Table of contents The Macro Scale I: Processing for Granulation 1. High Shear Granulation (G.K. Reynolds et al .). 2. Fluidized Bed Spray Granulation (L. Morl et al .). 3. Extrusion-Spheronisation (D.I. Wilson, S.L. Rough). 4. Drum Granulation Processes (G.M. Walker). 5. Roll Pressing (P. Guigon et al .). 6. Dry Granulation (Kazuo Nishii, Masayuki Horio). 7. Coating and Encapsulation Processes in Powder Technology (Khashayar Saleh, P. Guigon). 8. Modelling of Pan-Coating Processes for Pharmaceutical Dosage Forms (Preetanshu Pandey et al .). 9. Granulation Equipment (M. Jacob). 10. Online Monitoring (Satoru Watano). 11. Process Systems Engineering Applied to Granulation (I.T. Cameron, F.Y. Wang). The Macro Scale II: Applications 12. Agglomeration of Enzymes, Micro-organisms and Flavours (G.M.H. Meesters). 13. Agglomeration of Dehydrated Consumer Foods (S. Palzer). 14. Detergent Granulation (R. Boerefijn et al .). 15. Granulation Process Control – Production of Pharmaceutical Granules: The Classical Batch Concept and the Problem of Scale-Up (H. Leuenberger, G. Betz). 16. Tabletting (K. Pitt, Csaba Sinka). 17. Direct Pelletization of Pharmaceutical Pellets in Fluid-Bed Processes (P. Kleinebudde, K. Knop). The Meso Scale: Mechanistic Description 18. Shear-Induced Dispersion of Particle Agglomerates (D.L. Feke). 19. Scale-Up of High-Shear Binder-Agglomeration Processes (P. Mort). 20. Granulation Rate Processes (K.P. Hapgood et al .). 21. Breakage in Granulation (A.D. Salman et al .). 22. Fluidisation of Cohesive Particles (J.P.K. Seville). 23. Multi-Level Computational Fluid Dynamics Models for the Description of Particle Mixing and Granulation in Fluidized Beds (M. van Sint Annaland et al .). 24. Population Balance Modelling of Granulation (T. Abberger). The Micro Scale: Granules and Smaller 25. Granule Structure (D. Barrera-Medrano et al .). 26. Morphology and Strength Development in Solid and Solidifying Interparticle Bridges in Granules of Pharmaceutical Powders (G.I. Tardos et al .). 27. Liquid Bridges in Granules (S.J.R. Simons). 28. Pendular Capillary Bridges (C.D. Willett et al .). 29. Sub-Granule Scale Modelling (F. Štěpánek).
CONTRIB U TORS
1 1 09 255, 1 3 1 7 1 1 89 705 1213 255 673 499 1 071 673 1213 815 979 255, 323 897 21 289 979, 1 1 89 897 41 7 1317 779 779 673 1 071 3 705 897 897 555 1213 21 853 3 289 591 377 21 735 3, 979, 1 1 89
Thomas Abberger Michael J. Adams Daniel Barrera-Medrano Gabriele Betz Dafni G. Bika Gururajan Bindhumadhavan Renee Boerefijn lan T. Cameron Niels G. Deen Prasanna-Rao Dontula Leon Farber Donald L. Feke lan Gabbott Pierre Guigon Karen P. Hapgood Stefan Heinrich Masayuki Horio Michael J. Hounslow Simon M. Iveson Michael Jacob Simon A. Johnson Peter Kleinebudde Klaus Knop Reinhard Kohlus Hans J.A.M. Kuipers Phung K. Le Hans Leuenberger James D. Litster Lian X. Liu Gabrie M.H. Meesters James N. Michaels Lothar Mörl Paul Mort Amol M. Nilpawar Kazuo Nishii Stefan Palzer Preetanshu Pandey Mirko Peglow Kendal Pitt Gavin K. Reynolds
ix
x
CONTRIBUTORS
Sarah L. Rough Khashayar Saleh Agba D. Salman Jonathan P.K. Seville Olivier Simon Stefaan J.R. Si mons Csaba Sinka Yongxin Song Frantisek Stepanek Hong Sing Tan Gabriel I. Tardos Richard Turton Martin van Sint Annaland Gavin M. Walker Fu Yang Wang Satoru Watano Christopher D. Willett D. lan Wilson
1 89 255, 323 979, 1 1 89 255, 1 041 , 1 3 1 7 255 1 257 735 377 1 353 979 1213 377 1 071 219 499 477 1 31 7 1 89
PREFACE Granulation as a proeess has been the subjeet of ever inereasing interest over the past deeade. We think this arises beeause it is at onee a powerful teehnique for produet engineering of solids and a very interesting topie for aeademie investigation. We have attempted in this Handbook to give emphasis to both of these perspeetives - the praetieal and the theoretieal. Our vision for understanding granulation refleets in many ways the classie Chemieal Engineering paradigm developed over 50 years aga for the deseription of ehemieal reaetors. We seek to understand behaviour at some small length seale - perhaps that of a granule, or even a primary particle within a granule, and then use that to deseribe the emergent behaviour of the proeess - perhaps some eolleetive properties of granules or some produet property of individual granules. In this way we would naturally seek to develop understanding at a sueeession of length seales - whieh we usually term miero for the granules, meso for ensembles of granules and maero for whole proeess behaviour. One ultimate goal would be to quantify the behaviour at the miero and meso seales in terms of rates laws, apply them in a eonservation statement and then produee a deseription of the maero behaviour. In this ultimate state, the present Handbook would be logieally arranged from miero to maero. Inspeetion of the Contents page reveals that we have not yet reaehed our ultimate state. Instead we do the very reverse starting from the broader view of proeesses and applieation before deseending to the meso level and finally the miere level of individual granule properties. It is our hope that the material in this Handbook will provide guidanee of immediate praetieal and theoretieal benefit and that some time in future it will have given some landmarks so that navigation of the reverse journey from miero to maero beeomes possible. The Editors are very grateful to the large number of eolleagues who have helped in the preparation of this Handbook. These include the authors - who as ean be seen, are from around the world - and the members of the Partiele Produets Group at the University of Sheffield who eontributed so mueh to the praetieal arrangements of this large joint effort. Finally, we would like to thank
xi
xii
PREFACE
Professor Gabriel Tardos of The City College of the City University of New York whose efforts were the genesis of this book. A.D. Salman and M.J. Hounslow University of Sheffield, UK J . PK Seville University of Birmingham, UK
CHAPTER 1 H i g h S hear G ranu lation Gavin K. Reynolds * , 1 Phung K. Le2 and Amol M . N i l pawar2
Pharmaceutical and Analytical Research and Oevelopment, AstraZeneca, Macciesfield, Cheshire, SK10 2NA, UK 20epartment Chemical and Process Engineering, University of Sheffield, Mappin Street, Sheffield, S 1 3JO, UK 1
Contents
1 . Introduction 2. Effect of parameters and operating conditions on granulation rates 2. 1 . Effect of operating conditions 2 . 1 . 1 . Effect of amount of binder added (liquid to solid ratio) 2 . 1 .2. Effect of method of binder addition 2 . 1 .3. Effect of agitation 2 . 1 .4. Process time 2.1 .5. Other operating conditions 2.2. Effect of feed material properties 2.2. 1 . Binder properties 2.2.2. Primary particle size 3. Powder motion in high shear mixers 3. 1 . Horizontal axis ploughshare mixers 3.2. Vertical axis high shear mixers References 1.
3 4 5 5 5 6 8 8 9 9 11 11 11 13 18
I NTRODUCTION
There are typically four main types of wet-agitated granulating equipments, clas sified by the way the material is agitated: drum granulators, pan granulators, fluidised-bed granulators and mixer granulators. Mixer granulators or high shear granulators have a wide range of applications in the pharmaceutical, agrochem ical and detergent industries. They have the following advantages over other granulators [1]: • • • •
they can process wet, sticky materials, they can spread viscous binders, they are less sensitive to operating conditions than tumbling granulators, and they can produce small «2 mm) high-density granules. *Corresponding author. E-mail:
[email protected]
Granulation Edited by A.D. Sa/man, M.J. Houns/ow and J. P. K. Seville i 2007 Elsevier B.V. All rights reserved
4
Gavin K. Reynolds et al. Binding liquid through lance
+
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---
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Binding liquid through spray
Liquid add
Whirling bed
·
� ·
Impeller
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Airfilt er
�
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Fig. 1 . (a) Horizontal and (b) vertieal high-shear mixer granulators. Reprodueed with permission form 'Size Reduetion and Size Enlargement', Snow et al. Copyright © 1 997 MeGraw Hili [1].
High shear granulators in general fall into two c1asses, namely horizontal axis and vertical axis, and can be either continuously operated or batch operated. Typical configurations for horizontal- and vertical-axis batch high shear granula tors are shown in Fig. 1 . High shear granulators use an impeller to vigorously agitate the powder and produce high-density granules. They are commonly found in the pharmaceutical, agrochemical and detergent industries due to their ability to handle difficult feed formulations, including high viscosity binder fluids and fine cohesive powders. lmpellers rotate at high speed (between 1 00 and 1 500 rpm) on either a vertical or horizontal axis to create the agitation required for granulation. Typically, a seco ndary smaller impeller, called a chopper, is used. This rotates at much higher speeds (around 1 500 rpm). The role of the chopper in granulation is currently a matter of debate: it either fractures larger agglomerates or causes growth of smaller agglomerates, depending on the feed properties, operating conditions and the geometry of the mixer, impeller and chopper. Binder addition to high shear granulators can be in the form of a liquid spray or pouring. For melt gran ulation, binder can be added as a solid to a preheated high shear granulator.
2. EFFECT OF PARAMETERS AND OPERATI N G CONDITIONS O N GRANU LATION RATES
For many years and still to a certain extent currently, granulation design remains an essentially empirical process. In general, the majority of literature is concerned experimentally with the role of material properties and process conditions on the properties of the product granules. This section will present the role that a variety of material properties and operating conditions have been observed to play on the growth and properties of granules.
High Shear Granulation
5
2.1 . Effect of operating conditions
This section is concerned with the effects of process operating conditions in high shear granulators. Much of the wealth of literature concerning granulation con siders this area and as a result the experimental work encompasses a variety of types of equipments and different materials, depending upon the relative impor tance of these parameters to the industry on which they are focused. 2. 1. 1. Effect of amount of binder added (liquid to solid ratio)
Typically, granulation is induced by a liquid phase, and therefore a logical con sequence is that a larger amount of liquid results in a greater extent of gran ulation. An increased granulation rate is also observed when the liquid-solid ratio increases [2]. However if the liquid-solid ratio becomes too high, a phenomenon called overwetting may occur. In this case, granulation results in the formation of a paste [3]. Clearly this situation has to be avoided, because further processing (e.g. tableting) becomes difficult. The saturation of the granules, which can be defined as the ratio of liquid volume to granule-interstitial volume, increases when more liquid is added. A higher saturation is directly related to a larger average granule size [4,5] . Alternatively, if the saturation is too low no granule growth is observed. This implies that granules must exceed a critical saturation level in order to grow. This observation also explains the decreased period of no growth (consolidation) when the liquid content is increased, which was observed by Hoornaert et al. [6]. Owing to densification the porosity of the granules decreases resulting in an increase in saturation. If the saturation remains below the critical saturation no further growth will be observed. However, if the densification is sufficient to exceed this critical saturation growth will continue. This shift from no growth to growth will be observed at an earlier process time or higher liquid concentration. The particle size of the powder influences the effect of liquid con centration on granule growth. Keningley et al. [3] showed that the minimum amount of liquid needed for granulation increased when the size of the constit uent particles decreased. The same observation holds for the maximum amount of liquid that could be used for granulation. Fu et al. [7] presented the effect of the amount of liquid on product quality in terms of the size, binder content, porosity and appearance. In this work, the associated narrowing of the range of mecha nical properties for granules formed using an optimised procedure is exemplified by measurements of a number of parameters. 2. 1 . 2. Effect of method of binder addition
There are three main ways in which binder can be added to a high shear gran ulator: pouring, melting and spraying. The method of binder addition has been
6
Gavin K. Reynolds et 81.
found to greatly influence the properties of the resulting granular product. Holm et al. [8] found that liquid addition without atomisation gave rise to inhomoge neous liquid distribution (especially at low impeller and chopper speeds) and that atomisation of the binder led to better liquid distribution. Knight et al. [9] inves tigated all three binder-addition techniques. They found that where the binder was poured or sprayed on, the granule size distribution was initially bi modal and that the modal sizes were similar; at long granulation times the granule size distri butions were monomodel. However, the spray-on technique gave a lower pro portion of coarse granules and had a distinct tail of fine material in the granule size distribution at long times. The melt-in technique also produced a lower pro portion of coarse granules as compared with the pour-on technique, but the bimodal nature of the granule size distribution developed at long times. They conciude that, "the three methods of l iquid distribution differ in nature of the initial liquid distribution, but are fundamentally the same in that they all depend on prolonged mechanical mixing to give good uniform distribution". Knight and co workers also examined the effect of pouring on the compaction of the granules. They found that at short times, the coarse granules consist of three phases: air, liquid and solid. Also, the binder is not distributed evenly with granule size. This study is the first attempt to look at the properties of granules as a function of granule size and how these properties influence the granulation process. How ever, they did not investigate air or binder distribution with granule-size fraction for granules produced by other methods of binder addition. Another parameter confounded with the methods described above is the rate of liquid addition. Knight et al. [9] showed that the rate of liquid addition is also of importance. They observed a larger average granule size for the pour-on experiments compared to the spray-on experiments. If liquid was added very fast (i.e. pour-on) regions in the powder bed existed where the liquid concentration is high, resulting in over wetting. This led to the local formation of large granules or lumps, whereas a gradual liquid addition (i.e. spraying) led to a more uniform distribution of the binder. In this case the chance of over wetting was reduced, although the same amount of liquid was used. The general trend is that the faster the rate of addition of binder, the larger the granules become over time (e.g. Wauters et al. [1 0]). 2. 1 . 3. Effect of agitation
For a high-shear mixer, there are two ways of increasing the amount of energy input into the system, through the impeller and the chopper. The effect of both of these has been investigated. Schaefer et al. [1 1 ] found that the impeller speed produced no significant difference on the intra-granular porosity. Knight et al. [ 1 2] note that at high im peiler speeds, granule growth is limited by granule breakage. Kinget and Kemel [1 3] found that increasing the chopper speed mainly improves the homogeneity of the granulation due to the absence of fines. They do not
7
High Shear Granulation
define what is meant by homogeneity and so it is difficult to interpret what is meant; probably they are referring to the breadth of the granule size distribution. In contrast, using similar materials, Schaefer et al. [1 1 ] found that when the chopper was used the mean granule size was slightly smaller; there was no significant effect on the intra-granular porosity or the granule size distribution. Knight [2] found that the chopper aided in narrowing the granule size distribution, but the chopper was not used for the first 1 0 minof granulation and so no con clusions may be drawn about the influence of the chopper during nucleation. In addition to mixing the impeller and chopper are also responsible for the energy input in the process. The influence of the impeller and chopper speed therefore depends on how the granules respond to this energy input. If the in crease in impact energy results in more deformation of the granules, both the granule size and growth rate increase. Various authors reported this observation [2, 1 2 , 1 4]. Conversely, at high-energy inputs, where granule deformation leads to granule breakage, an increase in impeller speed leads to a decrease in granule size. This explains why sometimes a decrease in granule size is observed when the impeller speed is increased [4, 1 2, 1 5]. The influence of the energy input on granule growth was examined by Knight et al. [12]. Figure 2 indicates that for impeller speeds of 450 and 800 rpm, the growth rate is proportional with the energy input. The influence of the energy input on granule size is identical. At an impeller speed of 1 500 rpm the effect of the energy input is less pronounced. The authors argued that this was caused by an increased degree of breakage at this speed.
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15
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Fig. 2. Dependence of mean granule diameter on mixer energy input at impeller speeds of 450,800 and 1 500 rpm.The dashed line refers to a step change in the impeller speed from 800 to 1 500 rpm, resulting in a reduction in the granule mean diameter. Reproduced with permission. Copyright © 2000 Elsevier [ 1 2] .
8
Gavin K. Reynolds
et al.
2. 1.4. Process time
It would be expected that the general influence of a prolonged process time is increased granule size. Another influence of the process time is that the granule size distribution usually becomes narrower [9,1 2, 1 6]. However, it is not always the case that an increase in process time results in an increase in granule size. Hoornaert et al. [6] observed an initial period of no granule growth, sometimes followed by a rapid granule growth phase (Fig. 3). It was argued that during the no growth period granules become more densified (consolidation) due to the re peated impacts, while the saturation is still too low to cause granule growth. This period would last until the saturation is sufficient to promote granule coalescence. A logical consequence of the repeated impacts of the mixer arms on the granules is that the granules will densify. This densification occurs by the constituent particles within the granule becoming more closely packed, and hence reducing the interstitial volume. That is also the reason that usually a decrease in porosity is observed as a function of process time [9, 1 6, 1 7]. In particular during the initial time points the decrease in porosity is pronounced, whereas almost no change in porosity is observed at prolonged process times. 2. 1 . 5. Other operating conditions
Other operating conditions for high shear granulators can include temperature and mixer loading, Le., how much material is used for any one experiment. 1000 IlOO
i
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3
700 600 SOG 400 300 200 100 0
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,
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-17.8 wt,;. liquid -- 18.4 wt.� liquid --19.1 wt."4 liquid --19.8 wt.'lI. liquid -- 20.4 wt"4liquidl Fig. 3. Evolution of the mass-mean g ranule diameter for different amounts of binder (/1 3.9 M Pa.s for all experiments). ( 1 ) 1 7.8 wt% liquid (2) 1 8.4 wt% liquid, (3) 1 9. 1 wt% liquid, (4) 1 9.8 wt% liquid and (5) 20.4 wt% liquid. Reproduced with permission. Copyright © 1 998 Elsevier [6]. =
High Shear Granulation
9
Schaefer et al. [ 1 8] found that a decrease in the mixer load resulted in a sm aller mean granule size. They calculated the specific energy input as the time inte grated power consumption profiles normalised by the mass load, and found that the smallest granule size coincided with the largest specific energy input. They also state that the correct mixer load is crucial in obtaining a uniform and con trolled movement of mass in the mixer bowl. A low load will lead to a large amount of lumps and poor reproducibility. The effect of temperature is not discussed here as it serves to manipulate the properties of the feed materials (specifically binder viscosity). 2.2. Effect of feed material properties
Much of the granulation research work that has been carried out to date uses a variety of materials, making a generalised discussion on the relationship between feed material properties and granulation behaviour at best qualitative. However, despite this, trends have been found in the effect of feed material physical prop erties and granulation behaviour and may be of benefit if an operator or designer has some choice over the feed material properties. 2. 2. 1. Binder properties
Liquid binders exhibit a variety of properties that may affect the behaviour of the granulating system: •
• •
Viscosity. This will affect the viscous forces that can dominate in granule-gran ule interactions. This has been most widely studied as it is relatively easy to vary for a given system. Surface tension. This will affect the strength of the capillary forces. Contact angle. This will affect the wetting behaviour of the binder on the pow der. This has not been widely studied as it is difficult to change this property without changing the other properties of the material system.
Although listed separately here, surface tension and contact angle will not only depend on the binder but also on the solid phase in the system. 2.2. 1 . 1 . Binder viscosity
Schaefer and Mathiesen [ 1 9] granulated different molecular weight polyethylene glycols (pEGs) and two grades of lactose in an 8 1 high shear mixer using a melt-in technique. They found that the initial growth rate was lower for higher molecular weight PEGs but for that the subsequent growth rate was higher. They also found that lower weight PEGs gave rise to more spherical granules. Using a
10
Gavin K. Reynolds et al.
high-shear mixer, Hoornaert et al. [6] found that an increase in binder viscosity led to a larger extent of granulation in the nucleation and compaction regimes. The coalescence stage was characterised by faster growth. The time spent in each regime was also longer for higher viscosities. Overall, increased binder viscosity increased average granule size. However, the true value of the binder viscosity in the mixer could not be measured in their experiments as the binder partially dissolved some of the solid and the temperature rose over the course of the experiment, and hence the viscosity changes as weil. I n a drum granulator, Iveson and Utster [20] found that increase in binder viscosity de creased the rate at which intra-granular porosity decreases over the course of a batch granulation. Here, they pre-mixed the binder and powder to eliminate the effects of nucleation and achieve a uniform distribution of binder. However, for many granulating systems this pre-wetting cannot be used either the binder re acts with the powder (as in detergent manufacture) or because the binder so lidifies if the temperature decreases (e.g. in the production of pharmaceutical products where high molecular weight PEGs are used). This allows dissociation of nucleation from growth phenomena, but as nucleation affects the initial dis tribution of binder within the system, the pre-wetted powder would not be rep resentative of an industrial process. Johansen and SchCEfer [21 ] and Keningley et al. [3] showed that, depending on the primary particle size, a certain viscosity must be exceeded in order to obtain granule growth. When large primary particles were granulated with a low-viscosity binder, granule growth was limited. The work of Fu et al. [7] performed with different molecular weight PEGs showed that the critical viscosity to promote granule growth decreased with a decrease in primary particle size and that this observation was related to the granule strength. They explained that shear forces broke down weak granules that are obtained with a low viscosity binder and a large primary particle size. 2.2. 1 .2. Binder surface tension
Capes and Danckwerts [22] investigated the effect of binder surface tension in the drum granulation of sand. Due to the strength of the capillary bond in drum granulation, they found that there is a minimum surface tension necessary to granulate particles of a certain size. Iveson et al. [23] investigated the effect of binder surface tension on the dynamic yield strength of granules and found that decrease in the binder surface tension decreased the dynamic yield stress of granules. This result is expected from the analysis of Rumpf [24]. However, when they varied the surface tension of a more viscous binder, the binder viscosity dominated the yield-stress behaviour. Iveson et al. [23] further investigated the effect of the binder surface tension on the intra-granular porosity. They found that decrease in surface tension increase the minimum intra-granular porosity reached over the course of an experiment.
High Shear Granulation
11
2. 2. 2. Primary particle size
There is evidence to suggest that the primary particle size plays a role in de termining the amount of binder required for granulation. There is a general trend that more liquid is used when the primary particle size decreases. Schaefer et al. [1 8] also showed that less liquid is required to obtain an identical average granule size when a larger lactose size is used for granulation. The explanation that the liquid requirement is related to the primary particle size is as folIows. Granules are formed and increase in size due to the presence of liquid bridges between primary particles. More liquid is required to wet the primary particles when the size is smaller, since the surface area is larger. However, the liquid requirement is also influenced by other factors such as the porosity. As was stated earlier, the primary particle size also influences the critical viscosity that is needed to pro mote granule growth [3]. To prevent complete breakage, a higher binder viscosity is necessary when the primary particle size of the feed material is larger. 3. POWDER MOTION IN HIGH SHEAR MIXERS
Powder flow characteristics in high shear mixers are of paramount importance in understanding the mixing and collision frequency and magnitude between the powder, binder and subsequent granules. A number of studies have been made, qualitatively and quantitatively into these flow characteristics. This section will discuss measurement techniques and typical flow characteristics observed in horizontal axis and vertical axis mixer granulators, although specific flow char acteristics will inevitably vary with specific mixer geometry and material properties. Two principal techniques have been used to quantitatively measure bulk mo tion within high shear mixers, namely direct high speed optical imaging and pos itron emission particle tracking (PEPT). PEPT uses a single tracer particle that can be followed in time and space. The tracer particle is an artificial proton-rich isotope such as 1 8 F, 22 Na, 68 Ga and 64 CU. Such isotopes decay to produce a neutron, a positron and a neutrino. The emitted positron carries the energy of about 1 MeV and is annihilated in 1 ps by an inelastic collision with an electron in the surrounding medium. The collision produces two opposing collinear 'Y rays. Two detector plates placed at a specified separation detect the radiation. The direction of the y-ray emissions change rapidly and triangulation of two or more successive events enables the spatial location of the tracer to be determined. The time-averaged tracer position and velocity can be used to build up an impression of the bulk motion within the apparatus. 3.1 . Horizontal axis ploughshare mixers
Investigations into the motion of horizontal axis ploughshare mixers have been made typically using small-scale mixers. Forrest et al. [25] used PEPT to
12
Gavin K. Reynolds
et al.
Fig. 4. Radial sections of the granular bed in a ploughshare mixer: ( 1 ) 45-90°, base; (2) 90- 1 35°, bulk; (3) 1 35-1 80°, top; (4) 1 80-225°, free space. Reproduced with permission. Copyright © 2003 Elsevier [25].
investigate particle motion within 4- and 20-1 ploughshare mixers. The particles used were plate-shaped calcium hydroxy-phosphate of length 600 Jlm and width 1 00 Jlm for wet granulation and 600 Jlm resin beads for dry powder analysis. Figure 4 shows a radial cross section of a ploughshare mixer, with the different zones as defined by Forrest et al. [25]. For the case of wet granulation at a low ( 1 .3 Hz) and a high (2.5 Hz) blade speed a stationary zone of particles is observed, with some particles falling down from zone 4. The bl ade pushes particles through this stationary zone. For the case of dry particles, at a low impeller speed ( 1 Hz), the particles are pushed through the stationary zone, with little falling particles from zone 4. For a high impeller speed (2.25 Hz), there is no stationary zone, with many particles falling down from zone 4. They explain that the state of the particle bed is controlled by the ratio of the relaxation time of the system and the time between successive blades passes. If the ratio is less than one, the bed will come to rest and if it is greater than one, the bed will still be moving when the bl ade re-enters the bed. They also observed a low speed circulation zone where the material not carried by the blade falls down into the space created by the blade. Examining the axial profiles, they observed axial circulation zones caused by the co-operative action of the bl ades as each in turn enters the bed pushing material into the space created by the adjacent blade. Laurent et al. [26] performed PEPT experiments on a simplified horizontal axis mixer. Their apparatus consisted of a horizontal cylindrical shell stirred by a single long flate blade. A 600 Jlm radioactive resin tracer was used and had the same density as the powder. Figure 5 shows velocity fields for six different ranges of blade position. Figure 5(a) shows that as the blade enters into the particle bed a void is created behind the blade. Figures 5(b)-(d) show that as the blade passes through the bed, material is lifted and allowed to flow into the space between the bed surface and the agitator shaft. Figures 5(d) and (e) show a cascading flow
High Shear Granulation
�ection
����r-+----r
13 01 rotation
I- SQnm'sl d) 60•• 90°
b} 0° - 30°
e) 90° -120°
c) 30° - 60°
f) 180° - 210°
Fig. 5. Velocity fields i n cross-sectional view for six different blade positions i n a horizontal axis mixer with a level fill of 20% and a blade speed of 38 rpm. Reproduced with per mission. Copyr ight © 2000 AIChE [26].
pattern for the bed surface. When the blade is out of the bed, the free surface is left at angle of 1 5° to the horizontal, compared with the material angle of repose of 30°. 3.2. Vertical axis high shear mixers
Wellm [27] investigated the flow pattern in a 0.3 m diameter high shear mixer granulator using PEPT. The powder was found to be moving in the direction of the running blade with no exception. The powder was moving much slower than the blades, even near to the bl ades where the tip-speed was about 14.1 m/s. The velocities were calculated in a horizontal and a vertical plane. The particulate
14
Gavin K. Reynolds e t al.
mass was found to exhibit a toroidal vortex motion. The vortex motion was out ward in the lower regions of the mixer and inward in the upper regions, rising at the wall and falling near the axis of the mixer. These data were analysed with fast Fourier transform (FFT) that showed a peak at a frequency 0.9 S- 1 corresponding to a maximum tangential velocity of 0.85 m/s at the outer perimeter. With the FFT analysis it was found that the speed of the solids depends on blade speed and design, properties of the solids and level of fill. The tip speed and the speed of the powder had ratios as large as 1 00: 1 that became smaller with the smaller blade speed. For experiments done with a disc impeller at different speeds, the peaks for the horizontal motion were in an identical place. It was inferred that speed of the disc has no significant effect on the movement of the powder and so co efficient of friction is independent of the velocity difference between bl ade and powder. High-speed imaging has also been used to investigate particle motion within high shear mixers. Utster et al. [28] measured powder velocity in a 25 1 PMA Fielder mixer. The powder flow was filmed with a high-speed video camera at 500 frames/s. The camera was kept tilted at 45° centred on the spray zone. The flow pattern was measured for a batch of 6 kg dry lactose powder and wet lactose (approx. 6% moisture) at impeller speeds between 1 00 and 500 rpm. It was no ticed that the powder bed did not fluidize and its movement could be followed by using the natural bed structure, specifically lumps and cracks in the packed bed. The position of a lump of powder was followed over a number of frames and scalar velocity was calculated using image analysis. An average of all velocity results was used. They observed two distinct flow regimes. Firstly, 'bumping' flow in which the powder surface remains horizontal and the bed bumps up and down as the impeller passed underneath. Secondly 'roping' flow in which the powder from the bottom is forced up the vessel wall and then tumbles down towards the centre, similar to flow described as toroidal by Wellm [27]. The velocity in the bumping flow regime increased with increase in impeller speed, but was less sensitive to impeller speed in the roping flow regime (Fig. 6). A c1ear change in powder surface velocity was noticed in the transition from bumping to roping flow. Plank et al. [29] also used high-speed imaging to measure the surface velocity of powder beds in Aeromatic-Fielder high shear mixers of 25, 65 and 300 I vol umes fitted with plexiglass lids under numerous granulating conditions. Video clips were recorded for 5 s each. Only the tangential component of surface ve locity was calculated by tracking tangential movement of the powder frame-by frame. The frame of reference was established with the image of ruler positioned inside the mixer. The powder used contained a mixture of lactose monohydrate, microcrystalline cellulose, sucrose and pre-gelatinised starch with water used as a binder. Average surface velocity was measured as a function of impeller speed, amount of granulating liquid and fill ievel. Figure 7 shows their normalised powder surface velocity measurements. The surface velocities are normalised with
15
High Shear Granulation 1.2
�-------�--,
Bumping flow
Roping flow
1.0 Vl
l
Z. 0.8 ·0 o
�
� 0.6
�::::l
Oi 0.4 rJl
� [L
0.2 0.0 *'------,--r--"--j o 100 400 200 500 300
I mpeller speed ( rpm)
Fig. 6 . Powder surface velocities as a function of impeller speed for dry lactose i n a 25 1 vertical axis mixer. Reproduced with permission. Copyright © 2002 Elsevier [28].
:s
0.6
Z. .(3 o 0.5
---- 25 L
�
� äi 0.4 �
a.
-....
:s �
.g �
Q)
�
::::l (j)
0.3
t--I .. �
�300L
�t:::--
""'"
.....,
0.2 0.1 0.0 0.0
65 L
-+-
2.0
Lo
St, ndard/ Speed 4.0
�!-.
....
;....:><:::. �
i
I
I
t---..
�
t---
6.0
8.0
t-
10.0
�Stand
d HighSpeed
t---
�
12.0
-1 4.0
Impeller Tip Speed (m/s)
Fig. 7. Normalised powder surface velocity measurements for three different scale vertical axis high shear mixers. Reproduced with permission. Copyright © 2003 Elsevier [29].
impeller velocity. This figure shows that the velocity of the powder bed surface was significantly slower than the velocity of the impeller blades passing under neath the powder. This strongly suggests that impeller speed is not a reliable estimate for the speed of the powder surface and probably not for the bulk of the bed. Figure 7 also shows that the normalised surface velocity of the powder bed
16
Gavin K. Reynolds
et al.
1.2
� S
� '(3 0.8 0
äi > Ql 0.6 0 <11 't: :::l CI) Ql 0.4 +-------jrf---j ---.- Impeller speed Cl
� Ql
�
___
Impeller speed
=
1 50 rpm f-------i
=
300 rpm
0.2 0 0
5
10
15
20
25
30
35
Water Level (%)
Powdery
Sticky/Cohesive
Agglomerated
Fig. 8. Average powder surface velocity for different amounts of liquid addition in a 65 1 vertical axis high shear mixer. Reproduced with permission. Copyright © 2003 Elsevier [29].
remained relatively constant over a wide range of impeller speeds, whereas the smaller capacity mixers show a reduction with increasing impeller speeds. Plank et 81. [29] explain this as due to the change in the manner by which momentum is transferred from the im peiler blades to the powder bed. They observed a more toroidal bed motion in the sm aller capacity beds, where increasing impeller speed tends to transfer momentum more in the axial and radial directions at the expense of the tangential direction. They recorded that the toroidal motion was less pro nounced in the 300 I mixer. They also investigated the effect of liquid addition on the powder surface velocity, the results of which are shown in Fig. 8. Their results show a significant increase in powder surface velocity when the amount of liquid was increased to 7% w/w. The powder surface velocity then stabilised up to about 1 8% w/w liquid, where it was then found to increase up to a liquid addition of 30% w/w. Nilpawar et 81. [30] also used a high-speed camera for measuring powder bed surface velocities in a 1 0 1 Zanchetta Roto Junior high shear granulator fitted with a three-bladed impeller. They investigated the effect of binder viscosity on the powder motion by granulating Durcal 40 (calcium carbonate) with PEG 400 and glycerol. The liquids have viscosities of 93 and 890 MPa s at 25°C, respectively. They positioned the high-speed camera perpendicular to the powder surface during mixing and recorded images at 1 1 25 fps for approximately 2.7 s. At the impeller speed of 3 1 2 rpm (5.2 Hz), the images captured approximately 1 4
High Shear Granulation
17
revolutions of the impeller. The images were then processed using particle image velocity (PIV) analysis, with the powder surface providing sufficient texture for determination of surface velocities. They found a systematic variation of the ve locity magnitude with time due to the movement of the impeller blades. In both cases they observed a toroidal motion, with powder on the surface moving to wards the centre of the mixer. Performing Fourier analysis on the velocity signal, they observed a marked difference between the fundamental and third harmonic peaks. These peaks were found at 5.2 and 1 5.4 Hz, respectively, corresponding to the impeller frequency of 5.2 Hz and the individual blade frequencies of 1 5.6 Hz. In the case of the low viscosity binder, the third-harmonic peak was significantly higher than the fundamental, whereas the reverse was observed with the high viscosity binder. This suggest that the bulk motion of the powder bed is more responsive to the movement of each impeller blade in the case of the low viscosity binder, and less so in the case of the high viscosity binder. Transforming the velocities to the rotational frame using the fundamental frequency, they also observed this distinct difference between granules made with the two binder viscosities (Fig. 9). These c1early show how the powder bed surface velocity is influence by the passage of each of the three blades in the case of the low viscosity binder. Even a slight difference in the velocity magnitude imparted by each blade is visible in the plot (each blade had a slightly different angle). In the case of the high viscosity binder the influence of each impeller bl ade on the powder bed surface velocity magnitude is not obvious and the distribution of velocities is much less uniform, with half the bed moving at a higher velocity and half moving slower, leading to much less stable bulk motion.
: :1
.
e: 1.3 ::: 1.2 > - 1.1 1
t
(a)
..' :
, .
o
50
.
.
100
.
.
.
�-'
.
250
300
350
I
Fig. 9. Powder surface velocity magnitude in the rotational frame for granules made from (a) PEG 400 and (b) glycerol binders. Reproduced with permission. Copyright © 2006 Elsevier [30].
18
Gavin K . Reynolds
et al.
In summary, high-speed imaging of high shear mixers is providing valuable information on the motion of the powder. In addition, changes to that motion can be observed due to changes in impeller speed and granule properties. In par ticular high-speed imaging coupled with PIV is able to obtain high-resolution velocity fields of the bed surface. The disadvantage to this technique is that only the powder surface can be interrogated, and at best the bulk motion within the bed can only be conjectured. PEPT provides an excellent means to interrogate the bulk motion within the bed, but it is difficult to obtain high-resolution data spatially and also the temporal averaging required makes tracking the changes in bulk motion during a granulation process very difficult. REFERENCES [1] RH. Snow, T. A llen, B.J. Ennis, J.D. Utster, Size Reduction and Size Enlargement, in: R H . P erry, D.W. Green (Eds.) , Perry's Chemical Engineers' Handbook, 1 997, McGraw-HiII, USA [2] P . C . Knight, Powder Techno! . 77 ( 1 993) 1 59-1 69. [3] S.T. Keningley, P.C. Knight, A . D. Marson, Powder Techno!. 9 1 ( 1 997) 95-1 03. [4] T. Schaefer, P. Holm, H .G . Kristensen, Drug Dev. Ind. P harm. 1 6 ( 1 990) 1 249-1277. [5] P . Holm, T. Schaefer, H .G . Kristensen, Powder Techno! . 43 ( 1 985) 2 1 3-223. [6] F. Hoornaert, P AL. Wauters, G . M . H . Meesters, S.E. P ratsinis, B. Scarlett, Powder Techno!. 96 ( 1 998) 1 1 6-1 28. [7] J.S. Fu, Y.S. Cheong, G . K. Reynolds, M.J. Adams, AD. Salman, M.J. Hounslow, Powder Techno!. 1 40 (2004) 209-2 1 6 . [8] P. Holm, O . Jungersen, T. Schaefer, H.G. Kristensen, Pharm. lnd. 46 ( 1 983) 97-1 0 1 . [9] P .C. Knight, T. Instone, J . M. K. Pearson, M.J. Hounslow, Powder Techno!. 97 ( 1 998) 246-257. [ 1 0] P A L . Wauters, R B . Jakobsen, J . D . Utster, G . M . H . Meesters, B. Scarlett, Powder Techno!. 1 23 (2002) 1 66-1 77. [1 1 ] T. Schaefer, B. Taagegaard, L.J. Thomsen, H . G . Kristensen, Eur. J. P harm. Sci . 1 ( 1 993) 1 33-1 4 1 . [ 1 2] P .C . Knight, A . Johansen, H .G . Kristensen, T. Schaefer, J . P. K. Seville, Powder Techno!. 1 1 0 (2000) 204-209. [ 1 3] R Kinget, R Kemel, Acta P harm. Techno!. 31 ( 1 985) 57-62. [ 1 4] H . Kokubo, H . Sunada, Chem. P harm. Bull. 44 ( 1 996) 1 546-1 549. [ 1 5] J . S . Ramaker, M. A lbada Jelgersma, P . Vonk, N .w.F. Kossen, I nt. J. P harm. 1 66 ( 1 998) 89-97. [ 1 6] T. Schaefer, C. Mathiesen, I nt. J. P harm . 1 39 ( 1 996) 1 39-1 48. [ 1 7] AC. Scott, M.J. Hounslow, T. Instone, Powder Techno!. 1 1 3 (2000) 205-21 3. [ 1 8] T. Schaefer, B. Taagegaard, L.J. Thomsen, H .G . Kristensen, Eur. J . Pharm. Sci. 1 ( 1 993) 1 25-1 3 1 . [ 1 9] T . Schaefer, C . Mathiesen, I nt. J . P harm. 1 39 ( 1 996) 1 25-1 38. [20] S . M . Iveson, J . D . Utster, Powder Techno!. 99 ( 1 998) 234-242. [21 ] A Johansen, T. Schaefer, Eur. J . P harm . Sci. 12 (2001 ) 297-309. [22] C . E . Capes, P .V. Danckwerts, Trans. Inst. Chem. Eng . 43 ( 1 965) T1 1 6-T1 24. [23] S.M. Iveson, J.D. Utster, B.J. Ennis, Powder Techno! . 99 ( 1 998) 243-250. [24] H. Rumpf, i n: W.A . Knepper, (Ed.), Agglomeration, A lM E , Interscience, New York, 1 962, pp. 379-4 1 8. [25] S. Forrest, J . Bridgwater, P . R Mort, J.D. Utster, D.J. Parker, Powder Techno!. 1 30 (2003) 9 1 -96.
High Shear Granulation
19
[26] B.F.C. Laurent, J. Bridgwater, D.J. Parker, AIChE J. 46 (2000) 1 723-1 734. [27] A.B. Wellm, University of Birmingham, Birmingham, U K , 1 997. [28] J . D. Litster, K.P. Hapgood, J . N . Michaels, A. Sims, M . Roberts, S . K. Kemeneni, Powder Techno!. 1 24 (2002) 272-280. [29] R. Plank, B. Diehl, H. Grinstead, J. Zega, Powder Techno! . 1 34 (2003) 223-234. [30] A.M. Nilpawar, G . K. Reynolds, A.D. Salman, M.J. Hounslow, Chem. Eng. Sei. 6 1 ( 1 3) (2006) 4 1 72-41 78.
CHAPTER 2 F l u i d ized Bed S p ray G ranu l at i on Lothar Mörl , a Stefan Heinricha. * and M i rko Peg lowb
81nstitute of Process Equipment and Environmental Technology, Otto-von-Guericke University Magdeburg, Universitätsplatz 2, 0-39106 Magdeburg, Germany blnstitute of Process Engineering, Otto-von-Guericke-University Magdeburg, Universitätsplatz 2, 0-39106 Magdeburg, Germany Contents 1 . Introduction 2. Pneumatic behaviour of fluidized beds 2. 1 . Introduction 2.2. Geldart classification 2.3. Operation area of the fluidized bed 2.3. 1 . Minimal fluidization velocity 2.3.2. Elutriation velocity 2.3.3. Porosity of the fluidized bed 2.3.4. Operation area of the fluidized bed 2.4. Height and pressure drop of the fluidized bed 2.5. Air distributor of the fluidized bed 2.5. 1 . Equilateral triangle partition 2.5.2. Square partition 2.5.3. P ressure drop of segmented perforated plates with different opening ratios 2.6. Fluidized bed channel apparatuses 2.6. 1 . Setting of a constant bed height by a weir 2.6.2. Setting of a constant bed pressure drop by regulation of the discharge equipment 2.6.3. Setting of a constant bed pressure drop by regulation of the gas throughput for fluidization 2.6.4. Setting of a constant bed pressure drop by regulation of a secondary gas throughput 2.6.5. Setting o f a constant bed pressure drop b y regulation of a heightadjustable weir 3. Solid surface area and g ranule growth 3. 1 . Continuous fluidized bed granulation with ideal classifying particle discharge 3.2. Continuous fluidized bed granulation with ideal c1assifying particle discharge and monodisperse nucleation 3.2. 1 . Granule growth 3.2.2. Total surface area of all particles
* Corresponding author. E-mail:
[email protected]
Granulation Edited by A.D. Sa/man, M.J. Houns/ow and J. P. K. Sevi/le C 2007 Elsevier B.V. All riqhts reserved
23 24 24 25 26 26 29 33 34 36 40 44 45 45 46 47 49 50 51 51 53 53 59 59 59
22
4.
5. 6.
7.
L. Mörl
et al.
3.2.3. Size distribution in the fluidized bed 3.2.4. Residence time of the solid particles in the fluidized bed 3.3. Continuous fluidized bed g ranulation taking into account design parameters 3.4. Continuous f1uidized bed granulation with non-classifying particle discharge 3.5. Simplified modelling of the unsteady fluidized bed granulation 3.5. 1 . Batch process with increased bed mass 3.5.2. Semi-batch process with constant bed mass 3.6. Operation area of the fluidized bed granulation during unsteady process 3.6. 1 . Operation area of the batch process with increased bed mass 3.6.2. Operation area of the semi-batch process with constant bed mass Degree of wetting and heat and mass transfer 4. 1 . Modelling of the degree of wetting and of the transfer phenomena 4. 1 . 1 . Degree of wetting in the f1uidized bed 4 . 1 .2. Solid temperature in the f1uidized bed 4 . 1 .3. Heat and mass transfer between particles and gas f1uidized beds 4 . 1 .4. Example calculation 4.2. Influence of the mixing behaviour on the degree of wetting 4.2. 1 . Steady-state operation 4.2.2. Unsteady operation Fluidized bed granulation with superheated steam Fluidized bed spray g ranulation in closed or semi-closed systems 6. 1 . Closed systems with superheated solvent steam circulation 6.2. Closed systems with inert gas circulation 6.3. Sem i closed and self-inerting systems with gas recycle 6.4. Closed systems with heat pump 6.5. Closed systems with water vapour compression 6.6. Closed systems with rejected heat utilization for an u pstream evaporator 6.7. Concatenation of several closed systems Product examples of the university of magdeburg 7. 1 . Granulation of sticky products 7. 1 . 1 . Maize swell water 7.1 .2. Raw f1avour 7.1 .3. Cytosap 7.2. Granulation of paste-like products 7.2 . 1 . Calcium lactate 7.3. Granulation of microbiological producs 7.3. 1 . Fodder yeast 7.3.2. Rye starch 7.3.3. Lysine 7.3.4. Biosludge 7.4. Granulation of hard metals and magnets 7.4. 1 . Titanium carbides 7.4.2. Ferrite 7.5. Granulation of milk products 7.6. Granulation examples of chemical products
63 64 67 77 79 81 89 99 1 01 1 04 1 08 1 08 1 16 1 18 1 19 1 20 121 1 25 1 28 1 33 1 43 1 43 1 46 1 49 1 50 1 52 1 53 1 55 1 56 1 57 1 57 1 57 1 58 1 58 1 58 1 58 1 58 1 62 1 62 1 63 1 64 1 64 1 68 1 68 1 69
Fluidized Bed Spray Granulation 7.6. 1 . Potash 7.6.2. Activated carbon 7.6.3. Lead sulphate 7.7. Granulation of animal food 7.7. 1 . Sunflower protein 7.7.2. Swines blood 7.8. Granulation of fertilizers 7.8. 1 . Urea 7.8.2. Ammonium sulphate 7.9. Granulation of Glue sewage 8. Conclusions References
23 1 69 1 69 1 73 1 73 1 73 1 74 1 74 1 74 1 78 1 78 1 78 1 84
1 . I NTRODUCTION
Fluidized bed technology was founded in 1 922 by Winkler [1] for coal gasification, since that time the technology has been extended into many areas of applications that require different constructions of fluidized bed apparatus. Fluidized beds are used for physical processes like mixing, classifying, drying, coating, granulation, agglomeration, adsorption, pneumatic transport and heating and cooling of bulk solids. The plants for combustion, pyrolysis, gasification, gas cleaning, water pu rification, catalytic or gas-solid reactions belong to chemical fluidized bed proc esses. During the last years fluidized beds have been applied more commonly for the processes of environmental technology, for example adsorptive or absorptive gas cleaning or for the fluidization of immobilized micro-organisms in the liquid phase for the production of active substances in the cleaning of sewages. Fluidized-bed granulation in particular is very common, where atomizable liq uids (e.g. , suspensions, solutions, emulsions or melts) can be converted into free-flowing granular solids by integration of a number of processes like wetting, drying, size enlargement, shaping and homogenization or separation into a single step of the process chain by using high heat and mass transfer. This tailor-made particle design is used in a wide range of industries, including pharmaceutics, foodstuffs, fertilizers, detergents, mineral processing and specialty chemicals. Reviews on fluidized bed granulation are available in Refs. [2-6]. I n the literature, many attempts can be found to describe the particle forma tion in fluidized bed granulation in terms of population balances. Usually population balances describe the temporal change of particle property distribu tion. The influence of operating conditions on particle-size enlargement has been investigated by various authors [7,8] . For example, Watano [8] observed that the moisture content in solids is one of the most important particle prop erties to control the granulation process. For the authors interested in this re search [9-20] and especially for continuous granulation with high pro duct throughputs and possible self-sustained oscillations with external product
24
L. Mörl et al.
classification, much work is required for a complete understanding of the mech anisms involved. Alongside the granulometry and the pneumatics, the particle growth process is also strongly influenced by the thermal conditions in the flu idized bed. Our knowledge on the microprocesses of liquid injection, spreading, deposition and evaporation, as weil as the interactions with the gas-particle flow, is still limited. Nevertheless, some work was done to calculate the tem perature and humidity distributions in such liquid sprayed fluidized beds [1 5,21-24]. However, this article concerns the pneumatic behaviour, the particle growth, the heat and mass transfer as weil as different apparatus configurations regard ing the fluidized bed spray granulation by using simple analytical models. Gran ulation should be understood as layered growth of particles. Typical product examples explain the applicability of this technology for a broad range of particle processes. Using derived approximations, plant engineers are able to do rough calculations for a scale-up of the process.
2. PNEUMATIC BEHAVIOU R OF FLUIDIZED BEDS 2.1 . I ntroduction
Fluidization of granular solids (particles) occurs when the drag force exerted by the fluid (gas) on the particles exceeds the total weight of the particles. Above the minimal fluidization velocity the particles behave like a liquid, and the single solid particles start to move on stochastic streamlines. This state is characterized as fluidized bed. In particular the high heat, mass and impulse transfer in fluidized beds is offen used in a series of technical processes. It is weil known, that the heat transfer coefficient to a heating surface increases in a fluidized bed com pared with an empty tube by approximately an order of magnitude. Thus, a reduction of the dimensions of the fluidized bed apparatus is possible. Apart from the variety of fluidized beds for application in novel processes, a large number of fluidized bed apparatus designs are possible. From suit able literature searches it arises that the number of publications and patents for the area of the fluidized bed technology is already in 5-digit order of magnitude. It is no longer possible for a single expert to know all developments in this area. However, not all possibilities of the application of the fluidized bed technology are exhausted, and new applications are still arising. Morever, there is special interest in the area of fluidized bed spray granulation on which many quick developments have taken place during the last few years. Thus, from many application possibilities of the fluidized bed, this weil-chosen area is a subject of the present considerations. Therefore, the following executions refer primarily to this special application.
25
Fluidized Bed Spray Granulation
2.2. Geldart classification
In the literature, a huge number of works are available about the behaviour of disperse systems in the fluidization state, nevertheless, even today it can not be said for many complicated processes which appear with the fluidization of solid systems that they are fully understood. In particular the gas bubbles appearing in gas-solid systems provide a good mixing of the fluidized bed, but lead to un desired bypass currents of the fluidization gases, are still not accessible for an exact calculation. However, there is a huge experience with the application of the fluidized bed in the different areas that has resulted in a large number of phys ically reasonable, semi-empirical or empirical calculation methods. Such ar rangements allow the interpretation with sufficient exactness for technical purposes. Geldart [25] determined the fluidization properties of various particles through numerous experiments and classified them according to their density and diameter. He determined four groups of particles, which are described from smallest to largest particle as follows (Fig. 1 ): •
Group C (cohesive powders)
These particles are typically less than 50 )lm and are very difficult to fluidize because the interparticle adhesive forces are stronger than those, which the fluid can exert on the particle (drag force). These particles will tend to rise as a plug of solids in small-diameter beds and will not fluidize in larger diameter beds. To support the fluidization one can use mechanical stirrers, or vibration of the apparatus and pulsation of the gas, respectively. 10000
-
E Ob =. '0 a.
;;-'
§ ., u <= .,
_
1 -' r -, - ,- r ., - , r , " -, - ,- i _' _ '_ L
, ,
1000
�
.�
-
5
I
I
I
I
,
difficult to fluidize;
"0
I
I
I
,
::::
- - - - - -, - - - -, - - 1 - � - 1 - � i 1 1
100
10
I I
I I
I I
,
I
I
I
I I
, I
I I
" "
1 1
1 1
-
" "
, " ., r r
, " - - ,- r , , "
I I
1 000 100 mean particle diameter dp [-]
Fig. 1 . Geldart-classification [25] for air fluidization of powders.
10000
26 •
Group
A
L.
Mörl et al.
(aeratable powders)
The size of these partieles is typieally between 50 and 200 11m and their den sity ranges between 700 and 1 400 kg/m3 . One of the most important at tributes of these particles is that ean fluidize homogeneously at suffieiently low gas flow rates. When the minimum fluidization state is attained in the bed, these particle beds expand eonsiderably from their initial state. This dense phase ex pansion eontinues at a lower rate until the minimum bubbling velocity, Vb, is reaehed. In the bubbling state, the bubbles rise more rapidly than the rest of the gas and appear to split and eoalesee. The bubbles ean reaeh a diameter of 1 0 em. •
Group B (sandlike powders)
The size of these partieles is typieally between 40 and 500 11m and their den sity ranges between 1 400 and 4000 kg/m 3 . These particles do not undergo ho mogeneous fluidization. Bubbles begin to form at minimum fluidization. At higher velocities, small bubbles form at the distributor and . will grow and eoa lesee as they propagate through the bed. Most gas bubbles rise faster than the gas in the emulsion phase. The bubble size inereases with the bed height and ean reaeh the size of an apparatus diameter in fluidized-bed apparatuses with a large height to diameter radius (slugging fluidized bed). The size of the bubbles is proportional to the relative gas velocity, VG Vmf, and is independent of the partiele size. -
•
Group 0 (spoutable powders)
These are spoutable particles that fluidize poorly in deep beds. If the gas distribution is uneven, these particles will agitate and produee large bubbles or spout. Certainly all but the largest bubbles rise more slowly than the interstitial fluidizing gas, so that gas flows into the base of the bubble and out of the top, providing a mode of gas exchange and by-passing, eausing a heat and mass transfer between bubble and suspension phase. The bubbles eoalesee rapidly and become large. They rise more slowly than the rest of the gas. Partieles belonging to this group require a mueh greater gas supply than is required for the partieular applieation. This is usually solved by implementing a spouting bed. 2.3. Operation area o f the fluidized bed 2. 3. 1. Minimal fluidization velocity
If a paeked bed (or fixed bed) is flowed upwards from below, at a eertain gas velocity the minimal fluidization point oeeurs, where the fluidization starts. At this
27
Fluidized Bed Spray Granulation
point a force balance is achieved between the particle drag force as a result of the gas flow and the weight of the solids as a result of the gravity. With an increase of the gas velocity above this critical velocity, the relative porosity bed (void fraction) increases. Then, the pressure drop in a fluidized bed can be given as (1 ) The bed pressure drop of a fixed bed is calculable with a simplified flow model, which is based on the modelling of vertical gaps [26] based on the Ergun equation [27] PG v2 (1 - c;) 1 2 1 6 ( 1 - c;) 3.5 L1Pbed = Hbed (2) 2 G -c;3 -dp Re cos2 Clst
[
+ ]
where Cl = 45° is a correction factor which takes into consideration the change of the direction of the flow [26]. Equating both equations results in following:
-
(
gifp(ps PG ) = v�fd� � 1 08 ( 1 - c;) + 1 . 75 2 2 c; R COS2 Clst VG P G
3
vG
e mf
)
(3)
If the Reynolds number at the minimal fluidization point Remf vmfdp Remf - - VG
(4)
_
-
and the Archimedes number
Ar = 9d� �s PG vG PG are inserted into equation (3) folIows: (
Ar = Re2mf
(COS1 082 Clstc;(1 -Rec;)mf 3
)
+
(5)
1 .75 c;3
)
(6)
Rearranging to the Reynolds number at the minimal fluidization point and taking into account a statistical angle of Clst = 38° for the flow through the fixed bed follows [28] Re mf = 42.9 (1 - C;mf)
(
1+
c;�f Ar -1 2 (1 - C;mf) 321 4
)
(7)
The sphericity of the particle
28
L. Mörl
et 81.
From the literature, one more criterion is available for the calculation of the Reynolds number at the minimal fluidization, as for example by Rohsdostwenski [30] Ar Remf = ------==== (9) 2 1.75 1 -emt» ( 75 e� + e Ar �t Romankov [3 1 ] gives the following equation for the calculation of the Reynolds number at the minimal fluidization point Ar ( 1 0) Remf = 1 ( -emt) Ar 1 50 + 1.75 e�t � If the average value of 0.4 is used in equation (1 0) the porosity of the fixed bed is given by Gorosko et al. [32] Ar (1 1 ) Remf = 1400 + 5.22 ffi The approximation is easy to handle and is also often used in practice to calculate the Reynolds number at the elutriation point after modification (see equation (27)). In Fig. 2 the above mentioned calculation equations are compared. The dependence of the minimal fluidization velocity from the solid particle di ameter with the fluidization with air at 20°C with P = 1 bar, with the solid density as a parameter is shown as an example in Fig. 3 .
(
)
-----��
,
,
,, ,
1 � �--�----�-1000
100
I
-----
- -
- -
I
,
,
�" - - - - - - - - - � - - - - - - - - - : - ,
, ,
_
-
----- ---�---,
0,1
-
,
0,01
- - -
, '
10 1
, ,,
- - - - - - - - - r - - - - - - - - - T - - - - - - - - - -y - - - - - - - - - , - - - - - - - - - -, , , , , , , ,
-
- - - -
:-
-- ---�" ,
,,
:
- - - - -
,
,
I
,
1
,,
,
,
- - - , - - - - - - - - - � - - - - - - - - - 4- - - - - - - - - -
,,
- - - - - - - - • -
- --- - --
, , - - - - .. - - - - - - - - - .., - - - - - - - - - .. - - - - - - - -
- - - - - - .. - - - - - - - - - .. - - - - - - - - _ .. ,
- - - -
,
-0-
Ergun
--- Mörl -1r- Romankow
,
_ - - - - - - - - � - - - - - - - - -...- Rohsdostwenski
-+- Martin
0,001 -!-----i----i--t---t---l I ,E+06 1 ,E+07 1 ,E+08 1 ,E+04 1 ,E+05 1,E+02 1 ,E+03 I ,E+Ol Ar [-]
Fig. 2. Dependency of the Reynolds number at the minimal fluidization point from the Ar chimedes number for spherical particles according to different approximations.
29
Fluidized Bed Spray Granulation
---
-0----
·E 2 .5 >->
-I>-
o
�
�
.�
2
0
o
:ä .
Ps
800 kglm 3 3 = 1 200 kglm 3 = 1 600 kglm 3 = 2000 kg/m =
=
2400
=
2800
-+-
kglm33 kglm
1 .5
:; 4=: 03
.5
,
,
_ _ _ _ _ .1. _ _ _ _ _ _ .j,. _ _ _ _ _ _ .1. _ _ _ _ _ _ .l _ _ _ _ _ _
------
.S E 0.5
, , ,
1- - - - _ _ _ .. - - - - - - 1- - - - I r I I I
-- ------ -
,
..
..
• I
, , "
,
- - - - - .. , I
-- -- -- -- - -
.., I 1
O ���--�----��o
1 000
2000
3000
4000
5000
6000
7000
8000
9000
1 0000
particle diameter [)lI11]
Fig. 3. Dependency of the minimal fluidization velocity fram the solid particle diameter by var iation of the par ticle density (fluidization with air at 20°C and P = 1 bar ) .
The temperature of the fluidization medium has an influence on the density and the kinematic viscosity of the fluidization medium. Similarly, an influence on the Reynolds number at minimal fluidization point is expected. As an example of this dependency, the relation of the calculated minimal fluidization velocity at 20°C to the minimal fluidization velocity at 1 50°C with air as fluidization medium and as a function of particle diameter with the solid density as a parameter with 1 bar system pressure is shown in Fig. 4 [6].
2. 3. 2. Elutriation velocity
If the gas velocity is increased so that the settling velocity of the fluidized-solid particles is reached, these particles are elutriated fram the fluidized bed and the pneumatic transport of the particles begins. This is the upper limit of the operation area of the fluidized bed. The elutriation velocity of a spherical particle Velu with the diameter dp and the density P s in gas of the density Pa can be calculated from 4 (Ps - P G ) gdp (12) Velu = -3 PG � p(Reelu ) with the Reynolds number at the elutriation point Reelu
_
velu dp
-
--
VG
( 1 3)
30
L. Mörl et al. 1 .4 =
1 000 kglm3
-<>-
=
1 500 kglm3
-+-
=
2000 kglm3
-0-
=
2500 kglm3
-+-
=
3000 kglm3
-+-
1 .3
,
,
, ,
- - - - - - , - - - - - - ,- - - - - - - - - - - - - -
Ps
�
G 1 .2 ,
�
, , - - - - - - , - - - - - - , - - - - - - -,- - - - - - -
0
0 Ir)
-
'.../
E
;>
G
0
0
t!. E ;>
1.1
, , , - - - - - - , - - - - - - , - - - - - - - - -- - - - ,
1 .0
-
,
,
, , ,
, ,
0.9 0.8
, ,
- - - - - - '1 - - - - - - ., - - - - - - . . - - - - - -
, , -- - - ,- - - - - - - - - - - - - , ,
, ,
,
, ,
- - - - - - j - - - - - - r - - - - - - , - - - - - -
, , - - - - - - ,r - - - - - - r - - - - - - I - - - - - -
+---+--�-_+_-__+--+_-___+_--T__-_+_-____;-�
o
1 000
2000
3000
4000 5000 6000 particle diameter [11m]
7000
8000
9000
10000
Fig. 4. Relationship of the minimal fluidization velocity of solid particles at 20°C and 1 50°C as a function of particle diameter by variation of the particle density (fluidization with air at 20°C and P = 1 bar).
where �p is the drag coefficient, which can be distinguished for: Re < 0.25 24 = �p Re from Stokes [33] for 0 . 1 < Re < 4 1 03: 6 21 from Kürten [34] + In.: + 0.28 �p = Re v Re
(14)
x
(1 5)
24 4 from Kaskas [35] + 0.4 ( 1 6) Re vrn.:: Re The correlation between Reynolds number at the elutriation point and Archimedes number can be derived from a force balance around a floating sin gle particle, with: lifting force, gravity force, drag force and accelerating force. In Fig. 5, the direction of the forces is shown. Besides, the acceleration force can act in both directions, depending on whether the particle is accelerated or is decel erated. For a freely floating particle it can be considered zero. The forces can be expressed as follows (see Fig. 5): Lifting force
�p
=
+
( 1 7)
31
Fluidized Bed Spray Granulation
tttttttt
Fig. 5. Forces at a freely floating single particle.
Gravity force ( 1 8)
Drag force Accelerating force
FAc = M p CU
dVG
TC
( 1 9)
dVG = 6 Qpps CU _,3
The balance for the floating yields Fu + FGr + FD + FAc = 0 After remaining of three forces and some transformations, we have ?!. d� (ps PG) (p ?!. PG d�V;IU = 0 4 2 v� 6 VG
-
_
Now, the introduction of the dimensionless quantities Re and Ar yields 4 2 "3 Ar = ep R Eelu
(20) (21 ) (22)
(23)
It now the dependency ot the drag coefficient ep trom the Reynolds number is introduced, for the flow areas folIows: for Re < 0 . 25 trom Stokes [33] 24 4 Ar = "3 Ree2 1u = 1 8 Ree1u (24) Ree1
( u)
L. Mörl
32
(
et al.
1 03 from Kürten [34] 6 21 4 2 Ar = - ReeIU - + � + 0.28 (25) Reelu v Ree1u 3 for Re > 2 1 03 from Kaskas [35] 4 2 24 4 (26) Ar = - ReeIU - + � + 0.4 Reelu v Ree1u 3 From the literature a series of other criteria are known for the Reynolds number at the elutriation point as function of the Archimedes number, from which because of its simplicity and because of its validity for all areas the following is given according to Gorosko et al. [32]
for 0.1
<
Re
<
4
x
)
(
x
�elu
)
k
(ll) - 1 8 + 0.6 1 $r as weil as by Mushtejev and Uljanov [36] 1 .74Ar (28) ReeIu $r 3 1 .3 + In Fig. 6 the above relations are compared with each other, and it appears that the difference can be neglected for technical calculations. The curves for equa tion (27) and equation (28) are superposed. As an example the dependency of the elutriation velocity of a spherical single particle as a function of the particle diameter is shown in Fig. 7 with air at 20°C and 1 bar system pressure with the solid density as a parameter. _
- -=
I .E+12 I .E+ l l I .E+l0 I . E+09 I .E+Ü8 I .E+Ü7
"2
�
�
I .E+06 I .E+Ü5 I .E+04
,------.---,---,....---r--�-___r--=_-__, I I I , I , I , I I - - - - - -, I - - - - - - r - - - - - - - - - - - ,I- - - - - - -I,- - - - - - -I, - - - - - - -I, - - - - - - -,I - - - I I I I I I I , . - - - - - - Ir - - - - - - Ir - - - - - - I,- - - - - - - I,- - - - - - -I, - - - - - - -I, - - - - - - -I, - - - - - - -I - - - - - .,I - - - - - , I I I I I I I I - - - - - - Ir - - - - - - I,- - - - - - -c , - - - - - -I, - - - - - - -I, - - - - - - -I, - - - I I - - - - - -, - - - - - - - - - - - - I , , I I I . I I I I I I I I I I I - - - - - - r - - - - - - r - - - - - -� - - - - - -� - - - - - - ,- - - - - - -, - - - - - - - - - - - - � - - - - - - ,, - - - - - , I I I I I I " I - - - - - �I - - - - - - �I - - - - - - - - - - - r - - - - - - r - - - - - - r - - - - - - � - - - - - - ,- - - - - - -, - - - �I I I I I I I I I , , - - - - - - Ir - - - - - - Ir - - - - - - � - - - - - - � - - - - - - I - - - - - - -I - - - - �I - - - - - - �I - - - - - - �, - - - - - I I I I I I I I I I - - - - �• - - - - - - �I - - - - - - I� - - - - - - I� - - - - - - I� - - - - - -r - - - - - - I- - - -.- - - - �-----I I " " I _ _ _ _ _ _ � - - - - - - � - - - - - -� - - - - - -� - - - - _ _ _ _ _ _, _ _ _ _ _ _ �_ _ _ _ _ _ � _ _ _ _ _ _ J _ _ _ _ _ _ , , , - - - - - - � - - - - - - � - - - - - -� - - - - - -� - - - - - - - - - - o Stokes , , ,
0.1
10
1 00
Redu [-]
1000
10000
100000 1 000000
I E+07
Fig. 6. Dependency of the Reynolds number at the elutriation point from the A rchimedes number for spherical particles according to different approximations.
33
Fluidized Bed Spray Granulation
.....
35
]. 'ü o
C
---A--
30
-
25
-<>-
� 20
kg/m3 3 kg/m 3 kg/m kg/m3 = 4000 kg/m1 5000 kg/m3 6000 kg/m3 7000 kg/m3 800 = 1600 2400
P5 =
-<>-
.......
.� 15 '5
=
=
3200
=
---- -- --- , - ,- - -- , , --- -- - - -
= =
t:: o
�- - - - - - -: .
- -
�
- - - -
,
� 10
- -1-
-
5
.-...:r__....-
-r
-
- - - - -
t I I - - - - - - 1 T
-
I I
I I
--
- - - - - - - - - - - - - �I
------
- - -: ,
- - - - -
, I
- :- - - - - - I
,
O �---T----;---�--.--,r--,---� o
1000
2000
4000
3000
6000
5000
7000
8000
9000
1 0000
particle diameter [f.UTl] Fig. 7. Dependency of the elutriation velocity from the solid particle diameter by variation of the particle density (fluidization with air at 20°C and P = 1 bar).
The influence of the gas temperature on the Reynolds number at the elutriation point and on the elutriation velocity, including the influence of the particle diam eter, is shown as an example in Figs. and with air as fluidization medium at bar system pressure.
8 9,
1
-- -
(29)
1
0.38 ... 0.4
2. 3. 3. Porosity of the fluidized bed
The relative void fraction or the porosity of the fluidized bed Vyoid VYOid e - Vbed - Vyoid + Vp is the ratio of void volume to total volume of the entire fluidized bed. It grows from the minimal fluidization point and reaches e = at the elutriation point: < e < 1. The calculation can be done with the following expression -;-:-
e
Richardson and Zaki beds:
=
(18
Re
--:-:-
+ �·36 Re A
2
)
0.21
[32]:
(30)
[37] have found for the expansion behaviour of fluidized VG
-=
Velu
-
Vmf VG
Velu Vmf
f
E = - == E 1
fmax
(31)
34
L. Mörl et al.
1 .2 .------�---__._-_r_---�-__, . - - - - - -
, �
- - - - - - - - - - -
,
�
�
=
- - - - - - - - - - -
I
I
,
,
- - - - - - - - - - - i- - - - - - - - - - - i- -
0.6
c:::
cf 0. 4 =
_ _ _ _ _ _ _ _ _ _ _
c:::
0.2 0
� ,
" � , , , , , ,
- - - - - - - - - - -
�
- - - - - - - - - - -
, - - - - - - � - - - - - - - - - - - � - - - - - - - - - - - � - - - - - - - - - - - � - - - - - - - - - - -
°
�
- - - - - - - - - - -
,
::::: 0.8
U
�
- - - - - - - - - - -
� I , ,
, rI
-
-
,
- - -
I
_ _ _ _ _ _ _ _ _ _ _
- - - - - - - - - - -
�
Ir
I
_ _ _ _ _ _ _ _ _ _ _
- - - - - - - - - - -
100
50
0
- - - - -
I ,
� I ,
r
I
_ _ _ _ _ _ _ _ _ _ _
- - - - - - - - - - -
,
� ,
r
I
_ _ _ _ _ _ _ _ _ _ _
,
L
I
_ _ _ _ _ _
, , ,
- - - - - - - - - - -
I
I
1 50
200
r
I
- - - - - - - - - - -
I
250
300
gas temperature [0C] Fig. 8. Relationship of the Reynolds number at the elutriation point at a certain temper ature and at 20°C as a function of the gas temperature (fluidization with air at 20°C and P 1 bar, Ps = 2500 kg/m3 , dp 1 mm). =
=
with:
Vmf (32) and fmax = Velu whereby the exponent EE in this equation is given by Sathiyamoorthy and Rao [38] log ( 1 /fmax) , E = (33) log l:mf In Fig. 1 0 both equations are compared. 80th relations show a correspondence that is reasonable enough for technical interests. 2. 3. 4. Operation area of the fluidized bed
For the representation of the operation area of the fluidized bed there are different possibilities. For monodisperse particle mixtures, the ratio of minimal fluidization velocity to elutriation velocity as a function of the Archimedes number is shown in Fig. 1 1 . 8esides, the functional dependency can be calculated from [32] as folIows: Ar 1 8 + 0.61 (Ar)o.s Ar f. _ Re mf max Re elu 1 400 + 5.22(Ar)o.s 1 8 + 0.61 (Ar)o.s 1 400 + 5.22(Ar)o .s (34) _
(
)/(
)
_
35
Fluidized Bed Spray Granulation 1 .4 ....... -0-
J .3
....... -
1 .2
......
,
-0-
�
U l.l "......,
-+-
° 0
dp = O.OI mm = 0.05 mm = 0. 1 mm = 0.5 mm = I mm = 5 mm = IO mm
�
- - - - � - - - - - -
,
�
_ _
__
I
I , I _ _I _ _ _ _ _ _ - - - - - - � - - - - - - - - - - - � - - - - - - - - - - - � _
,
,
u :>
--" 0.9 ;;
_ _ _ _ _ _ _ _ _ _ _
,
-- - - - - - - - - - - - � - - - - - - - - - - - , - - - - - - - - - - - � - - - - - - - - - - - -
I
I
I
I
0.8
0.7
- - - - - - - - - - - � - - - - - - - - - - - -I - - - - - - - - - - - - � - - - - - - - - - - ,
,
,
,
,
0.6 +------r--�--+_--_r--� 250 300 150 200 1 00 o 50 gas ternperature [0C]
Fig. 9. Relationship of the minimal fluidization velocity at a certain temperature and at 20°C as a function of the gas temperature by variation of the particle diameter (fluidization with air at 20°C and P = 1 bar, Ps = 2500 kgjm3) .
...... Richardson and Zaki
0.9
-0-
Gorosko el al.
0.8
:s
0.7 _ _ _ _ _
2 0.5
_ _ _ _ _ _ _ _
1 _ _ _ _ _ _ _ _ _1 _ _ - _
-
- - _
-1
_ _
- - - - - - �-
- -- - -- -
, - - - - - I� - - - - - - - - II- - - - - - - - -II - - - - - - - - -I, - - - - - - - - �• - - - - - - - - �I - - - - - - - -
0.4
_
, L
,
0.3 0.2
. 1.
,
,
,
0.6
:> "0
I
I ,
_ _ _ _ _ _ _ _ L _ _ _ _ _ _ _ _ I_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
- -r -
------
-r - - - - - - - -1- I
,
---
-
-
-
-,- - - - - - - I
.. ,
------
-
�_
,
_ _ _ _ _ _ _
�
_ _ _ _ _ _ _ _
,- - - - - - - - , - - - - - - - ,
-1--=::+==+====-+----t---f-.---f.--1 o
2
3
4
5
6
7
8
gas velocity [rn/s1
Fig. 1 0. Comparison of the equations of Richardson and Zaki [37] and Gorosko et al. [32].
36
L. Mörl et al.
i--;---;---:--;-;--:I:====l ,, , I • _ _ _ ______ _ _ _ _ _ _ _____ _ _ _ _ _ _ _ _ _ _ _ _ ____ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _, ____ _ 0.1 ,, , I I , , , , , , , 0.08 ,, , I , I I I , , , , 0. 1 2
�
L
I
J
L I
I
J
I I ' 1 - - - - - , - - - - - - j - - - - - , - - - - - - j - - - - - , - - - - - - r -
�
,
" '" Q:;
-..
�
I I
I I
I
I
I
J
L
- - - , - - - - - - r - - - - - ' - - - - - - r - - - - -
I I
I
I
J
_ _ _ _ _ J _ _ _ _ _ _ L _ _ _ _ _ J _ _ _ _ _ _ L _ _ _ _ _ J _ _ _ _ _ L _ _ _ _ _ J _ _ _ _ _ _ IL _ _ _ _ _ J, _ _ _ _ _ _ IL _ _ _ _ _ ,
0.06
L
L I
___
0.04
L..I
,
I I
I I
e
"
e ti_ a rea On _ -,_-.J -, _
ra lar g_o p_ _ _
,
� �1
,
,
�
I
,
,
I
I
,I
I
I I - - - - - - r - - - - - ' - - - - - - r - - - - - ' - - - - - - r - - - - -
�
a �
a
----'lu
ea ar ion er top_ 1I _ Sm _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ L-_ � �
0.02
"
,
O +---�--�----r---�--_r--r_� 0.1
10
100
1 000
10000 1 00000 100000 I E+07
Ar
[-]
I E+08
I E+09
I E+ I O
Fig. 1 1 . Representation of the operation area of the fluidized bed by the relationship as a function of the Archimedes number.
fmax
The operation area of the fluidized bed can also be shown with the relative voidage as a parameter with direct dependence of the Archimedes number on the Reynolds number as shown in Fig. 1 2. The representations above are valid for monodisperse particle mixtures. In practice this case does not seem practical and for all particle mixtures with wide size distribution it must be taken into consideration that the sm all solid particles may not be elutriated, while the big particles should still be fluidized and may not remain Iying on the air distributor. In addition, their density must also be taken into consideration as another particle property. For such a case it is suitable to cal culate the minimal fluidization velocity and the elutriation velocity, in each case for smallest and the biggest particles present in the particle mixture. Figure 1 3 shows for an example (wooden particles and sand particles in each case with a minimal diameter of 1 mm and a maximal diameter of 3 mm ) , the dependency of minimal fluidization and elutriation velocities for a particle mixture with light small and large heavy particles. The operation area of such a fluidized bed is between the minimal fluidization velocity of the smalI, light particles and the elutriation velocity of the large, heavy particles. In this case it is possible to reach a stable fluidized bed for the entire particle spectrum. 2.4. Height and pressure d rop of the fluidized bed
The height of the fluidized bed determines the pressure drop that the gas suffers while flowing through the bed. The expansion behaviour of the bed is usually calculated with empirical correlations. In general, between the superficial velocity
Fluidized Bed Spray Granulation
37
l . E+ I O
I .E+09 I .E+08
,
,
,
"
I " , I 1 1
!
_ _ _ _ _ _ _ L _ _ _ a _ _ a _ � _ � _ L I , , I I I ' I I I I , I - - - - - -T r T r ' '
,
I
'
I
, I
I I
I
I
J � � _ _ _ _ _ _ _' _ _ _ _ L _ _ � _ L _ L � _ L L J _ _ _ _ _ _ � _ _ _ � _ _ � _
I
I I I I I
I , I I I
I ' I I I r I
I I I I I I I t I ' I I I I - -r l �' � - r -r ' -r r T - - - - I I I I I I I I "
I
' '
I
I
I
1
1
I
I
I
I
I
, , ,
I .E+07 I .E+06
�
, �
I .E+05 l .E+04 I .E+03 I .E+02
I .E+O I l . E+OO
I , t - - - - - - I r -- -T
I
I
- --
+-
-- -
I I I I I I I I I I I I I I I I - Ir I 1 1 - - - - - - - - - - - r t I - - i - � - - - I I
I I
, .. - - - -+" - - • - ...
I I
�
I I
I
I
__
10
I ' I 1 1 I I I 1 1
I ,
,
1
1
I
I
I I
I I
I I
... - � ... -'4 - - - - - - - ,- - - - '"" - - - - .. - .... ... -I- .. 1- -
���:�� : :�_L ' '� ' I
__ __ __
-
I , I I I r - r � -r r i
1 ��
1
,
t
,
l
I
1 1
I
�
__ __ __
100
�� I
__
I
-t:r-
=0.6
--0-
=0. 8
I I
I
I
I
I I I I ,
I I - _ 1_ ..... _ j,. ..... _1_
-D- E =0.4
I
I
I " I I I
- -,- -, - i "i -,-
I I I I , - -1- -1 - ... .... -1 -
��_L��========������� I
I
I
I
I
I
-<>-
= 1 .0
__
1 000
1 0000
Re [-] Fig.
12. Operation area of the fluidized bed as dependency Ar = f(Re).
10 -0- minimal
9 -tr-
tluidization velocity of small and light partic1es
minimal tluidization velocity of large and heavy particles
� elutriation
8
�
7
- -� - - - - - - - � - - - - - - - - - -
velocity of small and light particles
elutriation velocity of large and heavy particles
00
�
6
0 ·ü 5 0 �
I
;> '"
co bl)
I I , t I - - - - - y - - - - - - - -r - - - - - - - T - - - - - - - - - - - - - - - - T - - - - - - - - - I
4 3 2
o
I
( I - - - - -� - - - - - - - T - - - - - - - - - - - - - - - - T - - - - - - - - - I ,
,
,
- -, - - - - - - - j - - - - - - - - - -
- � -------� � ---- � - � -- g - -tt:--� operation area
of the fluidized bed
-
o
�
0.5
:
- - - - - - - _ -
-
1 .5
,
,
- -r - - - - - - - T - - - - - - - - - -
- - - - - -r
2
2.5
3
-
-- -- �
-
3.5
- - - - - -
4
partic1e diameter [mm]
1 3. Operation area of a fluidized bed with a particle mixture of light-small particles (wood spheres with a diameter of 1 mm) and large-heavy particles (sand spheres with a diameter of 3 mm) with air at room temperature as f1uidization medium. Fig.
38
L. Mörl et 81.
VG = Veff the corresponding bed height Hbed and bed porosity s and the same quantities at the minimal fluidization point exists an relationship - Smf Hbed Hbed.mf With this the dependence of the bed height at any operating velocities vG can be calculated
1
(35)
1 -S
(36) with
(37)
or
Hbed (Ar, Re) = Hbed,mf
1-C
Smf 8Re+2/6Re2 ) 0.21
1-
(38)
The dimensionless bed height Hbed can be written as (Re, Ar) L.ft (Ar, Re Hbed nbed Hbed,mf or Smf Hbed (Ar, Re) = Hbed,mf 0 21 - 8Re+2;36Re2 ) . C With this representation it must be pointed out to the fact that the dimenionless bed height is valid only in the operation area of the fluidized bed from = to In Fig. the dimensionless bed height is shown as a function of the Reynolds number with the Archimedes number as a parameter. It is recognizable that the dimensionless bed height rises to a non-finite value for certain values of Reynolds number. Then, these are the Reynolds numbers with a void fraction of related to the corresponding elutriation velocity. The pressure drop of a fixed bed increases with the gas velocity up to the minimal fluidization point. The pressure drop at this point can be given with as follows ( IX =
)
(39)
_
_
1-
1
1.0.
(40)
S 0.4
14
1,
38°):
[27]
(1 - s) 1 [ 150 (1 - S) + 1.75] S
d �Pbed = HbedPG VG --- 2 3 p Re cos IXst With further increase of the gas velocity after the minimal fluidization velocity has reached, the bed pressure drop of a monodiperse particle bed remains con stant. However, it is only valid for an open and non-limited bed height (Fig. If the fluidized bed has a weir as shown in Fig. the bed height can grow only up to limited height corresponding to the height of the weir. With further increase in .2
16,
(41)
15).
39
Fluidized Bed Spray Granulation
16 TT---'�----�---' 14
I . I -�--- - - - � - - - :- - - - - - - - � - - � , , .. , , : 1 - - - - t - - - :- - - - - - - - -: - : - - - - - - - � - - - - -
12
..: 01) 'ä}
,g
.c:: '0
I •
I
- - - • < •
_ _ _ _
c:
2
-
Ar = I000
- -
- - -
Ar = 10000
, , , ,
, ,
_ _ _ _ _ _ _ _ _ _ _ _ ..J _ _ _
: Ar = 100000 , : - - - -:. r - - - - - . - � - . - - - -- Ar = 1 000000 I I . I I I ' , .: , I I " I 1_ - - - - - - - - -I ': --------, -----I I I I, I I I , , , , I I ,IJ I I II I - - - 1 - - - -:- - - - - - - - -:�: - - - - - - - - - � - - - - - - - - - r - - - - - - - - - � - - - - - - - - - :- - - - - - - -: - I , I I I I : : : : I ;" : :I I , I I I -� --------�---------�---_ _: _ _ -1 _ _ _ _ _ : _ _ _ _ _ _ I •
8
4
•
-
I
.�c: 6 CI)
a '6
I
-
10
'" '" � '"
, '
.
•
I - : I I
1
•
I I I
•
- . - - - - •
- -1-
I - - - - - - - -i -
11
. - - - - - - - - - �
I
I
- - - - - - - - 1-
I
-
I
•
I
•
•
I
/� I' _ _
I
_
_ _ _ _ _ _ _ _
.J'.
I
_
'
,
� _" _'_" _ _ _ _ _ _ _','_ _ _ _ _ _ _ _ _ -: _ _ : I
_ _ _ _ _ �, _ ,. � _ '
-
I
I
_
-
I
-
_
_ _ _
I --------�---� - - - - - - - - - I� - - - - - - - - -II I :
: I
0 +------+--4--�--+_� 1400 1 200 800 1 000 200 600 400 o Re [-)
Fig. 14. Dimensionless bed height as a function of the Reynolds number by variation of the Archimedes number.
Fig. 1 5.
Bed behaviour with unlimited bed height.
the gas velocity solid particles are discharged over the weir, the relative voidage increases further and thus, the bed pressure drop decreases up to a value of zero until the elutriation velocity is reached. The bed behaviour is shown as an example in Figs. 1 7 and 1 8 for an unlimited bed height. In Fig. 1 7 the bed pressure drop and the bed height are illustrated as a function of the gas velocity for a fluidized bed with an unlimited bed height and Fig. 1 8 plots the bed porosity as function of the gas velocity.
40
L Mörl et al.
�1
'"";:: E >
t
J
Va,3 > Va.2 > Vmf
Fig.
1 6. Bed behaviour with limited bed height
If the fluidized bed is limited by its height by using a weir as is the case with most fluidized bed channels (horizontal fluidized beds), it extends after reaching the minimal fluidization velocity, firstly in the same way as the bed with unlimited height. This process goes on until the bed height is equal to the weir height. With further increase of the gas velocity solid particles are discharged over the weir, and the mass of the particles in the fluidized bed decreases, while the bed po rosity is increased. This process continues until the elutriation velocity is reached with which the bed pressure drop reaches the value of zero. In this limiting case only few particles are in the bed. As an example the dependency of bed pressure drop and bed height from the gas velocity is shown in Fig. 1 9 and Fig, il lustrates the dependency of bed porosity and bed mass from the gas velocity.
20
2.5. Air d istributor of the fl uidized bed
The air distributor of a fluidized bed strongly determines the functional behaviour of the bed. In particular with fluidized beds of large dimensions and with fluidized
41
Fluidized Bed Spray Granulation 15
3500 , - - - - - t - - - - - - - � - - - - - - -
3000
� 2500 e:.
_ _ _ _ _ _ _
0-
e "0 2000
� a '" 1 500 �
0"0 ., �
0
,
_ _ _ _ _ _ _
__ . _ _ __ I
_ _
- -
_ 1 I I
_
_
, ,
;
_ _ _
bed pressure drop bed height
---
I
_ _ _ _
_, __ .&..
, ,
_ _ _ _ _ .1 _ _ _ _ _
I
I
1
.!
_ _ _ .1 _ _ _ _ _ _ _ .1 _ _ _ _ _ _ _ . . _ _ _ _ _ _ _ !.. _ _ _ _ _ _ _ 1. _ _ _ _ _ _ _ _ _ _ _ I t I I I I I I
,
I
----
1000 500
:
, ,
- - - - - - - r - - - - - - - � - - - - -
,
I
I
I
I
I
, , ,
I
_ _ _ _ _ L _ _ _ _ _ _ _ � _ '
I
_
I
,
I
I
,
,
_
I
6
3
2
4
"E � ..c
I
_ _ _ _ � _ _ _ _ _ _ _ I
gas velocity [mls]
� ·0
- - ---
3
.-
��'�±=�==i'==1'��-J--J o
I Oll
---
I
I , I I I r - - - - - - I- - - - - - - - r - - - - - - - T - - - - - - - � -
_ _ _ _ _ � _ _ _ _ _ _ _ _ _ _ _ I
9
_ _
I
I
I
I
,
12
_
I
- - - r - - - - - - - 1 - - - - - - - , - - - - - - - -� - - - - - - - r - - - - - - - r - - - - - - - T - - I I I I - - - - r - - - - - - - , - - - - - - - � -
-
7
6
5
8
0
Fig. 1 7 . Dependency of the bed height and of the bed pressure drop from the gas veloci � with unlimited bed height (Aapp 1 m2 , = 300 kg , dp 2 mm , Ps = 1 500 kg/m , 9G = 20°C).
A4ed
=
€ �
0.8
0. 6
e
� .., o
.0
0.4
=
_
I I I I I I
- - - - - - - -
Fig.
I I I I I I
I I I I I I
�
- - - - - - - - -
�
- - - - - - - -
I I I I I I I I I I - - - - - - - - ,I - - - - - - - - - Ir - - - - - - - I I I I I I I I I I I I
I I I I I I
- - - - -� - - - - - - - - � - - - - - -
0
I I I I
_ _ _ _ _ _ _ _ �_ _ _ _ _ _ _ _ _ L _ _ _ _ _ _ _ _
I I I I I - - - - - _ 1_ - - _ _ _ _ _ _ 1 _ _ _ _ _ I I I I I I I I I I I I I I - - - - - - - -� - - - - - - - - t - - - - - - - -
.l- ----"
I I
-� - - - - - -
�
- - - - - - - - - � - - -- - - - -
I I I I I I I I I I I-I -1 ----+ 1 ----+-----4 ---� ----�------� --
�---�-o
I I I I I
I I I I I
2
3
4
gas velocity [mls]
5
6
7
8
1 8. De�endency of the bed porosity from the gas velocity with unlimited bed height 1m , = 300 kg, dp = 2 mm , Ps 1 500 kg/m 3 , 9G = 20°C).
(Aapp
=
A4ed
=
bed channels, the right construction of the distributor is very important. The sim plest (and often sufficient) constructions are perforated plates (sieve plates). The pressure drop of perforated plates can be calculated according to Hunt et al. [39] and McAllister et al. [40]. There are a series of other distributor designs, for example jet plates, CONIDUR@ plates that provide a directional airflow and bubble trays. The application of gas distributors with different opening ratios
42
L. Mörl
et 81.
3000 i--;::::;:====::;::==r----;---;---:---, 0.7 0.6 2500 0.5 ..:... 2000 ! 0.4 -:::6': � 1500 0.3 ; - bed pressure drop ]0. 1000 0.2 bedheight : � 500 � 0.1 , - - , - - - - - - - - r - - - - - - - " - - - - - - - -� - - - - - - -
, ,
, ,
• I I - - - - - - - - r - - - - - - - T - - - - - - - ,- - - - - - - - r
� �
I
,
I
, ,
-
,
_____
_ _ - - - - - -
_ - - - - - -
�
',;
I
- - - r - - - - - - -
-
..c: Oll
I - - - - - - , - - - - - - - -r - - - - - - -
�
- - - - - - - - - _ - - - - - -
- - - - - - -
, , ,
,
'" .0
- - - - - - - -r - - - - - - -
�
,
- - - - - _ _
I
O �--�r---�----_r--�--+--_+ O 0
2
3
4
gas velocity [m/s]
5
6
7
8
1 9. Dependency of the bed height and of the bed pressure drop from the gas velocity 2 limited bed height (Hweir 0.6 m, Aapp = 1 m , 300 kg, dp = 2 mm, 3 Ps = 1 500 kg/m , 9G 20°C). Fig.
with
A4ed
=
=
0.8 - - - - - - � - - - - - - -� � 0.6 :: ]R 0.4 + - ...<: -� -bed porosity 0.2 bedmass -
, ,
-
-
=
350 300 250 200 �
------�-
�
�
'Vi
- . ..
- - - - - - - -
-------�-- -
.0
- - - -
-
- -
:- - -
- - -
, --
""
�
1 50
;.. -
- - .. - - - _
-
100 50 80
dl .0
O �----r-----�--r_--�r_--�--_+ o
2
3 gas velo4city [m/s] 5
7
6
Fig. 20. Dependency of the bed porosity and of the bed mass from the gas velocity with 2 = 300 kg, dp 2 mm, Ps = 1 500 kgl limited bed height (Hweir = 0.6 m , Aapp = 1 m , 3 m , 9G 20°C). =
�ed
=
and a vertical incoming flow promises advantages; however, must be exactly calculated. Constructive specific features (heat strain of the plates, blockage of the holes) have to be considered. In the following, the pressure drop of a perforated plate will be calculated as the most common air distribution plate for fluidized beds. One distinguishes between two designs, explained in Figs. 21 , 22, 23, and 24, with d = hole diameter, S = air distributor thickness and Ss = spacing.
43
Fluidized Bed Spray Granulation
d
Fig.
21 . Hole diameter and air distributor thickness of a perforated plate.
1 .8 � � 1.6
.------r--�---�---__,.-__,
,
- - - - - - - - - - - - - - - - - - - -j- - - - - -
E
I
.g!l.. 1 .4
- - - -
.... o
- 1, -
I
-
,
I
- - -
-
- - -
- : ,
- - -
-
1 , ,
,
-
- -
_ _ _ _ - - - - - _ - - - - - - - - _
_ _ I_ _ _ _ _ _ _ _ _ _
I
-
---
_ _ _ _
�_
_ _ _ _ _ _ _ _ _
,
I
, , , ,
�_
., - - - - - - - - - - � - - - - - - - - - -
, ,
, ,
I
...
J
, , ,
J
-
- - - - - - - - - - .. - - - - - - - - - - I- -
_ _ _ _ _ _ _ _ _ _
I
_ _ _ _ _ _ _ _ _
... -
I
�
_ _ _ _ _ _ _ _ _ _
1
_ _ _ _ _ _ _ _
•
_ _ _ _ _ _ _ _ _ _
,
�
- - -
-
- - _ _ _
- - - -
-
_ _ _
_ _ _
•
, , , ,
l
_ _ _ _ _ _ _ _ _ _
0.8 o+--5 2 ratio3s/d 4 6----if--+--i--.;-..--l [-]
Fig. 22. Flow coefficient fram Hunt and McAllister [39,40] as a function of the ratio of the distributor thickness and the hole diameter.
Fig.
23. Spacing and hole diameter at equilateral triangle partition.
L. Mörl et al.
44
Fig.
24. Spacing and hole diameter at square partition.
Accordi n g to Hunt and McAllister [39,40] the pressure drop of the perfo rated plate can be calculated as folIows: 2 G [0.4(1.25 t/t) + (1 t/t)2] P (42) (�) K l1Pdislribulor 2 The opening ratio of the perforated plate distri butor t/t is equal to the ratio of the hole surface to the total cross sectional area of the distributor. The flow coefficient of the perforated plate distributor K = f(s/d) is taken from Hunt and McAllister [39,40] and plotted in Fig. 22. =
-
-
2. 5. 1. Equilateral triangle partition
Hole surface
Aho1e =
Triangular height
(43)
2
(44)
Triangular surface Opening ratio
t/t = Ahole = � d2
Aß
241t d
8
Aß
_2_ sshß
=
� if
8
=
sshß
(45)
2
2 2tan(300) 1ttan(300) d2 0.907 d2 (46) 2 s§ s§ Ss Ss =
=
45
Fluidized Bed Spray Granulation
2. 5. 2. Square partition
Hole surface
(47)
Surface of the square
Ao =
Opening ratio
!/t Aho1e =
Ao
=
s�
(48)
( n/4 ) d2 = 8S2
2 0 .785 8d2 S
(49)
2. 5. 3. Pressure drop of segmented perforated plates with different opening ratios
If the gas velocity on the perforated plate should be different, the distributor can be segmented. In this case, the single segments have different openi n g ratios and different hole dia meters. We can use the following calculations: Considering equation (42), for a segment n of the distributor folIows: [0.4(1.25 - !/t)2 - !/ti] (50) dlstnbutor,n 2 !/t Then, the pressure drop of the segmentes n is a function of the gas velocity (51) L'1 Pdistributor,n = distributor,n 0" n For a gas distributor with i segments (parallel connection) stands L'1Pdistributor,n = distributor, 0,,1 distributor,2 0,,2 = (52) distributor,3 0,,3 = . . = distributor/0,/ The total balance yields (53) A2 vG,2 A3 vG,3 with as the single surfaces of the segments and i s the correspondi ng gas velocities. Therefore the gas velocity on the respective segment can be fixed by suitable choice of the opening ratio of the single segments. We can also write 5 5 0 0 ) . ( ) . ( distributor distributor = = an d etc. (54) distributor, distributor,2 K
p . .
_
-
K
+ (1
PG
KP
KP
KP
1
.
VG
=
A1 VG,1 +
KP
=
KP
+ . . . + Ai VG,i
+
vG ,i
Ai
VG, 1
Ap
KP Ll
1
VG 2 '
Ap
KP Ll
L. Mörl et al.
46
A1 ( APddisislrlirbibuulolor,r ) 0.5 A2 ( APddisislrlirbibuluolor,r2) 0.5 A3 ( APddisislrlirbibuulolor,r3) 0.5 . . . (APddisisllrribibuulloorr,i) 0.5 With it the gas throughput is computable with given pressure drop or vice
Therefore folIows: VG
KP
=
KP
+
KP
+
1
+
+
A
KP
(55)
versa. However, it should be noted that for flu i dized bed channels with l i mited bed heig ht, the bed pressure drop also changes with the gas throughput by using weirs. 2.6. Fluidized bed channel apparatuses
Conti nuously operated fluidized beds for cooling or heati ng-up, for drying and also for granulation/agglomeration of particles channel-like fluidized bed apparatuses are used offen successfully. The principle of such an apparatus is shown in Fig. 25. The solid particles wil be fed (e.g., by a star feeder) onto a channel-li ke air di stributor. The fluidized particles that behave li ke a l i q ui d , flows through the channel in horizontal di rection to the particle outlet. Offen, weirs are arranged in vertical flow deriction to affect the longitudinal dispersion. These weirs can be flooded or an undercurrent flow can be realized. The solid mixing between two weirs can be assumed as ideal. At the end of the channel is a weir for the di scharge of particles in a discharge equi p ment (e.g ., star feeder). The pneumatic stability can be mai ntained by different ways, described in the following sections.
D
solid feed
0 1-------1
{
'" o
oo o
Fig.
inlet
weir
0
0
0
o
gas
0
0
0
0
0
'"
0
co
0
0
0
o
solid discharge D
25. Simplified schematic of a fluidized bed channel apparatus.
47
Fluidized Bed Spray Granulation
2. 6. 1. Setting of a constant bed height by a weir
The basic schematic of this control strategy is shown in Fig. 25. The height of the fluidized bed is kept constant by using an adjustable weir. If more solid i s fed, the weir discharges more soli d , and if no sol i d is fed, the fluidized bed remai ns stable, because in this case no solid is discharged over the weir. Moreover, the pressure drop is nearly independent of the solid particles throughput. Nevertheless, unli ke height-unlimited fluidized beds with a constant bed pressure drop, here the bed pressure drop depends strongly on the gas throughput. A wrong constructio n of the apparatus can lead to instabi lities in fluid ization. Such a worst case can appear if the characteristic curve of the fan has two or three intersection points with the total pressure of the fluidized bed plant. In Fig . 26, the fundamental pneumatic behaviour of such a fluidized bed is shown. The bed pressure drop rises progressively for the fixed bed range below the minimal fluidization point. After achievement of the mi n i m al fluidization point, the sol i d particles are discharged over a weir with a height corresponding to the bed height and the bed porosity increases. As a result, the bed mass decreases as folIows: (56) tvfj,ed = AappHbed (PS - p,)(1 - c) � BappLappHbed ps(1 - c) with Bapp as the width of the fluidized bed channel and Lapp as the length of the
fluidized bed channel.
6000 �---:----::--:---:--:-r=�====� 5oo . . . .. . ilProxcd bed 5000
�
!� ::l '" '"
� c..
- - - - - - - I--
I I - - - - - i-
I
, I
,
minimal fluidization point
- ilP,pp
- - - ilPbed
400
- ilPtOt
- bed mass
,
4000
,
- - - - - - - I,- - - - - - - - rI - - - - - - - I - - - - - - - -I - - -
,
I - - - - - - - r I - - - - - - - 1I - - - - - - - - - - - - - - - - r - - - - - - - - - - - �, - - - - - - - -�
3000
_ _ _
1 _
,
,,
_ _ _ _ _ _ _ t _ _ _
,' . - ' ,
___
, _J ,,
,
300
,
E "E
�
'"
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ L _ _ _ _ _ _ _
200 .0
I I I .�� _ _ _ _ � _ _ _ _ _ _ _ J _ _ _ _ _ _ _ _� _ _ _ I I I
2000
�
:� -_ _ L _
100
1 000
O +---�====��--�-----4--�� O o
3
2
4
gas velociry [m/s)
5
6
7
8
Fig. 26. Pneumatic behaviour of a fluidized bed channel plant with constant bed height for 2 an example (Aapp = 1 m , Hbed 0.5 m, � = 30, dp 2 mm, Ps = 1 500 kg/m3 , 9G = 20°C). =
=
48
L. Mörl et al.
[ (
)]
With equations (5) and (30), we can rewrite 0.21 2 18Re 0. 3 6Re .bed Bapp app be dPS 1 Ar If the pressure drop of the fluidized bed can be expressed as IV/p •
L
_
H
+
-
[ (18Re
)]
(57) (58)
0 .21 2 0. 3 6Re (59) bed - bedgps 1 Ar In Fig . 26 the progression of this function is shown. The pressure drop of the apparatus is (60) with � as function of the Reynolds number. The total pressure drop of the plant without the fluidized bed pressure drop permanently rises, while the total pres sure drop of the plant with the fluidized bed and apparatus pressure drop i s (61) LiPtot LiPapp LiPbed Normally, the increase of the apparatus pressure drop is so big that the de crease of the total pressure drop after reaching the mi n i mal fl ui dization point is uni mportant. However, in unfavourable cases a strong decrease of the total pressure drop after reaching the mi n i mal fluidization point occurs (see Fi g . 26), when the pressure drop of the fluidized bed is big compared to the apparatus pressure drop (tall fluidized beds). If now a fan is selected which has the characteristic curve, shown in Fig. 27, then three intersection points between the fan curve and the curve of the total pressure of the fluidized bed plant can occur. These would lead to three the oretical operation points. In the case shown in Fig. 27, the mi n i m um flui dization point cannot be reached after turni ng on the fan, if the fluidized bed channel apparatus is fil ed with soli d , characterized by the operation point 1. Nevertheless, the problem can be solved if the start-up phase begins without hold-up and if the particle feed is slowly decreased. Under these circumstances another stable operation point (point 3) appears. Nevertheless, such a system i s not to be recommended, because the apparatus cannot be started agai n if by an irreg ularity the entire fluidized bed has fil ed without gas supply with soli d . In such a case, only a part of the fl uidized bed material must be discharged to reach again we get
Ap
L.).
_
H
-
=
+
+
49
Fluidized Bed Spray Granulation 5� �
�,
4500
_ _ _ _ _
--
--
!
, �,
3�
_
�,
----�---...... ÖPr.,cd bcd �--r===== ==� -- ÖP,pp
_ _ _ _ _ _ _ _ _ _
,
, _ _ _ _ _ _ _ • _ _ _ _ _ _ _ _ _I _ _ _ _ _ _ _ _ � - - - - - - - -
---y-�-- -';' - �' n -
3500
8 2500 0..
�
_
- - -�
4�
�
'
,
--
-� -----
-!=-: minimal , fluidizatio? point !
---
" ,
;:';:
!,
!
- -
- -
- - - -
- - - - - -
.., ....
�
Mtot
-- -- - - -
-
, , , _ _ _ _ _ _ _ _ J. _ _ _ _ _ _ _ _
"'='
�
ÖPbed
--
-fan curve
- - - - - - - - - - - - - - - - - - ..., - - - - - - - -
- -
'"
2�
--
- - - - - � - - - - - - - - I- - - - - - - - -I - - - - : �� - � - - - - - - - - � � I I I � _' I I I I ,-_ I I I I I , I I I �_ I I I - - - - - - - - .- - - - - - - - - ,- - - - - - - - -. - - - - - - - - -, - - - - - ....... : - 1 - - - - - - - - 1 - - - - - - - - -
0..
1 500
I I
I�
_
500 0 0
I I I - _ ..' I , I ,...... - .. .. I I I I I _ _ _ _ _ _ _ L _ _ _ _ _ _ _ _ I_ _ _ _ _ _ _ _ � _ _ _ _ _ _ _ � _ _ _ _ _ _ _ _ J _ _ _ ::
:
:
:
:
I
I
I
I
2
3
4
5
I I I
:
I I
.J _
I
-
--
- - -
-------�--------1- --------:-------- � - ----�--------�-- - �:·;�o·t:·: ·-,�.� :
-
gas velocity [m/s]
"
'
"
_ _ _ _ _ _ _ l _ _ _ _ _ _ _ _ '"
elutriation point "-
6
7
8
Fig. Characteristic curves of the pressure losses of a fluidized bed plant with critical behaviour (parameters from Fig. 26) . 27.
a stable pneumatic operation range. The theoretical operation point 2 is an in stable point, which cannot appear in real plants. At this point it should be noted that such a system could react sensitively to changes in the particle size distributi o n. Due to growth, the particle diameter leads to a reduction of the relative voidage of the fluidized bed by which the pressure drop grows again. Furthermore, with an unfavourable fan curve, an undershooti ng of the mini mal fluidization point leads to a worst case regarding the pneumatic behaviour of the entire plant. 2. 6. 2. Setting of a constant bed pressure drop by regulation of the discharge equipment
Stable pneumatic conditions of a conti n uously operated fluidized bed channel apparatus can also be reached by regulation of the discharged particle through put correspondi ng to the bed pressure drop. In this case no discharge weir is necessary, however, a discharge equi pment (e.g., a star feeder) operates at the end of the apparatus, as it is shown in Fig. 28. Besides, pressure drop controlled discharge equipments may be star feeders (so called rotary valves), screw conveyers or double oscil ating flaps. An advan tage of this system is that the bed pressure drop is nearly independent from the product throughput, as weil as from the particle size distri bution. Therefore the critical pressure drop for a given fan curve cannot be exceeded. Si milarly, another disadvantage of the regulation by a constant discharge weir can be avoided with
50
-D
L. Mörl et al. solid feed
0 1------' o o o o
o
Fig.
we
0
g'O
<e
0
co 0
0
00 0
0
0
0
<9
0
0
0 0 0 0
�
---------�--------------� 0� air distributor o
gas inlet
( :0 o0g 100 0 0 00 0 1 0 cP g lg � 0 <ö 0 0 00 0 0 o0 0
g
0
0
I
,..
I
0
�::::�����e -D
28. Regulation of the bed pressure drop with the product discharge.
this discharge equipment. If a shut down process of the fluidized bed granulation occurs, all particles wil be discharged by the discharge equipment. Indeed, this operation has also disadvantages in respect to the fact that the discharge equip ment can be permanently full-fil ed with solid particles, leading to problems with sticky particles. Furthermore, bubbles can lead to bed pressure fluctuations. How ever, a suitable damping is very easy. 2. 6. 3. Setting of a constant bed pressure drop by regulation of the gas throughput for fluidization
If strong variations of the particle-size distribution of the fluidized product occurs, a regulation of the gas mass flow for fluidization is also possible, correspondi n g to the bed pressure drop. In this case, a stationary discharge weir is necessary. Figure 29 i I ustrates the schematic of such an operatio n. This regulation is independent of the particle size distributions and guarantees a constant mass. Besides, the feeding and discharge equipments are not full-fil ed with particles. The change of the gas throughput changes the porosity of the flu idized bed and the corresponding bed pressure drop and the bed height must be limited by a discharge weir. The bed pressure drop is nearly independent from the product mass flow and from the particle size distribution. The regulation of the gas throughput can occur by controlling the inlet or outlet gas stream or by a frequency control of the fan. However, compared with the weir regulation, this operation sig nificantly raises the control expenditure. Also, a change of the gas throughput is not favoured in many cases. Again , a suitable damping of the oscil ating signal is necessary.
51
Fluidized Bed Spray Granulation
D-
solid feed
O t-----..... o
:0 0 0 10 0 0 00 0 1 0 0 0 0<9 0 0 � 0 0 0 0 ----0 0 0 0 - ---- 00----------0 o
0
we
·CO o o�<:F � o( l g
o
o
0
--
air distributor
og
<07 -
0
0
g<0 0
0
co
0
-
0
00
r--------------------� 1
L...____ ..-____-� gas intet
Fig.
solid discharge
29. Regulation of the bed pressure drop by the gas throughput for fluidization.
2. 6. 4. Setting of a constant bed pressure drop by regulation of a secondary gas throughput
proven solution is the application of a secondary gas stream, which classifies the discharged particles (Fi g . 30). The product is led at the end of the channel over a weir directly into a discharge shaft, which is fed from below by a secondary gas stream. In its bottom thi s shaft has a non-c1assifyin g discharge equipment that guarantees a constant operation without full-fil ing with particles. The throughput of the secondary gas stream is so regulated that the bed pressure drop remains constant, Le., always the same bed mass is i n the fluidized bed. The particle size distribution and the product throughput have nearly no influence on the system. Moreover, the regulation of the secondary gas stream can occur with throttle equi pments and also with a frequency regulation of the fan of the secondary gas supply. However, it should be noted that a regulation of the particle size distribution is not possible, because the changes of the size distribution would influence the throughput of the sec ondary gas stream, but the mass and the pressure drop of the bed must remain constant. change of the particle size distribution can be reached only by a change of the growth mechanisms, e.g. by a change of the nuclei mass flow. A
A
2. 6. 5. Setting of a constant bed pressure drop by regulation of a height adjustable weir
Figure 31 describes the fluidized bed channel with height-adjustable discharge weir. With constant gas supply and constant particle size distribution, the pressure
52
L. Mörl et 81.
D 0
o
solid feed
�
c1assification
1------'
o
w r
ei
0 0 g '6 0 02 10 o ov- g o
o
o
,.n
CO 0 7
0
0
0
0
0
0
00 0
0
0
0
0
0 '0
1
0
0
o o
9
c;0 0 0 0 G 00 00 0
00
. o
�L_--a=i�rd:i:str�ib:u:to:r----_t--����-
gas inlet
o
0
�
Fig.
0
0
------ ---
----
0
------------
secondary gas inlet solid discharge
30. Regulation of the bed pressure drop by a classifying product discharge.
D 0
solidfeed exhaust gas
1------'
height adjustable
gas inlet
�L.:.:==--t---r�J L
Fig.
�-� o
___________
solid discharge
31 . Regulation of the bed pressure drop by a height-adjustable discharge weir.
drop of the bed is directly proportional to the fluidized bed height. If changes of the gas throughput or of the particle size distribution occurs, corresponding to a change of the relative voidage of the fluidized bed and of the bed pressure drop, a stable operation can be achieved by regulation of the height of the discharge weir.
Fluidized Bed Spray Granulation
53
The advantages of this operation are the independency of the bed mass from the particle size distribution and the non-full-fil ed discharge shaft. However, the mechanical adjustment of the height of the discharge weir can often stuck in the fluidized bed by clamped solid particles. 3. SOLID SURFACE AREA AND GRANU LE GROWTH 3.1 . Contin uous fluidized bed g ranulation with ideal classifying particle d ischarge
For the particle growth a model of Mörl et al. [4 1,42] was developed with the following assumptions: 1. Steady-state operation. 2. Spherical particles in the bed. 3. Fl o w rate Mp of monodi s perse external nuclei i n to the fl u i d ized bed (particle feed). 4. Flow rate Mp, out of monodisperse product partie/es from the fluidized bed (particle discharge). 5. Constant water content of the liquid. 6. Negligible formation of internal nuclei, e. g . by attritio n, overspray (drying of liquid droplets before they can wet a solid particle in the fluidized bed), break age, 7. Negligible elutriation of nuclei. 8. Uniform distribution of all the liquid (solution, suspension, melt) onto the total particle surface. 9. All particles are discharged from the fluidized bed after reaching a desired critical product diameter dp,out. Assumptions 1-7 agree with practical experiences, but assumption 8 is only achievable at high liquid injection rates. Assumption 9 can be described by using Fig. 32. The real granulator with classifying particle discharge can be split into (a) a fluidized bed with ideal mixing and into (b) a separator. All particles hits the separator (c1assifyin g tube), but only particles which achieve the diameter dp ou wil be discharged. The rest remains in the fluidized bed. Assumption 9 is act complished when the relationship of the particles with a critical diameter to the particles with a diameter below the critical value in the circulating product is nearly zero. In practice an optimal construction of the apparatus discharge (see Section 3.3) as weil as of the air distributor (see Section 2. 5 ) supports the abi d ance of assumption 9. According to the assumptions the particle growth can be described as fol Iows: The increase of mass of a particle with surface area Ap in an infinitesimal time
54
L. Mörl et al.
x
fluidized bed
M bed p
I
gas distributor
,
9i
I------l
� M
•
.1
,
�
--! � M,.2
-t-+---Pr' r-
_ _
"0
Fig . 32. Schematic of continuous f1uidized bed granulation with ideal c1assifying particle discharge.
segment dt (Fi g . 33) by assuming a uniform liquid distribution onto the particles is dmp = � ML(1 x) (6 2 ) dt I: Ap Assuming a constant particle density the change of mass can be expressed i n terms of particle volume dmp = Pp (6 3) dVp _
Ap(t) = n:[dp(t)f
The change of particle volume with respect to particle dia meter is defined by dVp = d((n:/6)cfp) = � d� (64) 2 ddp ddp
55
Fluidized Bed Spray Granulation d
Fig.
ddp
p+ dt ut -
A
33. Model of the linear particie growth.
Appling the chain rule we obtain for the growth rate of particles ddp ddp d Vp dmp dt d Vp dmp dt Combining equations we obtain the final expression for the particle growth rate ddp = x) G= dt Ap � ps = With the i n itial condition t to follows dp = dp,o. Thus, the time-dependency of the particle diameter is given by -
- . --
.
--
(65)
(62)-(65)
2 ML ( 1
-
(66)
(67)
Hence, the model of the linear particle growth folIows: dp (f)
-
-
2 ML(1 '\" 6
x) t + dP,O
Apps -
(68)
Analogous, a time-dependency of the surface and of the volume of a particle is with equation (66)
TC
Vp (t) = 6 (dp,o + Gt)
3
(69)
(70)
The total surface area of all particles i n the fluidized bed can be expressed as
(71 )
56
L. Mörl et al.
where I-np is the total number of all particles in the fluidized bed and Äp is the mean surface area of a particle, which is computeC\ from 1 t=tv
Ap -tv 1t=o Ap(t) dt =
(72)
The residence time t is the time which needs a feed nuclei with the diameter , at ti me t = to reachv the diameter dp,out. After reaching dp,out the nuclei wildpbeo discharged from the fl uidized bed by the ideal classifying tube. The integration of equation leads to ( 3) Äp = i { [(Gtv)2 + 3Gtvdp,0 + 3d�,0] Thus, with equation and t tv and dp = dp,out results 0
}
(72)
(68)
=
dp,out
+ dp,o or Gtv dp,out -dp,o I n serting equation in equation follows Ap- 1t [ ( dp,out - dp,o) 2 + 3 (dp,out - dp,o) dp,o + 3d2p,0] i (d�,out + dp,outdp,o + d�,o ) -d�,o) (3 dp,d�,ooutut -dp, o The mean surface-based diameter is then [ ] 3 d O P, o ut P, p 3 (dp,out -dp,o) =
Gtv
=
(75)
7
4
(7 )
(75)
(73)
= 3" =
= �
Ci =
_
rfr,
(76)
1 /2
(77)
Analogous, a mean volume of a particle can be calculated 1 1t=tv Vp(t)dt
Vp tv
(78)
t=o By inserting equations and into equation an integration folIows: -t3,0]} Vp 4 { [( Gtv)2 + 4( Gtv)2 dp,o + Gtv)2 d2p,o + 4 0p ;4 [(dp,out - dp,o) 3 + 4 (dp,out - dp,o) dp,o + (dp,out - dp,o) d�,o + 4ifp,0] ;4 (ifp,out + d�,outdp,o + dp,outd�,o + ifp,o) 4 (cfp,dp,ooutut --dp,cfp,oo) = -
(70)
-
=
=
1t
2
(75)
(78)
6(
2
6
=
1t
=
2
(79)
57
Fluidized Bed Spray Granulation
A mass bala nce gives Mp + ML(1 - x) = Mp,out With the assumption np = np,out we obtain . np
=
=
(80)
17,
Mp Mp,out ( n/6 ) cfp,ops - ( n/ 6 ) cfp ,outPS
Mp + ML(1 x) Mp - (n/6 ) d ,outPS � (n/ 6 ) d�,op s -
d�,out d�,o
Mp + ML (1 - x) Mp
[ . ] 1 /3
and the outlet dia meter can be expressed as dp, out
=
ML( 1
- x)
dp,° 1 + ---=:.. _...:. ..::..-,.. Mp
(81 ) (82)
(83)
(84)
Accordingly, to equation (71 ) the total number of all particles in the fluidized bed I. p must be cal c ul a ted. The mass of al l parti c l e s i n the fl u i d i z ed bed i s constant. Wen can write L: np = � = � (85) Vp Ps where Mp represents the mean mass of a particle. Considering equation (79), we get be M d
be M d
Mp
""
� np -
_
24M�ed
nps
(
dp ,out - dP,O 4 4 dp,out - dp,o
)
(86 )
The total surface area of all particles in the fluidized bed is computed with equation (71 )
(
)
= 8MPs�ed �d ,out -- dd�,o (87) p, o p,out Assumption 9 can be used to calculate the residence time of a particle to grow from the dia meter dp,o up to the final diameter dp,out. Thi s is the residence ti m e of a nuclei and not the residence time of a product particle in the fluidized bed. With equation (75) we obtain (88)
58
L. Mörl et 81.
By using equation (83) to get the ratio of the mass of a nuclei to the mass of a discharged particle
Mp cfp o = Mp Mp + ML(1 - x) Mp,out = cfp,�ut the residence time can be written as / 4 Mpbed [ 1 (�)1 3 ] [ 1 (�) ] Iv 4 � / ML(1 -X)Me1 - (� 1 ) Mp,out _
_
=
(89)
(90)
It is also necessary to calculate the fraction of the particle mass that stays longer i n the fluidized bed. Hence, we can define the corresponding time ts ts = tv - t
(91 )
The time-dependent single particle mass is related to the mass of the discharged particle This yields Mt>(t)
Mp ( f) 6 Mp (t) = M ( = � f) Mp,out ncfp,outPS
(92)
�
(93)
3 1 ML ( 1 - x) (tv - ts ) + dp,o ] = 0P,out [ Ps L Ap .
With
2ML(1 [ 4 4 L(1 1 M - x)(dp'out - dp o) 3 ' tS] M:.p ( t) - -- dP,out - M;ed 4 Ps (dp,out - dp,o ) x)
folIows:
(94)
.
ce P ( P,out
- d3P,out
_
ce ) P,O
(95)
The l i mits of these functions are ts = 0 and Mt> = 1, Le., 100% of the parti c i e mass have an resi d ence ti m e of tv = ts = 0 in the fl u i d i zed bed, and Le" the fraction of the nuciei mass of a particie = ts = tv Mt> = has a mean resi dence ti me in the fluidized bed wh ich is equal to the total growth time of a partieie tv. This simple model is capable for rough calculations. •
•
--'>-
(ddPp,out)3 MMp
P,out
,
59
Fluidized Bed Spray Granulation
3.2. Contin uous fluidized bed g ranulation with ideal classifying particle discharge and monodisperse n ucleation
In some eases (e. g . granulation of inorganie praduets) the internal formation of nuclei in the fluidized bed due to attritio n, spray dried liquid droplets (the so ealled overspray) or breakage of particles (see assumption 6) is not negligible. Henee, the following seetion derives an analytieal model for this formation of internal granules (nueleation) in the fluidized bed taking into aeeount the assumptions 1-5 and 7-9 of Seetion 3 . 1 [43]. 3. 2. 1. Granule growth
Aeeording to equations (62) and (64) the following expression is valid i n general terms for the volumetrie inerease of a particle in the fluidized bed (where y is the fraetion of the solid that is deposited onto the sphere) d �p = �6 [Cdp + d dp)3 cß.p] ML(1l:-Apx)ypsndp dt (96) With equation (66), a linear differential inerease of the di ameter of the granules with time is found x) dt d dp = 2ML(1 (97) p l: A ps Two separate eases must be eonsidered: Particles whieh arise fram the monodi sperse feed nuclei flowrate Mp , Particles whieh arise fram the newly-formed nuclei with the mass flow Md 1 x) .
_
2
=
-
•
•
(1 -y) .
-
If dp,Q is the diameter of the feed nuclei at the time of their addition, and dP,nuc is the diameter of the newly formed nuclei at the tim e of their orig in, then the dia meters, surfaee areas, and vol u mes ofthe granules (Table 1 ) ean be obtained as a funetion of the time fram equation (97). 3. 2. 2. Total surfaee area of all partieles
In equations (98-1 03), the total surfaee area of all granules is stil unknown, but ean be determined with equation (71 ) , whereby the total number of all particles in the fluidized bed is eomputable with (85). Thus, it is finally found that ( 1 04)
Cl o
Table 1 . Granule g rowth under consideration of monodisperse nucleation
Diameter
Feed nuclei
ML(1 - x)y 2 t d (t) = dP O + p
,
(98)
" L.. A P Ps
Surface area of a partic\e Volume of a partieie
\I,fed (f)
=� 6
[
]
(100)
ML(1 - x)y 3 2 t (102) dP,O + I: App s
Newly-formed nuc\ei M 2 L(1 - x)y t dnuc ( f) = dnuc + " A P Ps A nuc(f)
L..
(99)
]2 ] (103)
- X)y t = n: dnuc + 2ML(1 (101) I: A pPS
[ [
.
2ML(1 - X)y
t Vnuc (t) = 6 dnuc + I: A p ps n:
.
3
61
Fluidized Bed Spray Granulation
The mean surfaee area and the mean vol u me per particle for the two types of particles are as folIows: -
-
-
-
Ap Afednfed ++ Anucnnuc nfed nnuc V + Vnucnnuc Vp = fednfed nfed + nnuc
(1 05)
=
( 1 06 )
The assumption that all the solid particles leave the apparatus exaetly when they have reaehed the dia meter dp t gives the expressions for Ap and Vp for the two types of particles (Table 2). The residenee times of the solid partieles are then readily found fram equations (98) and (99) for the feed and newly-formed nuclei ,ou
� dp,o) L A pps t�ed = (dp,out2ML(1 - x)y
(1 1 1)
-:- dnuc) L Apps t�UC (dp,out2ML(1 - x)y
(1 1 2)
=
When equations ( 1 00-1 03) are introdueed, and allowanee is made for equation (1 07-1 1 0) , it follows fram equati o n (1 1 1-1 1 2) that Tabl e 3 ean be shown. The total number of nuclei i n the fluidized bed ean readily be obtained from the two fluxes of nuclei and the residenee time of a particle (Table 4). The mean surfaee area and the mean volume of a particle in the fluidized bed ean now be determined fram equations (1 05-1 1 0) together with equation (1 1 8) and equation ( 1 20). (1 2 1 ) Table 2. Integrals
Mean surfaee area of a particle Mean volume of a particle
Feed nuclei
1 A fed = f"" tved Jor v A fed (t)dt tled
Newly-formed nucl ei uc _
(1 08)
(1 07)
Vfed t Jor v Vfed (t)dt v 1
=
tled
ted
(1 09)
r�
A nuc = t�1UC Jo A nuc(t)dt V
nuc tv Jor v Vnuc(t)dt 1 = nuc
tnuc
(1 1 0)
62
L. Mörl et al.
Table 3. Solution of the integrals
Mean surface area of a particle
A-fed -
Mean volume of a particle
(
) ,0 )
Feed nuclei - �3
_
n Vfed = 24
)
d A- nuc - � �,out - �uc 3 dp,out - dnuc ( 1 1 4)
ifp,out - ifp,o dp,out - dp,o (1 1 3)
('
(
Newly-formed nuclei _
cfp out - cfp dp,out - dp,o (1 1 5)
v: - nuc
_
(
� cfp,out - �uc
- 24
)
dp,out - dnuc ( 1 1 6)
Table 4. Number of nuciei in the fluidized bed
Feed nuclei
nfed
fed ,tCi;ed
= 3n·
( 1 1 7)
Newly-formed nuclei nnuc
_
-
( 1 1 9)
3 (dp,out - dnuc) ( 1 - Y) ( 1 20) 3 n dnucY
( 1 22)
Hence, and with equation (1 04) the total surface area of all particles in the flu idized bed can be calculated. ( 1 23)
It should be noted at this point that another constrai nt on the quantities .o , dnuc and dp,oul stil exists, so that only two of these quantities can be freely seldpected at a given feed rate of nuclei and a given liquid flow rate. This gives ( 1 24)
63
Fluidized Bed Spray Granulation
-1 �jnLnn
60 .-----�--�----.--_.
� g
50
6.5
- - - - - - -.'� -. ,,: ... "f : : � .' , ,, , �, .,
_ _ 0
'" u
� 3 '" 40
�
'"
,
ü
.�0.. B
;.
.-
öl 30
7
- -
, , ' f ..
- - - - - - -
,,
...
-
-
- - - - - - -
6 - - -
5.5
5
- - - - - - -
4 4
I.... *
a .5 :a ti <'3
::l "0
e
0..
3 .5 3 2.5
20 0.5
0
1 .5
2
3
2.5
4
3.5
nucleation rate ( I -y) [%]
Fig. 34. Dependency of the total particle surface area as from equation (1 23) and of the product diameter according to equation ( 1 25) upon the nucleation rate (M$ed 25 kg, Mied = 2 kg(h, ML = 1 00 kg(h, X = 80 mass-%, dp.o = 3 mm, dnuc = 1 mm, Ps 1 200 kg(m 3). =
=
From equations the granules folIows:
( 1 1 3), (1 1 4), (1 1 8)
and
(1 20),
the outlet or product diameter of ( 1 25)
Hence, the assumptions that have been made permit calculation of the total surface area of all solid particles in the fluidized bed. As an exampl e , the re lationship for this surface area as weil as of the product diameter as a function of nucleation rate is shown in Fi g . Apart from providing an exact prediction of the discharge dia meter, equation is particularly suitable for determining the nucleation rate - y) in experimental investigations, since all the other quan tities in the equation can be calculated easily. 34. ( 1 25)
(1
3. 2. 3. Size distribution in the fluidized bed
According to the assumptions, all solid particles leave the fluidized bed through the c1assifying tube when they have reached the diameter dp,out. This assumption can not be satisfied exactly in a technical plant so that, i n reality, the di ameter dp,out must be regarded as the mean di ameter of a distribution, whose width, to a first approximation, is a function of the constructional parameters of the plant. On the other hand, when the size distribution in the fluidized bed can be [44],
64
L. Mörl
et al.
determined easily and exactly, the derivations above can be checked experi mentally under suitable conditions. In the calculation of the particle size distribution i n the fluid ized, two ranges of dia meters must be disti n guished: Gase dnuc dp,o : Range dnuc :( dp dp,o Range dp,o :( dp dp,out Gase dp,o dnuc : Range 1 dp,o :( dp dnuc Range dnuc :( dp dp,out Density di stributions related to the number, the surface area and the mass can then be determined theoretically in these ranges (referred to a unit mass of material) . Accordi n g to the assumptions, the following expression is valid in the first range of the first case: 1
2
<
:
1
:
<
2
:
<
:
<
:
<
<
:
2
=
M qo
nnuc j Mpbed = n. nuc tvnuc dP,out - dnuc ( dp,out - dnuc ) Mpbed
( 1 26)
From equations and we get equation By analogy, the surface area distri bution and mass density distribution can be calculated for this range as ( 1 20)
(1 23) ,
( 1 30) .
( 1 27) ( 1 28)
For the range dp,o ::::; dp dp,out, the effect of the feed nuclei must be taken into account. Accordi ng to the definition of the number density distribution <
M qo =
nnuc (dp,out dnuc) �ed . ..nuc nnuc1v (dp,out - dnuc) �ed _
+ +
np o (dp,out - dp,o) �ed . .Jed nfed lv (dp,out - dnuc) �ed
( 1 29)
Thus, equation folIows. Hence, the surface area distribution and the mass density distri bution i n this range can be calculated by equations and Analogously, the density distributions for case can also be estimated, summarized in Table 5. ( 1 33)
( 1 27)
( 1 28).
2
3. 2. 4. Residenee time of the solid partie/es in the fluidized bed
From equations 1 1 ) and 1 1 , with the help of equation the tim e requi red for an feed nucleus to grow from diameter dp,o to the diameter dp,o ut, or for a newly-formed nucleus of diameter dnuc to grow to the diameter dp,out, can be (
1
(
2)
( 1 23),
"Tl
C Cl:
Table 5. Summary of density distribution functions
§" 0..
Density distributions
Range Gase Range
dnuc < dp,o dnuc :( dp < dp,o
OJ (1) 0..
( 1 30) � ru '< G) ru ::l c
ru
(1 31 )
( 1 32)
Gase Range si m ultaneously: Gase Range
dn uc < dp,o dp,o :( dp < dp,out
and
( 1 33)
dp,o < dnuc dnuc :( dp < dp,out ( 1 34)
g
Table 5.
Range
Continued
Density di stri butions ( 1 35)
Case dp,o dnucdp Range dp, o � <
<
dnuc
( 1 36)
( 1 37)
( 1 38)
67
Fluidized Bed Spray Granulation
ealeulated explicitly ( 1 39)
( 1 40)
Henee, the two residenee times of the solid particles are direetly proportional to the ratio of their differenees from the diseharge diameter t�r
(dp,out - dp,o)
tvnuc - (dP,out - dnuc )
(141)
This predietion is partieularly important when dealing with temperature-sensitive materials, whieh should not stay in the fluid ized bed for longer than some spee ified time. 3.3. Contin uous fluidized bed g ranulation taking into account design parameters
Besides the proeess parameters, eonstruetional or design parameters of the ap paratus may have an influenee on the particle size distribution during granulation in a fluidized bed. The model of Seetion for the ealeulation of the surfaee area as weil as the residenee time negleets the fraetion of the particles whieh remains Ion ger than the time tv in the fluid ized bed. Effeetively, not all particles that reaeh the eritieal diameter are in the effeetive zone of the classifying diseharge tube. Due to their size distribution within the fluidized bed, their individual veloeities and streamlines, the partieles need a random distributed time until they reaeh the area nearly the classifying diseharge. The partieles grow also during this tim e beeause of the liquid injeetion and the solid depositi o n. The result is a eertain size dis tribution of the diseharged particles. Mörl et al. developed a model that prediets these influenee of design parameters on the particles size distributio n. The model assumes a eylindrieal apparatus with a radial inereasing opening ratio from inside to outside and a eentral loeated elassifying tube. The solid flow profile in sueh an apparatus is deseribed in Fig . The particles wil be trans ported upwards at the outer border of the fluid ized bed. At the top of the fluidized bed, the partieles falls into the eentre of the fluidized bed and wil be wetted by the eentral adjusted nozzle. At the bottom of the fluidized bed the wettest particles have eontaet with the hottest part of the air and wil be transported from the inner regions to the outer border before they wil be transported upwards agai n . 3.1
[44]
35 .
68
Fig.
L. Mörl et al.
35. Schematic of the probability model.
This model simplifies the stochastic movement of single particle. For the cal culation of the mean particle velocity in the flu i dized bed, an el li psoidal streaml i n e is approximated by a rectangular streaml i ne. A further assumption is that the probabil ity of discharge after the impact of a particle with dp > dp, t onto the classifying tube at one circulation is equal to the surface area ratio Asepou/Aapp, with Asep as cross sectio nal area of the classifying tube and Aa pp as total cross sec tional area of the flu i dized bed. With these assumptions we get with one-particle circulation for both events: peT) = �aseppp (partic/e impact onto the classifying tube) (142) A 1 - P( = 1 - sep (no particle impact) Aapp
T) (143) where Pis the probability of one impact of a particle onto the classifying tube. For ncirc ci r cul a ti o ns of the particle wi t h k as number of successful coll i s i o ns between a particle and the classifying tube, the following equation must be val i d : (144)
The probability of at least one col l ision P (x� 1 ) can be calculated with the prob abil ity of no collisions P (x < 1 ) P(x� 1 ) = 1 - P(x< 1 )
(145)
69
Fluidized Bed Spray Granulation
with k
=
0 P(x � 1 ) = 1
_
( nCirC ) (AAsep�p) O ( 1 o
_
)
Asep nCirC- O A �p
(146)
Hence, the number of circulations i , which are necessary for at least one i m pact with the probability P (x � 1) incs rc In[1 (- P(x :::: )1 )] (1 47) ncirc In 1 If a constant mean particle velocity vp is assumed, thus the necessary time for one circulation is =
_
Asep Aapp
2Hbed + Dapp t1 = Vp
and for ncirc
(1 48)
I n [1 ( P(x ::::)1 )] (1 49) In 1 The essential assumptions are that the diameter of the particle is much smaller than the dia meter of the classifyi ng tube, and that every particle that has an i mpact with the tube wil be discharged. Fig. 36 il ustrates for an example the time-dependency for at least one collision with the classifying tube at a certai n probability as function of the ration of the cross sectional area of the classifying tube and the total cross sectional area of the fluidized bed. Instead of the probabil ity P (x � 1 ) also the fractio n of the particles which are in the fluidized bed at time t 0 and that wil be discharged at time tn can be introduced. Thereby, only particles are taken into consideration for which is dp:::: dp,ou , i . e ., al l partic les whi c h may be di s charged. With these assumptions follows t I n ( 1 - �) 2Hbed + Dapp tnctrc (1 50) Vp In ( 1 ) where np,out is the number of particles, which wil be discharged from the fluid ized bed after the time tn by using the classifying tube and n:::.dp out is the total number of particles in the fluidized bed with the dia meter dp � dp,out. The fraction of the particles remaining i n the flu idized bed is then np,in np,out 1 (151 ) p ut p p n ,:,:d ,o n ,:,:dp,out tncirc
=
2Hbed + Dap p Vp
-
_
Asep Aapp
=
.
npedp,out
_
_
=
_
Asep Aapp
70
L. Mörl et al. 1 200 --- A",p/A,pp -<>-
1 000
--.-
-I>-
800
-+-4-
�
.§ '"
-+-
600
...q....
-><-
400
-+-
0.0 1 = 0.02 = 0.03 = 0.04 = 0.05 = 0.06 = 0.07 = 0.08 = 0.09 = 0. 1 =
-
, - - - - - - -�- - - - - - - - --- -- , - - - - - - - - - -
_ _ _ _ _ _ _ � - - - - - - - - - - - - - � - - - - - - - - - - - - - -I- - - - - - - - -
,
, ,
, ,
, ,
,
_ _ _ _ _ _ _ _ L _ _ _ _ _ _ _ _ _ _ _ _ _ � _ _ _ _ _ _ _ _ _ _ _ _ _ _ I_ _ _ _
,
,
,
,
- - - - - - - -� - - - - - - - - - - - - - { - - - - - - - - ,
- - - - - - - - - - - - - -, - - - - - - - - - - - - - - ,- - - , , , ,
200
I , , ,
- - - - - - - - - - - - - - -
O ��'������ o
0.4
0.2
-
0.8
0.6
p (x � I )
Fig. 36. Required time for at least one collision of a particle with the classifying tube as function of the statistical probability (Hbed 0.5 m, Dapp 0.5 m, vp 0.5 m/s). =
=
=
With both equations results the time-dependency of this fraction (152) These dependencies can be proved very easily by experiments [45], whereby the fictive particle velocity vp can be determined (see Fig. 37). Under steady-state conditions and with ideal particle mixing results for the unsteady case with np as particle flow d (� np�dp,out ) nP,in np (153) dt np ::: dp,out np:::dp.out This differential equation can be solved with the initial condition t 0 : npn:::P,indp.out 1 (154) by integration np.in- d (� 1-nP�dP.out np>-dp.out ) - 1 np (155) =
1
=
nPi' n nP:::dp,out
-
=
0 nP>dpout - , t
.
71
Fluidized Bed Spray Granulation
,
10 8 --------------
,, �,
_ _ _ _ _ _ _ _ _ _ _ J. _
- - - - - - t- -
�
- - - - - - - - -
- - - - - -
-f:r-0O �======�==���--��� 4
- - - - - - - - - - - - - - - - - - - -
-0-
2
vG = 7.62 mls vG = 6.74
- -
vp = 0. 1 4 m/s
-t
m/s -t
vG = 6.08 m/s
vp = 0.087 mls vp = 0.026 mls
-t
0. 1
Fig. 37. Experimental results of Jännert [46] for the fictive particle velocity at a fluidized bed plant with Dapp 0.4 m and Dsep 0.07 m. =
=
and solution of the integral
-,
n p in n p �dp.ou'
- '- =
np t ) exp (- --np�dp.ou'
(1 56)
With equations (1 52) and ( 1 56) the number of particles in the diameter range dp � dp,out can be written as np (2 Hbed + Dapp ) (1 57) n p �dp.ou' vpln ( 1 - �) =
A Aapp
_
By feeding of spherical and monodisperse nuclei of same density into the flu idized bed follows with equation (81 ) 6Mp (2Hbed + Dapp ) (1 58) n p �dp.ou' = ( A) ndp o Ps Vp In 1 - Asep where Mp is the feed particle flow, dp, is the diameter of the monodisperse particles and Ps is the particle density . Theo mass-based density distribution of the particles by using the apparatus configuration of Fig. 35 is shown in Fig. 38, whereby q't characterizes the number of particles at a certai n diameter related to the mass of 1 kg particles/m. 3
_
,
app
72
Fig.
L. Mörl et al.
38. Mass-based number density distribution and particle diameter as function of time.
At time tv all solid particles achieves the diameter dp,out and begin to fall out off the fluidized bed. For a better mathematical description the time 0 is introduced 0 = t - tv (159) corresponds to the time t in equation (152) and to the time t, which is past since the entry of a nucleus with the diameter dp,o into the fluidized bed. The function qr1(0) can be calculated with t7p0 ) qo (0) = exp ( - -(160) p n ?:dp,out with q� as mean mass-based number density distribution of the particles per kg and meter which is constant in the dia meter range dp, ut � dp � dp,o, because the absolute particle number is constant. Nevertheless,othe particles grow linearly from the diameter dp,o up to the diameter dp,out. Taking into consideration equa tion (157), we obtai n : ) 0vp I n ( 1 - AAsep app (161) q�(0) = q� exp o
M
%
-M
[
_
2 Hbed + Dapp
]
With the assumption of linear particle growth, we get: 0 = -tv and dp dp,o 0 and thus dp = dp,out =
=}
=}
o
dp - dp,out tv = dp ,out - dp,o
=
0
(valid for dp
2:
dp,out)
(162)
Fluidized Bed Spray Granulation
73
Now the density distribution as function of the diameter can be written as qo (1 63) q� Cdp) exp (Kwdp y expCKwdp) ,out This function is only valid for the range dp dp,out, whereas Kw summarizes some quantities: tvvp I n ( 1 �sep ) app Kw - ( (1 64) dp,out - dp,o ) (2Hbed + Dapp) The quantities q� and tv are stil unknown. With the assumptions the density distribution q� in the diameter range dp,o- dp,out and the total-residence time of a nuclei tv is calculable. If the number of particles in the fluidized bed in the diameter range dp,o-dp,out is much larger than the number of particles with a bigger dia meter than dp,out, the following equation can be written -M
=
�
_
_
(1 65)
Thus, with the total mass of the fluidized bed
M�ed
with
results
(1 66)
(1 67)
The mean particle volume Vp can be calculated by using the assumption np,dp o . dp,out » np.dP,out and equation (79). Now, q� i n the di a meter range dp dp,o ut can be calculated with 24 (1 68) qo (dp,out - dp,o) by using the residence time of a nucleus in the fluidized bed according to equa tion (88) 24 ex p (Kwdp) M(dp ) (1 69) (dp,out - dp,o) exp (Kwdp,out) �
-M
=
4
n
%
_
nps
4
4
Ps
4
(1 70)
L. Mörl
74 E
�
g-
600000 -r---,----,---..,---,---r--.--. - - - - - - :- - - f - - - ,- - - - - - - ,- - - - - - -,- - - - - - - - - - - - - - - - - - j, - - - - - - j - - - - - - j - - - - I I r ,
bI)
500000
I
'" o ';:J
B 400000
E::l
,' , ,I - - - - - I,,
I I
,
I - - - - - - r- -
300000
-
I
I
I I
200000 1 00000
.0 '" '" '"
E
o
I I
- - - - --r
I
-
:
I - r -
,
,
I
- - - - - -1 -
I I
I I
,
�
I
-
, -t---�' o
dp'o
0.002
_ _ _ _ _
,
- - - - -1 - -
, ,
I I
,
,
I I
,
I J_
f-+' 0.004
I I
I
-
,
,
I
,
�------�
- - - - - -
- - - - - -
,
�
- - - - - -
- -
,
,,
, - - - - - - , - - - - - - , - - - - - - T - - - - - -
_ _ _ _ _
--+----1 0.008 0.0 1
t--
-
--
I
_ _ _ _ _ _L _ _ _ _ _ 1_ _ _ _ _ _ _ 1_ _ _ _ _ _ _' _ _ _ _ _ _ , I I
I
, ,
,
i
,
I
l
, ,
-
I ( I - - I- - - - - - - , - - - - - - -,- - - - - - , - - I I i I I
.. - - - t- t
'"
1
�
I
"
I
'Ö
1l
I
I I _ _ _ _ _ _ � _ _ L _ _ _ � _ _ _ _ _ _ I_ _ _ _ _ _ _ _ _ _ _ _ _ �
.�
.� '" ., "0
et al.
- -
-
, �- --
- - -
-
- -
,
� -
- - - -
,
f-- --
,
I
0.0 1 6
0.0 1 8
-
-
0.006
0.0 1 2
0.0 1 4
0.02
particle diameter [ml Fig. 39. Mass-based number density distribution of the particies in the fluidized bed as function of the diameter for an example (!fbed = 0.8 m, Dapp 0.8 m, Dsep 0.08 m, vp 0.05 m/s, dp.o 3 mm, dp,out = 10 mm, ML 50 k9/h, x 80 mass%). =
=
=
=
=
=
This is the mass-based density distribution of the number of particles in the diameter range dp,out :::;; dp which is iI ustrated in Fig. 39 for an example. Fi g ure shows the influence of the diameter of the c1assifying tube on the number density distribution of the fluidized bed particles. Now, with the number density distribution the number of particles in the fluidized bed and the cumulative density distri bution can be calculated for both diameter ranges <
00 ,
40
0
1.
Range :
dp,o �dp�dp,out
np,dp,o .. dp,out = 0=
q�ddp dp,out � dp �
J:;:ut
2. Range :
np>dp - ,out
ldp,oP q�ddp d
q�(dp - �p,o)
+ J::'out eXP(K�dp,out)
=
=
q�(dp -dp,o )
exp(Kwdp)ddp
x
1 00
(1 71 ) (%)
1dp,out exp (Kwqo dp,out) exp(Kwdp)d d KwexprKwdp,out) [exp(Kwdp) -exp (Kwdp,out)]
(1 72)
00
-M
00
p
-M
(1 73)
75
Fluidized Bed Spray Granulation E
600000 .---�--�----.---�--'---�
� 500000 oJ)
-- - - - -...., I
,
c::
] 400000 .S2
'S :.c Vl
:> c::
]
- -
- - _
.... -
1
- - - - - - - - I
,
-
, ,
---
Dscp = 40 mm
-0-
= 60 mm
200000 . 1 00000 -
.... -
- -
- -
- - -1 - - - "1-
I
-
- -
-
I
- - - -
- -1I
- - - -
- -1 - - - - ,
- -
,
_ _ _ _ _ _ I... _ _ _ _ _ _ L. _ _ _ _ _ . 1... _ _ _ _ _ . . _ _ _ _ _ . I I I I ,
.� 300000 c:: ""Q.)
�
- - - - - _
- -
- - -
- - - - - - - - - - - - -:- - - - -
-
- ,,- - - - - - -,. - - - - - - -
= 80 mm
-
= 1 00 mm - -
-+--
= 1 20 mm
-0-
= 1 40 mm
o +-��==�==��--�--��� o 0. 002 0 .004 0 .006 0. 008 0 .0 1 0 .0 1 2 0.014 0.0 1 6 0.0 1 8 0.02 particle
diameter [m]
Fig. 40. Influence of the diameter of the ciassifying tube on the mass-based number density distribution of the particles in the fluidized bed for an example (Hbed = 0.8 m, Dapp 0.8 m, vp 0.05 m/s, 30 kg, dp.o 3 mm, dp.out 10 mm, flA 50 k9/h, x 80 mass%, Ps 1 500 kg/m ) . =
=
=
=
0-
Atff.e. d
=
=
=
(K d [exp(Kwdp ) - exp(Kwdp,out)] Kwexp w P,out)
=
-M
1 00 (%) - J:P,pou O t q�ddp + J:P,out exp(Kq�dP,out) exp(Kwdp )ddp X
W
(K d [exp(Kwdp ) - exp(Kwdp,out)] Kwexp w P,out) q- oM ( dp - dP,in ) - Ker� -M
=
X
1 00 (%)
( 1 74)
The resulting cumulative density distributions of the example in Fig. 40 are plotted in Fig. 41 . It is recognizable that the apparatus geometry has an important influence on the density distribution during granulation. Analogous, the density distributions for surface area, volume and mass can be written: 1. Range: dp, Q :( dp :( dp .out
qÖ(dp ) # f(dp) = q� q� (dp ) = q� n d� q�v (dp ) = q� � d� q�(dp ) = q� � d�ps
76
L. Mörl et al.
�
80
.tj
60
c o ';::l
E
:a o 'Vi
�
- - - - - - - - - - - � - - - - - - - - - ,
_ _ _ _ _ _ _ _ _ _ _ L _ _ _ _ _ _ _ ,
c
.�
öl :; E E
40
- - - - - - - -
,
�
- - - - - - - - - - -
T '
- - -
-0-
,
= 60 mm = 80 mm = 1 00 mm
20
= 1 20 mm
:::l U
O ����----�--��==�====� -4-
o
0.005
0.0 1
0.0 1 5 parlicle diameter [m)
0.02
= 1 40 mm
0.025
0.03
�ed
Fig. 41 . Influence of the diameter of the discharge tube on the cumulative mass-based number density distribution = 0.8 m, Dapp = 0.8 m, \lp = 0.05 m/s, = 30 kg, dp , o = 3 mm, dp,o ul = 1 0 mm, ML = 50 kg/h, x = 80 mass%, Ps = 1 500 kg/m ) .
(!:fbed
2. Range : dp ,oul � dp �
00
equation (169)
q�(dp ) = q�(dp) = q�(dp)d� q�v (dp) = q�(dp) � ifp q�(dp) = q� (dp) � ifpps
The above-mentioned equations are valid for the condition (175) The total number of all particles per kg in the diameter range from dp,oul to is (176) Taking into account equation (163), we get (177) np-> dP,out exp (:0 ) }{d ,out exp(Kwdp)ddp 00
=
d w P,OUI
-M
00
p
77
Fluidized Bed Spray Granulation
and the solution of the integral delivers
q�
ML (1 - x) (cfp,out - cfp,O) (2 Hbed + Dapp) np:o:dp,OU! = - Kw = - q-Mo 4/Vfred Asepp ) P (d3P,out _ d3P,O ) vp ln ( 1 _ Aa p *
(1 78)
For the total mass of all particles i n the diameter range dp,out to we obtain with equation (1 58), equations (1 68) and (1 78), 00 ,
np _ - * :O: dp,ou! MP :O: dp,ou! _ nP :O: dp,ou!
_
M. p ( cß,P,out - d3p,o) ed tv1?. d3P,O ML (1 - x) P
and with
(1 79)
(1 80) Mp>-dP,ou!
=
( 1 + d3 '
P,O ML
(1 -�)
(181 )
)
Mp (cfp,OU! - dp,o)
These assumptions yields the total number of all particles for both ranges dP, in < dp < dp ,out and dp ,out < dp < 00
(1 82)
and (1 83)
Analogous, the total surface area, volume and the mass of the particles in the ranges can be determi n ed. 3.4. Continuous fluidized bed g ranulation with non-classifying particle discharge
Basis for the calculation is the one-dimensional population balance for the conti n uous granulation aqÜ,bed L np aGqÜ,bed L np = qO,in n p,in - qO,outnp,out + at adp qü bed 'Lnp np,i n np,out *
.
*
.
(184)
describes the number density distri bution of the particles in the where fluidized bed related to the particle number, respectively include all
78
L. Mörl et al.
fluxes of the particles entering or leaving the granulator. The growth rate G is assumed as equal for all particles and independent from the di ameter, which means that a big particle gets more solid material per unit time than a smaller one (see equation), whereby the total surface area of all particles results from equation (71 ) with ( 1 85)
The assumption of constant bed mass leads to the fact that the sum of the feed and discharged mass flows is equal. This means, analogous to equation (80) that the discharged mass flow Mp,out is equal to the sum of i njected mass flow Ms and feed nuclei mass flow Mp . Taking into consideration a non-classifyi ng discharge of particles, the discharged particle flow np,out results from its dependency from the particle density distribution and the bed mass Ms Mp . " np,out = +ed qO,bed � np r-.j;.p *
(1 86)
Hence, from the population balance equation (1 84) follows under neglect of the ti me derivation " + Mp G 8qü,bed L np - np, m Ms .bed QO,bed � np 8dp IWp [dp,i; dp,i+1 ] Ip Qü bed n _
'
*
.
-
•
(1 87)
of the particle size, the number By integration over an interval can be substituted by the particle number np in the density distribution accordant interval . Ms + Mp G 8np = nP , in .bed np 8dp /VIp
( 1 88)
+ MP n P, . G np,i - np,i-1 - nP,m,1 Ms .bed I I1 dp IWp
(1 89 )
-
•
To determine the steady-state particle size distri bution, equation (1 88) must be solved. A possibility is the transfer of the partial differential equation by using the method of differences into a system of coupled ordinary differential equations .
. _
-
•
By transformation, we get the particle number in class I np,i =
,Gd np'i-1 + np ,in,i G + Ms +Mp
L}. p
8dp
(1 90)
M;ed p
The calculation of the particle number in a certain class occurs gradual starti n g with 1 to I. An explicit calculation of these expressions is not possi ble, because the surface-proportional growth rate G depends di rectly on the particle surface area. Nevertheless, equation (1 90) can be solved by a simple iteration (Fig. 42). i=
79
Fluidized Bed Spray Granulation
I I I I
estimate value I Ap
calculation
l
G
calculation np"
1
I I I
calculation I Ap,",w
end
Fig. 42. Computational sequence diagram of the continuous fluidized bed granulation with non-classifying particle discharge.
A selected calculation is shown in Fig. 44. A Gaussian normal distribution with a mean diameter dmean = 1 mm and standard deviation (J = 0.2 mm has been applied for the number density distribution of the nucieL The size distributions of the nuclei are il ustrated in Fig. 43. The resulting normalized number and mass density distributions of the bed material can be found in Fig. 44. By increasing the mass flow on the nuclei from 0.5 to 2 kgjh, Fig. 45 results. It is recognizable that the increase of the fraction + rlAp)/ M�ed leads to narrower particle size distributions. These ratio is equivalent to the mean residence time tv of the particles. For the limiting case tv 0, the particle diameter is constant. This means that the particle size distribution at the outlet of the system (product) is identical with the nuclei size distribution. (rIAs
-+
3.5. Simplified modelling of the u nsteady fluidized bed g ranulation
An advantage of the fl uidized bed spray granulation with a classifying discharge tube is the continuous processing with high product throughput and the possibi lity of process automation. Nevertheless, the unsteady behaviour is of interest for special cases, e.g., for the 1 coati n g of particles or production of spherical granul e s by si n gle-stage or multi stage batch processes,
80
L. Mörl 2.5
..;
E
�
iN -------i--b;j---
�-
2
e..
et al.
1 .5
1
------
-
- - -- - ----
-
-
-- ---- -- ----- - --- --
.
r- --
:
+
- - - - - - - - - - - - - -
-
-�----r---�--,
- - -
------ ------- ------ -----
e..
•
0; 0-
0.5
------ -------
- - - - - - - - - - - - -
- - - - - - -
o +---�--����--�--o 0.2 0.4 0.6 0.81 1 .2 1 .4 1 .6 1 .8 2 particle diameter [mm]
Fig.
Mp
43. Particle size distributions of the nuclei for the example calculation (Ms 0.5 kg/h, tvfped = 30 kg , Ps 1 500 kg/m3).
=
=
20 k9/h,
=
0.6
E .§ .
�
E .§
0-
�
- -- -- -�- -- --- � - -- --- �- -- --- �- ----- �- ----- r- -- - -- r- -- - --
0.5
I
I
I
I
I
I
q�.bcd
I
, �------�------�------�- -----�------+---- - - +------ ------�------
0.4
I
•
I
I
- - �- - - - - } - - - - - - � - - - - + -
0.3
-
-
-
I
0.2
I
-
-
- -
--�---- -+---
I
- - -
I
f-- --- ------�------
I
_ _ _ I.. _ _ _ _ _ _ L _ _ _ _ _ _ I.. _ _ _ _ _ _ 1. _ _ _ _ _ _ .I. _ _ _ _ _ _ .I. _ _ _ _ _ _ I I I I I I
,
_ _ _ _ _ _ .1 _ _ _ _ _ _ I
0-
0. 1
0 0
2
4
6
8
10
14
12
16
18
20
particle diameter [mm]
Fig. 44. Pa�icle size distriputions of the particles in the fluidized bed for the example calculation (Ms = 20 k9/h , Mp 0.5 k9/h, tvfped 30 kg, Ps 1 500 kg/m3). =
=
=
start-up phase during granulation of a fluidized bed consisti ng of particles of different material as the feed seeds or internal monodisperse nuclei with small particle diameters, and 3 transition period between cycle changes duri n g granul ation at conti n uous processi ng. 2
81
Fluidized Bed Spray Granulation
0.8 .---�----�--. 0.7
E 0.6
E :::; ." ß .-; * 0"
E E --
:g
o ·x· 0"
-
.. I
I
, , ,
-
--
- - -
... I
- - - - - -
I
_
-
I
I
- - - - -1- _ _ _ _ _ _ I
I
, , ,
_ _ _ _ _ _ _ l _ _ _ _ _ _ J _ _ _ _ _ _J . _ _ _ _ _ _ _ _ _ _ _ _ _
,
- - - - - - 1I - - - - - - �I - - - - - - - I- - - - - - I
0.5
-.
0.4
- - - - - ----- -,----
0.3
�
- -
--
I
T
- - - '-
, ,
- -
, , , -
, -
- - - - - -
- - - - -
, , ,
- - - - - � - - - - - - � - - - - - - -I- - - - - - -
0.2 - - - - - - -,. - - - - - - -
0. 1
2
4
6
8 10 12 particle diameter [mm)
14
16
18
Nfped
20
Fig. 45. Particle size distributions of the particles in the f1uidized bed for the example calculation with a quadruple nuclei mass flow (Ms 3 Ps 1 500 kgjm ).
=
20 kgjh, Mp = 2 kgjh,
=
=
30 kg,
In the following section, some modell i n g aspects based on investigations of Sachse as weil as Mörl et al. [45,47-49] wi l be explained regarding these 3 cases. 3. 5. 1. Batch process with increased bed mass
The batch process with increased bed mass for the coati n g of particles is very important for example for the production of pharmaceutical granules with retarded release of active i n gredients by using different coated layers of spherical form and an outer shell (Fig . 46) or of fertilizers with a long-term effect due to this alternating layering or for pelleted vegetable seeds. Fi gure 47 shows photos of coated landfil leachate granules of the University of Magdeburg with a cohesive shell of the coated layer. Figure 48 presents a schematic of the discontin uous coating process of particles. For the modelling the following assumptions are introduced: 1 . The total number of al l particles i n the fl u i d i z ed bed i s constant. 2. All granul e s are spheres. 3. Al l granules have the same di a meter, i. e ., the granul e s are monodi s perse. 4. There is no internal nuclei formation by attritio n, overspray or breakage and no elutriation of particles as weil as no agglomeration of particles.
82
L. Mörl et 8/. shell(coat)
layer I
core
coated granulate
spherical layered granulate
Fig. 46. Structure of a coated, respectively, spherical-Iayered granulate.
13
14
Fig. 47. Photos of coated landfill leachate granules.
The fluidized bed is ideal mixed. Thus, all particles are uniformly wetted with the liquid . 6. The amount and the concentration of the i njected l i q ui d is constant; and 7. The sol i d densities are constant. With the assumptions 1-6 follows for the time-dependent increase of the mass of a particle 5.
(191 )
where Mp time t = 0
=
Mp ,o
is the mass of a particle and dp
=
dp, o
is the particle diameter at (1 92)
83
Fluidized Bed Spray Granulation
l ,r M,
•
-
�
--
,-
..
� CI 1
�
-, -
-,�7/�!\.:S\
u \....
\ ,
<j
lf lf -
-
�/ !
-(
-
i
I
... '- '
-
1-
Cl
_
'_I
:S !I ü
� -
'-.) C... -
("'J .....
_
:-
_
C
fluidized bed bed Mp
gas distributor
\
M.
Fig. 48. Schematic of the discontinuous fluidized bed granulation with constant number of particles.
After integration the linear time-dependent solid mass growth can be written Mp (f)
=
MP,O
+
ML (1 x) f " L np -
(1 93)
In general, the total mass of all particles in the fluidized bed ��g is known. So, we get with P,O � "'"' n � p - Mp - d 3 ,o � p,op p,o _
M bed
_
M bed
[
bed MP,O
bed MP,O
]
(1 94)
the functional dependency of the particle mass from the ti m e Mp (t) = (3 dp,o Ps 1 + J[
3
ML(1 x) bed f MP,O -
(1 95)
With the spherical geometry according to Fig. 49 follows (1 96)
84
L. Mörl et al. dp ( l ) d�.o
P,,"oat
Ps Fig.
49. Structure of a granule.
By introducing the partie/es mass
(197) and a dimensionless ti me
[ML(1 - X)] _t
tvl;.,ed P,O
(198)
r
follows with equation (193) the dimensionless equation for the growth of the partie/e mass Mp(r) =
1
+r
( 199)
The dependency of the di mensionless partie/e mass fram the di mensionless time is drawn in Fig. 50. A bed mass of Mp = 3 Mp,o at the dimensionless time of r = 3 is i n a non-realistic order of magnitude. Normally, fluidized beds for coating operates in the range of Mp = (0. 1 . . · 2) Mp,o , Nevertheless, the dia gram il ustrates the sensitivity of the model. The dependency of the granulation from the pneumatic conditions and the l i m its of the disconti nuous process are explained i n Section 3. 6 .1, respectively. If equation (196) is inserted into equation (195) and if we consider that the core and the shell of the partie/e have a different solid density, we get x
x
(ddp,po)3 [1 ML(1 :;o x) PcoatPs ] Mt, =
+
t
(200)
85
Fluidized Bed Spray Granulation 4 .----------------,, ------------------------------� ,, ,
3.5
----------
� "
- ------ - -- -
� ,
- ----- - - ---
�
-----------
�
I
,, I
I
,
I I
I I
I I
I I
-----------
: , , ,
-----------
- - - - - - - - - - - T - - - - - - - - - - - t - --- - - - - - - -t - - - - - - - - - - -: - - - - -
3
., u 't; � 2 .5
,
-----------�-----------� , , ,
,,
2
,
, , , , , , , , ,, , , , , , - - - - - - - - - - - r, - - - - - - - - - - - T, - - - - - - - - - - -----r , ,
-----------�--------- -- I - --------
1 .5
-
T
-
-----
, , ,
l �------+---+_--+_--�--�
o
0 .5
1 .5
2
dimensionless time
2.5
3
[-]
Fig. 50. Dependency of the dimensionless particle mass from the dimensionless time during batch coating according to equation ( 1 99).
] 1 /3
Thus, we receive the dependency of the partide di ameter from the ti m e ML(1.bed x) Ps t dP ( t) dP,O 1 (201) IV/r,o Pcoal A dimensionless partide diameter can be written as (202) (:;J ifp Hence, the dependency of the di mensionless partide diameter from the di mensionless ti me duri n g the unsteady coatin g of partides with the ratio of the density of the core to the density of the shell Ps (203) Pp Peoal as dimensionless parameter occurs as folIows: (204) ifp('!) = ( 1 + P�'!) Figure 51 shows these dependency considering a constant number of partides and a complete evaporation of the total mass of the injected l i q ui d . For the calculation of the heat and mass transfer i n the flu i dized bed the total surface area of all particles in the bed is requi red (see Section 4.1). Assumi n g a constant partide number 'Lnp , the change of the total surface area of all partides =
[ . +
-
•
=
--- =
*
1 /3
86
L. Mörl et al.
2 .6 --
--0, " " E'" �
2.2
'ö " ü
.�<>on on
1 .8
p� = 5
=4
-.-
=3
-lr-
=2
--+-
=
1
-0-
=
0.5
--
= 0. 1
" t:
.�c
E 'ö "
2
1 .5
0.5
dimen ionle
s
2.5
time l-J
Fig. 5 1 . Dependency of the dimensionless particle diameter from the dimensionless time during batch coating according to equation (204) by variation of the dimensionless particle density according to equation (203).
in the bed during the particle growth reads as folIows:
(205) LAp(t) L npAp (t) = L np1td� (t) the derivations for 'Lnp and dp(t) into the equations above, we can =
Insertin g rewrite the time-dependency of these total surface areas 6M bed L Ap(t) = � dp,oPs
[ M' LM(1b: Ps ] 1
x)
+
p
0
Pcoat
t
2/3
By using a specific surface area which is based on the surface area at tim e and the di mensionless time, we obtain
(206) t
=0
(207)
Figure 52 shows the trajectories of this function with the di mensionless density ratio PS/Pcoat as parameter. The thickness of the shell respectively of the coated layer is Scoat dp -2 dp,o (208) _
-
87
Fluidized Bed Spray Granulation
7 1.=====��--�-----;--1 p;, = 5 -
=4 =
o
3
- -
----
-
- - - - - - - - - - -
-
- - - -
-
-
- - - -
1 .5
0.5
dimensionle
time [-]
r
, ,
- - - - - - - - - -
2
- ---
2.5
3
Fig. 52. Dependency of the dimensionless total particle surface area from the dimen sionless time during batch coating according to equation (207) by variation of the dimen sionless particle density according to equation (203).
We can rewrite equation (208) as dp 2scoat + dp,o (209) and insert these equation into equation (201) to get the time-dependent layer thickness Ps t) - 1 ] scoat(f) d2p,o [ (1 MLM(1bed x) Pcoat (210) Thus, a time-dependent dimensionless layer thickness, which is based on the initial diameter is calculable Scoatp,o = 21 [( 1 + Ppr - 1 (211) scoat(r = d Analogous to Fig . 51 , this dependency is drawn in Fig . 53. Contrarily equation (210) can be used to determine the ti m e which i s necessary to reach a certai n layer thickness scoat =
=
+
P,O
)
*
1 /3
-
*
) 1 /3 ]
3 d 2 ) [( Scoat tcoat(scoat) _ 1 ] M�� Pcoat M (1 Ps =
+ dP•o
dp,o
.
L - x)
(212)
88 1 .8 Ir===�==;---;' : P" = 5
-
-
-0-
�
]u
1 .6 -
:s
--
=4 =3 =2 =I = 0.5
I :I
----
-
i
:I :I :I
�--
-----
�:_
:I :I
-;-
-
,-
L. Mörl et al. ,
-
�
-
i.- ------ -:I
II I
II II
� _ _ _ _ _ _ _ _ _ _ _L __________ _
___
o
1 .5
0.5
2
3
2.5
dimensionJess time [-]
Fig. 53. Dependency of the dimensionless layer thickness from the dimensionless time during batch coating according to equation (2 1 1 ) by variation of the dimensionless particle density according to equation (203).
The mean particle density duri n g coating reads as folIows:
Pp = MVpp
(21 3)
-
(21 4)
_
-
Pp = (dp,dpo) 3Ps + [1 (dpdp,o) 3] PCt:Jat
With equation ( 1 96) and Vp = (1t/6)ifp, we receive a mean particle density _
whereby by considering of equation (202) stands Pp
= (opr3Ps + [1 (opr3] PCt:Jat -
(21 5)
and in dimensionless form
[ [ 1 (opr3] = 1 + (op ) -3 �- 1 ] = Pcoat = (opr3 �+ PCt:Jat Pcoat
P� Pp
_
Finally, we obtain with equation (203)
1
Pp(op 31 PP = +-) -*
-
(21 6)
(21 7)
89
Fluidized Bed Spray Granulation 10
- - - - - -- -- -- - - -f-- - - - - - - - - - : = = = : : : : : : : ::r- : : : : : : : : : : : 'rr : : : : : : : : : : : : : _ : : _ : : : : : : � - � -- - - - - - - - - - - . - - - - - - - - - - - - - - - - - - - { - - - - - - - - - - - - - - - - - - - - - - - t - - - - - - - - - - t - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - t - - - - - - - - - - - - - - - - - - - - -( - - - - - - - - - - - t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - { - - - - - - - - - - - - - - - - - - - - - - -t - - - - - - - - - - - } - - - - - - - - - - - - - - - - - - - - - - - - - - - - + - - -- -- - - --- ------ --- - - -:- --- - ----- --t-I - - - -
.� 5
- - - - - - -
- - - 1 - - -
- - - - - - - - - -
- - -
-
I , [: :: =�:�: =:=:=J:�t_:_=_ ==::�=�:::=�:: ==�: : :�E
T I
_
-
=
:=:
I
: ,
,
�
,
0. 1
-0-
=
- - - - - � - - -.-
- - - - - - - , - - - - - - - - - - - - :- - �- - - - - - - - - - - -� - -
-----------t: : - .. - - - - - - - - -t - - - - - - - - - - - :- - - -
e
c
:
- - - -==-=�====- ==- I_ -
----------t -----------�-- -
� § . Vj
=========
�
I
=
-4 :�:�::�:�j:�=�:�: _;=�::�_�::J� 3
2 0.5
I
---A-...:r-
=
'
-+-
= 1
�
=
:
I
- - - - - - - - - - - -
- - - - - - - -
- -
- - - -::=�:���:�� �_���- -�:�;t���-5�3 , I
I '
"0
- - - - - - -
= O. J
---
-,--- ---------
- - - - - -+ - - - - - - - - - - - -
-----i-- - - - - i - -_ _- - - - - - - - - : - -- -- - - - - i- - - - - :
__ _ __ .1 _
��-__+_---+__ ' ---J---== --: =:=::t===------i---.j 3 2. 5 o
0. 5
-<0-
1 .5
dirnen ionles time
1"-]
2
:
Fig. 54. Dependency of the dimensionless mean particle density from the dimensionless time during batch coating according to equation (21 8) by variation of the dimensionless particle density according to equation (203).
and the inserti ng of equation (204) yields a time-dependent di mensionless mean particle solid or particle density, il ustrated in Fig . 54 (218) p-* (r) = 1 + -:1pp+:-'--- -pp-1r We developed a nomogram (Fi g . 55), which is able to prediet the desired particle diameter, the bateh time or the layer thiekness and whieh is very useful to get fast results. P
-
3. 5. 2. Semi-batch process with constant bed mass
Normally, the bed material of the bed partieles at the begi n ni n g (hold-up) of the start-up of flu i dized bed spray granulation is different from the produet materi al . But a hold-up is neeessary to have a eertai n particle surfaee area for the particle wetti n g. We have two possibilities to solve this problem: 1. desi Use of bed particles of different material at the beginni n g in respeet to the red produet material: The foreign material deposited onto the produet partieles ean be separated by external erushing (i ntrieate) or ean be remains onto the surfaee of the produet (e.g. injeetion of proteins onto wheat and subsequent proeessi n g as foodstuffs .... )
L. Mörl et al.
90 0 001
0.2
0.4 0.• 0.8 1 .0
"'""� I"
I-
�K\ �< J>< - .'1 V �
���
1=;.' l7..k
� l:
2. 0
I-
4.0
l- V
8.0 8.0 '0
20
Il-
�
Ix
/<
V
t0'"" )Vv
��R>�k I'--..
V/1/
//
I"-... 'V ",""I> 10:: l)\ V �I?�
/
1/
I'
/
�
/
r0 � .�/x V , '-I> N)< K /r\bX/D< �::Xx 1"-""
,Q'
•
/
- -;; Vv l""" V j
://' V V-
/'
R< "V
01
V
/'
x x
V' 1= V/v �
40
- :0; .:0;
0 01
�
/ / /IX / /V l>< v
V 7 /1717 / jV
I?
1/ � �
V 1/
IX
I� ./
rI
IX
>-)<
AV/v
��
P>e?< J
/V /V
10
't
- x)/",*�3
=
0.5 h - 1 ,
Peoat/pS
=
0.8
-+
tcoat = 0.38 h).
/�
l,::/
f?/
E�& V �/'1/1///1/«:1/'
1/ 1/
� 1/ v:�./ 0� /I/�··�/Vl/1/'· / /":- �V
'i
_-
:>V /1/
//
� "'""" �
Fig. 55. Nomogram for the batch coating (example: Seoat = 0.3 mm,
ML(1
/
/V / V /'/ /r/ V / l/v
dp,o
=
8 mm,
2. Use of bed particles of same materia l at the begi n ni n g in respect to the desired product material: The particles of the starti n g material have a very small di ameter and were produced by a single batch vacuum drying with subsequent crushing and classifyin g. For both cases the unsteady start-up phase must be calculated. It i s appro priate to operate the fluidized bed plant with a constant bed mass by feeding the same amount of injected sol i d compared to the mass of the conti n uous dis charged particles. Figure 56 explai n s this disconti n uous semi-batch process. Based on these considerations, Schachova and Ritschkov [50, 5 1] derived a model for the granulation of urea from melts, which was used by Sachse [49] for the granulation of proteins from solutions (see Section 7.7.1). We consider the same assumptions (2), (3), (4,) (5), (6) of Section 3.5.1, but we add the following assumptions: 1. The total mass of all particles in the fluidized bed is constant. 2. Contin uous ideal classifyi ng discharge of particles, whereby the mass of the solid in the i njected liquid is equal to the mass of the discharged particles.
91
Fluidized Bed Spray Granulation
l.� M.
:J'_
J lr u
1------1
� M.,I
Fig. 56. Schematic of the discontinuous fluidized bed granulation with constant bed mass.
With these assumptions, we can write the equation for the feed and discharged solid mass in an infinitesimal time interval (219) This mass flow leads to the mass growth dMp of a solid partie/e withi n the tim e interval dt according to the modified equation (191) (220) and by using the timede-dependent total number of all partie/es in the fluidized bed 'Lnp with Afp�g = Afp = constant Ai:,ed p (t) " n (221) P � Mp(t)
92
L. Mörl
- x) d t
et 81.
We obtain with a modification of equation ( 1 94) dMp = or
r Mp =Mp JMp=Mp,o
M-pp(f)
ML(1
(222)
AJ;,ed
(223)
,o
- x) t=t dt Jt=o
With the initial conditions dp = dp and Mp = Mp ,o at t = 0 results dMp ML(1 = Mp Afped
( ) Afped t [ Afped- X) t]
and after integration the solution is In
- x) t
Mp M ML ( 1 = p,out = Mp,o Afped
(224)
(225)
[ Afped- x) t]
Finally, we receive the time-dependency of the mass of a single particle Mp(t) = Mp,oexp
ML(1
, psexp = 1t --
ifp o 6
ML(1
(226)
By using the dimensionless particle mass from equation (1 97) and the dimen sionless time from equation ( 1 98) a simple correlation for the particle mass growth can be written Mp(r) = exp[r] (227) This dependency of the dimensionless particle mass is shown in Fig. 57. According to Fig. 49 the inserting of equation ( 1 96) into equation (226) yields
(�) 3 dp,o
{ [ Afp:; X) t] } ' ( x ) t ( ::.. { [ L� ] - }) 3 =
1 + � exp Pcoat
ML(1
-1
(228)
1
(229)
Thus, the time-dependent particle diameter reads as dp(Q
�
dp,o 1 +
exp
M
The dimensionless particle diameter from equation (202) and the dimension less particle density from equation (203) gives the time-dependency of the
93
Fluidized Bed Spray Granulation w .-------.--.--r---,---�
� � - - - - - - - - - - - -� - - - - - - - - - - - , - - - - - - - - - - - -, - - - -
� 15 '" '" '"
Ei
"
Ü 'e � 10 � " c
.�"
- - - - - - - - - - - �- - - - - - - - - - - -
-----------
, - - - - - - - . - - - ,, - - - - - - .,.
o
Ei :a
5
O +-------�--_+--�r_--+--� 3 2.5 2 1.5 0.5 o
dimensionless time ( ) -
Fig. 57. Dependency of the dimensionless particle mass from the dimensionless time during the discontinuous start-up phase according to equation (227).
dimensionless particle diameter, illustrated in Fig. 58 with the density ratio as parameter � (T )
=
{ 1 + p� (exp[T] - 1 ) }
1 /3
= {1
-
p�(1 - exp[T])}
1 /3
(230)
Owing to the constant bed mass during the continuous particle discharge, the number of particles will decrease. At the beginning of the start-up process the total number of all particles in the fluidized bed is determined by the bed mass and the mass of a single particle according to equation ( 1 94). But the particle mass grows from Mp ,o upto Mp (t) , while the total bed mass is kept constant. Considering the number of bed particles from equation (221 ) and the time-de pendent bed mass from equation (226), the total number of bed particles reads as folIows:
M�ed exp 2: np (t) = � P,O
[
-
ML(1
]
x) Ml.ped t -
(231 )
This function is shown in Fig. 59. A universal function can be received by introducing the dimensionless time and a normalized particle number, which is based on the number of particles at time t = 0, presented in Fig. 60. '" �
np(t) = LLnpn(tp=(t) 0) *
=
exp[- ] T
(232)
94
L. Mörl et al. 45 . 4
Ir=== ===:=:::;-----;--;---�I .... p� = 5 -
� 3 .5 0) E '"
:.0
0)
Ü
.�c.. �
. C�
3
2.5
-0-
=4
- ---------
r
-----------
�
------------
=3 =2 =1
L.. -+-
---------
,
= 0.5 , ,, =� O.--' l - - - - - - - - - - � - - - - - - - - - - - �- - - - - - -
___
-0-
� ,, ,,
-----------
,,
------------
,, , r,
--------
�
�
:.0
1 .5
0.5
1 .5
2
2.5
3
dimensionless time [-)
Fig. 58. Dependency of the dimensionless particle diameter from the dimensionless time during the discontinuous start-up phase according to equation (230) by variation of the dimensionless particle density according to equation (203).
In order to obtain the time-dependent total surface of all particles in the fluidized bed
L Ap(t) = L np(t) Ap(t) = L np(t) 1tcfp(t) I:np (t) and
{ 1 - exp [M���X)p ] } ) 2/3 exp [M�l�X) ]
(233)
dp (t) have to be inserted to get 6MPbed
= __
LAp (t) dp oP , s
(1
-� Peo.!
t
.
t
(234)
A more general expression is derivable by using the dimensionless time and the specific surface, which is based on the surface at t = 0 � 6
A* (-r) = P
1 exp[r»}2/3 {1 - pp(exp[r] -
(235)
Figure 6 1 iIIustrates trajectories of this equation by variation of the dimension less particle density.
Fluidized Bed Spray Granulation
95
1 � �----�--,
_ _ _ _ _ _ _ _ _ _ _ _ _ ..l _
,
, - - - - - - - - -- - - - " - - - - - - -- - - - - - - - - - , ,
,
,
, , ,
,
- - - - - - - - - r - - - - - - - - - - - - - T - - - - - - - - - - - - -
= 50 kg =40kg = 30kg -- ==20kg L= 10 ==� kg --�--------�------�--� � ====== � 10 4 � 2 [hr) 3 -+-
M �"
1 00
- - - - - - - -
�, - - - - - - - - -
- - - - - ,r - - - - -
, ,
o
- - - - - --
,
- - -- - - - - - - - - --
, ,
5
time
Fig. 59. Dependency of the total particle n umber in the fluidized bed from the time during the discontinuous start-up phase according to equation (23 1 ) by variation of the bed mass for an example ( rIAL = 1 00 kg/h, x = 80 mass%, dp,o = 5 mm, Ps = 1 500 kg/m3) ,
0.8
I I I I - - - - - - , - - - - - - - - - - - - r - - - - - - - - - - - T - - - - - - - - - - - -, - - - - - - - - - - - - r - - - - - - - - - - -
E::l
" ,
,
,
.... "
c::
'Eos
..!:l
c.>
,
, ,. ,
.0
0.6
,
- - - - - - - - - - -
- - - - - - - - - - - - I-- - - - - - - - - - - - " - - - - - - - - - - - -1- - - - - - - - - - - - .. - - - - - - - - - - -
,
" I
I
: ,
p"
� " -= 0
E '6 ...
c
0.4
- � - - - - - - - - - - - � - - - - - - - - - - - -I- - - - - - - - - - - - � - - - - - - - - - - I I I I
,
,
,
"
0.2 O +-------�--�--�r_--� o
0.5
1.5
dimensionless time [-)
2
2.5
3
Fig. 60. Decrease of the total particle number in the fluidized bed during the discontinuous start-up phase according to equation (232).
96
L. Mörl et al.
1 .8 ::!:: 1:l
-t :J
�
---
p;
1--:---�--�----;--;===::::;::==::;-� -0-
1.5
=5
=4 =3 =2
1 .2
u
.€ '"
Li
Q.,
0.9
B
'"
� -a .o
0.6
;;; "
6
'Ö 0.3
o +-------+---� o 0.5 1.5 3 2.5 2 dimensionless time [-)
Fig. 6 1 . Dependency of the dimensionless total particle surface area from the dimen
sionless time during the discontinuous start-up phase according to equation (235) by variation of the dimensionless particle density according to equation (203).
[(
1 /3 (1 - x) ] [ML"4�3 t - 1 }) - 1 1
Equations (208) and (209) result into a time-dependent layer thickness Seoat(t)
dp,o 1 + Ps =2 Peoat
{
exp
seoat = 1 [(1 + { exp[r] - 1 }) 1 /3 - 1 = er] "2 Pp
(236)
which has in comparison to equation (21 1 ) the following form: *
s coalr)
P,O
*
(237)
Analogous to Fig. 53 the dependency of the dimensionless layer thickness fram the dimensionless time during the discontinuous start-up phase according to equation (237) by variation of the dimensionless particle density is shown in Fig. 62. A layer thickness of Seoat = 1 .7 dp , o at a high dimensionless time of r 3 is in a non-realistic order of magnitude. Usually, the typical layer thickness is only few micrameters or millimeters. Rearranging equation (236) yields the time, which is necessary to obtain a certain layer thickness x
=
[{
teoat(SeoaÜ = In
--- [ (
2Seoat +1 1 + Peoat P,O Ps d--
) 3 - 1 ] }] M. L(.b1 ed- x) • /VIp
(238)
97
Fluidized Bed Spray Granulation
--
,,
2 �------�--,
� 1 .6
() '" '" Q)
..Q :s 1 .2
-0-� �
p� = 5 =4 =3 =2
- - - - -
r,
- - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - -
.... Q) >.
�
�
Vl
C o ' iji
0.8
� Q)
E 0.4 '0
o l&�a��t=:= ==� o
3
2
dimensionless time [-]
F ig. 62. Dependency of the dimensionless layer thickness from the dimensionless time during the discontinuous start-up phase according to equation (237) by variation of the dimensionless particle density according to equation (203).
dp,out
The substitution of equation (238) leads to the time fend which is required for a start-up phase of the discontinuous semi-batch process and which predicts the duration until the first particles will be discharged with the diameter fend
=
ML�: x) { In [1 - P;:at (1 - �f�t) 1 }
(dp,--out) ]
(239)
An equal density of the core and of the shell yields fend
-
_
-
[
3�ed . In dp,o ML(1 x)
(240)
Based on equation (240), we developed a nomogram, which is shown in Fig. 63. By inserting the dimensionless quantities, we get
and respectively for
PcoaJPs = 1
rend
= 3 In (
cfp,out)
(242)
�.:
V;r/�
/ /
/
/
/
y / 1/
/ / / '/ / // / / 1// /� / / /v/r�/ /
/ V
/
/
/
3 2 5 2 1 8 1 .6 1 .4 1 .3 1 .2 1 1 1 0
10 8 8 5 4
I I I I I
II
/
V V
I
1
I
1/
/
/ 1/
/ / 1/ /
/
co <Xl
0.9
/ 1/ / / IV /1/ V/ /!/ / / 0.8 // / V
I 111 1// / IV/ I
0.6
1 .0
1.5
2.0
3.0
4.0 5.0
fend
7.0 9.0 1 0
15
1
2
3
4
t". [hl � 5
6
7
8
9 1 0 1 1 1 2 13 14
Fig. 63. Nomogram for the estimation of the growth time during semi-batch granulation according to equation (240) (e.g . dp, o
dp , out =
5 mm,ML (1
-
x) /��g
==
1 h- \
-t
=
6.9 h)
= 0.5 mm, ;;:-
99
Fluidized Bed Spray Granulation 5
�======�-:-----:--:---�
--- ( P;, t -0-
--
=
5
=
4
�
=
3
--6-
=
2
�
=1 =
05 .
o ������----�--� 2
1 .5
2.5
3
normali zed particle diameter of the product [-] Fig. 64. Dependency of the dimensionless time to reach a certai n product diameter from the normalized particie diameter of the product during the discontinuous start-up phase according to equation (24 1 ) by variation of the particle density ratio PcoaJPs.
Figure 64 shows the dependencies according to equation (241 ) regarding the dimensionless time, which is necessary to reach the final product diameter at different density ratios PcorelPs as parameter. Combining equations (21 5) and (21 7) leads in contrast to equation (21 8) to the mean dimensionless particle density as function of time Pp - * (r ) = 1 + (243) Pp 1 + p p (exp[r]
-1
_
1)
But with equation (21 6) we can express the mean particle density with real dimensions
pp (f) =
{
-;-[Md�_1-----,-t]-- ----c-1 ) } pcoat
1 + ___-;--"-�""' :"r at 1 .;;;x) � (exp + Peoa �
1
t
(244)
Figure 65 shows the dependency of equation (243).
3.6. Operation area of the fluidized bed g ranulation du ring u nsteady process
In supplementation to the theoretical considerations of Section 3.5 according to the particle growth during the discontinuous operation mode, the operation area
1 00
L. Mörl et 81. 1 0 �� -� - -�======� - -� -� - -� _�_� _� _ _� _� _ _,� - -� -� - -� -� - -� -� - -�-� -� - -� _� _ _� _ _� -� - -� -� - -� _� _� _ _� _� _ _� ,-� _ _ _ _ _ --p; = 5 ,( - - - - - - - - - - - - - - - -, , -----_____ -0=4 , , , , =3 _ _ _ _ _ _ _ _ _ _ - , - - - - - - - -6- - - - - - - - - - - 1- - - -
-
G . ;;;
c: o . ;;; c: .,
�
- - - - - - - - - - -
- - -
- - - - - - - - - - -� - - - - - - - -
- - - - - - - - - - -1 - - - - - - - - - - -
- - - - - - - - - - - 1- - - - - - - - -
, , 1
, ,
U
� ü;
- - - - - -
-
-----____________---
c: ., '" .,
1E"
-
- - - - - - - - - - -1-
1
�
=2
-+-
= 1
-0-
= 0.5
-+-
= 0. 1
;=:;i�:'�����=�=�= _��_�_-$,=������-,�-=��,�-�����
�I ��_-
__ = = = = = = = = = = = : = = = = = = = = = = _= � =_ _ _ _ _ __ _ _ _ _ _ _ __ _ __ __ __ __ __ __ __ _ _ _ _ _ _ _ _ _ _ _ _ __ =_ _ __ _= _= _= =_ =_ =_ L I
I
- - - - - - - - - - -1I
,
- - - - - - - - - - -1I I
,
_ _ _ _ _ _ _ _ _ -' _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ j..
_ _ _ _ _ _ _ _ _ _ -' _ _ _ _ _ _ _ I I
I
� t
J I
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .... _ _ _ _ _ _ _ _ _ _ _ 1
I
"
I
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .... _ I.. I I
1
I I
"
I
I I
________
______ ___________ J
, , ,
0 . 1 +=------�--_r--_+--r_--� o 2.5 3 1 .5 2 0.5 dimensionless time r - 1
Fig. 65. Dependency of the dimensionless mean particle density from the dimensionless time during the discontinuous start-up phase according to equation (243) by variation of the dimensionless particle density according to equation (203).
of the pneumatic behaviour as weil as of the heat and mass transfer behaviour must be taken into account. Concerning the dynamic operation, responses to changes of process parameters, like the increase of the fluidization gas mass flow for a stabilization of the fluidization of larger particles or the rise of the gas inlet temperature as weil as the reduction of the liquid injection rate regarding stable evaporation of the solvent, have to be considered. In respect to the pneu matic operation range, the operation velocity must be above the minimal fluid ization velocity and below the elutriation velocity. Due to the particle growth, one obtains a change of the mean particle density, according to the density of the core and of the shell. This should lead to an adjustment of the gas velocity during granulation in order to provide a constant bed porosity and thus a constant bed height. This requirement can be realized by an automatie process contro!. If the gas velocity is kept constant, the values for the porosity and the height of the fluidized bed would fall below the minimal fluidization point after a certain time due to the increase of the particle diameter and the change of the particle density. On the other side, the heat and mass transfer conditions have to be stable (for calculation see Section 4.1 ). The effective solid surface area is connected with the degree of wetting and grows in the case of the operation mode of Section 3.5.1 and grows or sinks in the case of the operation mode of Section 3.5.2.
1 01
Fluidized Bed Spray Granulation
The difference of the vapour pressure and the partial pressure of the solvent, the driving force of the drying, can be influenced by the temperature and the loading (humidity) of the gas. By assuming constant mass flow, temperature and humidity of the gas and with neglect of control aspects, the following sections concerns the operation areas with respect to the operation modes according to Section
3.5.
3. 6. 1. Operation area of the batch process with increased bed mass
P
Assuming constant process parameters (mass flow and inlet temperature of the gas) and monodisperse particles with . = Ps and an initial diameter the pneumatic operation area for a stable fluidization of the fluidized bed can be calculated for the dynamic process of Section The time-dependency of the particle diameter is given with equation the With the dimensionless quantities c!p , Pp and as weil as with equation time-dependent dimensionless particle diameter can be calculated. Also the mean particle density is a function of time if the densities of core and shell material are different. Combining equations and we received the mean particle density in dimensionless form according to equation Anal ogous to equation the Archimedes number must be computed to determine the minimal fluidization velocity P
dp•o , 01). ( 2 (204)
o
3 .5 .1.
'"[
(21 3) (215), (218).
(5),
_
gdkVppPG- PG) G
(245) For gas-solid fluidized beds we can assume (246) Pp> > PG Inserting the time-dependent particle diameter according to equation (201) and the particle density into the Archimedes number yields ] } pp(t) { dp,o [1 9 Ar (247) vG PG Using the dependency p p ( ) and replacing the quantities of real dimensions with dimensionless quantities, a linear dependency of the Archimedes number from Ar -
2
1 3 + ML( 1e-;;X) ..i!.L t /
=
M);.o
3
Peoa!
2
t
the time occurs
gifp,o ( 1
VG PG
(1
fi;�1,)Pcoat
+ Pp! ) + Ar = -----7" -- 2 -'--------'----'-or
Ar = Ar ( + !)
o1
(248) (249)
1 02
L. Mörl
et 81.
where gcft" o Ps Ar0 _ (250) - V2 P G G Now, the Reynolds number at the minimal fluidization point according to equation (1 1 ) can be obtained Ar Aro(1 + r) Remf(r) (251 ) 1 400 + 5.22,J,Är 1 400 + 5.22 JAro(1 + r) --------==
[
1
The minimal fluidization velocity can be written as Vmf(r)
mf(r) = Redp(r) vG =
() [
or
Vmf r =
Aro(1 + r) VG 1 400 + 5.2 2 JAro (1 + r) dp(r)
]
Aro(1 + r) VG 1 400 + 5.22 JAro(1 + r) dp o( 1 + p * r) 1/3
(253)
=
(254)
,
The minimal fluidization velocity at time t = 0 stands with Remf O VG ArO VG Vmf,O ' dP,O 1 400 + 5.22,JArO dp,o
The normalized minimal fluidization velocity related to the time t with .., vmf(r) vmf(r) - Vmf,O •
_
(252)
_
= 0 can be given
+ r) ( 1 400 + 5.22,JArO) [ 1 400 (1+ 5.22 JAro(1 + r)] ( 1 + pp r) 1 /3
(255)
Figure 66 shows the time-dependency of this dimensionless minimal fluidiza tion velocity. •
Gase 1 : P s > Peoat
Figure 67 shows the minimal fluidization velocity and the particle diameter as function of the dimensionless time for the case that the density of the shell material is higher than the density of the core material. At the beginning, the minimal fluidization velocity decreases, while further granulation causes a rise in the progression. For example, using an effective operation velocity of 1 m/s, the fluidized bed is stable only until the dimensionless time r 9.9. After this time, the granulation must be stopped. Figure 68 iIIustrates for the same example the time-dependency of the mean particle density and of the particle diameter. It is obvious that a maximal particle
=
1 03
Fluidized Bed Spray Granulation 3.5 i.= ====:::::;:----:--;--i
....... p�
= 10 2 � =1 'g 2.5 -
-0-
=
c--------------
5
,
;::-.
Ol >
.......
- - - r - - - - - - - - - - - - - - r - - - - - - - - - -
, ,
t;: �
§c 1 . 5 'E '" '" "
,
- - - - - - - - - - -
j, - - - - - - - - - - - - - - r, - - - - - - - - - - - - - ,
, ,
,
_ _ _ _ _ _ _ _ _ _ _ _ _ L _ _ _ _ _ _ _ _ _ _ _ _ _ _ L _ _ _ _ _ _
"2
o .� c
E
"
'Ö
0.5
- - - - - - - - - - - - - -
, �---,
, "
- - - - - - - � - - - - - - - - - - - - - - � - - - - - - - - - - - - - - � - - - - - - - - - - - - - -
O +-------�--�--r_--� o
2
4
dimensionJess
6 time [-]
8
10
Fig. 66. Dependency of the dimensionless minimal fluidization velocity fram the dimen sionless time according to equation (255) by variation of the dimensionless particie density during the batch pracess for an example (AA = 1 00 kgjh, x = 70 mass%, dp,o = 2 mm, 2 Ps = 2500 kgjm3 , 9G,in = 20°C, VG,in = 1 5 X 1 0-6 m js, PG ,in = 1 .2 kgjm3) . 1 . 2 -r------,---,---r- 0.008
1
i
.q �
g
.�
,
- - - -� - - - - - - - - - - - - r - - - - - - - - - - -
0.6
N
E '2 E
. :
0.006
I .... öl Eos "
_ _ _ _ _ _
�_
_ _ _ _ _ _ _ _ _ _ _ _
: , ,
'Ö ':;
�
,
,
0.8
c
t;:
0.007
• • • • • • • • • • • •• • • • •: • • • • • • • • • • • • • • • • •: • • • • • • •• • • • • • • • ••:•••••••••••••••• .J
- - -
�
,
_ _ _ _ _ _ _ _ _ _ _ _
:
L
:
_ _ _ _ _ _ _ _ _ _ _•
, � - - - - - - - - - - - - � - - - - - - - - - - - - - � - - - - - - - - - - - - � - - - - - - - - - - - :. " , , .
-0-
minimal fluidization velocity
-0-
particle diameter
- - -, - - - - - - - - - - - - r - - - - - - - - - - - .
, ,
, ,
0.005
: : .
. .
'Ö
�., "
0.004
a.
0.003
0 �------+---4---�--�--_+ 0.OO2 8 10 4 6 o 2
dimensionJess time [-]
Fig. 67. Dependency of the minimal fluidization velocity according to equation (253) and of the particle diameter according to equation (20 1 ) �rom the dimensionless time at Ps > Pcoat during the batch process for an example (ML = 1 00 kgjh, x 70 mass%, dp 0 = 2 mm, 2 Ps = 2500 kgjm3, Pcoat = 500 kgjm3, 9G•in = 20°C, VG,in = 15 X 1 0- 6 m js, PG in = 1 .2 kgjm3). , =
1 04
L. Mörl et al.
0.008�------�--. 3� 0.007 2500 :§: 0.006 2000 .� particle diameter � 0.005 1500 mean particle density .� 0.004 1000 e::0. E 0.003 -500 0.002�--o 2 4 6 8 10---�---r--� 0 dimensionless time [-) ................ ,. ............... ........... . . ,,. ............... , .......... . , , , - -- - -- -- -- - -� -- --- ------- �- --- -- --- -- -�- -- -- - -, , I
I �
.
... " "
'Ö " Ü
.
I
.
, .. - - - - . - - - - - - - - - - - - .. - - - - - - - - - - .... .. , , , , :
"'s 00 =.
-0-
" " ü .€ '"
- - :-
�
I
I
I
I
I
I
I
I
•
- - - � - - - - - - - - - - - - � - - - - - - - - - - - - 7 - - - - - - - - - - - - + - - - - - - - - - _ ..:..
0.
---------� , ,
- - - - - - - - - - -
�
- - -
---------�-----,
- - - - - -
:
- - - - - - - - - - -
e::
"0
'" "
� . :
Fig. 68, Dependency of the particle diameter according to equation (201 ) and of the mean
particle density according to equation (21 5) from the dimensionless time at Ps > Pcoat during the batch process for an example (ML = 1 00 kg/h, x = 70 mass%, dp 0 = 2 mm, 2 3 3 3 Ps = 2500 kg/m , Pcoat = 500 kg/m , 9G,in = 20°C, VG.in = 1 5 x 1 0- 6 m /s, PG ,in = 1 .2 kg/m ) .
diameter of 7.4 mm can be reached corresponding to a mean particle density of 540 kg/m 3 . •
Case 2:
Ps
<
Pcoat
If the shell density is higher than the core density no decrease of the minimal fluidization velocity occurs for low dimensionless times. Instead, the minimal flu idization velocity, the particle diameter as weil as the granule density grows permanent, expressed in Figs. 69 and 70. Hereby, the critical time where the unstable area begins is r = 8.8 corresponding to a granule diameter of 2.81 mm and to a mean granule density of 1 780 kg/m 3 .
3. 6. 2. Operation area of the semi-batch process with constant bed mass
The discontinuous operation according to Section 3.5.2 with a constant bed mass and a decrease in the number of particles is determined by equations (229), (230), (243), and (244) for the particle diameter as weil as for the particle density. These quantities (dp, pp ) can be inserted into equation (245) by using the
1 05
Fluidized Bed Spray Granulation
1.
minimal
=======�---:---:---1 4 1r= -0-
1 .2
-
-0-
fluidization velocity particle diameter
0.0035 0.003
.... � : .;:: - ------ � - - ., - , ---- --- � - .:. -----,. -- - - -- - - .,: -- - -- - - : , ---.. -
i
0 '(3 0 "il > c
0.8
- - - - -
� '6 0.6 ' :;
'E '2
.��,oQ<�.-l- 0. 0025 - - - - -
- - - - - - -
0.002 �
�
- - - - - - - - - - - � - - - - - - - - - - - - � - - - - - - - - - - - - �' - - - - - : - - - - - - - 0.001 5 -D 'ECIS 0. I . I ! � t 0.001 ' '6
- -
-
0.2 - - - - - - - -
-
-
t
- - - - - -
I
-
I
- - -
-
-
•
I
--
I
- ., - - - - - - - - - - - - ""'1- -
- -
:
-
-
- - -
- - -
- -
- - - - - - - - - -
:
•
-
- -
--
-
0.0005
O +----�---_+---��---+_��-� O
8
dim4ensionless time6[-)
2
o
10
69. Dependency of the minimal fluidization velocity according to equation (253) and of the particle diameter according to equation (201 ) from the dimensionless time at Ps < Pcoat during the batch process for an example (rIAL = 1 00 kgjh, x = 70 mass%, dp,o = 2 mm, Ps 500 kgj m3 , Pcoat 2500 kgjm3 , .9G,in = 20°C, VG.in = 1 5 x 1 0-6 m2/s, PG,in = 1 .2 kgjm3).
Fig.
=
=
assumption of equation (246) to get �=
gifp,o { 1 + pp(exp[r] - 1 ) } 2
[Pcoat { 1+p��;p�rl-1) + 1 } ]
VG PG
��
Again, using a modified Archimedes number Aro for the begining of the process according to equation (250), the time-dependency of the Archimedes number is obtained as Ar = Aro exp[r] (257) The time-dependent Reynolds number at the minimal fluidization point can be calculated with the time-dependent Archimedes number after Gorosko et al. [32]
Re f(r) m
-
- -=
Ar = 1 400 + 5,22 .JAr
-
(
Aro exp[r] 1 400 + 5.22JAro exp[r]
)
(258)
The time-dependent minimal fluidization velocity can be rewritten as Vmf(r)
=
Remfer) dp(r) V G
=
Aro exp[r] VG 1 400 + 5.22JAro exp[r] dp,o { 1 - pp( 1 - exp[rD } 1/3 (259)
1 06
L. Mörl et al.
,,
0.003 .,-----�---____r---�,...._---..,..__---, 2000
...
0.00275
'"
�
ö
'6
,
............... -:................ � ............... "
0.0025
.� 0.. '"
Ü
- - -
-
i
;;""
- - - - - - - - - - - - - -
- - - - -
0.00225
1600
,
,,
-
:-
-
1 200 C: .;;;
c Q) "0 '"
- - - -
800
�
.
-0-
partic1e diameter
-0-
mean particle density
.
,
.
Ü
0..
- - - - - - - - - - � - - - - - - - - - - - - � - - - - - - - - - - - -I- - - - - · - - - - - -
:
.�
400
E
0.002 �---_+_---_+----'f___---+---=--+ 0 10 8 6 4 o 2 dimensionless time [- J Fig. 70. Dependency of the particle diameter according to equation (201 ) and of the mean
particle density according to equation (21 5) from the dimensionless time at Ps < Pcoat during the batch process for an example (ML 1 00 kg/h, x = 70 mass%, dp o = 2 mm , Ps = 500 kg/m3 , Pcoat = 2500 kg/m3 , .9G,in = 20°C, vG,in = 1 5 X 1 0-6 m2/s, PG,in � 1 .2 kg/m3). =
A normalized Reynolds number which is related to the initial state can be defined as Remf(r) = *
Remf(r) (1400 + 5.22-JArQ) exp[r] :-::-::- =--= ::===7� Reo = � 1400 Jr.== Aro� exp[r] + 5.22
(260)
From this, the dimensionless minimal fluidization velocity reads as folIows: Remf(r)dP,O � (261) mf(r) Reodp(r) or (1400 + 5.22 JArQ) exp[r] (262) �ir) = 3 1 400 + 5.22 JAroexp[r] { 1 p p (exp[r] 1 ) } 1 / =
(
) +
-
Figure 71 shows the time-dependency of this dimensionless minimal f1uidization velocity. •
Gase 1:
Ps > Peoal
Figure 72 shows the minimal fluidization velocity and the particle diameter as function of the dimensionless time for the case that the density of the core ma terial is smaller than the density of the shell material. Again, at the beginning, the
1 07
Fluidized Bed Spray Granulation
,
100
---0-
0 'ü 0 ö
> c 0 'z:j oS
'S !;:: � E 'e 'E .!;:l
.......
10
-
p;
= 10 =5 =
1
:
-(r-
= 0.2
--
= 0. 1 '
,
-e
�
-
.�c
�,
- - - - - - - - - - - - -
� ,
- - - - - - - - - - - - - -
�
- - - - - - - - - - - - - -
E '6 "
O. l +-------�--_r--_+--�--� 4 o 2 6 8 10 dimensionless time [-)
Fig. 71 . Dependency of the dimensionless minimal-fluidization velocity from the dimension less time according to equation (262) by variation of the dimensionless-particle density during the semi-batch process for an example (M� = 1 00 kg/h, x 70 mass%, dp,o = 2 mm, 2 3 15 x 1 0- m /s, PG,in = 1 .2 kg/m3). P s = 2500 kg/m , .9G.in = 20°C, VG.in =
=
minimal fluidization veloeity deereases, while further granulation eauses a rise in the progression. By using an effeetive operation velocity of 1 m/s, the fluidized bed is stable only until the dimensionless time 2.4. That means, the gran ulation must be stopped earlier in eomparison to the example from the previous seetion. The reason is the higher partiele growth rate due to permanent deerease of the number of particles at eonstant bed mass. For fortifieation, Fig. 73 illustrates for the same example the time-dependeney of the mean particle density and of the particle diameter. The maximal particle diameter of 7.4 mm at a mean particle density of 540 kg/m 3 ean be reaehed after = 2.4 instead of 9.9 in eomparision to the example of Seetion 3.6. 1 . r
r
•
r
=
=
Gase 2 : P s < P eoal
In agreement with Gase 2 of the previous seetion, no deerease of the minimal fluidization velocity oeeurs for low dimensionless times when the shell density is higher than the core density. Instead, the minimal fluidization veloeity, the particle diameter as weil as the granule density rises permanently, expressed in Figs. 74 and 75. Hereby, the eritical time where the unstable area begins is = 2.35 cor responding to a granule diameter of 2.85 mm and to a mean granule density of 1 780 kg/m3. r
1 08
L. Mörl et al. 4 .-------r---.,...---.---� 0. 102 3.5
-<>-
minimal fluidization velocity
-0-
particJe diameter
--------
,
" "
_ _ _ _ _ _ _ _ _ _ _ _ � _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
.":'
�
� �
c:
� :a
� .§c: ·s
-------
2.5 2
-
-
- - -
-
_ _ _ _ _ _ _ _ _ _ _ _ J_ _ _
- - - - - " - - - - - - - - - - - -,,- - - - - - - - - - - - -
- - - - - -
, , , ,
- - - - - - - - - - - - �- - - - - - - - - -
_
-
0.082 _ _ _
_ _ _ _
-
� :
- - - - -
" E'" :a " v 0.042 'a ;;
- - - - -� - - - - - - - - - -
- -
'
-
g
0.062 �
-
1 .5
Ol
c..
0.022 0.5 o
����:;:J�--�---�---___+ 0.002 0
2
6 4 dimensionless time [-]
8
10
Fig. 72. Dependency of the minimal fluidization velocity according to equation (259) and of the particle diameter according to equation (229) from the dimensionless time at Ps > Peoal during the semi-batch process for an example (ML = 1 00 kg/h, x = 70 mass%, 2 dp•o 2 mm, P� = 2500 kg/m3 , Peoal = 500 kg/m3 , .9G,in = 20°C , VG.in = 1 5 X 1 0-6 m /s, P G ,in = 1 .2 kg/m ). =
4. DEGREE O F WETTIN G AND HEAT AND MASS TRANSFER 4.1 . Modelling of the degree of wetting and of the transfer phenomena
At fluidized bed spray granulation a permanent wetting of the particle surface and simultaneous evaporation and drying of the deposited liquid occurs. If we assume a laminar film on the particle surface, we can derive expressions for the ca Icu lation of the heat and mass transfer, drawn in Fig. 76. For the modelling we assume the following: 1 . All granules are spheres. 2. All granules have the same diameter, Le. the granules are monodisperse. 3. There is no internal nuclei formation by attrition, overspray or breakage and no elutriation of particles as weil as no agglomeration of particles. 4. The fluidized bed is ideal mixed (CSTR behaviour) . Thus, all particles are uniform wetted with the liquid proportional to their surface areas.
1 09
Fluidized Bed Spray Granulation 0. 1 02 _---�----r--___,-__r_---___r 3000 -0-0-
0.082
particJe diameter mean particle density r:
_ _ _ _ _ _ _ _ _ _ _ _ � - - - - - - -
I ö:i E�
� 0.062
I
, ,, ,, ..
,
- - - - - - - - - - - -
r I
- - - - - - - - - - - -
,
, :
- - - - - - - - -
2500
2000
_ _ _ _ _ _ _ _ _ _ _ _ 1- _ _ _ _ _ _ _ _ _ _ _ _ 1- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ I
" 0.042 '"
:a
�
_
I
,
:
1 500
,,
_ _ _ _ _ _ _ _ _ _ � _ _ _ _ _ _ _ _ _ _ _ _ L _ _ _ _ _ _ _ _ _ _ _ _ � _ _ _ _ _ _ _ _ _
0.
0.022
1 000
1. _ _ _ _ _ _ _ _
:
500
:
�
-'" .� " " 'Ü,:'" "E
bl)
e
"0
0. e �
1:�������!:::=--_L---�r__ ---_L8 ---___l100 6 · ·· ·· · ·· ·· · · · ·
0.002
- - - -
I
o
2
4
dimensionless time [-)
73. Dependency of the particle diameter according to equation (229) and of the mean particle density according to equation (244) from the di!Tlensionless time at Ps> Peoat during the semi-batch process for an example (ML = 1 00 kg/h, x = 70 mass%, 2 3 3 dp,o = 2 mm, P � = 2500 kg/m , P coat = 500 kg/m , 9G,in = 20°C, vG, in = 1 5 X 1 0- 6 m /s, PG i 1 .2 kg/m ) .
Fig.
,n
5. 6. 7. 8. 9. 1 0. 11. 1 2. 1 3. 14.
=
The fluidized bed has a constant porosity. The amount and the concentration of the injected liquid is constant. The injected liquid is totally deposited onto the particles. The solid densities are constant. The gas flows as ideal plug through the fluidized bed (PFTR behaviour). The secondary (classifying) gas flow fram the classifying tube is immediately mixed with the fluidization gas flow after passing the distributor plate. The process operates under steady-state and adiabatic conditions. There are no diffusion phenomena in the particles. The sensible heat of the injected liquid and of the solid is much smaller than the heat of evaporation. The water content of the feed nuclei and of the discharged granules is neg ligible.
Expressing the mass flux of vapour or water in an infinitesimal volume element as a function of pressures, we get with A = LA p d Mv = Ma d Y = P�Mv In RT
(PP _- PP�V) d � Ap '"
(263)
1 10
.-------,r--.,---r---..---r , --- --- - , - --- --- ------ -- --
L. Mörl et al.
6
-0-
5
� .� 4 öl
5 � 3 >
'ö 'S I;:: N
-
-
- - - -0-
-
0.037
minimal fluidizatiOll velocity
particle diameter
- -
-
- - - - - - - - - - - -
- - - - - - -
�
- -
_ _ _ _ _ _ _ _ _ _ _ _ _ L _ _ _ _ _
"
- -
- -
- - -
'
�
0.032 0.027
- - - -
- - - - - - - - - - - -
,,
-;; 2 E
'e
' ;:
i - - - - - - - - - - - - - r - - - - - - - - -
0.01 7 � 'ö
0.0 1 2 -
� § ...
0.022
1
0,007
o �ooo<"""'��E:=-_t----�---_+_---__J. 0.002 o 2 8 10
dim4ellsionless time6
[-)
Fig. 74. Dependency of the minimal fluidization velocity according to equation (259) and of the particle diameter according to equation (229) trom the dimensionless time at Ps < Pcoat during the semi-batch process for an example (!\AL = 1 00 kgjh, x = 70 mass%, 2 dp,o 2 mm, P� = 500 kgjm3 , Pcoat = 2500 kgjm3 , .9G,in = 20°C, vG,in = 1 5 x 1 O�6 m js, 1 .2 kgj m ). PG,in =
=
We can also define the mass flux of vapour as a function of moisture content. Using the relation y
-
-
Mv Pv Ra Pv - Rv P Pv - Ma P Pv _
with Pv
which can be inserted, we have
_
= (Mv /Ma
py
)+
y
(264)
(265)
(266)
111
Fluidized Bed Spray Granulation 0.037 ,-----�----,--___,--�---____. 3000 -<>-
particle diameter
0.032
�
0.027
.!i" 0.022 Eos
____
, I
. ..
____________
, . .. ,
�
_ _ _ _ _ _ _ _ _ _ _ _ _ 1_ _ _ _ _ _ _ _ _ ,
.
. , . , : - ; : - - - - - - - - - - � - - - - - - - - ;- - - - - - - - , , , : , . , , , - - - - - - - � - : - - - - - - - - - - 1 - - - - - - - - - - - - �- - - - _ ' , -
u
I
-
.
I
-
. •
0.01 2
,
0.007 ·· ··· ·· ··· · ·····
-
-
-
I
-
I
-
......
.
1 500
, - -
I
- -j
-
-
-
-
- - - - - - - -
1000
I
. .
� 8
� .� 5
"0
" u
.€os
0-
E
§ "
500
, , : , .
0.002 ;;;;,;;;;�iiQ9:� o 2
t
2000
. · · · · · · · · ·I· · · · ·· · · · · · · · · · · , · · · · · · ,
I I I . . . . ·· � . - - - - - - - - - - , - - - - - - - - - - - - , - - - - - - - - - - - - - ,- - - - -
I ------------�
'5 � 0.017
.�0.
. ... . .
4
��:=-�---�-----i-------l- 0 4 6 dimensionless time [-1
8
10
Fig. 75. Dependency of the particie diameter according to equation (229) and of the mean
particie density according to equation (244) from the dimensionless time at Ps > Pcoat during the semi-batch process for an example (AA = 1 00 kgjh, x = 70 mass%, 2 3 3 1 5 x 1 0- 6 m js, dp,o = 2 mm, P � = 500 kgjm , Pcoat = 2500 kgjm , 9G,in = 20°C, VG ,in P G, in = 1 .2 kgjm ) . =
(M(Y*v/Ma) (�v/Mv/�Maa Y*)
with a humidity-dependent Stefan correction factor
cPSY
=
-
In
Y)
+ +Y
(267)
A degree of wetting or wetting efficiency marks the ratio of wetted particle surface area to total particle surface area Awetted - Awetted (268) � Ap Atotal Thus, the effective surface area (Fig. 77) can be calculated by using the wetted part of the particles
ep -
_
_
A eff = Awetted
=
The unwetted part of the surface area is Aunwetted
=
(1
-
ep L Ap
(269)
ep) L Ap
(270)
Using a specific surface area (271 )
1 12
L. Mörl et 81. Ma
= M a,l + M a ,2
u
D �
YOUl ' 'ÖOUl
Y: _ _
_
o M p
•
• o
u D 'cf
Fig. 76. Schematic of the f1uidized bed granulation and drying model. and a dimensionless bed height
we obtain with
dL
Z
= Hbed
(272)
Ap = aAappqJdz
(273)
�bed
-
and with a specific gas mass flow or a gas mass flux
ma = AMappa ,
-
(274)
1 13
Fluidized Bed Spray Granulation
werted surface
unwerted surface
Fig. 77. Model of the degree of wetting.
from equation (266) dY CP sy{ Y'
-
Y)
_
-
ß
RT
MaP cpaHbed Y d rha �bed
(275)
If equation (275) is integrated into the boundaries z=
0:
z = z:
�bed = 0 and Y = Yin �bed = �bed and Y = Yin
results the dependency of the air humidity from the height of the fluidized bed. The following two cases should be distinguished •
•
Gase 1 : The partial pressure of the water vapour in the gas is negligible com pared to the total system pressure: P v < < P (e.g. at one time flow of ambient air through the fluidized bed). Then, a linear correlation between air humidity and particle vapour pressure according to equation (264) can be formulated with Y = (Mv / Ma )pv. Gase 2: It is essential that P v < P, but P v is not negligible compared to the total system pressure P (e.g. at recirculation of air).
For Case 1 , the Stefan correction factor CPSy, which is caused by the back flow of the gas from the phase interface (boundary layer), can be set to CPSy = 1 . Thus, after separation of the variables results (276) We can define a number of transfer units NTU (277)
1 14
L. Mörl et al.
so, after integration the equation (276) can be written in explicit form (278) This equation describes the dependency of the air humidity from the dimen sionless bed height. By introducing a modified drying potential of the gas or rather a modified drying efficiency (compare with the drying efficiency of equation (31 7)) Yf*
= Y*Y*-- YinY
(279)
a dependency of the modified drying efficiency of the gas from the dimensionless bed height can be transformed to (280) Figures 78 and 79 show these dependencies according to equation (280) at different degree of wetting. We can write for the gas outlet at (bed = 1 in dimensionless form (281 ) Yf�ut = exp (-NTUcp) Considering equations (277) and (278) we can also express for case P v < < P the gas outlet humidity with real dimensions Yout at a certain bed height a be (282) Yout = Y* - ( Y* - Yin) exp - ßPa cp H d rha The mean modified drying efficiency of the gas in the fluidized bed stand with ij*
=
1(';bebde=d=O1
(
exp(-NT UCP(bed ) d(bed
)
= NTU1 cp [1 - exp(-NTUcp)]
(283)
Again, we get in real dimensions Y* - Yin [1 - exp(-NTUcp)] Y = Y* NTUcp
(284)
where the quantities ß, a and cp are still unknown. Before we calculate these quantities we want to give some remarks concerning Case 2. Here, the Stefan correction factor is between 0 and 1 and not negligible, depending on the value of y* and Y. Starting with equation (266) and using the introduced quantities, we get analogous to equation (276) (285)
115
Fluidized Bed Spray Granulation
- -----��------- ; +......
,
-
0.8
>, <.) c <)
-
- -
:
:
-
-
-
- - -
-
,.
- - - - - - - - - - - - - - - - - - - -
, �,
- - - - - - - - - - - - - -
.... NTU = 0
'ü 0.6 iE
-0-
= 0.5
--A-
=1
�
-lr-
=2
<) 0.0 C
13
,
.
"'+
0.4
-+-
:g !C
E 0.2
=5
-0-
= 10
-+-
= 20
"""*"
=
50
, , ,
, , ,
_ _ _ _ _ _ _ _ _ _ _ _
L
, , , , , , "
, , , , , , , ,
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
!
, ,
_ _ _ _ _ _ _ _ _ _ _ _ _ _
l�========��--------�'----------+'----------�--------� -+-
o
, , , , , , , ,
_ _ _ _ _ _ _ _ _ _ _ _ L _ _ _ _ _ _ _ _ _ _ _ _ _ _I _ _ _ _ _ _ _ _ _ _ _ _ _ _ L _ _ _ _ _ _
o
0.2
0.4
0.8
0.6
dimensionless height of fluidized bed [-]
Fig. 78. Dependency of the modified drying efficiency from the dimensionless height of the fluidized bed according to equation (280) by variation of the number of transfer units according to equation (277) at ({J = 1 %.
0.8
I .... NTU = O
>, <.) c
.� iE
0.6
'" 0.0 C
' >, 0.4 .a
""2
:g !C
E 0.2
0.2
0.4
= 0.5
--A-
=I
-lr-
=2
-+-
=5
-0-
= 10
-+-
= 20
"""*"
= 50
-+-
= 100 0.8
0.6
climensionless height of fluidized bed
-0-
[-]
Fig. 79. Dependency of the modified drying efficiency from the dimensionless height of the fluidized bed according to equation (280) by variation of the n umber of transfer units according to equation (277) at ({J = 1 0%.
1 16
L. Mörl et al.
There exist no self-contained solution of the integral. Numerical methods are necessary to calculate the dependency of the air humidity from the dimensionless bed height according to equation (278). 4. 1. 1. Degree of wetting in the fluidized bed
The degree of wetting is necessary for the calculation of the height-dependent air humidity as weil as of the solid temperature. The following considerations were made •
•
The degree of wetting lies between 0 (no liquid injection) and 1 (total particle wetting) depending on the injected solvent mass flow. The maximal atomizable liquid mass is reached when all particle surface areas are wetted. A further increase of the injection rate leads to an increase of the liquid in the fluidized bed because the maximal loading capacity of the gas is exceeded.
Therefore, the maximal liquid mass is calculable with the solvent mass flow at
(286)
(287)
M
yOU!
.....:: +....
V
fluidized bed
gas
- - - - - - - - - - - - - - - - ,,/
Mp,ou'
Xp,UII' = O Fig. 80. Total mass balance of the fluidized bed granulation.
di tributor
117
Fluidized Bed Spray Granulation
For the case 1 the outlet humidity Yout is determined by the injected li q ui d mass flow. The dependency of the moisture content of the particles at the outlet XP, out from the degree of wetting i s negl i g i b l e accordi n g to assumpti o n 14. The replacing of equations (282) and (287) yields the degree of wettin g 1_ ln [ 1 - rlAx a In [1 rlAx - ßparhaHbed NTU Ma( Y* - Yin) (288) Ma(Y* - Yin) A degree of wetting nearly 1 would be very effective from the energetic poi n t of view. But in practice, these wet conditions would lead to a sticking of small particles, and thus to an agglomeration. Therefore, it is necessary to carry out experiments to find the critical value for the maxi mal possible degree of wettin g. Inserting 1 into equation (288) the specific solvent evaporation flow i s calculable, which is based on the maxi mal solvent evaporation flow at the com plete saturation of the gas . ML x 1 - exp(-NTU) (289) Mv* Ma( Y* - Yin) iI ustrated by Fig. 81 at different number of transfer units. It i s visible, that no water can be evaporated and thus no water has to be injected starti ng from NTU 6. Using equation (289), we also get the maxi mal l i q ui d loadi n g at complete par ticle wetti ng qJ =
qJ
=
1
.
qJ
=
1
.
_ _
=
=
= .
=
(290)
2 0.8
� o <;: c: o
.� 0.6
,
- - - - T - - - - - - - - - - - , - - - - - - - - - - - � - - - - - - - - - - - -.- - - - - - - - - - - I
] 'ü
�
0.2
I
,
,
, ,
, ,
, ,
, ,
� - - - - - - - - - - - + - - - - - - - - - - - � - - - - - - - - - - - � - - - - - - - - - - - -I - - - - - - - - - - - -
_ _ _ _ _
�
,
_ _ _ _ _
I
:-
u 0.;:;
I
- - - - - - - - - -
o 0. '" :'"
� 0 .4
I
-
_ _ _ _ _ _ _ _ _ _ _
'
I
I
, ,
, ,
-- - - - - - - - - � - - - - - - - - - - _ . _ - - - - - - - - - - � I
,
I
• _ _ _ _ _ _ _ _ _ _ _ � _ _ _ _ _ _ _ _ _ _ _ � _ _ _ _ _ _ _ _ _ _ _ _1- - - - - -
I
,
I ,
- - - - - - - - - - -
I
�----I
I
- - - - - -
�- - - - - - - - - - - t
0 +-------+---�--_r--�--_4 4 5 6 3 2 o [-)
number of transfer units
Fig. 8 1 . Dependency of the specific solvent evaporation flow according to equation (289) from the n umber of transfer units according to equation (277).
1 18
L. Mörl et a/.
and accordi n g to equation (290) the mi n i m al gas mass flow which i s necessary to evaporate a certai n liquid mass flow assumi n g 1 00% particle wetti ng . i.Ax (29 1 ) Ma,min = ( )] [ (y* - Yin) 1 - exp ßPaaAappHbed _
ma,mm
4. 1 . 2. Solid temperature in the fluidized bed
The advantage of the degree of wetting is the possibil ity to compute the tem perature of the solid particles in the fluidized bed. By assumi n g that the temperature at the liquid wetted surface area of the particles is determi n ed by the wet bul b temperature 90 which i s approximately equal to the adiabatic saturation temperature of the gas and that the temperature at the unwetted part of the surface area is characterized by a mean gas tem perature 9G of the fluidized bed (Fi g . 77), we can write for the mean solid tem perature (292) 9s = 90 cp + (1 - cp)9G (293)
The wet bulb temperature is a function of gas inlet temperature, gas humi dity as weil as molar mass of vapour and gas. For the calculation of the mean solid temperature, the mean gas temperature accordi n g to equation (293) is neces sary. Assumi n g plug flow of the ai r and constant air enthalpy, we can write hG = cpG9G + Y( cpv9G + Ahva)
(294)
to express the dependency of the gas temperature from the gas humidity as function of the bed height according to equation (272) with Y Y((bed) =
hG,in - Y((bed)Ahv "'G (i'Sbed) - cpG + Yi(i'Sbed ) cpv o
_
and finally in analogy to equation (278)
Y((bed) = Y* - (y* - Yin)
(295)
(296) exp(-NTUCP(bed) Insertin g equation (296) into equation (295) yields the gas temperature as function of bed height between 9G = 9G,in at the i n let of the flu i d ized bed (z = 0) until the outlet of the fluidized bed at z = Hbed C1 - Ahv[1 - exp( -NTUCP(bed)] (297) 9G ((bed) - 9G,in _
C1 + cp v[1 - exp(-NTU CP(bed)]
1 19
Fluidized Bed Spray Granulation
with the coefficient C1
(298)
According to equation (293), the mean gas temperature depending on the bed height is calculable �bed=1 (299) 9G = r O , G (�bed ) d �bed J�bed= The integratio n of equation (299) yields 1 (L':!hvü C2 ) [cpveXP(-NTUCP) - C3] C2 +' G - -cpv - C3 NTUcp -cpv + -C3 In C3 (300) with the coefficients C2 and C3 C2 = 9G,in C1 - L':!hvü (301 ) 9
-9
_
(302)
The mean solid temperature can be calculate with equation (292) within the boundaries 90 at the maximal l i q ui d injectio n rate (cp = 1 ) and 9G,in (without liquid injection), Equation (292) is not defined for the last case, 4. 1 . 3. Heat and mass transfer between partie/es and gas fluidized beds
Typical laws for the heat transfer may be given as empi rical nexpressions Nu = C Rem Pr" and for the mass transfer as Sh C Rem Sc . Accordi n g to the analogy, both laws have the same constant C=and identical exponents m and n. For the calculation of the heat and mass transfer we used the followin g model of Gnielinski [52] x
x
x
x
(303)
Sc = <>w,G � with the diffusion coefficient of water in air [53] <>w.G
( 9 + 273.1 5 ) 1.81 - 2.252 P 273 . 1 5 _
By using the followi ng expressio ns for the laminar and turbulent fractio n: Sh1am = 0 . 664Re; /2 Sc1/3
(304)
(305)
(306)
1 20
L. Mörl et 81.
037ReO �·8 Sc2 3 Shturb = 1 + 2 .40.43Re; (307) '\Sc / 1) we get the Sherwood number of a single particle Sh P,single = 2 + JN U�m + Nuturb (308) by which we can approximate the Sherwood number between all particles in the fluidized bed and the flu i dization gas Sh PG ßdW,Gp = [1 + 1.5(1 emf)]ShP,single (309) According to the analogy of heat and mass transfer, the Nusselt number NUPG IY.PAGG dp = ShpG Le( 1 /3) (310) can be determined by using the Lewis number AG Le cpGPGl5w,G (311) which is nearly Le = 1 for air-water mixtures. _
=
15 -
=
-
--
-
=
4. 1 . 4. Example calculation
An aqueous protein suspension has to be granulated in a fluidized bed by using ambient air. Table 6 contains the necessary and given parameters. After calculation ofthe apparatus diameter 1. 27m with equation (313), we have chosen a fluidized bed height of Hbed = 1.3 m (Table 7). After a complete calculation procedure of all parameters, the viscosity and the density of the gas concerning 9G,in have to be corrected in respect to .9G , and a new iteration should be started. For the calculation example the dependencies of the air outlet humi dity ac cordi n g to equation (287) as weil as of the degree of wetting accordi ng to equa tion (288) from the atomized liquid mass flow for a bed height of Hbed 1.3 m are plotted in Fig. 82. Figure 83 shows the dependencies of the mean temperatures of the sol i d and of the gas according to equations (292) and (300) from the atomized liquid mass flow. An injection larger than ML 1280 kgjh leads to an unstable area. Fig ure 84 explains the dependencies of the residence tim e accordi n g to equa tion (88) and of the degree of wetting according to equation (288) from the flu idized bed height at an atomized liquid mass flow of ML 1000 kgjh. Equations (292) and (300) may be plotted graphically to get the dependency of the mean solid temperature and of the mean gas temperature from the fluidized bed height. Dapp
=
=
=
=
1 21
Fluidized Bed Spray Granulation Table 6. I nitial parameters of an example calculation
Symbol Parameter Suspension mass flow ML x Water content Density of the solid in the suspension Desired granul e product diameter Diameter of the nuclei Temperature of the inlet air Humidity of the i n let air Desi red humi d ity of the outlet air Saturation temperature of the i n let air 90 Saturatio n humidity of the inlet air Moisture content of the product granules Moisture content of the nuclei Maxi mal wettin g efficiency (experimental determined) Specific heat capacity of the vapour Specific heat capacity of the ai r Average heat of evaporation in the operation range Kinematic viscosity of the inlet air Density of the i n let air Ps dp,out dp, o HG,in Yin Yout y*
XP,out
Value 1 000
80 1 200 10 3 1 50 0. 01 0.044 42 0 . 0536 0
CfJ m a x
0 45
cp v cpG Ahv
1 .9 1 2300
VG,in PG,in
28.29 0 .835
XP,in
kJjkg X
1 0-6
Unit kgjh mass%3 kgjm Mm Mm °C kgjkg kgjkg °C kgjkg kgjkg kgjkg % kJj(kg K) kJj(kg K) M2js 3 kgjm
These progressions are plotted in Fig. whereby an unstable area is below m. 85,
Hbed =
0 . 1 23
4.2. I nfluence o f t he mixing behaviour on th e degree of wetting
The drying in the fluidized bed depends on the properties of the solids. But nevertheless, the properties of the gas phase also play an important role. Besides the i n let conditions of the gas (temperature, humidity), the flow and mixing be havio ur has a large influence, because back mixing effects reduce the drying potential of the gas. The following section describes the influence of the two limiting cases (a) ideal plug flow (PFTR) and (b) ideal back mixing (CSTR) on the drying behaviour and in particular on the degree of wetti n g, Based on these considerations, rough estimations regardi n g the l i q ui d hold-up in the fluidized bed can be made by using the following assumptions:
1 22
L. Mörl
Table 7. Calculated parameters of the example
Equation
(5) (5) (1 1 ) (1 1 ) (27) (27) (4) (4) ( 1 3) ( 1 3) (312) (77) (5) (30) (287)
(31 3) (56) (87) (305) (304) (306) (307) (308) (309) (309) (80) (287) (288) (298) (30 1 ) (302) (300) (292) (88)
Parameter
Ar ( dp,o) Ar ( dp,out) Re mf ( dp,o) Remf ( dp,out) Ree1u ( dp,o) Ree1u ( dp,out) Vmf ( dp,o) = Vmf,mi n Vmf ( dp,out) = Vmf,max Velu ( dp,o) = velu,min Velu ( dp,out) = Velu,m ax Veff = ( Vmf,max + Velu,min )j2 dp R = Reeff Ar = Areff
e
G = Geff
MG
Dapp = [(4 VG ) /(nveff3600)] 1 /2 rvfcped L: A p .
(5w, G
Sc Sh1a m Shturb ShP,single ShPG
ß
Mp = ML ( 1 Mp,out Yout (j)
C1 C2 C3
9G 9s tv
-
x)(cf#, 01 cf#, out)
Val u e
475387 1 760691 2 95. 1 755.6 1 084 6831 0 .897 2. 1 4 1 0.22 1 9.33 6.2 6.8 1 490 55361 76 0.671 23529 1 .27 650 425 49.73 x 1 0-6 0.569 1 6.97 8.65 2 1 . 05 40.0 0.2925 5.4 205.4 0.044 9.46 23.37 1 205.7 25.27 98.82 93.44 8.93
Unit
mjs mjs mjs mjs mjs Mm M3jm3 kgjh M kg2 M2 M js mjs kgjh kg/h k9/kg %
°C oe
h
et al.
1 23
Fluidized Bed Spray Granulation
0.055
_ _ _ _ _ __r------,r__.____, � ---,--,--__--.--_
.,.-
-I 1
0.05
�
0.045 _ _
c..
.� 0.035 '0 'E ..5 0.03
0.025
.... - :;
0 .02
'::l :::l 0
0.015 0 . 01
,, , ,
-
� 0.04
.,
+____
_ _
, ,-
- - - - - - - - "!
,
,
m
,
,
" -� - - - - - - - - t - - -
____ _________ J
, , , , _ _ _ _ _ _, _ _ _ _ _ _ _ _ ,_ _ _ _ _ _ _ _ _ !, _ _ _ _ _ _ _ _ J, _ _ _ _ _ _ _ _ , , , , , ,, ,, ,, , , � � � � ,, , ,,
- - - - - - - -1-
------- 1
.
- -
__+_ m____i m___ +_ _ _ , ------- - - ,r- - - - - - - - - �, - - - - - - - -�-
-
- - - - - - � - - - - - - - - �-
- - - -
- - - - - - - � - - - - -
�
- - - - - - - � - - - - - - - - � - - - - - - -
- - - - - - - - -
- - - - - - - -
_
- - - - - - - -
- - - - - - - -
1 00 80
� Z'" '"
::::
t;
"
60 40
� .g
OJ)
., :;: '0 QJ
e
OJ) QJ '0
20
1::: :::.....�==d::===i===:===-_L--__l-�___l 0 o -
,
", - - -
�
@
�
�
I�
I�
I@
liquid m a s flow [kglhl
Fig. 82. Dependency of the air outlet humidity according to equation (287) and of the degree of wetting according to equation (288) from the atomized liquid-mass flow (pa rameters, see Table 6). 1. 2. 3. 4. 5. 6. 7.
Two phase model with a suspension phase with particles and a particle-free bypass or bubble phase. No heat and mass transfer between both phases. Two limiting cases for the gas phase: plug flow (PFTR behaviour) or total backmixing (CSTR behaviour). Perfect backmixing of the particles in the suspension phase (CSTR be haviour). Isenthalpic behaviour of the gas phase and thus, neglect of heat losses to the environment, of the heating-up of particles and of the liquid. The gas phase is quasi-stationary. The solid particles are monodisperse.
The liquid balance around a fluidized bed yields . d ML · Tl = Mnozzle - Mv
(3 1 4)
The equation can be rewritten by using the degree of wetting, the liquid film thickness onto the particles, and the density of the liquid . . d� 1 v) (31 5) M M o le n zz ( A L ptlhF The expression
dt = PL
ML.max,HoldUP = PL L AptlhF
(3 1 6)
1 24
L. Mörl et al. 1 50 ��------�---,--,---.---�---, 1 30
U
1 10
-
,
, , ,
,
90
50
-
- - - - - - - - �- - - - - - - - - - � - - - -
e.....
70
,. , ,
,
-
- - - - - - - - - . - - - - - - - - - � - - - -
- - -
� _ _ _ _ _ _ _ _ _ _ L _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ �_ I I I , • I I I ,
� ,
_ _ _ _ _ _ _ _ _ � _ _ _ _ _ _ _ _ _
b - t'}S
, , , ,
, , , ,
�- - - - - - - - - - L - - - - - - - - - � - - - - - - -
_ _ _ _ _ _ _I _ _ _ _ _ _ _ _ _ _ L _ _ _ _ _ _ _ _ _ 1 _ _ _ _ _ _ _ _ _ I I
, ,
, �_ _ _ _ _ _ _ _ _ _ � _ I I , ,
_ _
30 +-----�----_r--r_--_+--,_--�--� 4000 800 600 1000 2000 400 200 o
liquid mass [kglh] flow
Fig. 83. Dependency of the mean solid temperature according to equation (292) and of the
mean gas temperature according to equation (300) from the atomized liquid mass flow (for parameters, see Table 6).
�v !
12 ,-�r_----�-----.--__r l00 10
6 8 '" E '" () " '" "0 'öö
6
_
,
_ _ _ _ _ _ _
;
_ _ _ _
- Cf>
:
�
'" '"
:E os Ui
- - - - -
, , , �
- - -
---
-
�--
- -
:
, ,
1
.I.
_ _ _ _ _ . . � _ _ _ _ _ _ !.. _
, ,
, , , - - - � - - - - - - - �- - ,
-
-
-
- - - ,- - - - - -
" ::0
� 4
-
;
, -,
80
60 - -
--
- - -
40
- - - - - - -I- - - - - - - - � - - - - - - -
,
,
20
2
0 +------.---.--r---T---+ O 1 .6 1 .4 1 .2 0.8 0.4 0.6 0.2 0
fluidized bed heigh! [m]
Fig. 84. Dependency of the residence time according to equation (88) and of the degree of wetting according to equation (288) from the fluidized bed height (for parameters, see Table 6).
1 25
Fluidized Bed Spray Granulation
' --------r- g
1 50 �----�-----,
, : ,,,
1 20 U
: co
L 1::
:::l :;; 90
i:i 0.. 8 E
60
", 1;; C :::l
- - -
'
.
- - - - - - - -
-- �G
-
,,
- - - - -
-
�s - - - - -
- -
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1_ _ _ _ _ _ _ _ _
.-i. - --� - - �� '- :-::-:-:-:� :-:: : :-::-:-:":": - -� - - -� - -:-=-: - - --=-1 -
.; '-C-� -
-
--::-=": -
,
- -
-
-
- - -
,,
,
I I I I - - - - T - - - - - - - - , - - - - - - - - , - - - - - - - - � - - - - - - - - - I- - - - - - - - - r - - - - - - - -
30 +-----�----�--_4--r_--+--� 1 .6 1 .4 1 .2 0.8 0.6 0.4 0.2 o
fluicüzed bed height
[m)
Fig. Dependency of the mean solid temperature according to equation (292) and of the mean gas temperature according to equation from the fluidized bed height (for 85.
(300)
parameters, see Table 6).
characterizes the maximal accumulated amount of liquid in the system corre sponding at
1 : Analytical solution for PFTR behaviour The analytical solution for the drying efficiency assuming plug flow is NTU YOU1 - Yin ( 1 v) 1 exp 1]PFTR = v)
Gase
Y*
_
Yin
{
=
[
-
(1
_
with a dimensionless NTU-number analogous to equation
(277)
]}
NTU = ßPa d.''EJ A p
. .
(3 1 8)
Ma
.
Thus, the evaporated water mass flow is given as
{
Mv = Ma( You1 - Yin ) = Ma ( Y - Yin ) ( 1 - v) 1 - exp
Inserting the maximal evaporated water mass Mv.max
=
Ma (Y
-
Yin )
(3 1 7)
[
NTU -
(1
_
]}
v)
( 3 1 9)
(320)
1 26
L. Mörl
et
al.
(315) } ] 1 ( . - Mv,. max(1 -v) { 1 - [- NTU ) ep (1 -V) (321)
into equation yield the time-dependent degree of wetting d epPFTR exp dt = ML,max,Holdup Mnozzle
We can also define a dimensionless time a s relationship of the maximal liquid hold-up to the injected water mass flow
�ax,HoldUP r resp. dt ML,�ax,HoldUP d r = ML,Mnozzl e Mnozzle Replacing equation (321) leads to } ] d epP-'NTU Mv,-max-e (1 - v) { 1 - exp [- -----'-':drFTR-'-'-'- = 1 - -.Mnozzl ep PFTR ( 1 -v) t
=
(322) (323)
The ratio
8 = �nozzle
(324) can be defined as specific liquid loading of the fluidized bed between the limits 0 and 1. At 8 = 1, a complete saturation of the gas occurs d ep,--,:P,.:-: ( 1 8-v) { 1 - exp [- -FT,-,-,-R _ 1 - -_ (325) dr ( 1NTU- v) epPFTR] } Applying the separation of the variables, equation (325) can be integrated depPFTR - J dr (326) J1 exp [ _ NTU ",PFTR] Mv,max
( 1 -v) + ( 1 -v) 8
8
(1 -0)
m
{ [ 1 -V)} NTU V)] 1 1 ( I n 1 - (-- exp [ _ epPFTR] -- = r ] U N 8 8 (1 v) [1 _ T Converting into the dimensionless time yields [ NTU ex � -�] r} - 1 ) { P ( 1 ( -v) _ epPFTR - NTU In [--1 ] By neglect of the accumulation term in equation (325) 0 = 1 _ ( 1 8- V) { 1 _ exp [_ (1NTU-v) epPFTR] } we get the degree of wetting for the stationary operation (steady state) ( 1 - v) [ 8 ] epPFTR = - NTU In 1 - ( 1 _ v)
and solved
( 1 -0) 8
+
(327)
( 1 -v)
8 (1 -0)
(328) (329) (330)
1 27
Fluidized Bed Spray Granulation
The degree of wetting has to be much smaller than 1 for a stable operation of the fluidized bed. So, we have to accomplish that the NTU-number is bigger or equal the right-hand side of equation (330) NTU �
[
_
]
8 (1 - v) ln 1 - (1 _ - v)
-
Gase 2: Analytical solution for CSTR behaviour
(
(331 )
)
If we assume CSTR the drying efficiency becomes NTU
.
_
*
.
.
[
_
and solved -
(1 -
v/
8 NTU [(\:;1') - 1
{ r In
V
(
_
J1
_
_
_
(
(
)
[
and rearranging yields
_
( 1 - v) 8
dr J )
]
- 1
}
[
NTU ( 1 80) - 1
]
(334)
(335)
(336)
[
]
r +
1 -v
)]
-
The steady-state degree of wetting can be written with 0= 1
(333)
-
d
-( 1 - v) NTU
(
)
(332)
(337)
(338)
(339)
1 28
L. Mörl et al.
The minimal NTU-number requires a degree of wetting between 0 and
1 (340)
NTU �
[1 _B--.!L]
(34 1 )
(1 -0)
The liquid accumulated in the fluidized bed is obtained for both cases with
ML,HOldup = cP ML,max,Holdup
(342)
Figure 86 shows that a small specific liquid loading « 20%) leads to the same order of magnitude for the minimal NTU-numbers (degree of wetting = 1 ) of CSTR and PFTR. The bypass fraction has nearly no influence. The bypass frac tion reduces the maximum liquid injection rate. This bypass influence increases with increasing liquid loadings. As an example, a bypass fraction of 20% leads to a specific liquid loading of 0.8. The stationary degree of wetting is nearly equal for both mixing cases at specific liquid loadings smaller than 20% (Fig. 87). Again, the maximal liquid loading depends on the inactive bypass fraction, the liquid hold-up is smaller for the PFTR compared with the CSTR. Figure 88 shows the ratio of equations (332) and (3 1 7) regarding the drying efficiency, which characterizes the degree of saturation depending on the NTU-number at different bypass fractions It is obvious that the drying efficiency of the ideal mixed vessel is always smaller than the drying efficiency of the plug flow tubular reactor. In dependently of the mixing model, at high NTU-numbers lower bypass fractions yields a faster achievement of the saturation. u.
4. 2. 2. Unsteady operation
Gase 1: Analytical solution for PFTR behaviour
Considering equations (3 1 5) and written as d ipPFTR dt
=
1 /<'hF Ap L L P
{M
nozz[e
_
Ma
(Y*
(31 9)
_
the degree of wetting for PFTR can be
y:In)(1
_
v)
L Ap )] } [1 exp(- ßPaM�aPFTR (1 _
v)
(343)
1 29
Fluidized Bed S pray Granulation
. .. ., ;,! " .i .
10
1
.... ... ... .. .... .. .
.
..
.
_ ... .. . . . . . . . . . . . . .
.
L-
Q) .0
E
:::J C
° 10
I
=> IZ tU E 'c
"E
10
.1
--- PFTR v = 0
1 0" 2
o
PFTR v = 0.1
. . +. .
P FTR v = 0.2 CSTR v = 0 CSTR v
. . 0"
3 1 0-
0
0.2
0.4
0.6
=
0.1
CSTR v = 0.2 0.8
specific liquid loading B Fig. 86. Dependency of the minimal NTU-number from the specific liquid loading at differ
ent bypass fractions.
1 10
° 10
Cl C
� Ci :::
Q)
. 10 1
� 1 0"2 Q)
Cl Q) "t:I
... . e-. ..
3 1 0"
PFTR v = 0.2 CSTR v = 0
x
.. '0-' .. .
· 1 0' 0
0.2
0.4
0.6
specific liquid loading
B
CSTR v = 0.1 CSTR v = 0.2 0.8
1
Fig. 87. Dependency of the stationary degree of wetting from the specific liquid loading at different bypass fractions with NTU = 1 0.
1 30
L. Mörl et
0.95
al.
-------------
0.9
...!...
=
...... ,
-i>-
_ _ _ _ _ _ _ _ _ _ _ _ _ _1_ _ _ _ _ _ _ _ _
, ,
--4--
0.8 - - - - -
- - - - - - - - - ,- - - - - - - - - - - - , ,
0.75
-0-
....... -+-
0 1 .
=0.2 =0.4 =0.6 =0.8 =0.9 =
03
=
05
=
07
.
.
.
+-----+-----ir--t==---=-j
0.001
0.0 1
0. 1
NTU
[-J
10
1 00
Fig. 88. Dependency of the ratio of the drying efficiency of the CSTR model related to the drying efficiency of the PFTR model from the NTU-number at different bypass fractions.
Now, substituting by using the following variables K1 =
1
PL L: Ap l1hF
---:=--:--:-:--
K2 = Mnozzle K3 = Ma ( Y* - Yin ) ßP?Ap K4 = _
K5 = ( 1
Ma
-
v)
(344)
yields (345)
(346) (347)
1 31
Fluidized Bed Spray Granulation
A further substitution by using the variables
K6 = K1 K2 - K1 K3 K5 Ky = K1 K3 K5 K Ks = 4 K5
( 348)
leads to d ipPFTR
+ y
K6 K exp (KSipPFTR ) dt With the separation of the variables results the derivative integral
l
o
=
-
d
= xa - -ac1 I n [ a + b exp(cx) [
with the integration rule according to [54]
J
11
ipPFTR ----'--'-'--'-'--'---.,- - dt K6 + Ky exp (KSipPFTR ) 0
dx
a + b exp( cx)
----
-
(349)
(350)
(351 )
The absolute value can be neglected, because of the physical inanity t = ipPFTR K6
_
In (K6
+ Ky exp (KSipPFTR ) ) K6KS
( 352)
The initial condition t
=
0
+->
ip
=
0
In (K6 + Kye(KsipPFTR ) ) In(K6 + Ky) --+ K6 K6 Ks K6 Ks
t = ipPFTR
( 353) (354)
yields the degree of wetting in the steady-state
K6 + Ky exp (KSip PFTR,max ) = ipPFTR,max
= fa In
(- ��)
Case 2: Analytical solution for CSTR behaviour
0
(
(355)
)1
Considering equations (31 5) and (333), we get for the degree of wetting for ideal mixing ßPa
[
.
.
_
(356)
1 32
L. Mörl et al.
Replacing with the variables leads to (357)
�rR = K1 K2 - K1 K3K5
d4J
By transforming new variables
[(
- 5 K
� K4 4JCSTR) ]
(358)
(359)
we can express d
4J��TR
=
Kg - K7 [ (K1O 4JCSTR) ]
- rt dt
(360)
The separation of the variables produces a derivative integral
("' CSTR
Jo
d4JCSTR Kg - K7 K10 4JCSTR
with the solution t=
The initial condition
_
Jo
I n--,-( K 1 O_4J--=C:.::. ST .:. ) . .:.R.:..c. _g_- K7 K_
_ _
t
=
----:-:-:-::K7 K1O
O � 4JCSTR =
0
t = - In (Kg - K7 K1 0 4JCSTR ) + K7 K1 0
In(Kg) -K7 K10
(361 )
(362) (363) (364)
yields a degree of wetting for the stationary operation Kg - K7 K1 0 4JCSTR 4JCSTR =
Kg K7 K10
=
0
;(365) (366)
In the fOllowing, the model is compared with experimental results. We used a water sprayed fluidized bed containing glass spheres. Simultaneously, the air humidity at the outlet was measured by infrared spectroscopy. Concerning the dynamic operation, the unsteady start-up period with an increase of the air hu midity and a formation of a degree of wetting after water atomization until the steady-state was reached as weil as the shut-down period after stopping the water injection characterized by an entirely evaporation of the liquid film have
1 33
Fluidized Bed Spray Granulation
0.025 1--:---:--;--;:::=:::::===:;-1 0.02
�
�
0.015 0.01
"5 )-40
�
WI·...... �"'- ,: -,,
- - - - - - - - - - -� - - - - -
, .
: Mw = 15.8 ,
- �... "IJ � - - - - - - - - -
d-;-
-
,:
,
- -- - --
: .. : �lE , � ..
----------�
kg{h ,
- - - - - - - - - - - - - - - - - - - - - - ------------
0.005
,
Measurement model model
- - - - - - - - CSTR
,
�---- - - - - - - - - - - - t - - - - - - - - - - -
:, I"
�, ,
-- --
�
- P FTR
- - -
-
- - - - - - - - - - - � - - - - - - - - - - -
,
, �
,
,
O �------+_--r_--� o 200 400 600 800 I 000 1 200
time
[5]
Fig. 89. Measured dynamic response of the air h umidity at the outlet during water injection onto a fluidized bed of glass spheres and comparison with the mixing mod�ls at v = 0 and = 50 �m (Dapp O.4 m, ML 1 5.8 kg{h, x 1 00 mass%, MG O.28 kg{s, MF 9G,i n 1 21 .4°C, Yln O.06 kg{kg , y* O.03 kg{kg, M'ped 30 kg , dp,o 3.05 mm, 241 2 kg{m 3). pp =
=
=
=
=
=
=
=
=
=
been conducted. Figures 89-91 shows typical progressions. Both limiting cases PFTR and CSTR are solved in the time-dependent analytical form. Due to the higher drying efficiency of the PFTR, the steady-state air outlet humidity is reached faster. According to the total mass balance, both models yields equal humidities at the stationary operation point. 5. F LUIDIZED BED GRANU LATION WITH SUPERHEATED STEAM
The fluidized bed drying system using superheated steam as a drying agent and fluidization medium is widespread. The recirculation and reheating of super heated steam by using a closed circulation are only two of the advantages of superheated steam processing. These advantages imply that emissions coming from the drying product are not emitted to the environment, but will appear in the condensate. Only the amount of steam that corresponds to the amount of evaporated water will be removed from the c10sed circuit. Therefore, atmosphere in the process is inert, in the sense that no oxidation of the products and no fire or explosion risks exist [55]. The superheated steam transfers this heat to the wetted particles. Thus, the superheated steam temperature decreases until the saturation temperature of the solvent (water) corresponds to the system pres sure. Simultaneously, the transferred heat flux between wetted particles and
1 34
L. Mörl et al.
1-
I
7 �------�--�
6
1
5
- - - - - - - -
4 9-
,,
- -
V- - - -
3
2
-----
- - - - - - - -
1-
PFTR model
t- CSTR model ,
,
- - - - - - - - - t- -
,
- - - - r
,
- - - - - - - - - - -
,
- -
I
:� O +--------r-------+------��------�------+_------� 200
o
400
600
time
[sl
1000
800
1200
Fig. 90. Calculated dynamic response of the degree of wetting during water injection onto a fluidized bed of glass spheres and comparison with the mixing models at v = 0 and /1hF = 50 J.lm (for parameters, see Fig. 89).
2 �----�----�------�----_:--��====� 1.6 =
1.2
- - -
-
-
-
,
I
'r
, : Mw 15.8 kgJ/1
,
- - - - - - - -
-
_ _ _ _ _ _ _ _ 1 _ _ _ _
� 0.8
PFTR model
- CSTR model -
-
-
I
_ _ _ _ _ _ 1_ _ _
- - - - - - - -1 _ _ _ _
0.4
,: Mw = O kglh ,: ,
=
- - - - - - - - - f- -
O +-----�--�--��--
o
200
400
600
time
[sl
800
1000
1200
Fig. 9 1 . Calculated dynamic response of the NTU-number during water injection onto a fluidized bed of glass spheres and comparison with the mixing models at v = 0 and /1hF 50 J.lm (for parameters, see Fig. 89). =
superheated steam is used to heat up the deposited liquid up to the boiling temperature and to evaporate a part of the injected solvent. This generates an additional steam flow. A detailed description of the process is given in Section 6.1 .
1 35
Fluidized Bed Spray Granulation
In order to predict the superheated steam granulation in a fluidized bed, the following simplified model according to Fig. 92 has been derived by using the following assumptions: 1. 2. 3. 4. 5. 6.
continuous process, adiabatic operation, ideal particle mixing, homogeneous fluidized bed (neglect of bubbles), plug flow of the gas, availability of the degree of wetting model,
fluidized bed
-.----1
I � i
N
Ü Ü L
Ö I I
�
Ö
e e ____ gas distributor
D Ü 11
t------I
('-,...J Ms�1O,app · itSt,in,app
�
Fig.
MSt,in,sep itst,LD,sep .
92. Schematic of the fluidized bed granulation with superheated steam .
1 36
L. Mörl et al.
7 . mixing of the classifying gas and of the fluidization gas after passing the distributor, and 8. constant density and viscosity of the gas in the fluidized bed.
Heat balance around the volume element:
Mstcpv9st = ( Mst + d Mst) cp,st (9st + d 9st) + d Mst L'1hv
(367)
So, we get (368)
or d 9st cpv9st + L'1hv
The solution of the integration
8;t""8St d 9st ( + L'1hv cp 9st v 18st=8st.in yields
(
d Mst Mstcpv
=
MSt=MSt d Mst ( lMst=Mst.m Mstcpv
)
) (
(369)
. . L'1hv = - [In ( Mst L'1hv - In 9St,in + In 9st + ) - ln ( Mst,in ) ] cpv cpv respectively . 9St + dhV In �St,in In 9St,in + Mst
or
( (
(
c��v) = Cpv
MV 9St + c;9St,in + �::
(
. ) = (MSt,in ) Mst
)
)
(370)
(371 )
(372)
(373)
Now, we introduce the dimensionless temperature of the steam eSt =
with
(
9St + MV 9St,in + dh: cpv
Cp
)
(374)
L'1hv L'1hv 9St = ,9 st,in + Cpv eSt - Cpv
(375)
L'1hv d d 9St = 9St,in + Cpv eSt
(376)
(
)
1 37
Fluidized Bed Spray Granulation
the dimensionless temperature of the solid particles
with 9s
=
( 9s + ) Mv Cpv e; d( SI,in + !J.h
( 377)
I1hv (/JSl,in + I1hv ) ()s cpv cpv
(378)
()S
_
'
-
p
(
-)
I1h d 9s = 9sun + v d ()s cpv and the dimensionless generated steam mass flow
( 379)
.
MSI - MSI,in · MSI MSI,in *
_
(380) (381 )
(382) Combining equations (374), (382), and (373) leads to the dimensionless steam temperature according to Fig. 93 1 (383) ()SI = * 1 + MSt Taking into account equation (383) the maximal dimensionless evaporated water mass flow can be obtained
.
. *
MSt.max
()St.Sal = MSI,sal = 1 -SI,Sal --'.
*
()
--
(384)
where the dimensional steam temperal at saturation point is oSI,Sal
_ -
!J.hv 9SI Sal + cpv 9 . + Mv SI,1n c;'
( 385)
with the steam inlet temperature ,9 SI, i n and the steam temperature at saturation point 9SI,sal'
L. Mörl et al.
1 38
�
E" e
, , - - - - - - ,- - - - - - - - - - - - - , - - - - - - - - - - - - - , - - - - - - - - - - - - - r - - - - - - - - - - - - -
0.9
::l
0.
I
E 0.8
- - - - - - - - - -
B
,
- - - - - - - - - - - - -
, , , - - - - - - - - - - , - - - - - - - - - - - - - r - - - - - - - - - - - - -
� 0.7
, ,
, ,
"
-= .
r
o � c
,
� 0.6 'Ö
- - - - - - - - - - - - -r - - - - - - - - - - - - ,- - - - - - ,
0.5 +------r---T---;..---i--� o
0.2
0.8
0.6
0.4
dimensionless steam mass flow [-]
Fig. 93. Dependency of the dimensionless steam temperature from the dimensionless steam mass f10w according to equation (383).
Transferred heat in the volume element: The transferred heat in the volume element can be described as the change of the amount of steam
(386) where is the heat transfer coefficient, 9s the temperature of the wetted surface, and dLAp the effective surface area for the heat transfer. Using equation (27 1 ) for the specific surface area, we get for the cylindrical apparatus by inserting equation (273) into equation (386) r:J..
....
d MSI
=
Cl.aAapp
(387)
(9s1 - 9 s ) dz
By using a dimensionless bed height according to equation (272), one obtains dz = d� bed Hbed Inserting equations (375), (378) and (388) in equation (387) leads to Cl.
d MSI*
-
{ [(r,
0
+ f1hv
cP
)
(
e
_
] [(r,
f1hv
cP
0
)
+ f1hv
cP
)
eS
_
Cl.aAapp
f1hv C
p
(388)
] } d�bed
( 389) (390)
1 39
Fluidized Bed Spray Granulation
defi n ition of
ppepH bed (n . I'lhv ) . K - aaAa ""Stm + cpv I'lhvMSt,in the differential di m ensionless steam mass flow d M;t = K(est - eS)d �bed inserted in equation (383) and in equation (392) gives dMSt = K 1 + Mst - es d �bed
After
_
'
(1 )
. *
. *
(-.-, - es) = d �bed (1 + M�t) dM. -Kes d �bed St 1
(391 ) (392)
(393) (394)
1 + Mst
*
. *
I ntroducing the variables
MSt +
(Os- 1 )
=
(395)
�
-1 K2 = -es es in equation (395), the following relationship occurs
(396) (397)
(398)
and solved to get (1 - K2) In(K2 - M;t) + (K2 - 1) I n(K2) + M�t = - K1 �bed or
(400)
1 40
L. Mörl et al.
By simplifying (402) the implicit dependency of the dimensionless water evaporation from the dimen sionless bed height can be obtained J:b S ed =
In(K2 ) K
_
M�t K1
_
In(K2 + M�t) K
(403)
Now, we have to calculate the degree of wetting: for practical use the dimen sionless mass flow according to equation (380) can be set to rllst < < 1 . So, we can write by using equation (395) 1 d A/g, Kd ;b o (404) (G, es St + ---os
[M:
',]
� -
o
The following integration:
lM�, ( 1 ) dMst = - K1 l�bed =�bed d�bed �bed=O 1IIs. ,=o eF MSt + +s-1» . *
. *
yields
(fJ
(405)
(406) respectively (see Fig. 94)
.
*
MSt = -K2 [1 - exp( -K1 �bed )]
(407)
By using equation (407), the amount of evaporated water at a certain bed height can be computed. For z = Hbed is �bed = 1 , and thus Mst out - MSt in . MSt,out( �bed = 1 ) = ' = - K2 [1 - exp(-K1 )] MSt,in . *
'
(408)
By the explicit approximation of the steam mass flow, the unknown degree of wetting, inserted in the variable K1 , can be computed. For the further modelling we assume (Fig. 95): 1 . negligible sensible heats, 2. all granules and nuclei have no water content, and 3. adiabatic conditions (no heat losses).
141
Fluidized Bed Spray Granulation
0.07 �
� 0.06
0 c::
�
'"
0.05
<) t;; '" '"
0.04
E E '"
2 0.03
.�
=1 = 0.5 = 0. 1
c: <)
E 0.02 'Ö 0.01
--<>-
0 0
0.2
0.1
0.3
0.5 0.6 0.4 dimensionless bed height [-]
0.7
0.8
0.9
Fig. 94. Dependency of the dimensionless steam mass f10w from the dimensionless bed height according to equation (407).
..:..
•+ •
: +
V
••
fluidized bed
/
gas distributor
- - - - - - - - - - - - - - - - //
Fig. 95. Total mass balance around the fluidized bed superheated steam granulator.
Inserting the water balance (409) into equation (408), the explicit dependency of the degree of wetting fram the liquid injection rate can be obtained (see Fig. 96)
qJ = -
[
(
1) ( + -:-. "-L _-X )
flhj.tfsl'in !!.hv aaAappHbed 9s + c;-
In 1
_ M' MS1,inK2
(41 0)
1 42
L. Mörl et al. 1 00 .-------�--�--_,�
80
� $3
g,b 00
;: ..... o
�
,
40 · - - - - - - - , - · -
_ _ _ _ _ _ .1. _ _ _ _ _
Oll " .", ,
20
- • •
---�-------f ,
O ��_.----_r----+_--._--_.--T_--� o
0.005
().D )
0.0 ) 5
0.02
liyuid
mass
0.025
0.03
0.035
0.04
0.045
Oow [kg/s]
A-fp8d = 20 kg ,
Fig. 96. Dependency of the degree of wetting from the liquid mass flow for an example
(Dapp
pp =
= 0.4 m, 3 Mst = 0.42 1 kgjs, 1 500 kgjm ) .
IfSt.in
=
200°C,
dp,o
=
5.0 mm,
We assumed a mean steam temperature between 8St,i n and 8s regarding the viscosity and the density of the gas, so that we have to prove now the agreement between these temperature and the real mean temperature. The mean dimen sionless steam temperature can be calculated by equation (299) (4 1 1 ) Combining equation (383) and equation (407) implies the following equation: 1 1 - K2 [1 - exp(-K1 �bed)] Inserting of variable K2 (equation (397)) yields eSt (�bed) =
- 1�be=d=O 1 �bed
es d� d 1 - ( 1 - eS )eXp( -K1 �bed) be The solution of the derivative integral can be expressed as est =
(41 2)
(41 3)
(414)
1 43
Fluidized Bed Spray Granulation
The mean steam temperature in the fluidized bed in real dimensions follows with equation (375)
- (
,9S1 =
9S1 in ,
+
Ahv ) Ahv - In [eXP(K1 ) + - 1 ] - cpv cpv K1 0s
0s
0s
(4 1 5)
After completing of all parameters, the 9s concerning 9S1,in have to be corrected in respect to 8G, and a new iteration should be started, For these temperatures the density and viscosity of the gas as weil as the mean steam mass flow and the fluidization behaviour has to be corrected, Then, a new calculation procedure starts in order to compute the iterated values,
6. F LUIDIZED BED SPRAY GRANU LATIO N IN C LOSED OR SEMI-CLOSED SYSTEMS
In many cases it is advantageous to carry out the process of the fluidized bed spray granulation in a closed or semi-closed system, By a closed or semi-closed system should be understood that the whole fluidization medium or a part of it is led out in circulation. Moreover, water atomized in the fluidized bed and water evaporated from the surfaces of the particles must be removed in every case by condensation or by separation of a part of this medium. 6. 1 . Closed systems with superheated solvent steam circulation
The working principle of the fluidized bed spray granulation with superheated solvent steam is shown in Fig. 97. From a tank, the liquid (solution, suspension or melt) containing the solid, can be atomized by a suitable liquid dosage device and a nozzle into the fluidized bed. The fluidized bed consists of granulates and nuclei that are fluidized by superheated solvent steam. Figure 97 presents an apparatus with a classifying discharge. All the other already cited apparatus modifications can also be used. The medium that is supplied to the classifying discharge must also be superheated steam. By the gas distributor (e.g. sieve bottom) and the classifying discharge in the fluidized bed, inflowing steam delivers a part of his heat to the solid particles wetted with liquid in the fluidized bed. As a result, the vaporization of the solvent from the liquid takes place and the temperature of the superheated solvent steam sinks. An additional steam flow originates, which leaves the fluidized bed together with the supplied steam at the outlet into a combination of cyclone separator and filter which are used to separate as much dust as possible as shown in Fig. 97.
1 44
L. Mörl et al.
filter cyclone
ventilation and pres�ure regulation
cooling water oUllet
fan 2
cooling water inlel
condenser cOlldcns.1lC
liquid �upply
fan
4
97. Schematic representation of a fluidized bed spray granulation process with closed superheated solvent steam circulation and dry dust separation.
Fig.
The dust can either become part of the outlet flow, if it is desired as product, or it can be fed back pneumatically or mechanically into the fluidized bed where it can become a source for new nuclei in granulation. The c1eaned steam is trans ported by one or several fans in a heat exchanger where it is heated by indirect heat transfer to a higher temperature level and is supplied again to the f1uidized bed. By the constant generation of steam in the fluidized bed, a pressure increase would occur in the closed system if there is no discharge of steam , which is carried out by using a condenser after gas c1eaning either before or after the fan. In this condenser the steam is totally condensed by indirect heat removal, and thus removal of the heat of condensation to a coolant. The condensate of the solvent is separated as liquid. In this manner it is possible to carry out the fluidized bed spray granulation completely without producing exhaust gas flows. This is particularly advanta geous when the products to be dried or the solvents are harmful to the envi ronment, toxic, combustible or malodorous, as for example liquid manure, landfill leachate concentrates or various sewage sludges or industrial sewages. How ever, it must be considered that often small quantities of inert gases are dissolved in the liquid which would become free with the vaporization and accumulate in such a system. This would raise the system pressure, because these inert gases are not condensable. For this reason the condenser must be provided with an exhaust conduit about which these inert gases can become discharged.
1 45
Fluidized Bed Spray Granulation ventilation Qnd pressure regulation
lresh sotvent supply
condenser
vazzz
condenSSle
cooling wafer outlei
cool ing water intet
scrubber steam supply
liquid supply
98. Schematic representation of a fluidized bed spray granulation process with closed superheated solvent steam circulation and exhaust vapour scrubber with solvent.
Fig.
Normally, the absolute amounts of these inert gases are very low, so that their disposal, by feed into bio-filters or combustion is unproblematic. Moreover, the system pressure can be influenced. For the case where the substances to be granulated and to be dried produce dusty products or if a dry dust separation causes difficulties (e.g. bonding of filters), slight variation in the process can also be used as shown in Fig. 98. With this method the cleaning of the steam leaving the fluidized bed is done by a vapour scrubber. In this, scrubber solvent is finely sprayed at boiling temper ature and is brought in intensive contact with the exhaust gas stream. Moreover, the liquid droplets take up the dust particles and gather in the sump of the scrubber. With a rotary pump this resulting liquid is supplied again to the atom ization. This is continued until the solid concentration has reached a critical level in the liquid. Then the sump of the scrubber must either batch-wise de-sludged or reloaded with new solvent, or a part of the liquid stream is taken from the sump of the scrubber continuously and is fed again into the atomization of the fluidized bed. This part of the vapour scrubber cycle must be supplied with fresh solvent. A disadvantage of this process lies in the fact that the whole steam flow is cooled down to the boiling temperature of the solvent. Beside the problems of the supply of the saturated steam to the fan which requires possibly a heating-up of the steam flow after the vapour scrubber, the whole sensible heat of the super heated steam arising from the fluidized bed goes into the liquid, and hence, an additional steam flow that must be separated in the condenser. These losses will be high, if the solvent steam leaving the fluidized bed is away from the saturation state. Nevertheless, for reasons of the avoidance of condensation phenomena in
1 46
L. Mörl
et 81.
venlilalion and pressure regulation
fan 2
condenser condensate
cooIing waler outlel
cooling water inlet
liquid supply
fan 3 Fig. 99. Schematic representation of a fluidized bed spray granulation process with closed superheated solvent steam circulation and exhaust vapour scrubber with producl.
the conduits it is necessary to keep to a certain distance from the saturation state which should amount as a rule to 1 0-20 K. In addition, it is to be noted that by cooling of this steam to the saturation state, the additional evaporated solvent stream must be compensated with fresh solvent. The mentioned disadvantages of the vapour scrubber can be compensated partly by the fact that the liquid to be granulated and to be dried itself is used as a washing liquid as shown in Fig. 99. This is possible of course only in the case in which this liquid is sprayable and absorbs solids. Indeed, with this variation of the process additional solvent vaporization is also possible by cooling the steam flow from the fluidized bed to saturation temperature. Since this steam vaporization occurs from the liquid to be supplied to the fluidized bed apparatus, their solid concentration is raised and no additional solvent stream must be evaporated. In addition, the temperature of the liquid to be evaporated is raised which has a positive eftect on the viscosity and the atomization. 6.2. Closed systems with inert gas circulation
In many cases the fluidized bed spray granulation can be applied with inert gas circulation, when the materials are slightly combustible, explosive or when the media is sensitive to oxygen. The schematic representation of such a process is shown in Fig. 1 00. The fluidization medium is inert gas in a c10sed circulation. In most cases the inert gas
1 47
Fluidized Bed Spray Granulation
filter
cyclone
ventilation and pressure regulation
partial
condenser cooling water inlet
condensate
liquid supply
fan 1
g ranulate d ischarge
fan 3
Fig. 1 00. Schematic representation of a fluidized bed spray granulation with closed i nert gas circulation, dry dust separation and partial condensation.
should be free of oxygen. Often applied inert gases are nitrogen and carbon dioxide. After flowing through the fluidized bed where the inert gas transfers heat to the liquid-wetted particles, the gas reaches the dust separation section. In Fig. 1 00 this dust separation is shown as a combination of cyclone separator and filter. It must be seen to the fact that the evaporated water stream is only so big that the inert gas is still far enough from the dew point, otherwise condensation phenomena occur. Therefore, a Mollier diagram for the special system solvent inert gas is useful. After the inert gas and the contained steam have passed the dust separation, a pressure rise that is necessary to maintain the circulation which is carried out by a fan. After the fan 2 the steam loaded inert gas reaches a partial condenser where heat to a coolant is transferred by indirect heat transfer. A part of the steam contained in the inert gas is thereby condensed in the partial condenser and discharged. A typical example is the condensation of ethyl alcohol from a nitrogen circulation. About a second fan (Fan 1 ) the inert gas that is loaded only with little steam content is supplied to a heat exchanger. In this heat exchanger the inert gas is heated, e.g., with saturated steam again indirectly to a higher temperature, and thus enters about the gas distributor the fluidized bed. Thus, the gas circulation is c1osed. The nuclei supply and the discharge of granulate materials as weil as the recycle of dust from the dust removal systems into the fluidized bed occurs analogous to the process with superheated steam. The advantage of this method is that temperatures can be applied which are smaller than the saturation temperature of the solvent steam. Apart from the exclusion of oxygen, this is an important and essential aspect for a series of thermo-unstable substances.
1 48
L. Mörl et 81.
nuclei supply condensate (contaminated) fresh solvent liquid supply
fan 2
Fig. 1 0 1 . Schematic representation of a fluidized bed spray granulation with closed inert gas circulation and i njection condenser as a gas scrubber.
Another possibility of the f1uidized bed spray granulation with closed inert gas circulation is shown in Fig. 1 01 . In this case, the dry dust separation is substituted by gas cleaning (gas scrub ber) which works as a partial condenser. The injected washing water causes on one hand the partial condensation of the steam contained in the inert gas and, on the other hand, it cleans the inert gas of dust particles. The heat of condensation as weil as the heat for cooling the inert gas must be removed by a heat exchanger from the circulated liquid mass flow of the gas scrubber. The advantage of this system is the simplicity. Nevertheless, there are also three disadvantages which can lead to difficulties with the application of the system. The first disadvantage is that the condensate that is discharged from the gas scrubber circulation is more contaminated with dust, than in the process with dry dust separation. The second problem is the disposal of this circulated liquid mass flow. In addition, it encounters difficulties for a series of products to with draw the heat by indirect heat removal from a liquid strongly loaded with solid. It can lead to fouling of the heat transfer surfaces and thus to a reduced capability or to a functional disability of the heat exchanger. Thirdly, the exhaust inert gas from the gas scrubber is loaded with steam and is heated-up by an upstream heat exchanger, to prevent dew point undershooting in the conduits to the fan. All the other systems have to carry out similar to the superheated steam drying. By using the inert gas circulation, the problems during the discharge of granulates and of dust due to condensation below the boiling temperature of the solvent are more easily controlled in comparison to superheated steam drying.
1 49
Fluidized Bed Spray Granulation
6.3. Sem i closed and self-inerting systems with gas recycle
For temperature resistant granulates, whereby the contact of the product with oxygen should be minimized, especially the gas heating of the fluidization medium is suited by an upstream furnace chamber (burner) with partial recycle of the exhaust gas. The schematic representation of such a process with dry gas dust removal is shown in Fig. 1 02. For this case, gas with a very low lambda value is burned in an upstream furnace chamber. The high exhaust gas tem perature is lowered by fed of recycled exhaust gas in a mixing chamber to the desired gases inlet temperature of the fluidized bed. Thus, the mixture of flue gas and superheated steam flows into the fluidized bed, through the gas distributor and the classifying discharge tube and fluidizes the granulates and transfers heat to the liquid wetted particles. Thereby, an additional water mass flow evaporates, which flows into a combination of cyclone and filter as a dry separator (Fig. 1 02). The dust is separated as much as possible from the exhaust gas and is either fed back pneumatically or mechanically in the fluidized bed as nuclei or the dust can be discharged from the system as partial product. The gas stream generated by the almost stoichiometric combustion and the superheated steam flow in the fluidized bed due to water vaporization must be discharged in any case from the system. The water content of the circulation gas is determined by the relation of flue gas entering into the mixing chamber and the atomized liquid stream into the fluidized bed. If the above-mentioned advantage is partially renounced, the steam content of the circulation gas can be reduced by
exhaust gas to the cleaning sytem
liquid supply gas
fan 2
1 02. Schematic representation of a fluidized bed spray granulation with self-inerting circulation and dry dust separation.
Fig.
1 50
L. Mörl et al.
nuclei supply
exhaust gas to the cleaning sytem
gas
fan 2 Fig. 1 03. Schematic representation of a fluidized bed spray granulation process with self inerting circulation and gas scrubber.
increase of the A-value with the combustion in the furnace chamber or by direct feed of fresh air in the mixing chamber. Also for the process with a furnace chamber, the dust separation can occur through a gas scrubber as shown in Fig. 1 03. With this process all problems related to the dry dust recycle in the fluidized bed or to the dust discharge from the system are avoided. Nevertheless, the disadvantage is the liquid saturation of the gas from the scrubber. If the exhaust gas is far away from the saturation state, the biggest part of the heat, which is not used for the liquid vaporization can be gained back by the circulation. For the process with gas scrubber this is not possible because the exhaust gas of the fluidized bed comes into intensive contact with the circulated liquid of the scrub ber. Thus, the additional evaporated water evokes the saturation state. However, for the cases, where it is possible to use a partial stream of the liquid to be granulated as a washing liquid for the scrubber circuit as shown in Fig. 1 03, this heat flow is not separated and leads to a rise in the concentration of the solid and in the temperature of the liquid supplied in the f1uidized bed. Nevertheless, the requirement is that the liquid is still able to absorb solids without changing its consistency substantially. 6.4. Closed systems with heat pump
If for the fluidized bed spray granulation a c10sed system with superheated sol vent circulation or inert gas circulation is used as discussed above, the indirect
filter cyclone
�§1.··:··:· ·:�: : : : : : :�·r1 : I r���t! j�......i -J:
1 51
Fluidized Bed Spray Granulation heat exchange r lor heating-up 01 the heat pump circulation
liquid separator fan
1
\------, compressor � .. .
heat exchanger
condensate
lor cooling down 01 the heat pump circulation
liquid supply
fan 3 Fig. 1 04. Schematic representation of a fluidized bed spray granulation process with heat
pump and additional heating.
removal of the heat of condensation in a partial condenser and the direct supply of heat for the heating-up of the gas or steam stream before the entry into the fluidized bed apparatus is necessary. This means that on one hand a large heat flow must be withdrawn at lower temperatures from the system and otherwise a heat flow has to be supplied to the system at higher temperatures. This problem can be solved elegantly with the application of a heat pump as shown in Fig. 1 04. The gas er steam coming from the dust separation is led into a heat exchanger after a fan, where the heat is withdrawn which is necessary for condensation. Afterwards the condensate is separated in a liquid separator from the gas or steam stream and discharged from the system. The steam or the gas reach in the saturation state in the second heat exchanger where its temperature is increased again which leads to superheating of the steam or rather to the reduction of the relative gas humidity of the fluidization media. The main feature shown in the Fig. 1 04 is that a heat pump is used for supply and removal of heat. In this heat pump a fluid medium circulates. By the supply of mechanical energy in a compressor the medium gets a higher pressure, thereby its temperature also increases. With these parameters the circulation fluid is fed to the heat exchanger, which heats up the gas and accordingly the steam of the fluidized bed circulation. While on one hand the circulation medium of the fluidized bed circulation heats up at this point, other wise, the circulation medium of the heat pump GOols down and is expanded by a downstream throttle valve. Thus, a further temperature decrease occurs. This cooled circulation medium of the heat pump circulation flows through the heat
1 52
L. Mörl et al.
exchanger where the circulation medium coming from the dust removal section of the fluidized bed circulation is fed on the other side. By the indirect removal of the heat of condensation, the temperature of the medium of the heat pump circulation increases at this point, and it is supplied again to the compressor. Thus, the circulation is closed. The indirect temperature increase of the gas or rather of the steam of the fluidized bed circulation is also possible by using fresh steam in a second heat exchanger installed directly be fore the fluidized bed (Fig. 1 04). In this case a part of the energy supply occurs through mechanical energy (eompressor) and a part by heat energy (steam in the heat exehanger). However, it is also possible to feed the whole neeessary energy over the compressor into the system as shown in Fig. 1 05. The applieation of a heat pump for the deseribed heat transformation might be only worthwhile for big produet throughputs and heat flows and for produets with no big valence (wastes, sludges, liquid manure ete.) and pharmaeeutieal products with relatively smaller throughputs but high product valence, where the energy costs of the process are more important in eomparison to the investment costs associated with the heat pump. 6.5. Closed systems with water vapour compression
The water vapour eompression has advantages for processes with high produet throughputs and high water eontents of the atomized liquid. The prineiple eompression of the exhaust gas is strongly loaded with solvent steam. By this compression a condensation of a part of the solvent from the gas stream oeeurs. filter cyclone
f:,eh������.� ��:
"� i �§�§§Er I ��R" ': � i
e heat pump circulation
�1-------,
� �
1-1-----, compressor ! �> ..... .........
\J;;;;;
condensate
. .........
........
•
heat exchanger
for coolin9 down of the heat pump circulation
liquid supply
Fig. 1 05. Schematic representation of a fluidized bed spray granulation process with closed circulation with exclusive energy supply about a heat pump.
1 53
Fluidized Bed Spray Granulation
filter
gas discharge
cyclone
fresh gas supply
water vapours compression wlth turbine
liquid supply fresh steam supply
fan 2
heat exchanger
condensate to the steam producer
Fig. Schematic representation of a fluidized bed spray granulation process with water vapours compression and additional heating of the circulation gas about a heat exchanger. 1 06.
This condensed stream is discharged from the system by a separator. The gas with the reduced solvent content can be expanded by a turbine. Thus, a part of the compression energy is restored. At the same time, the absorption capacity of the gas for the solvent increases again. It must be pointed out at this point that for the application of this process, a very ca refu I removal of the dust in the gas or in the steam of the fluidized bed cir culation must occur in order to avoid impairing the functioning of the compressor and the turbine. A further rise of the absorption capacity of the gas for the solvent can occur through indirect heat supply by a heat exchanger. In Fig. 1 06 the f10wsheet of such a process with fresh gas supply, gas discharge and an ad ditional heat exchanger is shown. The system presents a partially closed circu lation. The flowsheet of a completely closed circulation that works in the superheated solvent steam is shown in Fig. 1 07. Here, the whole energy entry occurs about the engine of the compressor. For the application of the water vapours compression the same economic aspects are valid as mentioned for heat pumps.
6.6. Closed systems with rejected heat utilization for an upstream evaporator
For the disposal of a series of liquid rubbish as for example landfili leachate, liquid manure and industrial sewage sludges it is necessary to treat a liquid with rel atively low solid content so that in the end only a very dry granulate is produced.
1 54
L. Mörl et al. fi�er cyclone water vapours compression wrth turbine separator
Fig. 1 07. Schematic representation of a fluidized-bed spray granulation process with pure water-vapour compression.
Basically, it is possible to feed this liquid with low solid concentration into a fluidized bed spray granulation process. However, it must be considered that a big water mass flow containing a small solid stream must be evaporated and that the supplied heat can be used only once and is wasted afterwards in the con denser or with the exhaust gas to the environment. Beside the possibility of a multistage fluidized bed spray granulation process, there is also a possibility of using a multistage evaporation before the fluidized bed spray granulation proc ess, as presented in Fig. 1 08. Besides the fluidized bed spray granulation process use superheated solvent steam , the produced steam originating in the fluidized bed can be discharged from the system and used for heat supply for an indirectly heated evaporator (evaporator 2). The concentrate leaving from this evaporator is supplied directly to the fluidized bed, while the steam from evaporator 2 is used as a heat supplier for a second upstream evaporator (evaporator 1 ) and so on. Besides, the pressure must be setting up in both evaporators so that the necessary driving force is given with regard to the temperatures. Figure 1 09 shows that the condensation heat of the fed steam in the heat exchanger of the fluidized bed circulation is used three times, namely once in the fluidized bed even to the evaporation of the atomized solvent and two other times to increase the concentration of the liquid in the evaporator 1 and in the evap orator 2. In this manner, approximately 2.5 kg of water can be evaporated with 1 kg of fresh steam.
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Fluidized Bed Spray Granulation filter
caaling waler autlel
fresh steam
�
�Q)
o 0-
C\J
o ca (;
0'"
�
=I4-"""""--i
condensate ta the steam producer
liquid supply
Fig. 1 08. Schematic representation of a fluidized bed spray granulation process for salt solutions with upstream evaporation and rejected heat utilization.
Fig. 1 09. Schematic representation of a two-stage fluidized bed spray g ranulation process with use of the condensation heat of the 1 st stage.
The application of upstream evaporators which are heated with the rejected heat of the fluidized bed spray granulation process is advantageous only if the solid to be granulated is a product of low value and in low solid concentration in a solution or suspension. The ciassical case for such a product is, e.g., the gran ulation of landfill leachate. 6.7. Concatenation of several closed systems
In particular with big fluidized bed granulation plants with which big solvent streams, it is often suitable on the basis of scale up problems and also on the part
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condensate 1
Condensate 10 Ihe steam proucer granulate 1
granulate 2
granulate 3
condensate 3
F ig. 1 1 0. Schematic representation of a three-stage coupled fluidized bed spray granu
lation process with use of the condensation heat.
of the flexibility of such arrangements to carry out the fluidized bed spray gran ulation process in several parallel Iines. Then it is obvious to use the rejected heat of one plant for the heating of the second plant. This can be realized in various ways. One of these possibilities in the closed solvent steam circulation is the use of different pressure levels as shown in Figs. 1 09 and 1 1 0. The additive produced solvent steam in the fluidized bed plant 1 of pressure stage 1 (highest pressure stage) is supplied into the circulation heat exchanger of the downstream pressure stage with lower system pressure (pressure stage 2) and transfers its heat indirectly to the circulating steam etc. Theoretically many such plants can be coupled to each other with suitable pressure staging. The process has the advantage that with 1 kg of fresh steam several kg of water can be evaporated. The basic principle of this approach is applied successfully in the multistage evaporation of solutions. However, for fluidized bed plants this prin ciple has not been proved up to now and the reasons must be looked at. More over, the high investment costs and also the discharge of granulate materials under superheated solvent steam conditions at high temperatures and high pressures causes difficulties.
7. PRODUCT EXAMP LES OF THE UNIVERSITY OF MAGDEBURG
The fluidized bed spray granulation research at the University Magdeburg started in the 1 970s [41 ,45,47,48,56]. The main focus was on the granulation of different products as weil as on the modelling of heat and mass transfer. The following section iIIustrates some product examples of particles, which was granulated in Magdeburg by using different excipients and process parameters. For the visual characterization of the morphology, SEM micrographs and photos are used, completed with tables characterizing the process and granule parameters.
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7.1 . Granulation of sticky products 7. 1. 1. Maize swell water
Maize swell water (or maize starch) is the extraction water during the converting of maize into starch. It could be demonstrated that fluidized bed granulation is able to produce storable, strong and free flowing granules from concentrated maize swell water with a solid content of 35 mass% with a diameter of 3-1 0 mm [57]. The stickiness of the product caused by the hygroscopicity was a problem, but controllable by the use of feed maize powders with a throughput of 20 mass% in respect to the total throughput of the product. The parameters of the gran ulation are listed in Table 8 and pictures of the granules are shown in Fig. 1 1 1 . 7. 1 . 2. Raw flavour
Raw flavour is needed in dry from for convenience foods. The raw flavour is also hygroscopic and thus very sticky. Therefore, a mechanical stirrer was used to prevent that particles sticking together. The raw flavour suspension with a solid Table 8. Maize swell water - parameters and results of fluidized bed spray granulation
Apparatus configuration: Circulation Atomization Gas distributor
Seeds supply Waste gas purification Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
Open One two-fluid nozzle, lateral Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized Bed Classifying tube 6 m/s 95 °C 72 °C 90 kg/(cross section area hour), 0.56 k9/(kg bed mass hour) 50 k9/(cross section area hour) 3.3 h 3000-1 0000 11m; spherical, light blackberrylike Good Medium, dust-free 5-1 0 mass% 1 300 kg/m3 754 kg/m 3
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Fig. 1 1 1 . Maize swell water - form and surface of granulates.
content of 35.5 mass% was continuous atomized onto salt crystals [58]. Table 9 iIIustrates the parameters and a list of results of the experiment, while Fig. 1 1 2 explains the morphology of the granulated particles. 7. 1 . 3. Cytosap
The gentle drying of a concentrated cytosap suspension (solid content: 1 0-1 5 mass%) from plants and simultaneous granulation in a fluidized bed is very difficult, because the product is very hygroscopic and tends to be very sticky. Again, it was necessary to powder the granules with fodder lime and to use a mechanical stirrer [59]. A stable operation was realized with both measures, whereby the coating with external powders was more effective. Table 1 0 and Fig. 1 1 3 show the results. 7.2. Granulation of paste-like products 7.2. 1. Calcium lactate
With the product calcium lactate, a fluidized bed granulation of a paste-like ma terial was realized [60], based on the injection of a aqueous calcium lactate melt with 20 mass% solid content at 85°C. The parameters are listed in Table 1 1 and Fig. 1 1 4 shows the granules. 7.3. Granulation of m icrobiological producs 7.3. 1. Fodder yeast
The fermentation of molasses to fodder yeast is an example for a biological product, which was successfully granulated in a fluidized bed [61-64]. This
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Fluidized Bed Spray Granulation Table 9. Raw flavour- parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor
Seeds supply Waste gas purification Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation
Open One two-fluid nozzle, lateral Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 3.2 m/s 93 °C 76 °C 45 k9/(cross section area bed mass hour) 30 kg/(cross section area 6.9 h
x
hour), 0.22 k9/(kg
x
Specific granulate throughput: Mean residence time: Granulate: Particle size and form: Flowability: Stability: Moisture content: Solid density: Bulk density:
x
hour)
1 000-14000 ).lm; spherical, blackberry-like Medium Medium, dust-free 5-1 0 mass% 1 380 kg/m3 840 kg/m 3
Fig. 1 1 2. Raw flavour - form and surface of granulates.
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Table 1 0. Cytosap, powder-coated with lime - parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor
Seeds supply Waste gas purification Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability: Moisture content: Solid density: Bulk density:
Open One two-fluid nozzle, lateral Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) + lateral fodder Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 5.7 m/s 1 00 °C 35-40 °C 300 kg/(cross section area x x hour), 2.9 kg/ (kg bed mass x x hour) 30-50 kg/(cross section area x x hour) 2-3 h 3000-6000 Jlm; almost spherical Good Good, dust-free < 8 mass% 1 200 kg/m 3 720 kg/m3
Fig. 1 1 3. Cytosap, powder-coated with lime - form and surface of granulates.
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Table 1 1 . Calcium lactate - parameters and results of fluidized bed spray g ranulation
Apparatus configuration Circulation Atomization Gas distributor
Seeds supply Waste gas purification Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
Open One two-fluid nozzle, top down Opening ratio decreasing fram the outside inwards (22%, 1 0%, 5%) External seeds supply, top down Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 6-7 m/s 65-70 °C 40 °C 300-350 kg/(crass section area x hour), 1 .5-2 k9/(kg bed mass x hour) 70-90 kg/(cross section area x hour) 2-2.5 h 5000-1 0000 11m, almost monodisperse; spherical, light blackberry-like Very good Stift, dust-free 26-28 mass% 1 387 kg/m 3 635-697 kg/m 3
Fig. 1 1 4. Calcium lactate - form and surface of granulates.
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biomass was atomized as concentrated protein suspension with a content of 1 5-20 mass%. The granules were dust-free with a diameter between 3 and 1 5 mm, which is important because the produced enzymes are noxious. A certain temperature range was able to prevent the production of salmonella or other varmints. Table 1 2 and Fig. 1 1 5 summarize the parameters and pictures. 7. 3. 2. Rye starch
The obverse goal was the granulation of rye starch with a suspension solid content of 0 . 1 45 mass% to conserve the micro-organisms by adjusting a certain temperature range [65]. Fig. 1 1 6 shows granule pictures and Table 1 3 illustrates the experimental parameters and the granule properties. 7. 3. 3. Lysine
Lysin can be used as fodder for animals. The lysine suspension was granulated with a solid content of 1 5-30 mass% onto wheat grains [66-68]. Again, the strong Table 1 2. Fodder yeast - parameters and results of fluidized bed spray g ranulation
Apparatus configuration: Circulation Atomization Gas distributor
Seeds supply Waste gas purification Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation
Open Several two-fluid nozzles, bottom-up Opening ratio decreasing from the outside inwards External seeds supply, top down Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 2-1 0 m/s (depending on particle size) 1 00-300 oe (due to the low thermal resistance of the product) 70-120 oe 330-720 k9/(cross section area x hour), 1 .6-3.4 kg/(kg bed mass hour) 40-1 20 k9/(cross section area x hour) 1 .5-5.5 h x
Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
3000-20000 Ilm, almost monodisperse; almost spherical, blackberry-like Good Stift, dust-free 4-1 0 mass% 1 500 kg/m 3 900 kg/m3
Fluidized Bed Spray Granulation
Fig.
1 1 5. Fodder yeast - form and surface of granulates.
Fig.
1 1 6. Rye starch - form and surface of granulates.
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hygroscopicity was counteracted with powders of chalk or lime at simultaneously mechanical stirring. In a second step, the granules were coated with sodium silicate. The granulation parameters are listed in Table 14 and Fig. 1 1 7 char acterizes the morphology. 7. 3. 4. Biosludge
Biosludge was granulated with 90 mass% water coming from a fermentation of a liquid manure treatment [69-7 1]. The free flowing, dust-free and attrition-resistant as weil as water-resistant granules ( Fig. 1 1 8) with a high-bulk density can be used as animal feed or fertilizers. In a second step, the granules were treated by a temperature of 1 50°C and a residence time of > 40 min to reduce the spore
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Table 1 3. Rye starch - parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor Seeds supply Waste gas purification
Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
Open One two-fluid nozzle, lateral Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 4.6-5.3 mjs 65-126 °C 38-47 °C 1 30-350 kgj(cross section area x hour), 0.8-2. 1 kgj (kg bed mass x hour) 23-60 kgj(cross section area x hour) 2.8-7.2 h 1 000-5000 Jlm; spherical, light blackberry-like Good Medium, dust-free 5-1 0 mass% 1 050 kgjm 3 640 kgjm 3
forming anaerobic and aerobic bacteria. The used granulation parameters can be found in Table 1 5. 7.4. G ranulation of hard metals and magnets 7.4. 1. Titanium carbides
For the sintering of hard metals, strength and compact as weil as free flowing carbide granules with a diameter between 0. 1 and 1 mm are necessary. To get a very high bulk density, a broad particle size distribution was useful. Fluidized bed granulation experiments were carried out with an aqueous suspension (solid content of 50 mass%) by using an additional binder [72]. Granulation parameters are summarized in Table 1 6. A spray-dried product was used as hold-up material. Figure 1 1 9 draws pictures of the titanium carbide particles.
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Fluidized Bed Spray Granulation Table 1 4. Lysine - parameters and results of f1uidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor Seeds supply Waste gas purification
Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation
Open One single-fluid nozzle, top down Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 6.4 m/s 1 45-149 °C 1 20-1 30 °C 1 20-300 k9/(cross section area hour), 0.7-1 .8 k9/ (kg bed mass hour) 26-1 06 k9/(cross section area hour) x
x
Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
x
1 .5-6.3 h 3000-8000 11m; spherical , light blackberry-like Good Medium, dust-free 5-1 0 mass% 1 1 90 kg/m3 7 1 5 kg/m 3
Fig. 1 1 7. Lysine - form and surface of granulates.
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Fig. 1 1 8. Biosludge - form and surface of granulates.
Table 1 5. Biosludge - parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor Seeds supply Waste gas purification
Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
Open One two-fluid nozzle, lateral Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 6-1 0 mjs (depending on particle size) 1 40-1 50 °C 60-70 °C 1 000 kgj(cross section area x hour), 6-7 kgj(kg bed mass x hour) 90-140 kgj(cross section area x hour) 1 . 1-1 .8 h 3000-1 0000 flm, almost monodisperse; almost spherical, smooth surface Very good Stiff, dust-free 4-1 0 mass% 1 050 kgjm 3 630 kgjm3
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Table 1 6. Titanim carbide - parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor Seeds supply Waste gas purification
Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation
Open One two-fluid nozzle, lateral Constant opening ratio External seeds supply, top down (batchwise) Cyclone with recycle of the separated dust into the f1uidized bed Classifying tube 7.2 mjs 1 56 °C 60-90 °C 540 kgj(cross section area hour), 0.65 kgj(kg bed mass hour) 550 kgj(cross section area x hour) x
x
Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
1 .5 h 1 00-1 500 11m, almost monodisperse; spherical Very good Stift, dust-free < 1 mass% 6000 kgjm 3 3600 kgjm 3
Fig. 1 1 9. Titanium carbide - form and surface of granulates.
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lable 1 7. Ferrite - parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor Seeds supply Waste gas purification:
Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation
Open One two-fluid nozzle, top down Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 3.5-4.5 mjs 1 30 °C 60-70 °C 240-300 kgj(cross section area hour), 0:45-0.6 kgj(kg bed mass hour) 1 30-1 80 kgj( cross section area hour) x
x
Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
x
3-4 h 200-2500 /lm, almost monodisperse; spherical, smooth Very good Stift, dust-free 0.1-0.4 mass% 381 0 kg/m 3 1 800 kgjm 3
7.4. 2. Ferrite
Analogous to the production of carbides, for the production of magnets it is essential to design particles with a very low porosity and a very high-bulk density. The fluidized bed granulation of ferrite suspensions (solid content: 35.5 mass%) was able to produce such granules. The granulated preforms have very good magnetic properties (high-electric field strength) [73]. Table 1 7 and Fig. 1 20 summarize the results. 7.5. Granulation of milk products
Milk contains 85-91 mass% water, 3.4-6.1 mass% fat, 2.8-3.7 mass% proteins, 4.5-5 mass% lactose and 0.68-0.77 mass% minerals and many trace elements.
Fluidized Bed Spray Granulation
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Fig. 1 20. Ferrite - form and surface of granulates.
The fluidized-bed granulation of skim milk (solid content: 50 mass%) was realized to produce a free flowing, hydrophobie and storable (many years) anima I feed [74,75] . As hold-up material during the start-up, hackled milk granulates or casein particles with a diameter between 1 and 3 mm were used. Table 1 8 presents the parameters and Fig. 1 2 1 shows granule pictures.
7.6. Granulation examples of chemical products 7. 6. 1. Potash
Potash or potassium carbonate (K2 C0 3) is an important material for the glass industry. To prevent a demixing of the raw materials, a narrow particle size distribution is essential. Potash was atomized into a fluidized bed as aqueous solution with a solid content of 30-45 mass% [76-78]. The produced granules are monodisperse, attrition-resistant, free flowing and dust-free (Fig. 1 22). Again, Table 19 summarizes the parameters.
7. 6. 2. Activated carbon
The production of activated carbon from bones, wood or other renewable ma terials yields a fine activated carbon dust. We granulated this dust together with a binder suspension (solid content: 1 0-20 mass%) to get particles in a size range of 1-6 mm [79,80]. Table 20 explains the parameters, Fig. 1 23 shows the form of the granules. Subsequently, the activation of the granules was carried out by exclusion of air at temperatures between 600 and 1 000 °C.
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Table 1 8. Skim milk concentrate - parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor Seeds supply Waste gas purification
Discharge Parameters Superficial gas velocity: Gas inlet temperature Gas outlet temperature Specific evaporation Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
Open One two-fluid nozzle, lateral Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 2.8--3. 1 m/s (depending on particle size) 1 02-1 35 °C (due to the low thermal resistance of the product) 48-72 °C 1 00-1 1 0 kg/(cross section area x hour), 0.55-0.65 k9/(kg bed mass x hour) 1 00-1 1 0 kg/( cross section area x hour) 1 .6-1 .8 h 3000-8000 11m, almost monodisperse; spherical, light Blackberry-like Very good Stift, dust-free 1 .5 mass% 1 263 kg/m3 758 kg/m3
Fig. 1 2 1 . Skimmed milk concentrate - form and surface of granulates.
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Fig. 1 22. Potash - form and surface of granulates.
Table 1 9. Potash
_.
parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor Seeds supply Waste gas purification
Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation
Open One two-fluid nozzle, top down Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 3.3 m/s 1 65 °C 80-90 °C 1 1 0-380 kg/(cross section area hour), OA-1 A kg/ (kg bed mass hour) 60-250 k9/(cross section area x hour) x
x
Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
1 . 1 -4.5 h 1 000-31 50 Jlm, almost monodisperse; spherical Good Stift, dust-free < 1 mass% 1 990 kg/m 3 1 1 94 kg/m 3
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Table 20. Actibated carbon - parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor Seeds supply Waste gas purification
Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
Open One two-fluid nozzle, lateral Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 4.4 m/s 1 50-200 °C 60-90 °C 380-570 kg/(cross section area hour), 2.5-3.7 k9/ (kg bed mass x hour) 50-1 30 kg/( cross section area hour) x
x
1 .2-3.2 h 1 000-6000 J.lm, almost spherical Good Good, dust-free < 1 mass% 1 1 00 kg/m 3 660 kg/m3
Fig. 1 23. Activated carbon - form and surface of granulates.
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7. 6. 3. Lead sulphate
Lead sulphate is a stabilizer during the production of polyvinyl chloride. An aqueous suspension with a solid content of 50 mass% was injected into a flu idized bed granulator [81 ] to produce dust-free, free flowing and very strength granules. Table 21 contains the parameters and Fig. 1 24 shows the nearly ideal spherical particles with a narrow-size distribution. In a second step, a coating with stearate is possible.
7.7. Granulation of animal food 7. 7. 1. Sunflower protein
The fluidized bed granulation of a suspension of proteins from a sunflowers sus pension (solid content: 1 0-20 mass%) was realized in Refs. [44,49,82-84]. The large granules (2-20 mm) are spherical, storable (many decades) and water Table 21 . Lead sulphate - parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor
Seeds supply Waste gas purification Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
Open One two-fluid nozzle, top down Opening ratio decreasing from the outside inwards Without seeds supply, dust discharge, 50% dust production Cycione and filter with recycle of the separated dust into the fluidized bed Classifying tube 3-5 mjs (depending on particie size) 1 40-1 50 °C 90-1 00 °C 250-400 kgj(cross section area hour), 0.5-0.8 kgj(kg bed mass hour) 250-400 kgj(cross section area hour) 1 . 1-1 .9 h x
x
x
1 00-3000 Jlm, almost monodisperse; spherical, smooth Very good Stift, dust-free < 1 mass% 3900 kgjm3 2260 kgjm3
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Fig. 1 24. Lead sulphate - form and surface of granulates.
resistant. Spray dried proteins are water soluble and only few weeks storable. The granulation parameters can be found in Table 22. Photos are iIIustrated in Fig. 1 25.
7. 7.2. Swines blood
In slaughterhouses, large masses of swine's blood accumulate with a high con tent of proteins and minerals. This blood is only storable for a few hours. For an application as animal food, a blood suspension with a solid content of 1 0-1 5 mass% was granulated in a fluidized bed [85]. Salmonella as weil as pathogen sprouts was deadened. Table 23 and Fig. 1 26 show experimental pa rameters as weil as granule photos.
7.8. Granulation of fertilizers 7.8. 1 . Urea
Urea is an important nitrogen fertilizer and finds also application as animal food. The traditional use of prill towers (height: 40 m) for the solidification of urea melts (melting point 1 32.7 0c) produces only particles with 2 mm diameter. For fertilization by using an airplane, particles with a diameter of 4 mm are more suitable. The fluidized bed granulation of urea melts (95°C) with a solid content of 90-95 mass% was successfully realized [5,50,86-91], (see Table 24, Fig. 1 27). To influence the solubility, the granules were coated with c1ay in a second step.
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Table 22. Sunflowers protein - parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor
Seeds supply Waste gas purification Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
Fig.
Open One two-fluid nozzle, top down Opening ratio decreasing from the outside inwards (1 8.45%, 8.33%, 5.33%) External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 2--1 0 m/s (depending on particle size) 1 00-1 80 °C (due to the low thermal resistance of the product) 60-90 °C 400-1 000 kg/(cross section area hour), 0.5-3 k9/ (kg bed mass hour) 50-200 k9/(cross section area hour) x
x
x
1-4. 1 h 2000-20000 Jlm, almost monodisperse; spherical, smooth Good Stift, dust-free 4-1 0 mass% 1 500 kg/m 3 900 kg/m 3
1 25. Sunflowers protein - form and surface of granulates.
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Table 23. Swines blood- parameters and results of fluidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor
Seeds supply Waste gas purification Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation
Open One two-fluid nozzle, top down Opening ratio decreasing from the outside inwards (25%, 1 3%, 9.5%) Without seeds supply Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 5-1 0 m/s (depending on particle size) 1 40-1 60 °C (due to the low thermal resistance of the product) 1 00-1 30 °C 500-1 000 kg/(cross section area hour), 2-4 k9/ (kg bed mass hour) 50-1 50 kg/(cross section area x hour) x
x
Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
1 .3-4. 1 h 1 000-8000 �m; spherical, blackberry-like Good Medium, dust-free 1-3 mass% 1 1 00 kg/m 3 600 kg/m3
Fig. 1 26. Swines blood - form and surface of granulates.
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Apparatus configuration Circulation Atomization Gas distributor
Seeds supply Waste gas purification Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation
Open One single-fluid nozzle Opening ratio decreasing from the outside inwards External seeds supply, top down Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 4.4 mjs 35-60 °C 40-55 °C 1 5-55 kgj(cross section area hour), 0.08-0.3 kgj(kg bed mass hour) 290-530 kgj(cross section area hour) 0.4-0.7 h x
x
Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
x
1 500-7000 J.lm, almost monodisperse; spherical, smooth Very good Stiff, dust-free < 0.5 mass% 1 500 kgjm 3 900 kgjm 3
Fig. 1 27. Urea - form and surface of granulates.
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Fig. 1 28. Ammonium sulphate - form and surface of granulates.
7. 8. 2. Ammonium sulphate
Ammonium sulphate is also a nitrogen fertilizer, but more inactive than urea and will therefore be deployed before drilling. Ammonium sulphate was granulated in a fluidized bed by using an aqueous solution (solid content: 42 mass%) [92]. Figure 1 28 shows the form of the free flowing and dust-free granules, in Table 25 the parameters are summarized. The throughput could be increased when using higher temperatures. 7.9. Granulation of Glue sewage
Industrial glue sewages (solid content: 42 mass%) contain different ingredients, which may be obtained in concentrated form as dry substance due to fluidized bed granulation [93]. The produced particles are very stiff. The hold-up material was dry glue sewages powder as weil sand spheres. Table 26 presents the parameters, and Fig. 1 29 illustrates photos of the granules.
8. CONCLUSIONS
Normally, the granulation of particles in fluidized beds involves different kinetics such as formation of seeds, growth, breakage and agglomeration. The equations of these kinetics are usually non-linear, and this property in combination with continuous product classification and recycling of particle fractions can lead to
179
Fluidized Bed Spray Granulation
Table 25. Ammonium sulphate - parameters and results of fluidized bed spray granu lation
Apparatus configuration Circulation Atomization Gas distributor
Seeds supply Waste gas purification Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation
Open One two-fluid nozzle, top spray Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 6 m/s 1 45 °C (higher temperatures would be useful) 90-1 00 °C 1 60-250 kg/(cross section area hour), 0.5-0.9 k9/(kg bed mass hour) 1 30-1 80 kg/( cross section area hour) x
x
Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
x
1 .5-2.5 h 2000-6000 Jlm, almost monodisperse; spherical, smooth Very good Stiff, dust-free 0.1-0.4 mass% 1 770 kg/m 3 1 060 kg/m 3
self-sustained oscillations of particle size distributions and temperature and con centration progressions of the gas and solid phase. However, the focus of this article is to analyze simple approximations for the pneumatic behaviour, partic/e growth, particle wetting and their influence on the operation area of fluidized-bed granulation The aim is to show simple calculation procedures for scale-up of these types of granulator. The approximations are able to estimate particle residence times, partic/e surface areas, particle and gas temperatures, or time-dependent partic/e diameters, as weil as pneumatic operation areas for both operation modes: dis continuous and continuous granulation. So we introduced a surface proportional granule growth kinetic as weil as a surface proportional degree of wetting model.
L. Mörl et al.
1 80
Table 26. Glue sewage - parameters and results of f1uidized bed spray granulation
Apparatus configuration Circulation Atomization Gas distributor
Seeds supply Waste gas purification Discharge Parameters Superficial gas velocity Gas inlet temperature Gas outlet temperature Specific evaporation Specific granulate throughput Mean residence time Granulate Particle size and form Flowability Stability Moisture content Solid density Bulk density
Open One two-fluid nozzle, lateral Opening ratio decreasing from the outside inwards External seeds supply, top down (star feeder) Cyclone with recycle of the separated dust into the fluidized bed Classifying tube 5.6 m/s 1 48 °C (higher temperatures would be useful) 80 °C 400 k9/(cross section area x hour), 1 .8 k9/(kg bed mass x hour) 80 k9/(cross section area x hour) 3.5 h 1 000-4000 )lm; spherical, light blackberry-like Very good Very stiff, dust-free < 1 mass% 2000 kg/m 3 1 200 kg/m 3
Fig. 1 29. Glue sewage - form and surface of granulates.
Fluidized Bed Spray Granulation
1 81
For continuous granulation, models for the ideal c1assifying particle discharge as weil as for the non-c1assifying particle discharge were derived. For the first case, a discharge probability into a classifying tube was presented, using design parameters of the plant. The discontinuous granulation is described by case studies for the batch and semi-batch process, which are weil applicable to the coating of particles, for the start-up phase as weil as for the transition period between cycle process parameter changes. The time-dependent calculation of the layer thickness can help pharmacists to evaluate the quality of the coated layers. The mixing behaviour has an important influence onto the effectiveness of drying and thus on the granulation. Additionally, a model for the application of fluidized bed granulation with superheated steam has been developed. For the evaluation of operation modes, different c10sed or semi-c1osed systems were discussed. Notation
A A LAp �A� Ap Ar cp d, D dp
� F
9 G h H H* Ahv Ahvü K L
Le
M Mp
�
rh
M M* M n
specific particle surface (m2jm3 ) surface area (m2 ) total surface area of all particles (m 2 ) dimensionless total surface area of all particles related to t = 0 s mean surface area of a particle (m2 ) Archimedes number (m2 ) specific heat capacity at constant pressure (Jj(kg K)) diameter (m) mean surface based diameter of a particle (m) dimensionless particle diameter force (N) acceleration of gravity (m/s2 ) growth rate (mjs) specific enthalpy (Jjkg) height (m) normalized height specific heat of evaporation of the water (Jjkg) specific heat of evaporation of the water at O°C (Jjkg) flow coefficient of the air distributor length (m) Lewis number mass (kg) mean mass of a particle (kg) dimensionless particle mass mass flux (kgj(s m 2 )) mass flow rate (kgjs) dimensionless mass flow rate molar mass (kgjmol) particle number
1 82 NTU
ncirc 'L; np 'L; np np qo
q� %
-M
qü 'L; np -M q2 q3 q� M q3,V q3 'L; np p p
Pv P� LlP R
RRe
s Sc Sh S8 S�oat t T T tv v V
v v* Vp
V
x y
y Y* z
L. Mörl et al.
number of transfer units number of particle circulations total number of all particles dimensionless total number of all particles related to t = 0 s particle flow (1js) number density distribution ( 1 jm) mass-based number density distribution (1j(kg m» mass-based number density distribution in range d p , o ::::;; d p < dp,out ( 1 /(kg m» number density distribution related to the particle number ( 1 jm) mass-based surface area density distribution (m 2j(kg m» mass density distribution (k9/ (kg m» mass-based mass density distribution (kgj(kg m» mass-based volume density distribution (m 3j(kg m» mass density distribution related to the particle number ( 1 jm) collision probability system pressure (Pa) vapour pressure (Pa) saturation vapour pressure (Pa) pressure drop (Pa) specific gas constant (kgj(kg K» universal gas constant (Jj(mol K» Reynolds number thickness (m) Schmidt number Sherwood number spacing (m) dimensionless thickness of the coated layer time (s) hit temperature (K) residence time (s) velocity (m/s) volume (m 3) mean velocity (mjs) dimensionless velocity related to t = 0 s mean volume of a particle (m3) volume flow (m 3jh) water content (mass%) fraction of the sprayed solid which deposits on the granules (mass%) humidity (kg waterjkg dry air) saturation humidity (kg waterjkg dry air) length coordinate (m)
Fluidized Bed Spray Granulation
Greek symbols �
iXst
ß (j
� �h F E
I]
1]*
9
�o 9
o o o v
P Pp Pp Pp v
� �bed
(J r
cp CPs
CPSy Ij;
heat transfer coefficient (W/(m 2 K)) statistical fixed bed flow angle (0) mass transfer coefficient (m/s) diffusion coefficient (m2/s) difference liquid film thickness (m) porosity of the fluidized bed or void volume (m 3/m 3) drying efficiency modified drying efficiency temperature (0C) wet bulb temperature CC) mean temperature (0C) time function (s) dimensionless temperature mean dimensionless temperature kinematic viscosity (m2 /s) density (kg/m 3 ) mean particle density (kg/m 3) dimensionless mean particle density dimensionless particle density bypass fraction drag coefficient dimensionless bed height standard deviation (mm) dimensionless time degree of wetting shape factor of spheric form Stefan correction factor opening ration of the sieve boUom
Subscripts
a Ac app b B bed coat core CSTR
air acceleration apparatus bubbles width fluidized bed coated particle layer core of particle continuous stirred tank reactor o drag distributor sieve boUom resp. air distributor
1 83
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eff elu fed G Gr in
L
Li max mf min nuc out p
PFTR
S
Sat sep St tot v W 0
effective elutriation added gas gravity at inlet or input liquid litt maximal minimal fluidization minimal nuclei at outlet or discharge particle plug flow tubular reactor solid saturation classifying tube (separator) steam total vapour water state at time t = 0 or entry state
S uperseripts
fluidized bed added nuclei or seed
bed fed nuc
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[79] H .-J. Künne, L. Krell , L. Mörl, A. Lehnert, K. Radecke, Verfahren zur Herstellung konditionierter Adsorbentien, GDR Patent D D - WP C01 B/3 1 48 864, VEB Leuna Werke, 1 988. [80] A. Lehnert, Granulierung von Aktivkohlepulvern in der Wirbelschicht, Diplomarbeit, TH OUo von Guericke Magdeburg, 1 984. [81 ] M. MiUelstraß, H .-J. Künne, L. Mörl, L. Krell, Studie zur Trocknung und Granulierung von Bleisulfatsuspensionen in der Wirbelschicht, Forschungsbericht an der Sektion Appa rate- und Anlagenbau, Technische Hochschule Otto von Guericke Magdeburg, 1 978. [82] L. Krell, H .-J. Künne, J. KIiefoth, L. Mörl, Verfahren zur Granuliertrocknung von Pro teinhydrolysaten und Fleischaromakonzentraten, G DR Patent DD - WP A23L/2460 1 81 1 6, I nstitut für Getreideverarbeitung der Akademie für Landwirschaftswissenschaf ten der DDR Potsdam-Bomim, 1 982. [83] H .-J . Künne, Zur E ntwicklung und volkswirtschaftlichen Nutzung der Wirbelschicht technik, Doctoral thesis B, Technische Hochschule OUo von Guericke Magdeburg, 1 986. [84] J . Sachse, R. EIspaß, L. Mörl, Trocknung von Proteinsuspensionen, Forschungsbe richt an der Sektion Apparate- und Anlagenbau, Technische Hochschule OUo von Guericke Magdeburg, 1 972. [85] M. MiUelstraß, H .-J . Künne, L. Mörl, D. Schneider, J. Sachse, Trocknung von Blut in einem Wirbelschichtapparat, Forschungsbericht an der Sektion Apparate- und An lagenba u , Technische Hochschule OUo von Guericke Magdeburg, 1 976. [86] S.M. Danov, Trocknung und Granulierung von Harnstofflösungen in der Wir belschicht, Chimitscheskoje Promischlennost 6, Soviet Union, 1 966, 453-456. [87] H .-J . Künne, M. MiUelstrass, L. Mörl, J. Baruizki, D. Braumann, M. H uth, Chem. Techn. Rundschau 1 2 (2) ( 1 980) 1 3-23. [88] M. M iUelstraß, H .-J. Künne, L. Mörl, J. Sachse, Studie zur Granulierung von Harnstoff i n der Wirbelschicht, Forschungsbericht an der Sektion Apparate- und Anlagenba u , Technische Hochschule OUo von Guericke Magdeburg, 1 977. [89] M. MiUelstraß, H .-J. Künne, L. Mörl, J. Sachse, L. Krell , Studie zur Granulierung von Harnstoffschmelzen in der Wirbelschicht, Forschungsbericht an der Sektion Appa rate- und Anlagenbau, Technische Hochschule OUo von Guericke Magdeburg, 1 978. [90] M. MiUelstraß, H .-J. Künne, L. Mörl, J . Sachse, L. Krell, Studie zur Granulierung von FuUerharnstoff, Forschungsbericht an der Sektion Apparate- und Anlagenbau, Tech nische Hochschule OUo von Guericke Magdeburg, 1 979. [91 ] M. MiUelstraß, H .-J. Künne, L. Mörl, J. Sachse, L. Krell , Studie zur Granulierung von Harnstoff mit Wirkstoffzusatz in der Wirbelschicht, Forschungsbericht an der Sektion Apparate- und Anlagenbau, Technische Hochschule OUo von Guericke Magdeburg, 1 979. [92] H .-J . Künne, L. Mörl, J. Sachse, L. Krell , Studie zur Granulierung von Ammonium sulfat in der Wirbelschicht, Forschungsbericht an der Sektion Apparate- und An lagenba u , Technische Hochschule OUo von Guericke Magdeburg, 1 980. [93] L. Mörl, L. Krell, H .-J. Künne, J . Kliefoth, J . Schmidt, Studie zur Wirbelschichtgran ulation von Abwasser, Forschungsbericht an der Sektion Apparate- u nd Anlagenbau, Technische Hochschule OUo von Guericke Magdeburg, 1 986.
CHAPTER 3 Extrus ion-Sp he ronisation D . l a n Wilso n , * and Sarah L Rou g h
Department o f Chemical Engineering, University o f Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA, UK C ontents
1 . Scope and introduction 2. Equipment 2. 1 . Combination 2.2. Extrusion 2.3. Spheronisation 2.4. Drying and finishing 3. Mechanics and mechanisms 3. 1 . Rheology 3.2. Liquid-phase effects in extrusion 3.3. Extrusion-spheronisation interactions 3.4. Spheronisation 4. Formulation 5. Control 5. 1 . Combination 5.2. Extrusion 5.3. Spheronisation 6. Challenges and future developments Acknowledgments References
1 89 191 191 1 92 1 96 1 99 200 200 204 205 207 209 213 213 213 214 214 214 215
1 . SCOPE AND I NTRODU CTION
Extrusion-spheronisation (E-S) is used to manufacture spherical or cylindrical pellets by extruding a semi-solid wet powder mass through a single die, a series of dies or a screen featuring many holes, then breaking up and rounding the extrudate on a rotating friction plate. E-S is also known as extrusion-marumeri sation, where a Marumeriser is the name for the spheroniser originating from the Japanese for 'pellet', which appeared on the original Fuji-Paudal patent for their device. When optimised, the process yields a dense and quite spherical product with good integrity. These properties can be tailored via coating, which is *Corresponding author. E-mail: diw1 1 @cam.ac.uk
Granulation Edited by A.D. Salman. M.J. Hounslow and J. P. K. Seville ( 2007 Elsevier B.v. All rights reserved
1 90
D. I. Wilson and S. L. Rough
amenable to the spherical shape of the granules [1]. E-S is used widely in the manufacture of controlled release pharmaceuticals, polymers, detergents, ferti lisers and herbicides (particularly water dispersible granule forms). The spher onisation step is often omitted when cylindrical pellets are the desired product form, as in fertiliser and herbicide manufacture where the extrudates can be broken up in a fluidised bed drier to give products with the required size. This chapter will focus on the use of E-S in pharmaceutical granulation and related applications, where the material extruded is a wet powder mass and extrudate diameters are in the range of 500-1 500 flm. In practice, the largest particle sizes achievable are 5 mm. The free-flowing granules obtained by E-S are used in tabletting or in filling capsules for oral dosage forms. This particular process is favoured by the pharmaceutical industry since pellets formed with a small amount of active ingredient show a slower release profile compared to those made by other techniques. The closely related topic of pelletising, which employs similar devices to extrude drier materials to give generally larger gran ules, is not covered. The E-S process involves four steps, as iIIustrated in Fig. 1 : �
(i) Combination. The wet mass is prepared by combining particulate solids with a liquid binder. This is often termed 'granulation' in the E-S literature and employs standard granulation equipment, but the aim is to generate a well mixed material rather than a specific particle size distribution. (ii) Extrusion. The wet mass is compacted to a density approaching its saturation density (expelling entrapped air) and shaped into cylindrical extrudates by forcing it through circular dies or multi-holed screens. Non-circular dies are rarely used. The combination and extrusion steps can be combined in twin screw extruders. (iii) Spheronisation (or marumerisation). The extrudate is broken up into smaller rods and rounded by the action of a horizontal rotating friction plate, with typical operating speeds of 1 000 rpm. (iv) Drying and finishing. The pellets are then dried and coated as required. The pellets formed after spheronisation are quite firm and can be conventionally handled in this 'wet' stage; hence fluidised-bed drying is suitable for the removal of the granulation liquid. �
The influence of extrusion on the final granules is currently difficult to quantify: with many formulations one cannot form spheres from the wet powder mass directly - it first needs to be compacted and formed. The correct formulation will give spheres that are stable on the spheroniser plate for up to 30 min [1], and quality - quantified by granule shape and size distribution - will be relatively insensitive to variations in operating parameters. It is also difficult to predict
191
Extrusion- Spheronisation powders and liquid
wet mass
extrusion
extrudate
spheronisation
[
spheroid
'�I"g ao' "",,h'",
•
Fig.
granule or pellet
1 . Schematic of steps during E-S.
spheronisation performance simply from monitoring the extrudate quality, as not all smooth and well-compacted extrudates give good spheres [2].
2. EQUIPMENT 2.1 . Combination
Most types of powder mixers have been reported for preparing wet masses, including planetary, Z-blade, high-shear and paddle mixers [3]. The need to achieve homogeneous distribution of the liquid phase and a wet mass of uniform consistency applies, as for other granulation processes. The mode of combina tion can also affect the properties of the extruded material and spheroids as the packing and wetting of particles are sensitive to the extent of shearing applied.
1 92
D. I . Wilson and S . L. Rough
Schmidt and Kleinebudde [4] experimented with four types of granulator prior to extrusion (using a rotary ring die press), namely a planetary mixer, high-shear mixer, twin-screw with kneading elements, and twin-screw without kneading. They reported that higher liquid contents were required for successful E-S of material prepared in the high-shear devices. This water content requirement also affected the properties of the spheroids during and after drying. It is also nec essary to control the evaporation of liquid, especially in high-shear devices, where the viscous dissipation rate is high and may result in a noticeable tem perature rise, as liquid content is a key parameter controlling the rheology of the wet mass. Screw extruders, and particularly twin-screw extruders, are often used in con tinuous E-S applications since the combination step is performed alongside the extrusion operation. The extruder can be configured in separate zones, such as powder mixing, liquid addition, kneading then forming. 2.2. Extrusion
Extrusion of the wet mass represents an important densifying stage [5], as weil as a forming operation. Vervaet et al. [3] proposed that E-S devices can be clas sified as either ram or gravity fed, on the basis of the feed mechanism of the wet powder mass, but here we classify the extruders in terms of the mode of ex trusion, as this allows one to relate formulation and mechanisms more readily (Fig. 2). (a) Pumping action: ram, axial single and twin-screw. Here, the material is com pacted and conveyed in its dense form before being forced through a die plate or screen . The material is therefore held at a high pressure over some period of time and thus yields a dense product, but is subject to phenomena such as liquid phase migration owing to the extended duration of applied stress. The extruding pressure is generated by the auger or ram, and die land lengths can be large. Gear extruders, where the material is drawn into the gaps between intermeshing teeth, represent pumping action machines with a short contact time. (b) Wiping action: sieve and basket, roll, radial screen. In this mode, the material is compacted to its extrusion density and forced through a die or screen via a wiping action as a blade passes over the die entry. The screen usually flexes in response to the high stresses involved: this is a shorter time-scale process, where elastic effects are important and the operation is usually less sensitive to shear rate, except in a conveying section. The wiping action can be pro vided by a number of rotating parts. Little attention has been paid to the design and arrangement of the blades, with the noticeable exception of
1 93
Extrusion- Spheronisation (a) Pumping action (in a single screw extruder)
(b) Wiping action (in a screen extruder)
material densified -----� during approach to nip region
��III����I-
perforated screen W iPing blade
Fig. 2. Extrusion modes.
Vervaet and Remon [6], who modified the impeller design of a Niea E-1 40 (Aromatie Felder) radial basket extruder. They developed a new high-effi eieney bl ade design, with a longer eompression surfaee via a eonieal inner edge - this improved the feed eompression and evened out the pressure aeross the sereen. Several novel blade eonfigurations have also been pat ented (e.g. [7]). The use of sereens means the die hole lengths tend to be short (diameter 500-1 500 j1m, lengths O.5-2 mm). These deviees usually run at lower average pressures (but high stresses oeeur at the nip) and allow a greater throughput. The type of extruder will mainly influenee the density of the granules formed: frontal extruders (end-on, high pressure) produee relatively hard and dense granules; radial extruders produee medium density granules, with an 'overflow'; and dome extruders produee the lowest density and temperature rise [8]. Figure 3 illustrates the action of different deviees and Table 1 lists some of the manu faeturers of E-S equipment.
1 94
D. I. Wilson and S. L. Rough (a)
rotary pelJeLiser
(b) basket extruder (plan view) /
\:\
/
,
screen rotation
fixed / internal rollers ,,/
"
"
-- - ----
,,
- - - - - .. ...
,
,
,
,
,
\
\
\
I
\
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, "
/ , .. ... _ - -- - -
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(e)
/
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", ,. ,,
(dl
/
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,,/
gear extruder (end viewl
GO
radial screen extruder . _
.
�._ -
Fig. 3. Action of different extruders.
It is important to note that formulations which operate satisfactorily in one extruder type do not readily transfer to different machines [9]. For example, Fiel den et al. [1 0] reported that two microcrystalline cellulose (MCC)-Iactose formu lations (differing in lactose size) were both successfully spheronised after ram extrusion through long dies, but one failed to spheronise appropriately. Screen extruders are relatively insensitive to the solids particle size distribution in achieving good E-S, since they provide low average shear rates followed by a rapid deformation, and hence the material is close to its yield stress during its processing history. In ram extruders, low shear rates can lead to liquid phase migration. These two examples outline the fundamental differences in wet pow der mass handling, and Vervaet et al. [3] further rationalised the problem by relating the type of feed mechanism of the plastic mass, i.e. screws vs. gravity, to
1 95
Extrusion- Spheronisation
Table 1 . Manufacturers of pharmaceutical extrusion-spheronisation equipment (2005)
Spheronisation{ Marumerisation
Address
Manufacturer
Extrusion
Alekanderwerk
Cylinder Screen
Caleva
Screen Gear Mini-screw
Batch Twin Continuous M icro
www.caleva.co.uk Dorset, U K
Fuji-Paudal (Luwa in US)
Screen Screw Dome
Bench-top and floor standing
www.fujipaudal.co.jp Osaka, Japan
GEA Aeromatic Fielder (Nica)
Basket
Batch
www.aeromatic-fielder.com Switzerland, U K
Rotary pelletiser Pelletiser cascades
www.glatt.de Binzen, Germany{ Leicester, UK
Glatt
Hosokawa Bepex
Roll compactor Screen Screw Gear
Schlüter Machinefabrik GmbH
Screen{ring
www.alexanderwerk.com Remschiei, Germany
www. hosokawa.co.uk Osaka, Japan{ Cheshire, U K Batch
www.schlueter-neustadt.de Neustadt, Germany
the effeet on pre-eompaetion. They add that an axial serew feed produees a more den se material than a radial sereen, a lower throughput, and that the eorre sponding pellets differ in sphericity and size distribution (although different die land length to diameter ratios, LID, were used). A theoretieal framework for ex plaining sueh observations is not yet eomplete (see Seetion 3 - Meehanies and Meehanisms). For example, Raines [1 1 ] used the Benbow-Bridgwater ram ex trusion analysis [1 2] to identify formulations that produeed good-quality extru dates and those that did not. However, it was not possible to relate the rheologieal parameters direetly to the tendeney to form good spherieal granules. The movement of water during extrusion is eritieally important for ram extrud ers, and less so for eontinuously operating units Iike serew extruders. This being said, Newton [1] reeommends that if extrusion is to be earried out using a sereen system, then the water should be dispersed by a high-intensity mixing proeess. Preparations extruded with low-pressure systems ean be more suseeptible to water distribution problems sinee the extrusion stage will not eonsolidate and distribute the liquid, and henee require intensive mixing to ensure eonsisteney. The water aets as a glidant during extrusion [1 3], and is also related to the
1 96
D. I . Wilson and S. L. Rough
plasticity of the extrudates formed. With screen extruders, there is little internal moisture loss or movement of water within the extrudate. For example, a Nica™ radial screen extruder (basket type) as used by Hileman et al. [14], where the feeder and agitator rotate in opposite directions, affords a shorter compression zone, and thus the wet mass has a shorter exposure to high-shear gradients, with corresponding low heat (and thus negligible liquid evaporation) and product build up. A key parameter that does affect the extrudate quality is the thickness of the screen or die land length L compared to the die diameter D. Vervaet et al. [3] reported that a low LID, of "-'1 , produced rough, loosely bound extrudates due to the low extrusion pressure incurred. A higher LID can produce smoother extru dates and better densification [6], as weil as an increase in temperature. Vervaet et al. [3] reported that a gravity-fed system with LID = 2 allowed for a wider operability zone in forming decent quality spheres than that of a screw-fed system with LID = 0.9. Any alteration to the diameter of the perforations, either due to manufacturing methods or wear/abrasion, is thus an important consideration, as weil as the pre compaction stress. The longitudinal shape can be an issue with the holes in screen extruders, which are usually punched, drilled or laser drilled. These rep resent short dies, and rough hole finish, excessive taper or abrasion can promote surface fracture. Vervaet and Remon [6] investigated the influence of the method of screen perforation and perforation geometry on E-S. The perforation method affected the maximum amount of drug that could be processed (67% for punched screen, compared with 70% for drilled and profiled holes), whereas the profiled screen also led to a smaller amount of surface fracture. Examples of extrudates with and without surface fracture are shown in Fig. 4, and it is clear that the occurrence and extent of fracture for a given material depend on die geometry and extrusion velocity. The material used to make the screen or die can also affect the likelihood of fracture. Extrudates exhibiting gross fracture yield fines readily, while very dense extrudates can be resistant to breakage on the spheroniser plate. The presence of smalI, regular cracks has been demonstrated by Rough and Wilson [15] to aid the formation of regular sized granules since this can promote regular breakage. 2.3. Spheronisation
Figure 5 shows a typical spheroniser, which features a friction plate rotating at a controlled speed so that extrudate cylinders are broken up into short rods with lengths approximately equal to their diameters. Over time, following collision with the plate, walls and other particles, the pellet edges are rounded off and their overall shape changes from rounded rods to du mb-beils to ellipsoids to spheres
1 97
Extrusion- Spheronisation
(a)
(c)
LID = 48/3,
LID = 3/3.
V = 140 DUn s-J
V = 690 mm s- J
(b)
(d )
1 2/3, V = 690 (top), 1 40 (bottom) mm s- J
LID =
LID = 6/3, V = 690 mm s- J
4. Shape and fracture of extrudates from ram extrusion of 55 wt% water-MCC paste at various die land geometries (LID) and mean extrusion velocities ( V). Scale intervals O.5 mm.
Fig.
[3] (Figs. 6 and 7). Other workers report a twisting mechanism. The finished granules are designed to be greater than 0.5 mm in diameter, since extrusion holes less than this are difficult to manufacture, and spheronisation of granules greater than 5 mm is not straightforward due to the chopping and rounding proc esses [1]. In general, spheronisation is less dependent on equipment type, although plate design is important. Schmidt and Kleinebudde [1 6] reported that a rougher spheroniser plate applied more energy, thus reducing the water content required for spheronisation. The plates can be smooth, or grooved with radial- or cross hatching. Typical laboratory spheronisers feature a 1 20-225 mm diameter plate, operating at 1 200-400 rpm, and spheronisation usually takes 2-1 0 min; larger production units are available, up to 1 m diameter, and scale-up is often reported in terms of edge or peripheral velocity [3, 1 7]. Most spheronising equipment is manufactured from hygienic materials, such as 3 1 6 stainless steel. There is often an optimal spheroniser load and speed. Too low a load does not provide enough contact between the particles, and too high a load does not allow for enough interaction between the plate and the extrudate. Similarly, low speed
D. I. Wilson and S. L. Rough
1 98
lid
spindie
� I
chute with door
rotating friction plate
housing for variable speed motor
Fig. 5. Schematic of spheroniser.
Ca)
CA)
(h)
0 0 Ce)
( d)
o Ce)
� C=0 0 0 0 0 (B)
CC)
(D)
(E)
Fig. 6. Spheronisation mechanisms according to Rowe [58]: (a) cylinder, (b) round-edged cylinder, (c) dumb-bell, (cf) ellipse, (e) sphere; Baert and Remon [59]: (A) cylinder, (8) rope, (C) twisted dumb-bell, (D) spheres with cavity, (E) spheres.
changes rod shape slowly, while high speed can result in particle size reduction via unwanted breakage. The spheroniser process variables have been shown to determine the packing properties of the granules. Hellen et al. [ 1 3] showed that bulk and tapped densities increased with increasing spheroniser load, residence time and speed. Increasing the plate speed and residence time increases the granule density and roundness, or can produce more agglomerated pellets [16]. A system in which there has been insufficient consolidation during extrusion, or in which the extrudate has a high degree of surface impairment, will be more
1 99
Extrusion- Spheronisation
(a)
(e)
LID =
LID
=
1 2/3,
48/3,
V=
V=
140 mm S- I
350 mm S- I
(h)
L ID = 24/3, V =
140 mm S- I
(d)
LID = 48/3, V =
350 nun
s-I
7. Examples of pellet shapes obtained from ram E-S: water-MCC paste spheronised at 1 600 rpm for 2 min. (a-c) 55 wt%, (d) 50 wt%. (a) shows spheres, (b) ellipses, dumb beils and fines, (c) dimpled spheres, (d) dumb-bells and rounded rods.
Fig.
sensitive to the operating conditions in the spheroniser [1]. Thus screen extru dates are more sensitive to the spheronisation stage. Agglomeration of a slightly overwetted extrudate can be avoided by the use of a smoother friction plate andj or a lower velocity. 2.4. Drying and finishing
Fluidised-bed drying is widely practised for E-S granules. The degree of shrink age observed will vary with water content, and the common pharmaceutical ex cipient MCC gives pronounced shrinkage at higher water content. Bashaiwoldu et al. [ 1 8] demonstrated that the microstructural characteristics were strongly influenced by mode of drying, with freeze-drying yielding stronger pellets than fluidised-bed or dessicant drying. The drying stage is critical in controlling bac teria or other micro-organisms: Kouimtzi et al. [ 1 9] demonstrated that probiotic bacteria largely survived E-S before drying.
200
D. I. Wilson and S. L. Rough
3. MEC HANICS AND MEC HANISMS
E-S involves three distinct processing stages before drying, namely: (a) consolidation of the wet mass to a state which will allow it to be formed; (b) extrusion of the consolidated mass through the die(s) or screen; and (c) rupture and rounding of the compacted and shaped material. The level of detailed understanding and ability to perform quantitative predic tions of each stage varies, with the first stage being notably better established than the second and particularly the third. This is because the materials used in E-S, namely high solids volume fraction wetted granular pastes (as defined by Coussot and Ancey [20]), are complex systems whose rheological behaviour is determined both by the large number of particle-particle contacts and liquid phase phenomena. Without the liquid, the particle assemblies would be highly frictional and prone to locking in the extruder, require high stresses to deform and give brittle extrudates. The liquid phase provides interparticle cohesion, lubricates particle contacts, promotes wall slip and can also bear some of the stress. The rheology of these materials is relatively poorly understood compared to polymers or less dense suspensions. 3.1 . Rheology
An important feature of E-S materials that complicates their understanding is that they are not necessarily saturated, i.e. the voids between particles may contain gas (usually air) as weil as liquid. In the related field of ceramics manufacture, extensive degassing is employed to eliminate entrapped air, which promotes weaknesses and defects in extrudates, but this is rarely practised in E-S as it is seldom necessary. There are many similarities between the wet masses used in E-S and soils, particularly after the consolidation stage where the material will be close to its saturated state. The uniaxial compaction profiles in Fig. 8 show how the porosity of two materials - a microcrystalline cellulose powder commonly used in E-S, with and without the liquid phase - changes as they are com pressed. The initial decrease in porosity does not require large stresses as the particles rearrange. Above a joining pressure, larger stresses are required to change the porosity and in an extruder the material will often choose to flow instead. In the presence of the liquid phase the joining pressure occurs at a lower stress and is followed by a flatter profile as the system is now saturated and the liquid phase must be compressed in order to change its volume - the material will then prefer to flow rather than to consolidate further. This behaviour can be interpreted in terms of plastic flow, and the stress re quired to make the material flow is described as a yield stress as found in the O"J,
201
Extrusion- Spheronisation 0.8 r-------� ,
,
0.7
· · · ··
� '00 e 0.6 o Cl..
{jJ
{jJ
f
·. . ·· · · . . .
(dry MCC)
.
... . .. . .. . .
.-
�
. .. . . . .. . ... . . . . . . . . .
(wet MCC)
0.5
0.4 '-------'--'---' 3 4 7 8 5 6 o 2 Compaction stress I MPa
Fig. 8. Compaction behaviour of MCC: dotted line - compaction of dry powder; solid lines - compaction and relaxation behaviour of 4 5 wt% water-MCC paste. {}J indicates joining pressure.
metal-forming and soil mechanics literature. The yield stress is a measure of the work required to change the material's shape, and its relationship to the joining pressure observed in compaction testing is not straightforward (the description above is a simple one to communicate ideas). Nevertheless, many workers have used the techniques devised for measuring the yield strength of soils, metals and other plastics, such as cone penetrometers, to characterise the rheology of E-S materials, and this provides a useful quantitative tool for comparing formulations and assessing whether they will give cohesive masses suitable for extrusion (e.g. , Li et al., [21]). The plasticity approach is the basis of the characterisation method described by Benbow and Bridgwater (1 2), where the wet mass is compacted and then extruded by a ram at constant velocity through a cylindrical square-ended cap illary die as shown in Fig. 9. The force on the ram during extrusion, F, is reported as an extrusion pressure, Pe , which is related to the geometry and material by (1 )
where A ra m is the area of the ram in contact with the wet mass. Here, the die entry contribution P1 is described in terms of a simple plastic deformation model, which affords a yield strength parameter 0'0 and a rate dependent term (rxV m). The P2
202
D. I . Wilson and S. L. Rough
Extrudate
o
v
Fig. 9. Terms used in the Benbow-Bridgwater analysis of ram extrusion.
term accounts for shear in the die land and assumes that this is dominated by wall slip, characterised by a yield stress and rate term (ra and ß Vn , respectively) which are not necessarily the same as those involved in the extensional flow at the die entry. Newton and co-workers have made extensive use of ram extrusion to study E-S systems since it provides quantitative parameters for comparison of different formulations and also indicates conditions under which surface defect and liquid phase maldistribution phenomena can arise [1 0,22,23]. For example, Fig. 1 0 shows how the yield strength parameters i n equation ( 1 ) varied with water con tent for mixtures of MCC and water. The figure shows the range of water contents which could be reliably extruded and a marked reduction in strength with de creasing solids content, which is a well-established result in the soils literature. Table 2 lists sets of Benbow-Bridgwater characterisation parameters reported for some E-S materials. These strength parameters can be manipulated by the use of additives, particle size distribution, etc. A priori prediction of these parameters is not currently possible, even for the simplest systems, and leads to extensive empiricism in formulating E-S materials. The difficulty in predicting whether E-S materials will extrude and the forces involved is compounded by the fact that many extruders feature complex defor mation patterns which have yet to be modelIed in detail. The Benbow-Bridgwater approach, for example, provides parameters which can be applied readily to ram extrusion and other pumping mode devices such as single-screw extruders [24], but not to the feed section of twin-screw extruders and, in particular, wiping action devices. The latter have received Iittle attention apart from the work by Martin [8], with the result that the key deformation modes have not been identified and therefore the most appropriate rheological parameter(s) that need to be meas ured have not been established. E-S materials have also been studied using fluid constitutive models, but without modelling to link the parameters and extruder performance the data are effectively quantitative handles within an empirical framework. Delalonde et al. [25] used a compresso-rheometer to study the rheology of Avicel™ MCC pastes at different water contents, and reported simple power-Iaw shear thinn ing behaviour (r = Kr)")' with the lower water content formulation of 50 wt%
203
Extrusion- Spheronisation
1 0 ,-----,
-
.,0
"
0.1
'"
.
'00
. .. . ..
0.01 0.00 1 L�
Ii> : --� ____'_:-
__ _'_ _ _ � _ _ _ � _
�
�
�
W � Water content I wt%
-:!
_ _
m
Fig. 10. Benbow-Bridgwater yield parameters for extrusion of MCC pastes with varying water content. (Data from Rough et al. [32), reproduced with permission from Elsevier.)
Table 2. Benbow-Bridgwater characterisation parameters (equation pastes
Formulation
(jo
(all % wet basis) Water-MCC [32] 45 wt% 50 wt% 55 wt% 60 wt% 65 wt% Tale (vol. fraetion 0.49) Water + 39 wt% Surfaetants [56] 40 wt% water - potato starehes [57]
MPa
MPa (m/s) -m
1 .4 0.61 0.19 0.027 0.008 0. 1 5
5.8 4.7 2.7 0.40 0.057 1 .0
0. 1 1
1 .3
Cf.
(1 )) reported for E-S
ß
n
MPa
MPa (m/s) - n
0.21 0.28 0.34 0.37 0.26 0.23
0.39 0.080 0.051 0.01 1 0.00 1 2 0
2.0 0.61 0.42 0.076 0.0 1 6 0.22
0.59 0.29 0.37 0.42 0.37 0.26
0.33
0
0.30
0.36
m
TO
321 9 Pa SO. 38 , ; = 0.38) being more 'viseous' than the upper water content limit of 61 .54 wt% ( K = 453 Pa SO. 32 , ; = 0.32). MaeRitehie et al. [26] performed eontrolled stress rheometry of MCC/laetose formulations and related the results to ram E-S. They analysed their data using a viseo-elastie model. The apparent viseosity of mixtures deereased as the water eontent inereased, and they re ported that the range of water levels over which the elastic modulus GI and viscous (Ioss) modulus GI! were uniform corresponded to water levels which produeed the best extrudates. The ranges of GI, GI! and apparent viscosity re ported were of the order 3 1 07, 7 1 06 and 1 09_1 0 1 0 Pa s, respeetively. (K =
,
,
x
X
204
D. I . Wilson and S. L. Rough
3.2. Liquid-phase effects in extrusion
Galland et al. [27] studied E-S of MCC-water pastes in a simple axial screw extruder and identified 'hydric domains' for the extrudability regime, wh ich for their material lay between a 'hygroscopic limit' of 65% liquid (dry basis) and a 'fluidity limit' of 1 65%. They measured the porosity of the wet mass before and after extrusion at various rotational speeds and demonstrated that the level of unsaturation, i.e. the air content, of the wet mass generated in the combination stage was large at low liquid contents. The air content was almost completely removed in extrusion (Fig. 1 1 ). Above a threshold, corresponding to the capillary regime described by Newitt and Conway-Jones [28], the wet mass obtained after combination was close to saturation and this level did not change much on ex trusion. This study illustrated how, depending on the liquid content, extrusion can be simply a shaping process, or serve as a compacting process as weil. The wet powder mass fed to an extruder does not necessarily have to be saturated for extrusion, but for unsaturated feeds, the process must have sufficient time to compact the material. The threshold for saturated behaviour is strongly affected by the packing characteristics of the particulates - Heng and Koo [29] found a significant correlation between the void volumes in different MCC powders and their packing properties, and the water requirements for good E-S and pellet qualities (although this study used hand pressing through a mesh rather than mechanical extrusion). If the wet powder mass is consolidated and saturated, extended processing time can lead to liquid-phase migration, where the pressure on the liquid causes it to flow relative to the solids, leading to regions of high solids content, non-uniform extrudate composition, wet extrudate surfaces and, in the worst case, wholesale
1 .0 o
� (j)
o
e
o c..
0.5 50
1 50 1 00 Water content, wt% dry basis
Fig. 1 1 . Saturated (line) and measured porosity of wet masses (cireles), extrudates (squares) and pellets (triangles) during E-S via an axial screw extruder. (After Galland et al. [27], reproduced with permission from lehemE.)
Extrusion- Spheronisation
205
drainage. Boutell et al. [30] investigated the influence of liquid binder on the liquid mobility and preparation of spherical MCC/barium sulphate/surfactant granules by E-S, and they found that liquid phase migration was influenced more by the amount of liquid and the rate of extrusion than by the solids composition. Low liquid levels led to elongated pellets, whereas wet formulations produced larger, agglomerated pellets with a wide particle size distribution and a high porosity. Liquid-phase migration is exacerbated by slow extrusion speeds, so that the liquid has time to redistribute, and narrow particle size distributions that have a high permeability and therefore poor resistance to liquid-phase motion [31 ,32]. MCC does not dewater as readily as other non-absorbing solids: its water-binding behaviour has been described in terms of a gel and a super-molecular sponge by different groups. Various methods have been reported for studying liquid-phase migration, such as centrifugation [33], magnetic reSOnance imaging [34] and sectioning and drying of paste extrudates [32J, but this effect cannot yet be predicted without supporting experiments. 3.3. Extrusion- spheronisation i nteractions
Tomer et al. [35] reported that successful spheronisation requires extrudates that: (i) possess enough mechanical strength to retain their structure, but be brittle enough to break into short rods on the spheroniser plate; (ii) have enough plasticity in order to enable rods to roll into spheres; and (iii) be non-adhesive so that spheres do not agglomerate or stick to the spher onising equipment. The extrusion process therefore has direct impact on the subsequent spher onisation stage since extrusion defects, liquid-phase migration and extrudate ho mogeneity all affect spheronisation. Many workers have reported optimal combinations of geometry and operating conditions in order to extrude and spheronise a particular formulation. Figure 12 illustrates some of the factors in ram extrusion: short dies (small LID) require lower extrusion pressures but promote surface fracture, particularly at high extrusion velocities. Large LID values offen yield smooth extrudates, but these feature lower voidage owing to the higher extrusion pressures, and thus do not tend to break up readily and are prone to form dumb-bells during spheronisation. Low extrusion velocities can promote liq uid-phase migration, while high velocities can promote surface fracture owing to the uneven release of strains within the extrudate upon exiting the die land. It should be noted that surface fracture is not necessarily an undesirable phe nomenOn for spheronisation, unless it generates many fines. Rough and Wilson [1 5] have shown that evenly spaced circumferential fracture with small rupture
206
D. I . Wilson and S. L. Rough Quality
Knuckle-bones
.'
L .
Smooth and rigid
• • • • •
• •
. .
.
.
•. • •. . • .
• • • . .••• .. • .. .
.'
..
.'
.'
V ..
.. ••
• •• •
••
•
Gross fractures
�
.
Fig. 1 2. Schematic iIIustrating optimal operating conditions for extrusion prior to spher onisation.
depth (e. g. Fig. 4b) can promote regular break-up on the spheroniser plate. Domanti and Bridgwater [36] noted that these cracks often arise at a spacing of 012, giving the following relationship between final granule diameter dp and ext rudate diameter (ignoring compressibility effects): (2) This resonates with the observation by Harrison et al. [37] for an MCC-Iactose system that the diameter of the spheres was approximately equal to that of the extrudate diameter, although they did state that a smooth extrudate was required for good spheronisation. Figure 1 3 shows pellet size distributions obtained by sieving granules generated from ram extrusion of MCC-water masses and the link between the modal value of dp and 0 is evident. The generation of fines at smaller values of LID owing to fracture is also apparent. These sieving data do not, however, give an accurate account of granule shape as a significant pro portion of granules formed at larger LID are dumb-bells, but the minor axis allows them to pass through the '0' sieve and therefore count as pseudo-spheres. The strength of extrudates is determined by their degree of compaction, and cohesion
207
Extrusion- Spheronisation Dumb-bells 0.6
c 0
·ü
�
'" '" <11
:::i:
LID 01
0.4
0.2
., 2
(
0.71
04
.8 .16
1 .00
1 .40
1 .70
2.00
2.36
2.80
3.35
4.00
> 4.00
Upper sieve diameter / mn (a) D = 3 mm, V = 1 40 mm s-J 0.6
c
.2 Ü
� '" '" <11
:::i:
l-
0.4
0.2
0 0.60
(h) D
=
."..
1 rnrn, v =
0.71
n 0.85
LID D2
04 .8
r� 1 .00
1.18
1 .40
Upper sieve diameter / mm 690 rnrn s-J
>
1 .40
Fig. 1 3. Pellet size distributions obtained via sieving from E-S of 55 wt% water-MCC using different die diameters. (After Rough et al. [ 1 5], with kind permission of Springer Science and Business Media .)
provided by liquid surface tension. The strength also affects the friability of the extrudate, as illustrated in Fig. 14. 3.4. Spheronisation
The splitting and subsequent rounding of cylindrical extrudates on the spheroniser plate is a random process. In the absence of a preferred break-up pattern, for example the one promoted by regular fracture, detailed population balance models of this granulation process have yet to be developed. Since the extrudates are plastic masses, collision between particles either results in shap ing of individual particles via plastic deformation at the contact point or coales cence and subsequent shaping. Dumb-bells can be formed when long primary strands are shaped at each end, while hollow granules are formed from large units folding back on themselves. Break-up of individual granules is rarely re ported, although surface fracture can generate fines. Any means which tend to
208
D. I. Wilson and S. L. Rough - 3%
20 t-
'" a..
:2 C7; (/)
� Ui �
'üi c
2
.@
I0
I-
• --
0
• •
•
-
• 0
t-
-
•
• 0
0
Q) u
:J CI)
0············
• o
o
0
� :0
lt
'"
-
•
0 L-------� O% O wt% 1 00 wt% Fraction of MCC
Fig. 1 4. Schematic showing effect of formulation on granule properties. Solid circles surface tensile stress estimated from uniaxial compaction of individual spherical granules; open circles - friability, measured using air stream apparatus. (After Kleinebudde et al. [60].)
increase the deformability of moist agglomerates, e.g. reducing their tensile strength and improving plastic deformation, favours agglomeration by coales cence [31 ] . Packing densities are an important consideration and have been linked to increased surface plasticity - the faster the rounding of spheroids, the more surface water is generated and will result in further pellet growth. The shape of particles will evolve over the spheronisation stage and it is ac cepted that sieving techniques are not a reliable method for tracking the evolution of sphericity. Quantitative techniques employed include average aspect ratio, the one plane critical stability shape factor [38], two- and three-dimensional shape factors, eR and ec3 [39,40], chord and parameter analyses [41]. The progress of the spheronisation stage is largely controlled by the liquid content of the initial extrudate. The liquid distribution within a granule is often non uniform; liquid drawn in at the surface by capillary suction leaves the surface relatively dry, which is good for E-S. Excess liquid - which can arise as a result of extended consolidation of the granule - will appear at the surface and promote random coalescence. Fines are generated by the initial break-up of extrudate, and their persistence implies a reduction in surface moisture of the extrudate. Systematic studies of the rheology of the extrudate and its subsequent per formance are rare. Shah et 81. [42] studied MCC formulations using a parallel plate rheometer at strain rates down to 0.1 S -1 and also obtained yield strengths from a rotational shear tester. They reported that the initial breakdown of the extrudate into sm aller pieces is likely to be a function of tensile properties, while subsequent rounding of the pieces involves the material yield stress. A high-yield
Extrusion- Spheronisation
209
value gave spheres with a narrow particle size distribution, whereas formulations with lower values gave more spherical pellets. There is clear overlap, and need for further work, in this area with the mechanisms controlling pan granulation.
4. FORM U LATION
The equipment used in E-S is fairly standardised but the formulations employed vary, either to achieve a particular pellet functionality, such as dissolution rate or to incorporate particular compounds within the extrudate. These two aims are often connected, as in the case of the manufacture of water dispersible granules where dissolution aids need to be combined with an active ingredient. The main categories in a formulation are: (a) Primary solid phase, or excipient. In pharmaceutical and other applications, the major component, by volume, of the solids phase is normally an inert carrier which provides mechanical structure and allows extrusion by providing rheological stability, i.e. the plasticity and cohesiveness of the powder mass [43]. The excipient is usually insoluble or nearly insoluble in the primary liquid phase. Typical pharmaceutical excipients are calcium carbonate, tale, MCC and mixtures of MCC with other powders, particularly lactose. MCC is a well established agent with water retention properties which lends itself very weil to extrusion, and is often described as a supermolecular sponge or gel agent, able to hold large volumes of freely mobile water in the wet state (62.2 mLj 1 00 9 solid - [23]). Its properties are sensitive to particle size and source: several studies have demonstrated the variation in E-S behaviour between these parameters. Even for very insoluble materials, the lower the MCC content in a mixture of solids, the narrower the range of water contents at which E-S is successful [43]. Different brands of MCC cannot be inter changed without also adjusting the water content. (b) Secondary solid phases, or actives. The active ingredient may be present in large or small volume fractions (or even as a liquid). The properties of the actives are likely to be dictated by the desired functionality of the product, but it is important to consider the requirements of the E-S processing step in selecting these. A prime example is particle size and density to avoid seg regation during any mixing stage. Also, temperature is an important consid eration for thermolabile drugs [3], which may affect the liquid-phase rheology or induce a granule softening and promote evaporation of free water at the surface. (c) Liquid phase. The liquid phase serves to bind particles together as a cohesive mass in the combination stage and then lubricate and promote plasticity in the extrusion stage. The total liquid content should be considered, including any
210
D . I . Wilson and S . L. Rough
components dissolved during combination. Water and aqueous solutions are the most commonly used liquid phase in pharmaceutical applications. Many workers report different optimal liquid contents for processing the same ma terial through different types of extruder. (d) Secondary liquid phase. Some formulations employ a second liquid phase, either in the form of an emulsion or a layer that preferentially coats solids and aids lubrication. Secondary liquid phases can also arise when surfactants are added and not dispersed, so that local concentrations exceed the critical micelle content and give rise to locally high viscosities. (e) Surfactants and extrusion aids. Surfactants and lubricants can be added to reduce surface defects and power consumption [3], although this introduces mixing issues. The solidsjliquid ratio is the key parameter in developing formulations for E-S applications, as this dictates the rheology of the wet powder mass. Upper and lower limits exist on liquid content, closely mirroring the concept of the Attenberg plasticity limits for soils. The aim must be to achieve a plastic mass that can be extruded and shaped afterwards. Low liquid contents require higher forces to extrude and the drier extrudates yield noticeable fractions of dust. They will also faB to deform properly in the spheroniser. High liquid contents result in an over wetted mass which, when extruded, can rapidly become surface-wet and cause uncontrolled agglomeration in the spheroniser. The moisture content of the ext ru date ultimately has the greatest effect on the pellet size and shape, regardless of the type of granulator used [4]. With MCC, the sensitivity to water content varies with the amount of solid - a formulation with more MCC powder is less sensitive to a change in water content [1]. Recent studies using MCC and glyceryl monostearate (GMS) have shown that these systems require less water to give good performance [44]. Elbers et al. [45] showed that the amount and composition of granulation liquid were key factors in the mixing, extrusion and granulation of MCC pastes through a twin-screw screen extruder. They used a novel comb technique to estimate the plastic strength of the wet masses and were able to relate this to the power requirement for their extruder. Optimal liquid phase contents are often obtained by laboratory testing. Indi cations of saturated liquid content can be achieved by porosity measurements on the solids, but these are not absolutely accurate since the pore space involved in E-S is that obtained in a sheared and compacted material rather than that in a tapped density test. A noticeable feature of the soils and pharmaceutical literature is that liquid contents are reported on the basis of weight fraction rather than volume fraction, so that translating information between materials requires some extra calculation. In the case of waterjMCC, the calculation of volume fraction is not readily defined due to the water retention properties of this material.
Extrusion- Spheronisation
21 1
The liquid phase is usually aqueous, but alcohols and others are also reported [1]. Moisture-sensitive systems such as hydrophobie clays may require a non aqueous liquid phase such as an organic solvent. The essential feature is that the liquid is retained within the powder mass under the forces required for extrusion and spheronisation. The retaining component is often MCC for aqueous phar maceutical systems, and bentonite clays for aqueous and non-aqueous systems. The amount of MCC required (and the balance between other solid ingredients, such as lactose, calcium carbonate, calcium phosphate or bentonite) is depend ent on the active content and its properties (hydro-phobicity and hydro-philicity) [1 ]. Active levels < 1 0 wt% should not pose too many problems. The solubility of all components in the liquid phase is extremely important as this determines the amount of liquid required to obtain the required 'plasticity' [3]. Lustig-Gustafsson et al. [43] reported the effect of active agent solubility on op timal water content for successful E-S with MCC. Pellets were assessed on the basis of the two-dimensional shape factor (0 < eR < 1 ), and those with a value greater than 0.6 were deemed to be acceptable. The optimal water level, W, was found to decrease as the solubility of the drug increased, following W = Wo - In (solubility), although an increase in apparent water content requirement was needed to form good spheres above solubilities of 350-400 g/L. The viscosity of the liquid phase is an important parameter in systems where liquid phase migration may arise, i.e. pumping devices, as the rate of liquid redistribution is determined by its viscosity [30]. Liquid phase migration can be reduced by the use of a viscous liquid phase, but this parameter must be selected with due consideration of the mixing and drying required. The particle size distribution (PSD) has a significant influence on the extrusion characteristics (rheology) of the wet powder mass [23]. For example, increasing the PSD of lactose produces a larger pressure required for extrusion. Particle packing and therefore solids matrix strength are both controlled by particle shape and volume fraction, so that extrudate strength can be determined by these parameters. These also determine the porosity and pore size distributions in the mass and thereby the permeability (and likelihood of liquid phase migration) and drying characteristics of the extrudate. Fielden et al. [23] also showed that the particle size of lactose affects the sphere size - fine lactose gave no effect, whereas coarse lactose gave a significant time-dependent effect. So me oper ators spread finely divided powder ('dusting' with MCC, talc or starch) onto the surface of spheronising granules in order to stop agglomeration. Raines [1 1 ] and Tomer et al. [46] reported the variation in water retention capacity between grades of MCC. Colloidal grades exhibited the best quality extrudate surface, but at the expense of extrudate rigidity and difficulty in ex trusion. EI-Saleh et al. [47] also compared different MCC types that had the same chemical structure, but different microstructures. A colloidal grade extruded very weil, while powdered cellulose did not perform weil as an excipient. Powdered
212
D . I . Wilson a n d S. L. Rough
cellulose absorbs more water than MCC, and hence more water was needed to extrude it. The spheronisation behaviour of the two celluloses was very different with the same water content, the powdered cellulose pellets being rougher and more porous. Polymers can aid flow through an extrusion die and can add to the granule strength, but one has to avoid too cohesive a mass. Actives do not usually have lubricating qualities. Mesiha and Valles [48] evaluated 1 4 substances for use fulness in reducing surface defects, heat due to friction, and energy consumption for a water-based Avicel™ paste. Surfactants such as sodium lauryl sulphate were found to perform best, since they reduced the work input. Spheronisation studies were also carried out, and a wide range of results were obtained, in cluding unexpected ones. lIoariusi and Schwartz [49] investigated the effect of wax content on the extrusion forces for a water-based paste using an instru mented mini-extruder - the force required to extrude the wet mass was found to decrease as the wax content increased. Factorial designs are frequently employed in practice to identify suitable for mulations for E-S. The significance of each parameter varies between each extruder type and active/excipient combination. For example, Hileman et al. [14] studied a MCC-based material in a Nica screen extruder and reported significant variables to be MCC type and concentration, liquid content, spheroniser speed, residence time on the spheroniser and extruder screen size, while wet mixing time, extruder feed rate and extrusion speed were not significant. The results of such sweeps can be interpreted using regression models, or used to plot 'phase diagrams' as shown in Fig. 1 5.
L-
1 00 wt%
� __ __ __ __ �__ LL
__ __ __ __ __
1 00 wt%
MCC (Avicel PH 1 01 )
O wt%
Fig. 1 5. Schematic representation of triangular phase diagrams for MCC-Iactose-water formulations indicating zones where E-S produced pellets of acceptable quality. (After Vervaet et al. [61 ] , reproduced with permission from Elsevier.): Grey region - LID 2; dotted region - LID = 1 . =
Extrusion- Spheronisation
213
5 . CONTROL
E-S suffers from a lack of reliable and readily measured parameters for use in contro!. Granule product characteristics that are often measured or need to be controlled include active content, sieve analysisjPSD, shape, density and poros ity, crushing strength, water content, surface area and dissolution behaviour. Others are friability, hardnessjstrength, densities (bulk and tapped) and flow properties. 5.1 . Combination
Power consumption andjor torque is frequently used to provide quantitative in dicators of progress during mixing (e.g. [50]). Detailed analysis of the extent of mixing is not simple, particularly when unsaturated wet masses are generated. 5.2. Extrusion
E-S machines do not lend themselves readily to measuring extrusion forces and rate [1 0]. Baert and Down [51 ] were able to correlate the extrusion force on the screen of a basket extruder to power consumption, and found that both de creased as the paste water content increased, while lIoanusi and Schwartz [49] were able to develop plasticity maps by measuring the power consumption in a Luwa mini-ram extruder. Kristensen et al. [52] instrumented a rotary pelletiser in order to measure the torque; they found linear correlations between the torque increase and the MCCjwater content, and hence were able to use the torque to control the process. Since the water content in a formulation has to be tightly governed in order to control the pellet size, they established an end-point control system that enabled the formulation to reach an optimal water content. Schmidt and Kleinebudde [4] investigated different types of granulator, and found that less moisture content was required when using low-shear devices. The pellet shape was superior with low-shear devices, whereas the pellet size and crushing strength were better with high-shear. The energy dissipated during extrusion can result in noticeable increases in extruder temperature which must be controlled if: (a) there are thermolabile active ingredients; (b) the liquid-phase rheology is important, either due to liquid-phase migration being promoted by a reduced viscosity at higher temperature, or the formation of micelles; (c) particle softening may be an issue; and (d) evaporation of the liquid phase (i.e. water) from the extrudate, particularly from its surface, may aftect the spheronisation performance.
214
D . I . Wilson and S. L. Rough
The effect of speed in extrusion depends on the operating mode of the ex truder. High-extrusion speed can promote the formation of surface defects, often termed 'sharkskin' although these can differ noticeably in form from those ob served in polymer manufacturing where the term originated. The formation of surface defects can also be promoted by rough die holes, and reduced by the use of surfactants, smooth and countersunk die holes. For abrasive materials, ex truder speed is a key parameter determining wear on dies and screens. 5.3. Spheronisation
While the pellet size is ultimately determined by the screen or die diameter, pellet shape is dominated by the spheroniser conditions [53]. Spheronisation can be manipulated by speed and spheronisation time. The former affects a number of granule properties [3] - the speed is responsible for initial particle break-up (which affects the particle size distribution) and also the amount of collisions/ rounding off (which affects the pellet shape). The effect of the spheroniser load must also be considered. Key measures of spheroniser product quality are often granule sphericity (for coating) and flow behaviour (for capsule filling). 6. CHALLENGES AND FUTU RE D EVELOPMENTS
The main challenge in E-S is to understand the relationships which exist between formulation, processing and product quality, in order to remove the empiricism in formulation and uncertainty in scaling up between laboratory tests and manu facturing units, particularly when it requires a change of extruder type. While not considered in detail here, it should be noted that drying can introduce important effects. Excipients such as MCC shrink noticeably on drying (up to 14% [9]) and can introduce another level of tuning into the process. Co-extrusion is rarely used, but some workers have reported that this offers a route to generate encapsulated products. Pinto et al. [54] co-extruded non-com patible actives using a ram extruder, and reported that the outer layer of extrudate formed a complete outer shell on the spheroid. Finally, pharmaceutical products based on extrusion without spheronisation are being considered to deliver enhanced controlled-release characteristics. Carter et al. [55] describe the production of MCC-based monolith rods with in ternal channels and an external coating, which provide a uniform rate of release of active over time. ACKNOWLEDGMENTS
Discussions of paste extrusion with Prof. John Bridgwater and on E-S with Prof. Michael Newton are gratefully acknowledged.
Extrusion- Spheronisation
215
Nomenclature
Aram dp o
00
eR
ec3 F
G' GI! K L m n Pe P1 P2 V
WWo IY.
ß
y
A
O"J
0"0 T Ta
area of extrusion ram in contact with wet mass (m2 ) granule diameter (m) die diameter (m) ram extrusion barrel diameter (m) two-dimensional granule shape factor (dimensionless) three-dimensional granule shape factor (dimensionless) ram extrusion force (N) elastic modulus (Pa) viscous (Ioss) modulus (Pa) power-Iaw consistency (Pa Si ) die land length (m) Benbow-Bridgwater die entry velocity index (dimensionless) Benbow-Bridgwater die land velocity index (dimensionless) ram extrusion pressure (Pa) ram extrusion die entry pressure drop (Pa) ram extrusion die land shear pressure drop (Pa) mean extrusion velocity (m S- 1 ) level of water content (dimensionless) initial level of water content (dimensionless) Benbow-Bridgwater yield stress velocity factor (Pa m - msm) Benbow-Bridgwater wall shear stress velocity factor (Pa m -nsn) shear strain rate (S - 1 ) power-Iaw index (dimensionless) compaction joining pressure (Pa) Benbow-Bridgwater die entry yield stress (Pa) shear stress (Pa) Benbow-Bridgwater paste-die wall shear stress (Pa)
REFERENCES [1] J . M . Newton, i n : R. Grönig, P . C . Schmidt (Eds.), Entwicklungen in der pharmazeu tisch-technologischen Arzneimittelforschung, Deutscher Apotheker Verlag, Stuttgart, 1 999, pp. 39-43. [2] J . F. Pinto, G. Buckton, J . M . Newton, Int. J. Pharm. 83 ( 1 992) 1 87-1 96. [3] C . Vervaet, L. Baert, J.P. Remon, I nt. J. Pharm. 1 1 6 ( 1 995) 1 31 -1 46. [4] C . Schmidt, P. Kleinebudde, Chem. Pharm. Bull. 47 (3) ( 1 999) 405-41 2 . [5] A.M. J uppo, L. Hellen, V . Pullinen-Strander, K. Kaista, J . Yliruusi, E. Kristoffersson, Eur. J . Pharm. Biopharm. 44 ( 1 997) 205-2 1 4 . [6] C . Vervaet, J.P. Remon, Int. J . Pharm. 1 33 (1 996) 29-37. [7] J. Misselbrook, Apparatus and method for producing an extrudate, US Patent 6 , 1 26, 878, 2000.
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[8] P.J. Marti n , Meehanies of paste flow in radial sereen extruders, PhD Dissertation, U niversity of Cambridge, UK, 200 1 . [9] J . M . Newton, Powder Teehnology and Pharmaeeutieal Proeesses. D . Chulia, M . Deleuil, Y . Poureelot, (Eds.), Chapter 1 2 , Elsevier, Amsterdam, 1 994, pp. 391-40 1 . [ 1 0] K.E. Fielden, J . M . Newton, R.C. Rowe, Int. J . Pharm. 81 ( 1 992) 225-233. [ 1 1 ] C.L. Raines, The extrusion of various formulations of mieroerystalline eelluloses, PhD Dissertation, University of London, UK, 1 990. [ 1 2] J.J. Benbow, J. Bridgwater, Paste Flow and Extrusion, Clarendon Press, Oxford, 1 993. [1 3] L. Hellem, J . Yliruusi, P. Merkku, E. Kristoffersson , Int. J. Pharm. 96 ( 1 993) 1 97-204. [ 1 4] GA Hileman, S.R. Goskonda, A.J. Spalitto, S.M. Upadrashta, Drug Dev. Ind. Pharm. 1 9 (4) ( 1 993) 483-491 . [1 5] S.L. Rough, 0 . 1 . Wilson, J . Mater. Sei. 40 (2005) 41 99-421 9. [ 1 6] C. Sehmidt, P. Kleinebudde, Eur. J. Pharm. Biopharm. 45 (1 998) 1 73-1 79. [ 1 7] J . M . Newton, S.R. Chapman, R.C. Rowe, Int. J . Pharm. 1 20 ( 1 995) 95-99. [ 1 8] A B . Bashaiwoldu, F. Podezeek, J . M . Newton, Eur. J. Pharm. Sei. 21 (2004) 1 1 9-1 29. [ 1 9] M. Kouimtzi, R.J. Pinney, J . M . Newton, Pharm. Sei . 3 ( 1 997) 347-351 . [20] P. Coussot, C. Aneey, Phys. Rev. E, 59 (4) ( 1 999) 4445-4457. [21 ] J.-X. Li, Y. Zhou, X.Y. Wu , I. Odidi , A Odidi, J. Pharm. Sei. 89 (2) (2000) 1 78-1 90. [22] P.J. Harrison, J.M. Newton , R.C. Rowe, J . Pharm. Pharmaeol. 37 (1 985) 81-83. [23] K.E. Fielden, J . M . Newton, R.C. Rowe, I nt. J . Pharm. 81 ( 1 992) 205-224. [24] A. Englander, A.S. Burbidge, S. Blaekburn, Trans. IChemE. 78 (2000) 790-794. [25] M. Delalonde, B. Bataille, G. Baylae, M. Jaeob, S.T.P. Pharma. Sei. 1 0 (3) (2000) 205-209. [26] KA MaeRitehie, J.M. Newton, R.C. Rowe, Eur. J. Pharm. Sei. 1 7 (2002) 43-50. [27] S. Galland, B. Bataille, M. Delalonde, T. Ruiz, N. Bennaeer, C. Dupuy, Trans. IChemE. 81 (A) (2003) 1 237-1242. [28] D . M . Newitt, J . M . Conway-Jones, Trans. IChemE. 36 ( 1 958) 422-442. [29] PW.S. Heng, O . M.Y. Koo, Pharm. Res. 1 8 (4) (200 1 ) 480-487. [30] S. Boutell , J.M. Newton, J . R. Bloor, G. Hayes, Int. J . Pharm. 238 (2002) 6 1 -76. [31 ] K.E. Fielden, J.M. Newton, R.C. Rowe, Int. J. Pharm. 97 ( 1 993) 79-92. [32] S.L. Rough, J. Bridgwater, 0 . 1 . Wilson, Int. J. Pharm. 204 (2000) 1 1 7-1 26. [33] G. Tomer, J . M . Newton, Int. J . Pharm. 1 88 ( 1 999) 3 1 -38. [34] G. Tomer, M.D. Mantle, L.F. Gladden, J . M . Newton, I nt. J . Pharm. 1 89 ( 1 999) 1 9-28. [35] G. Tomer, F. Podezeek, J . M . Newton, Int. J. Pharm. 231 (2002) 1 07-1 1 9. [36] AT.J. Domanti , J. Bridgwater, Trans. I. Chem. E. 78 (A) (2000) 68-78. [37] P.J. Harrison , J . M . Newton, R.C. Rowe, J. Pharm. Pharmaeol. 37 ( 1 985) 686-691 . [38] S.R. Chapman, R.C. Rowe, J . M . Newton, J . Pharm. Pharmaeol. 40 ( 1 988) 503-505. [39] F. Podezeek, J . M . Newton, J. Pharm. Pharmaeol. 46 ( 1 995) 82-85. [40] F. Podezeek, J . M . Newton, I nt. J . Pharm. 1 24 (1 995) 253-259. [41 ] S. Almeida-Prieto, J. Blaneo-Mendez, F.J. Otero-Espinar, J. Pharm. Sei . 93 (3) (2004) 621 -634. [42] R.D. Shah, M. Kabadi , D.G. Pope, L.L. Augsburger, Pharm. Res. 12 (4) ( 1 995) 496-507. [43] C. Lustig-Gustafsson, H.K. Johal, F. Podezeek, J.M. Newton, Eur. J. Pharm. Sei. 8 ( 1 999) 1 47-1 52. [44] J . Chatehawalsaisin, F . Podezeek, J.M. Newton, Eur. J . Pharm. Sei. 24 (2005) 35-48. [45] J .A.C. Elbers, H W. Bakkenes, J.G. Fokkens, Drug Dev. Ind. Pharm. 18 (50) ( 1 992) 501-5 1 7. [46] G. Tomer, H . Patel, F. Podezeek, J . M . Newton, Eur. J. Pharm. Sei. 1 2 (2001 ) 321 -325. [47] F. EI Saleh, M. Jumaa, I. Hassan, P. Kleinebudde, S.T.P. Pharma Sei. 1 0 (5) (2000) 379-385. [48] M.S. Mesiha, J. Valles, Drug Dev. Ind. Pharm. 1 9 (8) ( 1 993) 943-959. [49] N.O. Iloafiusi , J.B. Sehwartz, Drug Dev. Ind. Pharm. 22 (7) ( 1 996) 667-671 .
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[50] P. Kleinebudde, J. Pharm. Sci. 84 ( 1 0) (1 995) 1 259-1 264. [51 ] L. Baert, G . R B . Down, I nt. J. Pharm. 1 07 ( 1 994) 21 9-222. [52] H . G . Kristensen, T . Schrefer, P . Kleinebudde, AAPS Pharm. Sci. 2 (3) (2000) 1 -8; (article 24). [53] GA Hileman, S.R Goskonda, A.J. Spalitto, S.M. Upadrashta, I nt. J. Pharm. 1 00 ( 1 993) 71-79. [54] J . F. Pinto, M . H . Lameiro, P. Martins, Int. J. Pharm. 227 (200 1 ) 71-80. [55] R E . Carter, J . M . Newton, A.M. Caminho, S. Mascia, Pharm. Tech. Europe 1 6 ( 1 2) (2004) 23-29. [56] P.J. Martin, D . I . Wilson, P.E. Bonnett, J. Eur. Ceramic Soc. 24 (2004) 3 1 55-31 68. [57] A. Cheyne, J . Barnes, D . I . Wilson, J . Food Eng. 66 (2005) 1-12. [58] RC. Rowe, Pharm. Int. 6 (1 985) 1 1 9-1 23. [59] L. Baert, J.P. Remon, Int. J. Pharm. 95 ( 1 993) 1 35-1 4 1 . [60] P . Kleinebudde, M. Schröder, P . Schultz, B.W. Müller, T . Waaler, L . Nymo, Pharm. Dev. Technol. 4 (3) ( 1 999) 397-404. [61 ] C. Vervaet, L. Baert, PA Risha, J.P. Remon, Int. J. Pharm. 1 07 ( 1 994) 29-39.
CHAPTER 4 D ru m G ranu l ation P rocesses Gavin M. Wal ke r*
Schoo/ of Chemistry and Chemica/ Engineering, Queen's University Be/fast, Be/fast BT9 5AG, Northern /re/and, UK Contents
1 . Introduction 1 . 1 . Granulation 1 .2. Drum granulation 2. Particle size enlargement in drum granulation 2. 1 . I ntroduction 2.2. Effect of moisture content on drum granulation 2.3. Effect of initial size distribution on drum granulation 2.4. Effect of drum rotational speed 2.5. Effect of residence time on drum granulation 3. Recent developments in drum granulation 3. 1 . Theoretical analyses 3.2. Effect of parameters on drum granulation 3.3. Growth regi me map 4. Mathematical modelling of drum granulation 4. 1 . I ntroduction 4.2. Granulation growth models 4.2. 1 . Mechanisms of g ranule formation 4.3. The population balance 4.4. The coalescence kernel 4.5. Solution of the population balance and estimation of the coalescence kernel 5. Drum granulation of NPK fertilisers (including own contribution) 5. 1 . Fertiliser granulation 5.2. Effect of solution to solid-phase ratio 5.3. Granulation kinetics 5.4. Effect of viscosity of binder solution 5.5. Effect of flight arrangement and critical speed 6. Future developments in drum granulation modelling 6. 1 . I ntroduction 6.2. Fundamental studies on granulation 6.3. Physically based drum granulation models 6.4. The modelling of granulation processes - future directions References
*Corresponding author. E-mail:
[email protected]
Granulation
Edited by A.D. Salman, MJ. Houns/ow and J. P. K. Seville ( 2007 B.V. '
Elsevier
All riQhts reserved
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1 . I NTRODUCTION 1 . 1 . Granulation
There are many processes where changing the size distribution of a powder are desirable, including the manufacture of pharmaceuticals and fertilisers. Granu lation is the generic name for particle size enlargement and is seen as a solution to different powder-flow problems, to ensure better results when mixing difficult powders, to reduce dust hazard problems, to ensure a uniform fill in tabletting and to obtain controlled release of nutrients in fertilisers [1 ,2]. The essential features of a granulated solid are: •
•
it is a solid composed of particles, which have been processed with the ob jective of improving one or more of the properties of the starting material, namely flow, handling, dustiness, strength, appearance, solubility or resistance to segregation; attainment of the objective entails restrictions on the size, shape and size range of the particle [3].
Granulation is the process of building up an optimum-sized, nearly spherical product from fines, melts or slurries. The granulation is brought about when a bed of solid particles moves, with simultaneous intensive mixing, in the presence of a liquid phase. This motion provides particle collisions and individual particles co alesce and bind together. Further granule growth takes place by layering on to these nuclei [1 ,2]. 1 .2. D rum g ranulation
The rolling drum granulator is one of the most widely used granulating equipment devices, in which size enlargement is achieved by collisions in a bed of moist particles undergoing rolling motion. The rolling drum is the simplest continuous granulation device, and is widely used in the granulation of fertiliser and in the balling of iron ore. A schematic design of a typical drum granulator is shown in Fig. 1 . It consists of a rotating cylinder, which is slightly inclined to the horizontal to facilitate the transportation of material through the drum. The drum is usually equipped with a dam ring so as to mini mise back-spill of the inlet material. At the outlet of the drum there is often another dam ring, which allows an in crease in depth of the bed inside the drum. Chutes, pipes or conveyors may be used to transport the granulate at the inlet and outlet of the drum. The solid material is normally wetted at or near the inlet of the drum, usually by spraying a fluid/binder onto the bed of tumbling solids. The design and number of the
Drum Granulation Processes
221
Fig. 1. The rolling drum granulator [3].
sprays varies between processes but is generally a function of the viscosity of the binder [3]. In most cases, drum granulators are fitted with a scraper bar that removes moist material from the drum walls, which would otherwise interfere with the rolling action and decrease the active volume of the drum. Stationary scraper bars or rotary scrapers are mostly employed and are designed to leave a thin layer of material on the shell to increase friction between the granulate and the drum, which allows a rolling motion to be established. Within the fertiliser indus try, knockers are often employed which hit against the outside shell of the drum to dislodge material adhering to the inside wall [3]. However, the use of knockers can adversely affect the shell wall and drive mechanism and are normally only used when absolutely necessary. Granulating drums are among the simplest types of agglomerating equipment. The first commercial plants using the technology were established in US in the 1 930s for the agglomeration of ion ore composites. Another early application of the technology was found in the fertiliser industry in which "granular" super phosphate fertiliser was initially produced (1 935) followed by mixed NPK ferti lisers. In the 1 950s, new drum granulation processes were developed. One process at TVA (US) sparged ammonia through a pipe under the tumbling bed to complete chemical reactions and to improve granulation. Fisons (UK) used a similar system using steam to maintain the temperature and therefore granulating conditions within the drum. In 1 960, the "Spherodiser" was developed by C&lj Girdler in which granules were agglomerated by spraying onto a falling curtain of particles formed by the incorporation of flights within the drum [4].
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2. PARTICLE SIZE ENLARGEMENT I N DRUM GRANU LATION 2. 1 . Introduction
Particle size enlargement has been described in granulation processes by the following basic mechanisms. Growth occurs either by the collision and successful adherence of primary feed particles into discrete granules or by growth centred around a nucleus onto which particles collide and attach themselves to form a layer. Again, this results in discrete granule formation [5,6]. In both cases, the particles are held together by cohesive forces at particle contact points. The overall strength of the granules is dependent on the mag nitude and nature of the cohesive forces, particle size distribution and the number of bonding contact points per particle [7,8]. It is essential that the fundamental mechanisms of particle growth are clearly understood if a greater degree of prediction in particle size enlargement process ing is to be achieved. It is, therefore, necessary to understand the roles of, first, the binding liquid and feed solids physical properties and, second, the reactor geometry and process conditions [3]. The overall mechanism of particle granule growth is not only responsible for the rate of growth, but it is also a key factor in determining the final properties and form of the product [8]. It is now generally accepted that the following three basic mechanisms, which have been observed apply to many granulating systems [5,9]: 1 . nucleation of primary particles by random coalescence [5,9, 1 0]; 2. a transition region dependent on either (a) coalescence in a preferential mode [9] or (b) crushing and layering [ 1 0]; and 3. a "ball" growth region [ 1 0]. Of these mechanisms, 1 , 2 (a) and 3 apply to wide distributions due to size independence, 1 and 2 (b) to narrow size distributions due to size dependence. The various possible mechanisms of granule formation are shown in Fig. 2 [5]. Nucleation occurs when non-particulate matter forms new particles. Layering is the addition of non-particulate matter to the surface of the particle. It is synon ymous to "growth" in crystallisation. Coalescence (aggregation, agglomeration) occurs when two particles successfully collide to form a single granule. The coalescence mechanism can be further sub-divided into random coalescence. The addition of small particles to the outside of well-formed granules is some times referred to as "Iayering" or "snow-balling", or "onion-Iayering" in the lit erature. Snow-balling is classified as a type of preferential coalescence [1 1 ] . Crushing and layering and abrasion transfer are other growth mechanisms that have been observed during the growth of weak, brittle granules [1 2].
Drum Granulation Processes
' + " "'
:.. �.. , ••
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•
. ., .:. �. .
-
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particulate
-particulate
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223
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-------..
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ce
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+
•
(f) Crushing and Layering
Fig. 2. Mechanisms of granule formation [5].
Kapur and Fuerstenau [1 3], using wide size distributions of limestone powder (irregular in shape and non-porous), observed from experiments carried out in a batch rotating drum, that nucleation of the primary feed particles took place in itially by rapid random coalescence. The transition region was also controlled by a coalescence mechanism which was size dependent, the growth rate passing through a maximum before falling off in the balling region. This was due to a decrease in the successful collision rate as the mean size of the granules in the process increased (Fig. 3) [5]. 2.2. Effect of moisture content on drum g ranulation
The key to successful granulation is a proper liquid to solid relationship, both as to the proportions of these materials in the drum and as to how weil the solids are wetted by the liquids. The main reason some formulations granulate better than others is that the liquids to solids ratio is nearly ideal [14] . This depends on the granulator type, formulation and temperature; the ratio cannot be determined without prior trials of the granulation process. A moisture content is often quoted as a simple percentage by weight or volume of water, of the total granulating mass. The volume ratio of the liquid to solid is preferable, however, as this correlates better to modelling of the granulation process [3]. Many researchers have identified the reasons why the liquid
224
G . M . Walker (a) d N
T
B
(b) dd dt
t Fig. 3. Granule growth in batch rolling drum experiments [5], (a) average granule size d vs. time, t; (b) differential growth rate (ddjdt) vs. time, t. (N, nucleation region; T, transition region; S, balling region).
and solid materials in the drum tend to agglomerate or granulate [ 1 5-1 8] . Two phenomena can be credited. One is the natural surface tension of the liquid that draws wetted solid particles into contact with each other and holds them together. The second is the mechanical forced contact of wetted particles as the drum rotates. These forces work together and must occur simultaneously. To explain the first phenomenon, the surface of water and many other liquids tends to form what can be described as an elastic film of molecules that hold tightly together. For example, water from an eye dropper forms drops rather than a steady stream and water placed on non-porous surface tends to bead up. In a drum granulator, this surface tension causes wetted particles to cling to one another, giving the resulting granules a degree of plasticity; in other words, they can be deformed or moved by mechanical action without breaking up. As the wetted particles roll around in the drum, they come in contact with each other. Surface tension from the liquid phase draws them even closer together. The continued rolling action causes them to grow larger (i.e., coalescence). If the mechanical contact continues in the proper liquid-solid environment, the granules will continue to form and grow until no small particles remain that have the proper surface area to mass relationship [14]. Newitt and Conway-Jones [1 9] first noted that the critical moisture content (solid:liquid ratio) required for granulation to occur, correlated with 90% of the moisture required to saturate the
Drum Granulation Processes
225
voidage in the powder being granulated, as measured by packed bulk density. The remaining volume was assumed to be taken up by entrapped air [ 1 9] . Many workers have observed that the rate of granule growth i s strongly dependent upon the liquid content of the granulating mass [1 , 1 9,20-24]. This is variously at tributed to the increased granule plasticity or surface moisture at higher liquid con tents leading to a greater probability that granules will stick together on collision [3]. When one or more of the materials being granulated is water soluble (e.g. in fertiliser granulation), it is the total volume of liquid or solution phase rather than the moisture content which controls the granulation behaviour [25-27]. The amount of solution phase is in turn a function of the temperature of granulation [28,29]. In fertiliser granulation, as granulation temperature increases, the sol ubility of the fertiliser salt increases. Therefore, for a given moisture content, the solution-phase ratio will be higher, thereby varying the extent of granulation. The more the solution-phase ratio, the higher the degree of granulation. 2.3. Effect of initial size d istribution on drum granulation
Feed characteristics have a pronounced effect on the behaviour of granulating devices. The majority of granulation studies have used narrow size distributions of primary particles much smaller in size than the granules produced. In such stud ies, the granulation rate increased with increasing primary particle size, but the strength of the product granules decreased [1 9,20,26]. The extent of granulation was found to increase with a decrease in bulk porosity of the particles [1 9,26]. In contrast, the feed to an operating drum granulator consists of a very wide size distribution of hard non-deformable particles. The higher fraction of this size distribution overlaps the size distribution of the product granules. There has been much less study on the granulation of such size distributions. An investigation into the granulation of iron ore sinter feed with broad size distributions found that most of the granulation occurred very quickly (within 5 min), with a small amount of further growth up to 25 min. Growth proceeded mainly by pseudo-Iayering of the small particles in the feed onto the larger ones. The size of the particles acting as layers was found to increase with moisture content. Researchers were able to predict the granule size distribution, giving the partition between layering and nucleation of the particles in the feed. However, the determination of this partitioning was not weil defined [30-33]. 2.4. Effect of drum rotational speed
In the operation of drum granulation systems, there are a number of process parameters that will affect the extent of size enlargement and physical properties of the final granulate. Many of these parameters (i.e., drum diameter, rotational
226 (a)
�
G . M . Walker
see-saw motion of bed with mass
rolling motion without cascading at
cascading motion at half the
relatively static at low rotational speed
higher rotational speed
critical speed
Fig. 4. Motion of material i n a rolling drum at various rotational speeds [34].
speed, angle of incline) affect the mean residence time of the particles within the drum. The parameter that can be most manipulated is the rotational speed. With low rotation speeds, the granulate slides about the boUom of the drum with Iittle agitation of the granules, with increasing drum speed the granule begins to roll, cascading occurs and the probability of agglomeration increases (see Fig. 4) [3]. It has been suggested that the optimum drum speed is half the critical speed, where the critical speed is defined as the speed at which the dry material will be carried around the drum by centrifugal force. The critical speed also corre sponds to the speed at which the Froude number is equal to unity, where the Froude number is the dimensionless ratio of the inertial to gravitational forces: Fr = n2 Djg (1) When the Fr = 1 , the optimum rotational speed then equals nFr = 42.4 D-0.5
(2)
where n = rotational speed (rpm); and D = drum diameter (m). In practice, good granulation can be achieved in drums containing no internal flights at speeds nFr 0.3-0.5. For drums containing internal flights, the optimum speed for good granulation is nFr 0.2 [9]. In the granulating drum, a mixture of fresh feed and recycle material are fed into the inlet end of the drum. At this end, drum separation of the granulate takes place due to natural segregation with the fine material concentrated at the boUom and the larger material concentrated near the surface. When the liquid/binder is sprayed onto the bed it preferentially wets the larger particles on or near the �
�
227
Drum Granulation Processes
surface, these larger particles then agglomerate with finer particles as they move through the bed. Only the strongest bonds between particles will survive the high shear forces found in the tumbling bed. The sprayer system may be located along the entire length of the drum or more normally along in the inlet section. The latter case is more commonly used because it lessens the potential of wet and over sized granules being discharged that may be the case with sprayers located in the entire length of the drum. Sprayers located at the inlet section generally lead to less oversize materials and drier and stronger granules [3]. 2.5. Effect of residence time on drum g ranulation
The mean residence or holding time within the granulator is probably the most important factor influencing the size of the granulation drum. Various studies have shown that the average granule size can be correlated to the number of drum revolutions. Figure 5 shows the growth behaviour of chalcopyrite powder granulated in a drum with variation in water (binder) content [35]. The data in dicate that the correlation between drum revolutions and mass mean diameter is complex. This system shows a typical induction-type growth behaviour with nu c1eation behaviour only occurring at low binder contents. Early studies on drum granulation residence time indicated that average gran ule size is a linear function of drum revolutions [ 1 9,20,36,37]. However, recently more complex growth behaviour has been found [1 1 ,21 ,38,39]. Three growth 12,000
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100
200
300
400
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600
700
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Fig. 5. M ass mean diameter VS. drum revolutions for chalcopyrite granulated with water
[35].
228
G . M . Walker
regions have been defined: 1 . the nuclei growth region; 2. a transition region; 3. ball growth region. Lister and Waters [31 ] proposed a two-stage growth mechanism. Initially, when water is added to the tumbling feed, the fine particles immediately layer onto the intermediate and large nuclei particles. Some intermediate particles also adhere to large nuclei particles. Following this stage, continued growth occurs as some intermediate particles change roles from nuclei particles to layer particles. This second stage is slow as a number of collisions may be necessary before inter mediate particles are successfully incorporated into the large nuclei particles. Eventually, equilibrium is reached where there is a balance between collisions, which dislodge particles from layers and those which add particles to them. At this point, the maximum stable granule size distribution is reached [21 ]. Thus, it is important to investigate the effect of residence time on the extent of granulation, in order to obtain an understanding of the growth mechanism(s) and to find the required residence time. Sommer and Herrmann [39] developed a model for the final size of agglomerates by assuming that the length of the bed surface where most of the growth takes place characterises this parameter. The total rolling distance, Sr, can be estimated by: (3) where: e = lifting coefficient which is a function of drum loading, tr residence time; n = rotation speed; and o = drum diameter.
=
During scale-up this characteristic must remain constant. Also, if the drum loading changes within typical limits ( ep = 0.1-0.3), the bed surface changes very little, while the relative amount of agglomerates travelling on the surface in creases inversely proportionate to the drum loading, ep ; thus sr �
or
(:)
trnO
= const.
(4) (5)
If, as for tube mills, the Froude number is kept constant during scale-up, i.e., and assuming that the residence time t, is also kept constant, the drum
os n ;:::;; O- . ,
Drum Granulation Processes
229
loading would change according to cp ;:;; 0° . 5 . This indicates that unwanted dens ification of agglomerates occurs in the deeper bed. Therefore, the drum loading is normally kept constant which requires a reduction in residence time according to tr oc O- O . 5 .
Another possibility to scale up (keeping tr constant) exists by adjusting the rotational speed and keeping the peripheral speed constant, Le., nO = constant or n oc O- 1 . Then according to equation (4) the drum loading cp is also constant. The two operating conditions: • •
n oc O- O. 5 Le., constant Froude number and n oc O- 1 Le., constant peripheral speed.
are the upper and lower limits. In reality, care must be taken to guarantee a rolling movement of the bed [39].
3. RECENT DEVELOPMENTS IN DRUM GRANU LATIO N
Research in drum granulation processes has increased significantly in recent years, with a considerable amount of work performed in order to understand and model growth behaviour during granulation. Two significant contributions to this field have been made by Ouchiyama and Tanaka [40] and by Ennis et al. [38]. Ouchiyama and Tanaka's model assumes that granulation takes place due to the deformation of particles when they come in contact, hence whether or not granulation occurs depends on the bond formed by the granule dumbbell and the forces it encounters. Ennis's model does not take into account particle deformation, but views particles as rigid spheres coated with a finite layer of binder. The model assumes that two granules stick when the viscous dissipa tion in the binder layer is equal to the relative kinetic energy of the two colliding particles. These two models assume different behaviour of the particles, Le., surface-dry, deformable granules and rigid granules with a liquid layer at the surface. In addition, Iveson and Utster [41 ] proposed a regime map for granule growth; incorporating a general framework in which the two extremes, as posed by Ouchiyama and Tanaka [40] and by Ennis et al. [38], were combined. Based on two properties of the granulating system, the growth regime map predicts what type of growth will occur. The two main types of growth that can be distinguished on the map are steady growth and induction-type growth. Steady growth occurs when particles are deformable and is characterised by a steady increase of the granule size with time; the growth rate increases when more binder is present in the system. In contrast, induction behaviour occurs when the granules possess low deformability and is characterised by no growth occurring during the first stage of granulation. During this stage, the granules
230
G . M . Walker Steady Growth Behaviour
Induction Behaviour
2 i:i5
"
:;
e
o
'------i�
Granulation Time
High Deformation System
8 Fig.
Granulation Time Low Deformation System
-. Rapid Coalescence Growth
6. Growth mechanisms proposed by Iveson and Utster [41 ] .
8
are compacted and liquid is squeezed from the interior on to the surface of the granules. Once the pores of the granules are saturated, they become surface wet and the liquid layer at their surface renders further growth possible. Increasing the amount of binder results in a shorter induction period [38]. In their work, Iveson and Utster [41 ] (see Fig. 6) cited a number of examples from several authors of both induction-type behaviour as weil as steady growth behaviour and they explain the differences using their regime map. In summary, the regime map provided a plausible explanation for the different growth types, using both Ouchiyama and Tanaka's theory as weil as that of Ennis et al. The following sections contain a literature review of recent studies into drum granulation. The first section looks at the application of models, particularly the Ennis model to drum granulation. The second section looks at more empirical approaches of some researchers, investigating the effect of process parameters on drum granulation. The final section looks in more detail at the application of the growth regime map to drum granulation. 3. 1 . Theoretical analyses
U u et al. [42] mode lied the coalescence of deformable granules in wet granulation processes such as drum granulation. The proposed model (an extension of the model of Ennis et al. [38]), which accounted for both the mechanical properties of the granules and the effect of the liquid layer at the granule surface. This model
Drum Granulation Processes
231
included factors such as granule plastic deformation during collisions and was written in terms of dimensionless groups such as viscous and deformation Stokes numbers and the ratio of granule dynamic yield strength to granule Young's modulus. The model describes the conditions for two types of coalescence - type I and type 1 1 . Type I coalescence occurs when granules coalesce by viscous dissipation in the surface liquid layer before their surfaces touch. Type 1 1 coa lescence occurs when granules are slowed to a halt during rebound after their surfaces have made contact [42]. Adetayo et al. [1 1 ] describe the effect of process parameters on the drum granulation of granular fertilisers using three fertiliser grades: ammonium sul phate (AS); mono-ammonium phosphate (MAP); and di-ammonium phosphate (DAP). They found that the extent of granulation increases with the available solution phase for a given fertiliser salt. However, they indicated that the differ ences in extent of granulation, using the three grades, cannot be explained by their differences in solubility alone. Other properties in the solution-phase binder, notably viscosity were also important. They also found that initial size distribution had a strong and complex effect on the granulation process. They proposed a two-stage mechanism based on the analysis regimes given by Ennis et al. [38] the first was a non-inertial regime, where successful coalescence is independent of particle size, followed by a second inertial regime, where preferential coales cence leads to a significant growth of larger granules. The proposed mechanism proved consistent with experimental results [1 1 ] . The experimental data i n the first study [1 1 ] was population balance mode lied by Adetayo et al. [24] with the granule coalescence described by a sequential two-stage kernei, with the first stage describing the non-inertial regime and the second describing the inertial regime employing a size-dependent kerne!. Using this two-stage kernei, the model was able to describe the shape of the granule size distributions over the full range of data [24]. Adetayo and Ennis [43,44] proposed a unified approach to modelling gran ule coalescence mechanisms. In their work, a physically based kernel for pop ulation balance modelling of granule growth by coalescence was presented. In this model, the kernel was size-independent in that all collisions with an effec tive average granule size less than a critical value are successfu!. Simulations based on this kernel showed that a variety of contradictory experimental obser vations can be modelled. The kernel described in this model clearly demonstrated the three regimes of drum granulation originally proposed by Kapur and Fuerstenau [21 ] . Lian et al. [45] described computer simulations of pendular state wet agglom erates undergoing pair-wise collisions. They found that the energy dissipated was associated primarily with the viscous resistance of the fluid and the interparticle friction rather than by liquid bridge bond rupture. It was further found that the structure of the resultant coalesced agglomerate was highly disordered and
232
G . M . Walker
depended on the impact velocity. Yang et al. [46] investigated the flow of particles in a horizontal rotating drum based on distinct element method (DEM) analysis and found that simulation conditions are comparable to those measured by means of positron emission particle tracking (PEPT). They further explained the effect that drum rotation has on granulation [46]. Venkataramana et al. [47] developed a mechanistic model for the industrial drum granulation of iron ore fines. The model is based on a layering-type mech anism and provides a piece-wise linear model for granulation kinetics. The model takes into account relevant process parameters such as feed size distribution and binder content. The kinetic parameters in the model were determined in bench scale studies, but the model has been successfully scaled up to predict the performance in a full-scale plant [47]. Wauters et al. [48] studied growth kinetics in drum granulators using chalcopyrite powder in bench-scale studies. Granule growth was found to occur in two stages, an initial induction stage followed by a rapid growth stage, which occurs when the surface of the granules becomes wet. The authors also investigated the compaction behaviour of the granulate. Further analysis indicated that the porosity of the granules decreased during the induction growth stage. Iveson et al. [49] developed a two-stage model to describe the penetration of liquid into submerged porous iron ore particles. In the first stage, liquid flow is driven by capillary pressure and the second stage concerns the dissolving of pressurised air through the pore liquid. The model indicated that the time taken for iron ore particles to become saturated with liquid is longer than the residence time in granulation drums, with implications for industrial iron ore granulation. 3.2. Effect of parameters on drum g ranulation
Walker et al. [50] investigated NPK fertiliser production in a bench-scale drum granulation unit. In this work, three factors are identified affecting the degree of fertiliser granulation, these were solution to solid-phase ratio, the binder viscosity and the optimal rotation speed of the drum. Experimental results indicated that a critical solution to solid-phase ratio was required for an increase in granulation in terms of mass-median diameter. Further work by this group [51 ] investigated the effect of process parameters on the crush strength of fertiliser produced from a bench-scale drum granulator. It was found that the granulation of the fertiliser took place in the growth regime. Crush strength analysis of the final granulate was undertaken and was correlated with particle size and fractional saturation. The experimental data and analysis in this study indicate that the rounded, reg ular-shaped granules produced by granulating with higher liquid-phase ratio and fractional saturation, result in granules having stronger bonds between sub granules and lower porosity. Reddy et al. [1] investigated the effect of operating
Drum Granulation Processes
233
variables, such as moisture content and feed rate, on the continuous rotary drum granulation of fertilisers. Granule consolidation was investigated by Iveson et al. [52] in a bench-scale granulation drum using fine glass ballotini as the model powder and glycerol water mixtures as model liquid binders. They found that granule consolidation during tumbling was complex and was controlled by the balance between the different mechanisms that resist granule deformation: interparticle friction and viscous dissipation. They indicated that the rate of consolidation decreased with the decreasing particle size. As liquid content increased, interparticle friction effects decreased but viscous losses became more significant. Thus, the effects of binder viscosity and liquid content were highly interactive. They proposed that unless the balance between the two mechanisms is accurately known for a given system, the effect of changes to binder parameters on granulation behaviour cannot be predicted, even qualitatively. To overcome these difficulties, the au thors proposed a new methodology for relating formulation properties to gran ulation behaviour, based on bulk powder properties measured by triaxial consolidation tests and the development of a new granulation criterion for de formable granules [51 ] . Gluba and Heim [53] investigated the drum granulation of ground dolomite with different particle size composition. The extent of granulation was found to be de pendent upon the amount of wetting liquid and particle size composition of the raw material. Further work by this group [54] investigated the effect of wetting, liquid droplet size on the growth of agglomerates during wet drum granulation of dolomite flour of selected grain-size composition. In this work relationships, determining the effect of wetting droplet size and particle size distribution of the raw material, on the rate of agglomerate growth during drum granulation were developed. The group lead by Seville and Adams reported the effects of changing the binder viscosity in rotating drum granulation using a narrow size fraction of an irregularly shaped sand [55]. It was found that the viscosity of the binder affected both the rate of size enlargement and the mechanism of size enlargement. It was found that the growth rate increased with the increase in binder viscosity up to maximum at a viscosity of about 1 00 mPa s. Enlargement occurred by a layering mechanism. With binders of viscosity greater than 1 00 mPa s, layering was not observed and growth was found to be by coalescence. Stokes number analyses of the internal deformation on impact and of the adhesion on impact of surface-wet granules were made and found to account, in part, for the effects of changing binder viscosity [55]. 3.3. Growth reg ime map
Iveson and Utster [41 ] introduced the concept of a regime map of granule growth behaviour based on granule deformation during collision. This regime map proposes that the type of granule growth behaviour is a function of two
234
G . M . Walker
dimensionless groups: the amount of granule deformation during collision (chara cterised by a Stokes deformation number, Stdef and the maximum granule pore saturation, smax) . (6) (7) where: U� Smax = W Yg
emin Pg PL Ps
inter-granule velocity (m S- 1 ) maximum pore saturation ( - ) granule liquid content (mass binder/mass dry solid) Granule plastic yield stress (Nm -2) minimum granule porosity granule density (kg m - 3) liquid density (kg m - 3) solids density (kg m -3)
Using this analysis, granule growth regimes such as steady growth, induction, nucleation, crumb and slurry were defined, with the regime map qualitatively ex plaining the variations in granulation behaviour. Iveson and Uster postulated two new granulation growth mechanisms, steady growth and induction-type growth (see Fig. 6). Steady growth occurs when the particles are deformable and induc tion growth occurs when the granules possess low deformability. Induction growth is indicated by the lack of granulation in the first stages of the process. During the induction stage, the granules are compacted and liquid is squeezed from the interior of the granule to its surface. Once the pores of the surface are saturated, the liquid layer at the surface of the pores makes further growth possible. Iveson and Utster used laboratory drum granulation experiments to test the regime map. Experiments were performed in a 0.3 m diameter drum using three sizes of glass ballotini (19, 31 and 60 11m) with water and glycerol as liquid binders [41 ] . Increasing granule yield stress by decreasing particle size and increasing binder viscosity caused the system to move from steady growth to induction behaviour as predicted by the regime map (see Fig. 7). Iveson et al. [56] further developed and validated the regime map concept and found that drum granu lation experimental data (from a number of sources) gave good agreement with the proposed regime map. The transition from nucleation or induction growth in drum granulation occurred at pore saturations between 80% and 90%. Rapid growth occurred for all pore saturations greater than 1 00%. The boundary be tween crumb and steady growth occurs at St(def) of order 0 . 1 and the boundary between steady and induction growth occurs at St(def) between 0.001 and 0.003. The steady growth results are all weil below the steady-crumb regime boundary of 0.2 proposed by Tardos et al. [57].
Drum Granulation Processes
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7. Growth regime map for drum granulation [56].
4. MATHEMATICAL MODELLING O F DRUM G RANU LATION 4. 1 . Introduction
Population balance models have been extensively used for modelling agglom eration in many granulation systems. These systems include aerosols [58,59], pelletisation [22,23,60] and crystallisation [61 ,62]. Various feed materials have been used to investigate the granulation kinetics, these materials include, sand [25,63,64], limestone powder [1 1 ,38] and other materials [22,65,66]. The use of ferti liser for study has also been used incorporating principles from the work using non-fertiliser feed material [23,67-69]. 4.2. Granulation g rowth models 4. 2. 1. Mechanisms of granule formation
To establish an understanding of the fundamental mechanisms of granule for mation,the forces involved in the collision of two spherical particles were inves tigated by Ennis et al. [38]. The capillary and viscous contributions were both found to significantly affect the bonding mechanism of colliding particles. The viscous Stokes number, St" , was defined as the ratio of the relative kinetic energy between colliding particles to the viscous dissipation brought about by the pendular bond,and is given by [38]: 8pg fV St" = ----g;;(8)
236
G.M. Walker
where:
V = velocity of granule collision (m S- 1 ); Pg = granule density (kg m - 3); r = effective granule size (m); - 1 1 = viscosity of binding fluid (kg m S- ).
p
Stv increases as the granule size increases or binder viscosity decreases. A critical viscous Stokes number Sr:; must be exceeded for rebound of colliding particle to occur,according to the following [38]: St; =
(1 + �) In (�)
(9)
where: e = particle coefficient of restitution; h = thickness of binder layer (m); ha = measure of granule's surface aspirates (roughness) (m). Three granulation regi mes were defined in terms of the magnitude of Stv in comparison to St� [38]:
1 . Stv « St: _ non-inertial regime (all collisions successful); 2. Stv � St� - inertial regime (some collisions successful); and 3. Stv » St: - coating regime (no collisions successful). The non-inertial regime is independent of granule velocity and all collisions between particles will cause successful granule formation. The inertial regime is dependent on granule velocity and therefore, a certain granule velocity is required to cause a successful collision between particles. In the coating regime, there are no successful collisions and it is a layering process [38]. For fine powders, growth typically begins within the non-inertial regime of granulation. As granule size and Stv increase during granulation, the process may pass through the inertial regime and finally end in the coating regime. The exact boundary between the regimes depends on the velocity of collision, the sizes of colliding granules and the properties of the binder. In general, the collision ve locities of granules within the process are difficult to ascertain. In the case of drum granulation, possible estimates are given by
V = rw V = rxRw where:
R = drum diameter (m); w = rotational speed (S - 1 ); and rx = numerical constant.
(10) (1 1)
Drum Granulation Processes
237
The estimation of St: with any great accuracy is problematic, this is due to the difficulty in finding the values of the thickness of the binding layer (h) and the measure of the granule's surface roughness (ha). The order of magnitude relationship between Stv and St: is however of interest [38]. Adetayo et al. [1 1 , 1 2] investigated the granulation kinetics of three types of fertiliser, MAP, DAP and AS. It was found that all fertilisers followed the first stage of granulation. DAP followed the second stage of granulation for all moisture contents above 2%. MAP followed the second stage after 5% moisture content, while ammonium sulphate followed only the first stage of granulation for all moisture contents tested. To account for the difference in solubility between the fertilisers, the concept of liquid-phase ratio (y) was defined by Sherrington [25] as the volume liquid phase per volume of solid in the granule: t y = (1w(1- Ws)P S)PI +
( 1 2)
where: W = weight percent of water in the granule; S = solubility of the fertiliser salt in water, (g g - 1 water); Pt density of fertiliser salt, (g cm - 3); and P I = density of fertiliser solution, (g cm - 3). =
4.3. The population balance
The population balance for a weil-mixed batch system undergoing coalescence alone can be given by [67]: (jn(v, t) (jf
100
1 ß v, t) neu, t) n(v, t) du N�T 0 (u, 1 ( OO + 2N� Jo ß(u, v - u, t) neu, t) n(v - u, t) du -
where: n(v, t) = number density function; ß(u, v, t) = coalescence rate kernei; NT = total number of particles at time, t; v = volume of granule, dimensionless; u = particle size, mm; t = granulating time, min; = 0, for free-in-space systems such as aerosols; and = 1 , for restricted-in-space systems such as granulation processes. IY.
IY.
(1 3)
238
G.M. Walker
The solution to equation ( 1 3), an integro-differential equation is not easy to determine as known analytical solutions are only available for special forms of the coalescence kernel with an assumed initial number density distribution [68]. Numerical solutions to this equation have been obtained by various methods, including moment [67], discrete [66] and sectional methods [69]. Hounslow et al., [61 ] using volume as the particle size coordinate, divided the particle size spectrum into geometric sections (Vi = 2 Vi- 1 ). Assuming that the number density distribution in each section is constant, they proposed a sectional population balance model . The change in the granule size distribution can be given by [61]: (14) where: Ni = number of particles in the ith interval; and ßij = collision rate function (coalescence kernei) between particles in the ith and jth section. Equation ( 1 5) gives the change in the number of granules of a certain size with respect to time [61]. 4.4. T h e coalescence kernel
An important parameter in population balance modelling is the coalescence kernei, ßi,j. A significant amount of research has focused on determining the appropriate form of the coalescence kernel. The coalescence kernel signifies the degree of granulation. A value of zero for the kernel represents no granu lation, whereas a value of infinity would give a large ball of all the particles being granulated. Ouchiyama and Tanaka [40,70,71] attempted a derivation of the kernel by conducting a force balance on the colliding particles. Owing to the complexity and lack of adequate knowledge of the forces involved in the gran ulation process, they could only propose a form of coalescence kernel with semi empirical adjustable parameters. The values of these parameters depend, in part, on the degree of plasticity of the granule and they determined the order and form of the kernel. Thus, the form of the coalescence kernel for granulation systems is not completely established. The available kerneis in publications are either purely empirical or semi-empirical [64,72]. It is commonly assumed that the granulation kernel can be divided into two parts: (15)
Drum Granulation Processes
239
The coalescence rate constant, ßo , determines the rate of granulation and is a function of the granulator operating conditions, including moisture contents, binder viscosity and drum speed. Higher binder content, greater binder viscosity, and faster drum speed, allow particles to adhere quicker, thereby increasing the extent of granulation. Therefore, it controls the rate of change of the mean gran ule size distribution. The dependence of the granulation process on the particle size is described by ß(Vj, Vj) which determines the shape of the granule size distribution [12]. It has already been mentioned that two stages of granulation have been iden tified and, therefore, it is expected that a two-stage granulation kernel would be required to adequately model the granule size distributions over a broad range of conditions. In the first stage of granulation (non-inertial regime), the probability of successful coalescence following a collision is independent of particle size and collision velocity and, instead depends only on the binder distribution. The prob ability of coalescence equals the probability of encountering the binder during a collision, with those collisions involving the binder being successful. In addition, it was assumed that the rate of collisions is independent of particle size and the first-stage mechanism becomes a random process [1 3] . This is a reasonable first approximation for a restricted-space concentrated system such as drum gran ulation. The first-stage kernel was defined as a constant: ( 1 6) Growth with a size-independent kernel has been described [1 3] with the total number of granules and mean granule size were both shown to vary: N = exp( -k1 t/2) ( 1 7) No ( 1 8) where: No = initial total number of particles; (0 = initial mean granule size, f.!m; ( = current mean granule size, f.!m; and t = granulation time, min. During the second stage of granulation (inertial regime), the granule size dis tribution widens. Therefore, particle deformation is important and, thus, collisions involving large granules are favoured due to their increased deformation upon impact. In order to describe this stage of granulation, it is necessary to obtain a size-dependent kernel. Empirical and semi-empirical kerneis of various order in volume have been proposed [72-78]. A number of first-order kerneis have been
240
G . M . Walker
evaluated by researchers. Golovin proposed the kernel [74]: ( 1 9) Thompson proposed the kernei: (20) The time scales in growth mechanisms vary, Adetayo sequential kernel for both stages of granulation:
et al.
[1 2] , proposed a
(21 ) where
�Y = given by equation ( 1 6); ��l = given by equation (1 9) or (20); t
t1 =
=
granulation time, min;
time required to reach the final equilibrium size distribution of the non-inertial stage of granulation, min. Experimental data for fertiliser granulation (5-25 min) published by Adetayo et al. indicated that, the first non-inertial stage of granulation was complete within 5 min (i.e., t1 < 5 min) [1 1 ] . Therefore, it was not possible to distinguish between differences in the rate of granulation and the first-stage rate constant k1 . It was noted that from equations ( 1 7) and ( 1 8), the group, k1 t is a measure of the extent of granulation and, in particular, k1 t defines the final extent of granulation occur ring within the first stage of non-inertial granulation. While it is not possible to determine k1 directly, it is possible to determine values of the extent of granu lation, or k1 t. Adetayo et al. [1 2] achieved this by using an arbitrary value for t1 (2 min), as the time for completing the first stage of granulation and for switching the form of the growth kerne!. By minimising the error between experimental granule size distributions and numerical solutions to the population balance equation, as discussed later, the values of k1 as weil as k1 t can be determined. Given the arbitrary selection of t1 the values of k1 are actually the measure of the extent of granulation at which the first stage of granulation is complete; however, differences in the values of k1 do not directly imply differences in granulation rate. Where the second stage of granulation does not occur, i.e., ��l = 0, the population balance solved for f> t1 giving the equilibrium granule distribution for coalescence in the non-inertial regime only.
Drum Granulation Processes
241
4.5. Solution of the population balance and estimation of the coalescence kernel
Various numerical solutions to known analytical solutions of the general popu lation balance equation, equation ( 1 3), have been established. Hounslow's sec tional model solution [61 ] equation (14), was found to accurately describe the behaviour of granulation processes. For given values of k1 and k2 , equation ( 1 5) is solved with the coalescence kernel given by equation (22) [1 2]. In a typical study [2], 1 8 size intervals were used with the first top size being 0.32 mm. Thus, a total size range of 0.32-1 7.46 mm was covered ensuring there is always at least one empty size interval at the top of the size range, so as to avoid finite domain error [68]. Equation (14) is a series of 1 8 ordinary differential equations (ODE), which can be solved using the Fehlberg fourth-fifth order Runge-Kutta method for a range of residence times [74]. The predicted size distributions at varying residence times can be compared to the measured ones and the best values of k1 and k2 , for a given set of data are estimated by non-linear regression. Adetayo et al. [1 2] used the Marquardt compromise method [75]. This routine combines the steepest descent and the Iinearization methods, and has the advantage of fast convergence as weil as being relatively robust. The best parameters are estimated by minimising the sum of squares error between the simulated and experimental cumulative size distributions [1 2]. 5. DRUM GRANU LATION OF NPK FERTILISERS (including own contribution) 5.1 . Fertiliser granulation
Granulation is an important process in the fertiliser industry. However, prior to 1 950 most fertiliser manufactured was produced in a non-granular form. In such form, the material caked when stored and was extremely dusty when applied in the field. About this time, a wide interest developed in the fertiliser industry for the manufacture of a granular, high-analysis fertiliser of improved physical properties [79]. Since this time various granulation processes have been developed. A schematic diagram of a typical granulation process is shown in Fig. 8. Recycle seed granules are fed to the granulator. New feed, which is in the solid or liquid phase depending on the process being used, is added to the seed granules, and granule growth occurs. Granules leaving the granulator are first dried and then screened to separate out the product size. Product size is normally very strict, e.g., 90% -4 mm + 2 mm [80]. Oversize granules are crushed and recycled with undersize granules.
242
G . M . Walker New Fecd
We! Granules
GRANULATION DRUM
Dry Granules
DRIER SCREENS
' '
Oversize
.;:: -0 -+-'---;;:::-...::.
-
Undersize
-+-
-
---..
-
Produc!
CRUSHER
Ree eIe Seed Granules
Fig. 8. Schematic diagram of a fertiliser granulation plant.
The operation of granulation plants is difficult because of two major problems. Firstly, often only a small fraction of the granules leaving the granulation drum are in the specified product size range. The recycle ratio, that is the ratio of the amount of material returned to the process, to that of the product, may be as high as 1 0-1 5, in high-recycle processes, and anywhere between 0.5 and 2 in low recycle processes. Processes using no recycle are practically non-existent, be cause there is always an undersize or oversize fraction of the product that has to be returned to the process [81 ]. Secondly, problems of non-uniform mass flow (surging) and non-uniform particle size (drifting) exiting the granulator coupled with the large dead time make it difficult to control the granulation plant at a steady state. In extreme cases these problems can result in plant shutdown [1 1]. Fundamentally, fertiliser granulation is similar to agglomeration in other sys tems such as pelletisation, flocculation, crystallisation and aerosols. Of these, the closest is pelletisation. However, because fertilisers are soluble, chemical com position of the particles significantly affects the agglomeration process. Com pared to soft and plastic pellets, recycled fertiliser granules are hard and cannot easily be deformed. These recycled particles have a very broad size distribution, which overlaps the distribution of product granules [3]. The following section describes the effect of process parameters on the drum granulation of NPK fertiliser in bench-scale batch systems. Although these data are specific for the
243
Drum Granulation Processes
fertiliser grade (27:6:6 in this case), many of the conclusions can be applied to general fertiliser granulation and indeed to other drum granulation processes. 5.2. Effect of solution to solid-phase ratio
The effect of solution to solid-phase ratio on NPK drum granulation is iIIustrated in Figs. 9 and 10 as a plot of solution-phase ratio vs. the mass-median diameter (d50) of the granulate at the end of each experiment. As with all fertiliser materials an increase in solution-phase ratio results in an increase in median granule size. The results also show a similar trend to those of other researchers in that gran ulation is weak, with a small increase in d 50, at low solution-phase ratios. At higher solution-phase ratios, depending on granulation time, d 50 increases sig nificantly, indicating a high degree of granulation [50,80]. Figure 1 1 i1lustrates the frequency size distributions for NPK fertiliser with in creasing moisture content. At all moisture contents (4-8% mOisture), almost all the fine material from the initial distribution was removed up to a critical size with this fine material agglomerated into granules having a broad size distribution. The relationship between moisture content and particle size distribution indicates that the finer material is removed but also gives an indication of how the granulation proceeds. At 4% moisture, the "s" curve is relatively shallow, but as the moisture content is increased to 6% the curve becomes steeper although the mass-me dian diameter remains fairly constant. At 8% moisture, the shape of the "s" curve is very similar to that of 6% except that the curve has been shifted towards the higher particle size range [50,80]. 4.5 -,-------,--,--, 4
3.5 3
� 2.5
.g.
2 1 .5
0.5
-+
--
1-
���----�i==-=�===
o �---+---�--�--� o 0.05 0.1 0. 1 5 0.2 0.25 y
Fig. 9. Effect of solution-solid-phase ratio on dso for variation i n granulation time (drum diameter 25 cm, four radial flights) [50]. =
244
G . M . Walker 7
6 f- - -.. - d
___tr_ d
�d
- 25cm
38cm 25cm (flights)
= =
5 0 4 -It)
Q.
" 3 2
:/ :1 ..11 ../ / •
�
--r
-o
0.05
o
0.1
I
0. 1 5 y
V
/
0.2
0.25
Fig. 1 0. Effect of solution-solid-phase ratio on d50 for variation i n flight arrangement and drum diameter (granulation time = 5 min) [50].
45
·
'1
35
:: ::
Ci
,
40
30 25
"if!. 20
15
·
.
·
,
rr----
-+- initial �8% '0- - 6% - 4% •
/ '\. , . '\. / , '\. }--, , / \ I ....... Li: . \ . . . / . \..'� .� .� ..... j .0 � ,
0-,
10
.
5
.
o o
2
4
6
8
10
dp (mm)
Fig. 1 1 . Effect of moisture conte nt o n particle size distribution (granulation time 25 cm drum, no flights) [50].
=
1 0 min,
5.3. Granulation kinetics
From Fig. 9, the transition in granulation occurs at a solution-phase ratio of between 0. 1 3 and 0 . 1 8 for a granulation time of 1 0 min and between 0. 1 8 and 0.24 for a granulation time of 5 min. Similar results were found by previous researchers with other fertiliser materials in that high degrees of granulation are dependent upon both solution-phase ratio and granulation time. The kinetics of fertiliser granulation have been described previously by Ennis et al. [38] in terms
245
Drum Granulation Processes
of the viscous Stokes number, which was defined as the ratio of the relative kinetic energy between colliding particles to the viscous dissipation about the pendular bond. Adetayo et al. [24] modified this original relationship (equation (8)) for drum granulation, yielding the following equation: 8p rwR Stv = g9/1 (22) where: Pg = granule density, kg m- 3 ; r = effective granule size, m; w = granulator speed, S- 1 ; R = granulator radius, m; and /1 = binder viscosity, kg m- 1 S- 1 . The three granulation regimes were defined in terms of the magnitude of Sty in comparison with St�. as before: non-inertial regime; inertial regime; coating regime. The results plotted in Figs. 1 2-14 i1lustrate these regimes quite neatly. Gran ulation with 4% moisture (Fig. 1 2) i1lustrates the non-inertial regime with similar distributions for 5 and 1 0 min indicating an equilibrium has been reached. Gran ulation with 6% moisture i1lustrates intermediate inertial regime with a narrowing of the distribution and a slight increase in particle size with time (Fig. 1 3). Granulation with 8% moisture (Fig. 1 4) shows the effect of the coating regime, with a significant increase in particle size with time caused by preferential coalescence. It was noted that in this granulation system preferential coalescence is undesirable with most of
:: ::
45 ,-
� �
J-
I =-l - -1 �
--� -------
initia� l o ns :: � ��s
----�--
--
-+-
--
15 10 5
o o�---��-+-+��--�----+ 2 4 6
8
10
dp (mm)
Fig. 1 2. Effect of granulation time on particie size distribution (moisture content 25 cm drum, no flights) [50].
=
4%,
246
G . M . Walker
45
40 I ..,
'1
1\ 11 \ \ .A \ j \ j I 1\/\ \.. / �/\ h-""
35 30 � 25 � � 20 0 15 10 5 o
i
o
j� 1\ 2
4
___ initial -0- 1 0 mins ---b- 5 mins
.J>..
---
dp (mm)
6
-
10
8
Fig. 1 3. Effect of granulation time o n particle size distribution (moisture content = 6%, 25 cm drum, no flights) [50].
45 r------,--�--�=c====� --- initial 40 +--"'�---+---�-----I -o- 1 0 mins 35
-Ir-
5 mins
30 �--+---+---����-n--�
-+�-4-+--��---��-� � 25 ���
o
2
4
dp (mm)
6
8
10
Fig. 1 4. Effect of g ranulation time on particle size distribution (moisture content = 8%, 25 cm drum, no flights) [50].
granulate above 5 mm in size, and thus would be termed oversize in most fertiliser plants [50]. 5.4. Effect of viscosity of binder solution
It has been shown that when water is added to dry seed particles the water dissolves some of the fertiliser salt so that the binding liquid is a saturated fer tiliser solution. It has been postulated that the viscosity of the saturated solution is a factor in the degree of granulation attained in a particular system [24]. To
247
Drum Granulation Processes 9
8 7
- 1�1 - -� - L
,-----,----,--�D�AP
1-
-
.-
-
--r
i-
2
o
- _I
f--
,
-
I
.-
__
L
j
L _K i -- i -
-
-
I
-1-
-------j
-
-
----l -
--+ -
-T - L _ L -1 L_ I - .
-
___
�--�-�I--�----4---� 4 6 5 2 3
o
dp 50 @ Y
=
0.1 5
Fig. 1 5. Effect of slurry viscosity on extent of granulation for fertiliser salts [50], after Adetayo et al. [24] . (AS, ammonium sulphate; MAP, mono-ammonium phosphate; and DAP, di-ammonium phosphate).
Table 1 . Solubility and viscosity of fertiliser materials [50,80]
(solubility 9 per 1 00 9 water)
Fertiliser salt Ammonium nitrate Mono-ammonium phosphate Di-ammonium phosphate Potassium chloride 27.6.6 fertiliser
Solubility 1 000e 871 .0 63.4
Solubility 200e 1 92.4 27.2
60
40.8
77.3 1 043
37.2 202
Sat. soln. viscosity 200e
5.5 cps
investigate this theory, the viscosity of the NPK saturated solution was deter mined with the granulation potential then compared with the work of previous researchers in Fig. 1 5, as a plot of viscosity vs. d50 at a constant solution to solid phase ratio of 0. 1 5. This analysis enables fertiliser salts with different solubility to be compared for granulation potential. The viscosity - d50 relationship follows c10sely that of a straight line with the NPK datum falling neatly between the published work [24]. This analysis appears to confirm that binder solutions having a high viscosity will result in a higher degree of granulation for a given solution phase ratio [50,80] (see Table 1 ).
248
G.M. Walker
5.5. Effect of flight arrangement and critical speed
To investigate the effect of drum flights and speed, two further pilot-scale drum granulators were developed, a 25 cm drum with 4 x 3 mm flights and a 38 cm diameter drum. The critical speed within drums is the speed at which material can be just carried around the drum by centrifugal action. In terms of the Froude number ( = n2 O/g) describing the ratio of inertial to gravitational forces, the crit ical speed can be defined in Section 1 as nF r = 42.4 O-o. s , where n is the ro tational speed (rpm) and 0 is the drum diameter (m). In practice, good granulation can be achieved in drums containing no internal flights at speeds nFr� 0.3-0.5. For drums containing internal flights, the optimum speed for good granulation is nFr� 0.2 [9]. Table 2 indicates the critical, operational and optimal drum speeds for the granulators used in this work [50,80]. Results from granulation with variation in speed and flight arrangement are iIIustrated in Fig. 1 0 as a plot of dso vs. solution-phase ratio. It can be seen from the plot that the non-flighted drums show a higher degree of granulation compared to the flighted drum for a given solution-phase ratio. Fur thermo re the non-flighted drums indicate almost identical granulation, with the 38 cm diameter drum granulating slightly better than the smaller drum. These results show good agreement with the optimum design speeds postulated in the literature for industrial rotating drums in that the operational speed for the flighted drum was almost twice the optimal speed, which resulted in poor granulation. 80th the non-flighted drums were operated at near optimal speed, which resulted in increased granulation. It was also noted that the larger drum gave a slightly better performance with a speed in excess of the optimal compared to the smaller drum was operated under the optimal speed. It must also be noted that operating a granulation unit to produce granules with dp50 in excess of 6 mm may not always be practical in a continuous fertiliser granulation process if the particle size of the product would be approximately 2-5 mm. However, these results iIIustrate that granulation to the product size range can be achieved with less solution phase in drums which are operated at the optimal rotation speed [50,80]. Table 2. Rotational speeds for drum granulators [50,80]
Drum diameter (m)
Critical speed (rpm)
0.25 0.38
84.6 68.6
Operational speed (rpm) 36 24
Optimal speed (rpm) 34 27
Drum Granulation Processes
249
6. FUTU RE DEVELOPMENTS IN DRUM GRANU LATION MODELLI NG 6. 1 . I ntroduction
Ennis and Utster have indicated that the advantages of granulated products include improved flowability, reduced dustiness and the co-mixing of materials that would otherwise segregate. Despite the fact that granulation processes have been employed in a number of industries for several decades, it is common that granulation plants operate below design capacity, due in part to high recycle ratios and unsteady-state processing conditions. Recycle ratios in granulation circuits can range from 2: 1 to 6: 1 [3] and even as high as 1 : 1 0 [80] in some instances. These problems are exacerbated by the nature of the granulation circuit operation in which changes in operating conditions are amplified and may eventually lead to the plant being taken offline with excess recycle material being removed from the granulation loop. Sastry [82] has illustrated that the develop ment of a process engineering approach to the design and control of granulation systems may alleviate many of these seemingly inherent problems. Although significant progress has been made in recent years on fundamental studies on granulation mechanisms, it is generally accepted that current mac roscopic models have not showed good correlation with plant data and are gen erally un-used in the design and control of granulation plants. The poor correlation is amplified by the granulation recycle loop, but three core problems have been highlighted by Wang and Cameron [83]: 1 . In granulation drums, the spraying of the liquid binder onto the surface of the powder creates a large number of relatively soft granules by a nucleation-type process. This initial nucleation is an important factor in determining the extent of further granulation in the drum and by extension the recycle ratio in the plant. This mechanism has yet to be included into models for granulation processes. 2. The process of granulation can be divided into a number of distinct stages, namely wetting and nuclei formation, compaction and consolidation and growth by coalescence. It follows that different granulation mechanisms will predominate in different sections along the length of the drum (not withstand ing issues of recycle). In most cases, however, a unified population balance model is conventionally used to describe drum granulation. 3. Within the granulation drum, the transport characteristics of the materials vary along the drum length with segregation and mixing of different-sized materials occurring. Furthermore, this transport problems may be further complicated by the inclusion of internal flights or dam rings within the granulator. Wang and Cameron conclude, "there exists a notable gap in knowledge bet ween microscopic level studies and plant scale modelling. Consequently, future
250
G.M. Walker
research work should focus on the construction of a bridge to link these two areas via the development of mesoscopic level models" [83]. 6.2. Fundamental studies on g ranulation
Ennis and Utster have identified four sub-processes within granulation: wetting and nuclei formation, compaction and consolidation, growth by coalescence and attrition and breakage. The first three sub-processes have received considerable attention, with notable micro-Ievel-based studies using liquid-bridge theory proposed by Ennis et al. [38]. This study has been extended by Uu et al. [12] to take into account plastic granule deformation during collision. These studies have lead to the development of Iveson's growth regime map [41 ,84] which identifies granulation processes based on granule deformation characteristics and fraction liquid saturation of the granulate. Nucleation kinetics and the characterisation of powder wetting have been compre hensively studied by Hapgood [85]. Within the area of numerical simulation, the discrete element method (DEM) has been successful in describing the phenomena of impact strength and breakage and impact coalescence. Despite these recent advances these models are not commonly used in industrial practice [83]. Conven tional population balance models using single-stage kemels are commonly solved by discretisation methods such as that developed by Hounslow et al. [61] and Utster et al. [86]. Some initial studies undertaken by Ennis et al. [38] and Uu et al. [42] have lead to the development of multi-stage coalescence kemels by Adetayo et al. [1 1 ] and unified kemels (Adetayo and Ennis [43] and U u and Utster [87]). 6.3. Physically based drum g ranulation models
The multi-stage coalescence kemel model developed by Adetayo et al. [1 1 ,24] (detailed in Section 4) was employed to simulate steady-state drum granulation processes. A laboratory-scale batch granulator was used to determine parameter estimation and for model validation. This was followed by a prediction for scale-up for a steady-state industrial-scale granulator. In a more recent study, Adetayo and Ennis have developed a unifying ap proach to modelling the coalescence mechanism, which was based on a suc cessful collision criterion. Liu et al. [42,88] have further improved and extended the method to more general granulation processes. It has been suggested, "these approaches have provided a starting point and baseline for further re search on dynamics, design and control of granulation processes" [83]. 6.4. The modelling of granulation processes - future d irections
The review of the modelling and future directions of continuous drum granulation, by Cameron and Wang, noted that the emphasis on drum granulation research
Drum Granulation Processes
251
should be concentrated on the modelling optimisation and control of the drum granulator itself, which they describe as the "bottleneck" in the entire granulation circuit. However, they also make a very valid point that a granulation circuit is a highly interactive system and without taking other processes such as crushing and size classification into account, it would be impossible to achieve optimal control of the granulation circuit [83]. They recommend that the future direction of drum granulation modelling should concentrate on the development of structure switching models, which incorporate models with a different structure for different parts of the granule formation proc ess. These models should account for the fact that a granulation drum can conceptually be divided into several zones, each represented by a different model structure. Nielsen and Villadsen [88] have described the development of pop ulation balance models with multiple particle properties, such as size, age and porosity. A multiple model has also been developed by Schroder and Cameron [89] to complex mineral processing. This new switching model could be incorporated into a model describing the overall granulation circuit taking into account solid and liquid transportation in rotary drums. Furthermore, Cameron and Wang suggest that a model hierarchy be developed with emphasis placed on the determination of control relevant models [83]. To develop an overall model studies on liquid-solid mixing, solid segregation and transport in the rotary drum are necessary. Wang et al. [90-92] have undertaken studies in heat and mass transfer and solid transport in flighted rotary drums based on rigorous mathematical analysis. Ottino and Khakhar [93] in a review paper have explained the current status of mixing and segregation research. Models relevant to drum granulation processes include random walk models [94,95], geometrical techniques for mixing in rotary drums [96]; discrete element methods and particle dynamic simulations [97,98]. Cameron and Wang further indicate that the final outcome of DEM research in this area may comprise of a set of simplified zonal models for the prediction of liquid and solid distribu tions in both the radial and axial directions to account for several zones with moisture contents and size distributions. REFERENCES [ 1 ] B.C. Reddy, DVS. Murthy, CD.P. Rao, Part. Syst. Charact. 1 4 ( 1 997) P257-P262. [2] H . E . M . N . Moursy, Granulation of Nitrophosphate Fertilisers, PhD thesis, Queen's University Belfast, 2002. [3] P.J. Sherrington, R. Oliver, Granulation, Heyden & Sons Ud., London, GB, 1 98 1 . [4] W . Pietsch, Size Enlargement by Agglomeration, Wiley, London, 1 99 1 . [5] K.V.S. Sastry, D .w. Fuerstenau, Powder Techno!. 7 ( 1 973) P97-P1 05. [6] P.B. Linkson, J . R. Glastonbury, G.J. Duffy, Trans. Inst. Chem. Eng. 51 ( 1 973) P251 -P259. [7] H. Rumpf, Chem. Eng. Tech. 30 ( 1 958) 1 44.
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[92] F.Y. Wang, ! .T. Cameron, J.o. Utster, V. Rudolph, Drying Techno!. 1 3 (5-7) ( 1 995) 1 26 1 -1 278. [93] J . M . OUino, D.v. Khakhar, Annu . Rev. Fluid Mech. 32 (2000) 55-9 1 . [94] S . o. Guptar, D.v. Khakhar, S.K. Bhatia, Powder Techno!. 6 7 ( 1 99 1 ) 1 45-1 5 1 . [95] S.J. Rao, S . K. Bhatia, D.v. Khakhar, Powder Techno!. 67 ( 1 99 1 ) 1 53-1 62. [96] G. Metcalfe, T. Shinbrot, J.J. McCarthy, J . M . OUino, Nature 374 (2) ( 1 995) 39-41 . [97] J.J. McCarthy, D.V. Khakhar, J . M . OUino, Powder Techno!. 1 09 (2000) 72-82. [98] PW. Cleary, Powder Techno! . 1 09 (2000) 83-1 04.
CHAPTER 5 Rol l P ress ing Pierre GUigo n , a , * Olivier Simon,a Khashayar Saleh ,a
G u ru rajan B i n d h u mad hava n , b M ichael J. Adams, b and Jonathan P. K . Sevi lle b
a Universite de Technologie de Compiegne, BP 20529, 60205 Compiegne, France b Centre for Formulation Engineering, Depanment of Chemical Engineering, University of Birmingham, Birmingham B15 2TT, UK Contents
1 . I ntroduction 2. Description of the roll compaction process 3. Roll pressing in practice 3. 1 . Types and arrangements of roll compactors 3.2. Roll type 3.3. Feeding systems 3.4. Sealing 3.5. Powder de-aeration 3.6. The overall picture: compaction behaviour and material properties 3.7. Common problems in roll pressing 4. Modelling 4. 1 . Johanson's model 4.2. Analogy with uniaxial compression 4.3. Other approaches to modelling 4.3. 1 . Finite element method approach 4.3.2. Discrete element method 4.3.3. Neural networks and genetic algorithms 5. Roll compaction simulators 6. Experimental investigations 6. 1 . Effect of powder properties and process parameters 6.2. Roll compaction using a screw feeder 6.3. Roll-press throughput 6.4. Roll-gap variation 6.5. Motion of the particles in the nip zone 6.6. Distribution of the compact heterogeneity 6.7. Novel techniques and improvements 7. Forward look Acknowledgements References
*Corresponding author. E-mail:
[email protected]
Granulation
Edited by A.D. Sa/man, M.J. Houns/ow and J. P. K. Seville r 2007 B.V.
Elsevier
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1 . I NTRODUCTION
Roll compaction is a continuous dry granulation process which is widely em ployed in the pharmaceutical, chemical, minerals and food industries in order to manufacture free-flowing agglomerates. An emerging application is the vast field of waste recycling and disposal. Although the process has been in use for many years, it has recently attracted renewed scientific attention, and usage in pharmaceutical operations is increas ing [1-3]. Several authors (as described in Section 4) have attempted to develop models of roll compaction in order to aid in the design and control of the process. However, as described later, there are many factors that contribute to the per formance of the process and a comprehensive model is not yet available. Most industrial roll compactors continue to be designed largely on an empirical basis. Roll compaction is conceptually very simple: the feed powder is passed through two counter-rotating rolls with the flow being induced by the friction acting at the surfaces of the rolls. The powder is subjected to high pressure in the narrow gap between the rolls, leading to the formation of a compact in the form of a continuous strip or discrete briquettes. This is sometimes the final product form. In the pharmaceutical industry, however, the compact is subsequently re duced in size by milling and screening in order to produce a granular powder which will flow easily in subsequent process steps, usually including tableting into a final product (Fig. 1 ). Roll compaction is designed to improve the flow properties, increase the bulk density and ensure the uniformity of particulate formulations, in order to prevent the segregation of pharmaceutical drugs, for example. It ofters advantages com pared with wet granulation for processing physically or chemically moisture sensitive materials since a liquid binder is not required. A further advantage is that it does not require a drying stage and is therefore suitable for use with compounds that either have a low melting point or degrade rapidly upon heating [1 ,4]. Against this must be set the fact that roll pressing itself generates heat, which must be removed in some applications. Roll compaction is a continuous process which can also be operated in a batch or semi-batch mode, while the other granulation methods are usually run in batch mode and are not readily adapted to allow continuous processing. The absence of a drying stage means that the throughput per volume employed is rela tively large compared with other methods. Except for electrical supply, service connections are not required. Wennerstrum [5] lists the advantages of the process as: •
uniform blends production of granules of uniform consistency and minimising segregation problems due to d ifterences in particle size, shape and density; -
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Roll Pressing Excipients
Active drug
I
�
Roll Compaction
I
1 1
MiLling
Tablening
Fig. 1 . Typical tableting process using roll compaction.
•
•
•
•
uniform particle size range roll compaction can assist in producing uniform granules of a specific size to meet precise requirements; improved f/ow properties compacted granules have improved flow charac teristics compared with powders and resist bridging and caking; controlled dust this can reduce waste and also improve safety by reducing operator exposure; increased bulk density increasing the bulk density will make it easier to han dle, transport and store the material. -
-
-
-
The key factor in roll compaction is that the binding of particles results from the compression forces alone. The choice of powder to be compacted is there fore critical. So me active ingredients can be compressed directly. Others may be processed in combination with another material, which is selected for its favour able compaction properties. Consequently, the bulk of the material to be com pacted often consists of an excipient or mixture of excipients, which are the materials that are mixed in with a drug in order to control drug delivery, to en hance patient acceptability and to aid in the tableting process. Pharmaceutical excipients may be any substances other than the active drug or prodrug, which have been appropriately evaluated for safety, such as microcrystalline cellulose, dicalcium phosphate and magnesium stearate.
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2. DESCRIPTION OF THE ROLL COMPACTION PROCESS
It is usual to consider that there are three zones of material behaviour in roll compaction, which correspond to the slip, nip and release regions [6]. The boundaries between the regions are defined by their angular positions (Fig. 2). The slip or entry region occurs before the nip region and is characterised by the feed partie/es slipping at the roll surface. Partie/e rearrangement and de-aeration can occur in this region, but the pressures exerted on the powder are relatively smalI. The powder behaviour in the slip region depends on the wall friction and inter-partie/e friction of the feed powder. The start of this region is defined by the entry angle8h, which is often determined by the feed arrangement. The nip region starts at a roll angle a , termed the nip angle, where the wall velocity of the powder becomes equal to that of the rolls. The powder is 'nipped' and densifi cation occurs due to the reduction in the gap width as the powder is dragged to the point of e/osest approach. This results in a substantial increase in the roll pressure (Fig. 3), up to a maximum at the neutral angle, which does not nece ssarily occur at the smallest roll gap because of wall slip and other factors. The
D
Slip region
D
Nip region
•
Release region
Fig. 2. Schematic diagram of the roll compaction process (vertical feed).
Normal
.-.i!!i!"!lll---- Compact
stress ==> Rolling direction
A n g le
Fig. 3. Stress distribution in the nip region (horizontal feed).
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Roll Pressing
nip region or compaction zone corresponds to a very small portion of the roll, often less than 1 0°, depending on the material characteristics and operating parameters. The release is initiated when the roll gap starts to increase again. The size of the release region depends on the stored elastic strain in the compact, the rate at which it is released and the roll speed. After ejection, the compact may increase in size due to elastic recovery, resulting in a larger strip thickness than the roll gap. In general, the maximum pressure applied in the nip increases with increasing nip angle, decreasing roll gap and decreasing roll speed. These effects are con sidered in more detail below.
3. ROLL PRESSING I N PRACTICE 3.1 . Types and arrangements of rol l compactors
Roll presses from all manufacturers consist of the same basic elements and have similar configurations. Commercially available roll compactors have rolls mounted in a horizontal, vertical or even inclined position as shown in Fig. 4(A-C).
A
(i)
(ii)
(iii)
Fig. 4. Configuration of roll presses - feed arrangements: i nclinations (A, B, C) and screw arrangements (i, ii, iii).
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P. Guigon et aJ. Roll Axe Bearing
Cantilever shaft design
Mill-shaft frame design
Fig 5. Bearing arrangements.
Feed may be by gravity or via one or more screw feeders, as in Fig. 4(i-iii). The relative merits of these configurations are still a matter of debate among manufacturers and practitioners. The issues are discussed further below by Bultmann [7]. Two different frame designs exist (Fig. 5), which are distinguished by the location of the press rolls with respect to the frame. In cantilever-shaft designs, the rolls are located outside the frame. This design is normally used for smaller machines and it allows easy access to the rolls for maintenance tasks. Larger machines use the mill-shaft frame design. This means that both ends of the two shafts are pivoted in bearings and the rolls are located within the frame. Generally, the bearings of one of the rolls are fixed in relation to the frame, while the bearings of the other movable (floating) roll are maintained in position by an adjustable hydraulic pressure. In some presses, however, particularly for small-scale experimental work, the rolls are fixed in relation to each other. 3.2. Rol l type
Rolls are available in different geometries (smooth, fluted, pocket design) and in different surface finishes for briquetting (Fig. 6), pocket shapes are optimised in order to diminish ejection problems and breakage of compacts. The maxi mum applicable stress on a compact depends greatly on roll diameter; greater stresses are generated on larger machines. The roll drive assembly must ensure a constant torque and an equal velocity of the two roll shafts in order to prevent early wear of the rolls and shearing forces that wil l fracture the compact. Particularly in the case of briquetting, both rolls must rotate with exactly the same speed.
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•
... Fig.
6. Briquetting in a roll press.
3.3. Feeding systems
The feeding system is an extremely important element of the compaction proc ess. It must achieve a uniform and continuous flow of material in order to fill the nip between the rolls correctly and sufficiently, so that the compacts formed are not heterogeneous. The feeding system frequently also serves to densify and de-aerate the powder. Two different types of feeding systems are used, depending on the flow prop erties, the density of the powder and the densification required to produce com pacts of sufficient quality: • •
gravity feed for free-flowing particles and force feed (powder is pushed towards the rolls by one or several screws).
If the powder shows good flowability, a sufficient bulk density and good com paction behaviour, gravity feeding is possible. However, problems due to feeding fluctuations and air escaping through the powder bed may occur, leading to compact heterogeneity and reduced roll velocity. Pietsch [4] gives some hints as to how to address these problems. For fine, light and/or poor-flowing powders such as those frequently encoun tered in the chemical and pharmaceutical industries, force-feeding is essential. The feeding screw controls the throughput, predensifies the powder and exerts a precompaction on the powder bed. The screw geometry and position depend on the manufacturer. The screw can be set vertically, horizontally or even inclined (Fig. 4(i-iii)) as mentioned previously.
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3.4. Sealing
In order to prevent the powder leaking from the compaction zone, the rolls have to be sealed at either side. This can be achieved either by a side-plate assembly ('cheek plates') or by use of rimmed rolls. In order to prevent metal-metal friction and wear, a sheet of low-friction material such as PTFE can be positioned between the side-plate and the rolls. Since the degree of densification is quite high in the compaction zone, the cheek plates can be deformed by the high lateral forces. This could lead to insufficient sealing, which would allow powder to escape from the compaction zone, leading to ribbons with weak andjor crumbling edges. The effects of such leakage on the pressure generation were investigated by Michel [8,9]. The rim roll assembly consists of one roll with two rims (one at each side of the roll), while the other roll runs within this cavity. Since the rims are mounted on the roll, they can resist high lateral forces without losing the sealing capability. This arrangement is also employed in roll-type comminution machines. 3.5. Powder de-aeration
The air fed with the powder can only escape by two paths: through the powder in a direction counter-current to the feed, and through the gap between the rolls and the cheek plates. Some air can be compressed inside the compact. This is a key factor limiting compaction production throughput and compact quality [1]. Vac uum de-aeration before the nip roll region is used to improve roll compaction of fine powders. 3.6. The overall pictu re : compaction behaviour and material properties
Figure 7 summarises the main factors influencing roll-pressing performance and the characterisation steps that are necessary in a full study. In addition to the process parameters discussed above, the properties of the feed powder are of great importance, particularly its frictional properties, compressibility and perme ability. These are all influenced by the size distribution (see for example, Seville et al. [1 0]). In order to measure the powder properties, it is necessary to employ a range of laboratory test equipment, including shear cells, uniaxial compaction cells and permeability testers. Dec [1 1 ] gives some schematic procedures and Mansa [ 1 2] discusses their use in a specific example of pharmaceutical roll pressing. 3.7. Common problems in rol l pressing
Figure 8 shows some of the problems which can occur in compaction between smooth rolls of fine and very fine powders; such problems are usually not found
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Roll Pressing Step... In fluderstand roll cOI1Ipocrioll
I.
I. Feed powder c1lOraClerisarioll
PanieIe size
Feed powder characterisation
Size distribution
2. Compac tion proccss characterisation
Angle of i n tern al
frietion
3. Prod uct ch.ractensation Angle of wall fnction Compressibility Bulk density 2. Compacrion process characterisatioll
ip angle 3. ProduCI dwracter;Slllioll
Roll gap
Compact strength Roll speed
Bulk density Roll surface friction Porosity
Pressurc profi l e
Microstructure analysis
Panicle velocity
Compact thickne s
Fig.
7. Characterisation of the overall roll pressing process.
A
B
c
D
E
F
G
H
Fig. 8. Common defects observed on compacts when using fine feed [1 1 ] . A, dense good quality compact; S, material release in powdery form, but with increased bulk density; C, compact breaks into regular pieces with v-shape cross section; 0 , no compaction on the edges; E, compact breaks in the middle into two separate strips; F, compacts shears into two parallel strips; G, non-uniform density across roll width; H, non-uniform density in the transverse direction.
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with eoarser, more permeable granular materials. The main problems are linked with defeets of feeding and too short an applieation of eompaeting stresses on the eompael. Feeding defeets are usually eaused by poor powder flowability or by perturbations due to air being squeezed out from the eompaet during the eom paetion proeess. Fine powders, whieh usually have low permeability and poor flowability, eommonly exhibit sueh problems. A detailed understanding of the behaviour of the powder at the exit of the serew and in the eompaetion region of the press is neeessary in order to optimise the properties of the eompaet (e.g. strength, homogeneity) and throughput of the press and also to minimise the produetion of uncompaeted material in powdery form. 4. MODELLING 4.1 . Johanson's model
Johanson [6] developed the first detailed model enabling a predietion of the behaviour of a powder undergoing eontinuous shear deformation bet ween rolls. The model improved the understanding of the relationship between the powder properties, the roll eompaetor geometry and the proeess para meters, and has been widely applied sinee. Johanson's ( 1 965) model [6] was based on the Jenike yield eriteria for steady state particle flow in silos and hoppers. The material is assumed to be isotropie, frietional, eohesive and eompressible and also to obey the effeetive yield funetion proposed by Jenike and Shield [1 3]. For the plane strain eondition between the rolls, the effeetive yield funetion ean be represented as in Fig. 9. The yield loeus was eombined with the equilibrium equations to give a system of partial hyperbolie differential equations, whieh ean be solved using appropriate boundary eonditions. Assuming slip oeeurs along the roll surfaees in the feed
J
Wall Yield Locus
Effective yield locus
2v ._---Fig.
a
----�)I
9. Jenike-Shield yield criterion for the slip region.
...---
Stress circle
aj
Normal Stress, Ci
Roll Pressing
265
region, Johanson showed that the pressure gradient (dO" /dx) in the slip region is given by the following relationship:
(dO")
dx slip
- � [1
40"(� - e - v) tan bE + � - cos 8] [cot(A - J1) - cot(A + J1)]
(1)
where e is the angular position at the surface of a roll, such that e = 0 corre sponds to the minimum gap, and the parameter A is given by A=
e+v+�
2
The acute angle, v, between the tangent to the roll surface and the direction of the major principal stress, 0"1 , is given by (see Fig. 9):
--
. sin 1> w - 1> 2v = n - arcsln w sin b
(2 )
In the nip region, a simplified material model was applied. It was assumed that no slip occurs along the roll surface and that all material trapped between the two rolls at the nip angle must be compressed into a compact with a thickness equal to the roll gap, as shown schematically in Fig. 1 0. For smooth rolls, the pressure, 0"0, at any e < Ci can be related to the pressure at the nip angle, by the following empirical pressure-density relationship: 0" = 0" [po]
o" x ,
e
x
Px
K
[(1(
]
1 + SjD - CoSCi) cos Ci K = 0"11 + SjD - cose) cos e
(3)
where K is the compressibility factor, which is determined from the slope of logarithmic plots of the density as a function of pressure in uniaxial compaction. An example of such a plot is given as Fig. 1 1 . Va
Fig. 1 0 . Geometry of the compression.
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...
�
7.2 ,------T--r---� ' : Peak pressure range obtained 7.1 : during roll compaction process , 7.0
oS
6.9
�
6.8
,, ,,
6.7 +------L--.---.---b--,� 3.7 3.2 5.2 4.2 4.7 In (0") Fig. 1 1 . Example of determination of compressibility factor,
K [14] .
The pressure gradient for the nip condition is given by:
(dadx)
Kao (2 cos e - 1 - S/D) tan e = nip � [(1 + S/D - cos e) cos eJ
(4)
Johanson [6] proposed that the pressure gradients in the slip and nip regions are equal at the nip angle, et, thus: (5)
The point of intersection of the pressure gradient curves (Fig. 1 2) then corre sponds to the nip angle. Hence, et can be deduced by solving equations ( 1 ) and (4): 4 (� - et - v) tan JE [cot(A - /1) - cot(A + /1)]
K(2 COS et - 1 - S/D) tan et GOS et
(6)
Thus the nip angle depends on the compressibility factor, K, the material flow properties, JE and o/w, the roll diameter, 0, and the roll gap, S. Bindhumadhavan et al. [14] present an example of the use of the theory in practice. Figures 13 and 14 show examples of experimental results compared with theoretical predictions for roll pressing of microcrystalline cellulose. In order to use the Johanson model, the following input parameters are required: • • • • •
effective angle of internal friction, JE, and wal l friction,o/w; compressibility, K; pre-compaction pressure, Po; roll geometry (face width, W, and roll diameter, 0); roll gap, S.
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Roll Pressing
Slip region Nip region
...
... ...
er,
e"
Angular position (6) Fig. 1 2. The pressure gradient as a function of angular position [6].
1 20 --'"
06 Q) .... ;:l CI> CI> Q) ....
0-
mm Olm 1. 2 - . - . 1.1.25 111Olm m mm . . . . - - 1.5 Olm --- 2 0.9
-- 0.9
80
o
60
:t::
40
t,.
20 0
(Ex pt) (Johanson) (Expt) (Johanson) (Expt) (Johanson) 2 01111 (Expt) 01111 (Johan on )
o
1 00
0
2
4
6
8
10
12
Angle (deg. ) Fig. 1 3. Effect of the roll gap o n the pressure profile [ 1 4]: the curves are calculated from Johanson's theory.
Using the input data, the following predictions can be made: • • • • •
nip angle, a ; pressure profile in the nip region; roll force and torque; effect of material properties on the roll compactor performance; effect of process parameters on the roll compactor performance.
An important factor that is ignored in Johanson's theory is the effect of roll speed. As explained earlier, as the powder is progressively densified, a fraction of
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70 �------�
� 60 6. 50
�
40
� 30 CI)
.e- 20
,f 1 0 nl
O +---�--�----�
10
12
14
16
18
20
Wall friction angle (deg) Fig. 1 4. The effect of wall friction on the peak pressure [ 1 4]; see reference for experi
mental details; the curve was calculated from Johanson's theory.
the gas initially contained within it may be expelled, thus disturbing the entering powder flow and leading to a non-uniform feed. It is easy to show [8] that the minimum fluidisation velocity of the powder can be exceeded, in which case the entry flow rate will be severely reduced. Bourseul [1 5] developed a semi-empirical adjustment to Johanson's theory that takes the effect of roll speed into account. In summary, Johanson's theory employs a mass-continuity relationship and a simple power law for the stressjdensity relationship in the nip zone. This ap proach enables the nip angle to be predicted, provided that the compaction be haviour of the powder is known. The main advantage of Johanson's theory is that it requires a limited number of experimental parameters for the powder: the wallj powder and internal angles of friction, and the compressibility factor, which is obtained from uniaxial compaction tests. The theory also draws an analogy be tween roll pressing and uniaxial compaction. For 8 < rx, the 'column' which is nipped by the rolls is compacted in a similar, but obviously not in an identical manner to that which occurs in confined uniaxial compaction. 4.2. Analogy with uniaxial compression
Direct measurement of the pressure in the nip region - using techniques described in the next section - allows the pressurejdensity relationship for roll pressing to be obtained. Figure 1 5 shows an example of the strip or compact density as a func tion of the maximum pressure for roll-pressing data, compared with the data from uniaxial compaction measurements of the same material - microcrystalline cel lulose. The results are shown to be in comparatively good agreement, despite the rather approximate nature of the analogy between the two compaction methods. Similar agreement has been shown for compaction of alumina [8] and Perera [1 6] has also shown close agreement between the roll pressingjdensity relationship and the Kawakita equation [1 7], which is a correlation originally developed for uniaxial compaction measurements. This suggests that uniaxial compaction is a
269
Roll Pressing 1 800 1 600
� � � � c
•
1 400
•
1200 1 000 800
y = 0 . 4583x + 1025
•
2 R = 0.951
600 400 200
•
Roll pressing ... Uniaxial compaction
O +-------�--�--__, 1 000 800 o 200 400 600
Pressure (bar) Fig. 1 5 . Density-pressure relationship for microcrystalline cellulose AV-1 02; roll pressing and uniaxial compaction data superimposed.
good means of testing materials for their roll-pressing properties, provided that their compression behaviour is not strongly rate-dependent. 4.3. Other approaches to modelling 4. 3. 1. Finite element method approach
Dec et al. [1 8] used the finite element (FE) technique to analyse the compaction of powder during rolling. A 2D FE model for the rolling process was developed using the commercially available ABAQUS code. FE modelling was carried out for a horizontally screw-fed roll compactor with a roll diameter of 1 00 mm. The position of the roll and the material mesh were defined for a prescribed gap of 2.0 mm. A pressure-dependent yielding plasticity model (the modified Drucker-Pragerjcap model) with linear elasticity was used as the constitutive model for the pow der. The calibration of this rate-independent model was based on a series of mechanical tests: diametrical compression, simple compression and compaction in an instrumented die. The internal friction angle was measured by shear testing. The simulation was conducted until steady-state conditions were reached, which was confirmed on the basis of constant values of the roll force and roll torque. The simulations were conducted to evaluate the effects of the friction coefficient at the rolljpowder interface and the feed stress on the process variables, namely roll force, roll torque, nip angle and neutral angle. From the simulation results, the following conclusions were made: the feed stress has a significant effect on the maximum roll pressure generated; • increasing the coefficient of friction for a given feed stress increase the max imum roll pressure; •
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the roll force and roll torque increase with increasing feed stress and friction coefficient; • the compact density increases with increasing friction coefficient and feed stress. •
These conclusions are in agreement with experimental findings. Dec et al. [ 1 8] also demonstrated the capability of the model for predicting the relative densities, material flow, deformation energy, shear stress distribution, pressure distribution, position of the nip angle and the neutral angle, and failure of the compact during release. The greatest challenge in the implementation of FEM modelling is obtaining reliable input data. This study highlighted the need for more accurate material models, which can realistically represent the behaviour of a powder through the wide range of densities encountered during compaction. Dec et al. [1 8] also reported that further work on fully 3D simulation and incor poration of various models of material behaviour in the feeding devices will be attempted. 4. 3. 2. Discrete element method
The discrete element method (DEM) is a simulation framework for particulate systems, first proposed by Cundall and Strack [ 1 9]. In this method, the behaviour of each individual particle can be calculated directly using Newton's equations of motion, taking into account the forces due to gravity, particle-particle interaction at each contact point and (where relevant) fluid-partide interaction. Although any particle interaction law can be incorporated into DEM, the most common approach is to use a spring, dashpot and friction slider to represent in a simplified way the physics of the contact interactions (see for example, Tsuji et al. [20)). DEM has been used to simulate the granular flows encountered in many different applications, including gravity-driven flows and fluidisation. Odagi et al. [21 ] developed a two-dimensional DEM simulation for the com pression of a powder during roll compaction. The method was based on the Tsuji DEM code [22], using Hertz theory to simulate the partide-partide normal in teractions and the Mindlin theory for the tangential interactions. The constituent particles were spherical and monosized. Odagi et al. [21 ] also introduced an additional adhesive force in order to simulate the effect of powder cohesiveness. In the absence of the adhesive force, the particles between the rolls did not compress into a compact during simulated compaction. By introducing the ad hesive force, it was possible to simulate the formation of coherent compacts. The predictions of the simulations were compared with experimental results from Michel et al. [9], with only qualitative agreement being achieved. There was a significant difference between the predicted and experimental pressure distri butions even with the indusion of an adhesive force, the deviation being ascribed
Roll Pressing
271
to the neglect of the interstitial gas and the use of a spherical approximation for the particle geometry. 80th of these restrictions can be removed in future work.
4. 3. 3. Neural networks and genetic algorithms
In practice, establishing cause-and-effect relationships in roll pressing is made more difficult by the large number of variables involved - both process param eters and formulation issues, since the powder to be compacted usually has several components, each with its own properties. This complexity has led some companies, particularly in the pharmaceutical industry, towards the use of arti ficial intelligence technology [23]. Intelligent software can be used in two ways: to establish relationships between causes and effects, and having established such relationships, in 'reverse' in order to establish the process conditions and other inputs necessary to produce a given set of outputs. In order for this type of software to function, it must be supplied with experimental data which cover the range of the possible cause-and effect relationships. Software for this purpose divides into rules-based types and numerically pre dictive models, often working together. Rules-based codes use the adaptive (Iearning) capabilities of neural networks and the Iinguistic capabilities of fuzzy logic [23,24] to produce simple linguistically expressed rules in the form of IF (condition 1) AND (condition 2) AND (condition 3), THEN (conclusion 1, with confidence factor x). Numerically predictive models can be developed using ar tificial neural networks (ANNs), which are mathematical systems that mimic the way in which the human brain processes information [23]. Each artificial neuron is a logic-processing unit that accepts one or more inputs and produces an output. The neuron computes the weighted sum of all the inputs and calculates, using an appropriate transfer function, an output to be forwarded to another neuron. Sub sequently, genetic algorithms are employed for optimisation in the multidimen sional space. It is usual to use only part of the data to train the model, retaining some for validation purposes. Inghelbrecht et al. [25], Turkoglu et al. [26] and Mansa et al. [27] have inves tigated the use of ANNs and genetic algorithms to predict the relationships between the process parameters, powder properties and product quality in roll pressing. Inghelbrecht et al. [25] attempted to predict final tablet friability, reporting significant deviations between predicted and experimental results. Turkoglu et al. [26] modelIed the effect of binder type, binder concentration and the number of roll compaction passes on the properties of compressed tablets using an ANN together with a genetic algorithm. The ANN methodology was used to predict and optimise tablet properties, namely the crushing strength, disinte gration time and ejection force.
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Mansa et al. [27] carried out roll compaction experiments on a 20 cm diameter experimental press over a wide range of process conditions, using two well characterised unblended and blended pharmaceutical excipients. Experimental relationships between powder properties, process variables and ribbon (product) properties were obtained . The commercial software package FormRules (In telligensys, Teeside, UK) was successfully trained so as to generate fuzzy rules to describe the relationships between the ingredient characteristics, process conditions and the output properties. Using the key inputs from FormRules a second commercial software package, INForm (Intelligensys, Teeside, UK), was trained and optimised. The trained model was successfully used to provide quantitative relationships between the same sets of inputs and outputs, and to estimate the process parameters which are necessary in order to obtain a desired product from a given starting material. The advantage of artificial intelligence methods is that they enable very large data sets to be handled and relationships to be extracted, indicating areas where further experimental work would be advantageous. Their limitation is that they do not provide physical insight and that they can only be used with confidence within the region of existing experimental data. 5. ROLL COMPACTION SIM U LATORS
A number of industrial suppliers and at least two academic groups - in Birming ham, UK and Compiegne, France - have developed small-scale instrumented roll presses for research and development work. Experiments performed with these presses are described in Section 6. The latest embodiment of the Birmingham experimental roll press is shown in Fig. 1 6. This consists of a fixed-axis solid roll and a moveable instrumented roll, each machined from stainless steel and 200 mm in diameter and 46 mm in length. They are separately driven by individual stepper motors, linked to a single quartz oscillator unit, which ensures a precise setting of the roll speed in the range 0-50 rpm and synchronism of the two drives. The instrumented roller is fitted with two flush-mounted miniature piezoelectric transducers, which provide continuous monitoring of the normal stress (0-700 bar) exerted at the surface. One trans ducer is mounted centrally on the roll surface and the other at a position 6 mm from one edge. Signals are transmitted by means of a slip ring assembly and sent to an analoguejdigital converter and thence to a logging computer. An absolute encoder mechanically coupled to the roller shaft measures the angular position of the pressure sensors simultaneously. An important distinction from industrial practice is that the gap width, the distance between the rolls at their dosest point, is fixed before each experiment, but adjustable via two bearing blocks. Two linear voltage-displacement transducers are used to check the gap (which changes
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273
Fig. 1 6. Birmingham instrumented roll press: 1 and 2, rolls; 3, adjustable bearing block; 4, displacement transducers; 5, slip ring assembly; 6, gap adjustment screws; 7, cheek plates.
slightly under load, due to the elastic response of the apparatus) and maintain the rolls in a parallel configuration. (As discussed earlier, in industrial roll presses it is usual for the rolls to be pressed together hydraulically, so that they are free to 'float', according to the load.) The press used at Compiegne is shown in Fig. 1 7; this is commercially available from the Komarek company. The roll press was equipped with rolls of 1 30 mm diameter and 50 mm width, vertically arranged. The press is specially instrumented in order to measure the compaction conditions, in a similar way to the Birmingham press. The upper roll is fitted with two flush-mounted piezoelectric transducers measuring the normal stress (0-200 MPa) exerted on the surface at 1 5 mm from each edge of the roll. The signals from the transducers are transmitted by means of high-precision slip rings to a charge amplifier, which is connected to a computer via a direct memory access AfD converter card. The position of the piezoelectric transducers is defined once per turn by a photoelectric Gell. The lower roll is fixed in position and the upper held against it by a hydraulic apparatus. The displace ment of the moveable upper roll is measured by a displacement transducer and recorded. The roll speed, the screw feeder speed and the hydraulic pressure are measured and recorded. The acquisition frequency of the recorded values is 1 000 Hz for the normal stress measured by the piezoelectric transducers and 2 Hz for the other data. The ranges of operating parameters are: • • •
the roll speed: from 2 to 1 6 rpm (0.01 3-0 . 1 08 m s - 1 ); the screw feeder speed: from 7.5 to 300 rpm; the hydraulic pressure: from 80 to 1 50 bar.
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b 4 2 -----l--t+--.
a 3
8
----'
Fig. 1 7. The Compiegne Komarek laboratory roll press 1 , roll ; 2, bearing block; 3, roll shaft; 4, supporting hydraulic system; 5, screw feeder; 6, Paddle mixer; 7, feed hopper; 8, cheek plate. (a) piezoelectric transducers, (b) displacement transducer.
Compaction Simulator
Roller Compactor
�
I
'
---------' O = R S in (C 'JI )
-
Fig. 1 8. Simulating a roller compactor using a compaction simulator [30].
Additional information about the laboratory roll press can be found in [28]. Zinchuk et 81. [29] developed a method for simulating the roll compaction process using a laboratory uniaxial press with sinusoidal movement of the punches, as shown in Fig. 1 8. This approach exploits the analogy with uniaxial compaction discussed earlier. The solids fraction and tensile strength were taken as the key parameters of the compact quality and were used in the evaluation of the simulation. It was found that real and simulated compacts of the same solids fraction produced
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using microcrystalline cellulose exhibited equivalent mechanical properties (ten sile strengths) and are thus expected to result in equivalent granulations. The simulation and key compact property approach proposed in the work can be used for process-specific prediction and scale up studies. Gereg and Cappola [30] developed a method to determine the suitability of a drug candidate for roll compaction. Optimum process parameters were deter mined for laboratory-scale equipment and these values were then used at the industrial scale. A hydraulic press with a flat-faced punch and die was used at the laboratory scale. The two methods for densifying lactose resulted in a product with similar density, compactability and suitable powder flow. The density and hardness of the tablets produced using the granules from both the methods were comparable, indicating a possible method for determining the suitability of pow ders for roll compaction. Loginov et al. [31 ] reported the development of a roll briquetting simulator for understanding the densification and performance of the roll compaction process. They also developed a mathematical model to relate the results obtained with the laboratory scale to industrial scale.
6. EXPERIMENTAL I NVESTIGATIONS 6. 1 . Effect of powder properties and process parameters
Michel [8] was responsible for designing the earliest version of the experimental press shown in Fig. 1 6 and carried out an experimental investigation using two smooth rolls of 1 00 mm diameter and 46 mm width, with gravity feed. The material was alumina (A 1 2° 3 , 2H 20) supplied by Pechiney. He used two different sampies of approximately 1 0 and 40 11m in size, in order to study the influence of com pressibility factor and flow properties, which were characterised using a uniaxial compaction press and shear tester, respectively. The major conclusions from his research work were as folIows: •
•
The pressure-density relationship obtained from the roll press is essentially similar to that obtained for the same material in a uniaxial compaction test to the same maximum pressure. Therefore, the pressure required to make a compact of given density in roll compaction can be estimated from the results of simple uniaxial compaction tests; simple semi-empirical compaction expressions such as that due to Kawakita [1 7] apply to both. If the same pressure can be achieved at the slipjni p transition, the resulting pressure profiles and compact densities are the same, independent of speed. (This is true for alumina, for which compaction is not rate-sensitive, but not true for materials that show rate-sensitive compaction behaviour.)
276 •
•
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The value of the neutral angle (the angle at which the maximum pressure occurs) was found to decrease with increasing roll speed and was independent of the roll gap, varying between 1 .0 and 1 .so. (This may, however, have been affected by the imprecision in the measurement of angle due to the finite size of the pressure sensor.) Using two pressure sensors, one mounted in the centre and another near the edge of the roll, it was found that the peak pressure was greater (typically by a factor of three) at the centre compared to the si des of the press. This was mainly attributed to the powder escaping from the edges of the rolls, past the cheek plates. (The Johanson model allows such losses to be taken into account if their magnitudes are known [8].) The roll speed has a strong influence on the compact properties and roll com pactor performance, an increase in speed causing a decrease in the nip angle and therefore in the maximum pressure applied. At higher throughputs, no coherent compact could be formed and the throughput-roll speed relationship is no longer linear - all these effects were attributed primarily to the effect of interstitial gas.
Bourseul [ 1 5] continued this work using a gravity-fed roll compactor with 200 mm diameter rolls, again with alumina as the material, and focussing on the effect of roll speed. He found that the experimental results obtained using smooth rolls fitted a relationship of the form:
Pm = A -BSw e
(7) D where Pm is the peak pressure, 0 the roll diameter, S the roll gap, the angular roll speed and the parameters A and B are constants. He proposed a modification to the Johanson theory in order to account for the air entrainment effect, thus enabling the prediction of the peak pressure and pressure distribution as a func tion of powder properties and press characteristics. The proposed model can predict the effect of roll speed, provided a measured gas permeability factor is entered and h/D> 0.0 1 . Using a n X-ray radiography technique, the densification i n the nip region was investigated. The results indicated that densification starts weil above the nip zone at low speed, which may indicate that high-speed conditions are too aerated for satisfactory compaction to take place. Bourseul [ 1 5] also investigated the effect of altering the friction coefficient of the powder on the rolls, by modification of the roll surface. He showed that the nip angle and hence the peak pressure both increase with an increase in the coefficient of wall friction. Perera [1 6] studied the compaction of the pharmaceutical excipients micro crystalline cellulose (Avicel PH1 0 1 , PH1 02 and PH1 05) and lactose (regular and w
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277
free flow). He made an extensive study of the analogy between uniaxial com paction and roll compaction, as mentioned earlier, and employed the empirical pressure-density relationships due to Heckel [32], Cooper and Eaton [33] and Kawakita [34]. Of the three, the Kawakita correlation showed the best fit to experimental data in both uniaxial compaction and roll pressing. The compact mechanical properties were studied using the three-point bend test to understand the influence of powder properties and process parameters on the compact strength. Bindhumadhavan [35] carried out further experimental investigations using pharmaceutical excipients on an instrumented roll compactor with an incorpo rated pressure transducer, particularly concerning the influence of powder prop erties on the roll-compactor performance. He showed that the particle size distribution has a strong influence on the compaction pressure applied and the final properties of the compact. An increase in the fines content can increase the peak pressure applied, and therefore the compact bulk density and compact strength. As summarised earlier, he also showed that Johanson's model is able to pro vide a reasonable basis for calculating the nip angle and pressure profiles de veloped in a roll press for a gravity-fed system. In principle, the current findings will apply to a screw-fed system but the additional complexity of a fluctuating feed pressure needs to be considered (see below). The major weakness of the model is the need to estimate the feed pressure at the nip since the complete pressure profile is very sensitive to this parameter. However, this boundary condition is likely to be a problem for any model unless a detailed analysis of the feed region is included. Such an extension might also be able to account for the entrainment of air. Briscoe et al. [36] attempted to validate the roll compaction parameters such as the roll force and roll torque predicted using Johanson's model with roll-mill experimental results. The effects of the roll-operating conditions - the roll gap, roll speed, feed material and friction ratio-on the roll force and roll torque were investigated. The model predictions were in close agreement with the experi mental results, again indicating that the simplified approach of Johanson [6] can be used to provide a quantitative prediction of the extent of the roll compaction performance and may be used to design optimal roll geometries and operating conditions. 6.2. Roll compaction using a screw feeder
When fine powders (Iess than about 50 Jlm) are compacted, press feeding is often a problem. As indicated earlier, this is the case firstly because fine powders de-aerate slowly, and secondly because fine powders often exhibit poor flowability
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so that gravity feeding is problematic. Screw feeders are therefore employed. In this case, the roll-press parameters include not only the roll speed and the roll gap but also the screw feeder parameters. Moreover the screw feeder interacts with the compaction process. These aspects have been extensively investigated by Guigon and co-workers [37-40], using the commercially available screw-fed lab oratory roll press (Komarek(K)B 1 OOQC) described in Section 5. Simon and Guigon [39] carried out experimental work to understand the influence of the operating parameters on the roll pressing of lactose and the interactions between the feed ing conditions and compaction. The measured stress applied to the powder was found to fluctuate significantly with time and position. The heterogeneity of the compact was correlated with the heterogeneity of the feeding pressure caused by the operation of the screw feeder. These aspects are considered further below. 6.3. Rol l-press throughput
The throughput of a roll press is principally limited not only by the rate of powder de-aeration, as noted above, but also by the elastic properties of the particles, which limit the compaction speed. In general, there is a limiting speed, above which poor-quality compaction takes place, for one or both of the reasons given above [4]. If the screw feeder is operated at a constant speed and the roll speed is varied, three conditions can be observed: •
•
•
sub-feeding, where the amount of powder that is provided by the screw feeder is too smalI. In this case, the particulate material is not compacted and no strip is formed. over-feeding, where the amount of powder provided by the screw feeder is too large. The compact is then extruded between the rolls and the roll gap in creases. In this case, the compacted material is of poor quality and a proportion of the powder is lost in non-compacted form . good compaction rate, which is an operating range between sub- and over feeding, corresponding to the production of a strip of compacted material that exhibits acceptable cohesion and mechanical strength.
Figure 1 9 shows the results of a series of such experiments, each at a fixed screw speed, where measured throughput is plotted as a function of roll speed, for conditions leading to good compacts. For a constant screw speed, the roll press throughput is approximately constant. Figure 20 presents the throughput against screw speed for all roll speeds, demonstrating a universal linear rela tionship. It should be noted, however, that the throughput resulting from the combination of screw feeder and roll press is considerably smaller than the
279
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20. Compactor throughput vs. screw speed for different roll speeds and comparison with throughput delivered by the screw when not coupled with the roll .
Fig.
throughput of the screw alone, which is also shown. This is because the coun terpressure created by the rolls modifies the friction between the powder and the screw barrel . Similar results were obtained subsequently by Lecompte [41 ] on a laboratory roll press of roll diameter 240 mm.
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6.4. Rol l-gap variation
If the upper roll can move vertically, the roll gap increases from its initial value to an equilibrium value when the powder is compacted. This equilibrium value, S, is a function of the mean stress applied by the rolls on the compacted material. It is also a function of the roll speed Vn the roll-press throughput Qe, the density of the compacted material Ps, the roll width L, and the extent of slip of the compacted material on the roll surface � [28]: (8)
If the roll gap is measured for many working points (sets of screw speeds, Vs, and roll speeds, Vr) then iso-gap curves can be computed, as shown in Fig. 21 . Depending on the powder being compacted, the curves are more or less straight; for alumina they are not perfectly straight, but curve slightly upwards. The local slope of the curve is the inverse of the working coefficient Cw, where 1 /Cw = VsfVr [42]. Lecompte [41 ] found a linear relationship between the gap and what he termed the predensification parameter R, defined as the ratio of the mass throughput to the product of the roll peripheral speed and the width of the roll. By
60
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Fig. 21 . Calculated iso-gap curves (mm) vs. roll and screw speed. Initial gap 0 . 8 mm. (alumina S H 1 00)
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Roll Pressing
0.8 0.6 -l----,.---,---,..----,.-,---,.---j 200 o 250 350 300 50 1 00 1 50 / Maximal normal stress MPa Fig. 22. Maximum normal stress measured with the piezoelectric transducers vs. roll gap. I nitial gap 0.8 mm. Solids:alumina (SH 1 00), salt, lactose.
taking the peripheral speed instead of the angular roll speed, he was able to take into account the roll size. In Fig. 22, the roll gap is plotted as a function of the maximum normal stress measured with the piezoelectric transducer embedded in one roll. The relation ship thus obtained is linear, which means that the iso-gap curves can be assim ilated to iso-maximum normal stress curves. Therefore for a given powder, the working range can be obtained in terms of the maximum stress. The working roll gap defines, of course, the thickness of the product strip and also the product properties or 'quality'. In order to obtain the same quality when varying the throughput, the operator must vary the screw and the roll speeds to remain on the same iso-gap curve. Some powders present straight iso-gap curves. In that case, using the same working coefficient leads to the same quality of compact.
6.5. Motion of the particles in the nip zone
Various investigators have attempted to follow the trajectories of individual particles within a press. One method is to observe the motion visually through a transparent cheek plate [28,42]. Markers added to the powder can be located and tracked on video using video analysis software. The position of a marker particle as a function of time (trajectory) represents a flow line. The speed of the particle can also be calculated along the trajectory in the x and y directions. Figure 23 represents the trajectories of 1 3 markers (the dotted lines show the roll surfaces). As expected, the dominant motion of the particles is in the x di rection. However, in the left part of the graphie (for x < 1 5 mm) the trajectories show discontinuities. The motion of the particles in this region is not continuous because of cyclic perturbations produced by the screw feeder. At every turn of the
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10 8 6 4 2 E E 0 >-2 -4 -6 -8 -10 -33
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-6
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':"C/l
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6
7
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position -33 < x < -28 and -2.5
feeding serew, the powder progresses locally and then stops. The trajectories are more ordered on the right side of the graphie (for x> 1 5 mm). The flow here is steady, determined principally by the friction on the rolls. Careful observation of the motion of traced partie/es e/ose to the cheek plate showed that their velocities varied periodically with time in a sinusoidal way, as shown in Fig. 24. These fluetuations have the same period as the feed serew and are in fact eaused by the motion of the last serew flight (Fig. 25). The
283
Roll Pressing
Feeding plane Stationary powder
ls e inside the ro___I�
_ _
Moving powder Fig. 25. Sketch of the feeding zone with screw feeder flights.
pressure at the exit of the screw is not uniform in the plane perpendicular to the direction of motion. This pressure is a function of the geometry and surface properties of the screw and of the compressibility of the powder. When the wall of the last screw flight is far from the feeding plane (the position corresponding to the top part of Fig. 25), the powder between the flight and the feeding plane is not compacted and the local pressure at the feeding plane is low. When the flight at this location moves forward, the powder first compacts without moving sig nificantly, progressively increasing its density and the local pressure at the feed ing plane. This is the cause of the discontinuous motion shown in Fig. 23. If the powder is less compressible, as is the case for sodium chloride, for example, the magnitude of these fluctuations is less pronounced. 6.6. Distribution of the compact heterogeneity
Most of the properties of the compacted strip depend on its density, so it is of interest to determine this as a function of position. This is particularly impor tant if a screw feeder is used, because this can, as shown above, impose a time dependent variation on the applied stress and can therefore be expected to influence the density in a time-dependent way. Various methods for measuring strip properties have been aUempted. Bourseul [1 5] made extensive use of three-point bend tests on pieces of the strip, as weil as measuring density. Lecompte [41] used the force needed to indent the slab and also measured the local density and porosity. Bindhumadhavan [35] obtained microstructural information on the cross-section of the compacts using X-ray microtomography. Simon [28] has used visualisation techniques to obtain qualitative indications of the stress variation, by incorporating either comminuted coal or sodium chloride into the feed powder. The former comminutes in high-stress regions and makes them look darker, while the laUer results in crystal orientation in high-stress
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I
160mm 50
Wicompact dth45mm
x / mm
Fig. 26. (top) Light transmitted through a sodium chloride compact (sodium chloride d50: 74 ).lm); (bottom) iso-grey-Ievels of the light transmitted through a sodium chloride compact [28].
regions, leading to greater light transmission. 80th methods have been used to study the oscillation in strip properties due to the feed screw. Figure 26 shows an example of the output of the latter method, with iso-contours of light transmission. 6.7. Novel techniques and improvements
Gaete-Garreton et al. [44] investigated the advantages of applying ultrasonic fields in the nip zone of a roll press. The presence of an ultrasonic field resulted in the reduction of the shaft torque required compared with the same operation without ultrasonic energy. It was also shown that the abrasive wear was reduced significantly using the ultrasonic field. Hirohata et al. [45] carried out experiments on metal powder compaction by differential speed rolling. There are two methods: using the same roll diameters but operating at different speeds, and using different roll diameters at the same speed. In this study, a compacted strip was fabricated from electrolytic copper powder by applying differential speed rolling with the same roll diameters under a carefully regulated powder feed volume. The roll diameter was 50 mm. The speed ratios were varied from 1 (conventional) to 1 .33. The effect of the roll speed ratio, initial roll gap, powder feed volume and strip speed at the roll exit on the rolling load, relative density and strip thickness were examined. The relative density was found to increase with differential speed rolling compared to conventional rolling for the same rolling load. It was found that the density of the strip was about 1 5% larger than that from conventional rolling. The difference in density between conventional and differential rolling becomes smaller as the rolling load is
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reduced. It was also found that a strip can be made with a small powder feed volume when a large roll speed ratio is used. The strip thickness increased with increasing rolling load and was directly related to the rolling load regardless of the roll speed ratio. Much remains to be done on the characterisation of roll-press products in response to different processing routes. Bultmann [46] investigated the effect of repeated compaction on the compact properties. Compacts were produced using microcrystalline cellulose and the sampies were recompacted by up to 1 0 passes. The amount of fines was found to reduce with the number of compactions. The powder flow properties were improved and the mean granule size was increased. However, the tensile strength of the resulting tablets was found to decrease with the number of passes, indicating the need to identify the optimum number of compactions in a particular case. Until recently, the extent of instrumentation applied to roll pressing was limited to pressure and torque sensors. Acoustic monitoring is a non-invasive technique widely used in powder metallurgy. Hakanen and Laine [47] used this technique to characterise the roll pressing process. It was found that the over-compaction of microcrystalline cellulose could be detected using this method, since it was ac companied by enhancement of acoustic emission in the region of about 1 7-23 kHz. In a later study, Salonen et al. [48] showed that acoustic relaxation emission (ARE) is a function of the compressive stress applied and is a char acteristic of the compacted powder. They compared microcrystalline cellulose with maize starch and suggested a possible relationship between the ARE and the mechanical properties of the powders. 7. FORWARD LOOK
The advantages of roll compaction compared with other granulation routes are likely to ensure its continued use in the pharmaceutical industry and new uses are emerging. Laboratory-scale test methods are now available to enable fea sibility studies to be carried out and scale up of industrial processes can be achieved. Future studies are likely to focus on the complex interactions between powder properties, process variables and product properties, especially in cases where the feed powder contains a mixture of components. Several new ideas have been proposed for enhancing the effectiveness of roll pressing, including the use of ultrasound and differential speed rolls, and these can be expected to be investigated further in the future. The direct measurement of stress in the nip region has been very important in understanding the process; further enhance ments in instrumentation can be expected. From a modelling perspective, several studies have shown the applicability of Johanson's model. To make further advances and, in particular, to model both
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the feed and the nip region will require 3D computational models. A promising approach here is the combination of DEM and FEM, allowing individual particle motion to be studied even in cases where extensive deformation is taking place. ACKNOWLEDGEMENTS
The authors thank the Region Picardie and the French Ministere de I'Education Nationale de la Recherche et de la Technologie for their financial support through the Pole Regional Genie des Procedes; and the industrial research organi sations of Rhodia, Pfizer, and Merck Sharp and Dohme. Nomenclature
roll diameter (m) roll gap (m) roll width (m) roll press throughput (kg S- 1 ) roll speed (rad S- 1 ) Vr screw feeder speed (rad S- 1 ) Vs velocity in x direction (mm S - 1 ) Vx main direction of motion of the powder X vertical direction perpendicular to x y horizontal direction perpendicular to y z nip angle (deg) rx density of the compacted material (kg m- 3) Ps max maximum of the normal stress profile (Pa) extent of slippage of the compacted material on the roll surface � entry angle (deg) e er release angle (deg) neutral angle (deg) D S L Qe
an Yn
REFERENCES [ 1 ] R. Miller, Roller compaction technology, in: D . M . Parikh, (Ed.), Handbook of Pharmaceutical Granulation Technology, Marcel Dekker, New York, 1 997, pp. 99-1 50. [2] R.W. Miller, P.J. Sheskey, Am. Pharm. Rev. 4 ( 1 ) (200 1 ) 24-35. [3] P. Kleinbudde, Eur. J. Pharm. Biopharm. 58 (2004) 31 7-326. [4] W. Pietsch, Size Enlargement by Agglomeration, Wiley, New York, 1 991 . [5] S. Wennerstrum, Ten things you need to consider when choosing and installing a roller press system, Powder and Bulk Engineering, 1 4(2) (2000) 37-50. [6] J . R. Johanson, ASME, J. Appl. Mech. 32 ( 1 965) 842-848. [7] J . M . Bultmann, http://www.jmbnet.de/brc/compare.htm. 2002.
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[8] B. Michel, Compactage en presse a rouleaux de poudres minerales, PhD thesis, Universite de Compiegne, 1 994. [9] B. Michel, J.P.K. Seville, P. Guigon, C. Sidawy, Experimental study of the roll compaction of powders, Proc. 6th Int. Symp. Agglomeration, (1 993) 790-795. [ 1 0] J . P.K. Seville, U. Tüzün, R Clift, Processing of particulate solids, Chapman & Hall, London, 1 997. [1 1 ] R Dec, Problems with processing of fine powders in roll press, 25th Biennial Conference, International Briquet. Assoe. , Philadelphia, 1 995. [ 1 2] R Mansa, Using intelligent software to predict the effects of formulation and process ing parameters on roll compaction, PhD thesis, University of Birmingham, 2006. [ 1 3] AW. Jenike, RT. Shield, J. Appl. Mech . 26 (1 959) 599-602. [ 1 4] G. Bindhumadhavan, J . P.K. Seville, M.J. Adams, RW Greenwood, S. Fitzpatrick, Chem. Eng. Sei. 60 ( 1 4) (2005) 389 1-3897. [ 1 5] F. Bourseul, Investigation on roll pressing as a forming operation, PhD Thesis, Uni versity of Birmingham, 200 1 . [ 1 6] L.N. Perera, Roll compaction of pharmaceutical excipients, PhD Thesis, University of Birmingham, 2004. [1 7] K. Kawakita, K.H. Ludde, Powder Technol . 4 (1 970/1 971 ) 6 1 -68. [ 1 8] RT. Dec, A Zavaliangos, J.C. Cunningham, Powder Technol. 1 30 (2003) 265-27 1 . [ 1 9] P A Cundall, O. D.L. Strack, Geotechnique 29 ( 1 ) ( 1 979) 47-65. [20] Y. Tsuji, 1. Kawaguchi, T. Tanaka, Powder Technol. 77 (1 993) 79-87. [2 1 ] K. Odagi, T. Tanaka, Y. Tsuji, J. Soc. Powder Technol. Jpn. 38 (2001 ) 1 50-1 59. [22] Y. Tsuji, T. Tanaka, T. Ishida, Powder Technol. 71 ( 1 992) 239-250. [23] RC. Rowe, RJ. Roberts, Intelligent Software for Product Formulation, Taylor & Francis, London, 1 998. [24] J.S.R Jang, C.T. Sun, E. Mizutani, Neuro-Fuzzy and Soft Computing, Englewood Cliffs, Prentice-Hall, NJ, 1 997. [25] S. Inghelbrecht, J.P. Remon, P. Fernandes de Aguiar, B. Walczak, D. Massart, F. Van De Velde, P. De Baets, H . Vermeerseh, P. De Backer, Int. J. Pharm. 1 48 (1 997) 1 03-1 1 5 . [26] M . Turkoglu, I. Aydin, M. Murray, A Sakr, Eur. J. Pharm. Biopharm. 48 (1 999) 239-245. [27] R Mansa, R Bridson, RW Greenwood, J . P.K. Seville, H . Barker, Int. Conf. Particle Technol. (PARTEC), Nuremburg, Germany, 2004, conference CD. [28] O. Simon , Etude experimentale de I'interaction alimentation-compaction dans une presse a rouleaux lisses alimentee par une vis horizontale, PhD Thesis, Universite de Technologie de Compiegne (2000). [29] AV. Zinchuk, M.P. Mullarney, B.C. Hancock, Int. J . Pharm. 263 (2004) 403-4 1 5 . [30] G.W Gereg, M.L. Cappola, Pharm. Technol. 26 (2002) 1 4-23. [3 1 ] Y. Loginov, S.P. Bourkine, NA Babailov, J. Mater. Process. Technol. 1 1 8 (200 1 ) 1 5 1-1 57. [32] RW. Heckei , Density-pressure relationships in powder compaction, Trans. Metall . Soc. A l M E 221 ( 1 96 1 ) 67 1-675. [33] AR Cooper, L.E. Eaton, J. Am. Ceram. Soc. 45 (1 962) 97-1 01 . [34] K. Kawakita, J. Soc. Mater. Sei. Jpn. 1 3 ( 1 964) 42-428. [35] G. Bindhumadhavan, Roll compaction of pharmaceutical powders, PhD Thesis, University of Birmingham, 2005. [36] B.J. Briseoe, AC. Smith, YA Yusof, Chem. Eng. Sei. 60 ( 1 4) (2004) 391 9-3931 . [37] A Petit-Renaud, C. Laroche, P. Guigon , Experimental study of the roll compaction of powders, World Cong. Particle Technol. 3, Brighton, U . K . , 1 998. [38] O. Simon, P. Guigon, Interaction between feeding and compaction during lactose compaction in a laboratory roll press, Kona Powder Part. 1 8 (2000) 1 34-1 38. [39] P. Guigon , O. Simon, Roll press design - influence of force feed systems on com paction , Powder Technol. 1 30 (2003) 41-48. [40] O. Simon, P. Guigon, Powder Technol. 1 30 (2003) 257-264.
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[4 1 ] T. Lecompte, Etude experimentale et numerique de la compression de poudre or ganique en presse a rouleaux, alimentee par une vis sans fin, PhD Thesis, Institut National Polytechnique de Grenoble, 2005. [42] E. Goidin-Jeröme, A. Delacourte, J.C. Guyot, F. Dehont, P. Hervieu, S.T.P. Pharma Sciences 2 (4) (1 992) 320-324. [43] O. Simon, G. Turini, P. Guigon, Determination of velocity of powder in the nip region of a laboratory roll press using video analysis, IBA Proceedings, 26, San Diego, California, USA ( 1 999) 67-77. [44] L Gaete-Garreton, Y. Vargas-Hernandez, A. Chamayou, JA Dodds, W. Valderama Reyes, F. Montoya-Vitini, Chem. Eng. Sei. 58 ( 1 9) (2003) 431 7-4322. [45] T. Hirohata, S. Masaki, S. Shima, J. Mater. Process. TechnoL 1 1 1 ( 1 -3) (200 1 ) 1 1 3-1 1 7. [46] J . M . Bultmann, Eur. J. Pharm. Biopharm. 54 (2002) 59-64. [47] A. Hakanen, E. Laine, Drug Dev. Ind. Pharm. 1 9 ( 1 993) 2539-2560. [48] J . Salonen, K. Salmi, A. Hakanen, E. Laine, K. Linsaari, Int. J . Pharm. 1 53 (1 997) 257-26 1 .
CHAPTER 6 Dry G ra n u latio n Kazuo Nishii,a, * and Masayuki Horio b
aNishii Gijutsushi Jimusho (Nishii Professional Engineers' Firm), Japan bGraduate School of Bio-Applications and Systems Engineering, Tokyo University of Agriculture and Technology, Tokyo, Japan Contents 1 . I ntraduction 2. Grawth Pracess and Mechanism 3. Operating Variables 3. 1 . Total granulation time 3.2. Superficial fluidizing gas velocity 3.3. Back pressure for downward gas flow 3.4. Durations of fluidization and downward gas flow periods 4. Material Properties 4. 1 . PSG from a single powder 4.2. PSG from hard-metal powder mixture 4.3. Co-granulation fram mixtures of pharmaceutical powders 5. Scale-up Considerations 5. 1 . Scale-up testing with a lactose powder 5.2. Scale-up testing with a hardmetal powder 6. Applications 6. 1 . Application to powder metallurgy industry 6 . 1 . 1 . Hard-metal materials of WC-Co with a lubricant 6 . 1 .2. Hard-metal materials fram WC-Co without lubricants 6.2. Application to pharmaceutical industry 6.2. 1 . A drug mixture with an excipient for dry powder inhalation 6.2.2. Powder coating of drug particles o n excipient granules for dry powder inhalation 7. Theory 8 . Summary References
289 291 294 294 294 297 297 298 299 300 301 303 306 306 307 308 308 310 312 313 314 319 32 1 322
1 . INTRODUCTION
Fine particles with sizes of less than several microns are mostly cohesive and are readily agglomerated by exerting pressure on them. Dry granulation utilizes their *Corresponding author. E-mail: vzy0451
[email protected]
Granulation
Edited by A.D. Salman, M.J. Houns/ow and J. P.K. Seville B.v. t) 2007
Elsevier
All rights reserved
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gas flow
Pressing
Extruding
Tumbling
Fluidizing
F i g . 1 . Typical dry granulation methods.
cohesive characteristics to form larger granules without using any binders but with pressure by extruding, tumbling and fluidizing powders as shown in Fig. 1 . 'Pressing' is performed mechanically or pneumatically. Roll compaction is the typical mechanical pressing method as described in a previous chapter. As a novel pneumatic method, Akiyama etat. [1] granulated superfine silica anhydride and diatomaceous earth by liberating air out of a pressurized chamber into a chamber containing the powders but evacuated initially. They reported that this method is applicable to powders whose bulk volume can be reduced by more than 40% by air compaction. 'Extruding' is conducted by scraping fine powders through a sieve or a per forated plate. It is an old-fashioned granulation method but is still used to some extent in industries as a simple and easy method. However, such equipments are difficult to automate. Another difficultiy is that the improvement in flowability is small because of the wide size distribution and rod Iike shape of the product granules. 'Tumbling' has also been applied over sixty years [2]. Meissner et at. [3, 4] investigated the agglomeration behavior of fine ZnO powders in a tumbling bottle. They reported that steady-state granules were obtained after revolutions between 40000 and 635000 at the speed of 1 1 0 rpm. Claussen et at. investigated the spheronization behavior with WC-1 0%Co powders of 1-2 f-lm in diameter for 1 2 hours and proposed a model for granule growth [5]. However, such granulation times are too long for commercial production. It is also difficult to obtain spherical and small granules of less than 1 mm because tumbling does not work effectively for small granules. 'Fluidizing' of fine cohesive particles has been recognized as a difficult process but known to form agglomerates as weil. The first report of the agglomerating tendency was made, as far as the authors' knowledge is concerned, by Sugihara [6] and Bearns [7] independently in 1 966. Sugihara investigated fluidization with fine particles of O.9�35 f-lm in diameter. He reported that the measured minimum fluidization velocity umfincreased with decreasing particle diameter in comparison with the Umf of primary particles calculated from the Kozeny-Carman equation.
Dry Granulation
291
He concluded that fine powders were fluidized in the form of agglomerates and estimated the agglomerate size. Bearns investigated the effect of cohesiveness of fine particies ranging from 2 to 200 flm in diameter on fluidization conditions. He defined a fluidizability index (FI) as a ratio of the calculated Umf and the measured Umf' However, such agglomerating behavior remained unnoticed until Chaouki etat. [8] of 1 985. They investigated the bed pressure drop and bed expansion of extremely light aerogels of CuOjAI 20 3 and CujAI 2 0 3 (bulk density: 66 kgjm 3) fluidized with gases of H 2 and N 2 in the temperature range from room temper ature to 473 K. They reported that the bed was changed from a packed state to a fluidized state at a gas velocity much higher than the calculated Umf of primary particles. An overall agglomerate size determined from photographs of approx imately 1 mm in diameter was observed. In many cases, the target of granulation is to produce free-flowing granules with a mean particie size of less than 1 mm in diameter. Granulation by fluid ization as a whole can produce smaller spherical granules within a shorter gran ulation time than tumbling. However, the reproducibility of product properties is difficult to achieve because of its insufficient capability to cope with the wide property distribution in the initial bed. In 1 989, Nishii et al. [9] reached the idea that this self-agglomerating tendency can be utilized for dry binderless granulation, while the attention of many workers was focused solely on the phenomenology. In 1 993 the idea was developed further into a novel granulation system named Pressure Swing Granulation (PSG) [10] . The advantage of PSG is the reproducibility of product properties that can be obtained by repeated fluidization and reverse pressure action for filter cieanup while maintaining the simplicity and functionality of fluidized bed granulation. The growth behaviors of dry granulations by extruding and tumbling are similar to those of the wet granulations that are described in other chapters. However, the growth behavior of dry granulation by fluidization is different from that of the wet granulation, which has never been discussed precisely in the literature. In this chapter, the dry granulation by fluidization is discussed on the basis of PSG results.
2. GROWTH PROCESS AND MECHANISM
In PSG, the periodic and sudden introduction of downward gas flow into the column of the normal fluidization operation unifies the quality of agglomerates as illustrated in Fig. 2. When gas is introduced upward into the bed of a fine cohesive powder, chan nels are formed in the bed or the bed is lifted up as a plug in the beginning. Then,
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t t t Upward gas f10w
Downward gas f10w
.! .! � Upward gas flow F l u i d izatlon
Com pactlon
Fig. 2. Principle of Pressure Swing Granulation.
the bed is partially fluidized with frag mental agglomerates of various sizes. If the gas velocity is further increased to improve the fluidization quality, the entrainment of fine particles also increases and the bed may still remains in the abnormal state. At this moment, if the fluidizing gas is shut down and downward gas flow is applied to the bed, the bed is compacted and the channels and large fragments formed during the fluidization period are collapsed by the downward gas pressure. At the same time, the fine particles accumulated on bag filters installed in the freeboard are recycled back to the bed. This period of downward gas flow is followed by the upward gas flow whose volume is more than that of the fluidizing gas flow and there the compacted bed is braken into smaller fragments. In the course of re peated fluidization, the fluidization quality is gradually impraved, fines are captured by larger agglomerates and agglomerates of irregular shapes andjor too large sizes are made more spherical and smaller through attrition. Eventually, after several hundreds cycles, the generation of elutriated fines decreases significantly and spherical granules of a narraw equilibrium size dis tribution with smooth surface morphology are obtained as shown in Fig. 3. The granules produced with this method have two kinds of internal structure as shown in Fig. 4; A core-shell structure (a). The core part has the same structure as the initial porous bed but is surrounded by a denser shell layer. These gran ules graw from cores composed fram the initial small fragments by the subse quent impaction and layering of fine particles. The second type is a uniform structure (Fig. 4(b)). In this case the whole granule's meso-structure is presum ably the same as the initial bed. Granules with the laUer structure are supposed to be obtained fram the large fragments broken in the early stage of granulation.
293
Dry Granulation
Fig. 3. Optical micrographs of ZnO powder during PSG granulation. (a), as received powder; (b), after 4 cycles; (c), after 8 cycies; (d), after 1 6 cycies; (e), after 32 cycies; (f), after 64 cycies; (g), after 1 28 cycies; (h), after 256 cycies.
(a)
(b) ----- 500 l!m
Fig. 4. Scanning electron micrographs of ZnO granules split with a needle. (a), core-shell structure; (b), nonnucieated structure.
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3. OPERATING VARIABLES
The characteristics of binderless granules are influenced by operating variables and material properties. In PSG systems, the major operating variables are durations of fluidization and downward gas flow periods and the chamber pres sure for the downward gas flow in addition to the total granulation time and superficial fluidizing gas velocity UD, which are common variables of conventional fluidization. In this section, these effects are discussed with the results of PSG experiments [1 1 ] . A fluidized-bed column of 1 00 mm in diameter, dehumidified compressed air, and ZnO powder (Miyazawa Chemicals), of which the median diameter dp,50 is 0.57 ).lm, were used for the experiments unless otherwise stated. 3. 1 . Total granulation time
As described in Section 2, the granule sizes tend to converge at a certain size through time. From the scientificjengineering point of view it is important to know the time required for it. The granulation experiment was performed using a small column of 44 mm in diameter with nitrogen gas (purity: 99.997%) to prevent the effect of moisture for 450 cycles, Le. approximately 2 h and the granules sampled out of the bed during granulation were evaluated. Figure 5 shows the size distribution change during granulation. A similar growth process has also been obtained by using a larger column with dehumidified compressed air as shown in Fig. 3. After 32 granulation cycles, the size distribution of agglomerates was still rather wide with a peak in the size fraction at 300 ).lm. As the granulation cycles were increased further, the peak progressively shifted and the PSD narrowed to near equilibrium ones. The size fraction between 350 and 500 ).lm reached approx imately 80 wt% after 450 cycles. This was achieved in a very short time in com parison with that of more than 6 h for the tumbling method. In addition, free flowing granules can be obtained after a hundred cycles, Le. approximately 30 minutes, when granules are not completely spherical. Such granules are already valuable since spherical granules with a uniform size are desirable but they are not always required, especially for intermediate products. 3.2. Superficial fluidizing gas velocity
Granule growth occurs mainly during the fluidization period. Therefore, the op erating velocity of the bed is supposed to have an important impact on this condition. Figure 6 shows the effect of the fluidizing gas velocity Uo on the median granule diameter obtained at 1 0 various velocities ranging from 0.354 to 1 .46 m/s
Dry Granulation
1 00 80
� 2n c: 0
�
:c
01
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295 0 0 o I::J.
: 82 010 1 . . : 1 28 010 1 . . : 225 c1C I . . : 450 01c l . .
60
40
20
500
Granule diameter b1m] Fig. 5. Size distribution change of ZnO granules with granulation cycles. 0 . 7 r-------, c:
C'O Q)
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0 :»
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.8I E C'O > I
Q)
Q) .0 -0
� :J
CI)
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o
0
o o
0.3 0 . 2 '--__--'-___1---__-' 1 .7 1 .2 0.7 0.2 SampIe charge. O.2kg
Fluidizing air velocity [m/s]
Fig. 6. Effect of fluidizing air velocity on mean granule diameter.
for a total granulation time of 900 cycies for each test [12]. The lower limit of the above range was determined based on visual observations. Below 0.354 m/s, fluidization quality was poor. The upper limit was simply determined by the ca pacity of the air compressor used.
K. Nishii and M . Horio
296
In the previous works on the growth rate of granules by fluidized-bed spray granulation [1 3] or attrition rates of particles in a fluidized bed [14] granule sizes were reported to reduce with increasing Ua. However, with the PSG system, the size of granules increased with increasing fluidizing gas velocity. Granules larger than 5 mm in diameter have been obtained from the circulating fluidized bed configuration with Ua of 2.71 mjs in the riser although their size distribution is rather wide [1 5]. This is because the higher gas velocity accelerates attrition of large size fractions and enhances the deposition of smaller particles. Figure 7 shows the effect of fluidizing velocity on the granule density. The granule density is determined based on the weight of 1 00 granules sieved be tween 0.5 and 0.71 mm in diameter with a mean diameter of 0.605 mm.The granule density is also found to increase as Ua is increased. This is considered to be the combined results of the attrition of core that had a density lower than the deposited layer, and the densification of deposited layer by increased and in tensified collisions. Note here that each core should have originated from the porous agglomerates formed in the early stage of granulation. The minimum fluidization velocity Umf and the terminal velocity Ut of granules were calculated using the size and density of the converged granules obtained at two values of the fluidizing gas velocity. For calculation of Umf, the Wen-Yu equation [1 6] was used and for Ut the Allen equation is used because of their Reynolds number of between 5.76 and 5 1 7. The granules produced at superficial velocity of 0.5 and 1 mjs had umf of 0.084 and 0.202 mjs and Ut of 2.50 and 4.06 mjs, respectively. From these results it is quite clear that attrition, deposition and collision mechanisms are essential in PSG process. 5000 E --
4000
.
3000
(')
�
=. (j)
>-
c: q) " � ::::I c: co .... C)
2000 1 000 0.2
Sampie charge: O.2kg
1 .2 0. 7 Fluidizing air velocity [m/s]
Fig. 7. Effect of fluidizing air velocity on granule density.
1 .7
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Dry Granulation
3.3. Back pressure for downward gas flow
The unique aspect of PSG system is the introduction of downward gas flow to readjust the bed structure to improve fluidization quality of fine cohesive powders. However, high back pressure cannot be applied to the bed when considering the negative effects such as clogging of the distributor plate and the longer operation time requirement caused by the formation of large and dense fragments. Figure 8 shows the effect of the initial back pressure for the downward gas flow between 0 to 50 kPaG on the bulk density of ZnO granules. The bulk density is slightly increased with the pressure as weil as the charge quantity w, i.e. the bed height. Consequently, the initial pressure of 30 kPaG and the bed height between 50 and 1 00 mm are typically adopted although less cohesive powders are oc casionally granulated with higher pressure. 3.4. Durations of fluidization and downward gas flow periods
In the initial stage of PSG, the bed has to go through a channeling or a partially fluidized state inevitably. The bed should be freed from such an initial stage quickly to minimize the loss of granulation time. In addition, since we have severe entrainment of fines in the early stage of granulation, bag filters should be frequently cleaned with downward gas flow. There a large volume of gas for downward flow is required in a short time interval, since a constant downward gas flow was found to be ineffective. Figure 9 shows the effect of durations of fluidization period on the median diameter and the bulk density of ZnO granules. The median diameter of the 1. 2
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D
1 . 0 � ".
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. •- 1
0. 0 o
2. 0
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0. 364 0. 546 0
0
X
A
4. 0
6. 0
Initial downward flow pressure [x1 0 kPaGj Fig. 8. Effect of intial pressure for downward gas flow on bulk density of ZnO granules
between 0 . 5 and 0.71 mm.
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E
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5
10
15
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� 0. 7 25
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Fig. 9. Effect of cyclic durations on median diameter and bulk density of granules.
granules is found to decrease with increasing duration of the fluidization period in the interval from 5 to 15 s. The shorter the duration of the fluidization period is, the heavier the attrition and fragmentation become. However, the median diameter of granules obtained from 20 s fluidization cycle was larger than that obtained from 1 5 s fluidization due to the growth of small agglomerates. The result for 900 cycles of 1 0 s fluidization with 0.5 s downward gas flow was similar to that for 450 cycles of 20 s fluidization with 0.5 s downward gas flow. The bulk density of the granules of sizes between 0.5 and 0.71 mm increased continuously with increas ing duration of the fluidization period. Since smaller and denser granules are required to realize a free-flowing sys tem, a cycle of 1 5 s fluidization with 1 .0 s downward gas flow has been adopted for normal operations. In summary, downward gas flow is effective to improve fluidization quality and recycling fine particles from bag filters into the bed, and the granule size con verges after a few hours in dry fluidized-bed granulation. The converged granule size and density increase with increasing uo. The bulk density slightly increases with the initial back pressure for downward gas flow as weil as the bed height.
4. MATERIAL PROPERTIES
Fine powders are cohesive but not all of them form granules of strength sufficient to handle in ordinary circumstances. In this section we discuss the upper size limit of fine powders for dry fluidized bed granulation for several different powders. For the lower size limit information is still quite insufficient. Due to their ex tremely high cohesiveness, agglomerates produced from nanoparticles and
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Dry Granulation
nanotubes in ordinary fluidized beds tend to be very porous. So, let us skip the issue of lower size limit now and try to review experiences on the upper size limit.
4.1 . PSG from a sing le powder
Takano et al. [1 7] has chosen lactose as the base material for their PSG inves tigation due to its common use in the pharmaceutical industry. Table 1 shows the properties of the primary particles they prepared. The particles were obtained by milling Pharmatose11; 200 M (DMV) using three different methods. For Powder L-1 a hammer mill, for L-2"-'L-5 a jet mill; and for L-6, a jet mill with a classifier was used, respectively. All granulation experiments were performed using PSG equipment for 1 20 min. Figure 10 shows the resultant micrographic images of the lactose granules formed and Table 2 lists their properties. All the powders belong to group C of Geldart's classification [1 8]. No granules were obtained from powders L-1 and L-2. The granules formed from powder L-3 was smaller and stronger than those from powder L-4. This is attributed to the specific surface area Sw,BET of powder L-3 larger than that of powder L-4, even though the particle size of powder L-3 was larger than that of powder L-4. Accordingly, the granule size decreased and the granule strength increased with increasing surface area SW,BET for powders L-3 to L-6. The size distribution of powder L-6 is rather narrow because it was classified after milling. Consequently, from this investigation, the upper size limit of lactose powders was roughly 8 )..tm . In case of milled alumina powders for abrasives, the granules were obtained from WA #8000 with the median diameter of 1 .2 ± 0.3 )..t m (JIS R6001 , 1 998) but not from powders with larger sizes such as WA #6000 and #4000. The upper size limit decreased because the density of alumina is higher than that of lactose. Table 1 . Properties of primary lactose particles
Powder L-1 L-2 L-3 L-4 L-5 L-6
dp,50 [)..t m ]
1 2.5 9.36 7.78 4.67 4.20 2.97
SW,BET [m2jkg] 0.86 1 03 0.73 1 03 1 .60 1 0 3 1 . 1 7 1 03 2.04 1 0 3 4.48 x 1 0 3 x x
x
x
x
Sw,ca/c [m2jkg] 0.75 1 03 0.79 1 03 0.82 1 0 3 0.95 1 0 3 1 .06 1 03 1 .52 1 03 x
X
X
X X X
Sw,Bä specific surface area measured by BET, Sw,calc: specific surface area calculated for a spherical particle.
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K. Nishii and M . Horio
(c)
(t)
- 1 mm
Fig. 1 0. M icrographs of PSG granules of lactose.
Table 2. Properties of lactose granules (uo
Powder L-3 L-4 L-5 L-6
da. 50
666 758 667 323
[flm]
[-] 0.493 0.601 0.596 0.579
Sa
=
0.351 mjs)
[N/m2] 2.00 1 04 1 .22 1 04 2.36 1 04 7.38 1 04 (J
X X
X
X
[kg/m3] 776 61 0 618 644 Pa
[kg/m 3] 4.2 1 02 3.4 1 02 3.1 1 02 3.5 x 1 02 Pbulk,a X X
X
da,50: median diameter of granules, ca: mean granule voidage, a : mean tensile strength of granules, Pa: mean granule density, Pbulk,a: bulk density of granules.
4.2. PSG from hard-metal powder mixture
In the case of hard-metal powders that consist of tungsten carbide (WC) particles coated with cobalt (Co) partie/es and paraffin wax as shown in Table 3, Nishii and Horio [1 9] obtained granules only from powder W-1 , but not from powders W-2 and W-3, at ambient temperature condition (Fig. 1 1 ). However, the upper size limit of the hard-metal powders was larger than that of alumina powders even
301
Dry Granulation Table 3. Compositions of hardmetal powders
Powder W-1 W-2 W-3
Co [wt.%] 7.0 9.0 14.0
WC [wt.%] 93.0 (dp,50 = 1 .5 11m) 9 1 .0 (dp,50 = 2.0 11m) 86.0 (dp,50 = 3.0 11m)
Paraffin wax [wt.%] 1 .5 3.0 2.0
Melting point of paraffin wax: 324 K.
(a)
(ua
(b )
--- O.5 mm
Fig. 1 1 . Scanning electron micrographs of PSG granules of hardmetal materials
= 0.531 m/s, total granulation time: 1 6 min).
though the density was exceedingly higher than the laUer. This is thought to be an effect of the large specific surface area Sw,BET as wet mixing with a ball mill was conducted for a long time before granulation to obtain highly uniform quality. These results imply that the specific surface area Sw,BET of powders can be more important than their initial powder particle size in dry fluidized-bed granulation. 4.3. Co-granulation from mixtures of pharmaceutical powders
Mixtures of two or more materials are common in pharmaceutical processes. Takano, Nishii and Horio [20] chose lactose as an excipient and a 2-ethoxy benzamide (ethenzamide) as a hydrophobic model drug and applied PSG to obtain granules of a uniform drug content. Table 4 shows the properties of the primary particles. Powder E-1 was pre pared by jet-milling ethenzamide powder (Junsei Pharmaceutical, Japan). Lac tose powders L-7 and L-8 are original Pharmatose 11' 325 M (DMV) and
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K. Nishii and M. Horio
Table 4. Properties of ethenzamide and lactose particies
Powder E-1 L-7 L-8 L-9
dp,1O ( 11m) 0.79 1 .96 2.72 2. 1 8
dp,50 (11m) 1 .94 1 5.4 1 1 .1 8.82
dp,90 (11m) 3.94 36.4 25.6 1 9.5
Sw,BET (m2/kg) 1 .71 1 03 0.33 1 03 0.86 1 03 0.72 1 03 x
x
x x
dp, lO: particie diameter of 1 0% cumulative undersize, dp,90: particie diameter of 90% cu mulative undersize.
PharmatosecE 450 M (DMV), respectively. Lactose powder L-9 was prepared by jet-milling and surface-modifying PharmatosecE 450 M (DMV) with a ball mill for 1 20 min. Figure 1 2 shows atomic force images and near surface cross sections of primary particles along lines indicated on the images. The surface roughness of powder L-9 was likely increased although specific surface area Sw,BET of powder L-9 was smaller than that of powder L-8. PSG experiments were performed for 60 min with the mixtures of various ra tios. Figure 1 3 shows the micrographs of agglomerates from individual powders E-1 and L-7 to L-9. Granules were obtained from powders E-1 and L-9 but not from powders L-7 and L-8. The granule size obtained from powder E-1 is much smaller than that of powder L-9 simply because SW,BET of E-1 is much larger as shown in Table 4. In the mixtures of E-1 and L-7, and E-1 and L-8 the maximum contents of lactose powders to produce granules are 37.5% and 75% as shown in Fig. 1 4 and 1 5, respectively. Powder E-1 works as a binder in these cases. On the other hand, in the mixture of powders E-1 and L-9 granules are obtained regardless of lactose contents as shown in Fig. 1 6. Figure 1 7 shows the experimentally determined ethenzamide content in indi vidual granules from powders E-1 and L-9. The content uniformity of drug in the product granules was examined by determining the quantity of ethenzamide in the sampled granules (0.35-0.50 mm in diameter) with a spectrophotometer (Hitachi, U-201 0), where absorbance at a wavelength of 290 nm that corresponds to ethenzamide was used. The drug content in sampled granules was within the accuracy of ± 1 5% for calculated values ranging from 2.5 to 75%. In their experiment, the powder pre mixing was done by hand before supplied into a chamber using two ejectors facing each other. In summary, mixtures of organic and inorganic materials with large Sw, BET were successfully granulated with dry fluidized-bed PSG. The granule size decreased and the granule strength increased with increasing Sw, BET. Powders with a nar row initial size distribution produce granules also with a narrow size distribution. A mixture of powders that can be granulated weil individually can also be co-gran ulated regardless of their mixing ratio.
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900
900
[nm]
[nm]
o
""-'-'---- 0 200 nm
382 . 1 6
[nm]
(a)
Fig.
12.
400x400 nm
387.51
[nm]
346.31
[nm]
(b)
Atomic force images and near surface cross sections of primary particles.
5. SCALE-UP CONSI DERATIONS
To apply the PSG method to commercial production, the product granule char acteristics for a given set of operating conditions should be repraducible for different scale equipments. Since the forces that contral the grawth of individual granules in the bed should be made identical irrespective of scales, it is logical to apply the same superficial velocity and bed height for different scale columns. Experimental tests were conducted to see if this understanding was appropriate.
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...... l mm
Fig. 1 3. Micrographs of agglomerates from individual powders E-1 and L-7 to L-9.
(a )
(b)
...... l mm
Fig. 1 4. M icrographs of granules from mixtures of powders E-1 and L-7.
Fig. 1 5. Micrographs of granules from mixtures of powders E-1 and L-8.
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(a)
(d)
Fig. 1 6. Micrographs of granules from mixtures of powders E-1 and L-9.
1 00
Ü
G ra n u le sam pie : 2mg
::> "0
e
Cl.
g�
"0
75
x
Q
:.;:: Cf) '" (/)
.gCI> E
u c 0 u CI> "0
(/) CI> ::> C '" �
50
'E Cl 2 5 '" N C CI> .s=
W
1 00 75 50 25 Ethenzamide concentration of starting powder mixtures (mass%]
Fig. 1 7. Content uniformity of ethenzamide in individual granules fram powders E-1 and L-9.
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K. Nishii and M. Horio
5. 1 . Scale-up testing with a lactose powder
An experiment was performed with a jet-milled lactose powder with dp,50 of 2.6 11m in three PSG granulators with column diameters of 1 00, 230 and 350 mm, respectively. All granulators are made of stainless steel. Oehumidified com pressed air was used for downward flow. In the case of the 1 00 mm granulator, dehumidified compressed air was used for fluidization. However, ambient air was used in the other two cases. The granulation conditions were all the same as shown in Table 5. As shown in Fig. 1 8, granules of fairly similar characteristics were obtained for the three PSG granulators of different diameters. The median diameters of the granules from 1 00, 230 and 350 mm 1 . 0. granulators were 0.45, 0.43 and 0.44 mm, and the bulk densities were 420, 340, and 350 kg/m 3 , respectively. The granule size seems to be converged within 1 20 minutes of the total granulation time. The bulk density of granules from 1 00 mm 1 . 0. granulator was slightly higher than from 230 and 350 mm granulators presumably due to the wall effect. Incidentally, the powder deposition was not observed on the stainless steel chamber wall during the tests. This is an advantage of stainless steel wall to satisfy the essential requirement of no deposition especially from the pharma ceutical industry. 5.2. Scale-up testing with a hardmetal powder.
Experimental tests were performed with a hard-metal powder of 1 .5 11m WC6wt. %Co-1 .8wt. % paraffin wax using the same PSG granulators as described in Section 5. 1 . The mixed dry material was provided from a hard-metal tool man ufacturer. The fluidizing air was heated at 70°C, which is above the melting point of paraffin wax (56°C), to reduce the fine particles generated at filling process to a die. The granulation conditions are shown in Table 6. Figure 19 shows the granules obtained in the testing. The bulk densities of product granules from granulators of 1 00, 230 and 350 mm I. O. were 371 0, 3800 and 3760 kg/m 3 , and the angles of repose were 34, 33 and 35°, respectively. In this case the similar overall bulk density of the granules was obtained for all Table 5. Scale-up testing conditions for a lactose powder
Bed height (mm) Superficial fluidizing gas velocity (m/s) Initial pressure of downward gas flow(MPaG) Ouration of fluidization period (s) Ouration of downward gas flow period (s) Total granulation time (min)
60 0.42 0.03 15 1 .0 1 20
307
Dry Granulation
(a)
(c) -
1 mm
Fig. 1 8 . Micrographs of lactose granules using three kinds of PSG granulators with the column diameters of (a), 1 00 mm; (b), 230 mm; (c); 350 mm.
Ta ble 6. Scale-up testing conditions for a hard-metal powder
Bed height (mm) Superficial fluidizing gas velocity (mjs) Initial pressure of downward gas flow (MPaG) Duration of fluidization period (s) Duration of downward gas flow period (s) Total granulation time (min)
1 00 0.64 0.03 15 1 .5 30
because the density of the hard-metal material was extremely high. The granule size was not evaluated since it is not so important for the evaluation of free flowing. However, as can be seen the mean diameters of granules were similar. The size distributions of hard-metal granules were wider than those of lactose granules. With a longer total granulation time this should be improved but will lead to an increase in costs. In the present case, the production cost was given priority over that of a narrower size distribution for the granules. In summary, the simple scale-up procedure of maintaining the same fluidizing air velocity and bed height successfully was applied to PSG granulators with column diameters from 1 00 to 500 mm. 6. APPLICATIONS
The granules obtained with dry fluidized-bed granulation are porous and their strength is approximately one or two orders of magnitude smaller than that of
308
(a)
K. Nishii and M. Horio
(b)
(c) -
O.5 mm
Fig. 1 9. Micrographs of hardmetal granules using PSG granulators with the column di ameters of; (a), 1 00 mm; (b), 230 mm; (c); 350 mm.
granules with wet binders because the wet binders once dried produce much stronger solid bridges while in dry granulation particles are agglomerated by only interparticle forces. It is thus inappropriate for us to build a large stockpile with granules from dry granulation or to handle them violently before use. Accordingly, this method seems to suit to small production andjor to intermediate process for products that require high purity, good compressibility, and good dispersibility into air and liquids.
6.1 . Application to powder metallurgy industry
In the powder metallurgy industry, binder granulation of fine powders is per formed before pressing to obtain free-flowing granules. For granulation of hard metal powders, spray drying has also been performed exclusively after wet mixing in a solvent such as ethanol and acetone. Accordingly, in spray drying the system becomes more complicated by introducing nitrogen gas circulation sys tem to prevent both oxidization of materials and solvent explosion. Combined with a vacuum dryer PSG systems can be much more cost-effective than spray drying systems, especially for small production volumes.
6.1.1. Hard-metal materials of WC-Co with a lubricant
In the formulation of WC-Co materials, mainly WC particle size and Co content are determined in accordance with the intended use of a tool. The WC size is
309
Dry Granulation
commonly selected from 0.5 to 1 0 )lm, and the Co content fram 6 to 25 wt.%. Paraffin wax of 0.5-3 wt. % is added as a lubricant for die pressing. Generally speaking, materials with coarser WC particles, larger Co and paraffin wax content tend to be more difficult to granulate. For materials with WC particles of sizes less than 1 .5 )lm, Co content less than 1 0 wt. % and paraffin wax content less than 3 wt. % can be successfully granulated by dry granulation as described in Section 4. Most of the materials have been smoothly granulated by supplying hot fluidizing air to utilize paraffin wax in a melt condition [1 9, 21]. Hot fluidizing air was applied to a PSG system for the conventional die pressing/sintering process (see Table 7) and found to be beneficial since it eliminates the generation of fine particles that causes pressing problems such as high friction between die and punches. Figure 20 shows scanning electron micrographs of PSG granules with various formulations of WC-Co materials. The angle of re pose of the product granules was significantly improved compared with those of the original powders as shown in Fig. 21 . Sintered bodies of 4 8 24 mm were prepared by die-pressing of granules at 1 00 MPa and were then sintered at 1 673 K in vacuum for 1 h. The density of the sintered bodies obtained from the granules were higher than 99% of the theoretical one. Figures 22 and 23 show RockweIl hardness and transverse rupture strength of the sintered bodies, respectively. They satisfy the cemented carbide industrial standard of Japan Carbide Tool Manufacturers' Association (CIS 01 9C-1 990). The PSG system has been employed so far by 16 manufacturers in four countries for granulation of har-dmetal materials not only for WC-Co-paraffin wax systems but also for other cermets-paraffin wax systems. PSG is applicable to other materials with the aid of melting additives such as paraffin wax. Further investigation is, however, needed to clarify its limitation. For instance, in the case of WC-Co systems granules are difficult to obtain when paraffin wax is added more than 3 wt. % even with hot air. If the surface of pow ders is completely covered with wax, the surface energy of powder is decreased and the granulation tendency is reduced. Even though the wettability of paraffin wax is low, it seems to be the reason for the difficulty we have experienced. Likewise, dry fluidized-bed granulation cannot be successfully performed in high moisture circumstances. x
x
Table 7. Compositions of hardmetal powders
Powder W-4 W-5 W-6
WC [wt.%]
93.0 (dp.50 = 1 .5 )lm) 85.0 (dp,50 = 1 6.0 )lm) 77.0 (dp,50 = 9.0 )lm)
Co [wt.%] 7.0 1 5.0 23.0
Paraffin wax [wt.%] 0.5 0.5 0.5
310
K . Nishii and M . Horio
(c)
- 0. 1 mm
Fig. 20. Scanning electron micrographs of PSG granules of WC-Co materials (uo 0.548 m/s, total granulation time: 1 6 min). =
70 .-----� o :Original powders
';j; 60 Q)
• :PSG granules at 348K
�
5l &. 50
�
-
o Q)
Cl c
«
/ so granules(70/0Co-20/0Wax)
40
* e e __ e ----
30 0�
5 �
--
� 1 O --1� 5--� 20 Co content [wt.%]
---
--
2 � 5--� 30
---
Fig. 2 1 . Angle repose of the granules of WC-Co materials.
6.1.2. Hard-metal materials tram WC-Co without lubricants.
Spark Plasma Sintering (SPS) is a new technology in powder metallurgy industry. The sintered bodies with higher hardness and transverse rupture strength can be obtained at lower temperature and pressure in a rather shorter time than those in the conventional methods. In this technique, the material without any lubricants is preferred since pressing and sintering is performed simultaneously if no de-wax ing stage is needed. Accordingly, products with high purity can be obtained.
31 1
Dry Granulation
�
95
� 90 tJl
.�
tJl GI c:;
'E CI! .c
...:�
��
85
Gi (J 0
80
•
• :Powder NO.l 0 :CIS V20 Ä :Powder NO.2 b. :CIS V50 • :Powder NO.3 0 :CIS V60
0:::
75
Granules :PSG al 348K Compacling: 1 tf/cm2 Sinlering : 1 673K. l h
0
5
10
15
Co content
20
25
30
[wt.%]
Fig. 22. RockweIl hardness of sintered bodies from the granules of WC-Co materials.
3500 �------� Granules :PSG al 348K Compacling: 1 tf/cm2 3000 Sinlering : 1 673K.l h Ä 2500 2000
.------ �
•
: Powder NO.l 0 :CIS V20 : Powder NO.2 6. :CIS V50 • :Powder NO.3 Ll :CIS V60 1 000 �--�--�----� 25 15 5 20 30 o 10
1 500
•
Ä
Co content [wt.%] Fig. 23. Transverse rupture strength of sintered bodies from the granules of WC-Co ma terials.
The authors [22] granulated 0.5 j.LmWC-6wt%Co mixture with PSG method using ambient air. The initial material was mixed in a wet ball-mill of ethanol with an agitator for 5 h and then dried in a vacuum mixer with an agitator before granulation. The methods of the upstream pracess were selected as an optimum for PSG. Figure 24 shows a micragraph of the granules. The yield of the granules bet ween 0 . 1 5 and 0.84 mm in diameter was 89%. Table 8 shows the properties of the granules in comparison with those made by spray drying. The hall flow of spray-dried granules was unable to be determined as da,5o was approximately 50 j.Lm and the granules did not flow out of a funnel with an orifice of 1 0 mm in diameter. The Fe and 0 contents for PSG granules are slightly higher than the spray dried granules but oxidization by the fluidizing air and Fe contamination fram the
312
K. Nishii a n d M . Horio
-
1 mm
Fig. 24. Micrograph of PSG granules of 0.5 IlmWC-6wt%Co (uo = 0.43 m/s, total granu lation time: 60 min).
Table 8. Properties of granules obtained
Bulk density (kg/m 3) Angle of repose (deg.) Hall flow (s/200 g) Fe content (wt.%) o content (wt.%)
Spray-dried 2000 50 No flow out 0.0020 0.34
PSG 2660 27 2.6 0.0028 0.36
stainless-steel container are tolerable in commercial production. Since in spray drying a binder shall be required, PSG can provide better process concepts. As far as the authors knowledge is concerned, two PSG systems have been employed for granulation of hard-metal materials not only for WC-Co but also only for WC in the manufacturer of SPS systems. For other advanced materials such as AIN and rare earth-based magnetic materials, granulation testing was also successfully performed but the system has not been employed in the industry yet. Some breakthrough is required for each process under consideration of its upstream and downstream. 6.2. Application to pharmaceutical industry
Dry granulation is finding new applications in drug designs as an alternative delivering method for systemic medications, e.9. peptides and proteins to avoid
Dry Granulation
313
the "first-pass effect", i.e. drug metabolism in the liver and unwanted systemic side effects. So far, there are three major delivery systems available, namely, (1 ) nebulizer, (2) metered dose inhalation (MDI) and (3) dry powder inhalation (DPI). In DPI system, dry drug particles have to be aerosolized and inhaled by the aspiratory effort of the patient and deposited on the target region of the lungs. DPI is now recognized to be in an advantageous position over the other meth ods; nebulizers are expensive and unsuitable for portable use and MOl requires chlorofluorocarbon propellant whose utilization has to be stopped due to their ozone depleting effect. In DPI, controlling particle cohesiveness is a key factor in its implementation because powders need to de-agglomerate into aerosol particles having a size range of 1 to 7 ).lm that can reach bronchi or alveoli in the lung. The applicability of dry fluidized-bed granulation to pharmaceutical powders has already been dem onstrated in Section 4, its product granules are suitable for DPI. This is because they are sufficiently weak for easy disintegration and dispersion but sufficiently strong to maintain their shape in the container until its use under practical conditions.
6.2.1. A drug mixture with an excipient for dry powder inhalation
The major formulation of DPI medication includes coarse excipient particles such as lactose with a diameter of approximately 60 ).lm that acts firstly to dilute the drug ingredient and secondly to obtain the free-flowing mixture. In this section, the effects of lactose particle size and its content on the di spersibility of PSG granules from mixtures of lactose and ethenzamide powders shown in Section 4 are discussed based on the work by Takano, Nishii and Horio [20]. The inhalation properties of the granules were evaluated with a cascade impactor (Tokyo Dylec, AN-200), a vacuum pump and a ball mill-like inhaler for Intal:IT, (Fujisawa Pharmaceutical, E-haler}') as shown in Fig. 25. 20 mg of the product granules (size range: 0.35-0.50 mm) was fed into a NO.2 HPMC capsule (Shionogi Qualicaps), inserted into the E-haler,j{ and then suctioned at an op erating airflow rate of 28.3L/min for 5 s. Afterwards, the capsule, the inside of the inhaler, throat, and each stage of the cascade impactor were rinsed with ethanol and analyzed with the spectrophotometer to determine the quantity of ethenz amide in each section. The respiratory fraction was calculated from the amount of ethenzamide collected in each section as a percentage of the amount loaded into the capsule. Figure 26 shows the results of the dispersion experiments, where the mass fraction of ethenzamide deposited on each stage is indicated. In addition, the total percentages of the deposition on stages of respirable size range from stage
314
K. Nishii and M. Horio
stageO:> 1 1 �l m f1='I' :l! "I': "" __ stag e 1 :7 ·1 1 �lm 1L=or ,.JI �___,.JI stag e2:4 . 7·7flm _ stage 3:3.3.4. 7j.l m � :l! stage4:2.1 .3.3j.l m f1='I' """I'::l! stage5: 1 .1 ·2.1 j.lm f1='I' :l! _ _ _ _
_ _ _ _
"""I': stage6:0.65·1 .1 j.lm .. stage7 :0.43.0.65j.l m -.......JI u.�� n ����.F i lter:<0.43�l m _ _
vacuum _ p ump 2r8� . 3;: m i H
_
Cascade Impactor
Fig. 25. Schematic of dispersion system for PSG granules, equivalent aerodynamic die ameters, and structure of E-haler® .
1 . 1 -2. 1 �m to stage 4.7-7 �m are shown in Fig. 26. The respirable fraction for the granules fram pure drug, i.e. powder E-1 was 8.4%, and those for the granules fram mixtures with powder L-7 or L-8 contributed to 1 0% of the total mass. The effect of lactose content on the drug dispersion can be found but was not very strang. On the other hand, for the granules obtained fram mixtures with powder L-9 the respirable fractions are largely improved up to 20-50%. As can be found in Fig. 27 there is a correlation between respirable fraction and compression strength for granules made with powder L-9. 6.2.2. Powder eoating of drug partieles on exeipient granules for dry powder inhalation
The drug powder blended with excipient carrier powders is successfully granu lated regardless of the carrier particle concentration. Nevertheless, when the drug content is as low as 2.5%, it is difficult to obtain a uniform mixture of drug and excipient particles. To cope with such a difficulty associated with low drug con tent, Takano and Horio [23] successfully tested a new particle design, i.e. coating the excipient granules with drug particles. The following example uses a jet-milled ethenzamide powder (powder E-1 ) within a respirable size range and surface-modified lactose powder (powder L-1 O) by treating Pharmatose ® 450 M (DMV) to ball-milling for 24 hours without de creasing their mean diameter. Table 9 shows the characteristics of the primary particles such as volumetrie diameter dp and specific surface area SW,BET. Granulation of powder L-1 0 was conducted for 60 min to obtain core granules with the PSG system. To obtain ethenzamide coated lactose granules, powder
Dry Granulation 60
50
315
(a) Jet-mi l led ethenzamide-Lactose 325M
cf2. 40 c: 0
n
�
u..
30 f-- I--20 f-- I--1 0 I-0
60 50
'#. 40
c: .Q Ü � u..
D E-1=1 00% 6 L-7=25% D L-7=37.5%
30 20
1
J3-.J
I ra, rEh
h
,
,
'
ra-. , .-cr1
(b) Jet-m i l led ethenzamide-Lactose 450M
,
rID
D E-1 =1 00% !3 L-8=25% � L-8=50% II L-8=75%
10 0
60 50
(c) Jet-mil led ethenzamide-Surface modified lactose 450 M
O E-1 =1 00% el L-9=25% 40 1----__ 12 L-9=50% • L-9=75% i?3 L-9=87.5% • L-9=90% I--�I I----__I 0 L-9=92.5% � L-9=95% 30 D L-9=97.5% n (I) .... 20 u..
� 2..... c: 0
10 0
Fig. 26. Dispersion characteristics of product PSG granules: Powder E-1 with (a) L-7, (b) L-B, and (c) L-9.
E-1 was mixed with the granules from powder L-1 0 in a stainless-steel tray and then charged into the PSG column. The coating operation was conducted for 60 min with the same system as that for core lactose granulation using two con centration levels of powder E-1 of 1 and 2%. It can be seen in Fig. 28 that both
316
K . Nishii and M . Horio 1 0 0 .-------, 0
80
60
40
•.,
.
..
.
.
••
...• . . •.
'
+---i
!l!
1m�11i i/i 1m 111
�*
1111
i�li!
lljj
!
r:m
r--+
-
•.. • . , r;lf:
20
••
!i I!·
II!il! i! 111 i!ji :1 im
!!1. 1!1
m" !�!
" I,
: ! 1: :
1'
11 ,,
40 60 80 1 00
co a.. =..
Öl c:: � Ci)
.r::.
� 'iij c:: Q) �
1 20
Fig. 27. Relationship between respirable fraction of ethenzamide and tensile strength for the PSG granules mixed with Powder L-9.
Table 9. Properties of ethenzamide and lactose particies
Powder E-1 L-1 0
dp,10 [).tm] 0.79 2.07
dp,50 [).tm] 1 .94 8.66
dp,90 [).tm] 3.94 24.0
SW,BET [m 2jkg] 1 .71 1 03 1 .1 7 x 1 03 x
core and coated granules show spherical shapes with narrow size distributions. Figure 29 shows the cumulative size distributions of the core and coated granules. The size distributions move to the right side after coating. This tendency can also be confirmed in Fig. 28. Such increases in the diameter (additional layer thickness � 22 and 82 ).tm for 1 and 2% drug addition, respectively) are much larger than the predicted thickness from the sole addition of powder E-1 . This indicates that the granules continue to grow even during the additional coating time Figure 30 shows the experimentally determined ethenzamide content of five granule sampies for each prescription. The ethenzamide content of the coated granules was between 0.92 and 0.96% (92.4 and 95.7% achievement) and be tween 1 .8 and 2.0% (92.0 and 1 01 % achievement) of that for 1 and 2% coating, respectively. Figure 31 shows the inhalation properties of the coated granules evaluated with the cascade impactor. The properties were determined with the same method as that used in section 6-2-1 . As can been seen, high dispersibility is achieved in both formulations. The fine particie fraction calculated from the sum of the amount of ethenzamide collected on stages from 2 to 5 as a percentage to the total amount of ethenzamide charged in capsules, estimated by the sum of those
317
Dry Granulation
(a)
Fig.
(b)
(c)
28. M icrophotographs of the core and coated PSG granules.
�
�
1 00 r-
------1I� I �__----,
-
Core 1 %coating 2%coating 1 000
2000
Granule diameter [�m] Fig. 29. Size distribution of the core and coated PSG granules. collected from capsules, the inhaler device, the thraat piece and all the eight stages of the cascade impactor is 53.9% for 1 % coating and 46.3% for 2%. The emitted drug fraction calculated fram the amount of drug emitted fram the inhaler device as a percentage to the total amount of drug charged is 89.8 ± 3.6% for 1 % coating and 83.2 ± 1 .6 % for 2%. Figure 32 shows the tensile strength of the core granules and of the Goated ones. The strength of the coated granules is as small as the one for the Gore granules. Although the strength of the 2% coated granules was raughly a quarter, the strength of those obtained from the mixture of 97.5% Powder L-9 and 2.5% powder E-1 in Fig. 26 the dispersibility was slightly impraved. The 2% coated
31 8
K. Nishii and M . Horio
-0
2
8 n:I
0
c Q)
C
0 0
�
2
0
Cf) Cf) n:I
.s Cf)
�
E � n:I
1
LU
O �------�--�
Q)
:2
N c: Q) .t=
:::l c:
Cl
Mean ± SD. [0/0) 1 0/0coating 0' 0.94 ±0.01 . 2"ö)�coating �: ' f95 ± Ö:öä
0
1
2
Ethenzamide content of initial mixture [mass%)
Fig. 30.
Ethenzamide content of the coated granules (n = 5).
60
;;R' e...
� c:
LL
50 40 30 20 10
H
I o 2%coating I
lllI 1 %coating
3.
lIiI
--
nn-, m,
I11I I
Hn�
.s.0 &.0"' O� �0 � � � � � � � � Jl�r::; /ßv � eP ..,,,"�...('\� �'\' �/'Y"J�/\..,,� '""�().ro
er
v
"
� ,, �,J '\ �'\. "J ' ')... ,,',' ,J
,J
t;
Equivalent aerodynamic diameter range
Fig. 3 1 . I nhalation properties of coated PSG granules evaluated with cascade impactor (da = 0.50-0.71 mm, n 3). =
granules might be too weak to maintain granules through the upper part of the inhaler down to the throat piece. The strength can be adjusted by changing the degree of surface modification to satisfy the shape-keeping ability during trans portation as weil as the dispersibility on inhalation. Now, only one PSG system has been employed for the development of DPI by a pharmaceutical manufacturer. Many of the DPI is still under develop ment and the dry fluidized-bed granulation is promising for granulation of DPI materials.
319
Dry Granulation
70
cu 0...
�
60
50
Öl c 40
..s:::.
Vi
Q)
"-
� rJ) c
Q) �
30
20
10 0
// Powder No. L-l O
Powder No. L- l O + 1 % drug
§ o
+
Powder No. L-l O + 2% drug
f
1 2 Drug addition [%]
3
Fig. 32. Tensile strength of product granules (0.50�0.7 mm in diameter) evaluated with
micro-compression testing machine (mean ± S. D . , n
=
1 0).
7. THEORY
Three models have been proposed to predict the size of agglomerates in ag glomerating fluidized beds as shown in Table 1 0 [24]. Chaouki et al. [8] assumed that the drag force due to gas flow, which is approximately equal to gravity force acting on an agglomerate, is equal to the van der Waals force of attraction bet ween primary particles. Morooka et al. [25] assumed that an agglomerate breaks if the collision energy exceeds the energy that is required to break it into two splits. lwadate and Horio [24] took into consideration of bubble hydrodynamics and agglomerate voidage, and assumed that the bed expansion force by bubbles is equal to the cohesive rupture force. Furthermore, Kuwagi et al. conducted two-dimensional DEM simulation to examine lwadate-Horio model [26]. The models and the simulation are based on the following assumptions: 1 . the gas velocity is only the factor of the destructive force, 2. van der Waals force is the dominant cohesive force and the cohesive force is constant during granulation. Conciusively, they reported the calculation results agreed with the experimen tal data. However, some results from models ciearly contradict to experimental
Table 1 0. Mathematical models for agglomerating size prediction
Aulhors Chaouki
Exlernal force/energy
Model et a/.
FGa
=
Fpp Force balance Fe.
Morooka et 81.
3 11 '6 dl pig
=
" Fpp ��;[1+ 8�;�,] =
van der Waals force I)etw�n primary particles
W �
gravity force"'drag force
Etotat (Ekin + E iarn) Energy balance =
=
E split
�
Fexp
=
Fcoh,rup Force balance
g OOlpont.On le
bub b
E:::;ef = 3�J.lU ,d1l2
E.OIlI =(Eltin+ EI.m)
V =U,..t
laminar
Iwadale and Horio
Cohesive force/energy
E. ,.,..,e:
shear
•
...
= mum,2/2
••
�,. . ffiE,olal
ElDlll
32ö\.dp
h,,(l ·€.o)dl =
v energy required to _
kinetic 'oree
0"0 = _ F
EIPIo!
break an
agglomerate
Fcoh fUP
P.
IIObp. g(-P.)d.
2
-'p =::''--'2 n.
bed expansion force
cohesive ruplure force
Commenls No bubble hydrodynamic effecls i ncl uded
No bubble hydrodynamic effecls i ncl uded If 3).1Umk hw
(1 -ea)/(32nodpea). negative da is obtained Bed exp ansion force caused by bubbles is equaled with cohesive ruplure force
?'
z (jj '
�
OJ ::J a.
s: I
o ::l. o
Dry
Granulation
32 1
results shown in the previous sections in terms of: 1. 2. 3. 4.
Umfof granules with the converged size is much smaller than Uo in granulation; the granule size is increased with increasing Uo ; the agglomerate size is increased with decreasing cohesiveness; and the cohesiveness is increased with surface roughness although it is said van der Waals force is decreased with surface roughness.
To construct a realistic model at least the following effects should be further considered: 1 . the effects of frictional charge and discharge due to collision between granule and granule, granule and particles, and granule and wall; 2. the effect of surface energy by surface modification; 3. the effect of the material density; and 4. the effect of collision on densification of granules.
8. SUMMARY
In dry fluidized-bed granulation spherical granules of which strength is sufficient to handle outside of a fluidized bed can be obtained from fine cohesive powders of organic and inorganic materials. The granule size converges after a few hours of the granulation, with the overall time that is needed much shorter than that of tumbling granulation. The converged size and density of the granules increased with increasing fluidizing gas velocity. The granule size is decreased and the granule strength increased with in creasing the specific surface area of the primary particles. The specific surface area is more important than the size. The granules with narrow size distribution are obtained from the powders with narrow size distribution. The granules are obtained regardless of their contents from a mixture of pow ders that can be granulated individually and one of the powders can be coated on core granules of another. A simple scale-up procedure applies to PSG as long as the same fluidizing air velocity and bed height are successfully maintained in the range of column dia meters from 1 00 to 500 mm. Pressure-swing granulation is one of the dry fluidized-bed granulation methods is employed to the production of hardmetal tools and is promising for granulation of DPI materials. For the wide spread use of dry granulation methods, surface modification of powders before granulation is encouraged.
322
K. Nishii and M. Horio
REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [ 1 0] [1 1 ] [ 1 2] [ 1 3] [ 1 4] [ 1 5] [ 1 6] [ 1 7] [ 1 8] [ 1 9] [20] [2 1 ] [22] [23] [24] [25] [26]
T. Akiyarna, T. Nagao, M. Kono, K. Nishirnoto, Powder Techno! . 8 1 ( 1 994) 9. E. Billings, H . H . Offutt, USP No. 2, 1 20, 540 ( 1 938). H . P . Meissner, A.S. Michels, R. Kaiser, 1 & EC Process Design Dev. 3 (3) ( 1 964) 1 97. H.P. Meissner, A.S. Michels, R. Kaiser, 1 & EC Process Design Dev. 5 ( 1 ) ( 1 966) 1 0. N. Claussen, G. Petzow, in Powder Metai!. Joint Group (eds), Third Eur. Powder Metall. Syrnp., 1 971 , p. 225. M. Sugihara, J. Res. Assoc. Powder Tech. Jpn. 3 (2) ( 1 966) 2 1 . M. Bearns, I & E C Fundarn. 5 (4) ( 1 966) 508. J. Chaouki, C. Chavarie, D. Klvana, G. Pajonk, Powder Techno!. 43 ( 1 985) 1 1 7. K. Nishii, Y. Itoh, N. Kawakarni, N. Moriya, JP No. 2958783, USP No. 5 1 24 1 00, E U P N o . 0429881 , 1 989. K. Nishii, Y. Itoh, N. Kawakarni, M. Horio, Powder Techno!. 74 ( 1 993) 1 . K. Nishii, PhD. dissertation, Tokyo University of Agriculture and Technology, 1 994. W. Chaiwat, BS thesis, Chulalongkorn University, 2002. P.G. Srnith, AW. Nienow, Chern. Eng. Sci. 38 ( 1 983) 1 223. H. Kono, AIChE Syrnp. Sero 77 ( 1 98 1 ) 96. M. Horio, A. Mukoyarna, Y. Iwadate, H . Karniya, K. Nishii, Circulating Fluidized Bed Technology VI, J. Werther (Ed), DECHEMA e V , 1 999, p. 579. C.Y. Wen, Y.H. Yu, AIChE J 12 (1 966) 6 1 0. K. Takano, K. Nishii, A. Mukoyarna, Y. Iwadate, H . Karniya, M . Horio, Powder Tech no! . 1 22 (2002) 2 1 2 . D. Geldart, Powder Technol 7 ( 1 973) 285. K. Nishii, M. Horio, Proc. 1 993 Powder Metai! . World Congress, Part 2, Kyoto, 1 993, p. 975 K. Takano, K. Nishii, M. Horio, Powder Techno!. 1 3 1 (2003) 1 29. K. Nishii , H. Sonoda, H. Karniya, M. Horio, J . Jpn Soc. Powder & Powder Metall . 41 ( 1 994) 1 288. K. Nishii , M. Horio, Powder Techno! . 1 30 (2003) 1 99. K. Takano, M. Horio, Powder Techno!. 141 (2004) 1 96. Y. Iwadate, M . Horio, Powder Techno!. 1 00 ( 1 998) 223. S. Morooka, K. Kusakabe, A. Kubota, Y. Kato, J. Chern. Eng. Jpn. 21 ( 1 988) 4 1 . K . Kuwagi, M . Horio, Chern. Eng. Sci. 57 (2002) 4737.
CHAPTER 7 Coating and Enca ps u l ation Processes in Powder Techno logy Khashayar Saleh * and Pierre G u igon
Chemical Engineering Department, CNRS-UMR 6067, Compiegne University of Technology, BP 20529, 60205 Compiegne, France Contents
1 . Introduction and Definitions 2. Industrial Applications of the Coating Process 2. 1 . Pharmaceutical industry 2.2. Biological industry 2.3. Food industry 2.4. Other fields 3. Principles and Classification of Coating Processes 3. 1 . Wet coating 3.2. Dry coating 3.3. Melt coating 3.4. Liquid-phase encapsulations 3.4. 1 . Interfacial polymerisation 3.4.2. Polymer-phase separation 3.4.3. Polyelectrolyte complex formation 3.4.4. Solvent evaporation process 4. Fundamental Aspects Involved in Coating 4. 1 . Phenomena occurring during dry coating process 4.2. Phenomena occurring during wet coating 4.3. Phenomena occurring during melt coating 4.4. Wetting and wettability 4.5. Interparticle forces in the context of coating processes 4.6. Work of adhesion 5. Coating Technologies and Equipments 5. 1 . Fluidised-bed coating 5.1 . 1 . Influence of divers parameters on fluidised-bed coating 5 . 1 .2. Influence of the properties of solid particles 5. 1 .3. Influence of the properties of the coating liquid 5. 1 .4. Influence of operating conditions 5 . 1 .5. Influence of the coater's specifications 5 . 1 .6. Design options for fluidised-bed coaters 5.2. Spouted bed coaters
* Corresponding author. E-mail:
[email protected]
Granulation
Edited by A.D. Sa/man, M.J. Houns/ow and J. P. K. Seville D 2007 SV
Elsevier
All rights reserved
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324 5.3. Wurster apparatus 5.4. Rotating drum, pan and disc coaters 6. Concepts in Modelling the Coating Process Conciuding Remarks References
K. Saleh and P. Guigon 362 364 366 372 372
1 . I NTRODUCTION AND DEFINITIONS
Coating of particulate materials is a fundamental operation widely practised in a variety of chemical industries including pharmaceuticals, food, fertiliser, cosmetics, biomedical, nuclear, etc. Generally, the coating process is performed to achieve one or several of the following objectives: •
• •
• • • • • •
to protect powders from oxygen, humidity, light or any other incompatible el ement, to delay andjor control the release of active agents involved in core particles, to confer desired interfacial properties to the particles making them more proper for the final target applications (e.g. dispersion in plastics, electrostatic pulver isation, etc.), to reduce the affinity of powders with respect to aqueous or organic solvents, to avoid caking phenomena during storage and transport, to improve appearance, taste or odours of products, to conserve nutrients contained in food products, to functionalise powders (catalysts, enzyme-coated detergents, etc.), and to increase the particle size.
In addition, coated particles can be subsequently pelletised or serve as a final product enclosed in a soluble gelatine capsules. The coating process involves the covering of particulate materials including seeds, agglomerates, pellets and powders with a surrounding layer of a coating agent (or coating material). The latter might be composed of a single, or of a multitude of inert or active com ponents, each having a specified function. The coating process can be applied to a variety of substrates ranging from submicron particles to very large objects. The coating thickness might vary from a few nanometres (chemical deposition) to several micrometres (film coating) or even several millimetres (e.g. sugar coating). According to the particular application, the active component can be contained either in core particles or in the coating material. There are several methods to introduce the coating agent into the system: dispersed or dissolved in an easily evaporable solvent, molten, or applied in the form of a very fine dry powder. In majority of cases, the final deposited layer (or coating layer) is a solid-phase material called a shell.
325
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43
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• (i)
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film coated (i) or powder coated fj) droplets
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Fig. 1 . Survey of coated products. In a few singular applications the coating layer can also be a liquid film. Some examples of coated products involved in particle technology are schematically depicted in Fig. 1 . Furthermore, the introduction of a liquid into a particulate system leads most often to formation of liquid bridges between wetted particles. This behaviour results in agglomeration phenomenon, which consists of adhesion of several elementary particles to form bigger entities called agglomerates. As the coating agent solidifies, liquid bridges are transformed to solid bridges leading to more resistant agglomerates. The solidification is promoted either by heating and evaporation of the solvent when the coating agent is introduced in the form of a solution/suspension or by cooling in the case of melt coating. However, as men tioned by Ormos [1], a lattice distinction between coating and agglomeration is not always possible. Usually, the process is labelled according to its main ex pected effect. For example, a coating process leading to coated agglomerates (Fig. 1 d) or agglomerates constituted of coated particles (Fig. 1 f) is called ag glomeration if the expected effect is size enlargement and coating if the objective is to cover particles to attain one of the several functionalities mentioned above. Another term subject to controversy in the technical and scientific literature is encapsulation, which is generally admitted to be a special kind of coating. For example, this term has been employed to differentiate either coating process leading to controlled release products or coating for dispersing an active agent on
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the surface of inert particles. However, in this chapter, the term encapsulation is used to distinguish one of the two following special cases: • •
the coating process is performed by immersion in a liquid phase and the products core is constituted of a liquid-phase formulation.
2. INDUSTRIAL APPLICATIONS OF THE COATING PROCESS
The coating of particulate products has been accomplished for hundreds of years using techniques as diverse as manually applying coatings to particulate mate rials to fully automated processing of tablets and compacts in various types of industrial coating devices. Today, a great diversity of products and processes are available for coating particular materials. However, the special functionalities to be achieved might vary basically from one application to another. The objective of this section is to portray an overview of coating operations as practised in various disciplines. 2.1 . Pharmaceutical industry
Among all industrial branches concerned with the powder technology, the phar maceutical industry has without any doubt experienced the most significant de velopments in coating processes. This is primarily due to high complexity of products and process specifications required in this discipline leading to the de velopment of high-performance coating techniques and agents. Although there are many reasons for coating pharmaceutical products, the main objective of modern coating processes is to manufacture controlled release granules and pellets. Actually, the principal goal in the pharmaceutical industry has been (and still remains) the synthesis of new and more efficient active agents. It is now generally accepted that the manner in which the drugs are administered is at least as important as the implementation of new drugs: "la maniere de donner est plus ,, importante que ce que I'on donne 1 as states a French proverb. The earlier applications of coating pharmaceutical products began with sugar coating, a technique largely borrowed from the confectionery industry. Sugar coating consisted of applying a relatively thick layer of sugar around particles. Over decades, the coating had a secondary position in the manufacturing of pharmaceutical products, as its foremost role was to mask the bitter taste of certain drugs "to taste ones medicine"! Indeed, the industrial nature of the coat ing process began in the 1 960s because of the development of a broad variety of polymer-based coating agents, in particular that of cellulose derivatives. These 1
The manner of giving is more important than that one gives.
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relatively recent coating products had the particularity to form a very thin coating layer presenting several advantages in comparison to sugar coating. In particular, this so-called film coating process provided better waterproofing and antioxidant effects. In addition, this type of coating allows engraving logo, identification num bers and names on the tablet core [2]. Consequently, since the introduction of polymers the coating process has had a remarkable development. The search for new products and the optimisation of existing ones have led to more and more complex and peculiar formulations. The conception of drugs able to resist to the gastric juices with the setting up of enteric coatings is an obvious example of the advances made possible by film coating. This type of coating permits to protect the stomach from irritant substances on the one hand and to guarantee the full effectiveness of the active principle on the other hand . Over the last decades, the coating process has become an unavoidable stage of drugs manufacturing. Indeed, one should recognise that if the required amounts (and thus the side effects) of some drugs have decreased considerably, this is partly due to the use of more controlled release and more targeted medi cations. Currently, the main concern for coating any drug should be to achieve the most adequate mode of its administration, in other words, to bring the right amount of the active ingredient to the right place at the right time. 2.2. Biolog ical industry
For powdery products, the majority of coating process applications in biological areas is similar to those used by the pharmaceutical industry. However, in the biological industry, it is not always possible to extract the active organisms from their native environment in a dry form. For example, to survive, aquatic bacteria require to be enveloped with the aqueous phase containing them. Consequently, in biological industry the coating is frequently performed by liquid-phase encap sulation. The coating agents are usually long-chain molecules, which are formed by polymerisation at the surface of emulsified droplets containing the active agent (Section 3.4). 2.3. Food industry
Compared to other industries, the food industry is characterised by the diversity of both coated and coating materials involved. Furthermore, this field requires the coating of pieces that are much larger and have complex shapes: centres as various as nuts, raisins, cherries, mint patties, crackers and gums are frequently coated with chocolate or hard and soft sugar shells. Breakfast cereals, pet foods
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and some snacks are offen coated with vitamin mixtures and sweeteners. Raisins may be lightly coated with oil to prevent clumping and inhibit drying. Generally, the requested effects are primarily preserving nutritious elements as weil as nutritional value and seasoning foods. For example, fried snacks, such as potato and corn chips, are coated with dry seasoning by hot surface frying fat to help the seasoning adhere but also to reach a moisture protective effect. As a consequence, the coating layer must provide a good moisture and oxygen protective effect with an immediate release of seasoning agents in the mouth. A recent review of existing technologies for encapsulation of food ingredients can be found in Ref. [3]. 2.4. Other fields
There are several other fields concerned by coating process, some of which are presented below: •
•
Detergent manufacturing Detergent industry is a main field of application of coating process. Generally, the objective is to functionalise the detergent particles adhering to active agents such as enzymes, flavours, fabric softeners and conditioners, etc. Agricultural products and fertilisers Fertilisers are generally coated to obtain a slow release of contained nutritious elements. In fact, the majority, if not all, of fertilisers is very water soluble and in regions with high precipitation the fertiliser may be leached from the soil faster than plants could assimilate it. For example, up to 75% of the nitrogen may be lost in areas with high rainfall [4]. A solution to avoid this problem is to coat the fertiliser granules with low water permeability shells that would retard the re lease of the fertiliser and therefore give plants more time for assimilation. The earliest application of this type of coating was the production of sulphur coated urea (SCU) which was the first coated fertiliser formulation sufficiently prom ising to reach large-scale commercialisation. The urea is highly soluble in water whereas sulphur is an advantageous coating material because it is water in soluble, biodegradable, abundant and relatively low cost. In addition, sulphur is an essential plant nutrient, which many soils lack. More recently, the use of coating process was extended to other agricultural products. For example, seeds have been coated with protective coat, nutrients, herbicides, bactericidal, insecticides and other materials that attraet or repeal moisture.
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Mineral industry Coated mineral powders are principally used as solid fillers in plastics man ufacturing or in paints. Industrial plastics are usually composite materials, con sisting of particles of one or more mineral materials, called solid fillers, suspended in a matrix of plastic materials. Commonly used fillers are clay, talc, calcium carbonate, marble, alumina, titan dioxide and silica. The use of these fillers in plastic systems has two main objectives: o diminishing the cost of product by incorporating a high percentage of a low cost material and o granting some desired properties to the system, i.e. opacity, vulcanisation, UV resistance, etc.
Accordingly, coating of mineral powders has one or both of the two following purposes:
•
o to improve the ease of dispersion of pigments in nonaqueous media and o to control their degree of flocculation in the final dispersion. Nuclear field The most important use of the coating process in the nuclear field is the neu tralisation of radioactive particles by deposit of a thick layer of an inert material.
3. PRINCIPLES AND C LASSIFICATION OF COATI NG PROCESSES
Coating of solid particles implies two joint conditions: primarily, particles must be thoroughly mixed and secondly the coating agent must be applied to the moving bed of particles in the appropriate manner and form. Powder mixing can be carried out either by mechanical actions (rotating drums and pans) or by pneumatic ac tions. In some cases, a combination of mechanical and pneumatic action is used (e.g. vibro-fluidised beds). In the particular case of liquid-phase encapsulation the dispersion of core particles is more often performed in stirred vessels. As for the coating agent it can be introduced into the system in diverse forms i.e. solid, liquid or suspension. Generally, from this point of view, coating proc esses can be classified as wet coating, dry coating and melt coating (Fig. 2). Generally, coating processes can be classified according to five main criteria (Table 1 ) : the phase in which core particles are dispersed, physical nature of the coating formulation, the dominant action used to promote the mixing, circulation of core particles and whether or not the process makes use of a solvent. The manner in which the coating formulation is introduced into the system might also be used as a criterion. This criterion concerns essentially wet and melt coating, which in the majority of cases employ a spray nozzle. Although the use of electro static pulverisation in dry coating techniques has been experienced recently, its use in industrial units is not yet practised.
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Coating operations
Fig. 2. Classification of coating processes.
Table 1 . Criteria in classifying coating operations
Criterion Dispersing phase Physical state of coating formulation Type of mixing action Circulation of core particles Use of solvent
Possible cases Gas Liquid (encapsulation) Solid (dry coating) Liquid (melt, solution or suspension) Mechanical Pneumatic Combined Conter-current or co-current single stage or multi-stage Solvent-aided solventless
3.1 . Wet coating
In this process, the coating agent is dissolved or suspended in an easily evap orable solvent. The resulting coating mixture is then progressively applied into a mixed bed of partie/es to be coated. This is usually done by means of a pul verisation system. The solvent is then evaporated, leaving behind a solidified layer of coating agent. The heat necessary to eva porate the solvent can be brought by a hot gas current or through the mixer wall (electric resistance, mi crowave, etc). Note that most of industrial coating processes rely on wet coating. Generally, a large variety of coated forms can be obtained. Some examples are sugar coating as weil as film coating of drugs, colouring and flavouring of foods, etc.
3.2. D ry coating
In this case, the coating agent is added to the system in the form of fine solid partie/es. The adherence of the coating layer on the substrate is guaranteed by van der Waals forces or by electrostatic forces (Section 4.4) although in some cases small amounts of binders are added to intensify the adhesion of coating
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powder. Consequently, the partieIe size of coating agent must be small enough (often less than 1 11m) to allow adhesion forces to overcome disruptive ones. This process is used for coating of powder paints or some mineral powders to improve their flowability. Another example is the incorporation of anti-caking additives to foods, fertilisers and mineral powders before their storage in hoppers. 3.3. Melt coating
This kind of coating uses a coating agent molten either prior to or during the coating step. Compared to wet processing, here the solidification of the deposited coating layer is carried out by cooling rather than drying. In addition, melt-coating processes use no solvent. The most widely used agents in this category are high-molecular-weight compounds such as polyethylene glycols, silicones, paraffins, etc. Melt coating can be carried out via two different procedures. The first one consists of spraying a hot melted agent in a cooled bed of partieIes at which it has sufficient time to spread before solidification. In the second procedure, the coat ing agent is introduced in the system prior to coating operation in a powdery form. The mixture is then heated up to a temperature e10se to the melting point of the coating agent at limited regions of the bed. This results in the coating agent being softened and spread over the substrate partieIes. Further cooling then solidifies the deposited coating layer. A representative example of melt-coating application is the production of sul phur-coated urea. Melt coating for taste masking, gastric resistance, acid resist ance, sustained release or bioavailability enhancement by polymers is also frequently used. 3.4. Liquid-phase encapsulations
Liquid-phase encapsulation has been the object of intense development over the past 20 years essentially due to increasing interest in the immobilisation of viable enzymes, live cells and biocatalyst systems. In liquid-phase encapsulation the active liquid to be coated is dispersed in an immiscible liquid (continuous phase). A continuous microcapsule wall is then formed by in situ polymerisation reactions surrounding the active liquid phase. There are four main techniques used in liquid phase encapsulation, which are summarised below. For more details see Ref. [5]. 3. 4. 1. Interfacial polymerisation
In this technique the aqueous phase containing the active agent to be encap sulated plus one or more reactants is dispersed in an immiscible organic solvent.
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Once dispersion is weil established, a co-reactant soluble in the organic phase is added to the system. The reaction between co-reactants contained in each phase leads to the formation of a polymer membrane on the aqueous/organic solvent interface. The most commonly used membranes are polyamides or nylons re sulting from reaction of diamines (water soluble) with diacid chlorides (organic solvent soluble). The organic phase is usually a solution of chloroform and cyclohexane with compositions ranging from 20% to 35% v/v [5]. 3. 4. 2. Polymer-phase separation
This technique relies on the so-ca lied interfacial precipitation phenomenon, which occurs at the interface of an aqueous/organic solvent system when each phase contains an appropriate polymer chain, e.g., 1 0% haemoglobin under alkaline conditions for aqueous phase and nitrocellulose as weil as polystyrene for or ganic solvent (diethyl ether or benzene). From a process point of view polymer phase separation is quite similar to the interfacial polymerisation (IFP) technique. The main difference concerns the nature of member-forming reagents. 3. 4. 3. Polyelectrolyte complex formation
In this process, an aqueous solution containing sodium alginate and the active substance to be encapsulated is dropped into an aqueous solution of calcium chloride. This leads to formation of a calcium alginate membrane, which rapidly appears around the droplet's surface. The calcium alginate beads are then transformed into microcapsules through a series of washes and treatments. 3. 4. 4. Solvent evaporation process
Also called in-liquid drying process or complex emulsion method, the solvent evaporation technique is based on the dispersing of active liquid phase in an immiscible volatile solvent, which contains a coating agent. Subsequent evapo ration of volatile solvent from the resulting emulsion produces microcapsules.
4. F U N DAMENTAL ASPECTS I NVOLVED IN COATI NG
Coating is a complex operation including a number of elementary phenomena, which take place in a multi-phase medium. Generally, several consecutive and competitive elementary steps such as particle mixing, liquid spreading, solvent evaporation, agglomeration, abrasion and fragmentation affect the coating proc ess. Each of these phenomena could interfere with the others. Therefore, the
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successful use of a coating process requires the understanding of the mecha nisms that govern the critical issues in coating, e.g. adhesion, uniformity, texture of the coating and surface appearance, particle growth and stability of operation. In this section, we will describe some theoretical aspects of phenomena in volved in coating operations. 4.1 . P henomena occurring during dry coating process
In dry coating, fine (guest) particles are attached onto the surface of relatively larger (host or core) particles by mechanical means without any liquid or binder [6,7]. Both discrete and continuous coating can be achieved depending on op erating conditions (processing time, weight ratio of guest to host particles), prop erties of both coating and coated particles and interactions between them. Furthermore, a homogeneous coating consists of either a particle layer (mono layer or multilayer), which is porous, or a continuous film coating, which is gen erally non-porous. In the majority of cases, if a continuous coating is expected the dry deposited layer must undergo a further treatment such as melting, polym erisation, etc. Also it is important to note that an even coating is not always desirable. For example, in dry coating of cohesive powders by flow conditioners (glidants) the optimum flowability is achieved before the host particles are completely covered [8-9]. This is related to the mode of action of glidants. In an intermediate cov erage level, coating particles lead to a higher roughness of host particles. This results in a decrease of the interaction forces because the presence of asperity on the particles surface increases the distance between interacting particles. Consequently, a more homogeneous coating characterised by a reduced surface roughness decreases the flow properties. A successful dry coating process requires two conditions to be satisfied: a good mix between guest and host particles and adhesion forces high enough to over come the disruptive forces. The former governs the homogeneity of coating on both a microscopic and macroscopic scale and the latter is responsible for a stable coating. In order to achieve a homogeneous and efficient coating the size of guest particles must be orders of magnitude smaller than that of host particles. In addition, as the main forces promoting the adherence of coating particles are the long action forces (van der Waals, electrostatic), generally the size of guest particles must not exceed a few micrometers. This condition guarantees that the adhesion force between particles prevails over the weight of the smaller particle, which will not be easily removed from the host. Because the main step of a dry coating operation is the mixing process, these two processes are c10sely related. In order to better understand the phenomena occurring during dry coating the literature on powder mixing, which is much more
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abundant than the literature on dry eoating, should not be overlooked (e.g. [ 1 0, 1 1 ]). Ideally, a mixing proeess should intimately blend the two species so that any sampie taken from the mixture would hold the same fraetion of the two eonstituents. This is usually referred to as ordered mixing. However, aehieving this ideal state of mixing is very diffieult (if not impossible). In addition, dry eoating is a more sophistieated proeedure beeause, besides the requirement for ordered mixing, some eomplementary eonditions must be fulfilled. In partieular, the guest partie/es must adhere onto the surfaee of host partie/es and be evenly distributed. Beeause the size of guest partie/es is very small the eoating powder is often eohesive and naturally forms agglomerates. Henee, a eonvenient eoating re quires breaking-up of agglomerates and rearrangement of elementary eoating partie/es. This is aeeomplished by means of a meehanieal aetion, whieh pro gressively splits the agglomerates on smaller fragments until a homogeneous eovering of eore partie/es is reaehed. The kineties and the quality of eoating depend on the relative magnitude of inter-partie/e forees exerting between host and guest partie/es. These forees de pend above all on the size of the interaeting partieles. However, the ehemieal nature of partieles plays also an important role. For example, Meyer and Zimmermann [9] found that the eoating proeess is more efficient when the in terfacial nature of guest partie/es is the opposite to that of the eore partieles: hydrophobie eoatings spread easier over a hydrophilie substrate. Generally, the dry eoating proeess involves the following eonseeutive-eompetitive phenomena: •
•
•
•
Coating or spreading: Coating oeeurs when primary guest partie/es adhere to the surfaee of host partie/es. As mentioned earlier, the spreading depends also on the ehemieal nature of partie/es. The surfaee eovering oeeurs either after a eollision between individual guest and host partie/es or by spreading of ag glomerates of guest partie/es already adhered to a host partie/e. Crushing or squashing: Crushing takes plaee as a result of the foree of impaet due to mixing. Agglomerates of the eoating powder break apart at strueturally weaker areas and spread over the surfaee of host partieles either in the in dividual form or in the form of small agglomerates. Peeling or abrasion: If during mixing relatively strong forees are applied to the partie/es, the fine partie/es may be peeled off from the surfaee of eore partie/es beeause of insufficient adhesive strength. The detaehed partie/es might be transferred to the surfaee of other host partie/es or adhere to eaeh other. However, due to low proportion of guest partieles with respeet to host partie/es, the seeond phenomenon is less probable. Embedding: When relatively severe operating eonditions are applied, the eharaeteristies of host and guest partie/es ehange due to their deformation. In some eases, beeause of stronger forees exerted onto eolliding bodies the guest partie/es are immobilised on the surfaee of host partie/es by embedding.
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335
However, for embedding to occur the guest particles must be harder than the host and also host particles should be deformable. An example of a model system reported by Iwasaki et al. [12] is spherical copper particles as host and submicron-sized alumina as guest particles. In addition, a minimum energy is required for the immobilization, which depends on the desired feature of par ticles and must be provided by a proper choice of operating conditions. Mechanofusion: In some cases, a considerable amount of thermo-mechanical energy is generated due to the mixing action. This can result in high local temperatures due to dissipated energy. If local temperatures higher than the melting point of the coating agent are attained, guest particles become softened and molten. The coating agent can then spread over the host particle's surface through fusion-solidification cycles. Compared to other dry coating mecha nisms, mechanofusion can lead to a continuous coating shell.
4.2. Phenomena occurring during wet coati ng
A common characteristic of wet coating processes is the use of a hot gas stream, which permits the evaporation and evacuation of the solvent. Several authors [1 3-1 7] have reported a description of the different phenomena occurring during wet coating. These phenomena are summarised in Fig. 3 and described below: Coating liquid containing a binder is applied, usually by means of a spray nozzle, into a moving bed of particles, which are wetted by liquid droplets. If excessive liquid is present or it is unevenly distributed so that the liquid droplets are larger than the particles, wet agglomerates develop by formation of liquid bridges. When the operation is performed in a fluidised bed, if wet agglomerates are too strong to be fragmented and too large to be fluidised then large regions of the bed may de-fluidise and stick together as large wet clumps. This phenom enon is termed wet quenching. Note that if the break-up forces exerted by the environment exceed liquid bridge strength, the wet clumps will be transformed into smaller wet agglomerates. Alternatively, if the droplet size is less than par ticle size, two situations are distinguished: •
•
Fast drying before a collision between wet particles. Consequently, the growth occurs by layering. Collision of two or more wet particles leading to the formation of a moving liquid bridges and wet agglomerates.
If the cohesion strength is weak in comparison with the break-up forces in duced by the moving action, the break-up of the bridges could lead to the for mation of individual wet particles that can be dried and grow by the layering mechanism. On the contrary, the solidification of liquid bridges occurs due to
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ATOMISATION
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Fragmentation (coating)
Fig. 3. Phenomena occurring during wet coating.
evaporation of the solvent and agglomerates become stabilised. Whether or not the particles remain together depends on the relative magnitude of the binding forces and the break-up forces arising from the movement of particles throughout the bed. If the cohesive forces are larger than the break-up forces, particle growth occurs by agglomeration. Once again, in the case of fluidised-bed coating if excessive particle growth occurs, the minimum fluidisation velocity of particles will exceed the operating velocity and "dry quenching" of the bed will follow. How ever, if the break-up forces completely predominate, the agglomerate may break down into smaller agglomerates or individual particles with a small amount of coating material attached to the surface of each. Note that a parasite phenomenon takes place during the spraying of the liquid corresponding to the droplets drying before the particles surface is attained (spray drying ) . This step favours the formation of fine solid particles that can be carried out by the drying gas or introduced in the bed and, in turn, grow or adhere to other particles.
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In addition, another parasite phenomenon taking place during spray coating is the rebound of droplets after their collision with particles. This phenomenon depends on the wetting parameters of the solid-liquid system used and the operating conditions. Whether or not the rebound of droplets occurs depends on the relative magnitude of the droplet inertia and dissipation and spreading energies [1 8]. Another common feature of wet coating operations is the existence of a local wetting region in the neighbourhood of the introducing point of the coating liquid. This leads to formation of a localised zone of relatively low temperature within the moving bed, the "wetting zone", which has a crucial role on the hydrodynamic aspect of the operation as weil as the uniformity of deposition. The presence of such a local wetted zone was initially established experimentally by Smith and Nienow by establishing the temperature contours in a fluidised-bed coater (Fig. 4a) [1 9]. Experimental works of some other authors [20-22] confirmed this observation. Recently, in a remarkable work Heinrich et 81. [22] established a mathematical model of the fluidised-bed coating taking into account the principal transport phenomena i.e. momentum, heat and mass transfer. The simulation results obtained by these authors showed that the model could reproduce the temperature gradients close to the spray zone (Fig. 4b).
4.3. Phenomena occurring d uring melt coating
There are two common ways to achieve melt coating. The first one corresponds to the injection of a molten coating agent onto the particles surface, wh ich is cooled by a cold gas stream. This case is analogous to wet coating provided that the heating is replaced by cooling and drying by solidification. In the second case,
0.1 2
I
0.1 0 0.08
.� 0.06 :E I
0.04
- ··_·
..
_
'-_
0.02
(a)
_
65
_
-"
__
�:/Jj;'��) !> t
·
··· .
..
) ····· !·· i.. ..- ....I ••••• • . . ... . J ---i·" '" • • �: ._' ;
..
._._
_
4 2 1 05 radial distance (m.1 02)
/
::::: :�:::: s :? _·····
(T
-1 5
)
C
Ts = 44°C
PL [-)
(,,-0.61 1 )
0.8
E 0.6 E
1 0-2
U-Umf = 0.525 ms-1 :u: 0.4 W = 2.1 x 1 0-4 kg S-1 0.2
(b)
1 0-4 0.5 I; [mim]
1 0-6
Fig. 4. Temperature gradients in a fluidised-bed coater. (a) Measured temperature profile in a diametrical plane of a bed of fluidised-bed coater established by Smith and Nienow [ 1 5) . (b) Calculated two-dimensional dimensionless local liquid loading of a start-up period in a liquid-sprayed fluidised bed (from Heinrich et al. [22)).
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the coating agent is added to particles in the solid state. The heating of the bed at temperatures close to the melting point of the coating agent causes the fusion and further spreading of the agent. Generally, the heating of the bed occurs locally and the rest of the bed is at a lower temperature, which permits the solidification of deposited coating layer. Therefore, the coating is carried out by successive wetting of particles by molten coating agent and the solidification of the deposited layer. Note that compared to wet coating processes, in melt coating the control of the heat transfer rate and the bed temperature is more important. 4.4. Wetting and wettability
From the physicochemical properties playing a role in the wet and melt coating process, the wetting parameters are probably the most important especially when using low viscosity liquid binders. In fact, both bonding and adhesive forces, which govern the growth mechanism and the coating efficiency respectively, depend on the liquid surface tension and liquid-solid contact angle. Wetting parameters mainly govern the mechanisms by which particles are coated and hence the resulting coating quality and morphology of the final product. Wettability describes the ability of a liquid to spread over the surface of a solid material. The wettability of a solid with respect to a liquid is a direct consequence of molecular interactions between phases coming into contact. Considering a liquid drop deposited on a flat solid surface; for wetting to occur, liquid molecules situated in the three phase interface must break off with their surrounding liquid molecules, push away the gas or vapour molecules adsorbed at the solid surface and adhere the solid by forming bonds with the solid's molecules. If the solid-liquid adhesive forces are stronger than both liquid cohesive and solid/gas adhesive forces, then sponta neous wetting occurs. Adhesive forces arise from different interatomic and inter molecular bonds which are established between the atoms and molecules in the liquid/solid interface. These forces can be classified with respect to their relative strength as primary, donor-acceptor and secondary bonds (e.g. [23,24]). The primary bonds involve chemical bonds (ionic, covalent or metallic), whereas the secondary bonds refer to hydrogen and van der Waals bonds. The donor acceptor forces include Bronsted acid/base and Lewis acid/base interactions. Generally, the most common bonds are the primary and donor/acceptor bonds. Generally, wetting can occur through various mechanisms, which are classified as "adhesive", "spreading", "condensational" (or "adsorptive") and "immersion" wetting [23]. However, sole spreading wetting is involved in wet coating process and is discussed below. Spreading wetting is a process in which a given amount of a liquid spreads over a solid substrate. The most widely used description of this type of wetting is the
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concept of sessile drop. Consider a horizontally positioned, ideally planar, smooth and chemically homogeneous solid surface in equilibrium with the vapour phase. When a liquid drop is deposited on such a surface, spreading wetting occurs during which the liquid forms a spherical cap and the solid/liquid interface, de limited by the so-calied "three-phase contact line", stretches pushing away the solid/vapour interface. The included angle formed at a given time at a point on the three-phase contact line between the solid/liquid interface and the tangent to liquid/vapour interface is known as the contact angle, 0 (Fig. 5). The spreading continues until an equilibrium contact angle, Oe, is reached for which cohesion interactions, which tend to conserve the spherical form of the drop, equal the adhesive interactions, which are responsible for liquid spreading. If the drop size is small enough such that the gravitational forces can be ne glected, the relation between surface energies and the contact angle at equilib rium is given by the classical Young equation [23-27]: COS Oe =
}'sv - }'SL hv
(1 )
where }'AB represents the interfacial tension defined as the energy required to create a contact interface of unity between the two phases A and B, initially com pletely separated. The subscripts S, L and V refer to solid, liquid and vapour, respectively. Equation ( 1 ) indicates that the equilibrium contact angle is unique and depends only on the three interfacial tensions of the considered solid/liquid/vapour system. Consequently, this parameter is an adequate quantitative measure of the wettability of solids with respect to a given liquid. Low contact angles imply that the liquid wets the surface and will spread readily across it, whereas high contact angles imply that the liquid does not wet the surface and will tend to form beads. For the special case when Oe = 0, the deposited liquid will spread spontaneously and wet completely the substrate. Hence, the wetting is called total or infinite. The liquid is called "wetting" or "non-wetting" if the contact angle is less than or greater than 90c, respectively. An important problem when using the Young equation to determine the contact angle is that i'sv and �! S L are not easily measurable. In order to overcome this
,,{LV
2. Vapor
1��<�==� �======� Fig. 5. Sessile drop spread wetting.
'Yg.
Solid
K. Saleh and P. Guigon
340
problem, several authors have proposed models to reduce the number of variables in equation (1). Antonow [25] and alternatively Bertholot [26], using two different approaches showed that equation ( 1 ) can be transformed to the following: cos Be = - 1
+ 2 rsv
YLv
(2)
For planar compact solid surfaces, the equilibrium contact angle can be deter mined quite simply from direct measurements by microscopical methods using goniometrie techniques or indirect force-based methods using microbalances, e.g., Whilhelmy plate method, tilt-plate method and capiilary rising method [27]. In contrast to plan ar surfaces, for finely divided solids, the contact angle and therefore the wettability assessment is not a trivial task even for ideaily smooth and homogeneous surfaces. Nevertheless, both direct and indirect methods exist to assess the wettability of powders with respect to liquids. For example, Fig. 6 shows a micrograph of a glass bead wetted by water further to water vapour condensation in the observation chamber of an environmental scanning electronic microscope (ESEM). It is out of the scope of this chapter to detail these different techniques but valuable information can be found in a recent review article [27]. 4.5. I nterparticle forces in the context of coating processes
As was emphasised in previous sections, the interaction between build-up and break-up forces and consequently the strength of solid and liquid bridges
Fig. 6. Micrograph of a glass bead wetted by water further to steam condensation in the observation chamber of an environmental scanning electronic microscope (ESEM) .
341
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between particles plays a crucial role in determining the mechanism of growth. In 1 958, Rumpf [281 presented a state of knowledge in the agglomeration field together with a complete synopsis of bonding mechanisms causing agglomerate cohesion. Rumpf used bonding mechanisms with and without material bridges as the basis of ciassification. Based on theoretical considerations Rumpf plotted the tensile strength of agglomerates due to different bonding forces as a function of particie size (Fig. 7). Bonding mechanisms without material bridges, i.e. van der Waals and elec trostatic forces, only are significant in the case of very fine particies ( < 1 00 j.lm). These forces can be neglected in the presence of binding agents (liquid and solid bridges) which are at least greater by one order of magnitude. The crystailisation of salts or drying of a deposited binder can form solid bridges. The strength of the bond arises from the molecular or atomic attraction in the solid state. Unfortunately, these types of forces are not so amenable to a theoretical approach and have been often estimated experimentaily. As para doxical as it may appear, this is not a real handicap where coating and agglom eration processes are concerned. In fact, the formation of solid bridges passes through liquid bridge formation. Generally, solid bridges are several orders of TracUon ftIIstmce
I,kg.cm2)
10°
10-1
o
10-1
101
1()2
1()3
ParUcle .Ize (pm)
Fig. 7. Tensile strength of binary agglomerates due to different bonding forces as a func tion of particle size [28].
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K. Saleh and P. Guigon
magnitude stronger than liquid bridges. Consequently, if the liquid bridges are strong enough to withstand the break-up forces, so are the solid bridges. It is out of the scope of this chapter to detail all attractive forces involved in particulate systems. Substantial literature exists on this subject and valuable information can be found in a number of excellent books and papers (e.g. [24,28,29]). Here, we will limit ourselves to a brief description of attractive inter partieIe forces involved in coating process Le. the van der Waals forces which are responsible for dry coating and liquid bridge bonding forces occurring during wet and melt coating. •
Van der Waals forces and dry coating In dry coating, the adhesion of coating agent on the surface of core partieIes is usually ensured by attractive van der Waals forces. These forces exist between molecules of any nature within very short distances up to 1 00 nm. Van der Waals attractive forces have been extensively described in the scientific liter ature. Several physical models have been established for well-defined geome tries (see e.g. Ref. [29]). Considering a perfectly spherical and smooth guest partieIe attached to a core partieIe (spherical and smooth as weil) according to Lifshitz theory the van der Waals force can be calculated from the equation R1 R2 Fvdw (3) 8nZ2 R1 + R2
_- � (
)
where C is the "Lifshitz-van der Waals constant" which depending on the ma terial characteristics and physical model used, takes values in the order of 1 0 - 2°_1 0 - 1 9 J. R1 and R2 are the radii of the guest and the core particles, re spectively. Z is the gap width between two partieIes which is equal to 4. 1 0 - 1 0 m for two particles in elose contact [29]. This equation shows that the van der Waals attractive force is proportional to the partieIe size and inversely proportional to the squared gap width. As long as the attractive forces remain superior to disruptive ones the particles stay together. In the absence of external forces, disruptive forces result from the gravity exerting on detachable partieIe which is considered to be the guest par tiele. Although the van der Waals forces increase with increasing partieIe size (equation (3)) the dependency of the gravitational force, Fg, on this factor is more pronounced (Fg R�). Therefore, increasing the size of the guest partieIe, a critical size is reached where the gravitational force is just equated to the attrac tive force. The balance between the attractive and disruptive forces is a criterion to predict whether or not the adhesion takes place: oc
(4)
343
Coating and Encapsulation Processes in Powder Technology
or
3C ( 1 ) (5) F; g where is the partieIe density and is taken as the ratio R1/R2 . This equation shows that for given values of Z and the ratio between attractive and dis ruptive forces is inversely proportional to the term 1) as weil as to squared partieIe size (R�). ratios greater than unity mean that in the absence of any other disruptive force than that of gravity, the guest partieIe wil spontane ously adhere to the core partieIe. Obviously, the model presented here is an over-si m plification and should not be used for desig n purposes. However, it does enable us to see how changes in some parameters affect the ratio , thereby increasing the tendency of guest partieIes to adhere. In particular, the two following important points can be drawn from this model: 1. For a given partieIe size, ratio increases with decreasing This evo lution is however insignificant for ratios smaller than 0.1 as the change becomes negligible compared to unity (see equation (5)). This means that the bonding forces between a guest partieIe and a core partieIe are higher than that of the two guest partieIes (for which 1 ). 2. For a fixed ratio , the probabi l ity of adhesi o n decreases si g ni fi c antl y with the size of guest partieIes. The ratio becomes smaller than unity for par tiele sizes of a few micrometers (whatever the value of other parameters is) even at very favourable conditions for adhesion (i . e . low density and narrow gap). This is the reason why the dry coati ng agents are always submicron powders. Note that a major difficulty when dealing with real systems l i es in the hi gh dependency of van der Waals forces on the di stance between partieIes. I n fact, the surface roughness and the presence of dust largely affect the attractive forces being exerted on the partieIes. In additi o n, the external forces imposed by the mixing system are not easily amenable to a mathematical description. Fi nally, depending on the nature of powders, the Lifshitz-van der Waals constant, C, can vary by an order of magnitude. These facts taken as a whole make it extremely difficult to establish reliable physical models to predict the behaviour of i n dustrial units used for dry coatin g. Li q ui d bridge bonding forces Accordi n g to models described by Rumpf [28] and by Newitt and Conway-Jones [30], for two i dentical touching spherical particles (Fig. 8) the bond strength due to a static liquid bridge can be related to the liquid surface tension, Fvdw
Pp
=
32n2 Z2 pp R; 1 +
IX
IX
pp,
(IX +
Fvd w/Fg
Fvdw/Fg
Fvdw/Fg
IX .
IX
IX =
IX
Fvdw/Fg
•
')I ,
344
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•
Liquid bridge bonding forces
(a)
Rumpfs model.
( b) ESEM micrographs of a binary agglomerate (glas beads/water).
Fig. 8. Binary agglomerate due to a liquid bridge. (a) Rumpfs model. (b) ESEM micro graphs of a binary agglomerate (glass beadsjwater).
and solid-liquid contact angle,
as folIows: F = nyd� sin 2 1/! + nydp sin I/! sin(I/! + e) e,
(6)
where dp is the particle diameter and I/! the liquid filling angle which depends on the volume of the liquid bridge. Recently, Mehrotra and Sastry [31 ] presented a review of existing models dealing with the tensile strength of binary agglomerates. They also extended the application of the Rumpfs theory to the case of not equally sized particles. Furthermore, experimental results from Adams et al. [32], Mazzone et al. [33] and more recently theoretical and experimental studies from Ennis et al. [34,35] demonstrated that the cohesive strength of the dynamic liquid bridges may ex ceed that of the static by at least an order of magnitude due to the additional energy dissipation resulting from binder viscosity. According to Ennis et al. [34] both the capillary and viscous contributions were found to significantly affect the bonding mechanism of colliding particles. The Ennis' findings underlined that the capillary viscous number, Cavis , which is a measure of relative magnitude of viscous forces to capillary forces, permits the estimation of the magnitude of the strength of a dynamic pendular bridge. For Cavis of less than 1 0- 3 , the dynamic bridge strength is of the order of a static bridge and is insensitive to liquid vis cosity. As a result, the strength of the dynamic pendular bridge is a superposition of Laplace-Young capillary and viscous dissipation forces. In contrast, bridge strength is insensitive to surface tension and linearly related to Cavis for capillary number in excess of 1 0. That is, bridge strength is only a function of viscosity at high Cavis . Note that under agglomeration conditions Cavis ranges from 1 to 1 00 and as a result the capillary contribution to the pendular bridge force can be neglected in this case. In contrast, for coating operations, generally low-viscosity liquids are employed and consequently the role of the viscous forces becomes secondary.
Coating and Encapsulation Processes in Powder Technology
345
Ennis et al. [35] linked these identified microlevel mechanisms to the macro scopic process variables and presented a significant understanding of different granulation regimes from an engineering point of view. In order to establish re gimes of granulation, Ennis et al. defined the viscous Stokes number, Stv, as the ratio of the relative kinetic energy between colliding particles to the viscous dis sipation brought about by pendular bonds: Stv =
8pdpUo 1 8.u
(7)
where Ua is the relative velo city of particles, Pp the particle density and .u the viscosity of the binding liquid. It is to be noted that the calculation of Stv presumes knowledge of the interparticle velocity, Ua, which reflects the effect of break-up forces imposed by granulation system. Ennis established some mathematical models to estimate this parameter for some of currently used techniques. For example, in the case of a fluidised bed Ua was estimated to be equal to 1 2 UBdp/dB as a maximum, and to 1 2UBdp/dB(j2 on average, where (j is the dimensionless bubble spacing and UB and dB are bubble velocity and bubble size, respectively. A critical viscous number Stv must be surpassed for rebound of colliding par ticles to occur: *
S� =
( + �}n (:J 1
(8)
where e is the particle coefficient of restitution, h the thickness of the binder layer and ha a measure of the particle's surface asperities. Three granulation regimes were defined in terms of the magnitude of Stv in comparison with St� : Stv � St� non-inertial regime (all collisions successful), Stv � St� inertial regime (some collisions succesfull), and Stv � St� coating regime (no collisions successful). Despite the limitation of theoretical analysis of Ennis due to a number of sim plifications, this theory can be used, at least qualitatively, with experimental re sults for fluidised-bed granulation. 4.6. Work of adhesion
Taking into account the analysis of phenomena governing layering, it can be concluded that for a given set of operating conditions, the coating efficiency depends on physicochemical properties which condition the liquid spreading and adhesion on the particles surface. According to Dupre's equation, the thermo dynamic work of adhesion, WA, required to separate a unit area of a solid and a
346
K. Saleh and P. Guigon
liquid phase forming an interface may be expressed by: WA = YLv (1 + cos ß) + ns (9) ns is called the equilibrium spreading pressure which represents the difference between solid surface energies under operating pressure and under vacuum. For an isobaric operation, the value of this term can be considered constant. Dupre's equation strictly only applies to a solid/liquid interface but by assuming that the surface free energy of a liquid does not change significantly when it solidifies isothermally and ignoring any shrinkage stresses, it may be applied to solid/ substrate interfaces [23]. The term ns in equation (9) is defined as Ys - Ysv, offen referred to as the equilibrium spreading pressure. It is a measure of surface energy reduction by vapour adsorption of the contacting liquid. For practical purposes ns is frequently considered negligible, mainly due to difficulties in its accurate measurement. 5. COATING TECH NOLOGIES AND EQUIPMENTS
Several coating technologies exist and a is variety of industrial equipments com mercially available. These could be divided into two categories: systems using mechanical agitation and those that use pneumatic solid mixing. Examples of the first category of apparatus are drums, pans and impeller mixers. The mixing of the solid is achieved by the movement of the apparatus itself or by use of an agitator. As for the second category, some examples are the fluidised-bed, spouted-bed or Wurster apparatus. Throughout this section we will be referring to these various coating technol ogies. Emphasis is however given to fluidised-bed coaters because this type of equipment is by far the most widespread in the industry to perform the coating of solid particles. In addition, the majority of trends relative to the influence of dif ferent variables on operation criteria holds up for other pneumatic agitation tech niques. Note that the dry coating technologies are not detailed here as they fall under powder mixing discipline and are described in several excellent works (e.g. [6, 1 0, 1 1 ]). 5 . 1 . Fluidised-bed coating
Employed as early as 1 926 for catalytic cracking of hydrocarbons, fluidised beds have successfully been used for coating solid particles such as pellets, granules and powders. However, it was not until the early 1 970s that its widespread use began, in particular due to its introduction in the pharmaceutical industry in the United States. Since then, this technique has been used on an industrial scale in the manufacture of many products, including detergents, fertilisers, foods, etc.
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In a fluidised-bed coater, core particles are fluidised by hot air in which the coating liquid in a solution or a suspension form is applied either directly into or onto the bed. This is often performed using a spraying nozzle. The nozzle may be positioned either above or inside the fluidised bed. In the case of solutions or suspensions, the solvent will be evaporated leaving behind the deposited solid material as thin solid layers. The heat of vaporisation of the solvent is mainly brought by the fluidising medium, which can be air, inert gas or solvent vapour. I n addition to desirable characteristics of conventional fluidised bed such as isothermicity, high heat and mass transfer rates and good particle mixing, flu idised-bed coating permits several elementary operations such as wetting, mixing evaporation and drying and sometimes granulation and classification to be carried out in a single piece of apparatus. Therefore, contrary to coating technologies relying on mechanical mixing (rotating drums and pans), there is no need for subsidiary drying units to evaporate the added solvent. However, these advantages, responsible for the successful use of fluidised beds in in dustrial operations, may be upset by some disadvantages when operating in the presence of spraying liquids, by de-fluidisation phenomena occurring due to formation of large agglomerates. Another problem when operating fluidised beds is the attrition phenomenon, which results in losses in coating agent dep osition and then operation efficiency. The latter, is an important parameter in the case of costly binders and indicates whether or not the operation is econom ically acceptable. This is a potentially serious problem that must be kept in mind for coating and agglomeration processes because when it occurs the behaviour of fluidised bed can change drastically and result in whole batches being rejected.
5. 1. 1. Influence of divers parameters on fluidised-bed coating
For optimal process development, it is imperative to understand the influence of process parameters and design as weil as product properties on the process performance and the fundamental mechanisms controlling the process. In this section, the influence of various parameters on the mechanism of growth based on works reported in the literature is reviewed. In fluidised-bed coating the growth mechanism and the properties of the end product depend on a variety of parameters. These parameters can be classified in four main groups: the properties of solid particles, the properties of the coating liquid, the geometry of the coater and the operating conditions. Note that the complexity of the process lies in the interactions between these various param eters. Accordingly, it is difficult to highlight the effect of each parameter in an independent way as none of them are autonomous.
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K. Saleh and P. Guigon
Prior to analysing the effect of process and products variables, it is helpful to introduce some important coating criteria. Generally, the extent of the growth is characterised by one of the two following criteria: •
•
Particle mean diameter: Generally, any characteristic diameter can be used but the Sauter mean diameter, d32 , and the median mean diameter, d50, are the most widely used. Growth rate: This dimensionless parameter determines the percentage of the particle size increase. This can be obtained by dividing the difference between the instantaneous diameter and the initial one by the initial mean diameter.
In addition, the following criteria take into account the efficiency of deposition and the loss of the coating agent by attrition and spray drying: •
•
Solute content: The solute content is defined as the mass fraction (or percent age) of the deposited coating agent to the support particles. Coating efficiency: This criterion is the ratio of the quantity of solute deposited on the solid particles during the time t to that introduced in the bed for the same duration.
5. 1 . 2. /nfluenee of the properties of solid partie/es •
Size and particle size distribution. Reported works in the literature agree on the fact that the dominant mechanism of the growth depends strongly on the initial particles size distribution. The presence of fine particles in the bed supports the growth by agglomeration [ 1 5,36-38]. For example Smith and Nienow [ 1 5] using a system having a weak tendency to agglomerate (i.e. glass beads-acid benzoic) showed that the in crease in the initial size of the particles allows a change of the mechanism of growth from agglomeration to layering. The same phenomena were observed when a more agglomerating coating solution (polyethylene glycol) was used but the growth rate was somewhat higher. Hence, the growth rate has, on the whole, a tendency to increase with decreasing particle size.
As for the influence of the initial particle size distribution, Jackson et 81. [39] and Vanacek et 81. [40] noted that using a narrow particle size distribution leads to an excessive formation of agglomerates. On the contrary, in the case of a relatively broad distribution, the particle growth is mainly controlled by the layering mechanism. In addition, the smaller the mean particle size, the greater the efficiency of operation [41 ]. This can be explained by the fact that smaller particles capture more binder than larger particles because of their greater specific area and more frequent contact with the spray in the atomizing zone.
Coating and Encapsulation Processes in Powder Technology •
349
Particle porosity So me authors [1 5,1 9,37,42--44] observed that the porosity of the support have a considerable influence on the mechanism of growth in fluidised-bed coating at low temperature. For example, Song et al. [44], carried out experiments using both porous (sodium tripolyphosphate) and non-porous (glass beads) particles. The coating liquid was a mixture of mono- and diorthophosphate of sodium. They observed that the effects of the fluidising velocity and the concentration of the solution on the growth rate are more significant for the porous particles than for the compact beads.
Smith and Nienow [1 5, 1 9] carried out coating experiments with porous alumina particles using solutions of benzoic acid (1 0% wjw). They noted that contrary to compact particles, the size of alumina particles remains practically constant throughout a long time called no-growth period. Beyond this period, the particle mean size increases noticeably either by agglomeration or by layering. These authors demonstrated that the no-growth period corresponds to the partial filling of the pores. Indeed, the specific surface area of particles decreased during the no-growth period and remained practically constant during the growth regime. Other workers [42--44] reported similar observations using other model systems. These works pointed out that the duration of the no-growth period is a function of a multitude of parameters such as the pore size distribution, the concentration and the viscosity of the solution, wetting parameters and the drying rate. Recently, Desportes [43] used the fluidised-bed coating technique to produce supported catalysts using highly porous silica particles as support and a coating solution containing organo-metallic precursors. He carried out a systematic study on the influence of the operating parameters on the coating of coarse porous particles in a fluidised bed. The reported results highlight that the coating process is governed by the balance between two elementary processes: drying and im pregnation by capillary wetting. This author defined two characteristic times, the first one relative to drying, tdry, and the second to penetration by capillarity, tcap . He postulated that for tdryjtcap ratios higher than 1 0 the deposition occurs uni formly at the internal surface of particles provided that the moisture content of particles remains greater than 1 0%. The deposition at the peripheral surface of particles begun when volume of pores is filled either by saturated coating solution or by solidified coating agent. •
Solubility of particles in the coating liquid Dencs and Ormos [45] carried out coating experiments in fluidised beds of six types of solids with aqueous solutions containing the same material that those constituting the bed. These authors noted that in the case of urea, the nitrate of sodium and potassium dihydrate carbonate, primarily layering develops the growth. The particle size distributions of obtained products at the end of the
350
K. Saleh and P. Guigon
operation were narrow. On the other hand, the coating of the sodium dichro mate, ammonium nitrate and potassium phosphate led to products having broad size distribution, Iying between 0.2 and 5 mm. In this case, the growth is carried out mainly by agglomeration. In addition, during the coating of sodium and iron sulphates, Mortensen and Hovmand [46J noted that the growth is done by layering for the first case, whereas in the case of ferrous sulphate it is controlled by the mechanism of agglomeration. In order to highlight the effect of the solubility and the absorptivity of the solid support on the mechanism of coating, Ormos et al. [47] studied the coating of various materials with an aqueous solution containing gelatine (6% wjw). These materials of initial size ranging between 0 . 1 and 0.2 mm are different by their solubility and their absorptivity (Table 1 ). These authors noted that the growth of the particles is more marked for the soluble solids in the solvent (water), as is the case for sodium chloride and nitrate. On the contrary, the growth is less marked for the glass beads and silica sand, both having good absorptivity. Finally, the speed of growth is very low when the material used has a low absorptivity, case of polyethylene. 5. 1 . 3. Influence of the properties of the coating liquid •
•
Liquid density The literature reveals no significant effect of the liquid density on the coating criteria. The only effect of this parameter concerns the coating of porous par ticles, in particular when the starting point for the growth regime is determined by the filling of pore volume by the coating liquid. In this case, the higher the liquid density, the longer the period of no growth. Wetting parameters First of all note that the wetting parameters are not inherent properties of the liquid but result from localised interactions between liquid and solid molecules (Section 4.4). Several works show that the extent of wetting is one of the most important parameters in controlling the quality of deposited layer. Indeed, the growth kinetics as weil as the operating efficiency are strongly dependent on the distribution of the liquid on the surface of the particles characterised by the contact angle. In addition, this parameter has an influence on the morphology of the final product.
Generally, the wetting of the solid substrate by the coating liquid is a function of three parameters, which are the contact angle, the surface tension of the liquid and its viscosity. The two first parameters govern the maximum (equilibrium) wetting which can be attained, whereas the third determines the wetting kinetics.
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The surfaee tension of the liquid governs the droplet size distribution as weil as the distribution of the liquid on the surfaee of the particles. Aulton and Banks [48] were the first to study the effeet of the wettability on the fluidised-bed eoating proeess. To modify the wettability, these authors used mix tures of two solid eomponents, the first one being hydrophilie (lactose) and the seeond hydrophobie (salieylie acid). The eoating liquid was an aqueous solution eontaining 5% in weight of polyvinylpyrrolidone (PVP). These authors noted that the inerease in the mass fraction of the hydrophobie eomponent results in a reduetion of agglomeration extent. Reeently, Saleh et al. [49] carried out a systematie study of the influenee of wetting parameters on the eoating eriteria by two types of experiments. The first one eonsisted of using hydrophobie glass beads prepared by a ehemieal grafting treatment. This type of operation has an advantage in being able to modify homo geneously the surfaee properties of solid particles without changing any other properties of solid particles (density, size, surfaee roughness) or of binder liquid (surface tension, viseosity, ete.). The seeond type of experiment eonsisted of adding different types of surfactant to aqueous solutions of lactose (1 0% wjw). In this ease, both untreated and ehemieally treated glass beads were used. The results showed that the eoating efficieney inereases with the produet of the liquid surfaee tension and (1 + eose). These results do indieate the direet relationship that exists between the eoating effieieney and the adhesion work (see equation 9). In addition, the work of Saleh et al. demonstrated that the agglomerate strength due to a liquid bridge (equation 6) ean suitably deseribe the extent of agglom eration. This is mainly beeause the eoating agent used by these authors was a low viseosity liquid. Another remarkable finding of these authors was that for eontaet angles higher than 90° the efficieney remained negligible « 4-5%) whatever the exaet value of the eontact angle was. This observation was attrib uted to the rebound phenomena, whieh beeome preponderant when the eontaet angle exeeeds 90° [1 8]. •
Liquid viseosity The viseosity of the eoating liquid has a major effeet on the predominant meehanism of the growth. Several experimental and theoretieal works show that the extent of agglomeration inereases with inereasing the liquid viseosity (e.g. [ 1 5, 1 9,32-35,50]). Generally, as deseribed in Seetion 4.5 at high liquid viseosity the eapillary forees do not govern the agglomeration and give up their plaee to viseous dissipation forces. Furthermore, the viseosity has a notieeable influenee on atomisation behaviour of the liquid and the resultant droplet size. The latter has a tendeney to inerease with inereasing the liquid viseosity.
In addition, the liquid viseosity plays a role in the quality of deposition. In the case of high viseosity liquids, the evaporation takes plaee before the liquid has
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time to reach the equilibrium contact angle. This phenomenon, similar to a poor wettability, alters the quality of deposition and the formation of nonuniform and rough coating layers. •
Concentration of the liquid The solution concentration is a parameter that affects the duration of the op eration as weil as the mechanism of the growth. However, while operating with highly concentrated solutions, the degree of saturation during drying can reach elevated levels. This leads to an increase of crystallisation or solidification rate of the solution on the surface of the particles.
In some cases, the concentration of the coating agent considerably affects its viscosity. For example, this is the case when using agglomerating liquids such as aqueous solutions containing polymers (Le. CMC, PVP, gelatine, etc.). For this type of coating solution the effect of the concentration appears through the var iation of the liquid viscosity. In the same manner, if the concentration affects the surface properties of the coating solution, the effect of the concentration becomes secondary compared to that of surface tension and contact angle. Generally, when growth by layering is the dominant mechanism (nonviscous liquids) the growth rate after a given time va ries linearly with the concentration [44,45,51 ,52]. For fixed operating conditions and for a given amount of coating agent introduced in the bed, the concentration seems to have no significant effect on the growth rate [1 7]. However, with high concentrations, evaporation and spray drying of atomised droplets becomes so fast that the coating efficiency deteriorates. 5. 1 . 4. Influence of operating conditions •
Atomising conditions The atomization air and liquid flow rates constitute key parameters in the flu idised-bed coating process. These parameters determine the droplet size, which in turn influence the mechanism and quality of deposition. Generally, it is accepted that the mean droplet size decreases with increasing atomising air flow rate or decreasing liquid flow rate.
Liquid flow rate The liquid flow rate is an important parameter in the coating process especially in batch operations, because it determines the duration of the operation and consequently the rate of production. Heating power must be taken into consid eration when choosing suitable parameters. In addition, it should be noted that, for a given atomising air flow rate, the increase in the liquid flow rate leads to an increase in droplet size [53-56].
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The effect of this factor on the particle growth rate has been studied in two different ways: the first one is to keep the duration of the operation constant and the second one is to keep the amount of the liquid (reduction in operation time) constant. For the first case, several works showed [45,57-6 1 ] that the increase in the liquid flow rate allows an increase in the particles size. This could be explained by an increase in the droplet size on the one hand and the enhancement of the amount of the coating liquid brought to the system on the other hand. These two phenomena support the growth by agglomeration. As for the second case, the results reported in the literature are not conclusive. Indeed, according to the physical properties of the liquid and in particular the liquid viscosity, two cases can be distinguished. In the case of highly viscous binders having a strong tendency to agglomerate, the increase in the flow of the solution allows an increase in the particle growth rate and a reduction in their brittleness [59]. For less viscous solutions, Saleh et al. [1 7] reported that for a given ratio of the solute introduced to the initial particle mass, the increase of the liquid flow rate influences neither the particle growth rate nor the operating effi ciency [1 7,62]. This was explained by the fact that, in their operating conditions, the droplet mean size did not vary significantly with the liquid flow rate. These results show that the influence of the liquid flow rate on the growth rate cannot be disconnected from the physicochemical properties of liquid and solid particles. Atomising air flow rate Generally, the effect of this parameter is expressed by means of NAR ratio, which represents the ratio of the volume or mass flow rate of the atomising air to that of the liquid. Several researchers [44,57,59,63] studied the effect of the air flow rate at constant liquid flow rate on the particle growth rate. The results showed that the increase in the atomising air flow rate results in a reduction of the average particle size. In addition, Shinee et al. [51 ] studied the kinetics of growth during the injection of a solution of sodium chloride in a bed constituted from NaCI crystals. These authors noticed that for low air flow rates (voluminal NAR = 500) the growth of the particles occurs by agglomeration, while for relatively high values of this parameter (NAR = 1 000) the growth by layering becomes dominant. Ormos et al. [64], using a solution of gelatine (6% in weight) and silica sand as support noted that the size of the particles increases for values of NAR (mass) ranging between 1 . 1 3 and 1 .7 then decreases between 1 .7 and 2.5 and remains constant beyond this value. As for the effect of the atomizing air on the coating efficiency, Saleh et al. [1 7] revealed the existence of an optimum air flow rate. They showed that starting from
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low atomising gas flow rates the operation efficiency first increases to attain a maximum value and decreases afterwards. It is interesting to note that the same trend was reported by Link and Schlünder [65] concerning the coating of a single freely suspended aluminium sphere with a 1 0 wt.% of hydrated lime (Ca(OHh) suspension. These researchers supposed that the binder deposition on the particle surface occurs in two steps: collision between liquid droplets and solid particles followed by droplet adhesion on the surface of particles. According to Löffler [66], the ability of a droplet to come into contact with the particle is determined by the impingement efficiency. After collision, the droplet can bounce or be captured. The efficiency can be calculated as the product of impingement efficiency and adhesion probability, wh ich governs the second step. By increasing the atomising gas flow rate at a constant liquid flow rate, impingement efficiency increases. In fact, due to both higher velocity and higher number of droplets more of them reach the particles surface before spray drying occurs. On the other hand, the adhesion probability is equal to unity (up to a critical velocity) because all kinetic energy possessed by the droplets is dissipated during contact. Beyond this critical value, the adhesion probability decreases because the collisions become inertial and the reflection and bounce of the liquid droplets occurs. However in the work of Saleh et al. [1 7,67] the efficiency decrease after the maximum point was not as pronounced as in Link's experiments because in a fluidised bed the bounced droplets from primary particles can still encounter other particles. In addition, Saleh et al. demonstrated that the quality of deposition can be significantly improved by increasing the atomising air flow rate. This was attrib uted to the decrease of droplet size in the one hand and to the increase of droplet momentum on the other, which lead to a more homogeneous and more impact deposition. •
Bed temperature The analysis of studies related to the effect of the temperature on the growth mechanism results in two distinct types of size evolution according to the range of temperatures used. For temperatures lower than 1 00°C, the results of var ious works are agreed on the fact that the size of the particles decreases with the temperature [59,60,68]. This effect was explained by the reduction in the solid moisture due to faster drying, which reduces the possibility of formation of liquid bridges between particles. Thus, higher temperatures tend to encourage the growth by layering [40]. However, Song et al. [44] attributed the reduction in the average size of the particles to the temperature gradient existing around the wetting zone of the coater, which leads to a fragmentation of the particles due to thermal shocks. This gradient is more important when the temperature is higher. In addition, in the range of higher temperatures, other researc hers [62,69] observed the same phenomena: the average size of particles
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decreases slightly with the temperature of the bed. During the drying and coating of calcium tetra hydrate nitrate, Markvart et al. [69] noted that for a bed temperature of 1 63°C, the dominant mechanism is agglomeration, whereas beyond 200°C, the layering mechanism prevails. For temperatures in between, the growth is done simultaneously by the two mechanisms. It is notable that, for temperatures higher than 300°C (temperature range used for radioactive waste processing and calcinations), the majority of the studies agree on the fact that the growth is governed by layering and that the average size of the particles increases with temperature [39,70-83]. For example, in the case of de-nitrification of uranyl nitrate, Philoon et al. [72] noted that the average size of the particles at a temperature of around 700°C is 2.5 times larger than that obtained at 600°C. This result was explained by the increase in the porosity of the bed with the temperature. Also, Jonke et al. [52] noted that the size distribution of the coated particles strongly depends on the temperature. At 31 0°C, the percentage of large particles is appreciably reduced, and that of fines (between 74 and 1 47 j.tm) is increased. According to these authors, at low temperature, the evaporation of part of the liquid is done in the porous solid leading to a fragmentation of the particles and a consequent formation of fines. On the other hand, at high temperature, the evaporation of the liquid takes place only on the external surface of particles. In an experimental study Saleh and Hemati [41 ] studied the coating behaviour of model particles (silica sand and glass beads) with aqueous solutions contain ing NaCI as the coating agent. They observed that the increase of the bed tem perature from 50°C (relatively wet conditions) to 1 30°C (relatively dry conditions) led to a highly porous and rough surface with sharp-edged crystal structures. This can be due to high drying rate in the system that causes the droplets to be saturated (or over saturated) when reaching the particle surface. This diminishes the wettability considerably and hence the spreading of liquid on the particle surface. In addition, an increase in the bed temperature has a negative effect on the coating efficiency because the loss of solute due to spray drying increases. Also the effect of the bed temperature is more pronounced for porous particles than compact particles. •
Fluidisation gas velocity The fluidising gas velocity is a parameter that influences both the operation stability and coating parameters. Hydrodynamic behaviour of the fluidised-bed coater is strongly dependent on the fluidising gas velocity. A proper choice of this parameter is essential to avoid unplanned agglomeration and to keep a stable operation for long periods. According to some authors [15,44,51] the fluidisation velocity can be considered as the principal parameter in the control
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of the growth of the particles. Generally, for low values of U/Umf ( = 2), the growth is mainly governed by agglomeration. As the ratio of U/Umf increases, growth by layering becomes more and more prominent. However, if the ag glomeration must be totally avoided fluidisation ratios between 1 0 and 50 are needed [83]. In addition, Smith and Nienow [1 5] showed that the choice of the fluidisation velocity depends primarily on the nature of the support and that of the coating solution. For example, when a methanol solution containing 1 0% of benzoic acid was injected into a bed of glass beads (270 11m) fluidised with a gas excess of 0. 1 5 m S- 1 , bed quenching took place after 5 min. Increase in the excess of gas to 0.65 m S - 1 made it possible to maintain a stable operation up to 600 min. In the latter case, the dominant mechanism was layering. Also, it is worthwhile to mention the work of Cherif [84] who studied the effect of fluidising gas velocity on the stability of the operation as weil as on the coating criteria. The operation stability was followed by means of the time evolution of total pressure drop. In fact, it is weil known that bed quenching is characterised by a rapid decrease in pressure drop, because most of the gas goes through the slumped bed. Consequently the bed quenching point can be determined by measuring the pressure drop through the bed [84]. The results showed that the lower the gas velocity, the faster the bed quenching takes place. To maintain a stable operation with layering as the predominant mechanism, fluidising gas ve locities higher than 6 times the minimum fluidisation velocity of initial particles was needed. However, a drop of about 30% in the coating efficiency was observed when increasing the fluidisation velocity from 2 to 6 Umf. This was attributed to the increase of attrition rate with increasing fluidising gas velocity. Several workers [1 5-1 7] have reported a direct relationship between the attrition rate in fluidised beds and the excess gas velocity. In addition, a higher fluidising gas velocity results in higher spray drying rate. •
Mass of the bed Experiments carried out by Dencs and Ormos [45] during the production of urea in a continuous fluidised-bed coater, showed that the average size of particles increases with the height of the bed up to a value close to 1 .25 times the diameter of the column. Beyond this ratio the growth rate became independent of this factor. These observations were explained by the fact that an increase in the bed height entail on the one hand, an increase in the average residence time of particles in the bed and on the other hand, by the development of the mechanical constraints which support a more marked attrition of the solid par ticles in the bed. For the bed heights higher than 1 .25 times the diameter of the column, these authors postulated that there is a dynamic balance between the growth and the disintegration of the formed particles.
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During batch coating, Ormos et al. [64] studied the influence of the bed height between 40 and 1 30 mm. The initial size of the support varied between 1 00 and 200 �m. During tests, they kept the ratio of the mass of the aqueous solution injected with that of the support constant. They noted that the average size of the particles decreases significantly with the height of the layer between 40 and 80 mm to remain constant beyond that. In addition, according to Saleh et al. [1 7] for a given ratio of the introduced mass of solute to initial bed mass, the growth rate and the coating efficiency are independent of the initial bed mass. These results together with those related to the effect of liquid flow rate indicate that particles wetting in a fluidised-bed spray coater occurs only in a limited volume of bed called "atomisation zone", which is independent of total mass of particles. The penetration depth of the spray de termines the size of this zone. This is a function of gas velocity, the nozzle position, physical praperties of atomising and fluidising gas and particles mo mentum. The existence of such a zone in the coater was reported by Smith et al. [1 5] by measuring the temperature gradients near the nozzle. Since the total bed weight has no effect in the penetration depth of the spray there is no effect of this parameter in the coating criteria.
5. 1. 5. Influence of the coater's specifications
Aside fram general requirements to ensure a suitable fluidisation [85] additional conditions must be fulfilled to maintain a stable coating operation. In particular, the introduction of the coating liquid within the bed renders the operation much more delicate than the conventional fluidisation. Among all coater's specifications the characteristics and the position of the spraying system and the use of auxi liary mixing aids are the most important parameters. Dencs and Ormos [45] studied the effect of mechanical agitation on coating and granulation in a fluidised bed equipped with a vertical agitator. They observed that increasing the number of revolutions leads to a linear reduction of the particle size. However, beyond a critical value of 1 80 rpm, the size varied moderately with this factor. The position of the spray is also a design parameter which can have an on the duration of a stable operation and on the mechanism of growth and the efficiency of the operation. Some researchers [57,59] announced that a rise in the spray height with re spect to the bed surface led to a reduction of the size of the coated particles. This was attributed to spray drying of atomised droplets. For example, the results of RankeIl et al. [57] obtained in a fluidised-bed coater of 0.3 m diameter showed that the average size of the particles passes fram 500 to 250 �m when the po sition of the spray with respect to the distributor increases from 0.75 to 1 .5 m.
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According to Mortensen and Hovmand [86] the size of the particles is maximised when the spray is immersed in the bed. Ormos et al. [64] studied the influence of the position of the spray with respect to the distributor in the range between 0.09 and 0.24 m. They noted that, under their operating conditions, this factor does not have any influence on the average size of the particles, but it influences the particle size distribution. Cherif [84] studied the influence of the characteristics of the pulverisation sys tem (i.e. the type of the spraying nozzle and the angle of dispersion of the spray) on the mechanism of growth. 80th internal mixing and external mixing nozzles producing similar dispersion angles were studied. The results showed that the extern al mixing atomiser led to a slower growth rate due to a finer atomisation. However, the operation becomes less stable as the external mixing nozzles present a higher risk of filling of the liquid nozzle's opening. The influence of the spray dispersion angle was studied by using two internal mixing systems providing two angles of 1 5 and 70orespectively. It was observed that an increase in the angle of dispersion favours the agglomeration extent and hence the growth rate. Cherif showed that the height of the spray nozzle has a considerable effect on the efficiency of the operation without modifying the growth mechanism. Finally, sev eral authors reported that the most adequate position of the nozzle is that for which the end of the tube is immersed in the bed. Doing so, the scouring action of the bed particles permits to avoid cakes formation on the outside of the nozzle. 5. 1 . 6. Design options for fluidised-bed Goaters
The operating arrangement of a fluidised-bed coater varies according to appli cation, feed type (melt, slurry, solution, etc.), spraying nozzle configuration and solid throughput. However, all of the possible configurations are modifications of a basic idea: particles to be coated are suspended by a hot gas stream and the coating liquid is applied as homogeneously as possible onto particles surface. Figure 9 assembles a survey of diverse design options available for fluidised bed coaters. Regarding the spraying of coating agent, three possible elementary configurations are commonly used which are top-spray, boUom-spray and side spray equipment. In some cases a combination of these options is used. The boUom spray configuration promotes a more regular circulation of particles through the weUing zone but its disadvantage is the clogging of the nozzle(s) that cannot be remedied easily since removal of the nozzle during a run is not pos sible. Side-spray systems are frequently used for waste and sludge incineration but rarely for coating operations. Heat for evaporation of the solvent is either supplied as sensible heat in the fluidising air or through the walls and/or by means of heat transfer surfaces inserted inside the bed. In some cases, the exiting air is recycled after dehu midification in order to reduce energy consumption of the unit (Fig. 9).
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t:=CC=� =��D=�fxI:::J air outlet +--- air
filters
coating solution
recycle (optional)
f 4-__ fines recycle (optional)
heater Fig. 9. Typical fluidised-bed coater.
(a )
� (b)
(c)
(d)
Fig. 10. Examples of specially designed distributors to improve particle circulation.
Dust removal systems (cyclones and/or filter bags or a combination of both) are usually used to separate fine dusty powder from the exit gases. Coating units can either be carried out continuously or in batches. Batch units are used for low solid throughputs but are versatile since the same apparatus might treat several types of solids. The coating mass distribution is however not as good as that obtained by continuous operations. This is because all particles do not have the same residence time in the wetting zone of the bed. The res idence time distribution (RTD) of particles within the spray zone can be tightened by a proper design of the column or the air distributor. For example, distributor designs presented in Fig. 1 0 provide a more regular circulating of solid particles
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within the bed and thereby a more uniform coating mass distribution. Continuous operations can be performed either in a single piece of apparatus or in a cascade of different pieces of apparatus. The former is easier and less costly but the latter results in a more uniform coating mass distribution because the RTO of particles shifts from mixed flow to plug flow as the number of coating chambers increases. I n the case of a single unit, partitioning the coating cell as illustrated in Fig. 1 1 could tighten the RTO. Note that option B is more adequate for agglomeration process because the passage of products from one compartment to another occurs through the gap distance between the air distributor and partition plates. Hence, due to segregation, coarser agglomerates have more possibility to leave a given compartment than finer agglomerates, which are retained during longer times. 5.2. Spouted bed coaters
Fluidised-bed coating would be a good choice for coating powders having small to medium sizes (up to 1 mm). Even though this technique can be used for larger particle sizes, its advantages will be largely disrupted as far as energy consid erations are concerned. For large particles (Geldart's class 0), the energy con sumption (calculated by the product of the gas flow rate and its temperature drop through the bed) is determined by the minimum fluidisation velocity rather than the net energy required to eliminate the solvent. Spouted beds have been de veloped into an effective alternative to fluidised beds for handling coarse par ticles, i .e. particles that exceed about 1 mm in diameter [87,88]. Since then they have been commercially used as a substitute for the fluidised bed, to process a great variety of coarse solid materials. A typical spouted bed consists of a cylindrical vessel usually with a conical base and a central orifice in the cone's bottom. The vessel is filled with solid particles and spouting gas is injected through the orifice with relatively high feed ,
feed •
to cyclons and/or filters
to cyclons .nd/or filters
Products removal
Air inlet
Products removal
(a)
(b)
Fig. 1 1 . Schematic view of continuous f1uidised-bed coating units.
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velocities, typically between 1 and 30 m S-1. The gas also flows into and upwards through the annulus. The high gas velocity causes a stream of solid particles to rise rapidly in a dilute central zone within the bed referred to as the spout. In the reason of diverging form of the spout the gas and solid velocities decrease along the bed height. Therefore, having reached a given height entrained particles fall back forming a fountain above the annular space around the spout. The particles form a loosely packed bed within the annulus space and slide down slowly and reenter the spout during their descending at different levels of the bed. Hence, a spouted bed has three well-defined characteristic regions (Fig. 1 2): •
•
•
The spout, characterised by relatively high velocities of both solids and gas stream, short contact times between gas and solid phases, high bed voidage and co-current solids movement with respect to upward gas stream. The fountain, where the solids movement with respect to the gas stream is nearly crosscurrent. The annulus (also called the down-comer) which, compared to the spout, is characterised by high solids concentrations, low gas and solids velocities, higher contact times and a counter-current solids movement.
In a spouted bed, a well-defined cyclic movement is thereby imposed on the solid particles. In order to avoid any lateral exchange between the spout and the annulus the latter is sometimes delimited by means of a draft tube. Both top-spray and bottom-spray spouted-bed coating processes can be used. However, the most commonly used configuration is the bottom-spray configuration.
(a) spouted bed coater Fig. 1 2 . Spouted-bed coating apparatus.
(b) spouted-t1uid bed
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In this ease, the eoating liquid is sprayed in the lower region of the spout where the spray droplets eollide with the bed partieles. Eaeh time a particle passes through the spray zone, it aequires an additional amount of eoating material. The deposited eoating liquid should solidify or dry outside the spray zone, either in the spout or in the annulus. This eireulation of solid particles is repeated until the desired eoat amount is deposited on the solid particles. Repetitive passages through the wetting zone inerease the eoating eontent and reduee eoat deficiencies due to uneven deposition on the surfaee. Consequently, the amount of eoating eontent of eaeh particle depends on the eoating applied in each pass and the total number of passes exeeuted by the particle during the operation. In almost all experimental works reported in the published literature, particle growth by layering is the dom inant growth mechanism. Industrial spouted-bed coating processes operate either continuously or dis continuously. The former is better matched for high produetion rates but produces less uniform eoating mass distribution due to the variation in the RTD of particles in the wetting zone. Unfortunately, despite its importanee, experimental data on RTD in continuous spouted beds are not known. As for batch processes, heterogeneity in coating distribution do exist due to variations in the number of passages through the spray zone and the amount of the coating liquid deposited in eaeh pass. However, recent works of Cheng [89,90] showed that the coating per pass distribution is responsible for the majority of the variation in the spouted-bed coating proeess. Note that the use of a draft tube eould however lead to a more uniform eoating. Regarding the top-spray spouted-bed eoating proeess, Robinson and Waldie [90] reported that the growth rate is dependent on particle size. They postulated that larger partieles spend a greater percentage of their time in the spray zone. Finally, note that the modifieation of standard spouted beds to include the charaeteristics of fluidised bed, ealled spouted-fluid bed, has also reeeived at tention due to its better solids mixing and heat and mass transfer rates. This kind of apparatus involves a substantial fluid flow through a single central inlet orifice, as in spouted bed, and an auxiliary fluid flow through a distributor surrounding the central orifice, as in fluidised bed (Fig. 1 2b). The auxiliary gas stream thereby keeps the annular zone lightly fluidised. 80th flat based or eonical based columns can be used. 5.3. Wurster apparatus
Wurster apparatus is perhaps the most eommon eonfiguration used for film coating. This apparatus is an air suspension coating introduced in the early 1 950s by Wurster. Industrial exploitation of Wurster coaters is more recent than fluidised beds and spouted beds. This system is a combination of the eoncepts of fluidised
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bed and spouted bed techniques (Fig. 1 3). A draft tube insert (Wurster partition or column) is placed coaxially in the bed to order the circulation of particles. The particles are carried by an upward gas stream in the draft tube and fall downward around it at the top of the tube. The coating solution is sprayed upward through a nozzle in the centre of the distributor plate placed at the bottom of the bed. The gas velocity inside the draft tube is significantly higher (gene rally between 3 and 20 ms- 1 ) than inside the annulus (0. 1 -1 .0 ms- 1 ). A gap between the distributor plate and the bottom of the draft tube allows powder to be picked up at this interface and accelerated by the high-velocity gas stream. Generally, the distributor is a perforated plate, with the size of perfora tions decreasing from the centre outward. The fraction of open areas of the Air outlet
F=::::::=::====i'-,
<=
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Atomizi ng a i r <=
Coating solution Fig. 1 3. Wurster coating apparatus.
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distributor beneath the draft tube and the annulus determine the relative amount of air flowing into these two sections. The liquid droplets are moving faster than the solid partieIes so the partieIes can be wetted and dried in the draft tube but the drying can also take place in the annulus. The solid movement in a Wurster coater is very similar to that of a spouted bed. The size of partieIes is however much smaller, elose to that used in fluidised-bed coaters. Compared to conven tional fluidised-bed coaters, in the Wurster apparatus growth by layering is en couraged. This is due to low solids concentrations and elevated heat and mass transfer rates within the draft tube. Industrial Wursters can be used for handling up to 500 kg of solids. The proc ess is extensively used in the pharmaceutical industry for precision coating and modified release drugs, e.g . , sustained release, enteric release and temperature controlled release. The literature on Wurster coating processes is less abundant than fluidised-bed coating. The fundamental mechanisms controlling the process are not yet weil understood and the optimisation is often based on operator experience. However, the knowledge from fluidised-bed coating could be used as guidelines as the majority of phenomena occurring are comparable in both operations. For exam pie, it has been reported that, similar to fluidised-bed coating, in the Wurster apparatus the smaller partieIes capture more coating than the larger partieIes [91 ] . In addition, the effect of the partieIe porosity is analogous to that observed in fluidised beds. Note also that the circulation time distribution can vary considerably depending on the partieIe properties, coater configuration and process variables such as air flow rate, partition gap, loading, atomisation air velocity, and distributor design. 5.4. Rotating drum, pan and d isc coaters
Rotating drum, pan and disc coaters are among the oldest and the simplest techniques used for coating particulates. Rotary pans were originally developed in the confectionery industry and adopted by pharmaceutical industry for sugar coating of drugs. The main characteristics of rotational coaters are their versa tility, flexibility, large throughputs and ability to handle a wide range of products. The common principal point of these techniques is that the motion of particles is maintained in a mechanically rotated vessel, while spraying liquid onto the mov ing bed of partieIes carries out coating. Figure 1 4 illustrates a schematic view of rotary coaters. These techniques are suitable for coating large partieIes, from a few millimetres to some centimetres. A main drawback of rotational coating techniques is the poor heat and mass transfer rates. Unlike the air suspension methods (fluidised beds, spouted beds, Wurster) a suitable control of the temperature is not possible when using
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(a) rotary drum
(b) rotary di c
Fig. 1 4. Schematic view of rotary coaters.
rotational apparatus. In addition, the holdup of rotary eoaters is small whieh re sults in bigger shell volumes eompared to pneumatie-based apparatus. Beeause of the large size of apparatus substantial filters must be used to eolleet the dust if neeessary. Generally, eoating pans operate diseontinuously, whereas dises and drums ean be used either in bateh or in eontinuous modes. A eonventional rotary pan eonsists of an ellipsoid vessel made usually of stainless steel and mounted on a gearbox shaft whieh is driven by an eleetrie motor. A hot air blower is usually used to irrigate the particies bed and improve the drying. The seleetion of a eoating pan depends on manufaeturer specifiea tions and may range from a simple modifieation of the eonventional eopper pan to specialised high-volume vessels. The operating mode of eoating dises and pans are very similar. The only major differenee is the geometrie design of the vessel, whieh makes rotary dises suit able for eontinuous operation. The diameter of industrial dises varies between 3 and 1 0 m and the height to diameter ratios between 0 . 1 and 0.3. Continuous dises are only suitable for short residenee times. For longer residenee times or when a eontrolled RTD is required rotary drums are preferred. Rotary drums are usually equipped with one or more ribbon-like baffles mounted to the inside surfaee of the front wall. In eontinuous rotary drums eoating agent is sprayed onto the bed, wetting the particies as they pass through the drum. Coating agent may be sprayed either at the entire length of the drum or only during the first seetions. The last eompartments of the drum are used for evaporation and drying and in some eases for eooling. A hot and dry gas stream generally traverses the drum. In some industrial designs, the drum may have a perforated or mesh wall for drying of the tablets. In this ease, the hot gas stream is direeted through the drum wall as the drum and the bed of particies are being rotated. This kind of design
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enhances gas to particle heat transfer and is suitable when high drying rates are needed. Note that rotary coaters are more suited to narrow size distributions. In the case of large particle size distributions, the coating distribution is less uniform due to natural segregation as separation takes place: fines concentrate near the bot tom of the kidney-shaped cross-section of the bed and the coarsest particles travel near the surface. The sizing of rotary drums is based on the average residence time t, which is calculated from the ratio of total mass of particles contained in the vessel (holdup), m, and mass throughput, C. The holdup, m, is a function of drum volume and drum loading, which varies between 0.1 and 0.3. Residence time depends mainly on three operating parameters: the angle of inclination of the drum's axis against the horizontal, the rotational speed and the drum's length. However, the angle of inclination is rather small (2-5°and only serves to provide the required axial movement. The rotational speed is usually fixed between 25% and 40% of the critical speed beyond which tumbling and centrifugation occurs. Unfortunately, the lack of the knowledge does not allow carrying out a priori sizing of rotary drums. For a given set of coating agent and substrate the sizing is based on experimental runs in pilot plants during which the appropriate operating conditions (angle of inclination, rotational speed, hOldup, liquid flow rate, con centration) are determined. The scale-up is then performed by know-how from the equipment manufacturer but some useful guiding rules exist [92]. 6. CONCEPTS I N MODELLING THE COATIN G PROCESS
Rational scale-up of coating units requires modelling of the growth phenomena by layering and agglomeration. A successful modelling requires knowledge of both mechanical and physicochemical phenomena occurring during the coating proc ess and presented in previous sections. Generally, the two main parameters that are chosen as modelling variables are either the particle size or the coating content of particles. Existing models in literature, aimed at predicting the evo lution of these target variables during simultaneous coating and agglomeration processes, may be broadly classified into two main categories: empirical and theoretical models. The first group involves models of "black box" type where the relationship between the particle mean size and key parameters in the process environment expected to govern the particle growth (Le. operating conditions and physical properties of solid and liquid) is given by an empirical expression. These models are quite simple but their use is restricted to the special cases and the domain of operating conditions at which the phenomena are studied. A very different process is used for theoretical models where one tries to take into account the physical phenomena occurring during the operation. Among the
367
Coating and Encapsulation Processes in Powder Technology
various theoretical modelling works on coating and agglomeration, two different approaches can be distinguished: simple approach and "fundamental" approach. The simple approach neglects the variations in particle size and solute content distributions considering that all particles have the same size as weil as the same residence time in the system. In other words, it is assumed that the size and the solute content of a single particle can be representative of the bulk properties of the powder. In this case, the targeted parameters can be predicted using con ventional heat and mass balances established for solids. In the case of mono size spherical particles with a uniform distribution of solute over particles the simple layering model leads to the following relations for estimating of the evo lution of the solute content and the mean particle size as a function of time: •
•
solute content
TS(f) =
particle mean diameter
dp =
[cf..
�·VL CI] t
P L Mo
_1]_ W'L
C Pp �o t]
pO 1 00 P L Ps M0 +
(1 0)
1 3"
(1 1 )
where Ps , Pp and PL are solute (coating agent) density, particle density and liquid density, respectively. vi.'L the coating liquid mass flow rate, t the operating time, Mo the initial mass of the bed, the coating efficiency and the concentration of the coating agent. dpo and dp are the initial particle size and particle size at time t, respectively. An important limitation of any theoretical model of coating processes is the difficulty of relating the coating efficiency to the process and product-related parameters. Note that this type of model is suitable and frequently used in the coating process by a solute but is not reliable when agglomeration is pronounced because the total number of particles varies with time. In the laUer case a simple model proposed by Sherrington could be used [93]. If the distribution of a given coating criterion rather than its mean value is to be predicted, more detailed description must be used based on a coupling conven tional heat and mass balances and population balance equations (PBEs). This is particularly the case for the film coating of drugs where even smali deviations in the thickness of the polymer film can significantly alter the properties of the final product. The population balance is a statement of continuity that describes how a given property of the population of particles changes with time and in space. In prin ciple, any common property of particles can be used but as mentioned above in
I]
C
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K. Saleh and P. Guigon
coating processes the more interesting parameters are the particle size and the coating content. PBEs were first introduced based on statistical mechanisms by Hulburt and Katz (1 964) [94]. Since, the PB Es were successfully applied for different par ticulate systems such as crystallisation, granulation, mixing, fluidisation, etc. PBEs describe how the rate of variation of the number of particles in a given interval of the target property (particle size, coating content, etc.) can be related to the rate at which particles enter and leave that interval by different phenomena occurring (Le. bulk flow into and out of the system, coating, agglomeration, breakage, etc.). In the most general case, for a continuous particulate system , the macroscopic population balance leads to the following expression [94,95]: 1 a(NTf) = a(Gf) Qoutfout - Qin�n + B 0 ( 1 2) _ ax NT NT at where G = axlat designates the mono-dimensional particle growth rate and f the population density function of particles defined on a number basis. More precisely f is a function of the spatial coordinates in the system, of the target property x of the particles and of the time, t. f is defined as the ratio of the number of particles, aN, in a differential neighbourhood around x, to the size of the neighbourhood, ax Q designates the number-based particle flow rate and the subscripts in and out specify the inlet and outlet flows. The variables B and 0 are the birth and death rates of particles number variation in a given x interval by such events as ag glomeration and breakage which change population density in a discontinuous fashion. The application of PBEs for modelling the simultaneous growth by lay ering and agglomeration in coating processes are abundant. These models can be classified in two main categories: _
•
•
_
_
Single-zone models: In single-zone models it is assumed that the particles are homogeneously mixed and the coating agent is evenly distributed throughout the bed volume. Equation ( 1 2) is directly applicable for single zone models. Generally, in a coating apparatus due to high intensity mixing of the particles the population density, f, is independent of spatial coordinates. In addition, usually the breakage rate is not detailed separately. This means that B and 0 in equation ( 1 2) correspond to the net variation of particles number by combined effect of agglomeration and breakage . Twin-zone models: Sheroney [96] and Wnulowski and Setterwall [97] were the first to propose a twin-zone model based on the PBEs for the fluidised-bed coating. In a twin zone model, the volume of the bed of particles is divided into two distinct regions: an active zone surrounding the spray nozzle and a mixing zone. This type of model is more reliable as it has been experimentally con firmed that such a distinct zone exists near the nozzle where the deposition of the spray on the particles and bulk evaporation of the solvents take place
369
Coating and Encapsulation Processes in Powder Technology
[1 5,17,1 9,21 ,22]. The size of this region is determined by the penetration depth of the spray, which depends in turn to operating conditions. It is considered that the coating mass deposited on the particles is directly proportional to the residence time of the particles in the spray zone, so that the coating mass distribution can be regarded as the RTD function. In a twin zone model the PBEs are applied separately for each distinct zone taking into account the internal flow of particles circulating between them: For the spray zone: •
1_ o NT.sprayfspray _NT,spray (
ot
)
=
_
o(G . fspray ) OX
_
aOoutfout - ßOinf;n
NT.spray
_
Oe ( fspray
- fdry ) + B NT,spray
_
0
(1 3a)
In this equation, is the number fraction of the spray zone and Qe the cir culating rate of particles between spraying and drying zones, which is considered to be the same for entry and exit flow. Note that even for a batch operation (Qin Qout 0) the internal zones must be considered as open systems as Qc#O. a
=
•
=
For the drying zone there is no growth by layering nor by agglomeration: 1 a(NT,dryfdry) (1 a)Qout fout - (1 - ß)Qinnn Qc (fdry - fspray) (1 3b ) at NT,dry NT,dry NT,dry -
-'-..:.----'---'-'--'
Simultaneous resolving of equations (1 3a) and (1 3b) results in the determi nation of fspray and fdry . Note also that if it is supposed that all particles have the same residence time in the wetting-evaporation zone (i.e. the particles pass regularly through a well defined spray zone) twin-zone models leads to the same predictions as single zone models. A difficult task while modelling the growth phenomena results from the com plexity of the PBEs. Although analytical methods of solving PBEs exist their use is limited to simple cases. Actually, analytical solutions are most often used to verify the persistence of numerical methods. Actually, numerical methods present two obvious advantages. First of all particle size distributions of any type can be dealt with and secondly discontinuous processes such as sequential feeding and solid removal can be taken into account. Extensive literature relative to numerical methods of solving PBEs is available. For a detailed review see Hounslow et al. [98] and Hogg [99]. The basic idea consists in breaking up the particle size distribution into a number of discrete x ranges. The population balance, described by an ordinary differential equation, is then established for each x interval and the resulting set of equations are solved by numerical methods.
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The most popular numerical method is that proposed by Hounslow et al. [98] mainly because it guarantees to predict the correct rate of change for first four moments; Le. total particle number, length, surface and volume (or mass). Note that the modelling of simultaneous growth by layering and agglomeration requires the introduction of the appropriate formulas for the particle growth rate, G, and agglomeration terms (B-O) into PBEs. •
Agglomeration term: In the majority of coating operations the main growth mechanism is the layering and agglomeration can be neglected. This is par ticularly true when the particle size exceeds a few hundreds of micrometers. In this case, the PBEs can be considerably simplified because both B and 0 are nil. For finer particles, the agglomeration can hardly be avoided and must be taken into account. Smoluchowski [1 00] was the first to develop a mathematical expression for birth and death rates by agglomeration. Considering that particle coalescence results from a series of binary collisions between them, he es tablished the following equations:
/2 ß(v
B= ( a
J
0 = f(v)
-
w, v)f(v - w) f( w)8w
100 ß(v, w)f(w)8w
( 1 4a) ( 1 4b)
where v and w are the volumes of the coalescing particles. The asterisk is used to signify that volume rather than size or coating content is chosen as the internal coordinate. The conversion of this equation to a length-based or a mass-based form is straightforward. If particle mass or coating content is chosen as x coordinate the equation ( 1 4) is directly applicable as: ( 1 5) u = m/p = mp(1 + Ts ) /p In contrast, if the particle size is used as x variable equation ( 1 4) can be ex pressed as follows (see Hounslow et al. [98]):
2 ß ( L3 _ 1I?) 1/3 , A)t/l( L3 - A3) 1/3) t{I(A)dA L B(L) - -2 { (L3 _ ,1,3)2/3 L
-
Jo
O(L) = t{I(L) 100 ß(L, A)t{I(A)dA
( 1 6a) ( 1 6b)
Besides the fact that this model considers only binary collisions, its main draw back is that it suggests that the total volume of agglomerating particles is con served. In equations (14) and ( 1 6), ß is a measure of agglomeration extent and is called the coalescence kernei, which defines the rate at which binary particle collisions
Coating and Encapsulation Processes in Powder Technology
371
result in successful coalescence. In general, this parameter is subdivided into two parts: ß(v, w) = KE
( 1 7)
where K is the frequency of binary particie coilisions between particies of volumes v and w. This parameter is a function of such parameters as apparatus geometry and operating conditions, which influence the hydrodynamic behaviour of the system. E is the probability of successful coalescence foilowing coilision between two particies of volumes v and w. This parameter is mainly conditioned by the balance between disruptive and attractive forces exerted during particie colli sions. Generaily, both K and E are size-dependent parameters but it is usuaily assumed that equation ( 1 7) contains two distinct parts, one independent of the particie size and the second dependent on it: ( 1 8) where ß 1 includes the functional dependency of the agglomeration kernei on the sizes of the coiliding particies. Several attempts have been made to develop a generalised expression for agglomeration kernei. However, despite the plenty of experimental results re ported in the literature none of these representations is completely reliable. Pro posed expressions are based on probabilistic considerations rather than a rigorous description of the coilision phenomenon [1 01]. At the moment, the most commonly used expression is the foilowing generic form proposed by Kapur [1 02,1 03]: _ (v + W) 8 ß1 ( v, W) ( 1 9) (vw)b -
In this expression, the numerator and denominator are approximate measures of the binary coilision frequency, K, and the probability of successful coilision, E, respectively. •
Coating term: For size-based PBEs the particie growth rate, G, in equation ( 1 2) is the rate of increase in particie size resulting from the deposition of the coating agent into the surface of particies. Assuming that particies belonging to different interval sizes receive ail the same amount of coating agent, G is given by w G = _1]_ liq C 3. (20) 1 00 P liq Pb S
This equation states that the coating rate is inversely proportional to the total surface area of particies in the system, S. This is a fairly realistic hypothesis because the coating process is a surface-dependent phenomenon.
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K. Saleh and P. Guigon
Note that equation (20) can also be written in a discretised form [36] more adequate for numerical solutions: 2 w Gi = � liq C (21 ) 1 00 PliqPb I: nNjL."j . J
2
Gi is the growth rate in the ith size interval. The efficiency 1] depends, more often than not, to the mean particle size inside the interval. The term I: nNjLJ is a measure of total surface CONCLUDING RE MARKS
The industrial scale-up and practise of coating powder materials can be suc cessfully performed provided that the optimal operating conditions and required residence time is determined prior to exploitation. Currently, a proper determi nation of operating conditions is only possible by conducting coating experiments in bench scale units. Although existing literature provides highly useful informa tion on the effect of different variables on the coating process, its use is Iimited to qualitative rather than quantitative analysis of phenomena. In particular, the effect of operating variables on the coating efficiency and agglomeration extent is not yet weil described. Consequently, an accurate and reliable determination of these parameters cannot be performed by theoretical considerations and more inves tigations should be carried out in this orientation. Finally, another major difficulty is the control of the coating quality and homogeneity both on a microscopic and a macroscopic scale. REFERENCES [1] Z. Ormos, Handbook of powder technology, vo!. 9, in: D. Chulia, A. Deleuil, Y. Pourcelot (Eds.), Powder Technology and Pharmaceutical Processes, Elsevier, Amsterdam, 1 994. [2] G. Cole, J. Hogan, M. Aulton, Pharmaceutical Coating Technology, Taylor & Francis, UK, 1 995. [3] S. Gouin, Trends Food Sci. Tech. 1 5 (2004) 330-347. [4] O.R Lundt, J. Agric. Food Chem. 1 9 (5) ( 1 971 ) 797-800. [5] C. Thies, in K.L. Kadam (ed.), Granulation Technology for Biproducts, CRC Press, 1 989, Boca Raton, FL, Chap. 7, Microencapsulated Enzymes and Live Mammalian Cells, pp. 1 79-206. [6] R Pfeffer, RN. Dave, D. Wei, M. Ramlakhan, Powder Techno!. 1 1 7 (2001 ) 40-67C. [7] A. Mujumdar, D. Wei, RN. Dave, R Pfeffer, C-Y. Wu , Powder Techno!. 1 40 (2004) 86-97. [8] C. Conesa, K. Saleh, A. Thomas, P. Guigon, N. Guillot, Prediction of flow properties of powder coatings used in automotive industry, "KONA" Powder Sci. Techno!. Japan, No. 22 (2004) 94-1 06. [9] K. Meyer, I. Zimmermann, Powder Technol 1 39 (2004) 40-54.
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R Turton, X.x. Cheng, Powder Techno!. 1 50 (2005) 78-85. P. J. Sherrington, Chern. Eng. JulyjAugust (1 969) 201-2 1 5 . H . M . Hulburt, S. Katz, Chern. Eng. Sci. 1 9 ( 1 964) 555-574. A.D. Randolph, M A Larson , Theory of Particulate Processes, Acadernic Press, New York, 1 971 . D . F . Sheroney, Chern. Eng. Sci . 36 ( 1 98 1 ) 845-848. P. Wnulowski, F. Setterwall, Chern. Eng. Sci. 44 (3) ( 1 989) 493-505. M.J. Hounslow, RL. Ryall , V.R MarshalI, AIChE 34 ( 1 1 ) ( 1 988) 1 82 1 -1 832. R Hogg, Powder Techno!. 69 (1 992) 69-76. M. Srnoluchowski, Z. Phys. Chern. 92 ( 1 9 1 7) 1 29. F.Y. Wang, I .T. Carneron, Powder Techno!. 1 24 (2002) 238-253. P.C. Kapur, Adv. Chern. Eng . 1 0 (1 978) 55-1 23. P.C. Kapur, D.W. Fuerstenau, I & EC Process Des. Dev. 8 ( 1 969) 56-62.
CHAPTER 8 M o de l l ing of Pan-Coating P rocesses for P ha rmaceutical D osage F o rm s Preetanshu Pandey8 , Yongxin Song b a n d Richard Turton b , *
aSchering Plough Research Institute, Oral and Respiratory Product Oevelopment, 2000 Galloping Hili Road, Kenilworth, NJ 07033, USA bOeparment of Chemical Engineering, PO Box 6102, West Virginia University, Morgantown, WV 26506, USA Contents 378 1 . Introduction 2. Modelling of mass coating variability 380 2.1 . Phenomenological modelling of the renewal process 380 2.2. Compartment and population balance models 382 2.3. Monte Carlo techniques 384 2.3. 1 . Monte Carlo simulation in a pan-coating device using video-imaging techniques 385 2.3.2. Video-imaging experimental set-up 386 2.3.3. Materials and methods 387 2.3.4. Results 390 2.4. Discrete element modelling (DEM) and computational fluid dynamics (CFD) 397 2.4. 1 . Spherical-particle DEM simulation 399 2.4.2. DEM method 399 401 2.4.3. Dynamic angle of repose 2.4.4. Average cascading velocity of particles in the spray zone 401 2.4.5. Effect of pan speed and pan loading 403 2.4.6. Tablet-shaped DEM simulation 403 2.4.7. Representation of tablet shape and contact algorithm 406 2.4.8. I mplementation of contact algorithm for tablet-tablet collision simulation 408 412 3. Conclusions and discussion References 415
* Corresponding author. E-mail:
[email protected]
Granulation Edited by A.D. Sa/man, M.J. Houns/ow and J. P. K. Seville (' 2007 El sevier B.V. All riohts reserved
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1 . I NTRODUCTION
The coating of pharmaceutical dosage forms has been practiced for many cen turies. Tablets are coated for a variety of reasons that include: • • • • • • • •
masking unpleasant taste and odour of drug; increasing shelf-life of drug by providing environmental protection; improving product identity; improving ease of handling; improving cosmetic appearance; controlling site (in the body) of drug release (enteric coating); controlling rate of drug release (sustained release coating); and coating of active drug on tablet.
The inter-tablet coating weight gain is extremely critical when the coating of the tablet plays an active role in the drug release process (enteric, sustained, active drug coated). With the advent of process analytical technology (PAT), a new FDA initiative, the industry is focusing on improving manufacturing efficiency and product qual ity. The goal of PAT is to adopt innovative technologies to increase product quality without raising concern that a new approach will lead to validation risks and production delays. One of the key components of this knowledge-based approach is to understand better the product manufacturing processes. With this in mind, the current review focuses on the different approaches to modelling a key unit operation in the pharmaceutical industry, namely coating. By incorpo rating one or more of the modelling approaches introduced here, the effects of variables used in pan-coating process can be quantified on a sound scientific basis and a rational method for process improvement can be formulated. The various types of coating equipment used can be classified broadly into pan coaters and fluidized-bed coaters. The fluidized-bed coaters, in general, provide more uniform coating and require shorter processing time but are limited to the use of relatively small particles (Table 1 ). The major criterion to decide between the use of fluidized bed and pan coaters is the size of the substrate. A rule of thumb is that if the product diameter is less than 6.35 mm (1/4 in.) then the Table 1 . Comparison of pan and fluid-bed coating methods
Coater type Pan Fluid bed
Advantages Low mechanical stress Simple operation Short processing time Low product variability
Disadvantages Longer processing time Greater product variability High mechanical stress High erosion
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preferred equipment for coating is the f1uid-bed coater [1]. The main reason behind this is the energetic product movement inside the fluid bed, which may cause attrition of the particles. Pan coaters are widely used in the Pharmaceutical Industry to coat relatively large particles or tablets. A good overview of the different kinds of pan coaters is provided by Porter [2]. It is simple in operation and offers low mechanical stress to the tablets. The main disadvantages of a pan coater are the long processing time and high product variability. Rotating drums or pans are also widely used in many engineering (chemical and metallurgical) processes, such as mixing, drying of granular and powder materials, milling, and granulation. In a typical pan coating process, a bed of tablets is placed inside a rotating drum. As the drum rotates, the bed cascades downwards under gravitational force, thus providing a fresh layer of tablets to come in contact with the spray and be coated with the coating solution (Fig. 1 ) . The coating solution is fed through a two-fluid air atomizing spray nozzle. Tablets get coated as they enter the spray zone and then cascade down and pass into the bulk of the tablet bed. At some point in time, the tablets re-enter the spray zone and the coating and drying processes are repeated. An important objective for the coating equipment is to promote the regular movement of tablets through the spray zone; however, tab lets may bypass the spray as they circulate or enter stagnant or slow moving regions of the tablet bed that reduce the frequency of circulation through the active coating area, namely the spray zone [3]. The most important parameter associated with coating operations is the variability of the applied coating. Mass coating variability (CV) refers to the variation in the mass of coating material that tablets receive.
Atomizing Air
/'
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•
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I
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Fig. 1 . Representation of a coating operation in a typical pan coating device.
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Although tablet coating is one of the oldest pharmaceutical processes, the process is still often considered more of an art than science. The underlying science of the coating process is complicated and the ability of the pharmaceu tical scientist to predict reliably the performance of a coated product a priori is often limited [4]. Different modelling approaches have been used to date to char acterize the mass coating variability. The most common approach in the industry is to study the effects of coating formulation and process parameters on coating mass variation through a series of designed experiments with the appropriate statistical analysis and regression. This type of modelling (or regression) results in information specific to a single formulation/product and is particularly useful for optimization purposes but ignores the physics behind the process. There are various techniques used to model the mass coating variability in a pan-coating process. These include: • • • •
phenomenological modelling; compartment and population balance modelling; Monte Carlo modelling; and DEM (discrete element modelling) and CFD (computational fluid dynamics) modelling.
A brief overview of each of these approaches for coating systems is provided in the subsequent sections with emphasis on Monte Carlo and DEM methods for pan-coating processes. 2. MODELLING OF MASS COATING VARIABI LITY 2. 1 . Phenomenological modelling of the renewal process
In this approach, the overall coating process is considered to be made up of many coating events where the tablet receives coating during each event. The final coating weight gain is the addition of coating received during all of these coating events. Thus the number of cycles a tablet completes in the spray or coating zone during the entire operation and the amount of coating received per pass through the spray zone determine the total amount of coating received by an individual tablet. The distribution of the number of cycles can therefore help to quantify the coating variability. Mann et al. [5] used concepts from probability theory to derive an expression for the mass coating variability (CV) in terms of the number of passes/cycles distribution, and the coating-per-pass distribution. They showed that the overall coefficient of variation for fluid-bed systems is given by: CV = O"lolaI = {llolaI
(1 )
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Modelling of Pan-Coating Processes
where fl and (i stand for mean and standard deviation respectively, subscript 'total' stands for the overall distribution, subscript 'x' stands for the coating-per pass distribution, and subscript 'n' stands for the number of cycles distribution. Mann [6] also showed that the number of passes distribution could be de scribed in terms of the circulation-time distribution. Using this transform, equation ( 1 ) can be written as equation (2). The circulation time is a much easier param eter to measure than the distribution of number of cycles. cv = (itotal =
fltotal
((ix) 2 flet ((iet) 2 flet flx
teoat
+
flet
teoat
(2)
where subscript 'cl' stands for the circulation time distribution. It is clear from equation (2) that CV is proportional to )1 jteoat for fluid-bed systems. Cheng and Turton [7] also derived this result using renewal theory for a Wurster fluid bed. This same effect of coating time on coating uniformity is also reported by Hall [8] for several types of industrial coating equipment. However, to the authors' knowledge, no such relationship has been published for pan coating. In order to characterize the mass coating-per-pass distribution, Shelukar et al. [9], and Subramanian et al. [1 0] injected a pulse of blue dye into the coating solution for a period equal to the average circulation time of the particles. The blue dye content on sampies of particles was used to estimate the coating-per-pass distribution. Shelukar et al. [9] found that the main contribution to the overall CV was from the mass coating-per-pass distribution (76-86%) and that the spread of the cycle time distribution had a much smaller effect on the overall CV. Cheng and Turton [7] concluded that, for the coating of 1 mm diameter non-pareils, the mass coating-per-pass distribution was even more important than for tablets with over 90% of the CV attributed to the sheltering of particles in the spray region. The cycle-time or circulation-time distribution has been measured experimen tally using various techniques for both fluid bed and pan coaters. Mann and Crosby [1 1 ] , Waldie and Wilkinson [12], Cheng and Turton [1 3] , and Shelukar et al. [9], all used a magnetic tracer particle and a detection coil in a draft tube or spouted fluidized bed. The distribution of cycle time was found by measuring the times at which the tracer particle passes through the detector coil (Iocated around the spouted region of the bed). Similar studies have been performed on rotating drums or pan coaters. Most of these studies have focused on understanding and quantifying the movement of tablets inside a rotating drum, and have not rigorously addressed the spray dy namics. Parker et al. [1 4] measured the movement of a radioactive particle using a positron emission particle tracking (PEPT) technique to determine the cycle or circulation time distribution. Nakagawa et al. [1 5] used magnetic resonance im aging (MRI) to measure the concentration and velocity profiles of particulate flows in a rotating horizontal cylinder. Turton and co-workers [ 16-1 8] used video-imaging
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techniques to measure the circulation time of a tracer tablet (identical to the re maining tablets except for colour) in a pan coater. This technique is also capable of quantifying the area of the tablet that is projected towards the camera or the spray nozzle in a coating operation. Thus, the amount of coating that the tablet would receive can also be estimated. It is important to point out that it is possible for the tracer to circulate a few layers below the top surface of the cascading layer and not be 'seen' or captured by the camera. Since the camera replaces a spray nozzle in a coating operation, the tablet will not 'see' the spray during such an event and hence will not receive any direct coating [1 7]. Thus, this experimental technique captures the dynamic nature of the cascading layer. Any model developed for the coating process, where a tablet is assumed to continue to remain at the surface, once it emerges, does not completely represent the true nature of the process. The video imaging technique allows quantification of the mixing level in the pan, and can be used to compare and optimize different baffle designs in order to achieve optimal mixing [1 9]. This technique is discussed in more detail in Section 2.3.2. 2.2. Compartment and population balance models
In this modelling method, it is assumed that the particles travel between different compartments in the equipment at a steady rate. Based on population balances and particle growth kinetics, several models have been proposed to predict mass coating variability for the particle coating in fluidized beds [20-24]. Recently, Denis et al. [25] developed a model for a rotating drum-coating de vice, which is similar to that proposed by Sherony [20] for fluidized-bed coaters. In this method, the particle bed is divided into two regions as shown in Fig. 2. Region 1 is the cascading region that is represented by a perfect single stirred tank in which coating material is applied evenly on all particles. Region 2 is a plug flow region that is represented by N-1 perfect mixers arranged in series. Coated particles in Region 2 get dried and mixed, then move back to the cascading region where they receive coating material. The assumptions on which this model is based include the following: • • • •
• •
Sizes of cascading and plug flow region are constant, Particles commute between these two regions at a constant rate, Only particles in the cascading region can receive coating material, Coating material is sprayed uniformly on the surface of the particles in the cascading region and the amount of coating received is directly proportional to the time spent in the spray region, There is no mass transfer of coating material between particles in any region, and The probability that a particle, with a given amount of coating material, leaves a given region and moves to a neighbouring region is proportional to the number of particles with that amount of coating material in that region.
-
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Modelling of Pan-Coating Processes
Region 1 cascade mixed flow
'------> l -ß
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-
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et al. [25) describing a pan-coating device.
In this model, Wo, W1 , ... , wNcare defined as the inereasing sueeession of eoat ing material amounts deposited on the particles, where the eoating material de posited on the particles are diseretized into Ne particle-mass bins. Therefore, there are Ne particle-eoating material ranges Ci : Ci = [Wi- 1 ;Wi], where i = 1 , 2, ... , Ne. So, in eaeh particle eoating material range, a eharaeteristie eoat ing material Wi deposited on the particle is defined as: Wi = (Wi- 1 + wi)/2. On the basis of the applieation of the population balance method in eaeh stirred tank, the resulting equations are as folIows: Cascading region: (3) Plug flow region: k = 2, . . . , N
where G is the growth rate (kg/h.number)) and is defined as Xs G = OI ßNt
(4)
(5)
Here, ß is the number fraction of particles in the easeading region, Nt the total number of particles in the eoating deviee, 01 the spray rate of eoating solution, Xs the eoating solution eoneentration, Oe the particle flow rate between the perfeet mixers, Ni the number of particles of class Ci at time t and ni the fraction in number of class Ci particles at time t, the superscript in the above equations refers the identification number of the perfect mixer, nJ = Ni / ßNt, and n� = [N�(N 1 )/(1 ß) NtJ.
-
-
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Numerical results were obtained by discretizing and solving the above N partial differential equations with an implicit scheme. There are two parameters that are difficult to predict a priori in this model. The first one is ß, the number fraction of particies in the cascading region, and the other one is Qe, the particie flow rate between two regions. Denis et al. [25] proposed experimental methods to predict these two parameters. The comparison of the coating mass distribution obtained from experiments and population balance model shows good agreement for an industrial scale batch operation. In addition, the effect of the number of perfect mixers on the coating mass distribution was investigated. Simulation results showed that the coating distribution is not affected significantly by the number of mixers when N> 1 0. 2.3. Monte Carlo techniques
Monte Carlo simulations capture experimental information and allow prediction of coating mass variability at the conditions of the experiments. The Monte Carlo method can be thought to be a quantitative exercise performed by ran domly sampling from the parameter probability distributions to predict the out come expected from theory and/or experiments. These parameters affect the events in the process in such a way that a probability distribution is obtained. This is achieved by sampling the parameters of the governing events several times. It is assumed that the average of all outcomes of the randomly sampled probability distributions will yield accurate estimates of the outcomes of real processes. Monte Carlo methods have been extensively used to simulate coating, trans port, dispersion or agglomeration/granulation of particies in fluidized beds [26-29]. Nakamura et al. [26] studied the effect of operating parameters on the coating mass distributions of seed particies in a tumbling fluidized bed coater using Monte Ca rio simulations. The coefficient of variation of coating mass was found to be in the range of 1 0.2-1 6 . 1 % depending on the operating parameters. They showed that the CV decreases with longer coating time, smaller hold up of particies and better mixing of the particies. The model showed that addition of a unidirectional flow (achieved by the rotation of the turntable) to a random walk is an effective method to achieve near perfect mixing. This helps to homogenize the coating mass distribution. They were not able to reproduce the effects of particie diameter nor were they able to predict effects of mixing aids, such as baffles on coating mass distribution. KuShaari et al. [27] developed a Monte Carlo technique to model the coating uniformity in a bottom spray fluidized bed, similar to the one used by Cheng and Turton [7]. They modelied the movement of tablets as a random walk. The steps in the vertical and the horizontal directions were estimated from the distributions of particie velocities, which were determined experimentally using image analysis conducted by Subramanian et al. [ 1 0] . The
Modelling of Pan-Coating Processes
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amount of spray received by a particle was determined from the local spray flux and the voidage profile between the particle and the spray nozzle. Hapgood et al. [30] studied the spray flux in wet granulation in an agitated gran ulator. They performed Monte Gario simulation on the spray zone. The Monte Garlo predictions were in good agreement with the analytical solutions for parameters such as proportion of nuclei formed from single drops (fsingle) and the fraction of the powder surface covered by drops (fcovered) as a function of dimensionless spray flux. They found that fSi ngle falls exponentially with increasing dimensionless spray flux. Also, it was shown that at low dimensionless spray flux, fcovered was equal to the dimensionless spray flux but as the dimensionless spray flux increased, the drop overlap became more dominant and the powder surface coverage levelled off. They observed that in the ranges covered, the results were independent of drop size, number of drops, drop size distribution and the uniformity of the spray. Monte Garlo has been used infrequently for simulating tablet movement in a pan coating device. Rogers and Gardner [31 ] , Black [32], Kohav et al. [33] used physical dispersion models with Monte Garlo method to simulate particulate transport and dispersion for powder flow in a horizontal rotating drum. The mod els were found to predict much less dispersion than that observed in experiments. The shortcoming was that these models neglected the contribution of particle collisions on the bed surface. Gahn and Fuerstenau [34] used Monte Garlo sim ulation to model axial dispersion of particles moving in a plane perpendicular to the axis of the drum. They studied the effects of drum speed and fill combinations on the average rotational speed of the bed and determined probability distribu tions of number of particles leaving sections of bed surface per bed revolution, particle movement direction, and the extent of axial movement. They concluded that a partieie was likely to leave a section and move a greater distance as the speed and fill were increased, but data for the average bed rotation and the distributions were not reported. 2. 3. 1. Monte Carlo simulation in a pan-coating device using videoimaging techniques
Monte Garlo simulations were used to simulate the movement of tablets in a pan coating device [35]. Both the tablet movement and spray dynamics of the system were taken into account. In order to model the coating variability, there were two main inputs used in the Monte Garlo simulation, as shown in Fig. 3. The first input is the information on the movement of tablets inside the coater, which is obtained from video-imaging experiments. This information includes centroid location dis tribution, circulation time distribution, projected surface area distribution of tablets as they pass through the spray zone, and velocity distributions of tablets in 2 directions. The other input is information on the spray dynamics of the system, which includes spray area, spray shape, and spray flux distributions in the spray zone. It should be pointed out that nozzle type, spray solution properties,
386
P. Pandey et al. Spray fIux data from pattemator
Exp. data from video-imaging •
Circulation time distribution
•
Projected surface area distribution
•
Velocity distribution (2-directions)
•
Spray shape
Centroid location distribution
•
Spray area
•
•
Spray fIux distribution
MONTE CARLO ALGORITHM
Coating mass:distribution I
Fig. 3. Monte Carlo scheme to determine the coating mass distribution in a coating op
eration.
atomizing air pressure, inlet air temperature, and tablet bed temperature also affeet the spray dynamies of the system, but are outside the seope of the work. 2. 3. 2. Video-imaging experimental set-up
The equipment used in the work was a 24 in. diameter pan and eonsisted of two transparent Plexiglas™ dises, 60 em 00, separated by a 1 0 em perforated alu minium strip, as shown in Fig. 4. A flexible fibre-optie light eable provided illu mination inside the pan. The position of the eamera was adjusted by a linear positioner, so as to point the eamera at the desired position relative to the tablet bed. The eamera was mounted inside the rotating drum in approximately the same position as the spray gun would normally be loeated in a pan eoater and was adjusted to sean an area eovering the normal spray zone during a eoating operation. This eamera takes images at a framing rate of 25 Hz and was eon neeted to a digital frame grabber board (Miero Dise, Ine., Yardley, PA). More details of the experimental set-up ean be found elsewhere [ 1 6, 1 7] . This video-imaging teehnique enables in-situ study of tablet motion a s the tablets pass under the spray gun, unlike most of the other studies eondueted from outside the side-wall of the pan. Another major advantage of this teehnique is that full frames of i mage data need not be stored for post-proeessing, and a 30 min experiment typieally generates a small-size data file (less than 1 Mb), unlike other high-speed imaging studies that are eapable of eapturing information for only a few seeonds due to the large file size generated. This teehnique provides a
387
Modelling of Pan-Coating Processes Li near Positioner
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Field of Vicw
Tablet B ed
R ubber Rollers
Fig. 4. Experimental set-up of the video-imaging system inside a pan coater to capture the movement of tablets through the spray zone [1 6].
scientific approach to evaluating mass coating variability rather than a case study approach that is generally used. The data generated were used as input to a mechanistic model to predict mass coating variability from measurements using Monte Carlo simulation. 2. 3. 3. Materials and methods
All of the tablets in the coater were first coated with 4% black OpadryTM (Colo rcon, West Point, PA) and then with 0.25% clear OpadryTM . An identical white tracer tablet was coated with 4.25% c1ear Opadry™ and introduced in the bed of black coated tablets [ 1 6]. The movement of this tracer tablet was recorded by the camera. The tablets used for this work were standard round placebo tablets (6.3, 7.9, and 1 0.4 mm) supplied by Mylan Pharmaceuticals Inc. (Morgantown, WV). Data on tablet centroid location (x- and y-directions), circulation time (time between successive tablet sightings at bed surface), projected surface area of tablet towards the spray nozzle or the camera in this case, and tablet velocities parallel and perpendicular to the cascading layer were obtained. Circulation time is defined as the time between first sightings of the tracer tablet in successive passes in the spray zone. A pass is defined as an event where the tablet cas cades down from the top of the tablet bed, passes through the spray zone where it receives coating, then cascades further down, and passes into the bulk of the tablet bed. The next pass is started when that tablet emerges from the bulk of the tablet bed, back to the top of the bed surface, and cascades down. The projected surface area of the tablet is defined as the surface area of the tablet projected towards the camera. This is critical in determining the amount of coating a tablet receives during each sighting in the spray zone, and can also be used to study the preferential orientation of the tablet, if any, towards the spray
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1/
Spray
nozzle
�
Fig. 5. Linear patternator used to determine the spray flux distribution inside spray region.
gun. Research to determine the preferential orientation of standard round tablets in rotating drum equipment is currently underway. The velocity of a tablet in the x- (perpendicular to direction of cascading layer of tablets) and y- (direction of cascading layer of tablets) directions was calculated by the ratio of displacements (determined from centroid locations) over time. A more detailed discussion on each of these calculations can be found elsewhere [ 1 6, 1 7]. The spray flux distribution inside the spray zone was obtained using a linear patternator, shown in Fig. 5 [35]. The patternator consists of a series of tubes that collect and record the volume of the spray solution at different locations. The volume of spray solution collected in each tube was used to generate a spray f1ux profile within the spray zone. The algorithm used to simulate tablet movement using Monte Carlo simulation is shown in Fig. 6. In short, a random starting location was selected from the centroid location distribution generated from the video-imaging experiments. The next tablet location was calculated by randomly selecting x- and y-velocities from the experimentally obtained velocity distributions using (6) where y is the centroid y-Iocation (in the direction parallel to the cascading layer flow) of the tablet, x is the centroid x-Iocation (in the direction perpendicular to the cascading layer flow in the plane of the cascading layer) of the tablet, M is the time increment, and Vx and vy are the randomly chosen components of tablet velocities in the x- and y-directions. The tablet-wall collisions were taken into account and assumed to be perfectly elastic. The time increment used was 40 ms, which is identical to the time taken by the camera to record successive images. Spray information including spray flux distribution, spray area and spray shape, was used in conjunction with the experimental data collected from video-imaging
389
Modelling of Pan-Coating Processes
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Fig. 6. Monte Carlo algorithm used in the current work to determine the coating weight gain of each tablet in the pan.
in order to predict the coating variability. The projected surface area values were randomly chosen from experimentally obtained projected surface area distribution. The movement was simulated for all the tablets in the bed for a coating time of 30 min and the weight gain of each tablet was calculated using equation (7). The coating weight variability between the tablets was calculated using equation (8). mi =
n
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Pass
cv = (Jm
Pm
X
1 00
(7) (8)
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P. Pandey et al.
where mi (g) is the coating weight gained by tablet 't, Aexp (mm2) is the projected surface area at each sighting of the tablet in the spray zone, Sflux (gjmm2js) is the spray flux at the centroid location of the tablet, CV is the weight gain coating variability, (jm is the standard deviation of the coating weight gain distribution, 11m is the average of the coating weight gain distribution, and n is the total number of passes taken by each tablet through the spray zone. Each 'pass' is defined by the appearance of the tablet in the spray zone before 'disappearing' into the bulk of the tablet bed. 2. 3.4. Results
The operating variables studied in this work in the experimental matrix include pan speed (6, 9, and 1 2 rpm), tablet size (6.4, 7.9, and 1 0.4 mm), pan loading (2 levels), spray shape, spray area, and spray flux (uniform, non-uniform) inside spray zone. The pan loading was quantified by using the fractional fill volume ( v) , defined as the ratio of volume occupied by the bed to the total pan volume, given by equation (9). It was varied at two levels (v = 0. 1 0 and 0 . 1 7), which covers the range of typical pan loadings used in the industry. volume of bed v = (9) pan volume The video-imaging data were used to generate distributions of circulation time, surface time (time spent in the spray zone per pass), projected surface area per pass and velocities in two directions for these conditions. These distributions are shown in Figs. 7(A)-(C), for 1 0.4 mm tablets at a pan speed of 9 rpm and a fractional fill volume of 0.1 0. It is c1ear from the figures that the distributions are non-normal in nature. However, the velocity distributions in 2 directions were found to be normal, as shown in Figs. 8(A) and (8) for 1 0.4 mm tablets at a pan speed of 9 rpm and a fractional fill volume of 0.1 0. The effects of average circulation time, surface time, projected surface area, and velocity as a function of tablet size, pan speed, and pan loading have been discussed in detail elsewhere [1 6, 1 7]. The main reason for the observed weight gain variability in the coating process is that all of the tablets in the bed do not behave in an identical manner over a given time period. For example, the number of passes each tablet makes through the spray zone is not the same. This is captured by Monte Carlo simulation and a typical result is shown in Fig. 9 for 1 0.4 mm placebo standard round tablets in a 30 min coating run at a pan speed of 9 rpm. It is desirable to have a 'narrow' distribution of circulation frequency between different tablets. This can be achieved by using mixing aidsjbaffles in the system [1 9]. --
--
2.3.4. 1 . Effect of coating time
The effect of coating time on CV was also studied. It was found that the CV decreases with increasing coating time, as shown in Fig. 1 0(A), for 1 0.4 mm
Modelling of Pan-Coating Processes
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392
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393
Modelling of Pan-Coating Processes
tablets rotating at a pan speed 1 2 rpm at a fractional volume fill of 0 . 1 0. It was also found that the CV is inversely proportional to the square root of coating time, as shown in Fig. 1 0(8) (equation (1 0)). 1 CV cx - (1 0) ,Jtcoal where tcoal is the total coating time. 2.3.4.2. Effect of spray shape and spray area
The effect of spray shape (eilipsoidal and circular) on CV was investigated. Initiaily, the spray area was maintained the same for both the cases. This meant that the entire pan width was not covered for the circular spray shape and ailowed 'bypassing' of tablets without getting sprayed/coated, as shown in Fig. 1 1 (A). This resulted in significantly higher CV values for circular spray shape, which, not surprisingly, shows that it is critical that the spray covers the entire pan width and ailows no or minimal bypassing [4]. In order to study the effect of spray shape alone, the spray area for the circular and eiliptical spray shapes was kept the same, and the entire pan width was covered. This was achieved by comparing two circular shaped spray regions with one eiliptical spray region, as shown in Fig. 1 1 (8) and (C). The ratio of the minor axis of the ellipse to the major axis was kept at 0.5, to maintain the same total
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394
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spray area. Figure 1 2 compares the results for the two spray shapes for 1 0.4 mm tablets at a fractional fill volume of 0. 1 0 at 3 different pan speeds. It is clear that the spray shape does not have a significant influence on the coating variability, as long as the spray area is kept the same. The effect of spray shape (circular vs. elliptical) on the coating quality (roughness) has been discussed by Porter [36]. He concluded that circular spray pattern produces smoother and glossier tablets, but there is a greater chance of localized overwetting, in comparison to the el liptical spray pattern. The effect of spray area on CV was studied. The circular-shaped (higher spray area) spray area was compared to the elliptical spray area (area of circle/area of ellipse = 4, for this case). Again the entire pan width was covered with the spray for these cases. The coating variability was found to decrease with an increase in spray area, as shown in Fig. 13 for 1 0.4 mm tablets at 3 different pan speeds (6, 9, 1 2 rpm) and a fractional fill volume of 0. 1 0. These results were observed for all the three sizes (6.3, 7.9, 1 0.4 mm) of round placebo tablets. 2.3.4.3. Effect of pan loading, pan speed , and tablet size
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x
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Modelling of Pan-Coating Processes
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pan speed (w), tablet diameter (dp), and pan loading (v), given by equation ( 1 2) [37]. Fractional fill volume (v) is a function of the number of tablets in the pan, N, the pan radius, R, and tablet diameter, dp. V
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396
P. Pandey et al.
A MATLAB™-based code was written for the Monte Carlo algorithm shown in Fig. 6. This was used to obtain CV values for the entire experimental matrix (3 tablet sizes, 2 pan loadings, and 3 pan speeds), with a total of 1 8 operating conditions. A statistical analysis of these results was conducted using JMP™ (SAS Institute Inc. Cary, NC) software. It was observed that CV was significantly dependent on dp (p< 0.000 1 ), w (p = 0.0002), and N (p < 0.000 1 ) [35]. The CV was found to be directly proportional to dp, and N, and inversely proportional to An increase in pan speed improves the mixing inside the pan, thereby resulting in lower CV values. The exponents a, b, and c were determined from statistical analysis using JMpTM and are shown in equation ( 1 4). w.
(14) where k2 is a constant. Good agreement (R2 = 0.90) was obtained between the CV values predicted from the model proposed in equation ( 1 4), and the CV values obtained from Monte Carlo simulations, as shown in Fig. 1 5. Incorporating the eftect of coating time into equation ( 1 4) by using equation ( 10), equation ( 1 5) is obtained [35]. ( 1 5) where k3 is a constant.
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The spray flux variation inside the spray zone was measured using the pat ternator shown in Fig. 5. The spray gun used was a two-fluid air atomizing nozzle (model 1 /8JAC + SU 1 1 ) fram Spraying Systems (Wheaton, IL). The normalized spray flux variation data obtained fram the paUernator as a function of distance (r1) fram the centre of spray zone is shown in Fig. 1 6. The atomizing air pressure used for this experiment was 40 psi with a gun-to-bed distance of 1 0.2 cm (4 in.). Figure 1 7 shows the results for 1 0.4 mm tablets, at a fractional fill volume of 0. 1 0 and at 3 different pan speeds. The uniform spray flux (no variation within the spray zone) was found to give a lower CV in comparison to the case where spray flux va ries with respect to the location (non-uniform flux) inside the spray zone. It should also be noted that the value of CV decreased with an increase in pan speed, as shown in Fig. 1 7. Setter mixing is obtained at higher pan speeds, which results in lower weight gain variability during coating. 2.4. D iscrete element modelling (DEM) and computational fluid dynamics (CFD)
As described in the previous sections, renewal, compartmental, and Monte Carlo techniques can be used to predict the mass coating variability. However, some model parameters should be either determined a priori experimentally or adjusted to obtain good agreement between simulation and experimental results. In prin ciple, this limitation does not exist for the application of the discrete element
398
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modelling (DEM) and computational fluid dynamics (CFD) methods. Much work has been done on DEM and CFD modelling and although exact predictions using these methods is still not possible without some parameter adjustments, these techniques provide a powerfuI and rigorous modelling framework to compare the effect of key operating variables on system performance. Most of the previous work using CFD methods has focused on the modelling of fluidized bed equipment. In CFD, equations describing the momentum and cont inuity of gas and solids flow in the equipment are solved numerically. In order to predict CV by using CFD methods, the spray plume from the spray nozzle should be combined simultaneously with the governing equations for gas and solids flow. Then the mass deposition of coating material can be calculated based on the interaction of the solids with the droplets from the spray nozzle. Rajabi-Siahboomi [38] used CFD to investigate critical process parameters for aqueous film coating in side-vented coating pans. Although this approach is capable of predicting CV using the current commercial CFD codes, much work must still be done to com bine the movement of gas and solids and their interactions with spray droplet for the application of CFD to model successfully the mass coating variability. The Discrete Element Modelling method is another useful tool to study granular flow in fluidized bed coaters and coating pans. Unlike CFD simulation, particles are tracked individually rather than as a continuum flow. Newton's equations of motion are solved numerically for each particle in the DEM method. In order to obtain accurate results, the time step should be kept very smalI. Therefore, the DEM method is a time-consuming approach, especially for a coating pan process in which, even for lab scale equipment, in excess of ten thousand particles are used. As computers continue to become more powerful and the contact algorithms for non-spherical particles become more efficient, this limitation will be eased.
399
Modelling of Pan-Coating Processes
2. 4. 1. Spherical-particle DEM simulation
As discussed in the Monte Carlo section, the coating process has two main components, namely the particle movement in the pan and the spray dynamics. Although there is not much work on modelling mass coating variability by DEM, particle movement inside the fluidized beds has been investigated by several researchers [39-41]. In addition, the DEM method has been used widely to study granular flow in rotating drums. Yamane et al. [42] used the DEM method to predict the distributions of circulation time, surface time, and the particle area exposed to the spray in a rotating drum. Mass coating variability can be estimated based on these distributions. Recently, Wassgren et al. [43] used the DEM ap proach to simulate the coating process for spherical particles and tablets in a pan coater. The effect of pan speed, pan loading, pan size and particle properties on the particle movement inside the coating pans can be obtained using DEM methods. This information can then be combined with that from the spray pattern analysis to predict mass coating variability. An introduction to the DEM method and the application of DEM to particle movement in rotating drums is discussed in the subsequent sections. 2. 4. 2. DEM method
Newton's equations of motion are used to track the translation and orientation of each particle in the DEM method. The basic equations for translational and rota tional motion of each particle are: cfr =v _
dt
dcö dt
r
1
( 1 6) ( 1 7)
where v is the velocity vector of the particle, r is the position vector of the par ticle's centre, F is the total surface force acting on the particle which includes the total normal forces and total tangential forces, 9 is the gravitational accel eration, m is the mass of the particle, cö is the angular velocity, r is the total torque acting on the particle, 1 is the moment of inertia of the particle, where 1 = 2/5 mr 2 for a spherical particle, and r is the radius of the particle. For non-spherical particles, the moment of inertia can be determined based on the geometry of particles. It should be noted that vectors are defined in the traditional global Cartesian coordinates. It is assumed that the values of the right hand side terms of the above two equations are constant over a very small time step, M. By integrating equations ( 1 6) and ( 1 7) over the time step M, equations ( 1 8) and ( 1 9)
400
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are obtained.
v vo + (g Fo) -
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(1 9) I where suffix 0 refers to the value from the previous time step. In order to solve these equations, the contact forces between interacting par ticles should be known. The solution yields the trajectory of each particle in the DEM simulation. Soth normal and tangential force models are required. There are several models that have been proposed to predict contact forces between in teracting particles [44-47]. A MATLAS™-based DEM code was developed (by IETek™ , Tacoma, WA) to simulate the spherical particle movement in a rotating drum [37]. Figure 1 8, shows a snapshot of the graphical user interface (GUI), which provides a picto rial representation of the simulation process. From Fig. 1 8, it is shown that it is very straightforward to change the particle size, pan size, operating conditions, and physical properties for the DEM simulation. The effect of these parameters on the dynamic angle of repose and average cascading velocity on the inclined surface have been investigated and compared with experiments using a video imaging technique, described in Section 2.3.2. The experimental conditions are �oecIlOI"I
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as foliows: •
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The diameter of the spherical polystyrene balls used in the experiment is 9 mm with a particle density of 0.99 gjcm3 . Young's modulus and Poisson ratio of the polystyrene balls are 1 28 1 09 Njm2 and 0.3, respectively. The coefficient of friction is 0.5. The thickness and diameter of the coating pan are 1 0.5 and 58 cm, respectively. Three levels of pan speed are used in the experiments (6, 9, 1 2 rpm). Pan loading is represented by using a fractional fill volume (v), which is defined as the ratio of volume occupied by the particle bed to the total pan volume (equation (9)). Two levels of pan loadings are used, v 0. 1 0 and 0. 1 7. .
x
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2. 4. 3. Dynamie angle of repose
The dynamic angle of repose is the angle formed by the inclined cascading surface and the horizontal and is illustrated in Fig. 1 9. A visual comparison of the dynamic angle between the experiments and simulations is shown in Fig. 1 9. Figure 20 shows the comparison of the dynamic angle obtained fram DEM sim ulation and experiments for two pan loadings and three pan speeds. Although the trends predicted by DEM were consistent with the experimental observations, the dynamic angle was found to be higher for the experiments. A possible reason for this difference is the 'wavy' shape of the cascading bed SUrface, which was observed to be more pranounced in experiments compared to simulations. 2. 4. 4. Average easeading ve/ocity of partie/es in the spray zone
The average cascading velocity of particles in the spray zone can be determined by using video-imaging methods as explained in Section 2.3.2. For the DEM
Fig. 1 9 . Comparison of simulation (A) and experiment (8) for 9 mm polystyrene balls in a 29 cm diameter pan. Parallel lines are shown in both figures to compare dynamic angles (slope) in both cases [37].
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simulations, the average cascading velocity of particles for any region on the inclined surface can be obtained. Figures 21 (A) and (8) show the average cascading velocity of particles in the spray zone for experiments and DEM sim ulations. From Fig. 2 1 , it can be seen that the average cascading velocity increases linearly with pan speed for both DEM simulation and experiments. For the lower fractional fill volume, the simulation results were in agreement with the exper imental results. The slope of the linear fit was found to be 2.00 (F?- = 0.98) trom experimental data and 1 .97 (R"2 = 1 .00) from simulation results as shown in Fig. 21 (A) for v = 0 . 1 0. Good agreement was obtained between the slopes ob tained from simulations and experiments. Figure 21 (8) shows results for v = 0.1 7, where the slope of the linear fit was found to be 3.1 (F?- = 1 .00) from experimental data and 2.25 (R2 = 1 .00) from simulation results [48].
403
Modelling of Pan-Coating Processes
2. 4. 5. Effect of pan speed and pan loading
Alexander and Muzzio [48] measured the velocity profiles along the cascading surface in a tumbling blender using a digital camera. Based on a dimensional analysis of the experimental data, they proposed that the velocity of particles on the inclined surface can be described by (20) where V is the velocity of particles at the surface of the bed, and the pan speed. The relationship in equation (20) and the effect of pan loading were investi gated through DEM simulation. Three different pan loadings were used to in vestigate the effects of pan loading on surface velocity of particles. The values of fractional fill volumes for the three different pan loadings were v = 0. 1 0, 0. 1 4 and 0. 1 7. Simulations using three different pan speeds were performed at each pan loading. Figure 22 shows the simulation results for all cases. In Fig. 22, the x-axis is the 'normalized distance from top of bed's surface', x = 0 refers to the top of the inclined surface and x = 1 indicates that the particles are at the bottom of the inclined surface. Using equation (20), the surface cascading velocities were first normalized by dividing by W2/3 , as shown in Fig. 23. From Fig. 23, it can be seen that the surface velocity scales weil with the pan speed (W2/3 ), as proposed by Alexander and Muzzio [48]. However, there is a significant difference for the surface cascading velocities at different pan loadings, which means that the surface cascading ve locities are significantly dependent on pan loading. Therefore, the fractional fill volume was also included in the dimensional analysis of cascading surface ve locity. As shown in Fig. 24, the simulation data were then normalized by ac counting for fractional fill volume and there was a good overlap of these simulation data when normalized by v 1 .8 [37]. Hence, w
(21 ) As shown i n equation (21 ), two parameters were taken into account for the surface velocity of particles in the cascading layer. This relationship provides important information for the pan coating scale-up process. Ongoing work fo cuses on verifying the effect of particle and pan size on the surface velocities of particles in the cascading surface, as proposed by Alexander and Muzzio [48] (equation ( 1 2)). 2. 4. 6. Tablet-shaped DEM simulation
As mentioned before, all results in the previous section were obtained for spherical particles for the DEM simulation. However, non-spherical particles are almost al ways used in the pharmaceutical industry. Therefore, the shape of these particles should be accounted for in the DEM simulation. For simplicity, Yamane et al. [42] used spherical particles to approximate the dynamic behaviour of non-spherical
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particles in DEM simulations. However, the accuracy of the simulations using this approximation is in doubt. Pandey and Turton [ 1 7] used video-imaging techniques (discussed in Section 2.3.2) to compare the movement of spherical particles with the movement of standard round placebo tablets. They found that the tablets move
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0 .. v • 0 •
0 ..
0.2
0.4
w=6,v=O. 10 w=9,v=O. 1 0 w=1 2,v=O.10 w=6,v=O. 1 4 w=9,v=O. 14 w=1 2,v=O.14 w=6,v=O. 1 7 w=9,v=O . 1 7 w=1 2,v=O. 1 7 0.6
?t
ej
� ..
0.8
1 .0
Normalized distance from top 01 bed surface Fig. 24. Cascading layer surface velocity norrnalized with fractional fill volurne and pan speed [37J.
at a higher cascading velocity than spheres with the same volume equivalent diameter. Therefore, it is important to model the shape of the partie/es in a more realistic way to improve the predictions of the DEM simulation. In order to simulate tablets in DEM, a contact algorithm is required to determine which partie/es are in contact with each other in multi-partie/e simulations. Since contact criteria are straightforward for spherical partie/es, multi-sphere represen tations of non-spherical partie/es are often used in tOO simulation. EI/iott et al. [49] used these methods to predict packing characteristics of non-spherical partie/es. The resufts showed that these methods are successful in determining the packing density of non-sphericaJ particJes. However, Song et al. [50] found that for the dynamic behaviour, there were large errors for single collisions of two tablets by
406
P. Pandey et 81.
using multi-sphere representations compared with experiments. Therefore, for sim ulating particle velocities the representation of tablet shape should be realistic, and yet the contact algorithms must not be too complicated otherwise simulation times become excessive. A method to represent the shape of standard round tablets, and the contact algorithm for these tablets was recently developed by Song et al. [50]. 2. 4. 7. Representation of tabtet shape and contact atgorithm
The intersection of three spheres is used to represent the shape of a typical round tablet, as shown in Fig. 25. From Fig. 25, the radii of the top and bottom surfaces (referred to Surfaces 2) are R2 and the radius of the side surface (referred to as Surface 1 ) is R1 . Other parameters used to define the geometry of the round tablet are shown in Fig. 25. On the basis of the above representation, there are three possible contact forms between the tablet and a flat surface, which are Surface 1 - Flat Surface, Surlace 2 - Flat Surface and Rim - Flat Surface as shown in Figs. 26(A) and (8). The corresponding contact criteria are also included in Fig. 26. In Fig. 26(C), S is the point on the rim of the tablet in contact with the flat surface. The location of .
.. . . . .
.
. .. . .. . .. . .... .. .
..
. .
.
.
. . .. ._. ... ........ ....... M . . ... . . . ..
.
.• • ... .
/\\
.. / ../
!
\.
1 !
/
; i
/
\ ..
.
.. ...
Rim of the tablet
" .
\'"
\.
Tablet
\.
\
\
\
i i
; !
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./ ... ....
..
.. . .••
.
'" .. .
... . . . ... . . . ..... .. ....... ...... .. ...... . . . .
. .
. .... .. . ......
Fig. 25. Representation of a tablet using three convex surfaces [50].
407
Modelling of Pan-Coating Processes p
Contact criteria for Surface Surface are:
..::..... . __ . o:::� ::: M
_ _ _ _ _ _
_ _ _
2-
Flat
Flat Surface
(A)
Contact criteria for Surface I Surface are:
- Flat
p . 90 - a $; y $; 90 •
d $; R ,
---'''''-t+ '' ...... -- Flat Surface
-
(8) p
Contact criteria for Rim - Flat Surface are: •
ß < y 90 - a
•
Axo + Byo + CZo + D $;
0
---------"'........ ... '-.. --- F1at Surface (C)
Fig. 26. (A) Schematic diagram of surface 2-flat surface contact, (B) schematic diagram of surface 1 -flat surface contact, and (C) schematic diagram of rim-flat surface contact [50].
point S is S(xo , Yo, zo) and the equation of the flat surface is Ax + By + Cz + D = O. In addition, there are three contact forms, which are Surface 1 - Surface 1 , Surface 1 - Surface 2 and Surface 2 - Surface 2 for the Tablet - Tablet contact shown in Fig. 27. Considering the Rim contact with the tablet, there are three more contacts, namely Rim - Surface 1 , Rim - Surface 2 and Rim - Rim for Tablet - Tablet contact shown in Fig. 28 (since Rim - Rim contact is not frequent,
408
P. Pandey et al. p
Contact criteria for Surface Surface I are:
(A)
•
y, � 90 - 0:
•
y, � 90 - 0:
•
0,0, < 2R,
I
-
M p
Contact criteria for Surface 2 Surface 2 are:
•
y, ::; ß y, ::; ß
•
MP < 2R,
•
(B)
-
M
Contact criteria for Surface 1 Surface 2 are: •
1', � 90 - 0(
•
1', ::; ß
•
O,M < R, + R,
-
(e)
Fig. 27. (A) Schematic diagram of surface 1 -surface 1 contact, (8) schematic diagram of surface 2-surface 2 contact, and (C) schematic diagram of surface 1 -surface 2 contact [50].
it is not shown in Fig. 28). All contact criteria are shown in the related contact forms in Figs. 27 and 28. 2. 4. 8. Implementation of contact algorithm for tablet- tablet collision simulation
The contact criteria for tablet-shaped bodies were implemented in MATLAS™ code to model a collision between a moving tablet and a stationary tablet fixed to
409
Modelling of Pan-Coating Processes
Contact criteria for Rim Surface I are:
p
(A)
.0,
Contact criteria for Rim Surface 2 are: •
•
y<ß PS < R2
M
(B)
Fig. 28. (A) Schematic diagram of rim-surface 1 contact, and (8) schematic diagram of rim-surface 2 contact [50].
a tlat surfaee. In addition, a MotionPro™ high speed digital imaging system trom Redlake MASD, Ine. (San Diego, CA) was used to reeord the images ot one tablet hitting another tixed tablet. The images were then analysed by using the spread sheet analysis module included in the system [50]. Since the angular velocity measurements are very sensitive to the partiele shape and the eontact algorithm, only the angular veloeities were used to eompare the results trom the simulations to the experiments. Table 2 shows the results trom both DEM simulations and experiments. The four eases considered correspond to different starting positions for the tablet being dropped. It was found that there is good agreement between the simulation and experimental results using this eontact algorithm. In order to verify the efficieney of the current representation of tablet shape, simulations using multi-sphere representations were carried out. Four different representations, whieh were composed of 1 0, 26, 66, and 1 78 identieal spheres, respectively, were used as shown in Fig. 29. First, the eomputational time for a single eollision of two tablets were eompared for different representations of
410
P . Pandey et 81.
Table 2. Comparison of simulation and experimental results for angular velocities of two contacting tablets [ 1 ]
Angular velocity (radis) Ca se 1 Case 2 Ca se 3 Case 4
Experiment 1 70 89 209 251
C D)
Simulation 1 66 90 1 87 236
% Error 2% -2% 11% 6%
(E)
Fig. 29. The tablet shape and the multi-sphere representation of tablet shape; (A) tablet shape, (8) 1 0-sphere representation , (C) 26-sphere representation, (D) 66-sphere repre sentation , (E) 1 78-sphere representation [50].
tablet shape. Figure 30 shows the computational times along with the time for a single sphere-sphere contact. From Fig. 30, it can be seen that the computational times for the 66- and 1 78-sphere representations were significantly greater than that for the tablet representation using three convex spheres. The simulation time for the tablet was about 1 .5 times more than that for a single sphere contact. In addition, Song et 81. [50] showed that the angular velocities using multi-sphere representations were different from those of the tablet simulation even when more than one hundred identical spheres were used in the multi-sphere repre sentations. Recently, the contact algorithms for tablet-shaped bodies have been imple mented to simulate multi-tablet movement in a rotating drum using the MAT LASTM-code. The size of the tablet can be easily reset. Figure 3 1 shows the surface velocity profile along the inclined surface for tablet and spherical particle simulations in a rotating drum. In this simulation, 1 500 tablets and 1 500 spherical particles were used. The volume of the spherical particle was equal to the volume
Modelling of Pan-Coating Processes
41 1
80 �------, 70
::§: 60
�
Q)
tii
.§
50 40
1ii
� 30 E o
ü 20
single sphere
Tablet
10 spheres 26 spheres 66 spheres
1 78
spheres
Fig. 30. Computational time comparison for different tablet-shape representation methods shown in Fig. 29 [50].
E
Ci>
I
12
.3. 1 0 � '0 o 8 Q)
�I
>
'V •
V
'<1
l
v
7.5 mm spheres 8 mm tablets
• v
v -
•
'<1
"
'<1
•
•
•
•
•
•
'V
-
� 'V •
•
0.2
0.4
0.6
0.8
1 .0
Normalized distance from top of bed surface Fig. 31 . Comparison of surface velocity profile along the inclined surface between tablet and spherical particles. The diameter of the drum used was 29 cm and the pan speed was 6 rpm.
of the tablet and all other physical properties were kept the same. The diameter of the drum was 29 cm and the pan speed was 6 rpm. From this figure, it can be seen that the surface velocity of tablets is much larger than that for spherical particles, which is consistent with the findings of Pandey et al. [37]. In principle, the weight gain CV can be estimated from a combination of data obtained from DEM. Specifically, the tablet area exposed to the spray zone, the spray flux distribution and the velocities of the tablets can be used to find CV, as
412
P . Pandey et al.
was discussed in the Monte Carlo section (Section 2.3). In a recent study by Wassgren et al. [43], it was shown that mass coating variability can be estimated in laboratory-scale equipment and the effect of particle shape, vessel configu rations, and the coating solutions on the CV can be simulated by the DEM method as weil. Their simulation results showed that there was an inverse frac tional power law relationship between mass coating variability and number of rotations. Although the number of rotations of the drum was quite low, due to the long simulation time, it appears that these results are consistent with renewal theory. 3. CONCLUSIONS AND DISCUSSION
A discussion on different modelling approaches is provided, with emphasis on Monte Carlo and DEM approaches. All of the discussed models provide a rea sonable picture of the processes that take place in coating equipment. These models vary from simple to a very complex approach and give reasonable agreement with experimental data. All the models show that CV is inversely proportional to the square root of coating time. Even though in actual practice this may not be the most practical way to reduce the CV of the process due to time constraints, this can still be used effectively for situations where an active drug is coated on the tablets and low CVs are extremely critical. Among the different approaches, the Monte Carlo method covers both the tablet movement and spray dynamics aspects of the coating process. The CV model proposed can provide a basis for adjustments in process parameters re quired during a scale-up operation or in situations where the tablet size, pan loading, or pan speed is changed, in order to achieve the same CV. The Monte Carlo approach is also able to study the effect of spray shape and area on CV, which was not quantified in any of the previous approaches. The spray shape was not found to affect the CV of the process significantly, but an increase in the spray area was shown to promote lower CVs. Although not discussed in the current work, the internals or baffles that determine the mixing inside the pan have a significant effect on the value of CV. This can be quantified by the video imaging technique [1 9]. Moreover, mixing inside the pan can be captured by the Monte Carlo simulations. However, the Monte Carlo simulations discussed in the current work require experimental data from the video-imaging system, and hence a priori prediction is not possible. The DEM approach, on the other hand, can be used as an independent predictive tool and was shown to predict the movement of tablets inside the coater. Recent work has shown that the effects of pan geometry, such as the design of baffles, can be effectively simulated by DEM. In the future, a combination of DEM with the spray dynamics of the system may, in principle, allow a priori estimates of CV.
Modelling of Pan-Coating Proeesses
413
Although DEM simulations of production-scale coaters are still beyond the limit of current computers, simulations of smaller, laboratory-scale equipment (with up to 1 5,000 particles) in which non-spherical particles and vessel internals are included are now feasible. A combination of DEM and CFD approaches will also allow the heating and drying of particles to be modelled. In addition, by incor porating the forces associated with formation of liquid bridges in the DEM code, phenomena, such as local overwetting, twinning, etc., may be modelied and a first step towards the modelling of membrane morphology might be made. Therefore, there are certain process analytical tools that exist in the form of these modelling approaches. These can be used to predict and control the CV of the coating unit operations and put analysis of the coating processes on a more scientific footing. Nomenclature
Ni Ne
01
Oe
R R1 R2
Sflux
V
Wi Xs
Z a,b,c d dp 9 k1 , k2 , k3 m ni n
projected surface area (mm2 ) coating material range (g) total surface force acting on the particle (N) growth rate (gjsjnumber) moment of inertia of the particle (gm2) number of perfect mixers or total number of particles in the coat ing device number of particles of class Ci at time t number of particle coating material range spray rate of coating solution (gjs) particle flow rate between the perfect mixers (numberjs) pan radius (em) radius of the smaller sphere in Figs. 25-28 (mm) radius of the larger sphere in Figs. 25-28 (mm) spray flux (gjmm 2js) cascading layer velocity (cmjs) characteristic coating material deposited on the particles (g) coating solution concentration (gjg) distance defined in Fig. 25 (mm) real number exponents distance defined in Fig. 26 (mm) diameter of particles (mm) gravitational acceleration (mjs2 ) constant mass of the particle (g) fraction in number of class Ci particles at time t total number of passes by each tablet in the spray zone
414 r
r r1 tcoat L1t 11
x
Y Wi
P. Pandey et 8/.
position vector for the centre of particle (m) radius of the particle (m) distance from centre of the spray zone (m) total coating time (s) time increment (s) linear velocity vector (m/s) centroid x-Iocation (m) centroid y-Iocation of the tablet (m) coating material deposited on the particles (g)
Greek symbols !Y. (J J1
ß r v
W
w
angle defined in Fig. 25 standard deviation mean number fraction of particles in the cascading region or angle defined in Fig. 25 total torque vector acting on the particle (N.m) fractional fill volume pan speed (rpm) angular velocity vector (radIs) angle defined in Figs. 26 and 28 angle defined in Fig. 27 angle defined in Fig. 27
Subscripts
ct m n total x y
cycle time distribution coating weight gain number distribution total mass of coating material on a particle coating mass distribution or direction perpendicular to the di rection of cascading tablets direction parallel to the direction of cascading tablets
Abbreviations
CCD CFD CV DEM F DA GUI MATLAS™ PAT
charged-coupled device computational fluid dynamics mass coating variability discrete element modelling food and drug administration graphical user interface registered trademark (software) of the MathWorks™ Corp process analytical technology
Modelling of Pan-Coating Processes
415
REFERENCES [ 1 ] R. Campbell, G. Sackett, Pharmaceutical Unit Operations: Coating, Va!. 3, K Avis, A. Shukla, R. Chang , I nterpharm/CRC 1 999. [2] S. Porter, Coating of Pharmaceutical Dosage Forms, Chapter 9 1 , Remingtons Pharmaceutical Seiences, 1 7th Edition, 1 985 pp. 1 633-1 643. [3] R. Turton, Powder Techno!. in press, 2006. [4] P. Pandey, Ph.D. Dissertation, West Virginia U niversity, Morgantown, WV, 2006. [5] U . Mann, M . Rubinovitch, E.J. Crosby, AIChE J. 25 ( 1 979) 873-882. [6] U. Mann, Ind. Eng. Chem. Process Des. Dev. 22 ( 1 983) 288-292. [7] x.x. Cheng, R. Turton, Pharm. Dev. Techno! . 5 (No. 3) (2000) 323-332. [8] H .S. Hall, Granulation Technology for Bioproducts, Chapter 1 1 , K.L. Kadam (Ed.), CRC Press, Boca Raton, FL, 1 990. [9] S. Shelukar, J. Ho, J. Zega, E . Roland, N . Yeh, D . Quiram, A. Nole, A. Katdare, S. Reynolds, Powder Techno!. 1 1 0 (2000) 29-36. [ 1 0] G. Subramania n , R. Turton , S. Shelukar, L. Flemmer, Ind. Eng . Chem. Res. 42 (2003) 2470-2478. [1 1 ] U. Mann, E.J. Crosby, Can. J. Chem. Eng. 53 ( 1 975) 579-581 . [ 1 2] B . Waldie, D . Wilkinson, Can. J . Chem Eng. 64 ( 1 986) 944-949. [1 3] X . x . Cheng, R. Turton, Pharm. Dev. Techno! . 5 (No. 3) (2000) 3 1 1 -322. [ 1 4] D.J. Parker, A.E. Dijkstra, PA McNeil, Chem. Eng. Sci. 52 ( 1 997) 201 1 -2022. [ 1 5] M. Nakagawa, S. Altobelli, A. Caprihan, E. Fukushima, E. Jeong, Exp. Fluids 1 6 ( 1 993) 54-60 . [ 1 6] S. Sandadi, P. Pandey, R. Turton, Chem. E n g . Sei. 5 9 (No. 24) (2004) 5807-581 7. [ 1 7] P. Pandey, R. Turton, AAPS Pharm. Sei. Tech. 6 (No. 2) (2005) E237-244. [ 1 8] P. Pandey, R. Turton, Proceedings of AICH E Annual Meeting, paper # 3c, San Francisco, CA, Nov. 1 6-2 1 , 2003. [ 1 9] P. Pandey, R. Turton, AAPS 6 (Si ) (2004) . [20] D.F. Sherony, Chem. Eng. Sei. 36 ( 1 98 1 ) 845-848. [21 ] P. Wnukowski, F. Setterwall, Chem. Eng. Sei. 44 ( 1 989) 493-505. [22] S.J. Maronga, P. Wnukowski , Chem. Eng. Sci. 52 ( 1 997) 291 5-2925. [23] H . B . Eldredge, D.C. Drown , Chem. Eng. Sci. 54 ( 1 999) 1 253-1 264. [24] L.X. Uu, J . D. Utster, Powder Techno!. 74 ( 1 993) 259-270. [25] C. Denis, M. Hemati, D. Chulia, J .-Y. Lanne, B. Buisson, G. Daste, F. Elbaz, Powder Techno! . 1 30 (2003) 1 74-1 80. [26] H. Nakamura, E . Abe, N . Yamada, Powder Techno!. 99 ( 1 998) 1 40-1 46. [27] K. KuShaari, R. Turton, paper 309d, presented at the Annual AIChE Meeting, I ndianapolis, Nov. 3-8, 2002. [28] K. KuShaari, P. Pandey, Y. Song, R. Turton, Powder Techno!. 1 66 (2006) 81-90. [29] M.S. Choi, A. Miesen, Chem. Eng. Sci. 52 ( 1 997) 1 073-1 086. [30] K. Hapgood, J. Utster, E. White, P. Mort, D. Jones, Powder Techno!. 1 4 1 (2004) 20-30. [31 ] R. Rogers, R. Gardner, Powder Techno!. 23 ( 1 979) 1 59-1 67. [32] J. Black, Ph. D. thesis, Edinburgh U niversity ( 1 988). [33] T. Kohav, J . Richardson, D . Luss, AIChE J . 41 (No. 1 1 ) ( 1 995) 2465-2476. [34] D . Cahn , D. Fuerstenau, Powder Techno!. 1 ( 1 967) 1 74-1 82. [35] P. Pandey, M. Katakdaunde, R. Turton, AAPS Pharm. Sci . Tech. 7 (4) (2006). [36] S. Porter, Pharmaceutical process scale-up , M. Levin (Ed), 1 1 8, Marcel Dekker I nc., 2002 275-276. [37] P. Pandey, Y. Song, F. Kayihan, R. Turton, Powder Techno!. 1 6 1 (No. 2) (2006) 79-88. [38] A. Rajabi-Siahboomi, Advances in Film Coating symposium, AAPS Annual Meeting, Baltimore, M D , 2004. [39] Y. Maguruma, T. Tanaka, Y. Tsuji, Powder Techno! . 1 09 (2000) 49-57.
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P. Pandey e t 81.
[40] S.T. Nase, W.L. Vargas, AA Abatan , J.J. McCarthy, Powder Techno!. 1 1 6 (2001 ) 21 4-223. [41 ] K. Terashita, S. Natsuyama, I . Nishimura , H . Sakamoto, J. Jan, Soc. Powd. and Powd. Meta!. 47 (2002) 1 306-1 3 1 1 . [42] K. Yamane, T. Sato, T. Tanaka, Y. Tsuji, Pharm. Res. 1 2 ( 1 995) 1 264-1 268. [43] K. Wassgren, J . Perez, K. Morris, paper presented at Eng. Conf. Intern.-Particulate processes in the Pharmaceutical Industry, June 26-30, Montreal, Canada 2005. [441 PA Cundall, O . D.L. Strack, 29 (No. 1 ) ( 1 979) 47-65. [451 o. Walton, R. Braun, J . Rheology 30 (No. 5) ( 1 986) 949-980. [461 o. Walton, Mech. Mate. 1 6 ( 1 993) 239-247. [471 C. Thornton, J . App!. Mech. 64 ( 1 997) 383-386. [48] A. Alexander, F. Muzzio, in: M. Levin (ed), Pharmaceutical Process Scale-up , Marcel Dekker, New York, 200 1 . [491 J A Elliott, A.H . Windle, J. Chemical Physics 1 1 3 (No. 22) (2000) 1 0367-1 0376. [50] Y. Song, R. Turton , F. Kayihan, Powder Techno!. 1 61 (No. 1 ) (2006) 32-40.
CHAPTER 9 G ranu l at i on Eq u i pment M ichael J acob *
Glatt Ingenieurtechnik GmbH, Nordstrasse 12, 99427 Weimar, Germany Contents
417 1 . General overview of equipment for granulation and coating processes 2. Granulators and coaters using mainly convective heat and mass transfer and low 426 agitation 426 2. 1 . Fluidized-bed granulators and coaters 2. 1 . 1 . General design aspects 426 428 2 . 1 .2. Processing options 430 2 . 1 .3. Processing gas handling 2. 1 .4. Gas distributors 439 2 . 1 .5. Dry material charging and discharging systems for batch and continuous operation 443 453 2 . 1 .6. Dry material handling/recirculation/production of seeds 455 2 . 1 .7. Liquid handling and spray systems 461 2.2. Spray dryers 461 2.2. 1 . General design aspects 461 2.2.2. Processing options 464 2.2.3. Processing gas handling 2.2.4. Dry product treatment 464 465 2.2.5. Liquid handling and atomization 466 2.3. Control and instrumentation 3. High shear granulators 469 3. 1 . General design aspects 469 3.2. Processing options 472 475 4. Summary References 475
1 . GENERAL OVERVI EW OF EQUI P MENT FOR GRANU LATION AND COATING PROCESSES
In the literature many articles are published dealing with general introductions in granulation and coating processes and related equipment [1-5]. This article fo cuses on the relationship between product form and equipment to create the desired product properties. On the basis of the differences in product structures *Corresponding author. E-mail: [email protected]
( 2007
Granulation Edited by A.D. Salman, M.J. Hounslow and J. P.K. Seville Elsevier SV All rights reserved '
418
M . Jacob
particulate products
agglomerates homogeneous structure
homogeneous structure
composite
porous structure
porous structure
Fig. 1 . Structures of particulate products.
and forms the selection of related equipments and technologies is explained. Moreover the differences in operating principles of each type of equipment and their influence on product properties are summarized. There are a lot of tech nologies established in all kinds of industries to produce solid product forms. In Fig. 1 , the most used product forms are summarized. Depending on the technology used to create these products, they have differ ent inner structures. A e/assification of particulate products is not possible e/early due to the fact that different industries use their own definitions and terms to describe processes and product forms. In the following chapters these definitions are used to define a solid product form: Single particle
Grains Agglomerates Capsules Tablets
The term "single partie/e" represents a homogeneous partie/e of small or medium size produced directly in a single-step process. Other used terms: prill A "grain" is a homogeneous partie/e of medium or larger size produced using a layering growth process. Other used terms: pellet The product form of an "agglomerate" is created by coalescence of single partie/es, grains or agglomerates of smaller size. "Capsules" contain one or more solids (single partie/es, grains, agglomerates) in an outer shell. Widely used wall materials for capsules are hard or soft gelatin. If single partie/es, agglomerates or grains are pressed together they form a tablet.
These are the definitions of the individual processes [6]: Agglomeration
spraylng
wetting
solidifving
agglOmerate
.\
...
.. binder- powder dropleI
liquid
bridges
solid
bridges
"raspbeny" slructure
419
Granulation Equipment
Wet granulation
liquid addition
wetting
compactionl drying
powder
liquid bridges
solid bridges
binder
Pelletization
Spray granulation
Spray coating
final granule
"snowball" structure
spheronizing
agglomerate or wet granule
pellet
"snowball" structu re
spreading
spraying
sprayed seedsl droplet powder
welling
spraying
final granule
solidifying
solidified shell
"onion" structure
solidifying
coated particle
cl
Powder layering
coating droplet
granule
rolling up
spraying
�
q binder droplet
powder
pellet
drying/ solidifying
liquid bridges
solid bridges
seed
To carry out these processes different equipment can be used. Especially for agglomeration and wet granulation, different apparatuses are available from labo ratory scale to large-scale production. The main differences are in the main mechanisms of particle growth, intensity of agitation, use of compaction forces and processing time. In Fig. 2 a short summary of size enlargement processes is shown.
420
M. Jacob
size enlargement processes tor dry products
powder layering spray granulation spray coating
how pressure
high pressure
Fig. 2. Classification of size enlargement processes.
Basic principles often used for granulation and coating equipment are sum marized and explained in this chapter. For growth and tumble agglomeration a variety of apparatuses can be used. To produce relatively dense agglomerates the different technical versions of mixers are used as wet granulators. For in stance, in the fertilizer industry, rotating drums are often used (Fig. 3). Rotating drums are also used for spray granulation and coating processes. Depending on the current application, the liquids are sprayed on the particulate phase or the solid feed is pre-mixed with the homogeneous liquid phase and fed pre-agglomerates to the drum where the solidification and drying takes place. For coating applications mainly in the pharmaceutical and food industries drum coaters are prevalent [7]. In Fig. 4, the operation principle of a batch wise op erating drum coater is explained. Here a perforated drum is rotating and this leads to a mixing of the material, which was loaded. A processing gas flow (typically heated air) enters the drum and flows through the particle bed. Coating liquids can be sprayed on the particles using nozzle arrays and the coating film is dried by the processing gas which picks up the moisture and leaves the drum via bed and perforated drum. Another often used type of equipment is the mixer. There are a lot of technical executions available for both batch and continuous mode of operation. For i n$tance, when high capacities are needed at low production cost, mixing technologies are a
421
Granulation Equipment
ventilation
solid drying energy
product Fig. 3. Principle sketch of a rotating drum for agglomeration.
drum rotation .....,---. liquid feed ..,. - .... .... / perforated drum , "' .k' \ .k' I \ � process gas in I:.�... .k' l:,!:,!... I .......... . .. .. .k' i":"":"":" .. .. . � .. .k' \!:.!:.!:'!:.'. .JIt'
process gas out .k' ....!:.!:!::,!�.t;'... .k' �� .�.�.�.�.�
.��":�� -._
�
I I
,
Fig. 4. Processing principle of drum coater.
good choice. The main field of application in this area include the food (instant products, sauces, soups, teas . . . ) and detergent (complete blends . . . ) industries (Fig. 5). In Fig. 6, two principles of mixers used for continuous wet granulation are explained. Especially in pharmaceutical industries, if small or medium size product quan tities are to be produced, batch processing is preferred. In general there are two basic design concepts for batch wet granulators. They can be distinguished by the mounting of the mixer shaft. In Fig. 7 left, a bottom driven mixer is shown in principle. In that case the seal of the mixer shaft is product contacting and needs additional design efforts. The other option is a top-driven mixer as shown in Fig. 7 right. It is advantageous that the shaft seal is not directly product contacting but the shaft itself has to be sized Ion ger and more resistent against torsion compared to bottom-driven systems due to the longer distance between product and drive. In any case vibration has to be avoided and high stress resistance must be ensured. Seetion 3 deals with these topics in more detail. Wet (high shear) granulators produce typically not very spherical particles. For this reason, wet granulated products are pelletized when smooth surface structure
422
M . Jacob
Fig. 5. Drum coater in pharmaceutical execution for film-coating application (Glatt/ Germany).
solid liquid feed feed
drying energy
ventilation
liquid feed
solid feed
product product
Fig. 6. Principle sketch of wet granulators for continuous processing.
and improved density is required. Additionally pelletized products have a more narrow size distribution and lower dust content. The operation principle of pelletization is explained in Fig. 8. Such equipment is used to handle pre-formed solids from wet granulation or extrusion. The solids are circulated in a helical rotating flow, established by the superimposition of gas flow through the ring gap, centrifugal and gravitation forces. Owing to the attrition between product, housing and rotor disk the shape of particles changes [8].
423
Granulation Equipment
ventilation solid feed
liquid feed
chopper
���==��I
product
mixing blade
shaft Fig. 7. Principle sketch of wet granulators for batch processing. batch pelletizer
pelletizer cascade for continuous processlng discharge orilice
solid leed
1<,. gas leed
"
0
"�ct� �=·:':::"= �'.
gas leed
Fig. 8. Design and operation principle of pelletizing equipment.
..<.�I . OW iiTi� . J
o
discharged product
Pelletization can be carried out both in batch and continuous processing. In batch processing the pelletizer is charged with a certain amount of pre-formed raw material. After a defined process time the process stops and the shaped product is emptied. A continuous pelletization can be established using a cas cade of individual pelletizers. They are arranged in line and a continuous solid flow goes from one to the other. The residence time per unit can be defined by size, process parameters and position of discharge orifice, which is used as an overflow to downstream units. In contrast to the high and medium agitated wet granulation equipment as explained before convective drying technology uses low or no agitation. One of the oldest and very widely used drying technologies is spray drying. A simple spray dryer setup is sketched in Fig. 9. In a typical spray drying process liquid raw materials are transformed to dry products by drying. A wide range of technical executions are available to create different dry product forms. In general a spray dryer consists of a drying chamber in which a liquid feed is atomized. A conditioned ( mostly heated) drying gas enters the drying chamber where solidification and particle formation process takes place. A more detailed explanation about spray drying equipment follows in Section 2.2.
424
M . Jacob
!:;::;=j-- liqUid feed
_ .-_ _ _
---+:;=;:
heater
cyclone ,--_+{
exhaust drying gas
ventilator
spray dryer
M
rotary valve
fines drying gas inlet
M
rotary valve
product Fig. 9. Spray drying setup.
cyclone
exhaust drying gas ventilator
fluidized bed apparatus
M
rotary valve
fines liquid feed
heater
ventilator }---- drying gas inlet
Fig. 1 0 . Fluidized-bed setup .
Over the last 50 years fluidized-bed equipment was developed for spray gran ulation, agglomeration and coating applications. In contrast to spray drying, liquids are not sprayed into a low particie loaded drying chamber. The liquid is always sprayed into a dense bed of fluidized particies. In Fig. 1 0, a simplified fluidized-bed setup is shown. In the figure, a batch process is sketched where the liquid is sprayed onto fluidized particles. The de dusting of the drying gas is carried out by a downstream cycione. In Section 2. 1 more details of fluidized-bed (FB)-systems are explained.
425
Granulation Equipment
:1
Ci)
raw material feed
:0:
.----- I
shaft ----.
I
I I I \
\ \
;' ... -[
;
"
rotor
�
I I I ,
...... \�
\, � ,I
extrudates
1
raw material feed
......
extrudates
\
\
� ...... ......
�
'
- conical hole sieve
-
,
I
,' '--..
' '--.. ,'
" --.. '--..
extrudates
�
Fig. 1 1 . Operation principles of low pressure extruders.
�'P I ' " L
raw material feed
G
1
housing
' cu11'mg mechanlsm (optional)
!
extrudates
Fig. 1 2 . Sketch of a axial screw extruder.
The main processes using higher pressure are extrusion, compaction and tabletting. The range of extrusion processes is wide. There are low-pressure extruders available as weil as high-pressure versions. In Fig. 1 1 , two principle sketches of low-pressure extruders are included. These types of equipment are typically used if heat and pressure sensitive extrudates have to be produced. The feed raw material is usually done by means of gravity. Feed screws are less commonly used to feed low-pressure extruders. An example of high-pressure executions is the screw extruder shown in Fig. 12. Here the material is pressed axially through a hole-plate. Depending on the application, formulation, downstream treatment and type of product, cut ting devices are occasionally used. Especially in the food industry the particles break due to gravity into more or less irregular pieces. This pre-formed product can then be shaped in a downstream pelletizing step, for instance, as sketched in Fig. 8. Screw extruders are very often used in food and detergent applications. Depending on the process and product properties they can be cooled or heated. Also multi-step processing is possible where as, for instance, different raw
426
M. Jacob
materials are blended, a liquid is added as a binder and the wet mass is then extruded. 2. GRANULATORS AND COATERS USING MAIN LY CONVECTIVE H EAT AND MASS TRANSFER AND LOW AGITATION 2.1 . Fluidized-bed g ranulators and coaters 2.1.1. General design aspects
Fluidized-bed granulators and coaters are widely used in many industries to produce speciality products as weil as bulk products. Considering the general design of fluidized-bed units a general structure can be summarized as shown in Fig. 1 3; only typical options are included which are related to granulators and coaters. This chapter will focus on this kind of equipment only. Specialties, for instance, a heat exchanger, integrated into the process chamber are not con sidered here. Methodology of gas-fluidized-bed granulators and coaters exhaust chamber
no internals with filter system
shake filter cartridge filter bag filter
spray system
top-spray
on bed in bed
bottom-spray
with inserts without inserts
tangential-spray process chamber
batch operation
constant cross section
ö
continuous operation expanded cross section
batch operation continuous operation
gas distributor
porous I perforated plate
circular shape rectangular shape
rotating non-porous plate gas inlet chamber
single chamber divided chamber
Fig. 1 3. Methodology of gas-fluidized bed granulators and coaters.
circular shape
427
Granulation Equipment Main parts of gas-fluidized-bed systems
eXhaust \=J exhaust chamber
spray system �--.,..
-,
-
gas distributor fluidization gas inlet q Fig. 14. Main parts of gas-FB-systems.
process chamber
}
gas inlet chamber
Following the direction of fluidization gas flow the gas inlet chamber, gas dis tributor, process chamber, spray system and exhaust chamber can be defined as main parts of any fluidized-bed granulator or coater (Fig. 1 4). For individual main parts different design options can be selected. Here, not only processing options have to be considered. In addition, the mode of operation (continuous or batch) has an influence on the plant setup and mainly on the eurrent design of the process ehamber. Depending on the use of equipment and principle of processing, different setups can be used to build tailor-made FB systems. In the following section the individual exeeutions of main parts are explained in detail. The gas inlet chamber is the lower part of a fluidized-bed unit. Here the processing gas enters. Depending on the design and the use of the unit this ehamber can be exeeuted as single or divided. In case of a divided gas inlet ehamber different fluidization gas flows can enter the unit. These flows can be eonditioned, for instance, with different temperatures and flow rates. This prin ciple beeomes important in case of continuous operating units where the product has to pass different proeess conditions (for instanee, agglomeration and an additional drying step). Between the gas inlet chamber and process chamber the gas distributor is installed. In most applications statie perforated or porous plates are used to distribute the fluidization gas aeross the whole cross section of the processing chamber. Depending on the general design of the unit, circular or rectangular versions are typical. Rotating plates are only used in combination with tangential spray systems. In that case the circular plate is non-porous and the fluidization gas enters the process chamber through a ring gap between proeess ehamber wall and rotating disko
428
M. Jacob
The process chamber itself can have a constant or an expanding cross section in the vertical direction. Both options are available for batch as weil as for con tinuous operation. Under the subject spray system the nozzles and feed lines for spraying liquids into fluidized beds are summarized. The available executions depend on processing options and are described in more detail. Also the aspects of the exhaust chamber design are explained more in the chapter on gas handling. 2.1.2. Processing options
In general, the main processing options can be characterized mainly by spray nozzle orientation and by design principle of fluidization gas distribution into the processing chamber. When a fluidized-bed unit is used for granulation and coat ing one or more liquids have to be sprayed in the process chamber. To create different product properties different processing options were developed. These options are: • • • •
top-spray processing; bottom-spray processing; Wurster-processing; and Rotor-processing (tangential spray).
In Fig. 1 5, the basic options are shown in principle. In the simplest case of "Top-spray processing" the spray nozzle is installed in the upper part of the process chamber above the fluidized bed. The liquid is sprayed on top of the fluidized particles in the process chamber. In "Bottom-spray processing" the nozzle sprays upwards into the fluidized bed. In contrast to that, the nozzle can be mounted horizontal or with a slight rise or fall. Depending on processing options the function and process stability of the nozzle varies. In Table 1 , the characteristics of the individual options are top-spray -----\-----, tangential-spray --�� gas distributor ---\0.' . fluidization air
Q
Fig. 1 5. Standard processing options.
-"1--- fluidization air L---t---- bottom-spray
429
Granulation Equipment Table 1 . Standard processing options Top-spray processing
- uniform gas inlet velocity, - solid mixing and dispersion by rising gas bubbles, - tendency to spray drying or spray crystallization, and - increased risk of caking on spray nozzles.
- agglomeration of powders to produce grains with low and medium bulk densities, and - coating.
Bottom-spray processlng
Characteristics - uniform gas inlet velocity, - solid mixing and dispersion by rising gas bubbles, - reduced tendency to spray drying or crystallization, - high impact of bed mass on spray nozzles, and - "c1eaning effect" of bed mass minimizes cake formation.
Typical applications - agglomeration of powders to produce grains with medium and high bulk densities, - spray granulation of liquids, and - coating.
Tangential-spray processlng
- uniform gas inlet velocity, - solid mixing and dispersion by rising gas bubbles, - reduced tendency to spray drying or crystallization, - lower impact of bed mass on spray nozzles, - "c1eaning effect" of bed mass minimizes cake formation, and - spray is influenced by fluidization gas.
- spray granulation of liquids, and - coating.
summarized together with their typical applications. In process development the focus is on the following topics: • • •
tendency to spray drying; risk of product build-up on nozzles and supporting structure; and influence of fluidized bed on spray pattern.
430
M. Jacob
�--- bed mass tangential-spray --...... ..:.....-7----,--"-=__;" rotating disk ---t--" (non-perforated) '----- ring gap
process air
q
Fig. 1 6. Rotor-process.
I
�
In the 1 980s special fluidized-bed processes were developed with a focus on fine particle and tablet coating. Targets of these activities were the optimi zation of wetting characteristics in the spray zone and particle movement in the process chamber. On the basis of the work of Prof. Wurster the so called "Wurster-process" was developed based on the "Bottom-spray" option. A special development to produce very compact particles by agglomer ation and layering is the "Rotor-processing" option shown in Fig. 1 6. As briefly explained in the previous section, this process uses a rotating disk as lower part of the process chamber and the fluidization gas enters via a ring gap. The spray nozzle is fixed tangential to the process chamber wall. This option combines the use of mechanical forces together with the drying capacity of fluidized beds. 2.1.3. Processing gas handling
All convective granulators and coaters have in common that they need additional equipment for processing gas handling. Depending on installation and application different setups are typically used in practice. In Fig. 1 7, a simple flow diagram of gas handling processing steps is shown. In process development the current execution of the individual steps has to be defined as weil as number and arrangement of ventilators for metering the processing gas flow. In the process development phase some general points have to be considered. These are, for example: • •
kind of processing gas (air, nitrogen, gas mixtures); volume of processing gas (flow rate, total output to environment);
431
Granulation Equipment
, 1 1 1 l
------ ------, 1- - - - - - - - - - - - - splitting 1 1 _ _ _ _ _ _
_ _ _ _ _ _ _
:
1
granulator or coater
- - - - - - y- - - - - - -1
1 l
processi�g gas recycling
1
_ _ _ _ _ _ .., _ _ _ _ _ _ _
inlet gas handling
: 1
1------
------1
mixing
:. - - - - - - - - - - - -1 1
l _ _ _ _ _ _ _ _ _ _ _ _ _ _
fresh gas in Fig. 1 7. Flow diagram of processing gas handling. • • • •
quality parameters needs of processing gas at granulatorJcoater inlet (temper ature, dust load, water content); quality parameters needs of processing gas at granulatorJcoater outlet (tem perature, dust load, water content); energy consumption of process; maximum parameters of pollutions to environment (dust load, total emissions, temperature);
432 • • • • • •
M . Jacob
explosion protection aspects; mode of operation (batch, continuous, semi-continuous); field of industry (pharmaceutical industry, food industry, fine chemicals); product quality control issues (product hygiene, contamination risks); personal safety issues (protection of operators); and degree of automation.
Typically, standard fluidized-bed plants for granulation or coating are designed as fresh air systems. That means the processing gas passes all gas handling equipment in a single pass from the inlet to the outlet. In that case no processing gas is recycled partly or completely to the fluidized-bed apparatus. Typically, processing gas recycling is done due to the use of special gases (e.g. nitrogen) or plant operation using superheated steam as a fluidization me dium. The use of these gases can be effected by: • • • •
the need of protective measures in case of explosive products; oxygen sensitivity of the product; energetic aspects; and strong emission limits, especially regarding odor.
If a certain amount of processing gas is recycled, additional measurement and control measures are needed. In the following section the individual gas-handling steps are explained in more detail. Fresh processing gas, in most cases ambient air, enters fluidized-bed plants passing a coarse filtration step, for instance, to avoid entrance of dirt, foreign bodies. Downstream the processing gas is con ditioned to fit desired process conditions. Here, different sub-systems can be installed: Pre-filtration De-humidification Humidification
Heatingjcooling
Here the processing gas is filtered to avoid pollution of downstream equipment and product contamination. A typical application of de-humidification steps is the increased of drying capacity due to the reduction of moisture load per mass dry processing gas. In special cases of very sensitive processes or strong demands on process reproducibility the moisture level of processing gas is controlled. In combination with de-humidification a constant, weather independent, inlet moisture of the fluidized bed can be established. Various types of heaters can be used to heat-up the processing gas to process level. Depending on desired temperature level, product properties and available utilities direct or indirect heating equipment.
Granulation Equipment
Final-filtration
433
If the process needs any kind of cooling the heating step is replaced by cooling. This is the case, for instance, in hot-melt processing. Downstream moisture adjustment and heating additional final filters are integrated in the process gas line to avoid any contamination of the process chamber. This setup is widely used in pharmaceutical and food industry. In most ca ses static two-step filters are used.
heating medium
eondensate
eooling medium
Fig. 1 8. Example for a typical inlet processing gas-handling setup.
In Fig. 1 8, a typical processing gas handling equipment arrangement is shown as an example. The processing gas, in most cases air, is pre-filtered by means of a F5 static filter before it passes a downstream de-humidification and heating combination. In this example the de-humidification is realized by a cooler, which cools down the gas to a certain dew point. Here, for instance, cold water can be used with 6°C inlet and 1 2°C outlet temperature. The heating can be realized using saturated steam. Finally, the gas is filtered in additional final filtration steps. In the example a F9 static filter and a F 1 3 HEPA-filter is shown. The arrangement shown in Fig. 1 8 is a typical setup of inlet gas handling in the pharmaceutical and food industry. In Fig. 1 9, an example of an air handler in mono block design for the use in food industry is shown. The outlet gas handling can be done in several ways. Here a first de-dusting of processing gas inside the fluidizing unit is preferable. In this case contamination risks of product and environment can be minimized. As shown in Fig. 1 3 and Fig. 14 the upper part of fluidized-bed units, the exhaust chamber, can be equipped with filter systems. These internal filters can be designed in different ways. In Fig. 20, the integration of back purge filter elements inside the exhaust chamber of a fluidized-bed unit is iIIustrated. In case of the use of back purge filters, the known standard filter systems can be used. These are, for instance, textile bag filters and any kinds of pleated or un pleated cartridges. The cleaning of the filter elements during plant operation is done by reverse gas jets (back-purge) and the dust falls down to the fluidized-bed
434
M. Jacob
Fig. 1 9. Gas handler in food grade execution during manufacturing (Paradair/Germany). compressed air
pressure vessel
exhaust chamber
Fig. 20. Integration of filters in fluidized-bed exhaust chamber.
process chamber. Another option is the use of textile shake filters inside the exhaust chamber shown in Fig. 21 . Characteristic for shake filters is the use of mechanical filter shaking to clean the textile filter sacks. During operation the gas flow is adjusted to a desired process value and the exhaust flap is fully open (Fig. 21 lett). When the filter is to be cleaned, the processing gas flow is stopped by closing an exhaust flap and the shaking of filters starts (Fig. 21 centre). After a certain cleaning time the shaking stops and the process gas flow is restarted by opening the exhaust flap (Fig. 2 1 left). The left two sketches in Fig. 21 shown a single chamber execution. This
435
Granulation Equipment r'----+----,
D
D
�" shaking! active
Shakin flap open
flap closed
D
Fig. 21 . Setups of integrated shake filter systems.
Fig. 22. View i nto integrated filter systems of production scale fluidized-bed granulators (Glatt) .
execution has the disadvantage that the process gas flow has to be stopped regularly. This can lead to process performance problems especially in agglom eration processes. To overcome this disadvantage double-chamber shaking fil ters were developed (Fig. 21 right). In this case the exhaust chamber is divided to install two separate shaking filters. During cleaning of one of the filter segments the other part of the filter is operating as process filter. So the continuous process gas flow is secured and the processing safety is increased. The control of the shaking and of the two exhaust flaps is typically realized by time sequences. Some examples of integrated filter systems in production scale fluidized-bed granulators are shown in Fig. 22. On the left the single chamber and in the centre the double chamber executions of textile shake-filters are shown. The right pic ture in Fig. 22 shows a back-purge filter system equipped with un-pleated metal cartridge elements. This filter system is designed for real CIP (cleaning in place) in pharmaceutical and food industry. As an alternative the de-dusting of outlet process gas external filters or wet scrubbers are widely used. Moreover, these options can be combined with in tegrated filter systems for further reduction of dust content and as a safety issue
436
M. Jacob fluidized bed unit with integrated back-purge filter
( static police filter )
�ID----'_ c:::) outlet gas outlet gas handler
� inlet gas : inlet gas handler
Fig. 23. Typical fluidized-bed setup for food application.
(as a police filter) in case of filter malfunction (e.g. filter rupture). In Fig. 23, a fluidized-bed system with inlet and outlet gas-handling equipment is shown. This kind of arrangement is typical for applications in food and pharmaceutical industry. Another major point in process development is the selection and the arrange ment of ventilators. By the integration of one or two ventilators in the processing gas stream the pressure inside the fluidized-bed apparatus can be adjusted de pending on the position of the ventilator(s) in relation to the fluidized-bed appa ratus itself (Fig. 24). Depending on application, product and peripheral equipment, the right pres sure level inside the process chamber must be selected. For instance, the pres sure difference between process chamber and ambient pressure (e.g. in the building) affects the contamination risk. Here it must be distinguished between contamination of product or contamination of equipment, personal or building. If any contamination of product is to be avoided then flows of any gas (e.g. air) into the process should be minimized. In that case an operation using overpressure prevents flow to the inside e.g. due to leakage. But on the other hand there is an increased risk of contamination of the outside. In the process development phase all factors have to be balanced. Of course if the product is dangerous, for in stance, due to high toxicity the suction mode is preferred. The combined mode using two ventilators is a more expansive one but from the pressure profile point of view it is an optimized setup. By having ambient pressure inside the process chamber the risk of cross contamination can be minimized. Additionally, the in terfaces to upstream and downstream equipment can be designed in a simple way or sometimes open inlets or outlet for solids can be used. This situation has positive side effects, for instance, when sticky or stress-sensitive products must be charged into a fluidized-bed apparatus and rotary valves are unsuitable.
437
Granulation Equipment
a) suction mode
pressure increase
b) overpressure mode
overpressure
vacuum
c) combined mode
atmospheric pressure
Fig. 24. Arrangement of ventilators and related pressure profiles.
If process gas recycling is an option then the position of the ventilator in the loop plays an important role. For instance, the inlet of fresh gas must be located at a point with a lower pressure level than the feed pressure to ensure a gas flow to the loop. The outlet gas must leave the loop at a point of higher pressure. Gas recycling is often used due to: • • • • • •
Using nitrogen as processing gas (e.g. due to explosion protection); the use of dangerous products, to minimize outlet gas treatment; malodorous outlet gas to minimize pollution of the environment; reduced energy consumption; using superheated steam as processing gas; and Iimited amount of outlet gas (e.g. limited approval from government).
In Fig. 25, a simplified cIosed-loop setup is explained. In the figure the total processing gas flow leaving the fluidized-bed apparatus is de-dusted using two filter steps. Passing the filters the gas stream is cooled to condense a certain amount of solvent (e.g. water). The cooled and de-humidified gas is recycled to the inlet gas heater by a ventilator. In most of the ca ses a certain gas flow must
438
M. Jacob fluidized bed unit
purge
-+�:::::;:�I----.l
<=:J inlet gas
q outlet gas
spray
Fig. 25. Example of a closed-Ioop setup.
purge
-+:;::��J.----.J
J-....-----ID--. q
outlet gas
outlet gas handler
spray <=:J
inlet gas
ventilator
Fig. 26. Example of a partially recycling of processing gas.
be vented. This out/et gas f/ow is needed to keep the mass balance in the /oop. There are a/ways gas streams, which are fed to the /oop, for instance, purging gas (e.g. for filters, sealing) and fresh in/et gas (e.g. nitrogen to keep the oxygen /evel below a desired value) Depending on the spray rate, the solvent concentration at the out/et of the condenser and the feed rate of in/et gas, a certain steady state solvent concen tration will be reached. Particu/ar/y for the case of sticky or hygroscopic products, the drying kinetics can be affected by the recircu/ation compared to a standard system. If on/y a certain amount of the processing gas is recyc\ed a setup, such as that shown in Fig. 26 can be used. In that case, a condensation of the out/et gas is not always needed. Depending on the temperature profile (especially the out/et temperature of the f1uidized bed) and spray rate the recircu/ation rate and the outlet gas f/ow (sp/it ratio) can be optimized. /n the design of such a /oop the dew point must be considered to avoid, for instance, fou/ing problems and hygienic risks.
Granulation Equipment
439
2.1.4. Gas distributors
The main function of the boUom part of the processing chamber is to distribute the fluidization gas across the whole cross section of a fluidized-bed unit. De pending on the processing option the gas distributor design is used to create special gas velocity distributions, for instance, in "Wurster-processing". Moreover the gas distributor can be used for charging and discharging of process cham bers. In that case, the part has to have a "transport effect". This means that the gas distributor has to work as a simple conveying system and can be used to blow particles into a certain direction. Typical requirements of gas distributors are defined from the construction, process and maintenance point of view. Examples are as following: • • • •
mechanical stress resistance; prevention of passage of particles through the distributor; low pressure drop; and easy cleaning.
From the literature a large number of air distributor types are known. Here, the only versions considered are ones that are widely used for fluidized-bed coaters and granulators. Special designs for fluidized-bed reactors will not be explained. All types are used for fluidized-bed granulators based on the following basic versions: • • • • •
porous plates; perforated plates; sintered plates; wedge wire plates; and CONIDUR
Common for all types of gas distributors is that they are characterized by a pressure drop as a function of gas velocity. In Fig. 27, two simple diagrams explain pressure drop dependencies from open area of plate (left) and of gas velocity (right).
CPplate
Fig. 27. Basic properties of gas distribution plates.
440
M. Jacob standard version - low thickness of plate - big openings - punched holes -
special version - high thickness of plate - small openings - drilled holes -
�:7: � � ���
: - :' ,: - � :, .
.
:., :, .. . -:. . . � .: oe :
. - . . - . . - . - . - - . - . . - . . - . - . . •
-
-
.
Ct
-
.
- . .
.
.
.
-
•
.
Fig. 28. Examples of hole-type gas distributors (photographs [9]).
In accordance with processing requirements and size or design of the fluidized bed unit the pressure drop has to be specified correctly to guarantee the desired gas velocity distribution across the whole cross section. Moreover, the stress resistance must be high enough to avoid vibrations or breakage of the gas dis tributor. At the industrial scale the gas distributor plate itself has to be equipped with a support structure. Porous plate gas distributors are widely used in research and development to study the bubbling behaviour of gas-solid fluidized-bed hydrodynamics. Simple perforated plates are commonly used for many kinds of fluidized-bed applica tions. The main advantages are the low price, easy manufacture, the variety of specifications and the possibility of tailoring the plates to fit special demands (for instance, segmented design). In Fig. 28, two examples of perforated plates are shown. On the left side in Fig. 28 an example of a typical perforated plate is shown. This kind of plate is commercially available with relatively low thickness, for ex ample, 1-3 mm. Owing to the method of manufacturing the openings the min imum size of holes is of the same order as the plate thickness. That means small holes, which are needed to avoid passage of particles, can only be achieved with thin plates. In that case, an additional supporting frame below the hole-plate is needed for the structure to have sufficient stiffness and strength. To get more stress-resistant gas distributors the wedge-wire plates were in troduced in fluidized-bed processing (Fig. 29). This type of plate consists of profiles, which are welded direct on supporting profiles. The gap between the individual profiles determines the maximum size of openings. The advantage of such gas distributors is the very high stress resistance in combination with sm all opening sizes. Additionally these plates are also easy to clean. Standard perforated plates and wedge-wire plates are designed to create up wards gas flows (vertical to surface of gas distributor). That means the particles in
441
Granulation Equipment standard version without transport effect
fIWWl
special version without transport effect
Fig. 29. Examples of wedge-wire type gas distributors.
� standard version with transport effect
a)
b)
Fig. 30. Examples of plates with transport effect.
the fluidized bed are not blown or conveyed in a certain direction. To have (
442
M. Jacob
Table 2. Improved processing options Bottom-sprayprocessing
Characteristics - non-uniform gas inlet velocity, - non-uniform gas inlet velocity, - solid transport next to the nozzle due - solid transport inside Wursterto high gas velocity, partition by pneumatic transport, - solid mixing and dispersion by rising - solid mixing and dispersion by rising gas bubbles in the outer bed, gas bubbles in the outer bed at - less impact of bed bass on spray low turbulence, - "controlled" solid circulation nozzle, and - improved wetting behaviour. between Wurster-partition and outer bed, - less impact of bed bass on spray nozzle, and - optimized wetting behaviour. Typical applications - coating of fine particles, grains and - agglomeration of powders to produce grains with medium and tablets, and - spray granulation of liquids. high bulk densities, - spray granulation of liquids, and - coating. mainly in Wurster-processing as shown in the sketches of Table 2. These spe cially designed gas distributors are segmented to have different open areas over the whole cross section of the fluidized-bed apparatus as shown in Fig. 3 1 . Below the Wurster partition the plate i s designed with a higher open cross section compared to the outer bed region. This results in a higher gas velocity inside the Wurster-partition than in the outer region and a kind of up wards pneumatic transport of particles in the partition can be achieved. The gas velocity in the outer bed region is adjusted in such a way to have a slowly bubbling bed behaviour. In Fig. 32 a picture of a typical Wurster-type gas dis tributor is shown. In the same figure on the right is a top view into a processing chamber.
443
Granulation Equipment outer plate ( hole plate ) (open cross section q, 1 )
�Pplate
. . : . : . : . : . : . : . ' . ' : ' : ' . inner plate ( hole plate ) .' . : . . : . : : : : : . : . : . : . : (open cross section q,2> q, l ) .
.
.
.
'
�Pplate
plate
Fig. 31 . Principle of segmented gas distributors for Wurster-processing.
Fig. 32. Bottom and top - view on Wurster-process chamber (Glatt/Germany).
2.1.5. Dry material charging and discharging systems for batch and continuous operation
It is obvious that particles (products) have to be charged or discharged in any fluidized-bed application. In the development phase of fluidized-bed plants the general mode of operation, batch or continuous, is an important consideration. In batch processing the solid handling is usually organized in sequences. Contin uously operating plants' solids have to be discharged and charged all the time in a certain production campaign. For batch units several solid flow concepts are in use in industrial and small scale . The handling options are: • •
exchangeable material containers; charging and discharging by means of pneumatic conveying (use of vacuum); and
444
M . Jacob
exhaust � exhaust chamber including filter
spray system -c
gas distributor -c
�aICh nO.2 �XChani>
fluidization gas inlet q
U ·.-.· ••· • •·;.·ii• .
.. . ......... ..
" ,W.�;;:
1o.
charging
and dlschargmg
}
}P' }
expansion chamber od"" ooola;o"
gas inlet chamber
Fig. 33. Solid handling in case of use of an exchangeable material container. •
charging and discharging using gravity (for instance, by means of discharge chutes, folding down gas distributors or turning gas distributors).
In the simplest case the unit is designed with an easy exchangeable process chamber (Fig. 33). This exchangeable part is then often called as product con tainer. The advantages, including a very simple design and a rapid changeover from batch to batch are compromised by a need to open the apparatus. This can lead to contamination risks for personnel and products. Open material handling leads always to higher cleaning activities compared to closed systems (Fig. 34). A way to overcome open solid handling is, for instance, the use of turning gas distributors. This handling philosophy allows charging and especially discharging procedures without opening the processing unit. In Fig. 35, the principles are explained. The key feature of such fluidized-bed apparatuses is the rotating gas distribution plate and a docking system using the inlet gas chamber. The inlet gas chamber is equipped with a discharge flap on the boUom side. The gas inlet pipe can be closed using a second flap. During charging of the unit the fluidization gas flow is shut-off and the gas inlet flap is closed. The bulk of solids which shall be charged into the process chamber can be filled in, for instance, by gravity using a chute at the side of the chamber. A flap is integrated to open or close the feed system. In operation the charge and discharge flaps are closed and the fluidized-bed plant can operate as usual. After processing the fluidization is stopped and the discharge flap opened to connect the gas inlet chamber with downstream solid handling, for instance, a material container. Afterwards the gas distributor is turned to a vertical position and the solid batch flows down to the discharge flap passing the gas inlet chamber. After emptying, the discharge flap is closed and the gas distributor is turned back to its horizontal position.
445
Granulation Equipment
Fig. 34. Batch fluidized-bed u nit with exchangeable material container (Glatt/Germany). in process
charging
� �
q
�
�
q
",,"
...... ... ......
"" ... . .. . .. .... . �::�� ��:.-:
--
-=:J
*
discharging
�
�
.� �
.lJ.
Fig. 35. Solid handling in case of use of a turning gas distributor.
The production cycle can be restarted again by charging the fluidized bed unit with a new batch of solid raw material. The right picture in Fig. 36 shows an example of a rotating gas distributor. The picture includes a bottom view and was made in the workshop. Owing to the pharmaceutical execution including CIP (Cleaning in Place) a wedge-wire plate
446
M . Jacob
Fig. 36. Solids feed system including flap and wedge-wire turning gas distributor (Glatt! Germany). f----+(
�
throttle flap
c:=:> outlet gas
ventilator
on/off flap heater
<:;=::J inlet gas
Fig. 37. Charging of f1uidized-bed units by pneumatic transport.
was selected. The left picture shows a charging port with an open/close flap flushing with the inner wall of the process chamber. This flap is also designed for CIP of the fluidized-bed plant. Another option for charging and discharging is the use of pneumatic transport. I n Fig. 37, a simplified flow diagram of such a system is shown. Owing to the vacuum created by the process gas ventilator, solid raw materials can be sucked into the processing chamber. The throttle flap in the gas inlet pipe can be either closed or partially opened to adjust a minimum fluidization. An on/off flap in the suction pipe between material container and process chamber is used to close the fluidized bed after charging. Advantages of this charging principle are closed solids handling the horizontal product flow. It needs less total height of the plant compared to a product flow by gravity. For empting very often side discharge systems are used in combination with pneumatic charging (Fig. 38).
Granulation Equipment
1-----+1
447
�
throttle flap
c::::::) outlet gas
ventilator
heater material
� inlet gas
Fig. 38. Side discharge system for FB-systems.
Fig. 39. Side discharge system (GlattfGermany).
I n this case a discharge flap is mounted on the housing of the process chamber elose to the gas distributor. After the discharge flap, a chute can be used to connect a material container. This container must be sealed from the atmosphere to ensure a comparable pressure level in process chamber and material con tainer. Otherwise air will be sucked into the fluidized-bed apparatus and no product will be discharged. With side discharge systems very often gas distributors with transport effects are used. These distributors blow the bed mass to the discharge port. Specially designed distributor plates can create defined product flows and ensure a good emptying result. In Fig. 39, a typical side discharge system of an industrial scale fluidized-bed granulator is shown. On the left side a top view of the gas distributor is shown. Here a segmented design made of CON I DUR (I\'--plates is used to give a tangential product flow next to the chamber wall. Owing to this setup all product is trans ported to the opening of the side discharge. The right picture in Fig. 39 shows an outside view of the discharge flap.
448
M. Jacob solid raw material
dosing system
53-"1 M� n
discharge of product Fig. 40. Basic principle of continuous processing.
In contrast to batch processing, in the continuous operation of fluidized-bed plants raw materials and product have to be charged and discharged all the time. There are a few basic concepts of charging and discharging systems, which are explained here. To change a batch apparatus to continuous, processing feed and discharge equipment must be added. In Fig. 40, a flow diagram of raw material and product feed and discharging of a continuous fluidized-bed granulation plant is shown. In the figure a dosing screw is used to feed and metre a solid raw material (for instance, a powder) to the granulator. A fixed speed rotary valve ensures the pressure disconnection to atmosphere. The continuous product discharge is done by a variable speed ro tary valve mounted on a discharge chute. This rotary valve can be used to adjust the (volumetric) discharge rate depending on the feed rates of solid and liquid raw materials to satisfy the mass balance. Especially for continuous product discharge a wide variety of systems are in industrial use. To ensure a constant height of fluidized bed, simple overflows in different executions were developed. In Fig. 41 , two examples are explained. In both cases fixed speed rotary valves are used for disconnection to atmosphere or to downstream equipment. The left sketch shows a typical setup for horizontal (plug-flow) fluidized beds with rectangular cross section of the process chamber. On the outlet side of the apparatus an end weir is mounted which divides the fluidized-bed section from the product discharge chute. When the fluidized-bed height is increased, for instance, due to additional raw material feed, solids flow over the weir and into the discharge chute at an in creased rate. It has to be taken into consideration that a fluidized bed also ex pands when the fluidization gas velocity increases. That means there is a relationship between hold-up mass and bubbling behaviour of the fluidized bed.
449
Granulation Equipment r··-··_··_··_··_··_··_··_··'
fluidized bed
weir i gas inlet chamber+-
'-------1
discharge chute
rotary �IE--!-{ valve
discharge product
01
rotaryHH-{ valve
discharge product
01
Fig. 41 . Design principle of overflows.
The correct setup is chosen based on scale-up trails or during the start-up phase of a plant. Another possibility is the use of discharge pipes. These pipes are mounted at a certain height above the gas distributor to keep a desired bed mass nearly constant. The main advantages are the simple design and the possibility to integrate more than one discharge per fluidized-bed apparatus. A disadvantage of such systems is the need for additional openings for emptying the fluidized bed in shut down procedures. To drain the whole bed, underflow flaps are integrated into overflow weirs or additional side discharges or discharge chutes are used. All discharge principles shown in Figs. 40 and 41 have in common that the whole particle size range of the fluidized-bed mass is discharged. This means that, for instance, in spray granulation plants, d ust or undersized grains can leave the apparatus. These fractions must be recycled to the granulator again as seed material to grow further. To overcome this disadvantage classifying discharge systems were developed. In Fig. 42, two examples of classifying product outlets for fluidized-bed granulator are shown. In general any kind of sifting devices can be used in combination with fluidized-bed apparatuses. In the simplest case the discharge pipe shown on the right in Fig. 41 , can be modified to have a classifying function. To get this functionality the top end of the discharge pipe has to be installed in level with the gas distributor. Additionally, a separate gas flow is to fed into the discharge pipe. During operation of the flu idized-bed unit, all particles can pass the upper end of the discharge pipe and can enter this from the top. Inside the discharge pipe a classification process takes place due to the counter current upwards gas stream. The gas velocity in the discharge pipe can be changed, by adjustment of the flow rate of classification gas. Depending on particle size, the sinking velocity of particles varies. That means all particles which are too small are blown back into the fluidized bed by
450
M . Jacob r" -" - " -" -" -" -" -" -'"
undersized particles weir
--,r-tr-_..L
i whole particle size ranges
gas inlel chamber
discharge pipe particles 01 desired size rotary valve discharge producl
01
discharge of product
Fig. 42. Options of classifying outlets for f1uidized beds.
the classifying air stream. Particles that are large enough sink down and are discharged. Using this principle a dust free product is ensured. Another option is the use of zig-zag-sifters as shown on the left in Fig. 42. The advantage of zig-zag-sifting compared to simple counter current sifting is the improved efficiency. The discharged particle size range is closer. The reason for the improvement is that shadow effects and clouds of particle in the separator are avoided. Owing to this behaviour the separation probability is increased. The costly design is a disadvantage. By combining different continuous charging and discharging principles a large variety of apparatuses can be designed. But in general, two different basic types of continuous fluidized-bed units are used in all kind of industry. Very popular are horizontal fluidized-bed units, characterized by a rectangular design of the proc ess chamber. In the past this type was used mainly for drying and cooling proc esses. Later they were developed further for granulation, agglomeration and coating processes. In Fig. 43, a typical setup of a horizontal fluidized-bed apparatus is explained. In the case shown in the figure a simple inlet chute is used to charge the fluidized bed with solids in continuous operation. A rotary valve is used for disconnection to upstream processing steps. The discharge of product is realized by means of a discharge chute equipped with a speed adjustable rotary valve on the outlet. All known spray options shown in Fig. 1 5 can be applied. Very often internal filter systems are used to keep any dust and fines in the apparatus. This design minimizes the need for peripheral equipment for outlet gas handling. A most useful option is the possibility to feed different conditioned inlet gas flows to a unit. Owing to this, different processing steps can be carried out in one single unit, for instance, spray granulation, after-drying and cooling. Moreover processing
451
Granulation Equipment outlet gas
r-1 r-1 I I I I I L _ .' L _ -' '- _ -'
r-1 I I L _ -'
rolary valve
••.
I I I I
I I I L _ -'
'- _ J
I I
I I
'- _ J
;�.
...:. .. . ... .. . ........ ... ... .... ................ . ... ......... ...... .. . .. . .. ... . .. . .. ... ... ... . .-: • -:::�:.-::.-::.-:.:-::.-::.-::.-::.-:::::.-: Fluidized bad �-::.-::.-::.!:.-::.-::.-::.-::.-::.-::.-::
·-:":1:::;.-:;.-:;.!:.::�·-:;,.���-:��':.�· ..:��-:;;:.!:�·-'!i..
·
�S
... . .:. . . ..
�
}
spray system
discharge chule
.:�
g� i�� chamber(s)
inlel gas slream 1
inlel gas slream 2
inlel gas slream 3
Fig. 43. Horizontal fluidized bed for continuous processing.
conditions of single step processes can be optimized in the fluidized bed by adjusting, for instance, inlet gas flows and temperatures. Also temperature pro files and variations in spray rate can be used (Fig. 44). Compared to fluidized-bed units having a circular design of the process chamber the dynamic behaviour is different. Depending on process conditions (e.g. capac ity) and geometrical dimensions (e.g. length and width of the process chamber) the residence time distribution of solids in the fluidized bed can be homogenized. That means a horizontal fluidized bed type shows a more plug-flow-like behaviour in stead of a weil mixed one, which is typical for circular fluidized-bed apparatuses. In [121 more detailed information about residence time behaviour can be found. For spray granulation and agglomeration processes a configuration shown in Fig. 45 is often used in the fine chemicals and detergent industries. In this case the circular fluidized-bed principle is equipped with a continuous classifying outlet, which was introduced in Fig. 42. This type of plant commonly operates at higher fluidization velocity to produce more den se and compact products. Owing to the level of gas velocity no internal filters are used (Fig. 46). Typically external filters, cyclones or wet scrubbers are used downstream to clean the outlet gas and the dust collected in filters or cyclones are normally recycled to the process. This flow of fines and dust is often needed as seeds for further particle growth.
M" Jacob
452
Fig. 44. Industrial scale horizontal fluidized-bed granulator GFG 500 with internat bag filter system (Glatt/Germany)"
outlet gas expansion chamber
g'-'-
process --+chamber • •
_
:-:":-':'"fluid ized bed ':�:-",.ioj. " .... �.�.�.�.�.�.�.�.�.�.�. • • •• _• • .ß._• �• • _•• _• • • •• • ••
i
S
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r-
.
. -- - -
L spray Jsystem
-- I"nlet for soll"d
raw materials
gas inlet chamber discharge pipe
"Inlet ----+�-----,
classifying gas
Fig. 45. Weil-mixed f1uidized bed with classifying outlet for continuous processing"
Granulation Equipment
453
Fig. 46. Industrial scale weil-mixed fluidized-bed granulator AGT 2200 (Glatt/Germany).
2.1.6. Dry material handlingjrecirculationjproduction of seeds
In fluidized-bed granulation processes the discharged grains have to be treated downstream. For instance, in continuous spray granulation processes seeds (nuclei) are needed for steady state particle size distribution. Seeds have to be generated in process or have to be fed from external sources. Generally speak ing, seeds can be produced in process by: • • • •
spray drying or spray crystallization (overspray); attrition; breakage of particles; and recycle of mi lied or crushed oversized grains.
A very stable and reproducible method of seed formation is the recycling of mi lied or crushed oversized particles. In Fig. 47, a simplified flow diagram of external seed production is shown. All particle size fractions are discharged un classified from the fluidized bed, for instance, by means of a chute and a rotary valve. Downstream of the rotary valve a two-deck sieve is installed to separate oversized and undersized particles. If a certain amount of undersized product (or dust) is not allowed in the final product, these undersized grains can be recycled
454
M. Jacob t:::> outlet gas
external solid feed q -------,
spray liquid q
�
_ _ _ _ _
may contain solved or unsolved solids
recycle
e.g. air q for conveying
blower
( RV
=
rotary valve)
Fig. 47. Principle of external seed production - conveying of seeds.
to the granulator as seeds. The oversized fraction also can be used if they are milled or crushed to a smaller size and returned to process. The fraction between the two sieve decks is defined as final product. External seeds are produced in additional processes. Typically powders can be used for further size enlargement in granulation plant. As an example, fine par ticles produced in spray dryers can be fed to a granulation plant where they will be enlarged by agglomeration, spray granulation or coating. The product flow and conveying of seeds can be done using typical solid transport principles like pneumatic transport, gravity, belts or screw conveyors. In Fig. 47, the discharged particles are fed to sieve and mill by gravity. This principle requires a certain minimum height below the fluidized-bed unit. The seeds are blown back to the granulator by pneumatic conveying. The conveying air is han dled by a blower, which produces enough overpressure for transportation. This principle is called dilute phase conveying. The conveying gas (mainly air) enters the fluidized-bed granulator. The filter system of this apparatus is used to handle this gas stream. The disadvantage of seed conveying by overpressure is the risk of dust for mation or contamination in case of a leak in the transport line. An alternative philosophy is to convey all discharged product upwards and then design the classification and millingjcrushing based on gravity. In Fig. 48, this principle is shown. The advantage of this setup is, in principle, easier conveying of discharged material due to its good flowing behaviour. Moreover less height below the gran ulator is needed. All downstream processing to handle final product and seed material can be based on flow by gravity. Because of this fine particle and dust conveying by pneumatic transport can be avoided. A disadvantage is the sig nificant increase in size of the conveying system. Here the total discharge stream
455
Granulation Equipment outlet gas <:::;
filter or other separator
outlet gas �:::}----- -
mill or crusher
external c:::> -------, solid feed spray liquid .----'\
may contAln L..--,.f solved or unsolved solids
�
_ _ _ _ _ _
discharge e.g. air c:::> tor conveying
-f:,
tluidizäti on gas conveylng line blower
Fig. 48. Principle of external seed production - conveying of discharged product.
has to be transported in contrast to only seeds conveying. Depending on process conditions, a smaller amount of discharge grains has to be recycled in a number of industrial applications. But there are also processes installed where the ma jority of discharge is recycled (in that case mainly undersized particles) and only a small percentage is the final product. This ratio varies from process to process and should be optimized during process development. 2.11 Liquid handling and spray systems
In most fluidized-bed processes for granulation and coating one or more liquids have to be added depending on the process. To have good process conditions for particle growth by coalescence of (smaller) particles, layering by spray granu lation, powder layering or coating in nearly all cases very small droplets are needed. Different types and sizes of spray nozzles are in use to transform the continuous liquid stream(s) into disperse drops. For atomization, in general, two basic types of spray nozzles are in use. These are pneumatic (binary) and hy draulic (pressure) nozzles as shown in Fig. 49. If spray nozzles have to be selected or designed for fluidized-bed applications, some general parameters have to be taken into account. These factors include: • • • •
drop size distribution or average drop size (e.g. Sauter-diameter); spray pattern (full cone, hollow cone, flat jet); spray angle; liquid feed rate (minimum, operation, maximum);
456
M . Jacob hydraulic (pressure) nozzle
pneumatic (binary) nozzle
gas cap
atomizalion gas liquid nozzle -----j:J\
.f..I--W-- spray liquid --M-I" ring gab L---- liquid outlel -----' Fig. 49. Nozzle types. • • •
drop velocity distribution or average drop velocity; feed pressure of the liquid; and atomization gas feed pressure and flow rate in case of pneumatic (binary) nozzles.
In Fig. 50 the different spray patterns are sketched. The spray pattern has an influence on the particle wetting and on the local liquid distribution in the fluidized bed. Owing to this the spray pattern and all the nozzle parameters have an effect on particle growth kinetics, type of particle size enlargement (e.g. layering or coalescence) and product properties (e.g. porosity, surface roughness, size, particle density). In fluidized-bed applications in the fine chemical, pharmaceutical or food in dustries, pneumatic nozzles are typically used. This type is also called a binary nozzle. This nozzle atomizes the liquid flow using a high velocity gas flow. As shown in Fig. 49 left, a liquid nozzle with relatively big bore is covered by gas cap. Between the gas cap and the liquid nozzle is a ring gap where the atomization gas is led to the nozzle tip. On the nozzle tip the relatively slow flowing liquid comes in contact with the very high velocity gas stream. Owing to the high shearing forces the liquid stream is atomized, producing a very fine mist. In Fig. 51 two basic gas-Iiquid-mixing principles are explained. The standard case is shown on the left where the liquid to gas contact takes place just in front of the nozzle tip. This kind of pneumatic nozzle design is ca lied external mixing. In case of internal mixing (Fig. 51 right) the tip of the liquid nozzle is inside the gas cap and liquid and gas are mixed before the mixture leaves the circular arranged spray bores (Figs. 52 and 53). In contrast to pneumatic (binary) nozzles, hydraulic nozzles atomize the liquid stream due to high feed pressure. The drops are formed because of the very high
457
Granulation Equipment
/\
/ \ / \
,/�;\.,
.t.":... -
4::��; •_
��. .
... . \, .. .......:·-�·-�··��: .,.�"!..."! ...:- ... . .. ...... ..
i •• �
../
!
:*• • �-.�� • • .,. _ __
.... ....�-.�"Io
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/':..-...................... .-......\.\ !
!
.
.
.
\
\ // .'•.. : .-..... ..:... ,.-......."",; .... .. : . .;:.;_... :�...
flat jet
hollow cone
full cone
\
i���;:·:'\
Fig. 50. Forms of spray pattern. pneumatic (binary) nozzles internal mixing
external mixing
1--1-......;. ---- liquid ------ftI..-tt-l Ho!lf---- atomization gas ---Mf'
---'I
". "T i_ _
:'i : '.\ / : :, \, \, I
'I� \((
, ,
I I
' I
I I
I,
\
\ \
,:
mixing zone
spray cone --...:-,..
\ \ \ \ \ \ \
,
'
Fig. 51 . Basic gas-liquid-mixing principles of pneumatic (binary) nozzles. (Adapted fram Schlick [ 1 6].)
velocity inside the bore. In Fig. 54 an example of such a spray nozzle is shown. The simple design and the mechanical robustness are some of their advantages. In a lot of applications ceramic liquid inserts are in use due to the very high flow velocity inside the bore. Especially if suspensions or other abrasive liquids are to be sprayed, special construction materials are needed. Depending on the liquid feed pressure different drop size distributions and spray rates are achieved. Owing to the direct dependency between spray rate
458
M. Jacob
Fig. 52. Pneumatic (binary) nozzles with external mixing - left single nozzlejright multi head nozzle (SchlickjGermany) [ 1 6] .
F i g . 53. Pneumatic (binary) nozzle modified for internal mixing (SchlickjGermany) [ 1 6] .
Fig. 54. Pressure (hydraulic) nozzle (SchlickjGermany) [ 1 6] .
and drop size pressure nozzles have to be designed for a weil defined operation point. For a good spray pattern a certain minimum spray rate is required and has to be considered in start-up procedures of spray systems. In Fig. 55, two photos of spray pattern produced by pressure (hydraulic) noz zles are shown. On the lett is a standard nozzle type with a very uniform spray and the right photo explains a special nozzle with multiple holes, which are arra nged in a circular pattern.
459
Granulation Equipment
Fig. 55. Examples of pressure (hydraulic) nozzle spray pattern (Spraying Systems Co./US).
!height diameter
nozzle array
Fig. 56. Nozzle arrangements.
multi head nozzle
center nozzle
In pilot and industrial scale fluidized-bed processing several spray nozzles are typically installed in one granulation or coating unit. In Fig. 56, different options of nozzle arrangements are shown. In the simple case one single nozzle is installed in the centre of a fluidized-bed unit. Depending on the process the spray rate of this nozzle can be very high and large differences in the local moisture distribution in the bed can be the result, especially in large-scale processes. A way of im proving the wetting properties across the bed surface is the use of multi-head nozzles. Here the simple liquid feed system can be combined with a more uniform distribution of the spray.
460
M. Jacob (a)
(c) 1+--1::'<1---"-----.---1><1-_ nozz[e
nozz[e f-------i::'
'L-_..J--I>o:r-+ nozz[e open/e1ose
f-------i::'
(b)
(d) nozz[e
nozz[e nozz[e nozz[e
nozz[e
flow
nozz[e
contro[
10
nozz[e array
Fig. 57. Spray liquid feed principles.
A very good liquid distribution is achievable by using multiple single nozzles. Here an optimum of process safety is possible but this setup needs the highest expendi ture in the liquid feed system. In Fig. 57, different principles of liquid feed systems are summarized. In general, a liquid feed system has to fit the following demands: • • •
safe metering of liquid to the nozzle; controllability of liquid flow rate to nozzle; and possibility of recognizing of nozzle or feed malfunction.
Especially if suspensions or melts have to be metered and distributed to noz zles the liquid feed system must be designed to: • •
Avoid settlement of solids in liquid line (e.g. in case of suspensions). Minimize dead ends or dead zones (e.g. in case of melts or suspensions).
Independently of the nozzle type being used, an individual liquid stream has to be fed to the nozzle(s). To metre the flow rate different options can be used, summarized in Fig. 57. Version "a" shows a very simple example of a ring pipe spray system. The liquid pressure level is controlled by means of a control valve.
Granulation Equipment
461
The circulation pump (e.g. a centrifugal pump) is running with fixed speed. The flows to the nozzles are not controlled. Each nozzle gets a liquid flow depending on their pressure-flow-characteristics. In version "c" additional flow controllers are inserted into the feed lines to the individual nozzles. By means of these flow controllers the spray rate can be adjusted per nozzle. The pressure control valve in the ring pipe is used to realize nearly constant pressure conditions upstream of the control valves. Compared to version "a" this setup offers a much higher level of process safety and transparency. When a high number of nozzles are needed the version "c" can be extended to version "d" where nozzle arrays are connected to a single control valve. This version can be used to reduce the number of control loops. On the other hand using this setup several nozzles are connected to each other and in case of malfunction or blockage of a nozzle the other nozzles tend to compensate. Owing to this behaviour the error detection needs additional efforts. Another option is the use of separate spray pumps for each nozzle as shown in version "b". In that case the flow can be controlled by the speed of the pump. Especially if the number of spray nozzles is very high, this option is very expensive. 2.2. Spray dryers
In the following section some basic information about spray drying principles are summarized. There will be no complete explanation of all details and back grounds. This section will focus on the technology in general and its differences to fluidized-bed technology. For deeper information, for instance, [1 3] can be used. 2.2.1. General design aspects
Spray drying equipment is widely used to transform solid containing liquids into dry products by evaporating the solvent (normally water). There are many tech nical versions available beginning with lab equipment up to large industrial scale. In Fig. 58 a simplified methodology of spray drying equipment is summarized following the processing steps from liquid to final product. The solidification step in particular can be realized in many ways. In the sim plest case the liquid is atomized into a drying chamber and a powdery product is formed. To reduce the amount of fines and to increase the final particle size spray drying plants are often equipped with fines recycling. Depending on the gas-solid flow pattern inside the drying chamber more or less agglomerated products can be achieved. In Fig. 59 the main parts of a typical spray dryer are sketched. The most visible construction element of a spray dryer is the drying chamber. 2.2.2. Processing options
To produce different particle structures and forms, various options of spray dryer configurations can be used. The main differences are in the flow regime inside
462
M. Jacob Methodology of spray drying equipment post-processing
fluidized bed
internal extern al
fluidized bed fines recycling conveying I storage
offgas treatment
bag filter
external
cyclone cyclone
*
a.
cartridge filter
internal
Cl C ·w
bag filter
'" Q) u
discharge
e
direct from chamber
batch operation continuous operation
a.
from deduster
total discharge secondary discharge
with particle presence
solidification
recycled particles external particle feed
L-
_�
om at� at� n� io i z= � � �
_ _
without particle presence
�� L.J
�
noZZle ============== rotary
Fig. 58. Methodology of spray drying equipment.
liquid leed => ------, drying gas inlet =>
->I r-�--+---'----,
-
atomizer {
)- gas distributor
drying chamber exhaust
<::= ----_\.
n
product Fig. 59. Main components of a spray dryer.
)- discharge
463
Granulation Equipment co-current
co-current
cou nter-cu rrent liquid in
liquid in liquid in
... ,.
/
-'
.
....
gas in gas out
. .
.
.
. ....
• • •
gas out
IJI. • •
• product out
• product out
product out T
Fig. 60. Co-current and counter-current spray dryer flow models.
gas in
liquid in
liquid in
. ...
,..
gas out
gas out
•
product out
•
product out
Fig. 61 . Mixed flow spray dryer flow models.
the drying chamber and so in the droplet or particle to gas contaci. On the basis of general information from [ 1 3] basic processing options can be sketched as shown in Figs. 60 and 6 1 . Roughly speaking, different particle structures can be created using co-current or counter-current contacts between processing gas and droplet/particle due to the differences in drying (or crystallization if the liquid is a melt) kinetics.
464
M. Jacob
The individual flow patterns have an influence on the design of the drying chamber. Owing to this dependency the flow type has to be fixed in the process development phase before the dryer design phase starts. More complex flow models can be established if, for instance, a fluidized bed is integrated into the bottom section of a spray drying chamber. In Fig. 6 1 , two examples of mixed flow systems are explained. On the left side in the figure a system is sketched where the liquid is atomized in an upwards direction, co-current with the gas flow. At a certain height the flow direction of the particles turns and they fall down against the gas flow. The other option show right as a co-current dryer configuration where the particles fall direct into a fluidized bed for further treatment. This ver sion is often used in food industry where instant products (e.g. drinks, milk prod ucts) have to be produced. Here, the fluidized-bed option can be used for after drying of agglomerated particles. Owing to this, for instance, the amount of fines can be reduced. Especially in the last few decades a big number of modelling algorithms and tools were developed to simulate and optimize spray-drying principles. For in stance, the coupling of CFD-codes with population balances is promising and a lot of basic research work is ongoing. But nevertheless the right selection and design of these equipments needs experimental studies and the specific know how of the manufacturer. 2.2.3. Processing gas handling
The processing gas (typically air or nitrogen) treatment in general include com parable components and is based on the same philosophies explained in the previous Section 2. 1 .3 for fluidized-bed applications. 2.2.4. Dry product treatment
In most applications of spray drying the dried material has to be handled in the dryer itself or in additional downstream processing steps. The after drying or agglomeration of spray dried particles in additional equipment are typical cases. A widely used setup of such a two-step process is sketched in Fig. 62. In the example a co-current spray dryer is connected with a horizontal fluidized-bed system (explained above in Section 2. 1 .5). Here the dryer is used to transform the liquid raw material to a solid form. Very often the dried product is of small particle size and contains a bigger amount of dust and fines. To reduce the dust load and to increase particle size very often downstream agglomeration is used. Depending on installation the solids coming from the spray dryer can be dis charged directly to the fluidized-bed unit or additional equipment can be used for pressure disconnection or metering. In Fig. 62 a configuration is shown where the spray dryer and the fluidized bed are operating at the same pressure level. Owing to this the solids can be transferred directly to the agglomeration step.
465
Granulation Equipment r_ _ _
�l- liquid feed
exhaust gas
---l=r=;:
fines
spray } system rotary valve discharge of final product Fig. 62. Spray dryer two-step processing.
As explained in Section 2. 1 .3 different arrangements of ventilators and throtlle flaps effect different processing gas pressure profiles in the plant. In the sketch combinations of two pressure ventilators (one for spray dryer and one for fluidized bed) and one suction ventilator for both process units was selected to balance the operating pressure inside the two process chambers and to control the individual gas flows. The offgas from both is de-dusted using a cyclone. The separated fines can be recycled to the spray dryer or to the inlet of the fluidized-bed agglomeration. In the fluidized bed, for instance, a binder liquid can be sprayed to create particle growth by coalescence. Other typical applications of such setup are coating or instantization processes in food industry. There are many more different configurations in industrial use. In particular, the process gas cleaning and dust or fines recycling has to be designed specifically for each application, taking the product properties and the field of industry into account. Spray drying equipment with integrated filters were developed to keep all fines and dust inside the drying chamber. 2.2.5. Liquid handling and atomization
In general spray drying equipments require an atomizer to transfer the liquid raw material into droplets. There are a lot of technical solutions available on the market. Nozzle atomization is an example of a frequently used atomizing tech nology. The nozzle principles and types explained in Section 2.1 .7 can also be used in spray dryers. Such types are used mainly in fine particle formulations due to the ability to reach very small droplet sizes.
466
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liquid in
1
7 -r-----' wheel / disc '--
-
-
openings or nozzles
Fig. 63. Principle of rotary atomizer.
Another atomizing principle is the rotary wheel or disc type. Here the liquid stream is centrifugally accelerated to high velocity and is discharged to the drying chamber. In [ 1 3] a complete overview on atomization for spray drying is sum marized. In Fig. 63 a very simplified sketch of a centrifugal atomizer is shown. There are many technical versions of atomizers using centrifugal energy avail able. For instance, the wheel can be executed bushed, vaned or bored. Also pin wheels and vane less designs can be used. For more detailed information the reader is referred to [ 1 3]. 2.3. Control and instrumentation
Each type of spray drying, granulation or coating equipment based on convective heat and mass transfer can be characterized by a certain temperature profile and related processing gas flow. The difference between gas inlet and gas outlet temperature depends on the actual water (or the current solvent) evaporation capacity and the heat losses of the plant. To observe and control granulation and coating plants different measurements can be used. That means the main proc ess streams and their parameters must be characterized. Some of the main parameters are summarized below: Stream Basic parameters Additional parameter Relative humidity inlet Flow rate Processing gas Inlet temperature Relative humidity outlet
467
Granulation Equipment
Outlet temperature Flow rate Feed pressure Dry matter concentration
Temperature Viscosity Density Chemical properties Solid feed from external Flow rate (continuous process) Particle density Particle porosity Mass (batch process) sources Particle size distribution Chemical properties Bulk density Moisture content Flow rate (continuous process) Particle density Solid discharge Particle porosity Mass (batch process) Particle size Chemical properties distribution Bulk density Moisture content
Spray liquid
In addition to the parameters of the main process streams, the technical pa rameters and conditions have to be considered. In particular, the atomization has an important influence on process stability and product properties. This means that the spray system of a fluidized-bed plant as weil as the atomizing section of a spray dryer requires special attention. Constant and reproducible processes can only be carried out if the liquid raw material feed is of constant quality. On the basis of this the processing gas stream and the inlet and outlet gas temperatures have to be controlled or at least observed as shown in Fig. 64. On industrial scale equipment, control systems of spray drying, granulation or coating plants become more and more complex due to the need for automated operation characterized by minimum or no manual activities, automatic detection of malfunctions, self-regulating concepts and the ability to react on, for instance, fluctuation in feed stream capacity and quality. Owing to this, different control concepts were developed. It is impossible to list and explain all these concepts in a general form. Nevertheless, some basic principles are explained for the example of fluidized bed granulation or coating. In the developing phase of control system the basic functionalities must be determined and fixed. For instance, the relationship be tween spray rate and parameters of processing gas must be taken into account. In Fig. 65, two simplified examples of concepts to adjust spray capacity, process ing gas and temperature profile are shown. It is assumed that the fluidized-bed unit is operating at a certain fixed processing (fluidization) gas flow, meaning that the fluidization velocity is independent of spray liquid feed and other parameters like particle size distribution. This is valid when the process reacts slowly to capacity fluctuations and no major changes in particle size distribution occur.
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---I I I I
flow control
flow I------{ Fe control
dryer granulator coater
spray liquid pump
TI temperature indication
temperatur control heater
processing gas Fig. 64. Typical processing gas and liquid feed streams instrumentation.
flow
TC temperature control
spray liquid
spray liquid
temperature TC contro!
processing gas
processing gas
Fig. 65. Basic control principles.
On the left in Fig. 65, a principle is sketched where the fluidized bed runs at a controlled spray rate. This can be a constant or stepwise changing flow. In con tinuous operation the target is to run a certain time-independent capacity. Changes are necessary in case of starting and shut-down procedures, turn-down operation and if upstream or downstream malfunctions occur. To guarantee a constant temperature level inside the processing chamber the processing gas inlet temperature is adjusted. In the figure the flow of heating medium to the heater is controlled in dependency to the processing chamber temperature. A constant flow of spray liquid is advantageous due to the very often flow rate
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469
depending spray systems. For instance, changes in liquid flow will always effect changes in droplet size distribution of hydraulic (pressure) spray nozzles. These differences have influence, for instance, on binding behaviour in agglomeration or on spreading in case of spray granulation or coating processes and so the prod uct properties. The disadvantage of such a control concept is the larger, more slowly reacting heating system. Owing to the heat capacity of heater, piping and process unit the system reacts with a certain delay. Especially in continuous plants that principle can be used because of the normally steady-state like op eration where only small fluctuations will happen. A second option is shown right in Fig. 65. Here the liquid feed is adjusted depending on the actual temperature inside the processing chamber. As men tioned before constant and reproducible atomization must be ensured and needs additional efforts. The advantage is the possibility to establish faster control due to lower heat capacity of the total spray system. Such systems are often used in batch-wise operating plants where the processing unit must be heated up and cooled down frequently due to different processing sequences or due to product changeover. Additional technical parameters as weil as utilities can have importance and influence on the process. As an example the rotation speed of an atomizer wheel of a spray dryer determines the drop size distribution and due to the drying principle also the product particle size.
3. HIGH SHEAR G RANULATORS
This section includes information about high shear granulation with focus on batch equipment as weil as single pot processing. Not all operation principles and design versions can be discussed and explained here. 3.1 . General design aspects
As explained in Section 1 there are a huge number of technical executions available for high shear granulation. In the following part, top and bottom-driven granulators will be described for the batch processing option. In Fig. 66, a sketch of a bottom-driven high shear granulator is shown. The basic element is the mixing bowl, also calied the working vessel. Into this vessel the one or more solid raw materials are fed by gravity. For instance, the lid of the vessel can be flipped up in case of small sized granulators or swivelled to the side on bigger production scale equipment. The rotor is used to move the product and specially designed versions, especially the Z-rotor (Powrex/Glatt) can create optimized product motion (Fig. 67). Together with the geometrical shape of the
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filter cleaning system
H---- cartridge filter system (optional)
it'�m����
____ _ _
Iid
,;-=-.-----":---- spray nozzle double jacket for thermal treatment
discharge Fig. 66. Schematic sketch of a bottom-driven high shear granulator (Glatt/Germany).
Fig. 67. Technical features of high shear granulators - patented Z-rotor and chopper (Glatt/Germany).
vessel (vertical or conical ) the right design of the rotor can achieve uniform product circulation inside the vessel. Integrated choppers are frequently used tools for process optimization. They homogenize the size distribution by breaking up lumps in the wet mass and also support the liquid distribution. In most of the applications liquids have to be added for particle size enlargement. This addition can be done by means of spray nozzles. As known from fluidized-bed processing and spray drying there are different spray patterns available. In high shear granulation full or hollow cone sprays can be applied as weil as special executions like fan-shaped jets [14].
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Fig. 68. P i l ot and lab-scale high shear granulators (Glatt/Germany). -
Discharge of the product from the working vessel is often done by a side discharge port where a wet sieve can be installed downstream for further homo genization. Integrated drying inside the granulator is also a processing option. The drying can be realized, for instance, by heated walls (e.g. double jacketed design of vessel and lid), gas stripping or vacuum. The evaporated moisture leaves the granulator by a venting system. The outlet gas can be de-dusted by means of an optional cartridge filter system to minimize downstream contamination. Mainly in the food and pharmaceutical industries automatie cleaning systems are required. To clean working vessels and product discharge in place cleaning nozzles can be installed as a technical option. In Fig. 68, two examples of small scale high shear granulators are shown. These kinds of units can be used in product and process development or op timization by changing processing options as weil as technical executions like size and shape of working vessel. As mentioned in chapter 1 , top-driven granulators are also available [1 5]. In Fig. 69 a schematic sketch of such a system is shown. The picture includes possible processing options and illustrates a typical setup for a pharmaceutical application. It can be seen that all mechanical sealing of mixer and chopper are located in the lid of the working vessel and by means of this principle, product contamination can be minimized. Particularly in single pot processing where drying is also carried out inside the working vessel this apparatus ofters a lot of options. There are specially devel oped gas inlets integrated into the bottom section of the working vessel to feed a wide range of gas streams to the process. The outlet gas can be cleaned directly on the working vessel by means of a filter system (e.g. equipped with metal cartridge elements for CIP-cleaning). Solid raw material is sucked in from drums by vacuum. A special discharge port is located at a low position in the bottom
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vacuum pump
module
dry liquid
Fig. 69. Schematic sketch of a top-driven high shear granulator (GlattjGermany) [ 1 5] .
section of the working vessel to discharge the final product. The rotor supports the discharge process. In Fig. 70, a new special optimized design of a high shear granulator in phar maceutical execution is shown. Here the granulator is designed for through-the wall installation. That means all technical equipment is located and mounted behind the wall in a technical area. During process working the vessel is lifted up to close the process room. The process unit can be charged without opening by vacuum. On the left in Fig. 70 the high shear granulator is shown with lowered working vessel. In that position the agitator blades and the chopper can be inspected easily. On the right in Fig. 70 the top-drive-granulator is shown with maintenance hood opened. 3.2. Processing options
High shear granulators are very often used together with FB-systems for drying or for additional processing steps like coating. Also these types of granulators are installed to feed downstream processing units. Some examples are given after wards. In Fig. 71 a typical setup of a combination of batch high shear granulator and batch fluidized-bed dryer is shown. In such cases an additional wet milling step can be used to homogenize the product coming from the granulator. As an alternative the granulated product can be discharged to drums or con tainers for further processing. Homogeneous blends of different solid raw ma terials in an agglomerated product form can also be achieved using high shear granulators. For instance, these pre-products can be further treated in low pres sure extruders and finally pelletized in batch processing as sketched in Fig. 72.
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Granulation Equipment
Fig. 70. Top-drive granulator designed for through-the-wall installation for pharmacH,ticai application (Glatt/Germany).
fluid bed dryer
Fig. 7 1 . Installation of high shear granulator with downstream wet mill and fluid-bed dryer (or alternatively container).
After pelletization the product is frequently charged to fluidized-bed process units for drying and coating if needed. Various handling and storage principles are installed to transfer materials fram one pracess unit to the other. In simple cases gravity can be used and a vertical layout concept must be selected. Mainly in batch pracessing in food and pharmaceutical industry containers are very
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vertical granulator
material container for fluidized bed drying
Fig. 72. Principles of pellet manufacture.
Fig. 73. Charging of a production scale high shear granulator VG 600 (Glatt/Germany).
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popular. As an example Fig. 73 shows the charging procedure of a batch high shear granulator by means of a container handled by a post hoist. Binding Iiquids are metered by standard dosing systems as previously ex plained in Section 2. 1 .7. Also process gas conditioning uses comparable prin ciples to those used in fluidized-bed processing.
4. SUMMARY
This chapter provides a short introduction into drying, granulation and coating equipment. Owing to the very wide field of applications and processes a huge number of equipment types have been developed. Because of this some exam pies of equipment basics were explained here in more detail and other types were mentioned only as an overview. In the developing phase of processes and also of products equipment suppliers should be contacted to select the right type and size of equipment and to optimize processes. Additional standard literature references contain information about other processing principles and types of equipments (e.g. [2-5,1 0]). REFERENCES [1] W. Pietsch, Systematische Entwicklung von Verfahren zur Kornvergrößerung durch Agglomerieren, Chem. Ing. Tech., Wiley-VCH, Weinheim, (74), (2002) S . 1 5 1 7-S. 1 530. [2] R.H. Perry (Ed.), Chemical Engineers Handbook7th edition, McGraw-Hill, New York, 1 997. [3] W. Pietsch, Agglomeration Processes: Phenomena, Technologies, Equipment, Wiley-VCH , Weinheim, 2002. [4] J. Litster, The Science and Engineering of Granulation Processes, Kluwer Academic, Dordrecht, 2004. [5] G. Heinze, Handbuch der Agglomerationstechnik, Wiley-VCH, Weinheim, 2000. [6] Glatt: I nnovative Technologies for Granules and Pellets.- Glatt Ingenieurtechnik GmbH, WeimarjGermany (company brochure), 2005. [7] Glatt: Drum Coating Systems - GC Master.- Glatt Maschinen&Apparatebau AG, PrattelnjSwitzerland (company brochure), 2002. [8] Glatt: Extruder, Spheronizer, Pelletizer.- Glatt GmbH Process Technology, Binzenj Germany (company brochure), 2006. [9] Andritz: High-Tech Perforation.- Andritz Fiedler GmbH & Co. KG , Regensburgj Germany, 2004. [ 1 0] Hein&Lehmann: CONIDUR Fine Hole Sheets.- H E I N ,LEHMANN Trenn- u nd Fördertechnik GmbH , KrefeldjGermany, 1 995. [1 1 ] Andritz: ConiPerf - Das außergewöhnliche Feinlochblech.- Andritz Fiedler GmbH & Co. KG , RegensburgjGermany, 2004. [ 1 2] D. Reay, Fluid bed drying, i n : G. Geldart, (Ed.), Gas Fluidization Technology, Wiley, Chichester, 1 986. [ 1 3] K. Masters, Spray Drying in Practice.- SprayDryConsult I nternational ApS, Denmark 2002.
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[ 1 4] Glatt: Vertical Granulators.- Glatt Systemtechnik GmbH , DresdenjGermany (com pany brochure), 2005. [ 1 5] Glatt: Top Drive Granulator.- Glatt Systemtechnik GmbH, DresdenjGermany (com pany brochure), 2005. [1 6] U. Weiß, Atomizing technologies of SCHLICK - For fluid bed processing. TTC Work shop, Weimar, March 2000.
CHAPTER 1 0 Onl ine M onitoring Satoru Watano *
Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531, Japan Contents 1 . Introduction 2. Online monitoring of process variables 2. 1 . Measurement of torque and power consumption 2.2. Moisture content 2.2. 1 . Sensors available for monitoring moisture content 2.2.2. Online moisture measurement by infrared sensor 2.3. Pressure 2.4. I mage processing 2.4. 1 . Continuous monitoring of granule growth by image processing 2.4.2. Feedback control of granulation process by image processing 3. Conclusions References
478 478 479 480 481 481 485 489 490 493 498 498
1 . I NTRODUCTION
Control and optimization of granulation processes is a basie requirement, espe cially for industrial scale production. The productivity depends largely on the con trol of the processing time or the amount of binding liquid. Even if the operational variables are precisely controlled, the granule growth is sometimes very sensitive to the change in feed material properties and external conditions (humidity, temperature, etc.). This necessitates precise measurement of process variables, monitoring of granule growth and detection of the optimal operational end-point. So far, extensive investigations have been carried out regarding different devices for monitoring and controlling granule growth during granulation process. 2. O N LI N E MONITORING O F PROCESS VARIABLES
In the following sections, monitoring of process variables in wet-granulation processes is described. In particular, torque and power consumption measure ments in high-shear granulation, monitoring of moisture content in fluidized-bed * Corresponding author. E-mail: [email protected]
Granulation E, '%d by A.D. Sa/man, M.J. Houns/ow and J. 1-' K. 3eville ( 2007 Elsevier SV All rig hts reserved
478
s. Watano
granulation, monitoring and contral of pressure in extrusion granulation and im age pracessing for online monitoring and contral of granule grawth in high-shear and fluidized-bed granulation pracesses are described in detail. 2. 1 . Measurement of torque and power consumption
In the field of agitation and kneading granulation, monitoring of agitation torque and power consumption has become common in order to determine the optimal operational end-point. So far, Lindberg et al. [1 ,2] measured agitation torque of the main shaft during high-shear granulation. Measurement of power consumption was described by Leuenberger [3,4], who showed records of power consumption and torque were in good agreement. Holm et al. [5] measured power consumption and temper ature changes during high-shear granulation. In most cases, the monitoring of torque or power consumption became useful tools to monitor granule grawth and to determine the optimal operational end-point. Figure 1 shows typical curves of torque and power consumption during high shear granulation. The agitation torque and power consumption were in good agreement and both parameters indicated large values in the initial stage of gran ulation, followed by gentle decrease with some fluctuation. According to the pre vious study [1-5], the optimal operational end-point based on the torque and power consumption measurements should be near at constant values. From this figure, it is difficult to discern their constant values. Generally, there are many cases where the torque and power consumption curves cannot determine the optimal operational end-point. Watano et al. [6-8] proposed a method to determine the 1 .0 .---.---�--�--,----.---.---. 30
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479
Online Monitoring
operational end-point by using a frequency analysis of power consumption. By means of this technique, determination of the operational end-point and analysis of the granule growth are possible even in such cases as shown in Fig. 1 . By using a fast Fourier transformation (FFT) analysis, the frequency behaviour of power consumption data can be obtained. The specific peaks are found where frequency multiplies integrally against the rotational speed of the main blade (agitator blade). According to the previous analysis by Watano et al. [6-8], the specific peak had its origin in the collision of granules against the agitator blade, thus the granule growth influenced the intensity of the peak greatly. Figure 2 indicates intensity of the specific peak that was obtained by the FFT analysis of power consumption. Figure 3 also shows granule growth (mass me dian diameter and geometrie standard deviation) during high-shear granulation. The intensity of the specific peak was large at the initial stage of granulation, followed by a rapid decrease. After reaching the minimum value, the intensity increased again. At the initial stage of granulation, a large energy was required to distribute the binder liquid and force that the agitator blade received against granules was localized due to the broad granule size distribution. This caused remarkably large intensity of the specific peak. After achieving uniform distribution of binder, the shape of granules also be came spherical and flowability improved. This caused uniform distribution of force that the agitator bl ade received against granules, indicated by a small peak in tensity. At the minimum intensity, where granule growth was most stable, the optimum operational end-point was determined. The reason why the intensity of
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the peak increased after reaching the minimum value originated from secondary agglomeration, where granulated particles themselves adhered together. The torque and power consumption measurements roughly correspond to the granule growth and are useful for the determination of the optimal operational end-point. To get more precise information from this monitoring, the frequency analysis is a very useful tool, which determines the optimum operational end point and predicts granule growth with a high accuracy. 2.2. Moisture content
Granulation processes are mainly categorized into wet and dry processes. Wet granulation is defined as a size enlargement, which sticks powder particles using liquid binders to produce granules having desired properties, such as size, shape and density. In the wet-granulation process, the physical properties of granules are very sensitive to the degree of wetness (moisture content). Even in dry-granulation processes (compaction, direct tabletting, etc.) moisture content sometimes causes problems. Generaily, powder materials contain mois ture to some extent as water of hydration, bound water, etc., which exist on the powder surface or between powder particles as liquid bridges. Moisture on the powder surface greatly changes the powder properties such as flowability and internal friction, leading to handling problems. The liquid bridge generates ag glomeration of powders and adhesion onto the vessel wall. In both wet- and dry-granulation processes, monitoring of moisture content and its control are required to produce desired product continuously.
Online Monitonng
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2. 2. 1 . Sensors available for monitoring moisture Gontent
Table 1 Iists moisture sensors available for wet-granulation processes. In wet granulation processes there are no sensors that can measure moisture content directly. Therefore, moisture content is determined by using the correlation be tween indirect parameters (absorbance of spectrum, dielectric constant, etc.) and moisture content that has been previously measured by a direct method (drying or titration). So far, electrical, optical and radioactive ray methods have been available for wet-granulation process. Among them, optical method has been widely used in the industrial and practical applications. In the fOllowing, the optical method for continuous monitoring of moisture content during fluidized-bed granulation proc ess is described. 2. 2. 2. Online moisture measurement by infrared sensor
In general, the optical sensor utilizes the principle that physical values (concen tration, distance, etc.) are indirectly detected by using the absorbed/reflected energy of spectra when the spectra are radiated to an object. The so-called "spectra" are categorized into ultraviolet, optical and infrared (IR) rays depending on the wavelength, and each sensor uses specific wavelength, which fits char acteristics of the measuring object. Figure 4 shows I R absorption characteristics [9]. Water absorbs IR spectra markedly at the wavelengths of 1 .43, 1 .94 and 3.0 �m, due to the resonance with atomic vibration between oxygen and hydrogen in a water moleeule [9, 1 0]. Since energy of IR spectrum is absorbed remarkably at these wavelengths in proportion to moisture content, moisture content can be detected by measuring the differ ence between the irradiated and the reflected energy. Since the absorption spectrum measurement alone is easily disturbed by the object surface conditions and fluctuation in beam length, a reference method that calculates the reflected energy ratio of the absorbed spectrum (1 .94 �m) and of the bilateral unabsorbed spectrum (reference spectrum of 1 .78 and 2. 1 4 �m) has been adopted. This cancels out any disturbance, since the disturbance affects the absorbed and unabsorbed spectra equally. Details of the IR moisture sensor are illustrated in Fig. 5. The continuous light from the source is condensed by a condenser, then changed to a chopper beam by passing through a rotating sector with four optical filters composed of the different selective spectra of 1 . 94 �m for absorption, the bilateral 1 .78 and 2.14 �m for unabsorbed references and a visible spectrum for targeting. When these portions of the spectra are irradiated to the object, the absorption spectrum is absorbed in proportion to moisture content of the object, while the reference spectra are fully reflected [9, 1 0]. These spectra are transformed to electric sig nals, and the degree of absorptivity, defined as the ratio of energy absorbed to
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Table 1 . Moisture measuring methods and their principles
Electric method
Methods Electric resistance method (DC) Method applying high frequency
Method applying dielectric constant (electrostatic capacity) Method applying IR-ray
Optical method
Method applying microwave Method measuring moderationjscattering Method measuring attenuation strength Balanced relative humidity
Radioactive rays
Other method
0,
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x ,
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Principle of measurement Measure electric resistance change (direct current) due to moisture increasejdecrease Measure electric current (high frequency) change due to moisture increasejdecrease Smaller quantity of water can be detected than the DC method Measure dielectric constant change due to moisture i ncreasejdecrease Measure absorbance of I R-ray at absorption bands ( 1 .43, 1 .94 Ilm) of water near IR Measure attenuation of microwave due to water Measure moderationjscattering of neutronjy-ray due to water Measure attenuation strength of ß or y-rays due to water Calculate moisture content by relative humidity, which is balanced with circumstances
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the supplied energy of the spectrum, is calculated. Based on the degree of ab sorptivity, the absorbance X, the output from the moisture sensor, is calculated based on the following equation: (1)
484
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where V1 , V2 and V3 show the absorptivities at 1 .94, 1 .78 and 2.1 4 )lm IR spectra after temperature compensation; and ko , k1 and k2 indicate the calibration co efficients, respectively. Although IR moisture sensor is able to measure moisture content continuously without touching the object and is not influenced by powder density and packing condition, it measures the moisture content on the surface or just below the surface of the object due to the long wavelength. Normally, there exists moisture distribution inside powder material, leading to different moisture content at sur face and core. Therefore, in order to measure moisture content correctly by the IR sensor, a calibration curve between sensor output (surface moisture content detected by IR sensor) and total moisture content measured by a drying method, etc. [9] is required. Figure 6 iIIustrates a system that measures and controls moisture content by using an IR moisture sensor in a fluidized-bed granulation [9-1 1 ]. The I R detector and fluidized-bed vessel is connected with optical fibres and a heated purge air is blown at the extremity of the sensor (the place where the optical fibres are con nected at the vessel wall) to prevent powder sticking. Based on the moisture monitoring, the amount of binder liquid is controlled to maintain the desired moisture content. After feeding the pre-determined amount of binder liquid, the controller stops the pump, leading to shift to the drying process automatically. Co mpressed air
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Moisture conte nt [kg-water/kg-solid] Fig. 7. Relationship between granule mass-median diameter and moisture content.
Figure 7 indicates the relationship between granule mass-median diameter and moisture content when powder sampies composed of lactose, cornstarch and hydroxypropylcellulose (HPC) are granulated by purified water (binder). As seen in Fig. 7, the relation between granule mass-median diameter and moisture content was expressed by a linear equation, and granule growth can be divided into two stages: stage I ( O < W< O. 1 7) and stage 11 (W> O. 1 7). •
•
Stage I. Liquid bridges are partly formed and remarkable granule growth is observed in this stage. The fact that granule growth is linear indicates that the granule growth is directly proportional to the number of liquid bridges. Stage 11. The surface of the particle is saturated with binder solution. Owing to the large number of liquid bridges on the surface of the granule particles, rapid granule growth takes place. In addition, secondary granulation, in which ad equately granulated particles themselves adhere to each other, accelerates the rapid increase in granule size.
The linear relationship between granule median diameter and moisture content suggests that granule growth can be controlled by measuring and controlling the moisture content. In the Japanese pharmaceutical industry, automatie manufacturing of phar maceutical particulate drug is commonly conducted by fluidized-bed granulation with moisture control, and uniform properties are maintained [1 2]. 2.3. Pressure
An extrusion granulation is widely used in the pharmaceutical, agriculture, food, chemieal, forage and fertilizer industries. It is because the uniform granules can
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be produced continuously at low cost. It is, however, known that the properties of extruded granules are sensitive and easily influenced by the initial powder prop erties and the operating conditions. Also, the recent trend in granulation tech nology is towards an improvement of process efficiency, stability of product quality, safety manufacturing and labour saving. However, there are many trou bles such as screen breakage because of the high extrusion pressure. With such improvements and the demands for granulation, there is a great need for a re liable system for process monitoring and control of extrusion granulation. In this section, extrusion pressure was measured during extrusion granulation and the relationship between the properties of extruded granules and the extru sion pressure was investigated [1 3 , 1 4]. The extrusion feedback control system composed of a computer, PID controller, controllable powder feeder was then developed and applied to extrusion granulation [15]. The dynamic characteristics of the extrusion-granulation process were analyzed and an extrusion pressure feedback control system was developed. Figure 8 shows a schematic diagram of extrusion pressure-measurement sys tem . In the extrusion granulation, a kneaded mass was fed into the granulator from a powder feeder and then extruded through an extrusion granulator. Inside the granulator, the kneaded mass is moved forward by the screw rotation and is then extruded through the screen. Under compression forces and tensile-stress plastic deformation of the mass occurs. Onto the hemispherical dome-type screen, a hole (5 mm) was made and a semiconductor pressure sensor was placed so as to measure pressure as the wet mass passed through the screen.
Kneaded mass
Extrusion paddle Motor Pre ssure sensor
Fig.
8. Schematic diagram of extrusion granulation with pressure-monitoring system.
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The measured pressure was amplified and converted into a digital signal, which was processed by a personal computer. In the personal computer, parameter setting, data input/output, individual calculation and manipulated variable to pow der feeder were controlled. After the extrusion granulation, the obtained pellets were dried in a fluidized-bed dryer. The heated air temperature during drying was kept at 353 K. The obtained granules were evaluated by their strength. The strength of the granules was analyzed by a strength measurement system; a punching Iid moved down from the top at a speed of 1 cm min - 1 and pressed a granulated particie on a flat stage. The applied force and pressed displacement were measured continuously. The strength of the granulated particie was then measured by the force when the granulated particie was crushed [16]. In this experiment, starting materials consisted of lactose, cornstarch and crystalline cellulose. Dry HPC was adopted as a binder, which was mixed into the starting materials before granulation. Purified water was used as a binder solution. Figure 9 investigates the relationship between granule strength and extrusion pressure. Seen from the figure, granule strength increases Iinearly with an in crease in the extrusion pressure. This implies that the extrusion pressure, Le. the resistance, which the wet, kneaded mass experiences when passing through the pores of the screen, determines the granule physical strength. The Iinearity also suggests the possibility of practical control of granule strength by means of the extrusion pressure. To control the extrusion pressure in the extrusion-granulation process, its dy namic characteristics should be fully understood beforehand . The step response of the extrusion-granulation process was thus analyzed by using a semiconductor
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pressure sensor. Stepwise input difference was generated by a personal com puter then its output response was investigated (Fig. 1 0). From this trial, the dynamic characteristics of this process was assumed to be described by a sim plified transfer function G(s) composed of a first-order lag element including dead time as Ke- Ls (2) G(s) = 1 + Ts where K, L and T are the gain, dead time and time constant, respectively. By using a curve fitting, each parameters in the above equation can be determined as K = 1 , L = 1 9.0 s and T 1 0.7 s. The inverse Laplace transform gives the numerical output response against the unit step input. In the fOllowing, a feedback control of the extrusion pressure is attempted by using the transfer function G(s). The PIO controller has a transfer function composed of P(proportional), I(in tegral) and 0 (derivation) elements as =
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Figure 1 1 shows the result of PID feedback control of extrusion pressure when the moisture content of the kneaded mass suddenly changed from 22 to 25% as external disturbance. To compare this control performance with no-control ex periments, experimental results without control are also indicated in the same figure. Here, the desired value was set at 0.3 M Pa and the sampling interval was 20 Hz(0.05 s). Without control, the extrusion pressure suddenly decreased when the moisture content changed from 22 to 25%. However, in the PIO control, the extrusion pressure almost maintained the desired value after changing the moisture. The granule strength under the control had almost the same property as the initial granule despite the moisture change. By contrast, without the control, the prop erty changed awfully due to the change in moisture content of the kneaded mass. This result suggested that the control of extrusion pressure could conduct stable operation regardless of the changes in the powder properties. 2.4. Image processing
In the previous sections, several monitoring techniques such as torque, power consumption, moisture content and pressure have been described. In most cases, these techniques are useful in detecting granule growth during granula tion. However, these are the indirect methods, which measure parameters and correlate with granule growth. In so me cases, reproducibility of the measurement is poor due to the changes in feed material properties or external disturbances (humidity, temperature, etc.), since these are the indirect methods and they cannot account for these changes.
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Contrary to such indirect methods, image processing of granules during gran ulation process is considered to be the ultimate method, since it provides granule properties directly. In this section, direct monitoring and control of granule growth during wet-granulation process is described. So far, Tanino et al. [ 1 8] have de veloped a granule growth control system in fluidized-bed granulation by meas uring the percentage of granule fragments on a trapping tape located on the side wall of the column by using an image-processing system, and then correlated with granule growth. They have succeeded in the automatic production of di gestive medicine. Watano et al. [1 9,20] have developed an advanced image-processing system. They have used it for the measurement and control of fluidized beds [ 1 9,20] and high-shear granulation processes [21-23]. In the following sections, application of image processing to the wet-granulation process is introduced. 2. 4. 1 . Continuous monitoring of granule growth by image processing
Figure 1 2 illustrates a schematic diagram of the developed particle image probe, which looks downs from above [1 9,20]. Its main body is a cylinder made of stainless steel, comprising a CCO camera, optical fibers for lighting, telephoto lens and a purge air unit. A stroboscope with a high-energy Xe lamp gives flashing light at 1 J.ls intervals; the optical fibers transmit the light to the image probe extremity. At the extremity, a slit is equipped so as to light up the plane at an angle with respect to the centre axis of the CCO camera. Since the CCO camera focuses the plane, only granules on the lit-up plane can be detected and their sizes can be measured correctly. By this success, granules out of focus, or granules overlapped behind the lit-up granules reflect a considerably smaller quantity of light, and therefore, can be removed in binarization. The binary images thus obtained here have no or very few overlapped granules. This Wall of vessel
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Fig. 1 2. Schematic diagram of particle image probe.
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sharply reduces the labor needed to segregate the overlapped granules. If the overlapped granules still exist, methods such as a circle pattern matching or an eight-neighbour erosion method can segregate the overlapped granules completely [ 1 9]. As shown in Figs. 13 and 14, the probe is attached to the sidewall of the upper tapered vessel. The heated purge air is blown to prevent powder adhesion. I mage processing, such as labelling, binarization, segregation of overlapped particles and computation of particle properties are done in an image processor using parallel processing. The image data are statistically treated in a host computer to yield granule-size distribution, median diameter, shape factors and yield. This image-processing system can process 4096 granules per second. The
Fig. 1 3. I nstallation of particle image scope onto fluidized bed.
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Fig. 14. Automated fluidized-bed granulation system with image-processing system . 1 , Agitation fluidized bed; 2, bag filter; 3, spray nozzle; 4, blower; 5, heater; 6, motor; 7, agitator blade; 8, slit plate; 9, image probe; 1 0, image-processing system; 1 1 , host com puter; 1 2 , controller; 1 3, pump; 1 4, binder.
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photographing speed was 0.5 s and output interval (control output) of the image analysis was set at 1 0 s. During each output interval, at least 500 granule pictures were taken and analyzed. It was confirmed that the measurement of granule properties could be carried out reliably if at least 200 granules were analyzed in each interval. Figure 15 shows the plots of granule mass-median diameter as a function of operational moisture content. In this figure, closed circles indicate Feret diameter calculated by the image processing system and open circles indicate granule mass-median diameter obtained by a conventional sieve analysis. Since granule size distribution obtained by the image-processing method is a number-based distribution, it cannot be compared with data by conventional sieve analysis since that is a mass-based distribution. Fortunately, since granules obtained by fluidized-bed granulation have a sharp granule-size distribution and also obey a log-normal distribution, the obtained number-based size distribution can be transformed into mass-based distribution using a following Hatch's well-known equation [24]: In(MMD) = In(NM D) + 3(1n 2 g )
(5)
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where MMD, NMD and O"g show mass-median diameter, number-median diam eter and geometrie standard deviation, respectively. From Fig. 1 5, a close agreement is obtained between the results of image processing and sieve analysis. I mage processing can detect granule growth in a low-moisture-content range, while the sieving method cannot, because the soft agglomerates are broken into fine powders during sieving. It can also detect rapid granule growth in the high-moisture-content range. Figure 1 6 shows pictures of granules taken by the image probe during gran ulation. Pictures A-H agree with the same symbol marked in Fig. 1 5. Owing to the 500 .----.-l---.-l---,l----�1--'1,---� E 400
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slit lighting, each picture has almost no overlapped granules in the depth direction and shows a very clear image of well-dispersed granules from initial to final stage of granulation. Figure 1 7 represents shape factor plots as a function of operational moisture content. In this figure, circles indicate circularity and squares the granule aspect ratio; closed circles and squares indicate the continuous measurement by the image processing system; open circles and squares show manual analysis of granule microphotographs obtained after drying. Circularity and aspect ratio both increase with the moisture content. This shows that granules were made spher ical in the progress of granulation. It is also found that the circularity expresses shape factor better than the aspect ratio. 2. 4. 2. Feedback control o f granulation process by image processing
Granulation in a high-shear mixer is widely used in many fields in order to pro duce spherical and well-compacted granules. In addition to the granule proper ties, this type of granulation has significant process advantages that the operation
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can be completed in relatively short time and the equipment itself is very simple in construction. It is, however, found that granulation in a high-shear mixer is very sensitive to even minor changes in moisture content, amount of binder and the operating conditions. Consequently, there is a great need for reliable instrumental methods for process monitoring and determination of the operational end-point. In the previous section, monitoring of high-shear granulation process by means of torque and power consumption measurement was described. Although many different studies on the measurement of high-shear granulation have also been conducted, all of them were based on the indirect methods, thus they were easily affected by the changes in powder properties and the operating conditions. It is definitely clear that no reliable tools have been developed so far to monitor the granule growth directly, much less to self-control the granulation process. In the following section, continuous monitoring and self-control of the granule growth in high-shear granulation by means of image processing and a fuzzy control system is described. Figure 1 8 shows a schematic diagram of the experimental apparatus used. A high-shear mixer was used for wet granulation [21 -23]. The bottom of the vessel was equipped with an agitator bl ade (main impeller) rotating horizontally, which promoted agglomeration and compaction. A chopper bl ade was also provided on the sidewall so as to break up wetted mass into small granules. The image probe was installed on the sidewall of the vessel (Fig. 1 9(A)). At this positioning, the probe could take the clearest and most distributed image of granules [21 ] . It is also possible to install the image probe via an observation glass window at the top lid of the vessel (Fig. 1 9(8)).
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Com puter Particle image probe
Image processi ng system
Computer tor measurement
com puter for con trol
Fig. 1 8. High-shear granulation system with image processing system.
(A) Installation at the side wall
(8) Installation from the top lid
Fig. 1 9. Installation of image probe in high-shear mixer.
From the previous experiments, granule-size measurement by the developed image-processing system is found to have a lag element, and dynamic character istics of granule grawth are so complex that it is difficult to construct a model-based system for granule growth. However, if the process characteristics are understood fram past experience, application of fuzzy logic to the contral system is very effective [25]. Therefore, removal of excessive granule grawth and impravement of contral stability and response are attempted by using linguistic algorithms employ ing if-then rules, in which granule size, its changing rate and pracess lag element are taken into consideration [25].
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Figure 20 shows a block diagram of granule-size control system based on a fuzzy logic [25]. Deviation D(t), the difference between desired (Dd) and meas ured values (Dm (t» of granule size, and its changing rate AD(t) were adopted 8S input variables (no smoothing method was applied to the input variables); they were defined as follows (6) AD(t) = Dm(t) - Dm(t - 1 )
(7)
The result of fuzzy reasoning V(t) was used to control the output power of liquid feed pump. Here, K1 and K2 represent gains of the input variables. For the membership functions, a typical triangular representation was used. The following five fuzzy variables were used for the fuzzy reasoning: ZR (zero), PS (positive smalI), PM (positive medium) and PL (positive large). I n the fuzzy controller, fuzzy reasoning with a minimum-maximum composition method using triangular-shaped membership functions and if-then rules was conducted [26,27]. The resultant fuzzy reasoning was defuzzified by using a centre of grav ity method [26,27]. Figure 21 illustrates temporal change in granule size and pump output, re spectively as a result of fuzzy reasoning. The excessive granule growth was fully removed and excellent control stability was achieved throughout the granulation; at the initial stage of granulation, granule size was small enough that the pump fed maximum output power. At 600 s, decrease in the pump output was observed to reduce granule growth rate. When granule size was closely approaching the desired value (750 s), output power of the pump decreased significantly and finally stopped at 900 s. Owing to the previous suppress of pump output, granule growth was very gentle when the measured diameter was near the desired value. Consequently, no excess granule growth was observed. Figure 22 illustrates the accuracy and reproducibility of the contro\. Deviation of the data represented the maximum and minimum values of the producl's size obtained by several batches of granulation under the same desired value. Seen from the figure, the producl's size was weil controlled and accuracy of the control
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was within ± 5%. However, it showed the tendency that the larger desired value resulted in a slightly larger product's diameter. The small and light-compacted granules became smaller because small fragments (most of the cases were cornstarch particles) were peeled off from the surface during the drying process, while the large granules became large due to the adhesion of small particles by the leached water during the drying. To increase in the accuracy of control, granule growth mechanism during drying process should also be considered. As a result of the fuzzy control, it was found that high-shear granulation could be weil
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controlled without any excessive granule growth by means of the developed fuzzy control system. 3. CONC LUSIONS
Monitoring of process variables in wet-granulation processes is described in this chapter. Monitoring of process variables and control of granulation process are very important in maintaining product quality. It is expected that a more reliable and advanced system for precise monitoring and control of granulation processes will be developed in the near future. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [ 1 0] [1 1 ] [1 2] [ 1 3] [ 1 4] [ 1 5] [1 6] [ 1 7] [ 1 8] [ 1 9] [20] [21 ] [22] [23] [24] [25] [26] [27]
N.O. Lindberg, Pharm. Acta Helv. 1 4 ( 1 977) 1 97-204. N.O. Lindberg, L. Leander, B. Reenstierna, Drug. Dev. I nd. Pharm. 8 (1 982) 775-782. H. Leuenberger, Pharm. Acta Helv. 57 ( 1 982) 72-82. H. Leuenberger, Pharm. Acta Helv. 29 ( 1 983) 274-280. P. Holm, T. Schaefer, H.G. Kristensen, Power Technol 43 ( 1 985) 21 3-223. S. Watano, K. Terashita, K. Miyanami, Chem. Pharm. Bull. 40 ( 1 992) 269-271 . S. Watano, K. Terashita, K. Miyanami, Adv. Powder Technol. 6 (1 995) 91-1 02. K. Terashita, S. Watano, K. Miyanami, Chem. Pharm. Bull. 38 ( 1 990) 3 1 20-3 1 23. S. Watano, H . Takashima, Y. Sato, T. Yasutomo, K. Miyanami, Chem. Pharm. Bull. 44 ( 1 996) 1 267-1 269. S. Watano, H. Takashima, Y. Sato, K. Miyanami, T. Yasutomo, Adv. Powder Technol. 7 ( 1 996) 279-289. S. Watano, T. Fukushima, K. Miyanami, T. Murakami, T. Sato, Chem. Pharm. Bull. 42 ( 1 994) 1 302-1 307. S. Watano, A. Yamamoto, K. Miyanami, Chem. Pharm. Bull. 42 ( 1 994) 1 33-1 37. S. Watano, J. Furukawa, K. Miyanami, Y. Osako, Chem. Pharm. Bull. 49 (200 1 ) 64-68. S. Watano, T. Okamoto, M. Tsuhari, I . Koizumi, Y. Osako, Chem. Pharm. Bull. 50 (2002) 34 1-345. S. Yoshimura, S. Watano, Y. Osako, Proceedings of the 2nd Asian Particle Technology Symposium, NO. 1 , Penang, Malaysia, 2003, pp. 561 -566. S. Watano, E. Shimoda, Y. Osako, Chem. Pharm. Bull. 50 (2002) 26-30. J.G. Ziegler, N.B. Nichols, Trans. ASM E 64 ( 1 942) 759-768. T. Tanino, Y. Yawata, S. Otani, H. I noue, K. Sato, T. Takeda, T. Mizuta, Proceedings of the Sixth International Symposium on Agglomeration, Nagoya, Japan, 1 993, p. 548. S. Watano, K. Miyanami, Powder Technol 83 ( 1 995) 55-60. S. Watano, Y. Sato, K. Miyanami, Chem. Pharm. Bull. 44 ( 1 996) 1 556-1 560. S. Watano, T. Numa, K. Miyanami, Y. Osako, Chem. Pharm. Bull. 48 (2000) 1 1 54-1 1 59. S. Watano, T. Numa, K. Miyanami, Y. Osako, Powder Technol. 1 1 5 (200 1 ) 1 24-1 30 S. Watano, T. Numa , I. Koizumi, Y. Osako, Eur. J. Pharm. Biopharm. 52 (200 1 ) 337-345. H. Masuda, K. Higashitani, H . Yoshida (eds), Powder Technology Handbook, 3rd edition, CRC Press, FL, 2006. L.A. Zadeh, I nform. Control 8 ( 1 965) 338-353. M. Sugeno, Inform. Sci. 36 ( 1 985) 59-83. E.H. Mamdani , I nt. J. Man-Machine Stud. 8 ( 1 976) 669-678.
CHAPTER 1 1 P rocess Systems Eng i neering A p p l ied to G ranu l ation I . T. Cameron * and F .Y. Wa ng
Partic/e and Systems Design Centre, Schoo/ of Engineering, The University of Queens/and 4072, Australia Contents 1 . Key issues 1 . 1 . Why a systems perspective in granulation? 1 . 1 . 1 . Viewing reality through a systems framework 1 . 1 .2. The life cycle concept and its impact 1 . 1 .3. The importance of a process systems approach 1 .2. Multi-scale, multi-task perspectives in granulation technologies 2. Process systems engineering: selected applications 2. 1 . Steady state and dynamics of granulation systems 2 . 1 . 1 . The role of steady-state analysis 2 . 1 .2. The role of dynamic analysis 2. 1 .3. The role o f mathematical modelling 2. 1 .4. Development o f linear models and multiple model approach 2 . 1 .5. The role o f measurement 2.2. Operational aspects of granulation systems 2.2. 1 . Process optimization 2.2.2. Statement of steady state and dynamic optimization problems 2.2.3. Control relevant models 2.2.4. Objective functions for system optimization and open-Ioop optimal control 2.2.5. Dynamic optimization algorithm 2.2.6. Selected simulation results and discussion 2.3. Control design, analysis and performance 2.3. 1 . Black-box controller design 2.3.2. Model-based controller design 2.3.3. Multi-level control of granulation processes under uncertainty 2.4. Diagnostic and guidance systems for granulation process operations 3. Future challenges in process systems approaches to g ranulation References
*Corresponding author. E-mail: [email protected]
. 2007 Elsevier
Granulation
Edited by A.D. Salman, M.J. Hounslow and J. P.K. Seville S.v. .
All rights reserved
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1 . KEY ISSUES
In this chapter, we outline key issues relevant to a process systems engineering (PSE) perspective on granulation. These issues are set within the context of the product and process life cycle, which provides an important framework to high light key PSE areas. The current application of process systems approaches to product and process engineering can be vast. They encompass key synthesis, analysis and design methodologies and the application of advanced computa tional tools across the Iife cycle phases. Hence, in this chapter we provide an overview of the importance of PSE approaches, highlight their past and potential impacts, and then select a few areas for detailed comment in relation to gran ulation systems. In particular, we show a number of control, optimization and process diagnostic applications to granulation systems as prime examples of PSE in action. 1 . 1 . Why a systems perspective i n g ranulation?
Granulation is both product and process focused. The various chapters in this handbook bear ample testimony to the importance of granulated products in modern society as weil as the processes that seek to make those products efficiently and effectively. It is vital that we understand the "systems perspective" on product and process. A useful process systems definition can be an assembly of equipment, human and software components that work to gether in an organized manner to achieve a desired goal. This definition highlights key aspects of a systems view, namely an appreci ation of the complex nature of designed systems that must integrate equipment with software systems and human interaction in order to achieve a desired goal or a set of goals. It highlights, too, the necessity of synthesis and analysis within PSE and the ever-growing importance of understanding software systems and human factors in design and operations. In this respect, PSE shares much in common with the field of requirements engineering [1], which addresses similar issues mainly in the area of software development. In the preface to his 1 96 1 seminal book Systems Engineering for the Process Industries Theodore Williams of Monsanto [2] wrote about the importance of process industry examples to the systems field that . . . should show the advantages of systems engineering over conventional methods. It should detail the differences in procedures, the necessary new information, the required tools, as weil as actual increases in return on in vestment from the plant due to increased throughput, higher overall product quality, decreased plant investment, or a combination of these.
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Process Systems Engineering Applied to Granulation
Written almost a half a century ago, the importance of an i ntegrated , multi faceted approach to modern granulation systems is just as relevant. It is easy to show that such views take on even more importance in the 2 1 st century because of the increased global competition, an emphasis on time-to-market, increased concerns with product and process safety and higher quality demands of a so phisticated and differentiated market. The thrust of Williams' arguments was that systems engineering brings a multi-scale, multi-disciplinary approach to solving industrial problems through a fundamental reliance on mathematics and advanced computational techniques. Has much changed in 50 years? In our depth of un derstanding, clearly "yes"! In the commitment to systems concepts, it is evident that we have refined and extended the basic ideas, tools and approaches. The impacts of the application of PSE to any process can yield significant rewards - in terms of economics, product and process design, product quality, process safety, improved control and diagnostics. A detailed understanding of the physics and chemistry of granulation is absolutely essential but is easy to get isolated in these areas and not see the bigger "systems" picture of the whole system. This is the challenge of PSE to appreciate the roles of all the individual components and to design, operate and optimize these into a coherent system for a desired purpose. To do this, Sections 1 . 1 . 1 and 1 . 1 .2 put the systems approach firmly within the life cycle of product and process, while Section 1 . 1 .3 shows the importance and impact of these approaches. 1.1.1. Viewing reality through a systems framework
One of the powerful techniques of systems engineering is the methodology of conceptualizing reality in a form amenable to systematic synthesis and anal ysis. The "systems" approach views a process in terms of concepts such as states, inputs, outputs and disturbances. This view is seen in Fig. 1 , which cap tures the principal aspects related to systems approach es [3]. States are related to mass and energy hold-ups in the system under consideration. Inputs are the manipulations used to "steer" the system in some manner. Outputs are those disturbances
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variables often measured for quality or control purposes, that is, the desired values. Disturbances are regarded as outside inputs, which are uncontrolled or essentially unknown. In some cases they can be measured and techniques exist to anticipate system changes to these disturbances. The importance of this formalism is seen in the various problems that can be tackled using this generic view of the system. These include: •
•
•
•
•
•
•
Steady-state analysis and simulation. Given the model of the system S, and an operating point Xss compute the outputs y, knowing the inputs u, the distur bances d and the system parameters p. Dynamic analysis and simulation. Given a model structure for S, predict the outputs y knowing the time-varying behaviour of the inputs u, disturbances d and the parameters p. The design problem. Estimate the set of parameters p, for a given fixed struc ture of S, desired outputs y and specified inputs u. The optimization problem. Estimate the optimum values of the states x for a given objective function FObj involving states, parameters and inputs. Regulatory control or state-driving applications. Estimate the input u for a given S, y, d and p. This is a standard control issue. System identification. Find a structure for the system S with its parameters p using inputs u and outputs y. State estimation problem. Find the internal states x of the system S knowing inputs and outputs.
This approach can be applied to systems at various length scales in a hier archical manner down to the smallest scale of interest. This is the focus of Sec tion 1 .2. Hence the systems perspective allows a wide range of problems to be concisely formulated and understood within a formal generic structure. By so dOing, all the power of modern systems analysis tools are at the disposal of the analyst. It is clear that this perspective can be applied across the "life cycle" and this is discussed in the following section. 1.1.2. The life cyc/e concept and its impact
Life cycle concepts now dominate product and process engineering activities across almost all commercial operations. The ideas are not new but the recent formalization iso This is attested by new i nternational life cycle standards such as ISO/IEC1 5288 "Systems Engineering - System Life Cycle processes". The generic life cycle phases involve [4]: •
•
concept - analysing needs, identifying key concepts, developing potential so lutions; development - engineering a product and process;
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Process Systems Engineering Applied to Granulation
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production - manufacturing the product; utilization - operating or using the product; support - maintaining and supporting the product and process; retirement - retiring, disposing or archiving the product and process.
The process life cycle is clearly a related concept. It is characterized by a number of sequential stages as shown in Fig. 2. These stages are contrasted with the generic phases of 180 1 5288. Accompanying the process life cycle phases are key activities associated with each phase. Of prime importance throughout the life cycle perspective are the issues of raw materials, wastes and emissions, energy consumption, generation and reuse. These issues are necessarily part of a truly integrated framework [5]. From a process systems perspective we can consider an expanded set of activities typical of industrial life cycle analysis. These include: • •
strategie planning research and development activities
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conceptual product and process design detailed engineering designs installation and commissioning operations and production decommissioning of process remediation of process related facilities.
Some of the individual activities or considerations of the life cycle phases illustrate the many applications areas in which PSE plays a role, iIIustrating the current breadth of a process systems perspective. These are seen in Fig. 3. Granulation operations are equally subject to life cycle processes and systems engineering provides the tools and techniques to address key aspects across the process life cycle. In each phase there will be separate challenges related to granulation processes and granulated products. Some of the generic issues in this area include: •
•
•
•
•
developing a holistic approach to product and process design in line with life cycle principles; the effective use of new, deeper insights into granulation mechanisms and equipment behaviour in process and equipment design as weil as overall op erations; the effective use of appropriate models at each life cycle phase to improve overall performance of these systems; the development of goal-driven models and their use across the life cycle phases - from concept to the grave; integrating the socio-technical issues in product, process design and opera tions. This includes the important area of human factors in design and oper ations related to routine operations and also to abnormal situation management (ASM) and fault diagnosis.
The impact of the life cycle perspective is that corporations need to take a "cradle-to-the-grave" approach to product and process design. The early deci sion-making processes will have long-term and far-reaching effects on the rest of the life cycle phases. Poor decision-making at the early stages can create difficult or intractable problems for design, operation and retirement. This can be expen sive in terms of personnel time, project costs and time to market. In contrast, when a life cycle approach is taken, early life cycle phase decisions take into account long-term perspectives and help lead to optimal solutions. 1.1.3. The importance of a process systems approach
The life cycle concepts covered in Section 1 . 1 .2 are the prelude and context to applying PSE principles to granulation processes.
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PSE is ultimately concerned with improved decision-making procedures across the product and process life cycle mainly through the use of computational methodologies and tools. It has become a "model-centric" activity, where models in their various forms are used as a basis for this decision-making process. The goals of that decision-making process are focused across the whole productj process life cycle seen in Fig. 3. An extensive review of modelling and model applications is given by Cameron et al. [6]. PSE has its origins in the generic field of systems engineering but with a focus on processes that were predominately in the chemical and petroleum industries. The approaches used in those sectors have rapidly spread to a wide range of industrial processes that encompass particulates, biologicals, pharmaceuticals, food and consumer products. There have been numerous significant impacts brought via PSE approaches. Table 1 , adapted and expanded from Grossmann and Westerberg [7], lists some of these accomplishments. Most we now take for granted as standard approaches. It can be seen that the accomplishments have addressed a wide range of challenges across the product or process life cycle - from concept, through process design to operations. How to effectively utilize such techniques and tools still remains an ongoing challenge for those working in the area of granulation systems. 1 .2. Multi-scale, m ulti-task perspectives in g ranulation technologies
Not only is PSE concerned with the life cycle phases of a product or process but it is essentially a multi-scale approach that considers the relevant length and time scales at which the dominant behaviour takes place. This has always been an implicit focus of PSE but it is now explicitly addressed through the growing ap plication area of multi-scale systems [8]. It is a current area of rapid growth from a scientific and commercial perspective. A multi-scale perspective on product and process design spans the whole life cycle, since key decision-making across the phases necessarily must incorporate time and length scales from the early concept phases through to the retirement of the product and process. As an example, the time and length scales for drum granulation are weil displayed on a scale map as seen in Fig. 4 [9]. Here the scales refer to typical characteristic length 1 0-6-1 03 m and accompanying time scales of 1 0-2-1 04 s. In the context of granulation, particles and granules occupy the lower length scales, whereas the plant and supply chain populate the larger length scales. We see particles associated with very small characteristic times while the plant typically has very much larger time constants. Similar maps apply to other forms of granulation technology including high shear, pan and fluidized bed systems. The traditional approaches to studying particle technology are
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Table 1 . Significant accomplishments of PSE.
Process design
Process operations
Synthesis of energy recovery networks Synthesis of distillation systems (azeotropic) Synthesis of reactor networks Hierarchical decomposition of flowsheets Superstructure optimization Design of multi-product batch plants
Scheduling of process networks Multi-period planning and optimization Data reconciliation Real-time optimization Flexibility measures and flexible design Fault diagnosis
Process control
Supporting tools
Model predictive control (MPC) Controllability measures Robust control Non-linear control Statistical process control Process monitoring Thermodynamics-based control
Sequential modular simulation Equation-based process simulation Artificial intelligence and expert systems Large-scale non-linear programming (NLP) Optimization of differential algebraic equations (DAEs) Population balance modelling and solution methods Mixed-integer non-linear programming (MINLP) Global optimization methods Multi-scale systems analysis
typically focused on two length scales: the macro-scale (unit operation level) and the micro-scale (particle level), with little efforts spent on the intermediate scale [1 0]. Advances in the design, optimization and control of particulate processes require filling of this gap in knowledge. The challenges in multi-scale granulation applications are weil discussed by Ingram et al. [8] who emphasize the following challenges: • • •
deciding which length scales are appropriate for a specific application or model; developing or selecting appropriate models at the scales of interest; choosing suitable frameworks to link or integrate the partial models.
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The choice of length scales is often dictated by •
• • • • •
the key physico-chemical phenomena related to atoms, molecules, particles and thin films; phases that exist in the system; process equipment and unit operations that are considered; complete plant analysis; company sites for integrated studies; business enterprise considerations across national and multi-national operations.
In targeting key scales a number of factors are often important, including insight and experience, the system geometry, analysis of experimental data and pre vious experiences with similar modelling. More analytic approaches are now be ing developed to address the scale incorporation issue by means of goal-directed modelling approaches but this remains in the area of current research [1 1). Choice of partial models at the scales is dictated by the quantities that the models can predict, the inputs required, the applicability range of the model and its accuracy and finally the cost and time to set up such a model. Modelling techniques such as molecular mechanics, molecular dynamics, front-tracking systems, computational fluid dynamies, flowsheeting and enterprise supply chain
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modelling span the nano to mega scales [1 2-15]. Despite the current interest in many modelling and solution techniques there still remains little advice on the best approaches to an application. The final area of multi-scale modelling involves the way that partial models at the different time scales are integrated. Work in this area has started to develop an understanding of integration frameworks [8, 1 6]. A number of important inte gration frameworks for multi-scale models exist as seen in Fig. 5. Each of these frameworks allow quite distinct ways of information transfer between two partial models at different scales. These information structures also have a direct impact on computational complexity and computation times. The decision on the "best" integration framework is not easy and the development of metrics that capture properties of both partial models and the composite, multi scale model is one means of providing guidance to model developers. In the case of granulation, the scale map of Fig. 4 suggests a number of natural levels of analysis and multi-scale modelling. These include: • •
• •
particle scale level with particle interactions being important; a volume element of powder characterized by mixing with its kinetic mecha nisms and rates; the vessel scale that characterizes mixing and residence time phenomena; the plant level scale for process design, control, optimization and operator guidance.
These challenges are currently being met through various multi-scale model ling and simulation approaches that use a wide variety of techniques already mentioned. PSE approaches bring powerful analysis and synthesis tools to bear on the multi-scale nature of granulation and provide a holistic focus on design, control and other operations challenges. In the next sections we outline some important systems perspectives in granulation, centred mainly on batch and
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continuous drum granulation of industrially relevant products. A similar focus applies to other granulation modes - the applications may change but the ap proaches used are very similar. 2. PROCESS SYSTEMS ENGI NEERING : SELECTED APPLICATIONS
In this section we select a number of important application areas where the power of PSE approach es is evident. As mentioned in the introduction, PSE applications across the life cycle are numerous and ubiquitous. To establish the context of the selected applications in control, optimization and diagnostics, we first discuss the importance of studying the process from both steady state and dynamic situations. 2.1 . Steady state and dynamics of g ranulation systems
80th steady state and dynamic analysis of process systems is important. The consideration of both is vital in order to provide comprehensive solutions to many modern processing problems. Failure to consider the dynamics of systems at several stages in the life cycle has in numerous cases meant costly redesigns or retrofits. In some cases, companies simply have to live with sub-optimal operations for the complete life cycle of the product or process. Undergirding the application of modern optimization and control methods is the extensive use of models in various forms. Modern PSE is strongly "model-cen tric" and this emphasis will only continue to grow. However, the models should be goal-driven, such that the application area will determine the model form and complexity needed for the job. This issue is addressed in following sections. We first start by considering the roles of steady state and dynamic analysis. 2.1.1. The role of steady-state analysis
This includes: •
•
Determination of operating points for the development of linear models in control applications. The linear models are normally developed from non-linear models using first-order Taylor series expansion around certain operation points. An obvious selection of operation points for continuous processes is the steady state conditions. The linearization method will be described in Section 2.1 .4. System optimization and parameter estimation. The time-independent design and process parameters can be identified using system optimization algorithms for steady-state operations, which will be explained in Section 2.2.2. The steady state determined by system optimization is used as a target for state-driving operations.
Process Systems Engineering Applied to Granulation •
•
•
51 1
Sensitivity analysis followed by the determination of possible manipulative varia bles. Two frequently quoted pioneering works on steady-state analysis of con tinuous granulators published by Han [1 7] and Han and Wilenitz [1 8] have provided convincing evidence for the roles played by steady-state analysis. Interaction analysis of decentralized contral systems using relative gain array (RGA). In process engineering, a decentralized, multi-Ioop control scheme is frequently used for the ease of implementation, in which one output variable is controlled by only one manipulated variable. In order to design effective de centralized control systems, the following two items of information are essen tial: ( 1 ) a measure of process interactions and (2) a recommendation concerning the most effective pairing of controlled and manipulated variables. The broadly used RGA method developed by Bristol [1 9], which requires only steady-state information, provides the aforementioned items of information. The RGA method is easy to understand and simple to implement with detailed explanations in popular textbooks on process control [20]. Development of effective numerical schemes for the solution of population bal ance equations (PBE). It will be shown in Section 2. 1 .3 that a generalized population balance model involves at least three dimensions: time (t), space (z) and size (v) domains. In order to reduce the complexity in the development of numerical schemes, the researchers commonly solve steady-state problems together with an assumption of perfect mixing, leading to an one-dimensional model with particle size as the only independent variable [21].
As early attempts to address steady-state operations of complex granulation processes, Han [ 1 7] and Han and Wilenitz [1 8] imposed a number of restrictive assumptions to the systems under their studies. These include: ( 1 ) The granule growth rate is uniform, such that granules grow at the same rate, independent of their size. (2) Granules travel through the granulator at a constant forward ve locity. (3) Crushed particles are the predominant source of new granule forma tion, so that the formation of new granules due to attrition within the granulator is negligible. (4) The granule size from the crusher discharge is uniform and it is smaller than the smallest granule size of the granulator discharge stream. (5) Sieve efficiency is 1 00%. (6) Layering is the only granule growth mechanism, so that coalescence between granules in the granulator is negligible. In spite of the very restrictive assumptions used in the model development, good agreements were achieved between simulation results and experimental data. Furthermore, reported results have clearly demonstrated the significance of steady-state anal ysis. A number of conclusions drawn more than 30 years aga are still valid at the present time. These include: ( 1 ) Granulation processes with significant recycle streams are not self-regulatory, namely they will not be returned to desired steady states without proper control actions when deviations occur. (2) The product size
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distribution is very sensitive to the crusher discharge size and efficiency. (3) The effective regulatory control can be achieved by adjusting the rotation rate of the crusher in the granulation circuit. 2.1.2. The role of dynamic analysis
This includes: Prediction of dynamic behaviour for processes under uncertainty andjor ex temal disturbances. Real steady states without any deviations from specified operational points can hardly be realized in process engineering due to uncertainties, disturbances, as weil as changes in product specifications. Con sequently, it is important to predict the dynamic behaviour of processes when steady-state operations are disturbed. Among the others, the most important issue in dynamic analysis is the determination of stability conditions. In the cases that steady state and dynamic analyses lead to conflict conclusions, the priority should be given to stability concerns. • Design and operation of batch processes. Since there are no steady states in batch processes, dynamic analysis is inevitable for the prediction of process behaviour. The operational points in batch processes for the development of local linear models (see Section 2.1 .4) are also determined by dynamic analysis using some special measures such as the gap metric method [22,23]. • Development of hierarchical models. The development of multi-form models with various complexities for different applications relies on dynamic analysis. These models include mechanistic, black box, hybrid, non-linear, linear, local linear and reduced order models. The fitness between the model and its ap plication is assessed by the difference between the prediction error of a given model and the error tolerance of a specified application, as weil as the com putational time. • Process control with sensitivity and interaction analysis. It is weil known that effective control requires dynamic information. This point will be further ex plained in Section 2.3.2. It has also been realized for sometime that results from steady-state sensitivity and interaction analyses could be misleading with counter examples [20]. In some cases, direct extensions of the steady-state analyses to treat dynamics are possible with certain assumptions, such as dynamic RGA [20]. However, these extensions should be used with caution. • Dynamic optimization. Dynamic optimization is also denoted as optimal control in this chapter. It is the upper-Ievel control, which provides target profiles (set points) for the lower level, model predictive control (MPC). Dynamic optimiza tion methods will be described in Sections 2.2 and 2.3.3 for processes without and with significant uncertainties, respectively. • Fault diagnosis and troubleshooting. These will be explained in Section 2.4. •
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2.1.3. The role of mathematical modelfing
The role of mathematical modelling is comprehensively analysed by Hangos and Cameron [3] with the following summary of application areas: • • • • • • •
process design process control soft sensor development troubleshooting on operations process safety operator training environmental impact.
In contrast to gas and liquid systems, characterization of particulate processes involves the determination of particle number and property distributions, such as size, shape, moisture and porosity distributions. Consequently, in addition to heat, mass and momentum balances, studies on population balances are es sential to granulation processes. Basic concepts and techniques for the deve lopment and resolution of general PBE are weil explained by Randolph and Larson [24] and Ramkrishna [25]. One- and multi-dimensional population balance models (PBMs) are defined based on the number of property coordinates (in ternal co-ordinates). In this work, we mainly address one-dimensional PBMs for both batch and continuous systems with particle size as the only internal coor dinate. Multi-dimensional PBMs are reviewed by the authors elsewhere [6J. As major case study examples, one-dimensional , batch and continuous drum gran ulation processes will be analysed in detail. The model structures are applicable to other popular granulation equipment, such as high-shear mixers and fluidized bed granulators. 2 . 1 .3. 1 . One-dimensional population balance equations For a weil-mixed batch system with only one internal coordinate v (particle size) is described as folIows: a a n(v, t) = [Gn(v, t)] + B 0 (1 ) at av where n is the one-dimensional number density, G the growth rate, B and 0 are the birth and death rates due to coalescence, respectively, which are represented as -
1 Jr
-
B = 2. o ß(v - v', v')n(v - v' , t)n(v', t)dv' 0=
n(v, t)
100 ß(v, v')n(v', t)dv'
(2) (3)
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The PBE for continuous systems with one internal and one external coordinates is given by a a . o [Zn(v, z, t)] - [Gn(v, z, t)] + B 0 n(v, z, t) = (4) av at az where the spatial velocity is defined as . dz . (5) Z= E R dt The representations of the birth and death rates are similar to that for batch processes, except that they are spatial dependent described as folIows: -
B=
-
� 1v ß(v - v', v')n(v - v', z, t)n(v', z, t)dv' 0 = n(v, z, t) 100 ß(v, v')n(v', z, t)dv'
(6) (7)
Continuous granulation processes are commonly encountered in the fertilizer and mineral processing industries, whereas most granulation operations in the pharmaceutical industry are performed as batch processes employing either high shear mixers or batch fluidized-bed granulators. There are a number of effective numerical techniques for the solution of PBEs, which will be reviewed in this book by other authors. We only described a few relevant ones used in our research projects. Hounslow et al. [21 ] developed a relatively simple discretization method by employing a M-I approach (the mean value theorem on frequency). The main advantage of Hounslow discretization method is that it is easy to understand and simple to implement with relatively small number of size classes. Consequently, it has been used in the control studies carried out by our research group, which will be described in some detail later. Kumar and Ramkrishna [26,2 7] developed a discretization method by using a grid with a more general and flexible pattern with fine or coarse discretizations in different size ranges. A comparative study was carried out by Balliu [28] to investigate advantages and disadvantages of the methods, developed by Houns low etal [21 ] and Kumar and Ramkrishna [26]. The wavelet-based methods are relatively new numerical schemes for solving PBE consisting of both differential and integral functions [29,30]. The most important advantage of these methods over other numerical techniques is their ability to effectively deal with steep moving profiles. There is a long history in studies on the application of Monte Carlo methods to particulate processes. The first serious research paper on a Monte Carlo treatment for systems involving population balances could be cred ited to Spielman and Levenspiel [31]. Since then, a significant number of pub lications have appeared in the literature on the solution of PBEs using Monte Carlo methods [25]. Comprehensive Monte Carlo treatments are described in the literature [25,32]. Monte Carlo methods allow artificial realization of the system behaviour, which can be divided into time- and event-driven simulations. In the
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former approach, the time interval M i s chosen, and the realization of events within this time interval is determined stochastically. In the laUer case, the time interval between two events is determined based on the rates of processes. In general, the coalescence rates in granulation processes can be extracted from the coalescence kernel models. The event-driven Monte Carlo can be further divided into constant volume methods in which the total volume of particles is conserved [33], and constant number method in which the total number of par ticles in the simulation remains constant [34,35]. The main advantages of the constant number method for granulation processes are identified as the popu lation remains large enough for accurate Monte Carlo simulations and the elim ination of the renumbering effort. Monte Carlo methods are applicable to multi dimensional PBM [35,36], and also effective in sensitivity analysis in addition to solution computations [37]. Another recent development in solution techniques has been presented by Immanuel and Doyle 1 1 1 [38]. This technique is based on a finite-element discretization of the particle population, and tracks the total par ticles within each of the bins. The equation representing the total particles within each bin is derived from the PBE in a straightforward manner (partial analytical solution). The particle population in each bin is updated employing a two-tier hierarchical solution strategy, enabling orders of magnitude improvement in the computation times. The individual rates of nucleation, growth and coalescence in each bin are computed in the first tier of the algorithm (at each time step), and the particle population is updated in the second tier. Because of the separation of the three rates in computations, the differences in their time scales are incorporated into the algorithm. The other major factor that contributes to the improvement in computation time is the off-line analytical solutions, which can be computed just once at the start, leading to a substantial reduction in the computational load. The method can also be applied to multi-dimensional PBMs [39]. We now explain the numerical method developed by Hounslow et al. [21 ] i n some detail, which has been extensively used in dynamic optimization and model-based control by a number of researchers [6,40]. The PBEs, such as equations (1 )-(3), are normally developed using particle volume as the internal coordinate. Because of the identified advantages of length-based models, Hounslow et al. [21] performed the coordinate transformation to convert the volume-based model to a length-based model. In the length-based model, the birth and death rate functions described by equations (2) and (3) are converted into (8)
0=
n(L, t)
100 ß(L, },)n(A, t) d A
(9)
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where L and A denote the eharaeteristie length of partieles. The Hounslow method is based on a geometrie diseretization with the following ratio between two sue eessive size intervals: (1 0) where L and v represent the eharaeteristie length and volume of partie/es, re speetively, the subseripts i+ 1 and i denote the size e/asses. Using Hounslow's diseretization method, the PBE for a bateh system given by equation ( 1 ) ean be eonverted into a set of diserete PBEs. Sinee the number-based PBEs are more frequently used in the literature, whereas the mass-based ones are more eon venient for contral and optimization studies, we show both representations together. The diseretized forms of equation ( 1 ) are represented as folIows: d 8 n; - (Gn;) + B; 0; dt 8L
= :t M = - q � ;
(G�)
-
+ Bm_; - Dm_;,
i = 1 , 2, . , imax . .
(1 1 )
where n and M are partie/e number and mass (kg), respeetively, subseript i stands for the ith size interval, subseript m_i represents mass-based value in the ith size interval, i 1 , 2, . . . , imax, in whieh imax is the total number of size intervals. The mathematieal representations of B;, Bm_i, Di and Dm_i are given by
=
(1 2)
(1 3)
where ß;j is equivalent to the representation ß(L;, L) and the growth term is rep resented as
(14)
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Consequently, an original PBE described by a partial differential-integral equa tion is converted into a set of ordinary differential equations. A continuous pop ulation balance model can also be discretized using a similar strategy. For example, the discrete population balance model for a perfect mixing, continuous granulator is described by
d - M·
dt 1 i = 1 , 2, . . . , imax
( 1 5)
( J)
where F and Fm are the number and mass flow rate, respectively, the subscript t indicates the total value and the superscripts identify the inlet and outlet streams. The representations of B i , Bm_i, Di, Dm_i, a�(, and Ir. G are also given by equations (1 2)-(1 4). I
2. 1 . 3 . 2 . Coalescence kerneis
It is easy to see that a coalescence kernel is affected by two major factors: ( 1 ) collision probability of the specified pair of particles and (2) successful coales cence or rebounding after collision. The first factor mainly depends on the particle sizes, granulator configurations, particle flow patterns and operating con ditions. The second issue has been intensively studied by Uu et al. [41 ] with the identification of the following four most important aspects affecting the success of coalescence: elastic-plastic properties, viscous fluid layer, velocity collision and energy balance. The authors have also observed that there are two types of coalescences distinguished by particle deformations. That is, the Type I coalescence is not associated with any particle deformation during the collision, whereas the Type 11 coalescence is accompanied by particle deformations. Uu and Utster [42] further proposed a new physically based coalescence kernel model based on the criteria developed earlier [41]. From these fundamental studies, it can be determined qualitatively that the coalescence kerneis should depend on particle sizes, energy consumptions, particle deformability and, most importantly, the moisture content (viscous fluid layer). A historical summary of the proposed coalescence kerneis is given in Table 2, which is an extension of the table originally presented by Ennis and Utster [43] with the new coalescence kernel developed by Uu and Utster [42] and another kernel from aerosol dynamics [44]. 2 . 1 . 3 . 3 . Reduced order models
In many PSE applications, reduced order models are highly desirable because they are computationally efficient and contain the requisite functionality for
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Table 2. A summary of proposed coalescence kernel in the literature.
Kernel
ß = ßo
0 0
ß = ß (u+v)a (uv/ (U2/3+V2/3) ß - ß 1 /u+ 1 / v ß = a(u + v) 2 ß = a (U_v) (u+v) k, t < ts ß - a(u + v), f > ts
{
{
k, constant; ts , switching time k, w < w* ß= O , w > w* W - (u+v)a (uvt k, a, b, constants ß = ßo ( 1 l u + 1 Iv) 1 /2 (u1 /3 + V1 /3) 2 ß = ßO (U-1 /3 + V- 1 / 3) (U1 / 3 + V1 /3) ß1 Types l and 1 1 without permanent deformation ß lu,v = ß2 Type 1 1 with permanent deformation rebound o
References Kapur and Fuerstenau [45] Kapur [46] Sastry [47] Golovin [48] Golovin [48] Adetayo et al. [49] Adetayo and Ennis [50]
_
{
Friedlander [44] Uu and Utster [42]
the application. The authors have reviewed a number of model order reduction techniques applicable to granulation processes [6]. These include reduced order models using the concept of lumped regions in series, model order reduction for multi-dimensional population balances and reduced order models using the method of moments. The method of moments has been frequently used in control and optimization for crystallization processes [51 ,52]. However, it is not com monly used in granulation processes because of the difficulties involved in the computations of fractional and negative moments. In the cases where the type of size distribution is more or less known, such as the log normal distribution, the moment models are also very effective for control and optimization of granulation processes [53]. 2.1.4. Development of linear models and multiple model approach
Most industrial processes, including granulation plants, should be represented by non-linear models. However, the well-established theory and techniques for
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Process Systems Engineering Applied to Granulation
process control and systems analysis are largely based on linear models. Non linear systems theory and methods are mathematically complicated and difficult to implement in real plants. Consequently, development of approximate linear models from non-linear models is a common practice in modelling of non-linear processes. A general non-linear process without uncertainty is described by the following differential algebraic equations: dX = fex, u) ( 1 6) dt y = h(x, u)
{
where y and u are the vectors of controlled and manipulated variables, respec tively, x is the vector of state variables, and f and h are vectors of smooth functions. Using the Taylor series expansion around certain operation points, the non-linear model described by equation ( 1 6) can be linearized as folIows: dbx bu = Abx + Bbu bx + ---r = --,= � ou d t ox (1 7) Oh bx = Cbx by = T OX
at ! X=Xo,U=Uo at ! X=Xo,U=Uo ! X=Xo,U=Uo
The symbol b in front of x, u and y is omitted for notational simplicity in most cases. The readers should keep in mind that the linear models developed from the first-order Taylor series expansion deal with deviations from operation points rather than real values. If the deviations from a specified operation point are too large, a single linear model is not sufficient In this case, a multiple model ap proach should be applied. That is, the original non-linear model is approximated by a number (say, m) of linear models, each of which is only valid in a narrow operation region i (i = 1 , . . , m) represented as foliows:
d�;= O�T ! X=Xi O,U=U,o bx + O�T ! X=Xi O,U=Ui O ,
I
bu = A;bx + B;bu
oh by = bx = C bx OXT x=xw,u=u/,o
( 1 8)
I
The multiple model approach has been applied to advanced control of non linear processes by the authors [22,23]. 2.1.5. The role of measurement
The role of measurement is summarized as follows with some brief explanations: •
Model validation with parameter identification. Steady state and dynamic data are essential for the identification of structure and parameters of respective steady state and dynamic models. Schroder and Cameron [54] developed a
520
•
•
• •
I .T. Cameron and F.Y. Wang
technique for model structure validation using non-linear and mixed-integer optimization (NLMIO) method. Parameter identification using measurement data will be explained in detail in Section 2.3 as applied to the development of multi-level control schemes. Glosed-Ioop control. 80th black-box control and model-based control require dynamic measurement data, which will be stated in Section 2.3. On-fine optimization and model modification. The control targets (set-points) should be updated using optimal control techniques based on the on-line mod ified models. The model modification is realized through the minimization of the differences between the measured and predicted data, which will be described in Section 2.3. Fault diagnosis and troubleshooting. This role will be explained in Section 2.4. Safety protection through risk assessment. It is easy to see that the abnormal measurement data provide warning signals for risk management. "
As a basis of on-line monitoring and diagnoses, reliabre on-line measurements of particle size distribution and moisture are important. The commonly used technique for on-line determination of particle size distribution in granulation is based on i mage analysis. A typical i mage analysis system consists of a GGO camera, lightning unit, telephoto lens and computer. An image probe is normally installed within the high-shear granulator to receive the image, which has been described in detail by Watano etal. [55,56]. A study of on-line size measurement based on image analysis using an OptiSizer unit [57] has been carried out at the University of Queensland for drum granulation processes [53]. The experimental set-up is shown at the URL: http://www.cheque.uq.edu.au/psdc. In contrast to the installation of a probe for the high-shear granulator, a sampling system can be developed for drum granulation processes to allow the measurement of a rel atively small sampie stream using the OptiSizer unit. In the case where the particles are wet, technical difficulties may occur due to the temporary agglom eration and reduced flowability induced by the particle stickiness. A modified strategy is to dry the particles before the measurement. However, this will lead to a further time delay. Solid moisture can be measured on-line by using near-infrared (NIR) spec troscopy [58] or microwave-based techniques. A microwave technique for the measurement of solid moisture in batch sam pies has been developed by Shah hosseini et al. [59]. Its extension to continuous sampies encounters similar diffi culties to that of OptiSizer units due to the particle stickiness. Further work is needed to develop improved sensors for both particle size and moisture meas urements. It can be seen from the literature that the direct measurement of particle char acteristics, such as particle size d istribution, moisture contents and deformability, is still a challenging research area. In order to cope with measurement difficulties,
Process Systems Engineering Applied to Granulation
521
some indirect monitoring parameters have been adopted as the indicators of particle characteristics. A commonly accepted monitoring parameter in the pharmaceutical industry is the power consumption, which has been successfully used to control the particle size in high-shear mixers at the end-point [60,61]. Based on a series of investigations carried out by Leuenberger [60], the energy dissipated per unit volume d W/d V in a high-shear mixer is related to powder porosity E , which can be used to calculate the powder saturation level S. As soon as the powder saturation level is determined, the average granule size can be estimated [62]. This indirect monitoring technique has been successfully applied to the control of high-shear mixers [60], which will be further explained in Section 2.3. 1 , which deals with black-box controller design. 2.2. Operational aspects o f granulation systems 2.2.1. Process optimization
Process optimization and open-Ioop optimal control of batch and continuous drum granulation processes are described in this section. Open-Ioop optimal control can also be denoted as dynamic optimization, which provides the set points (targets) for the lower-Ievel c1osed-loop contro!. 2.2.2. Statement of steady state and dynamic optimization problems
In process optimization, the adjustable variables are defined as "decision pa rameters", which are not time dependent. On the other hand, the goal of optimal control calculations is aimed at the determination of time-dependent "manipu lated variables" in order to reach optimal output trajectories. Both steady state and dynamic optimization studies are carried out by the authors, which consist of: (i) construction of optimization and control relevant, PBMs through the incorpo ration of moisture content, drum rotation rate and bed depth into the coalescence kerneis; (ii) investigation of optimal operational conditions using constrained op timization techniques; and (iii) development of optimal control algorithms based on discretized PBEs. The objective of steady-state optimization is to minimize the recycle rate with minimum cost for continuous processes. It has been identified that the drum rotation rate, bed depth (material charge) and moisture content of solids are practical decision (design) parameters for system optimization. The objective for the optimal control of batch granulation processes is to maximize the mass of product-sized particles with minimum time and binder consumption. The objective for the optimal control of the continuous process is to drive the process from one steady state to another in a minimum time with minimum binder consumption, which is also known as the state-driving problem. It has been known for some time that the binder spray rate is the most effective control (manipulated) variable. Although other process variables, such as feed flow rate
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I .T. Cameron and F.Y. Wang
and additional powder flow rate can also be used as manipulated variables, only the single input problem with the binder spay rate as the manipulated variable is addressed here to demonstrate the methodology. It can be shown from simu lation results that the proposed models are suitable for control and optimization studies, and the optimization algorithms connected with either steady state or dynamic models are successful for the determination of optimal operational con ditions and dynamic trajectories with good convergence properties. It should be pointed out that only open-Ioop optimal control issues for gran ulation processes without uncertainty are addressed in this section. The integra tion of open-Ioop optimal control with closed-Ioop, non-linear model predictive control (NMPC) for uncertain processes has been reported elsewhere by the authors [63] and outlined in Section 2.3.3. A typical batch drum granulation process is schematically shown in Fig. 6. There are two operational strategies: ( 1 ) pre-mix the fine particles with the proper amount of liquid binder followed by the rotating operation until the desired size distribution is achieved and (2) simultaneous mixing and granulating by spraying liquid binder (and fine powders in some cases) on the moving surface of particles inside the rotating drum. The first strategy involves system optimization without any control action. The optimization problem can be stated as: to determine the optimal moisture content, initial size distribution, rotating rate and bed depth (drum charge), such that the desired size distribution can be obtained within a minimum time tf. Optimal control techniques can be applied to the second strat egy, which can be stated as for the specified initial conditions, maximize the mass of product-sized particles in minimum time with minimum energy consumption by adjusting the manipulated variables, such as binder spray rate and drum rotation speed. We will discuss the optimal control problem with the binder spray rate as the single manipulated variable in detail. A continuous drum granulation process with an additional fine powder stream is shown in Fig. 7. The additional fine powder stream is used to improve the controllability of the process, which is not seen in the conventional design. Our studies on continuous drum granulation include the steady-state optimi zation and optimal state driving from one steady state to another. The objective for steady-state optimization is to achieve minimum recycle rate with minimum
_ _ .. .
t"'1r
Fig. 6. Schematic diagram of batch drum g ranulation.
Process Systems Engineering Applied to Granulation
523
Liquid Spray (Rw) Solid Feed (Fs)
Solid Output Fig. 7. Schematic diagram of continuous drum granulation .
cost through the determination of optimal operational conditions, such as rotat ing rate, binder spray rate, feed flow rate, bed depth and drum inclination angle. The optimal state driving attempts to drive the system from one steady state to another in a minimum time with minimum energy consumption by adjusting the time-dependent manipulated variables, such as binder spray rate, feed flow rate and optionally additional fine powder flow rate. 2.2.3. Control relevant models
A control relevant model was developed by Zhang et a/. [64], in which the co alescence kernel is a function of the moisture content. In the newly developed kernel models reported by Balliu [28] and Wang eta/. [40], in addition to moisture content, the bed depth and drum speed are also incorporated. Two kernel mod els, namely size-independent kernel and size-dependent kernei, are used in op timization and control simulations. The size-independent kernel is given by ßo = ao ' [(xw )n' e- a IXW ] . [(Bd t2 e- a2 Bd ] . ( S�3 e - a3 Sd ) ( 1 9) ßm_O = boßo where Xw is the moisture content in particles, Bd the bed depth, Sd the drum rotating rate, aO-a3 and n1-n3 are constants determined through parameter identification techniques based on the measurement data and bo the conversion factor. The size-dependent kernel is represented as [44]
(20) where ßo and ßm_o are also defined in equation (1 9). Since the main mechanism determining the growth rate G in equations (1 1 ) and (1 5) i s layering of the fine powders o n the surface of particles, it can be deduced that the growth rate is a strong function of the powder fraction and moisture content. The following correlation, which is an analogy to the well-known
524
I .T. Cameron and F.Y. Wang
[
]
Monod model in biochemical engineering [65], is used to calculate the growth rate
Mpowder . exp - a(xw - xwc)2 G = Gm '" M1. + Mpowder ' k . L.
(21 )
where Gm i s the maximum growth rate, Mpowder the mass of fine powder below the lower bound of the particle classes, Mi the mass of particles in the ith size class, Xwc the critical moisture, and k and a are the fitting parameters. Studies on powder mass balance lead to the following equation for batch processes:
L m ax i [ (Mi Mi )] � Finpowder - 23 G '"' f2 (Li - Li-1 ) --c + Li--11
dMpowder = in 3G ('XC> M(L) dL F powder dt Jo _
(22)
and the following equation for continuous processes:
L � [(L. L. ( · L L.
M ML dMpowder = in 3G (OO ( ) dL Fpowder _ powder tR dt Jo Mpowder � G Mi + Mi- 1 in � Fpowder � ) 1 1 1 tR 2 i=2 1 1- 1 _
_
_
_
)]
(23)
In equations (22) and (23), F�owder represents the inlet powder flow rate, and tR is the retention time. The inlet powder flow rate can be used as an additional manipulated variable. The liquid mass balance for batch processes is given by
d x w � Rw dt - Mt
(24)
where Mt is the total mass of solids in the drum and Rw the binder spray rate. Similarly, we can develop the liquid mass balance for the continuous process as
dxw = 1 [Fin in FM w + Rw] Tl Mt MXw - X
(25)
where F� and FM are inlet and outlet mass flow rates, respectively, and x� is the moisture content in the feed solids. In summary, the equations in the control relevant model for batch systems are discretized PBEs given by equation (1 1 ), powder dynamics described by equa tion (22) and liquid dynamics represented by equation (24). The corresponding equations for continuous processes are equations ( 1 5), (23) and (25). Both cases share the same kernel models given by equations ( 1 9) and (20), and growth rate model described by equation (21 ).
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Process Systems Engineering Applied to Granulation
2.2.4. Objective tunctions tor system optimization and open-Ioop optimal control
The objective function for system optimization of batch granulation is (26)
S.t. equation (1 1 )
The objective function for batch granulation with the binder spray rate as the only manipulated variable is given by Min Rw
{
-Wl Mp (lr )+W2 fa/r Rwdl Ir
}
W1
S.t. equations (1 1 ), (22) and (24)
(27)
In equations (26) and (27), Mp is the mass of product-sized partie/es, and W2 are the weighting functions. The objective function for steady-state optimization of continuous granulation is Sd.Bdpn Rw
Min
{-W1Fp + W2 R } w
(28)
S.t. equations (1 5), (23) and (25) with left-hand si des replaced by zero
Fp
where is the mass flow rate of product-sized partie/es. For the state-driving study, we carry out steady-state optimizations for two different product specifications: the product range for steady state 1 (SS 1 ) is 2.0-3.2 mm, whereas that for steady state 2 (SS2) is 3.2-5.0 mm. The objective function for this optimal state-driving problem is described as 2 Mj (tf) - M?S2 + W2 I�f Rw d t + W3 tf ��n J = L: (29) S.t. equations (1 5), (23), (25) and zero derivatives at final time where M,{ tf) andM?S2 denote the mass of partie/es in the ith size interval at the final time and for SS2, respectively.
{
[wu(
)]
}
2.2.5. Dynamic optimization algorithm
It is not difficult to solve the steady-state optimization problems with constraints represented by algebraic equations by using commercial software packages. We mainly explain the dynamic optimization methods used in this work. The basic structure of the algorithm employed in this paper is shown in Fig. 8. In the dynamic optimization algorithm depicted in Fig. 8, a control parameter ization technique [66] is used to discretize the originally continuous control var iables. That is, a control (manipulated) variable u(t) is represented by a set of
526
I .T. Cameron and F.Y. Wang Set J=O and initial guess for Ui
,...---"'--=-"'---+1 J=J+1
Conslrained opllmlzatlon algorithm Aigebraic conslrainlS Objecllve function
Initial conditions
....
..... DAE-ODE solvers state values Ui
_ _
...
_
Yes
Terminate
Fig.
8. Basic structure of the dynamic optimization algorithm.
piece-wise constants, Ui, i = 1 , 2, . . . , q. These constants are treated as param eters to be determined by using dynamic optimization algorithms. Since the MATLAB software packages with Optimization Toolbox provides both effective ordinary differential equation (ODE) solvers as weil as powerful optimization algorithms, the dynamic simulations reported in this paper are car ried out by using the MATLAB Optimization Toolbox [67]. 2.2.6. Selected simulation results and discussion
Simulations for both batch and continuous granulation processes are based on a pilot plant drum granulator with the following parameters: length 2 m, diameter 0.3 m , nominal hold-up 40 kg, rotation rate 25-40 rpm, retention time range 6-1 0 min. The particles are classified into 20-size classes specified as: [0.250, 0.31 5, 0.397, 0.500, 0.630, 0.794, 1 .000, 1 .260, 1 .587, 2.000, 2.520, 3 . 1 75, 4.000, 5.040, 6.350, 8.000, 1 0.079, 1 2.700, 1 6.000, 20.1 60] with units of mm. Other process parameters are available in a recent paper by the authors [40]. The simulated optimal profiles for the batch processes are shown in Figs. 9(a-c) with two datasets with and without constraints on control action. The control con straints restrict lower and upper bounds on the control variables (Iower bound
Process Systems Engineering Applied to Granulation
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9. Optimal Control of Batch Drum Granulation.
o kg S-1 ,
upper bound 0.015 kg S-1 ) , as weil as the gradient of the control actions ( I Rw / tl < 0.0003 kg S- 1 ) . It can be seen from Fig. 9(d) that if the normal con straints on the control variable are replaced by a high-upper bound of control variable (0.036 kg S-1 ) as the only constraint, very high-spray rates at the early operating stage with very short-spray time leads to the minimum objective function given by equation (27). However, if the normal constraints are activated, the control variable moves smoothly rather than suddenly with the price of a Ion ger operational time. The difference between final times in the two cases is about 1 04 s (283-1 79 s), which is quite significant. The results clearly have implications on equipment design and specifications that could allow the constraints to be moved out thus approaching the best-operating policy. Through steady state optimizations using the objective function described by equation (28), optimal binder spray rates for two different specifications on prod uct size ranges are obtained. These are: Rw = 0.050 kg S-1 for 2.0-3.2 mm as the product size range, and Rw = 0.075 kg S-1 for 3.2-5.0 mm as the product size range. Figures 1 0(a) and 1 0(b) show the profiles using an optimal control policy and a constant spray rate policy. The change of the cumulative mass between
528
I .T. Cameron and F.Y. Wang c: Optimal Cummulative Mass
a: Dynamics of Product Mass
40 ,-----, 16 o � E 14
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d: Control Profiles
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14 0
500
1 000
1 500
2000
6 �--�----�--� 1 500 2000 1 000 500 o
Time (seconds) Fig.
.� .
Time (seconds)
1 0. Optimal Control of Continuous Drum Granulation.
initial and final times under optimal control policy is shown in Fig. 1 0(c). The control profiles are depicted in Fig. 1 0(d). The optimal control policy leads to about 50% reduction on the objective function given by equation (29). The optimal spray rate policy can be stated: "Gradually increase the spray rate from the first steady state (0.005 kg S-1 ) to achieve a relatively high-spray rate (0.0084 kg S-1 ) followed by gradual reduction of the spray rate until the spray rate of the second steady-state value (0.0075 kg S-1 ) is reached, which will be maintained for the rest of the operational period". From Fig. 1 0, the significance of optimal control stud ies can be demonstrated by observing the facts that the optimal profiles approach the second steady state faster, and the optimal control strategy is easy to im plement with smooth movement. It should be pointed out that the small difference between two control policies shown in Fig. 1 0 is due to small difference between two product specifications (product ranges from 2.0-3.2 mm to 3.2-5.0 mm). It can be predicted that if the two steady states are far away, profound economic benefit can be achieved. Optimal control strategies are particularly important to plant start-up and shutdown operations. Figure 1 1 shows the dynamic profiles of optimal state driving from SS1 to SS2 with different levels of constraints. Dynamic changes of product mass,
Process Systems Engineering Applied to Granulation c: Dynamics of Moislure Conlenl
a: Dynamics of Producl Mass
16
529
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Cl
Cl C E 14
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0.1
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0.08
3 d: Control Profiles X 1 0. 10 ��------------------�
Dynamics of Under Sized Mass
Loose Constraints Loose Conslraints E
2 18
Cl .!: �
�
-i..
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!
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14 o
500
1000 Time (seconds)
Fig.
1
1500
2000
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1 1 . Effects of Constraint Tightness on Optimal Control of Drum Granulation.
undersized mass and moisture content are shown in Figs. 1 1 (a), 1 1 (b) and 1 1 (c), respectively under two constraint levels. Figure 1 1 (d) depicts control profiles for these two cases. In addition to the constraints on control actions, the final time constraints to ensure the final steady-state status is imposed on the system. That is, the left-hand sides of equations ( 1 5), (23) and (25) should be zero at the final time. However, it is not necessary to achieve zero exactly for the derivatives at the final time. We normally impose the final time constraints as Idx(tf)jdtl < I> in which x represents general state variables, such as number of particles, mass of powder and moisture content, and 8 is a very small positive number for practical applications with the value depending on the tightness of constraints. The I> val ues are chosen as 1 0--6 and 1 0-3 for tight and loose constraints indicated in Fig. 1 1 , respectively. It can be shown in Fig. 1 1 that the control strategy with loose constraints leads to shorter operational time than that with tight constraints (1 827 s vs. 1 925 s). However, the moisture dynamics show severe offset and oscillation. In optimization simulations, only final time constraints are changed for the two cases. It is interesting to note that the programme with tight constraints leads to small and smooth controller movements even though the constraints on the control variable are not altered explicitly. It seems that the loose constraints
530
I .T. Cameron and F.Y. Wang
allow too much manipulative variation that drives the system into a region (xw 0. 1 ) where moisture variations have significant impact on the granulation per formance. A marginal benefit identified by 5% time reduction is achievable using loose constraints with a price of process oscillations. Consequently, a control strategy with tight final time constraints is superior to that with loose constraints in this particular application. Through an analysis on the simulation results, the following conclusions can be drawn: ;::::::
1 . Population balance modelling provides an important basis for optimal design and operations for both batch and continuous granulation processes. 2. The effects of liquid content, bed depth and drum rotation rate on the coa lescence behaviour can be quantified through the development of new kernel models with the structure described by equations ( 1 9) and (20). The simulation results are qualitatively consistent with industrial experience in large-scale fertilizer production. 3. An optimal control strategy and algorithm using commercial optimization soft ware packages connected to reliable DAE/ODE solvers are successful for the determination of optimal trajectories with good convergence properties. This implies that under certain conditions, the more complicated optimal control algorithms, such as that based on the well-known Pontryagin's maximum principle, could be avoided. 4. Since start-up and shutdown operations are frequently encountered in gran ulation plants with huge financial impacts, studies on optimal control strategies can lead to significant economic benefits. 2.3. Control design, analysis and performance 2.3.1. Black-box controller design
There exist a number of practical control schemes in granulation plants, which do not rely on mathematical models. These include simple feedback control with or without feed-forward compensation and fuzzy-Iogic control systems. One of the most important issues for the effective control of granulation proc esses is the development of fast and reliable measurement techniques for the characterization of particulate systems. As pointed out previously, because of the difficulties associated with the direct measurement of particle characteristics, such as particle size distribution, moisture contents and deformability, some in direct monitoring parameters have been adopted as the indicators of particle characteristics. Leuenberger [60] and Faure et al. [61 ] have adopted a technique to use power consumption as an indicator of particle properties for control of particle size in high-shear mixers. Leuenberger [60] has proposed an approx imation to correlate the energy dissipated per unit volume in a high-shear mixer,
531
Pracess Systems Engineering Applied to Granulation
d W/d V, with the powder porosity as folIows: 1 -3 dW = {l(JcK CX -(30) 3 dV where W is the power consumption, V the granulator volume, {l the apparent coefficient of friction, (Je the cohesive stress, K the dimensionless shear rate and 3 the porosity of the powder mass. It is easy to show that the power consumption is related to the saturation level S defined as folIows: S
= H(1 3- 3) p
(3 1 )
where H i s the mass ratio of Iiquids to solids and p the density of the particle relative to the density of the liquid ( p = P s/pd. Furthermore, Kristensen and Schaefer [62] pointed out that the saturation level defined by equation (31 ) could be related back to the average granule size. Consequently, the power consumption, the saturation level and the granule particle size are i nterrelated , which forms a technical basis to use power consumption as a monitoring parameter for the characterization of particles within the high-shear mixer. A detailed description of the control strategy using power consumption as the in dicator of particle properties in high-shear mixers is also provided in Leuenbe rger [60]. Mort et al. [68] pointed out that "With recent development in particle sizing technology, the agglomerate size distribution can be measured in-li ne at any number of points in the process." The main measurement technique is image analysis by mounting high-speed cameras and lighting systems in appropriate locations. Since the direct measurement data of particle sizes are available, the controller design can be based on these data without relying on the indirect indicators under the condition that the rate of binder addition is sufficiently slow to allow for image data to be collected, processed and fed back. This concept has been used for batch granulation processes in fluidized beds. The same authors [68] also proposed a feed-forward control strategy to compensate the fluctuation of the recycle rate. The simple feedback control with feed-forward compensation scheme is shown in Fig. 1 2. Recycle rate
�'<,
Setpoint ;::;
�
Fig.
I
I
Feedback controller
1 "I 1
I
Feedforward controller
)+
+'C
I
-1
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1 I
Measurement data
1 2. Simple feedback contra I scheme with feed-forward compensation.
532
I .T. Cameron and F.Y. Wang +
Setpoint D,
'------� Host computer
Fig.
Image processing system I_--.....J
1 3. Block diagram of granule size control system. (After Watano
et al. [55,56].)
The measurement data in Fig. 1 2 could be the indirect monitoring parameters [60], or the explicit particle size distribution [68], depending on the relative speed of the measurement system and process dynamics. Watano et al. [55,56] have developed a novel system to control granule growth in a high-shear mixer. The system basically consisted of image processing and a fuzzy controller as shown in Fig. 1 3. In Fig. 1 3, D(t) is the deviation between the desired value (Dd) and measured value (Dm) of granule size, and !!D(t) denotes the change rate of measured values, which are mathematically represented as folIows: D(t) = Dd - Dm(t) (32) !!D(t) = Dm(t) - Dm(t - 1 ) Other notations in Fig. 1 3 are explained as folIows. V( t) is the result of fuzzy reasoning used to control the output power of liquid-feed pump, K1 and K2 rep resent gains of the input variables. In the methodology developed by Watano et al [55,56], four fuzzy variables were used, namely ZR (zero), PS (positive smalI), PM (positive medium) and PL (positive large). The values of D(�, !!D(� and V(�, all were classified into these four categories. Ten rules were proposed to relate measured D(� and !!D(� with V(�. Consequently, V(� can be quantified using the if-then statement. An example is given as folIows: If D(t) = PS and !!D(t) = PL then V( t) = ZR (Rule 2 in Table 2 of Watano et al. [56]). In such a way, all the combinations of D(t) and !!D(t) can be connected with V(t) for the effective control of the process. The technique can be considered as highly successful with the experimental justifications. 2.3.2. Model-based controller design
Edgar [69] has pointed out that "Significant potential benefits can be realized by using a combination of MPC and real time optimization (RTO)." The integra ted configuration of the two methodologies is shown in Fig. 1 4, which is an extension of scheme reported by Seborg et al. [20]. Since the control scheme consists of two levels: one for the determination of set-points, another for the
533
Process Systems Engineering Applied to Granulation Upper-Level Optimal Contra! .-------.---------------.-------------------------i
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---------------
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1 4. Configuration of model predictive control using real time optimization.
simultaneous determination of uncertain parameters and manipulated variables, it is defined as multi-level model predictive control (ML-MPC). This configuration is applicable to both linear and non-linear model predictive control of granulation processes. Pottmann et al. [70] demonstrated the control of granule density and the gran ule size in continuous operation of industrial granulators. They proposed a model predictive control strategy in which the control of the granule size is achieved through the control of the 5th percentile and the 90th percentile of the particle sizes. In their granulation system, they employ three-binder addition ports with spray rate n1 , n2 and n3 as the manipulated variables, each of which influence the bulk density (PB) , and the 5th and the 90th percentiles of the particle sizes (d5 and dgo). They point out that independent control of both the 5th and the 90th per centile is not possible. Thus, to avoid infeasibility, they seek to set one-sided constraints for these two variables (rather than require set-point tracking). Even though the process is non-linear, an approximate linear model relates the three manipulated inputs to the three outputs was considered appropriate by them for the purpose of control system design depicted in Fig. 1 5. They employ a linear MPC framework based on a discrete time first-order plus time-delay transfer function model described as Y(Z- 1 )
=
[
g (r1 ) 11 g2 (r1 ) 1 g3 (r1 ) 1
]
g 1 2(r 1 )
9dr 1 )
g22 (r 1 )
g23 (r 1 ) U (Z- 1 )
gdr 1 )
g33 (r1 )
( 33)
534
I .T. Cameron and F.Y. Wang °1
PB (P B = pB*)
.. ...
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..
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°3
cis (ds � dL) d90 (d90 ;:O: du)
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in which
[pa -p� l [ l
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-1
_
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•
_
-
_
-
n2
-
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where the hat over y is used to distinguish the model prediction from actual process data and the superscript 0 indicates the nominal values. The control problem is defined as folIows:
p
pBd(k)5(k) d(k)L (35) � g u (k) d d o S.t. n;nin �ni(k) �n;na\ for i= 1 ,2, 3 where P Ck) is the bulk density at the discrete-time instant k, Pa(k)the set-point value at the same time instant and niCk) the binder addition rate at time instant k through nozzle i. The optimization problem underlying the MPC strategy is given = �
a
;;0
��� { / = teT(k + i)We(k + i) + �UT(k + i)QU(k + i)} (36) where eCk + i) is the vector of error in the output at time instant k + i, and u (k + i) the input at the same time instant, P and C the prediction and control horizon, below
respectively. The objective seeks to minimize the deviation of the output from the desired value with the minimal variation of the inputs from their nominal values. They simplify the above optimization problem by separating the effects of the past control actions on the evolution of the outputs from those of the future control actions (the future control actions being the decision variables for the optimization problem). This results in the following formulation:
��� {I = UT(k) [MTWM + Ö] U(k) - 2XT(k)WMU(k) + XT(k)WX(k)} (37)
535
Process Systems Engineering Applied to Granulation
X(k) and E(k) are defined as X(k) yr(k) - 'l(k) - \jI(k) (38) E(k) X(k) - MU(k) The matrix M is related to the process mode!. The constraints on the inputs and
where
=
=
the outputs (bounds on the particle size) are set as folIows: 1 -I
[
]
[ ] U(k) :::: u�ax . . . u�ax -u�ax . u�ax limes limes [ -MM J U (k) - [ -YmYmaxin+-XX((kk))-+yryr((kk)) ] "-v----' C
<
.
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.
v
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(39)
(40)
In their study, they identified the need for the prioritization of the objectives, as weil as the need for relaxing hard constraints at the initial steps of the prediction horizon to avoid infeasibility of the optimization problem. The proposed MPC strategy has been tested via simulation on a specific granulation process. Its performance indicates that the desired control objectives can be met effectively by using this approach. Gatzke and Doyle 1 1 1 [71 ] proposed a model predictive controller based on two novel strategies to both account for the prioritization and to avoid the infeasibili ties in the optimization problems. One of these is based on a soft constraint contro!. The other is based on a prioritized control strategy so as to avoid un attainable set-points as weil as to tackle the more important objectives first and the less important ones later. Along the lines of Pottmann etat. [70], they develop controls for the bulk density along with the 5th and 90th percentiles of the particle size. Also, as in Pottmann et al. [70], they required reference (set-point) tracking for bulk density, while the 5th and the 90th percentiles of the particle sizes were constrained between set limits. In order to address infeasibility concerns in op timization problems, Gatzke and Doyle 1 1 1 [71] proposed two alternative Model Predictive Control strategies. The first strategy is a direct extension of traditional MPC, with either a quadratic or a linear objective function, and constraints (either one- or two-sided) for the objectives on particle size. subject to the constraints:
(41 ) (42)
In addition to constraints described in equation (42), soft constraints on the outputs, also known as asymmetrie objectives should be incorporated in
536
I .T. Cameron and F.Y. Wang
the Quadratic Programming (QP) algorithms. The soft constraint formulation is given by (43) r(i) - y( t) � ey(i) ; - r(J) + y(i) � ey(J) V i = k, k + 1 , . . . , k + p In the above equation, r(i) is the vector of reference or set-point values at discrete-time instant i, Y(/) the vector of measurements at time instant i, k the current time instant and P denoted the prediction horizon (the number of time instants into the future over which the error is sought to be minimized. For the objectives on the 5th and 90th percentiles on the particle size, they have envisaged the need for asymmetrie constraints, for which they propose the following asymmetrie bounds: ro(i) - Yo (i) � 1Y.6eyo(i); - ro(i) + Yo(i ) � lY.ü eyo ( i) V i = k, k + 1 , . . . , k + p (44) In the above equation, the subscript "0" refers to a particular control objective. A suitable choice of the values of 1Y.6 and lY.ü will ensure the realization of the necessary asymmetrie bounds on the control objectives. The second control strategy is based on a prioritized objective formulation. This is inspired by the need for prioritizing the objectives (economical vs. product properties) or to enable a step-by-step facilitated approach to the set-point value. In this strategy, they specify a series of control objectives and assign priorities for each of them. The objective function in the formulation is given by (45) (46) In equation (45), the last two terms represent the traditional output error and move suppression terms. The first two terms are added to prioritize the outputs. The binary variables Pj and Oj in equation (46) are elements of vectors p and 0, respectively. Variable Oj assume a value of 1 if the control objective j is satisfied (for any given solution u). If any particular control objective i is not satisfied, then the corresponding priority Pi is set to a value of 0 (in addition to 0i being 0). Further, the priority variables Pj for all other control objectives of a lower priority than the said control objective i is also set to O. These logics are represented by the following constraints: P1 � 0 1 ; P2 � 02 ; · · · , PN � ON (47) P2 � P1 ; P3 �P2; " " PN- 1 � PN In these constraints, the subscripts refer to the N control objectives of de creasing priority. The weight P1 is assigned a larger value than the weight P2, and both of these are maintained higher than typical values of the output error and move-suppression
537
Process Systems Engineering Applied to Granulation
terms (through suitable choice of weights ry and r ) Thus, the solution u seeks to maintain the ordered priorities of the control objectives foremost, then ensures as many control objectives are satisfied as possible, and finaily addresses the errors in the reference tracking and the move suppression terms. It can be seen that the techniques developed by Pottmann et al. [70] and Gatzke and Doyle III [71 ] are based on linear, input-output (black-box) models without incorporating PBMs. We now describe the non-linear model pre dictive control (NMPC) strategy using PBMs. NMPC schemes consist of simultaneous determinations of manipulative variables and uncertain parame ters. The previous work reported by Patwardhan et al. [72] and Patwardhan and Edgar [73] has demonstrated the applicability of NMPC to complex chemical processes described by partial differential equations known as distri buted parameter systems. The integration of open-Ioop dynamic optimization with closed-Ioop control with on-line parameter identification has accomplished by Rawlings et al. [52] and Miller and Rawlings [51 ] with particular applications to crystallization processes. In these developments, PBMs originally described by partial differential equations were reduced to low-dimensional models using the method of moments, leading to the control of average size rather than size distribution. Immanuel and Doyle 1 1 1 [74] and Crowley et al. [75] have carried out detailed studies on NMPC of particle size distribution in emulsion co-polymer ization processes using PBMs. The direct application of NMPC to a pilot-scale granulation plant has been reported by the authors [63]. We first describe basic concepts of NMPC followed by explanations of particular applications to the granulation process. A general non-linear process is described by the foilowing differential algebraic equations: u .
{
dt = fex, u; p)
dX
y=
h(x, u; p)
(48)
where y and u are the vectors of the controlled and the manipulated-variables, respectively, x is the state variable vector and p the set of model parameters, which may include disturbances. The NMPC algorithm normally consists of two sub-optimization problems: one for the estimation of parameters and another for the determination of manipulated variables. The objective function for the pa rameter estimation is given by (49) where y is the vector of real output variables, y the vector of predicted output variables, Wp a diagonal matrix of weighting functions, wpi the ith diagonal
538
I .T. Cameron and F.Y. Wang
Wp,
element in Nm the numbers of measured variables and Nd the number of sampies of each measured variable up to time t, the subscripts i and j identify output variables and sampling times. The objective function for the determination of manipulated variables is described as M in {
(50) where Nf is the total number of discrete intervals in time domain, subscript u identifies control-relevant variables and the superscript "set" indicates set points. The optimization problem with objective functions described by equations (49) and (50), subject to the dynamic model equations and process constraints, can be solved using dynamic optimization algorithms for the simultaneous de termination of uncertain parameters and manipulated variables. Again, we use the batch drum granulation process to demonstrate the ML-NMPC strategy. We specify the product size c1asses as c1asses 1 0-12 (2.000-3. 1 75 mm). The desired trajectories are determined through the minimization of the following objective function, which is an alternative representation to equation (27). M !n
{J
=-
I: W1 ,iMi(tf) + W2 J�f Rwdt + W3 tf
}
(51 ) 8.t. equations(1 1), (22)and(24) In equation (51 ), w1-w3 are the weighting functions. The objective function for c1osed-loop control is described as Rw
i=10
��{ J = llf [ (Mp - M;fW1 (Mp - M;) + R ] d + } (52) where Mp = W1 is a weighting function matrix and the superscript "* " signifies the desired trajectory. The interconnection between the two control W2
W
t
W3tf
[M10, M1 1 , M1 2]T,
levels is shown in Fig. 14. The c1osed-loop performance using NMPC will be shown in Fig. 1 6 in the next sub-section. 2.3.3. Multi-level contral of granulation pracesses under uncertainty
The optimal control study carried out so far is based on nominal models with out accounting for system uncertainties. However, control relevant models for chemical processes are normally subject to significant uncertainties. Unfortu nately, conventional open-loop optimal control techniques, such as that based on well-known Pontryagin's maximum principles or dynamic programming algo rithms, require highly accurate models. Otherwise the obtained optimal trajec tories used as set-points for c1osed-loop control are no longer optimal, leading to performance deterioration, or even process instability. The common practice in
Upper-Level Optimal Contro! under Uneertainty
Model for Optimal Contro!
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1------'--., Model Outputs
540
I .T. Cameron and F.Y. Wang
the process industries is to adopt a two-Ievel control strategy with different time scales, namely the upper-Ievel optimal control with large-time scales counted by hours or even days, and the lower-Ievel closed-Ioop control with fast dynamics adjustable in seconds. Obviously, significant profit losses are inevitable if major process disturbances andjor parameter uncertainties occur without a subsequent adjustment of set-points. That is, during a very long-time period, the upper-Ievel passes set-points to the lower level without modifications, which is considered as a one-way connection. In an attempt to design optimal dynamic systems under uncertainty, Mohideen et al. [76] proposed mini-max optimization algo rithms. The methodology is incorporated in the two-Ievel optimal control scheme by the authors together with the development of other practical methods [63]. These methods include the combination of uncertain parameters with state or manipulative variable to form pseudo-control variables, classification of uncer tainties into fast, intermediate and slow modes for the implementation of various techniques based on time scales, and the construction of optimal profile library, which can be selected on-line using logic rules. All of these new characteristics are incorporated in the ML-NMPC framework with two-way connections between control levels shown in Fig. 1 6. The proposed methods are applied to drum granulation processes described by PBEs. Uncertainties under study are se lected as both feed condition variations as weil as parameter perturbations. The practical methods for handling uncertainties for drum granulation proc esses have been tested by the authors [63], which are briefly summarized in this sub-section. It has been found that each method possesses advantages and disadvantages, which is only suitable for particular cases. However, if an inte grated framework is developed, the system is able to select the most suitable trajectories from the trajectory library, based on the measurement data. 2 . 3 . 3 . 1 . Mini- max optimization strategy
As pointed out previously, the mini-max optimization provides worst-case out comes. The objective function for the upper-Ievel optimal control is given by
{
{
Min max E[J(X(tf) , x(t), u (t) , p, d)] } u d p.
}
(53)
where E is the expectation operator, p and d are vectors of uncertain parameters and disturbances. This strategy could be very conservative when the worst-case does not dominate the operation. 2 . 3 . 3 . 2 . Method based on pseudo-manipulated variables
In the case that an uncertain parameter (Pm) is connected with a state variable (Xn) , and a pseudo-manipulated variable (up) can be formulated as folIows: (54)
541
Process Systems Engineering Applied to Granulation
Consequently, uncertainties can be partly removed in the upper-Ievel optimal control. The value of up obtained from optimal control allows the computation of the desired trajectory xn* with on-line identified parameter Pm in the lower-control level. This method will be demonstrated in a case study on granulation processes. 2 . 3 . 3 . 3 . Time-scale classification of uncertainties
Similar to state variables, uncertainties can also be classified into fast, intermediate and slow modes. For high-frequency uncertainties (fast mode), a mean-value ap proach is acceptable. The conventional one-way connection between two control levels may not lead to severe performance deterioration for uncertainties with very slow dynamics. Major attentions should be paid to uncertainties with intermediate frequencies (say the period is about 1/5-1/2 of the retention time). In this case, two-way connection is necessary with on-line set-point modifications. As an illustrative example, we choose parameter 8 1 in the kernel model de scribed by equation ( 1 9) as the uncertain parameter. It has been identified that the parameter 8 1 may change ± 5%. Since 8 1 is included in an exponential function, tremendous changes in overall coalescence kernel are observed. Figure 1 7(a) shows the increases of the mass in product-sized classes in three optimization 'Ci 30 � '"
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1 7. Open-Loop Optimal Control under Parameter Uncertainty.
300
542
I .T. Cameron and F.Y. Wang
simulations: ( 1 ) nominal 81 value, (2) 5% 81 reduction, and (3) mini-max opti mization between two 81 values. Corresponding manipulated variables are shown in Fig. 1 7(b). It can be shown that although an acceptable performance is ob tained, mini-max optimization cannot reach the real optimality. Figure 1 7(c) compares product trajectories between two cases: (1 ) optimization based on known parameters and (2) a pseudo-control variable consisting of the unknown parameter. The pseudo-control variable is given by (55) where c is a computable constant. Figure 1 7(c) indicates that the pseudo-control variable can lead to real optimality. In the case that the known parameter can be identified on-line, the real control variable can be determined using the model, which is shown in Fig. 1 7(d). The closed-Ioop behaviour predicted by NMPC is shown in Fig. 1 8. It is as sumed that the parameter 81 is reduced by 5% at the 4th-sampling interval out of total 20-sampling intervals. Figures 1 8(a) and (b) show that if the model used in the upper-Ievel optimal control is not modified, the process can also be forced to follow the specified trajectory, which is no longer optimal. If the modified model is used, about 47% reduction of the operational time can be achieved (283-1 50 s).
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1 8. NMPC for Batch Drum Granulation under Uncertainty.
250
300
Process Systems Engineering Applied to Granulation
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The necessity of the two-way link between upper- and lower-control levels can be justified using these simulation results. Wildeboer [77], in his PhD dissertation at the University of Queensland, de veloped an effective strategy for operation and control of granulators based on regime separation. In this strategy, he proposes the separation of the various processes that determine the granule properties, namely wetting and nucleation, aggregation and growth, and breakage and attrition, into separate vessels. It is clear that this approach provides better handles and enhances the attainable region. A similar strategy was successfully applied for emulsion polymerization problems [74], resulting in a facilitated approach for the underlying complex non-convex optimization problem. Thus, this regime-separation strategy is prom ising for future non-linear control developments. 2.4. Diagnostic and g uidance systems for granulation process operations
Stable operation of granulation systems, especially continuous drum granulation has continued to be a major challenge. With the advent of detailed models of granulation circuits, it is now feasible to develop convincing monitoring and dia gnostic systems that address the area of abnormal condition management. Early work in this area was carried out by Saelid et al. [78], where they con structed operator support through the use of models of various units within the plant, in this case a phosphate fertilizer operation in Norway. The work combined models of the process with fault trees and the use of Kaiman filters to estimate unmeasured states as a background to a diagnostic system built with the real-time expert system G2 [79]. The system assumed certain primary causes of disturbed operation and then the system monitored events to detect abnormal states. A backward search was conducted to find primary causes. If none were found then the operator was prompted to report conclusions or in the case of ambiguous outcomes the operator makes a decision on the likely cause. The work was done through plant simulations with no direct plant implementation at the time. The work by Scheibach [80] developed a real-time expert system based on root-cause analysis derived from a comprehensive HAZOP study of a granulation circuit. It used deep knowledge on granulation derived from an understanding of the mechanisms that play a role in particle formation and breakage. The diagno stic system was implemented in G2 and tested using a detailed dynamic simula tion of a commercial granulation circuit [81]. This showed the utility of such a system in detecting faulty states and then seeking to isolate the principal causes of such abnormal situations. Pattern recognition techniques are effectively applied to fault diagnosis. Tra ditional pattern recognition methods are suitable for one-to-one or many-to-one
544
I .T. Cameron and F.Y. Wang
mappings [82]. It can be seen from previous sections that granulation processes consist of four major regimes, namely, wetting and nucleation, consolidation, growth, and attrition and breakage with very different, or even confliet in the desired operating conditions. For example, binder size distribution from spray nozzles is very important in the wetting and nucleation regime with insignificant effects in other regimes. On the other hand, particle collision frequency and energy are essential in growth regime without major impact on other mecha nisms. Consequently, patterns in variables of granulation processes can be interpreted in different ways, which is classified as one-to-many mapping. An attempt has been made to remove this hurdle using a context-based recognition method [82], in which the current process regime (the context) is taken into account in the interpretation of an observed pattern. In pattern recognition, fea tures are classified into two categories: primary feature and contextual feature. Through the incorporation of contextual features, some ambiguous or erroneous characterizations can be clarified. It should be pointed out that the feature clas sification is not unique. For example, in two-dimensional PBM, both particle size and porosity are classified as primary features. However, in one-dimensional PBM, porosity is treated as one of the contextual features. This implies that model dimension reduction can be achieved through incorporation of proper diagnostic systems. We have applied the context-based recognition approach in an intuitive manner for granulation processes. A systematic study in order to develop a generalized algorithm and software package should be carried out. In a further development, Nemeth et al. [83,84] developed a hierarchical col oured Petri net (CPN) approach to the diagnosis problem by using a multi-scale view of the process that relied on a series of increasingly detailed models from circuit to equipment to mechanisms. This again relied on process models coupled with qualitative failure models that allowed the system to monitor operations and determine possible reasons for detected faults. Figure 19 shows a part of the CPN representation of the system. The figure shows some details of the wet granulation drum and the key symptoms, indicated in the hexagons, as part of the CPN system . Accompanying such a representation is the systems' fault logic tree based on HAZOP or Failure Mode Effects Analysis (FMEA) studies that allow extraction of symptoms and potential root causes. This logic tree is seen in Fig. 20 and consists of basic logic gates ("AND" and "OR") that capture the dependencies in the system. This logic provides the basis for construction of operator guidance systems (OGS) for abnormal condition management. The OGS can be constructed using integrative software systems such as Gensym's G2 real-time expert system. Such a system constructed using G2 is seen in Fig. 21 . Here the overall structure shows the principal tasks and functionality of the system. The G2 sys tem connects to both a simulation system containing a comprehensive dynamic model of the complete circuit and a PLC system that drives a drum granulation
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22. G2 operator interface to granulation plant diagnostic system.
pilot plant [85]. Figure 22 shows a typical operator interface screen that displays trends as weil as abnormal condition information. These systems require signifi cant time and effort to develop, especially the appropriate interface displays. The extended Kaiman filter (EKF) is one of the most popular model-based techniques for fault detection and diagnosis [86,87]. It has been realized that faults can be detected through the observation of changes of state variables as weil as parameters. This allows the unification of fault diagnosis with model based contro!. It can be shown that EKF can be integrated into a multi-level control framework described in Sections 2.2 and 2.3 with some additional efforts. In order to reduce the computational load, Chang and Hwang [86,87] have developed a simple procedure to decompose the filter model according to the precedence order of the state/parameter estimation processes. In their proposed approach, uncertain parameters are treated as additional state variables through the development of additional ordinary differential equations (dp/dtwhere p is the vector of parameters), allowing the application of Kaiman filter-based state es timation methods. In NMPC algorithms, on-line dynamic optimization techniques are implemented for the simultaneous determination of control variables and uncertain parameters with satisfactory results. So far, it appears that there are few commercial real-time diagnosis applica tions in granulation plants. They tend to be expensive to develop in terms of time and effort and require significant background studies to fully understand the sys tem failure dependencies and the dynamics associated with those failure modes. However, the current developments in academe and the interest in industry provide a high possibility of providing advanced monitoring and model-based diagnosis in commercial operations. These examples of diagnostic systems show the potential to apply systems engineering approaches to complex operational problems such that operators are
Process Systems Engineering Applied to Granulation
549
weil informed, are able to quickly diagnose abnormal conditions, test quickly possible solutions via detailed simulations and then proceed to apply corrective actions. They will become effective tools as the benefits are realized by the granulation industry as production margins tighten. 3. FUTURE CHALLENGES IN PROCESS SYSTEMS APPROACH ES TO GRANU LATION
The previous sections have given a brief outline of the breadth and depth of some PSE approaches to granulation systems. The potential areas of application are enormous and are spread across the life cycie of product and process. These areas have been identified and the contributions of PSE in general engineered systems have been highlighted. In particular, we have concentrated on the ap plication of operation al PSE techniques such as advanced control and diagnosis systems in this chapter. Many other relevant areas can be tackled by these holistic methods firmly based on systems concepts. The following comments summarize the key challenges in process systems applications in the granulation area. They inciude: •
•
•
•
•
•
An increased awareness by industry, and in particular senior managers in commercial and industrial organizations of the benefits to be derived by the application of systems approaches to granulation design, operation and proc ess evolution. Advanced control, for example, can routinely deliver a benefit of 5% of turnover costs, even for well-operated processes, let alone for those that are poor performers. A life cycie perspective on product and process development that takes a holistic view from cradle-to-grave, such that early life cycie phase decisions are done with ciear consideration of the implications on later stages such as the operation al phase. The appreciation, analysis and use of both steady state and dynamic analysis of granulation systems in order to improve existing process designs, enhance operational stability, improve quality control and optimize the system. The development of robust multi-scale methods for the modelling, solution and analysis of granulation systems as a means of improving existing designs and the generation of innovative new designs for granulation, such as regime sep arated devices [77]. The intimate linking of new theoretical findings in granulation mechanisms and kinetics into a coherent modelling framework such that deeper understanding of the contributions and interactions of these key aspects are appropriated for design and operation. This is an inherent systems approach. The application of linear and non-linear model-based control to a wide range of granulation systems for the improved control of product quality, system stability
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and increased thraughput in the face of raw material variations and systems disturbances. The key issue of reliable, in situ, on-line measurement methods is crucial to advanced contral applications. This covers particle size distributions, moisture, segregation patterns, phase determinations in reacting systems and the like. PSE has a central role to play in advancing granulation practice across many industry sectors. The power that such an approach affords has been recognized and utilized in many other application areas. Its further application in granulation technology and practice is long-overdue. REFERENCES [1] M . E.C. Hull, K. Jackson, AJ.J. Dick, Requirements Engineering, Springer, UK, 2004. [2] T.J. Williams, Systems Engineering for the Process Industries, McGraw-HiII, New York, 1 96 1 . [3] K.M. Hangos, I .T. Cameron, Process Modelling and Model Analysis, Academic Press, San Diego, 200 1 . [4] I .T. Cameron, Computer-Aided Chemical Engineering Series Volume 20: European Symposium on Computer Aided Process Engineering- 1 5, L. Puigjaner, A Espuna (Eds.), Elsevier, Amsterdam, 2005, pp. 3-1 9. [5] K.S. Rosselot, D.T. Allen, Chapter 1 3: Life-Cycie Concepts, Product Stewardship, and Green Engineering, in: DT Allen, D. Shonnard (Eds.), Green Engineering: Environmentally Conscious Design of Chemical Processes, Prentice-Hall PTR, Upper Saddle River, NJ, 2002. [6] LT. Cameron, F.Y. Wang, C.D. Immanuel, F. Stepanek, Chem. Eng. Sci. 60 (2005) 3723. [7] I. Grossmann , A Westerberg , Research Challenges in Process Systems Engineer ing, unpublished paper, Carnegie Mellon U niversity, USA, 200 1 . [8] G.D. Ingram, LT . Cameron, K.M. Hangos, Chem. Eng. Sei. 5 9 (2004) 2 1 71 . [9] G . D. Ingram, LT. Cameron, Proc. APCChE 2002jChemeca 2002, Christchurch, New Zealand, 2002, Paper No. 554. [ 1 0] J . N . Michaels, Powder Technol. 1 38 (2003) 1 . [1 1 ] LT. Cameron, Proc. 1 4th I nt. Drying Symp. (lOS 2004), (2004) 3-1 7. [ 1 2] W. Marquardt, Comput. Chem. Eng. 20 (6j7) ( 1 996) 591 . [ 1 3] K.K. I rikura, D.J. Frurip, ACS Symp. Ser. 677 ( 1 998) 2-1 8. [ 1 4] J.J. McCarthy, J.M. üUino, Powder Technol. 97 (2) (1 998) 9 1 . [ 1 5] P T Cummings, Proc. ESCAPE-1 1 , R Gani, S.8. J 0rgensen (Eds.), Kolding, Denmark, (200 1 ) 1-1 2. [ 1 6] C.C. Pantelides, Proc. ESCAPE-1 1 , R Gani, S.8. J 0rgensen (Eds.), Kolding, Denmark, (200 1 ) 1 5-26. [ 1 7] CD. Han, Chem. Eng. Sci. 25 ( 1 970) 875. [ 1 8] C.D. Han, I. Wilenitz, Ind. Eng. Chem. Fundam. 9 (3) (1 970) 401 . [ 1 9] EH 8ristol, IEEE Trans. Auto. Control AC-1 1 ( 1 966) 1 33. [20] OE Seborg, T.F. Edgar, DA Mellichamp, Process Dynamics and Control, Wiley, New York, 2004. [21 ] M.J. Hounslow, RL. Ryall, V.R MarshalI, AIChE J 34 ( 1 1 ) ( 1 988) 1 82 1 . [22] F.Y. Wang, P . 8ahri, P.L. Lee, I .T. Cameron, i n Comput.-Aid. Chem. Eng. 1 58: Proc. 8th Int. Symp. Process Syst. Eng. (PSE 2003), 8I Chen, AW. Westerberg (Eds.), Elsevier, Amsterdam, 2003, pp. 1 064-1 069.
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[23] F.Y. Wang, P. Bahri , P.L. Lee, I.T. Cameron, Computer-Aided Chemical Engi neering Series Volume 20: European Symposium on Computer Aided Process En gineering-1 5, L. Puigjaner, A. Espuna (Eds.), Elsevier, Amsterdam, 2005, pp. 1 1 1 1 -1 1 1 6. [24] A. D . Randolph, M A Larson, Theory of Particulate Processes, 2nd edition, Academic Press, San Diego, 1 988. [25] D. Ramkrishna, Population Balances: Theory and Applications to Particulate Systems in Engineering, Academic Press, San Diego, 2000. [26] S. Kumar, D. Ramkrishna, Chem. Eng. Sci. 51 ( 1 996) 1 3 1 1 . [27] S. Kumar, D. Ramkrishna, Chem. Eng. Sci. 51 ( 1 996) 1 333. [28] N. Balliu, An Object Oriented Approach to the Modelling and Dynamics of Granulation Circuits, PhD Thesis, School of Engineering, The University of Queensland, Australia, 2004. [29] Y. Liu, I .T. Cameron, Chem. Eng. Sci. 56 (200 1 ) 5283. [30] Y. Liu, I .T. Cameron, Powder Technol . 1 30 (2003) 1 8 1 . [31 ] LA Spielman, O . Levenspiel, Chem. Eng. Sci. 20 (1 965) 247. [32] B . H . Kaye, Powder Mixing, Chapman and Hall, London, 1 997. [33] J . R.P. Gooch, M.J. Hounslow, AIChE J 42 (7) ( 1 996) 1 864. [34] M. Smith, T. Matsoukas, Chem. Eng. Sci. 53 (9) (1 998) 1 777. [35] P.A.L. Wauters, Modelling and Mechanisms of Granulation, PhD thesis, The Delft U niversity of Technology, The Netherlands, 2001 . [36] M.J. Goodson , M. Kraft, S. Forrest, J. Bridgewater, Proc. 2nd I nt. Conf. Popul. Balance Model . , Valencia, Spain, 2004. [37] A. Vikhansky, M. Kraft, J. Comput. Phys. 200 (2004) 50. [38] C.D. Immanuel, F.J. Doyle 1 1 1 , Chem. Eng. Sci. 58 ( 1 6) (2003) 368 1 . [39] C.D. Immanuel, F.J. Doyle 1 1 1 , Powder Technol . 1 56 (2/3) (2005) 2 1 3. [40] F.Y. Wang, X.Y. Ge, N. Balliu, I .T. Cameron, Chem. Eng. Sci. 61 (2006) 257. [4 1 ] L.x. Liu, J.D. Litster, S.M. Iveson , B.J. Ennis, AIChE J 46 (3) (2000) 529. [42] L.X. Liu, J.D. Litster, Chem. Eng. Sci. 57 (2002) 21 83. [43] B.J. Ennis, J.D. Litster, Chapter 8: Size Enlargement. In: R.H. Perry, DW. Green, J.O. Maloney (eds), Perry's Chemical Engineering Handbook, 7th edition, McGraw Hili, New York, 1 997. [44] S.K. Friedlander, Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics, 2nd edition, Oxford University Press, New York, 2000. [45] P.C. Kapur, DW. Fuerstenau, Ind. Eng. Chem. Pro. Des. Dev. 8 ( 1 969) 56. [46] P.C. Kapur, Chem. Eng. Sci. 27 (1 972) 1 863. [47] KVS. Sastry, Int. J . Mineral Process. 2 ( 1 975) 1 87. [48] A.M. Golovin , Sov. Phys. Dok!. 8 ( 1 963) 1 9 1 . [49] A A Adetayo, J.D. Litster, S.E. Pratsinis, B.J. Ennis, Powder Techno!. 82 (1 995) 37. [50] A.A. Adetayo, B.J. Ennis, AIChE J 43 ( 1 ) ( 1 997) 927. [51 ] S.M. Miller, J.B. Rawlings, AIChE J 40 (8) (1 994) 1 3 1 2. [52] J.B. Rawlings, S.M. Miller, W.R. Witkowski, Ind. Eng. Chem. Res. 32 ( 1 993) 1 275. [53] F.Y. Wang, I.T. Cameron, Powder Techno!. 1 24 (2002) 238. [54] A. Schroder, I.T. Cameron, Proc. AusIMM'98 - The Mining Circle, Mount Isa, Australia, 1 998 37 1 -380 [55] S. Watano, T. Numa, I. Koizumi, Y. Osako, Eur. J. Pharm. Biopharm. 52 (2001 ) 337. [56] S. Watano, T. Numa, I. Koizumi, Y. Osako, Powder Techno!. 1 1 5 (200 1 ) 1 24. [57] PA Webb, C. Orr, Analytical Methods in Fine Particle Technology, Micrometrics I nstrument Corporation, 1 997. http://www.micrometrics.com. [58] K.R. Morris, S.L. Nail, G.E. Peck, S.R. Byrn, U .J . Griesser, J.G. StowelI, S.-J. Hwang, K. Park, Pharm. Sci. Technol. Today 1 (1 998) 235. [59] S. Shahhosseini, I .T. Cameron, R.B. Newell, F.Y. Wang, E.T. White, E .T. , Proc. 25th Australia and New Zealand Chem. Eng. Conf., CHEMECA'97, New Zealand, 1 997.
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[60] H. Leuenberger, Powder Technology and Pharmaceutical Processes, in: D. Chulia, M. Deleuil, Y. Pourcelot (Eds.), Handbook of Powder Technology, vol. 9, Elsevier, Amsterdam, 1 994, pp. 337-389. [61] A Faure, P. York, RC. Rowe, Eur. J. Pharm. Biopharm. 52 (200 1 ) 269. [62] H.G. Kristensen, T. SChaefer, Drug. Dev. Ind. Pharm. 13 ( 1 987) 803. [63] F.Y. Wang, LT. Cameron, Proc. 7th World Congr. Chem. Eng. (WCCE 7), Glasgow, Scotland, 2005. [64] J. Zhang, JD. Lister, F.Y. Wang, I .T. Cameron, Powder Technol. 1 08 (2000) 1 22. [65] J . Nielsen, J . Villadsen, G. Liden , Bioreaction Engineering Principles, 2nd edition, Kluwer Academic, New York, 2003. [66] K.L. Teo, C.J. Goh, K.H. Wong , A Unified Computational Approach for Optimal Con trol Problems, Longman Scientific and Technical, New York, 1 991 . [67] MA Branch, A Grace, MATLAB Optimization Toolbox User's Guide, The Math Works Inc., Natick, 1 996. [68] PR. Mort, S'w. Capeci, J ,W. Holder, Powder Technol. 1 1 7 (200 1 ) 1 73. [69] T. F. Edgar, Comput. Chem. Eng. 29 (2004) 4 1 . [70] M . Pottmann, B A Ogunnaike, A A Adetayo, B.J. Ennis, Powder Technol. 1 08 (2000) 1 92. [71 ] E.P. Gatzke, F.J. Doyle 1 1 1 , Powder Technol. 1 21 (2001 ) 1 49. [72] AP. Patwardhan, G.T. Wright, T.F. Edgar, Chem. Eng. Sci. 47 (4) ( 1 992) 721 . [73] A P . Patwardhan, T.F. Edgar, I nd. Eng. Chem. Res. 32 ( 1 993) 2345. [74] CD. Immanuel, F.J. Doyle 1 1 1 , AIChE J 49 (9) (2003) 2383. [75] T.J. Crowley, E.S. Meadows, E. Kostoulas, F.J. Doyle 1 1 1 , J. Process Control 1 0 (2000) 4 1 9. [76] M.J. Mohideen, J.D. Perkins, E.N. Pistikopoulos, AIChE J 42 (8) (1 996) 225 1 . [77] WJ. Wildeboer, Design and Operation of Regime Separated Granulators, PhD Dis sertation, U niversity of Queensland, 2002. [78] S. Saelid, A Mjaavatten, K. Fjalestad, Proc. Eur. Symp. Comput. Aid. Process Eng. 1 , Eisinore, Denmark, 1 992, pp. S97-S 1 08. [79] Gensym, 2005. http://www.gensym.com/. [80] D. Scheibach, Development of Granulation Circuit Diagnostics for Gensym's G2 In telligent Control System, Thesis, Department of Chemical Engineering, U niversity of Queensland, 2000. [81] N. Balliu, LT. Cameron, RB. Newell, Proc. 6th World Congr. Chem. Eng., Melbourne, Australia, 2001 , Paper No. P3- 1 38. [82] R Srinivasan, C. Wang, WK. Ho, K.W Lim, Chem. Eng. Sci. 60 (2005) 935. [83] E.R Nemeth, K.M. Hangos, LT. Cameron, Hierarchical CPN Model-Based Diagnos tics Using HAZOP Knowledge, Tech Tep. Sys & Control Lab SDCL-002/2004, MTA SZTAKI, Budapest, Hungary, 2004. [84] E. Nemeth, LI. Cameron, K.M. Hangos, Comput. Chem. Eng. 29 (4) (2005) 783. [85] E. Nemeth, R Lakner, K.M. Hangos, I .T. Cameron, Computer-Aided Chemical En gineering Series Volume 20: European Symposium on Computer Aided Process En gineering- 1 5, L Puigjaner, A Espuna (Eds.), Elsevier, Amsterdam, 2005, pp. 535-540. [86] C.T. Chang, J . 1 . Hwang, AIChE J 44 (6) ( 1 998) 1 392. [87] C.T. Chang, J.1. Hwang, Chem. Eng. Sci. 53 (22) (1 998) 3853.
CHAPTER 1 2 Agg l omeration of Enzymes , M icro-organisms and F l avo u rs Gabrie M . H . Meesters8, b , *
aOSM-Food Specialties, P.O. Box 1, NL-2600 MA Oelft, The Netherlands bOelft University of Technology, Julianalaan 136, NL-2628 BL Oelft, The Netherlands Contents 1 . Agglomerated enzymes, micro-organisms and yeast hydrolysates for food applications 1 . 1 . Micro-organisms and enzyme formulations 1 . 1 . 1 . Micro-organisms 1 . 1 .2. Solid yeast formulations 1 . 1 .3. Formulated bacteria 1 .2. Enzyme formulations 1 .2. 1 . Detergent enzyme formulations 1 .2.2. Starch degrading and glucose isomerizing enzymes 1 .2.3. Enzyme formulations for the baking, beverage and dairy industries 1 .2.4. Enzyme formulations for the feed industries 1 .3. Conciusions 2. Hygienic design of food equipment and process lines 2. 1 . Hygienic design and certification 2.2. Materials of construction for equipment processing dry materials 2.3. Validation and certification 3. Drying of sticky materials such as yeast extracts 3. 1 . The production process 3.2. Drying of a yeast extract liquid 3.3. Conciusions References
555 557 557 557 557 559 559 568 569 570 573 574 576 578 579 580 583 583 588 588
1 . AGGLOMERATED ENZYMES, MICRO-ORGANISMS AND YEAST HYDROLYSATES FOR FOOD APPLICATIONS
In many food applications micro-organisms, enzymes, proteins or hydrolysed pro teins and nucleotides are used. In many cases these additives increase the stability of a product, improve the taste or texture of the product, or otherwise modify the food product. * Corresponding author. E-mail: Ga [email protected]
Granulation Edited by A.D. Salman, M.J. Hounslow and J. P. K. z; Elsevier BV All rights reserved
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Micro-organisms are typically used in the baking field. Here the bakers yeast Saccharomyces Cerevisiae is among the most produced organisms. The func tion is to produce gas, to allow the dough to expand and to produce certain enzymes, which help the dough to develop in the right way. Lactic acid bacteria are produced for their use in the production of yoghurts and cheeses and for the production of probiotics. For the production of yoghurt the main activity is to acidify the milk and to make it more viscous. Due to this action the fermented milk can be kept for a longer period of time. The flavour and mouth feel of the yoghurt is also influenced by the type of the culture that is used. During the manufacturing of cheese the main function of these bacteria is the formation of flavour-producing enzymes. These enzymes are released during the growth of the organisms and when they fall apart and die. The probiotic bacteria are used to increase the gut health of humans and some animals. Here the micro-or ganisms have to survive the journey through the stomach and the small intestine to be able to grow out in the large intestine, where they employ their beneficial qualities. All these micro-organisms need to be formulated in such a way that they are able to be stored in for application, days, weeks or months, after they have been produced. When they are to be used in a few days, the liquid formulations are most often employed. When they need to be stored for a longer period of time, these micro organisms are mostly dried and formulated such that they will show new growth in their final application, even after a year of storage. Enzymes are, on an industrial scale, mostly produced by yeast, fungi and bacteria. Enzymes are proteins that catalyse specific reactions. Typically, these enzymes are used to hydrolyse starch, convert glucose into fructose, hydrolyse proteins, phytate etc. By doing this they perform the reactions that we want, but often the result of the reactions catalysed by these enzymes change structure of cheese or dough, enhance colour, remove stains etc. Specifically, these enzymes are typically formulated to their application field. Often the formulation helps the enzyme to survive the application environment, which can be harmful for the enzymes. The specific areas of application and their specific formulation needs will be discussed in the following chapters. Several enzymes are used to hydrolyse proteins and nucieotides, which after the hydrolysis will be used as flavour enhancers in foodstuffs. These hydro Iysed products are mainly obtained by hydrolysing yeast proteins and nucieo tides. The hydrolysed products are put in all kinds of savoury products like soups and sauces, but are also used on chips and snacks. They can be given a speCial taste (beefy, chicken, roasted), depending on the enzymes used for hydrolysis. The following chapters will deal with the specific needs for agglomeration to formulate the above-mentioned products in a way that they will be able to show the desired activities in their applications.
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1 . 1 . Micro-organisms and enzyme formu lations 1. 1. 1. Micro-organisms
There are different ways micro-organisms can be formulated into a dry form. The reason for these dry formulations is mainly stability (also called viability). The micro organisms are kept in a kind of resting state, so that as soon as they come to be used and there is water present they will hydrate again and start to grow again. Most of the solid formulations of micro-organisms are found for yeast, especially bakers yeast, and bacteria, mostly the bacteria used for making yoghurts, probiotics and cheese. 1. 1.2. Solid yeast formulations
The use of yeast for baking bread goes back more than 1 0,000 years. A lot of yeast used for baking purposes was made as liquid or a pressed block; these are called the fresh compressed yeasts. Active dry yeast were also developed, but the invention of instant dry yeast by DSM Bakery Ingredients some 30 years aga was based on extrusion and drying the yeast pellets. This product is in a dry state, and the yeast becomes active when water activity rises. Since it is so easy to use and requires no pre-soaking, many industrial but also artisanal and ho me bakers are using it. Normally, the viability of fresh yeast is only a few days to a week or two. The viability of the instant yeast formulations is at least two years, when stored in a cool place. These instant yeasts need to dissolve quickly in dough and disperse easily when the dough is kneaded. At the same time the yeast have to become alive quickly, within less than half an hour. The main action here is to concentrate a fermentation broth containing the yeast by centrifugation. After a subsequent filtration, the wet cake is processed through an extruder where the extrudates are cut off at the end of barrel, at the die-plate and dried in a fluidized bed. After packaging the product is marketed as Fermipan�R: [1]. 1. 1.3. Formulated bacteria
Most of the formulated bacteria are found in the field of dairy applications. Spe cific bacteria are grown and concentrated to be added to the curds of cheese to enhance the ripening or give specific taste. Also the production of yoghurts is started by adding starter culture. Depending on the strain used, different types of yoghurts will be produced. These bacteria are either cultured and formulated as concentrated liquid, as freeze-dried powder or as a frozen liquid. Also fermented sausages like salami are made by adding bacteria, which enables the fermen tation of the meat. Another category is probiotics [2]. They are live micro organisms (like Lacto bacilli and Bifidobacterium species) that, when administered in adequate
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amounts, benefit the gut-health of the persons using them. Here too liquid for mulations are sold, which can be kept for a maximum of a few weeks (e.g. Yakult ® and Actimel ®). Also, probiotics mixed into yoghurts are found. Solid formulations can be found as weil , which can be kept for several months without loosing too much of the viability of the bacteria. The freeze-dried cultures are offen compacted and put into capsules or are tabletted. The capsules and tablets are sold in bottles or in blisters (see Figs. 1 and 2). Companies producing these cultures are Chr. Hansen, Rhodia, Danisco, Rosell-Lallemand, DSM-Food Specialties and others. The probiotic market is a
Fig. 1 . Capsule formulation.
Fig. 2. Tablet formulation.
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500 .------,
_ EU 400
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USA
300
:J c
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200
1 00
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3. Probiotic markets in the EU and the USA [3) .
fast-growing market, which fits into the fast-growing field of neutraceuticals. Figure 3 shows how the market is developing in Europe and USA. The solid probiotics formulations are often freeze dried and granulated or spray dried and granulated powders. Often stabilizers are added to ensure proper vi ability, survival through the stomach and enhanced storage stability. The survival through the stomach is the most critical. After passing the stomach, these pro biotic bacteria can survive easily in the gut. To be able to pass the stomach, the dried cultures are often put in a capsule or are tabletted and optionally coated with an acid-resistant coating. Viability losses during freeze-drying are mainly caused by the osmotic shock and membrane failures due to ice-crystal formation and recrystallization of these crystals. During spray drying the cells are mainly damaged by heat and rapid dehydration. Protectants for the bacteria during drying can enhance the viability of the cultures. Many cryoprotectants can be used, like sugars (trehalose, maltose, lactose and sucrose), polysaccharides (maltodextrins and starches), glycerol, ascorbate etc. Typical solid formulations of the dried cultures are fat-containing gelatine-coated capsules (e.g. Jintan company), hard gelatine capsules (e.g. ehr. Hansen, Denmark), multi-Iayered tablets and powders (e.g. Lactiferm from Medipharm AB in Sweden). 1 .2. Enzyme formulations 1 . 2. 1. Detergent enzyme formulations
The large-scale use of formulated enzymes started in the early 1 960 by the addition of these proteins into laundry detergents. These enzymes were mainly
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proteases, which help the removal of certain stains during the washing of clothes. The enzymes were made using large-scale fermentation processes, from which the proteins were recovered by acetone precipitation or by liquid concentration. The dried enzymes were added to the detergent formulation in a powder form. The main producers of these enzymes were Novo-Nordisk in Denmark and Gist brocades in the Netherlands. By the end of the 1 960s it showed that these powdered enzymes caused major allergic reactions at the end-users, mainly women at that time, in the United Kingdom. This resulted in a major problem for the enzyme producers. The market then collapsed to almost zero. The solution came by granulating these enzymes into larger low-dusting particles. Novo-Nordisk developed first a prilling process, shortly followed by an extrusion spheronization process) [4]. Gist-Brocades developed a prilling process [5]. The first prills were marked without an outer coating. This changed quickly into a coated prill formulation when it showed that the coated reduced the amount of airborne enzyme dust enormously. The enzymes are dissolved or dispersed into the molten liquid. The composition of the Novo-Nordisk extrusion-spheronization formulation is given in Table 1 , the Gist-brocades prill formulation is given in Table 2. The enzyme powder consists of pure solid enzyme, salt and stabilizers. The extruded mass is spheronized to get small spherical particles in a so-ca lied Mar umerizer at around 500-2000 rpm. Marumerizing is a spheronization technique, which aims at the generation of nearly spherical particles from extruded cylinders. Often the particles are near spherical or rounded-off cylinders. The prill mixture was heated to 60-80°C and continuously prilled over a wheel (spinning disk) producing many droplets that fall down in a tower, where they are cooled below the melting point (around 55-60°C) and collected at the bottom of the tower. Figure 4 shows the spinning disk used. These prills where in a separate machine coated with a waxy-unctuous coating, containing paraffin oil and stearic acid. The amount applied to the prills was 1-5 wt% of the prill weight. The coating was applied batch wise by mixing the prills in a Nauta Blender (Hosokawa), where the waxy material is distributed over Table
1. Novo-Nordisk extrusion-spheronization formulation [4]
Compound Enzyme powder Binder (e.g. PVP, sugars) Water-soluble salts Water-insoluble salts Coconut mono-ethanol-amide Ti0 2 Water
Wt% 5-30 1-10 40-60 5-20 4-7 0-4
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Table 2. Gist-brocades prill formulation [5]
Compound Non-ionic or PEG 6000 Soy oil Ti0 2 BHT PVP CaS04 . . 1j2 H 2 0 Enzyme powder Builder (Na2 S04) ·
Wt% present in formulation 42-56 0.6 0.1 1 .5 5 25 (maximum) 1 7-63
N B : O N LY HA L F OF. THE TOUl NUIo4 BE R OF S LOTS ARE SHOWN FOR C LARITY .
Fig.
4. Drawing of the rotating wheel used in the Gist-brocades prilling process.
the prills, after which about 1 wt% of Si0 2 (aerosol) was added to make the prills free flowing again. A process overview is given in Fig. 5. During the 1 970s, the Gist-brocades prill formulation was further optimized to reduce the formation of enzyme dust during handling. Novo-Nordisk switched to a
562
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!"" c - 'T'IQ I t
G. M. H. Meesters
-i?1� -
r
CO l d
a i r'
t::::=== coer5e
Fig.
5. Schematic overview of the Gist-brocades prill process.
new formulation based on batch high-shear granulation. This technology proved to be more robust than the extrusion spheronization technique. Novo-Nordisk formu lated the new granules by adding fibres to the formulation [6,7]. These fibres (which were cellulose based) increased the strength of the formulated product enor mously. After high-shear granulation, the product is dried in a fluid-bed drier after which a coating of Polyethylene Glycol is applied as a melt in another high-shear granulator or as a solution of dissolved PEG in water in a fluid bed. They gave the product the name Granule T. This process is more flexible than the prill process of Gist-brocades, since liquid enzyme formulations as weil as solid enzyme powders can be used. Table 3 shows the typical formulation recipe and Fig. 6 the process. In the 1 980s, the enzyme-dust levels, which were allowed in the air during handling at the detergent manufactures became even more strict. The end users no longer had any allergie reaction problems, but cases were being found at detergent manufacturing sites. This pushed Gist-Brocades to develop a contin uous process to manufacture a formulated enzyme product that was highly flex ible and did not break during loading. A fork-lift could run over these granules causing them to flatten, but the particles were so flexible that the initial shape returns after the load is removed. These granules were proven to result in very little airborne particles containing enzymes. The name of this formulation was MOM [8]. The formulation is found in Table 4.
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Table 3. Novo-Nordisk High Shear formulation (Granule T) [6,7]
Compound Enzyme powder or liquid Cellulose fibres Water Filler (e.g. Na2 S04) Colouring agent
Wt% of final product 5-90% (in practice 5-40%) 2-40% 1 0 (maximum) 0-70 1-3
enzyme
wat.er
f l lJ I d
...
b i nder
bed dr-yer-
r l bbon b l ender-
Fig.
6. Schematic overview of the Novozymes high shear granulation plant.
In the 1 980s, more enzyme producers came into the market. Novo-Nordisk stuck to the Granule T concept, which was copied by Showa Denko with the difference of using artificial fibres instead of cellulose-based fibres. Table 5 shows the Showa Denko formulation recipe [9, 1 0].
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Table 4. Gist-brocades MOM formulation [8]
Compound Modified starch Enzyme powder Sugar Sorbitol Ti02 Glycerine Paraffin Non-ionic (Lorol C-1 8)
Wt% of final product 45 20 16 6 4 4 3 2
Table 5. The Showa Denko formulation [9]
Compound Enzyme Artificial fibres Waxy materials (binder) Fillers Colorants
Wt% 1 7-1 9 1-1 0 1 0-35 42-69 4
Solvay enzymes developed a formulation similar to the old Novo-Nordisk ex trusion spheronization technology. Their typical composition is given in Table 6. Clearly, a very complex and expensive formulation. Miles enters the enzyme field by using a fluid-bed coating layering technique. By the end of the 1 980s, many players were competing in the field of enzyme formulation, mainly for use in laundry detergents. This continued into the early 1 990s. Henkel joined the field by using a con tinuous pressure extrusion technology, different from the old Novo-Nordisk and Solvay formulations [1 2-1 4]. At the same time Gist-brocades saw the end coming for its prilling technology, since the formulation cost was too high and only en zyme powders can be used in the formulation. The use of powders remained a health risk during manufacturing. Because of this risk water-based enzyme re covery lines were developed, resulting in a concentrated enzyme liquid. The MOM technology was developed for use of enzyme powders, although liquid could be applied. This MOM technology also proved to be too expensive to compete with the other formulations and methods used. In the mid-1 990s, Genencor International entered the field of enzyme produc tion , using the Miles technology [15] to make layered enzyme granules. A sche matic drawing of a top spray fluid-bed coater is given in Fig. 7.
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Table 6. Typical Solvay Enzyme's formulation [1 1 ]
Compound Cellulose Kaolin CaC0 3 Flour Starch Na2 S04 Polyethylene glycol 3000 Polyvinylpyrrolidon K-90 Lactose Ca-formiate Enzyme (Water content during extrusion)
Wt% 23 11 6 8 13 9 11 0.8 4.5 2.2 1 1 .5 (30)
Fig. 7. Schematic drawing of the top spray coater as used by Genencor International for their Enzoguard formulation (courtesy from Glatt GmbH, Binzen, Germany).
Gist-brocades was developing a similar technology at the time. The Genencor formulation was named Enzoguard. The composition is found in Table 7. The technology used is a batch top-spray fluidized-bed process 1 6 , 1 7]. A Schematic diagram of the Enzoguard formulation is given in Fig. 8, a picture of a multi-Iayered particle in Fig. 9.
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G. M. H. Meesters
Table 7. Enzoguard formulation of Genencor International [ 1 6 , 1 7]
Compounds Core material (sugar or salt based) PVA-coating Enzyme layer Scavenger layer ((NH4 hS04) Outer coating (pigment and PVA) Neodol over coating
Wt% of the final formulation 20-80 01-2 0.1-20 5-50 1-20 0.1-5
Enzoguard™
• • • • • •
Solid core PVA-Iayer Enzyme layer (NH4hS04 lay Polymer + pigmen Neodol coating
. . . . . . 20-80%
. . . 1 -2%
Fig. 8. Schematic drawing of a fluid bed coated particle, representing the typical layers as found in the Genencor International formulation ca lied Enzoguard [ 1 6 , 1 7].
Fig. 9. Cross section of a fluid-bed-coated layered particle (courtesy Glatt GmbH, Binzen, Germany).
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Table 8. Typical Granule TX formulation of Novozymes [ 1 8 , 1 9]
Compound Bentonite ASB 350 Fibrous cellulose Arbocel BC200 Carbohydrate binder Crystalline enzyme Amorphous enzyme Filler; Ground Na2 S04
Wt% 10 15 11 2 9 54
During the mid-1 990s, several companies were bought by others. Novo-Nor disk acquired Showa Denko, while Genencor International acquired the industrial enzymes divisions of Gist-Brocades and Solvay. Owing to these takeovers, at the end of the 1 990s two-major players were left in the field, Novo-Nordisk and Genencor International, both with a market share of around 40%. Henkel stayed in detergent enzyme manufacturing as weil; mainly for there own captive use. The enzyme formulations at that time were further optimized. Novo-Nordisk developed a new generation of detergent enzymes called Granule TX, based on the old Granule T concept [1 8, 1 9] A typical TX formulation of Novozymes is given in Table 8. The advantage of using crystalline enzymes in the formulation is the higher stability of the enzymes, as weil as higher enzymatic content that can be contained in the granules. Genencor International stayed with fluidized-bed coating and layering as their preferred technology. They developed a new one, more matrix type of formu lation, using the same fluidized-bed technology [20,21] . By dispersing the en zyme more through the granule, instead of having a concentrated enzyme layer, less dusting problems were seen. Table 9 gives an example of this formulation. Henkel continued producing their granules by the extrusion technology they de veloped in the early 1 990s. The main driver for these companies when entering the 2000 era was opti mization towards less dust formation, enzyme stability and detergent compati bility. Not only there were several variations of proteases formulated using these techniques but also other enzymes including different types of amylases, cellu lose and lipases. Each of these enzymes has its own specific problems with respect to stability and allergenicity. Also the field of applications has broadened. Next to laundry detergent powders and tablets, automatie dish wash detergent powders and tablets are using enzymes. During this tabletting process the en zyme granules have to be strong enough to withstand the tabletting process and are not allowed to break.
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G. M. H. Meesters
Table 9. Typical example of the Genencor I nternational Matrix granule using a fluid-bed
technology [20,21]
Compound Core: sucrose Enzyme layer corn starch Sucrose UF concentrate solids
Wt% 25 1 7.8 1 7.8 5.2 20
2nd layer MGS04 .7 H 20 3rd layer Purecote 790 Methyl cellulose A 1 5 Neodol PEG 600 Ti02
2.5 2.5 1 .5 1 .7 6
• • •
•
• • • •
Novo-Nordisk, which changed their name to Novozymes at that time, and Genencor International are currently at a stage that these formulations are nearly perfect with respect to dust formation and stability. Enzyme dust issues are now more a question of proper handling of the detergent manufacturers than the fact that these granules are not good enough to do their job. 1 . 2. 2. Starch degrading and glucose isomerizing enzymes
To degrade starch to sugar monomers and to isomerize glucose into fructose, enzymatic processes have been developed. These processes and enzymes run at elevated temperatures of 50-70 °C and operate in highly concentrated subst rate conditions. Typically these formulated enzymes are immobilized and remain in the reactor for several weeks or even months. The driving factors for formu lating these enzymes are the cost of producing the formulations as weil as the lifetime of these granules. In the 1 970s and 1 980s, Novo-Nordisk used an extrusion process to make granules, which were subsequently cross-linked chemically to prevent these granules from falling apart in the reactor. Gist-brocades used a prilling process where the gelatine-based prills were made by using a liquid submerged nozzle [22-24]. The liquid gelatine prills were hardened in the liquid (water immiscible liquid) due to cooling, after which they were cross-linked with glutaric aldehyde.
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Miles used a system similar to Novo-Nordisk, an extrusion process, but they used two cross-linking agents instead of one [25]. Another process was de scribed by Anheuser Busch [26,27], where glucose isomerase is mixed with agar. This mixture was hardened with an organic solvent, after which the gelled par ticles were dried. Owing to the takeover of Solvay enzymes and Gist-brocades Industrial en zymes division, Genencor International became the largest producer of these types of enzymes, with Novo-Nordisk the second largest player in that field. During the 1 990s less of these enzyme formulations were used, and the starch and glucose producing industries turned to the use of ion-exchange base enzyme reactors. Here, the enzymes were coupled to an ion-exchange resin, which was kept in the reactor. When the enzyme activity drops, the enzymes are washed out by, e.g., increasing the conductivity or changing the pH value. After removal of the old enzymes, a new batch of enzymes was simply loaded into the reactor by coupling them to the ion-exchange resins at the proper con ductivity and pH. 1 . 2. 3. Enzyme formulations for the baking, beverage and dairy industries
In the baking industry, most of the enzymes are added as solids in so called 'bread improvers'. These bread improvers are added to the flour to enhance the structure of the bread loafs and reduce the dough rising time. Major producers of these enzymes for bread are Novozymes, DSM (who took Gist-brocades over), Danisco (who acquired Genencor International in 2005) and AB-enzymes. Typically the diameter of the particles should be below 200 J.1m. The reason for this is that often some of these enzymes are pre-blended by the millers of grains to enhance the quality of the flour. Since flour is sieved through a sieve of 250 J.1m, larger enzyme granules will be sieved out. Another important issue is the solubility of the granules. The granules should fall apart and disperse easily in the dough. Instant particles are required. Particles as used in the de tergent industry would dissolve too slowly and the enzyme activity will not be dispersed weil enough throughout the dough. For use in bread improvers the size of the granules is of less importance, but they still have to exhibit an instant behaviour. Most of the enzymes were until recently spray dried from concentrated ultra filtrates. At this moment most of the products are made using spray driers with integrated fluid beds, with connected fluid beds or with fines return system. These systems are called multi stage driers (MSD), since the drying is performed in the spray-drying unit as weil as in the fluid-bed part. The (vibrating) fluid bed installed under the drying chamber acts as an after cooler to reduce stickiness and GOols the product down to below its sticky temperature. A spray drier is a
570
G. M . H . Meesters
single stage drier. These MSD lead to granules that are much less dusty and have a high-instant character. These granules are mainly developed using MSD to re duce the dustiness and therefore the risk of allergie reaction to the bakers using these enzymes. Most of the enzymes in dairy and beverage applications are formulated as liquids. However, a small fraction is granulated using the multi stage drying techniques such as those used in the baking industry [28-30]. Figures 1 0 and 1 1 three-schematic pictures of commonly used techniques to granulate these enzymes. The spray is created by a rotary atomizer or a set of nozzles. These designs of MSD are useful for products, which are difficult to dry (hygroseopie andjor sticky substances). Companies such as Niro, who design these units, have several design configurations available. So-called two stage driers and driers with an integrated fluid bed in the spray tower (three-stage drier). The location of the fluid bed in the drying chamber of the spray drier permits drying at lower temperatures, which results in better thermal efficiency and easier drying of sticky products, since the temperature of the product leaving the spray drying chamber can be set lower than the 'sticky temperature' of the product. In all cases the external vibrating fluid bed is used as a further cooling unit and to blow out the fines from the final product. These fines are blown back into the spray-drying chamber close to the nozzles or the wheel. These fines will collide with the freshly formed droplets that are drying. Due to the fact that these drying droplets pass through a regime of stick iness, the returned fines will stick to these drying droplets to form agglomerates. This process will repeat itself until the aerodynamic diameter of the agglomerates is so large that they are not blown back into the spray-drying chamber anymore. This is the product that is collected as the final product from the vibrating fluid bed. 1 . 2. 4. Enzyme formulations for the feed industries
The application of enzymes in the animal-feed sector is relatively new. The de velopment of these enzymes started in the 1 990s. The best-known product is called Natuphos @ developed by Gist-brocades. Novozymes later developed a similar enzyme. What is important for the enzyme formulations in this field is that these en zymes are added to the feed pellets for pigs, chickens, etc. During the production of these pellets, the meal (the mixture which is formed into the feed pellets), consisting of dry feed compounds including nutritional products, grains, vitamins, minerals, oils and enzymes, is steam heated prior to pelleting to about 70-90DC for a few minutes. The formulation should be such that the enzymes survive this short period of high temperature and moisture. Many enzymes are relatively stable at high temperatures when there is little or no moisture present. The formulations of Gist-brocades and Novozymes are developed in such a way that
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571
(a)
(b)
Fig. 1 0 . (a ,b) Spray drier with connected fluid bed for fines return (courtesy Gea Niro, Soborg , Denmark) (two-stage driers).
external coating prevents the uptake of moisture during that few minutes of high temperature and high-moisture content [25,31 ,32]. The formulation of Natuphos )l; [31] is made using an extrusion spheronisation technique. The enzyme liquid is mixed with starch and some stabilizers and this
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G. M . H . Meesters
Fig. 1 1 . Spray drier with integrated fluid bed (annular ring around the air outlet at the bottorn of the spray drying charnber) and connected fluid bed (courtesy Gea Niro, Soborg, Denrnark) (three-stage drier). Table 1 0 . The Nathuphos® forrnulation as developed by Gist-brocades
Compound Enzyme liquid Starch Stabilizing salts Outer PEG-6000 coating
[33,34] Wt% 1 5-30 65-80 0.1-5 1-10
mixture is extruded through a low-pressure basket extruder. The dried product is coated with a PEG-6000 coating. Novozymes uses a Granule T type of formulation, as described in Section 1 .2. 1 . regarding detergent enzymes, and applies multi-Iayered coatings to these particles [25,32]. These layers are made of a fatty core followed by a talcum coating, after which several layers of fat and talcum are applied successively. 80th formulation coatings have to withstand the steam and water prior to the pelleting, but still have to dissolve in the stomach of an anima!. Table 1 0 describes the Natuphos ® formulation developed by Gist-brocades, and Table 1 1 details the Novozymes formulation. Figure 1 2 shows an SEM picture of an uncoated Natuphos ® granule and Fig. 1 3 of a coated particle.
573
Agglomeration of Enzymes, Micro-organisms and Flavours Table 1 1 . The Novozymes formulation [32]
Compound Core Sodium sulphate Cellulose fibre Kaolin dextrin enzyme dry matter Coating (Iayered) Hydrogenated beef tallow Filler (Mg-silicate) Hydrogenated beef tallow Filler (Mg-silicate)
Wt% 71 (weight of core) 8.9 3.0 5.0 1 1 .1 4 (percent based on core) 1 2.5 4 1 2.5
Fig. 1 2. A n uncoated starch based, extruded a n d spherionized, enzyme granule of Gist-brocades.
The major challenge in this field is to make granules, which can withstand the extreme conditions encountered during pellet manufacture. The focus of the for mulation development is aimed at this. Better coatings are being developed and increased enzyme stability is required. The major producers of feed enzyme are BASF, DSM and Novozymes. 1 .3. Conclusions
Since the 1 960s there has been great progress in the field of enzyme formu lations. The drivers have been dust reduction in relation to the allergenic nature of
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G. M. H . Meesters
Fig. 1 3. Sampie of the final coated Natuphos :K enzyme granules.
enzymes, especially in the field of detergent enzymes. It is this field of formulation that is developed the furthest. Here too the enzyme stability in the detergent matrix was an important driver for product innovations. This industry is only fine tuning the current formulations and methods which are proven to be most suc cessful; namely the fluidized bed coating/layering technique of Genencor Inter national and the high-shear granulation technique of Novozymes. For starch degrading enzymes, most particle formulation work based on mak ing immobilized enzymes for use in continuous columns has stopped since the introduction of ion exchange columns. In the dairy, beverage and particularly baking industries, the formulation tech nique used by almost all producers is based on a multi stage drying technique, resulting in instant enzyme granules. Here the issue of enzyme dust reduction is under discussion at this moment. In the near future, this will be an important product innovation driver. Cost is another important issue in this field. The feed enzymes business is dominated by Novozymes with a high-shear product and BASF with an extrusion spheronization technique, which came from DSM (who acquired Gist-brocades). Here, pelleting stability at even higher tem peratures will be the driving force behind product innovations. 2. HYGIENIC DESIG N OF FOOD EQUIPMENT AND PROCESS LlNES
In the food industry many different types of dry materials are being produced and handled. This requires different design criteria for specific process equipment and process-lines in relation with the various food safety requirements of each material.
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575
The following organizations provide information and resources for various as pects of the food industry, including standards bodies: 1 . Ameriean Dairy Produets Institute (ADPI): ADPI membership includes man ufacturers of evaporated and dried milk, cheese and whey products; firms that provide supplies and services to processors; and many companies that either use these manufactured dairy products or are otherwise involved in the industry. ADPI represents companies across the U.S. and more than 1 5 other countries. www.adpi.org 2. European Hygienie Equipment Design Group (EHEDG): EHEDG is a con sortium of equipment manufacturers, food industries, research institutes and public health authorities. EHEDG aims to promote hygiene during the processing and packing of food products and assists industry in complying with European hygienic machinery directives. EHEDG certifies equipment and process lines. www.ehedg.org 3. 3-A Sanitary standards Ine: The non-profit organization combines all facets of the 3-A sanitary standards program, including the 3-A standards writing process. It also maintains oversight of the 3-A Symbol used to identify equipment manufactured to 3-A Standards. 4. International Assoeiation of Food Industry Suppliers (IAFIS): IAFIS is a trade association whose members supply the food, beverage, dairy and related sanitary processing industries. www.iafis.org 5. International Association for Food Proteetion (lAFP): IAFP is a non-profit association of food safety professionals, dedicated to the education and service of its members, as weil as industry personnel. wwwJoodprotec tion.org 6. International Dairy Foods Association (lDFA): IDFA represents more than 500 dairy food manufacturers, marketeers, distributors and industry suppliers across the United States and Canada, and in 20 other countries. www.idfa.org 7. United States Department of Agriculture www.usda.gov 8. United States Food and Drug Administration www.fda.gov 9. International Organization for Standardization (ISO): ISO is a worldwide fed eration of national standards bodies from some 1 30 countries, one from each country. ISO is a non-governmental organization designed to promote the development of standardization and related activities in the world. ISO's work results in international agreements, which are published as International Standards. www.iso.ch 1 0. NSF International (NSF): NSF International is committed to public health safety and protection of the environment by developing standards, by pro viding education and by providing third-party conformity assessment serv ices, while representing the interest of all stakeholders. www.nsf.org
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G. M . H . Meesters
2.1 . Hygienic design and certification
Among others, EHEDG certifications can be obtained for equipments and even process lines for good food grade hygienic designs. Several documents like the ones from ADPI, 3-A and EHEDG, deal with processing of food powders, ag glomerates and granular material. Typical aspects of hygienic-equipment design involve cleaning of equipment, prevention of contamination, and microbial growth in relation to dry materials. Sometimes other procedures (such as dry cleaning) need to be used and these too are described in these documents. The design criteria for dry materials especially when handling of product in and dry cleaning of equipment can be less stringent compared to liquid material han dling, but design must consider the eventuality of disassembly/accessibility for cleaning and inspection. However, when there are high moisture-content levels present in the powder, design criteria for liquid processes must be applied. Product moisture content and method of processing influence the design criteria of the equipment in addition to the required cleaning procedure. Safety aspects in processing dry materials have to be taken into account, especially where forma tion of dust, exposure to it, and the hazards of dust explosions are concerned. There are specific documents that focus on design criteria of equipment and process lines, liquid to dry solid processes (Iike spray drying, fluid-bed coating and agglomeration), but also wet solid to dry solid processes (like fluid-bed drying and mixing).
• • • • • • • •
Examples of typical equipment used in process handling of dry materials are: agglomerators and granulators • mills charge hoppers • mixers/ blenders • particulate collectors (dry/wet) coaters • particulate dosing systems containers • particulate flow promoters conveying systems coolers • powder valves • sieves driers filling and packing systems • silos
Aspects relating to equipment operations involving the handling of dry mate rials include: • air filtration • abrasion • cleaning • bearings • construction materials • connections • fans/blowers • drives • inspectability and accessibility • fire and explosion suppression • sensors • seals • surface treatment • shafts
Agglomeration of Enzymes, M icro-organisms and Flavours
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All these subjects are or will be described in the documents of e.g. EHEDG, 3-A and the NSF. The criteria for hygienic design of equipments and plants for dry materials handling depends upon the moisture content of the dry material and the method of cleaning [35,36]. The choice of cleaning procedure depends upon whether the plant or equipment to be cleaned is a designated a dry- or wet-processing area or zone. The ability to clean equipment used in the processing of food material is essential to maintain standards of hygiene and dry material quality by: • • •
Preventing cross-contamination and/or co-mingling of material during a pro duction change to another material. Preventing degraded material arising from deposits remaining in the equip ment. Preventing material remaining in the equipment under conditions that would cause microbial growth with possible contamination.
Good housekeeping standards require the ability to clean areas in and around equipment so as to prevent the accumulation of dirt that attracts microbial growth and/or presence of vermin/insects. The frequency of cleaning depends upon the dry material and processing equipment involved. As long as dry material is being produced that meets all quality specifications at rated equipment capacity, plant shutdown for cleaning is not required. However, as soon as conditions arise leading to creation of sources of dry material degradation or problems in meeting steady-state-plant operation, plant shutdown for cleaning is required. Therefore, equipment should be cleaned at appropriate intervals to prevent malfunction and dry material contamination that would adversely affect both the quality of the dry material produced and a safe equipment operation. Deposit formation increases the frequency of cleaning. Suitable cleaning procedures for dry food material processing plant include both dry and wet methods, and relate to the type of food material involved [35-39]. Microbial growth possibilities are low and can be rated as neg ligible with powders having a water activity below 60%. When only dry powders are handled, dry cleaning only should be performed. This ensures the safest cleaning with respect to unwanted microbial growth. Moist p owders: Microbial growth possibilities are high, especially in warm and humid conditions if the water activity of the powder exceeds 60%. Wet cleaning procedures are necessary and product contact surfaces of stainless steel or equivalent are required. Drainage and fast drying after cleaning help to prevent microbial growth after the cleaning operation. When wet spots remain after cleaning, dry material may stick to these spots on start up, possibly causing unwanted microbial growth.
• Dry powders:
•
578 •
G. M. H . Meesters
Oi! and (at containing (non-water related) sticky powders: Possibilities exist for deposit formation on product contact surfaces and dry material quality degra dation through heat andjor mechanical handling. Wet cleaning procedures are necessary and product contact surfaces of stainless steel or equivalent are required. Here too, proper drainage and drying of the cleaned equipment en sures good hygiene.
2.2. Materials of construction for equipment processing dry materials
Construction materials coming into contact with food (including associated ad hesives) must be food grade (FDA-approved or national equivalent). Selection of construction material depends much upon the dry materials, method of cleaning and cleaning agents to be used [35,37]. Fabrics and non-metallic filter materials used in connection with the cleaning of air involved in dry materials handling systems must be non-toxic, cleanable, and not impart contaminating smell to the dry material. Glass is a hygienic material, but should not be used due to risk of breakage and subsequent difficulty in detecting broken glass in dry materials. It is recommended to replace the glass by another material e.g. Polycarbonate. As stated before, the criteria for hygienic design of equipment for dry materials handling depends upon the moisture content of the dry material and the mode of cleaning. When wet cleaning is used, directives in documents on liquid process ing [37] also apply. However, dry materials handling must take into account the possibility for material lump formation, creation of dust explosion conditions, high moisture-deposit formation in the presence of hot air, and material remaining in the equipment after plant shutdown (even if a degree of self-emptying is achieved). More details can be found in [35]. Two examples of hygienic design will be given below. One deals with static flanges and the other with flexible connections, which are often seen and used in food processing plants. Static seals should be of an elastic material, have a non-porous surface and be cleanable. They should be mounted to create a flush surface without any crevice with the surrounding metallic body. Misalignment of ducts should be avoided as dry material can be entrapped on the misaligned ridges (Fig. 14b). Assembly of seals and gaskets for vessels of large diameter require special attention to prevent operational problems, especially air and liquid (washing) leakage and material dust emissions to atmosphere. PTFE can be used as a static seal in combination with an elastomer (food grade, FDA-approved or national equivalent). The PTFE should be of high-density resilient quality. Metal-to-metal contact duct assemblies (Figs. 14c and 1 5) and paper-type gaskets between flanges can be applied where a plant operates at atmospheric pressure and requires no wet cleaning.
Agglomeration of Enzymes, Micro-organisms and Flavours
579 R'F'''9''hc centering
metal to metal contact Fig. 1 4. Examples of static flange seals for dry products: (a) hygienically designed seal usable for wet cleaning, (b) seal creating a gap and misalignment, c) metal-to-metal flange joint (only for dry cleaning). From EH EDG [35].
pipe end
l
......
-
m
�
/ rn
metal to meta l co ./ or gap
metal sleeve Fig. 1 5. Static clamp joint without elastomer seal and axial compression (hygienic risk). From EHEDG [35].
The second example deals with flexible connections (Figs. 1 6 and 1 7). Flexible connections between duct ends are always liable to cause dry material build-up between the flexible material and metal-duct surface. Telescopic connections should be avoided because of gaps at the duct ends (Fig. 1 6) causing hygienic and operational risks. A build up of material between the ducts cannot be avoided, but must be minimized. Ring clamps for mounting flexible connections should be placed close to or at the end of the duct in order to minimize dead areas for dry material build-up as demonstrated in Fig. 1 7. The plastic sleeve must allow small axial and radial movements without generating axial forces. The flexible material should have a smooth surface that minimizes sUrface build-up of dry material. 2.3. Validation and certification
Contrary to 3-A and the NSF, EHEDG [38] can validate and certify process equipments and components for food grade use. Figure 1 8 shows the validation scheme as used by EHEDH and Fig. 1 9 shows the certification scheme.
580
G. M. H . Meesters detail A
end of _-r;::�'1 pipe
flexible sleeve
Fig. 1 6. Telescopic moveable connection between duct ends causing hygienic risks. From EHEDG [35].
detail A
end of pipe
detail A
end of pipe
end of pipe
fixing clamp
flexible sleeve
fixi ng -=f,E+l1-liID clamp clamp sheet 10 avoid /��--I crevice flexible . flexible crevlce sleeve sleeve possible
avoided crevice
Fig. 1 7. Examples of flexible connection duct ends (right). One ring clamp close end used for smalJer diameters; crevice not totally avoidable (Ieft). Application of two clamps, one of which is mounted directly at the end to avoid any crevice (middle). From EHEDG [35].
3. D RYIN G OF STICKY MATERIALS SUCH AS YEAST EXTRACTS
Yeast extracts are a natural product that enhance flavours in savoury products or give products a specific flavour such as beefy, chicken or pork. Yeast extracts are produced by hydrolysing fermented yeast cultures. Mostly bakers or brewing yeast cultures are used. At the end of the fermentation process the yeast are hydrolysed by an autolysis step. Sometimes bacteria or enzymes are used to hydrolyse yeast components in a specific way to get a desired flavour. The components that are hydrolysed are cell wall components (proteins) but more
Agglomeration of Enzymes, Micro-organisms and Flavours
581
Validation Scheme Process Equipment & Components
4.
Cleanability Testing
f.-!.!'��_
(duplo)
Rejected for further testing
good
Rejected tor further testing
7. CleanabiJityTesting
d _____, f-"'0"' o"-
good
Fig.
18. Validation scheme as used by EHEDG for process equipment and components [38].
importantly the DNA, RNA and other cell components; the hydrolysed nucleotides are the main flavour components. The insoluble parts are removed to obtain a fully soluble product. Many of these products are used in soups, sauces, and flavour for snacks and for the manufacture of stock cubes. Producers of yeast extracts include. Bio Springer, DSM-Food Specialties, Lesaffre and Quest Inter national.
(J1 CXl N
Certification Scheme for process equipment and components
Altecnatlve route: Customer $ubmits appltcation form to institute. PrOduct expett complotes wilh internat offer and sends 10 notifkKf body
Institute 1 1 .1 Report 10 notified body Assessmenl report by ptoduct expert
11.2 Report on certification advice by produCI expert
12. OecJaratlon assessment casts 10 notifled body Notlfled body
18. Asse$S1 contra! certificate
Fig. 1 9. Certification scheme as used by EHEDG for equipment and components [38].
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3. 1 . The production process
Figure 20 shows a typical production process for the manufacturing of yeast extracts. In a fermentation vessel a yeast culture (baking or beer yeast) is grown. At the end of the fermentation process the yeast is concentrated by a centrifugation step, after which the concentrated broth is hydrolysed at elevated temperature with optionally the addition of bacteria or enzymes. The hydrolysed mass is passed through a centrifugation step once more to remove the remaining insol uble solids, like cell wall components. The resultant c1ear liquid is evaporated to high dry-matter content. Part of this is formulated as a liquid, slurry or paste by the addition of salts such as NaCI. The remaining amount is spray dried to form a solid product. This dry formulation will be discussed in the following section.
3.2. Drying of a yeast extract liquid
The process used for drying yeast extracts is the so-called multi-stage drying technique (it is discussed in a previous chapter on agglomerated enzymes, SecBalanced nutrients
Mollasses Ammonia I)hosphates
Fermentation vessel
Sterile air Control of ·Temperature ·pH concentrated yeast
Autolysis vessel
20. A schematic layout of typical yeast extracts plant (courtesy of DSM-Food Spe cialties, Delft, The Netherlands). Fig.
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G. M. H . Meesters
Fig. 2 1 . Picture of a blocked fluid bed, caused by the sticking of yeast extract to the walls and bottom plates of the drier (DSM Food Specialties).
tion 1 .2.3). Often a simple two-stage drier with fines return is used. This results in a dust-free product. One of the major problems of drying yeast extracts is the stickiness observed during the drying. When the proper conditions for drying are not met, fouling or even blockage of the drying unit can be observed. This will result in extensive cleaning, often with a lot of manual labour involved. This is illustrated in Fig. 21 , where total blockage of the fluid-bed drier has occurred, for which manual cleaning is the only remaining option. This costs at least a day in down-time of the unit. The stickiness temperature, Ts, is the temperature where the structure of the amorphous powder changes irreversibly. Ts depends on the composition of the product, the relative humidity of the drying air, the temperature of the product, the surface viscosity and the operating parameters of the drier (slow or fast drying rate). In Fig. 22, the sticky region is shown. When drying a liquid (liquid, non-sticky region), the water will evaporate from the liquid. At a certain point the liquid be comes very concentrated and an amorphous solid is formed. This product is sticky. By further drying of this product, the moisture content will become lower and lower, and at a certain point a solid, non-sticking product is formed. A drying droplet in a hot air stream of a spray drier goes through all these stages. During its path through the drying chamber of a spray drier, a droplet becomes sticky, but has to be non-sticky when it hits the wall and falls down into the cone of the spray drier and enters the fluid-bed drier. When the process is not weil set, or the product is a complicated mixture of components, it may be that the granule is still sticky when it hits the wall. This results in the granule sticking to the wall and ultimately fouling the equipment. Figure 23 shows a typical stickiness curve of a yeast extract.
585
Agglomeration of Enzymes, Micro-organisms and Flavours Thermal de<:omposition
CONTINUUM (liquid)
(non-sticky TegIOfl)
curve
DISCRETE (partlculates)
(non-sticky TegKJII) MOISTURE CONTENT
Fig. 22. The relationship between the temperature and the moisture content showing the sticky region of a product during drying [40].
- -- �: _�-+ + -- . 1-- +- +- - t---i - ��t � l �,=�-�-�-,st-ex-L-S-) I t, 1- 1 -+-= I r---1 1 +-_ --t +- -1---' l-T Stickiness
1 80 1 60 1 40
�
1 20
...
1 00
7ä ...
E
80
Cl) :l
Cl) a.
Cl) �
60
-
, -=-
-------1 -
---
40 20 0.0
--
--
o +-
- - +- -
,
-
-
- --� '
-
_ '
--
___
--,--- . , - -- L ;� ---vl -- --
�---+
5.0
-
1 0.0
�
1 5.0
�
20.0
+_
25.0
'atl
H"mldity (%)
_r
_+
�
30.0
35.0
40.0
Fig. 23. Stickiness curve of a yeast extract (DSM-Food Specialties).
By plotting the stickiness CUNe into a Mollier diagram a new representation is obtained, as shown in Fig. 24. The Mollier diagram is based on the relationship between heat content and water vapour content of air. The heat, or energy, content is difficult to measure directly, so the diagram is distorted to give the illusion of being based on the relationship between temperature, relative humidity and water vapour content since these parameters are more easily measured. The water vapour concen tration is expressed in the Mollier diagram as kgjkg of dry air [40].
586
G.
M. H. Meesters
1 80 •
1 60
- - -
Yeast Extract type 2: sticky Yeast Extract type 1 : free flowing
1 40
�
1 20
Q) Cl.
80
Q) I-
60
ü 0
� :l
E
1 00
40 20 0 0.00
0.01
0.02
0.03
0.04
0.05
Water content. kg/kg dry air Fig. 24. Stickiness curves in a Mollier diagram.
What can be seen from Fig. 24 is that the product is non-sticky inside the area of the curves, but is sticky outside the curve area. The lines drawn in the Mollier diagram show the product temperatures of the drying droplet. Firstly, the droplet is heated up when it enters the spray drier (heating air in Fig. 24). Then, the droplet starts to evaporate and the air-cools down (liquid drying in Fig. 24), after which the product reaches a final temperature and moisture content as indicated by 'Product' in the diagram. Clearly the conditions are such that yeast extract 1 (dashed curve) gives a non sticking product, since the product point lies within the area of the curve of product one. Were yeast extract 2 (solid curve) dried under the same conditions, the final-product point would lie outside the area of curve 2, resulting in a sticky product. For this product a much lower air inlet temperature is needed in the spray drier to dry this product. These curves for stickiness can be influenced by changing the production conditions like the air temperature and the drying rate. By changing the salt content, the amount of residual sugars, pH and amount of organic acids present, the drying behaviour of the liquid can be influenced enormously. Products that are normally difficult to dry can be dried by changing the drying conditions. In the situation that the product remains difficult to dry, an alternative multi stage drying technique can be used, called a Filtermat drier. Figure 25 shows a schematic drawing of such a drying unit. In the Filtermat set up, products can be dried which are extremely sticky. Some of the yeast extracts that are very difficult to dry can be dried using this equip me nt. The filtermat drier is a spray drier with an integrated belt. The spray is created by nozzles and liquid is sprayed co-currently with the hot air stream. The
Agglomeration of Enzymes, Micro-organisms and Flavours
587
Fig. 25. Filtermat two-stagedrier of Niro (Courtesy of G EA, Niro, Soborg , Denmark).
water evapo rates, and the dry particles fall down on a belt at the boUom of the spray drier. Since the product is very sticky, a moist, porous cake of several centimetres is formed. In the after drier the cake is further dried, because the belt slowly moves the cake away from the spraying zone. Hot air is passed through the belt and cake, where the cake is dried until the moisture content reaches a low-enough value for the product to be non-sticky. At the final stage, air cools the product down to ambient temperature, after that the cake is collected and milled until the required size range is obtained. Any fines are recycied back into the drying chamber to agglomerate with the drying droplets. Since products such as the dried yeast extract remain hygroscopic after drying, they must be packed in sealed boxes or bags that prevent moisture uptake from the ambient air. Too much water uptake will result in lump formation and in the extreme case, the whole box or bag becomes one large agglomerate.
588
G. M. H. Meesters
3.3. Conclusions
Drying sticky products Iike yeast extracts requires the measurement of product stickiness. The stickiness may vary considerably, depending on the product and/or the process. The stickiness information can be translated into a Mollier diagram in order to find the best conditions in which to dry the producl. When the conditions are not favourable, changing the operating conditions of the plant may give a more favourable drying characteristic. In cases where the product remains difficult to dry, other techniques like the Filtermat may solve the problems of drying. REFERENCES [1] Fermipan horne page: wwwJermipan.eom. [2] G.R. Gibson, Probioties & prebioties and their funetion, Functional nutrition 2 (2) (2003) 1 1-1 3. [3] Finaneial Magazine, 26( 1 ) (2004) 1 . [4] Novo Nordisk AIS patent, British Patent 1 .362.365, and DE-21 37043, 1 970. [5] Gist broeades NV. patent: Duteh patent NL-1 48807, 1 976. [6] Novo Nordisk AIS patent: German Patent 2730481 A 1 , 1 977. [7] Novo Nordisk AIS patent: EP 0304331 A2, 1 988. [8] Gist-broeades NV. patent: US 4.242.21 9, 1 980 and UK 30556, 1 977. [9] Showa Denko patent: AU A 48508, 1 985. [ 1 0] Showa Denko patent: EP 02561 27, 1 986. [1 1 ] Solvay Enzymes patent: EP 0656058 B 1 , 1 993. [ 1 2] Henkel patent; OE 3344 1 04, 1 985. [ 1 3] Henkel patent: O E 4007601 , 1 99 1 . [ 1 4] Henkel patent: WO 92/1 1 347, 1 992. [ 1 5] Miles Corp. patent: EP 0 1 93829, 1 986. [ 1 6] Geneneor International patent: EP 082001 7, 1 996. [ 1 7] Geneneor I nternational patent: WO 9 1 /06638, 1 99 1 . [ 1 8] Novo Nordisk AIS patent: WO 9 1 /09941 , 1 991 . [ 1 9] Novo Nordisk AIS patent: EP 050679 1 , 1 990. [20] Geneneor I nternational patent: WO 02078737, 2002. [21 ] Geneneor International patent: EP 1 372713, 2002. [22] Gist Broeades NV. patent: Duteh patent 72 1 2445, 1 972. [23] Gist Broeades NV. patent: British patent 1 404933, 1 972. [24] Gist broeades NV. patent: US patent 3838007, 1 972. [25] M iles laboratories I ne: EP 90276, 1 983. [26] Anheuser-Buseh Ine.:US 4230802, 1 976. [27] Anheuser-Buseh Ine.: US 4208482, 1 976. [28] Novo Nordisk AIS patent: WO 01 /04279, 2001 . [29] Novo Nordisk AIS patent: WO 0 1 /254 1 1 , 200 1 . [30] Novo Nordisk AIS patent: WO 0 1 /254 1 2 , 200 1 . [31] Novo Nordisk AIS patent: E P 0569468, 1 992. [32] Novo Nordisk AIS patent: WO 92/12645, 1 992. [33] DSM Patent: EP 98631 3, 1 998. [34] DSM Patent: EP 990026, 1 999. [35] EHEDG Doeument 1 3 : Hygienie design of equipment for open proeessing , 1 996. [36] EHEDG Doeument 22 "Hygienie design eriteria for the safe proeessing of dry partieulate materials", 2001
Agglomeration of Enzymes, Micro-organisms and Flavours
589
[37] EHEDG Document 1 0 : Hygienic design of closed equipment for the processing of liquid food, 1 993. [38] EHEDG Document 8: Hygienic equipment design criteria, 1 993. [39] EHEDG Document 26: hygienic engineering of plants for processing of dry particulate materials, 2003. [40] R.H. Perry et al. , Perry's Chemical Engineers' Handbook, 7th edition, McGraw Hili, New York, 1 997.
CHAPTER 1 3 Agg lomerat i o n of De hyd rated Consumer Foods Stefan Palzer*
Nestle Product Technology Centre Lebensmittelforschung GmbH, Lange Strasse 21, 78224 Singen, Germany Contents 1 . I ntroduction 2. Properties of food particles and main adhesion principles 2. 1 . Chemical composition, supra-molecular and microscopic structure of food particles 2.2. Hygroscopicity and hygrosensitivity of food powders 2.3. Mechanical properties of solid food substances 2.4. Adhesion principles relevant for food agglomeration 2.4. 1 . Low-viscosity liquid bridges 2.4.2. Solid bridges obtained by drying 2.4.3. Sintering 2.4.4. Solid bridges built by melting of fat 2.4.5. Increasing adhesion forces due to increasing contact area and/or distance between the particles 3. Agglomeration processes used by the food industry 3. 1 . Agglomeration of food powders during spray-drying 3.2. Steam jet agglomeration of food powders 3.2. 1 . Steam jet agglomeration systems integrated into spray-driers and stand-alone agglomeration towers 3.2.2. Steam jet agglomeration in a fluid bed 3.3. Fluid-bed agglomeration of food powders 3.3. 1 . Pneumatically fluidized bed 3.3.2. Mechanically fluidized bed 3.4. Pressure agglomeration of food powders 3.4. 1 . Extrusion of wet powder masses 3 .4.2. Roller compaction 3 .4.3. Tabletting of food powders 4. Agglomeration technologies for different product groups 4. 1 . Dairy powders 4 . 1 . 1 . Composition of dairy powders 4 . 1 .2. Agglomeration of dairy powders during spray-drying
*Corresponding author. E-mail: [email protected]
Granulation Edited by A.D. Salman, M.J. Houns/ow and J. P.K. Seville :j; Elsevier All rights reserved
2007
B.V.
592 593 593 598 601 605 606 607 608 610 61 1 613 613 617 617 619 619 619 624 627 627 629 637 644 644 644 646
592
S. Palzer
4.1 .3. Agglomeration of dairy powders during spray-jbelt-drying (filtermat drying) 647 4. 1 .4. Agglomeration of dairy powders in an external fluidized bed 647 647 4 . 1 .5. Lactose crystallization during agglomeration 648 4.2. Dehydrated convenience foods 649 4.2. 1 . Composition of dehydrated convenience foods 4.2.2. Agglomeration of convenience food in mechanically or pneumatically 650 fluidized beds 4.2.3. Extrusion of wet powder masses 651 4.2.4. Roller compaction of culinary powders 652 4.2.5. Tabletting of culinary powders 654 656 4.3. Dehydrated beverage powders 4.3. 1 . Composition of beverage powders 656 657 4.3.2. Agglomeration of beverage powders during spray-drying 657 4.3.3. Steam-jet agglomeration of beverage powders 659 4.3.4. Fluid-bed agglomeration of beverage powders 4.4. Confectionery and sugar-based products 660 4.4. 1 . Composition of confectionery and sugar-based products 660 4.4.2. Tabletting of confectionery 661 4.4.3. Manufacturing of compressed sucrose based sweets 662 4.4.4. Agglomeration of sucrose-based products 663 4.5. Agglomeration of breakfast cereals and manufacturing of cereal bars 664 4.5. 1 . Composition of cereal products 664 4.5.2. Manufacturing of cereal bars 664 4.5.3. Extrusion of breakfast cereals 665 4.5.4. Granulation of breakfast cereals 665 5. Undesired agglomeration of food powders 665 5. 1 . Caking of amorphous food powders 666 5.2. Post-hardening of agglomerates 668 References 670
1 . I NTRODUCTION
Foods are dehydrated to reduce their transport weight and to increase their shelf life. Various dehydrated food products are currently offered to the consumer. Amongst them are dairy powders, infant formulas, bakery mixtures, beverage powders, dehydrated convenience foods, kitchen aids, confectionery, granulated sugar, tabletted sweeteners and cereal-based products. Most of these products are agglomerated. Agglomeration by definition is a process during which primary particles are fixed together to form larger, porous secondary particles. Within these agglomerates individual primary particles are still visible. Freely dosable powders are agglomerated to provide superior instant properties. They should re-hydrate or dissolve quickly without forming lumps. In addition, the flowability of powders is improved by agglomeration. Good flow ability is especially important for precise dosing of powders as required in vending machines. Food products are also offered as pre-dosed quantities in the form of
Agglomeration of Dehydrated Consumer Foods
593
tablets. Tablets are agglomerates, which can have a distinctive, easily recogni zable shape. In all of these applications product features are improved by means of agglomeration. Sometimes undesired agglomeration effects can be observed while processing dehydrated food powders. Caking of powders or post-hardening of agglomerates during storage deteriorates the product quality significantly. Stickiness and en crustation of equipment is observed during processing (wh ich can be considered as an undesired agglomeration) and requires increasing cleaning efforts. How ever, desired and undesired agglomeration of food products can be explained by the same basic principles and kinetics. These mechanisms are strongly linked to the material properties of the food particles. 2. PROPERTIES OF FOOD PARTICLES AND MAIN ADHESION PRINCIPLES
To understand the adhesion mechanisms it is necessary to know the chemical composition, the molecular arrangement and the microseopie structure of the particles. Furthermore, as in most agglomeration processes, moisture plays an important role, the interaction between water and the food substance has to be investigated. 2. 1 . Chemical composition, supra-molecular and microscopic structure of food particles
Food powders are mainly composed of carbohydrates, proteins, lipids and vari ous acids. In addition, they contain minerals, flavours, vitamins, additives and a small amount of water. Although the water content is low, moisture is very im portant for the physical behaviour of solid food materials. In food systems, two basic supra-molecular structures can be found: amorphous systems in which the moleeules are in disorder and crystalline structures in which the atoms and mole cules are highly ordered. Fat in food products is a polymorph material because it crystallizes in several different forms. The different fats found in food materials are normally a mixture of various tri-glycerides. Thus, they solidify gradually upon cooling. If the tri-glyc eride mix contains a high amount of saturated fatty acids, it solidifies at higher temperatures. The solid fat content (SFC) is the amount of solid fat based on the total fat content at a certain temperature. The temperature at which 1 00% of the fat turns liquid is defined as melting point. Cocoa butter e.g. has a melting point of 30-40cC, milk fat of 25-35°C and hydrogenated palm oil melts at 35-55°C. Hydrophilie water-soluble substances can be in the crystalline or the amor phous state. Siow cooling or drying of such substances results in crystalline
594
S. Palzer
structures. The longer the molecules are and the faster the cooling or drying is performed, the more difficult it gets for them to arrange themselves into a highly ordered crystalline structure. Since various dehydrated food materials are dried or cooled by rapid processes, they are transferred into a super-cooled amorphous melt. Upon drying or cooling, the viscosity rises forming a thick syrup and even tually an amorphous solid. Such a continuous change is referred to as a second order phase transition. Additionally, amorphous structures can be formed while grinding crystalline sucrose during the manufacturing of icing sugar. Conse quently, various food components are in the amorphous state. Their molecules are randomly distributed within a more or less rigid molecular matrix. Such an amorphous matrix is called a glass if it has a high viscosity and storage modulus. In contrast to liquids, glasses can support their own weight under the force of gravity. While heating such a glass, it gradually transforms into a rubbery structure and finally it Iiquefies. The following water-soluble food components are often in their crystalline state: • • •
Low molecular carbohydrates: Sucrose, dextrose, lactose, polyols Organic acids: citric acid, ascorbic acid Salt: sodium and potassium chloride. Various amorphous substances are found in food products:
•
• •
•
Carbohydrate mono- or oligomers: dextrose, fructose, galactose, maltose, isomaltose, lactose, sucrose Carbohydrate polymers: maltodextrines and dextrose syrup, amylose Amino acids, di- and oligopeptides: gluten, animal and plant proteins Organic acids: citric acid, malic acid, lactic acid, tartaric acid.
So me food materials like starch and amylopectine are semi-crystalline. They are partly amorphous, but they also contain crystalline regions. Furthermore, crystallization of single components might be inhibited by the presence of poly mers. This effect is used while manufacturing boiled candies, which contain a blend of sucrose and dextrose syrup. Amorphous structures are generally meta-stable systems. With increasing storage time they are gradually transformed into crystalline structures. The velo city of crystallization depends on the molecular mobility and, thus, especially low molecular weight substances exist in their crystalline state. Crystallization as such is a combination of two processes: nucleation and crystal growth. At high concentrations (high viscosity) diffusion and, therefore, also nucleation is Iimited. At low concentration (Iower viscosity) crystal growth is Iimited. Above the melting temperature the propagation rate is zero. Thus an optimal substance-specific moisture content or temperature exists for crystallization. Various authors [1] applied the WLF (Williams, Landel and Ferry) equation (see equation (1 3)) to model crystallization of sugars. Others used a simple Arrhenius
595
Agglomeration of Dehydrated Consumer Foods
approach to predict crystallization [2]. However, the most popular approach is to model crystallization kinetics according to Avrami [3]: (1)
Cer i s the volume fraction of crystalline material, kA the crystallization rate con stant, t the time and n the reaction order of the crystallization process. Crystallization and the formation of amorphous structures is strongly linked to the molecular mobility. Molecular mobility within crystalline or amorphous struc tures can be expressed as free volume available for the motion of the molecules. The free volume is the non-occupied space in a molecular matrix. If, due to thermal fluctuations, a critical free volume is accumulated near a molecule, it can leave its fixed position. With increasing temperature the molecular mobility and the free volume within amorphous and crystalline structures increases differ ently. While heating a crystalline system the molecules are vibrating about their position in the lattice until the crystalline structure breaks down at a defined temperature, called the melting point. If the resulting melt is chi lied slowly enough, it can crystallize again. Such a discontinuous change happening at a constant temperature is called a first-order phase transition. For amorphous systems no melting point exists. While heating an amorphous glass the free volume increases steadily. However, above a certain temperature interval the gradient with which the free volume increases changes significantly. Molecule clusters are set free and start to rotate and slip past each other. The lower border (onset) or the mean (midset) of this temperature interval is defined as glass transition temperature Tg . Figure 1 iIIustrates changes of free volume due to increasing temperature for crystalline and amorphous structures. While exceeding the Tg , the viscosity decreases from 1 0 1 1 _ 1 0 1 2 Pa s to ap proximately 1 08-1 09 Pa s [4]. The glassy and brittle material becomes more and more ductile. Further increasing of the temperature liquefies the rubbery material successively. In parallel to the described thermal expansion, the specific heat and the dielectric constant change. Accordingly, the glass transition temperature can be measured by various methods while heating the product: differential scanning calorimetry (DSC - changes in specific heat), dynamic mechanical analysis (DMTA - changes in mechanical properties) and nuclear magnetic resonance spectroscopy (NMR - molecular relaxation). The value obtained for the glass transition temperature depends on the method and the temperaturejtime gradient applied. The glass transition temperature also depends on the molecular weight. The glass transition temperature of linear monodisperse homopolymers is pro portional to the inverse of their molecular weight Mn. This effect can be described using equation (2) developed by Fox and Flory [5]: Tg
=
Tg •oo
-
A
Mn
(2)
596
S. Palzer
molecule- Clu ste r rz;==;:::---,
i�:J '�:
E �
'0 > 0 u E \;::: 'Ü M
8. E
i
I\.
liquid
1 W �i�ItSIO?Cf W
'';bbe
Q)
rJ)
,� "",
chilling
E
crystalline glass transition
tempo T9 o
temperature I K
melting temperatura Tm
Fig. 1 . Free specific volume in crystalline and amorphous structures depending on changes in temperature.
A is a constant parameter and Tg, oo the value for Tg obtained by extrapolation to infinity. Equation (2) was applied by Roos and Karel [6] to describe the relation between molecular weight and glass transition temperature of maltodextrines and dextrose syrups. Different authors publish the glass transition temperatures of various water-free food powders as shown in Table 1 . Knowing the glass transition temperature Tgj of the different components and their mass fraction Wj, the Tg of a homogenous mixture of different amorphous substances can be estimated according to Fox [5]:
1
_ _
Tg m
=
�� Tgj i=1
(3)
Equation (3) is only valid for a powder in which the different components are equally distributed amongst and within the obtained particles. This is not always the case. Some food particles are structured, which means that their components are not equally distributed within the particles. If food powders are manufactured by blending different powdered ingredients, the components are not equally distributed amongst the particles. The physical behaviour of the powder mix depends on the properties of the dominating powder component. To predict the macroscopic properties of such a disperse system, it is
Table 1 . Glass transition temperature of different water-free food su bstances
Substance Fructose Glucose Lactose Maltose Trehalose Sucrose Maltodextrin DE20 Maltodextrine DE 1 0 Maltodextrine DE5 Starch Skim milk powder Water
Glass transition temperature (0C) 5 31 1 01 87 1 00 57 141 1 60 1 88 250 1 01 -1 35 -143
Gordon&Taylor constant 3.8 4.5 6,7 6.2 6.5 5.4 6.8 7 7,7 5.2 6.5 6,7
Wheat gluten (0,004% water) Soft wheat flour
1 63
Tomato powder
50-58
5.5
Whole milk powder Hydrolysed fish protein
101 72
8.6
1 28
»
(Q (Q
Method Onset DSC (5°Cjmin) Onset DSC (5°Cjmin) Onset DSC (5°Cjmin) Onset DSC (5°Cjmin) Onset DSC (5°Cjmin) Onset DSC (5CCjmin) Onset DSC (5üCjmin) Onset DSC (5°Cjmin) Onset DSC (5CCjmin) Onset DSC Onset DSC Onset DSC Vapour-deposited amorphous water Pressure-amorphized ice Midpoint DSC (1 0°Cjmin) Midpoint DSC (5°Cjmin) Extrapolation of onset from DSC Onset DSC (5°Cjmin) Midpoint DSC (5üCjmin)
Author Roos & Karel [6,7] Roos & Karel [6,7] Joupilla&Roos [8] Roos & Karel [6,7] Roos & Karel [6,7] Roos & Karel [1] Roos & Karel [9] Roos & Karel [9] Roos & Karel [9] Roos [6,7] Vuataz [1 0] Jouppila & Roos [8] Sugisaki et al. [1 1 ]
0" 3
?l CD
5'
:::l
0
-
0 CD ::J" '< 0. öl CD 0. 0 0 :::l Cf> c
3
CD
.....
"Tl 0 0 0. Cf>
Johari et al. [1 2] Hoseney et al. [1 3] Doescher et al. [14] Palzer & Zürcher [ 1 5] Vuataz [1 0] Aguilera et al. [ 1 6]
(J1 co --.I
598
s. Palzer
necessary to consider the mass fraction and the particle size distribution of its main components. 2.2. Hygroscopicity and hygrosensitivity of food powders
Since water or water-based binder solutions are often used in food agglomeration to increase the adhesion forces between the particles, it is required to know the hygroscopicity and the hygrosensitivity of the different food powders. Hygroscopicity describes the tendency of a material to adsorb water from the atmosphere. The sorption isotherm shows the amount of water ( w ' ) a food ma terial contains at a defined temperature and water activity 8w if it is in equilibrium with its environment. The 8w is the vapour pressure in the headspace of the product divided by the vapour pressure of pure water. In equilibrium the relative humidity (RH) of the surrounding air and the water activity of the product are equal. The sorption isotherm of a product can be modelled according to Guggenheim, Anderson and deBoer (equation (4); GAB) or Brunner, Emmet and Tellauer (equation (5); BET) using the parameter C, K and w ' m : ' CK8w w (4) w' m (1 - K8w)( 1 = (C - 1 )K8w) ' w ' wm
C8w (5) (1 - 8w)(1 = (C - 1 )8w) ' w m represents the water quantity (dry-basis) required for a monomolecular water layer on the solid surface. For C = 1 the GAB equation is transformed into the BET equation. Water-soluble crystalline substances nearly adsorb no water until they dissolve completely at a specific RH (sodium chloride at 73-75% RH; crystalline sucrose at 83-85% RH). Amorphous hydrophilic substances adsorb increasing amounts of water with increasing RH, which is stored within the amorphous matrix and no critical humidity, at which the particies might dissolve, can be defined. Accord ingly, re-crystallization of amorphous substances liberates moisture, which af fects the crystallization velocity of the remaining amorphous fraction. The liberated moisture might lead to caking of the powder. Due to crystaliization it is rather difficult to establish the sorption isotherm of amorphous substances with a low molecular weight at high humidity. Figure 2 shows the sorption isotherm of dextrose syrup (wh ich is amorphous), amorphous sucrose, crystalline sucrose and sodium chloride. In addition to the moisture inciuded in a sorption isotherm established for non-porous structures, water might be bound in smali pores. Below a specific pore diameter de, condensation can even occur spontaneously. This critical
599
Agglomeration of Dehydrated Consumer Foods 1 5 .----,--r--, .... sodium chloride • crystalline sucrose • amorphous sucrose • dextrose syrup
dextrose syrup DE 20-21
C .$ c:
8 ....
.$
C1l
3:
•
5
,, ,, ,, ,, ,,
•
,, ,, ,,
..
sodium chloride crysta lline sucrose
amorphous sucrose (Makower & Dye 1956)
,, ,,
re-crystallisation
0.1
......-, 0.4 0.6 0.5 0.3 water activity aw / - ( 22 °C) • •
0.2
0.7
0.8
0.9
Fig. 2. 22°C-sorption isotherm of different amorphous and crystalline food materials (water content determined according to Karl-Fischer).
diameter can be calculated according to equation (6). For the calculation the following parameters are needed: surface tension y of water, wetting angle e between water and solid, temperature T, Kelvin constant R (8.314 J/mol K), vapour pressure Pv , absolute pressure p and molar volume of water V ( 1 8 1 0 -6 m 3jmol). x
'}' cos(0)V dc < 2 RT ln (pfpv)
(6)
Capillary condensation is also one of the reasons for the observed hysteresis between the sorption and desorption isotherm. Changes in the physico-chemical properties of food materials linked to changing water content are referred to as hygrosensitivity. Amorphous materials are more hygrosensitive than crystalline substances. Crystalline substances preserve their texture with increasing hu midity until they dissolve at a certain critical RH of the surrounding air (see Fig. 2). The resulting solution has, in most cases, a low or medium viscosity because the molecular weight of crystallizing substances is normally smalI. Amorphous materials are hygrosensitive. Such substances, which can be re garded as super-cooled liquids, do not really dissolve. They already have a liquid like molecular structure. Amorphous substances absorb moisture depending on
600
S. Palzer
the humidity of the surrounding air. The absorbed water has a plastifying effect on the amorphous matrix. With increasing moisture content the glass transition temperature decreases. The decrease of Tg caused by an increase of moisture can be modelled using the Gordon and Taylor equation [1 7]. For calculating the Tg of a moist substance, the glass transition temperature of the water-free sub stance Tg, s , the glass transition temperature of water Tg,w , the water content w (wet-based) and the Gordon & Taylor constant k have to be known. T9
_
(1
-
w)Tg,s + kwTg,w - w) + kw
-
(7)
(1
Figure 3 shows the glass transition temperature of different food powders at varying water content. In a powder mix the water activity is the same for all com ponents although they might have different water content. Therefore, it is useful to measure the glass transition temperature of the different powder components depending on their water activity. Obviously, the powder fraction with the lowest glass transition temperature at a defined water activity is the most sensitive com ponent within the powder blend. Combining equations (4) and (7), the dependence
1 50 A
�
Cl
•
•
1 00
• •
I�
�
E
Q) c..
$
50
c 0 ."
'e;;
§ c
CfJ CfJ
5!1
0
Cl
•
0
5
• •
soft wheat flour dextrose syrup skim milk powder
•
• • • •
•
soft wheat flour ( D oescher et al. 1 987) ..
reaction flavour
-50
•
native wheat starch (Zeleznak & Hoseney 1 987)
•
��
:::J
reaction flavor wheat starch tomato powder
10 water content (wb) / %
dextrose syrup tomato powder
15
20
3. Glass transition temperature of various food powders depending on their water 1 content (Tg is defined as DSC onset at a heating rate of SOC min- ; water content ac cording to Karl-Fischer; Gordon & Taylor constant k and Tg, s as included in Table 1 ). Fig.
Agglomeration of Dehydrated Consumer Foods
601
of Tg on the water activity can be mode lied according to equation (8) [15]: (1 - Kaw )(1 + (C - 1 )Kaw ) Tg + kwm CKaw Tgw T9 (aw ) - ���������--�-=�� - (1 - Kaw)(1 + (C - 1 )Kaw) + kwmCKaw
(8)
2.3. Mechanical properties of solid food substances
For optimizing pressure agglomeration of food powders it is important to fully understand the mechanical behaviour of the powder. Liquids already deform at very low stress. The shear stress generated within liquids is proportional to the strain rate, and the factor of proportionality is the viscosity of the liquid. So me food substances deform plastically, which means a critical stress has to be exceeded before the material starts to flow. Furthermore, the achieved strain is proportional to the applied stress and after the stress is released, the strain remains. Other food substances like crystalline materials or amorphous substances in their glassy state show elastic behaviour according to Hookes law. Exposing elastic solids to a shear stress FjA leads to a proportional shear strain !J.xjy. The constant of proportionality is the shear modulus G. Alternatively, a compression or elongation of the material can be achieved by applying a normal stress FjA. The achieved strain Mjl is proportional to the stress and the constant of proportionality is the called Young modulus or modulus of elasticity E. The shear modulus G and the Young modulus E are connected via the Poisson ratio v.
Elastic behaviour
Viscous behaviour
Shearing Compression or elongation If the stress generated in such materials due to shearing or compression ex ceeds a certain limit, the particles will break. However, a number of food sub stances have viscous (Iiquid-like) and elastic (solid-like) features. Such materials, including various amorphous food substances, are called visco-elastic. In their glassy state and while exposed to a high strain rate, they behave more like elastic solids whereas in the rubbery or viscous state or while they are deformed slowly, they show liquid-like properties. Mechanical models for visco-elastic substances include a parallel or a serial combination of a spring (representing the elastic component) and a dashpot (representing the viscous component). A serial combination of the spring and the dash pot is known as the Maxwell model whereas a parallel combination is referred to as the Kelvin-Voigt model (see Fig. 4). Since these simple models are
602
S. Palzer E
E,
Tl
Kelvin-Voigt model
four-parameter model
Maxwell model
Fig. 4. Different viscoelastic models for solid food materials.
often not sufficient for describing the behaviour of complex food systems, more sophisticated models (e.g. a four-parameter model) can be obtained by combi nation of several springs and dash pots [18, 1 9]. By applying a constant stress over a defined time, a progressing deformation of the material, which is called creeping, is observed. In case of a Kelvin body no instantaneous deformation is given while exposing the system to such a constant stress (see equation (3)). Applying a Maxwell model an instantaneous strain and a linear increase of the strain with time is obtained (see equation (1 0)). er
�; set) = ( 1 - e -t�) (J (Jt (Ja (J = - + set) = + - t E 11 11
= Es + 11
::::}
So
::::}
Kelvin - Voigt Maxwell
(9) ( 1 0)
is the time dependent strain and (J is the normal stress applied. The Maxwell model cannot account for a retarded elastic response. On the other hand the Voigt model is not able to describe the observed stress relaxation of real food systems. Based on the Maxwell model, the stress relaxation can be described according to equation (1 1 ): s
-(
= (Jo eT
(1 1 ) The relaxation time T, calculated as the ratio between viscosity and Young modulus, indicates how fast the strain decreases after the stress is released. It can be calculated as the ratio between viscosity and Young modulus. For liquids, a relaxation time of 1 0 - 1 2 _ 1 0- 1 0 s is typically found. However, often the relax ation of real systems can only be described using a relaxation time distribution. The ratio between the relaxation time and the observation time is defined as Deborah number, D. If 0 is large, no relaxation is observed during the experiment and the visco-elastic material appears to be more liquid-like. If 0 is very smalI, the material seems to behave solid-like. The relaxation time is influenced by temperature. Empirically, it was found that the temperature dependence of all relaxation times follows the same pattern. According to the time-temperature superposition principle, the ratio between two relaxation times is defined to be the (J(t)
Agglomeration of Dehydrated Consumer Foods
603
shift factor Etr. Below Tg and over 1 000e above Tg this shift factor va ries with temperature according to the law of Arrhenius: aT
e Ea/ R(1 / T - 1 / To) =� Ta =
( 1 2)
where Ea is the activation energy, R the Kelvin constant, T the temperature and Ta a reference temperature. Between Tg and Tg + 1 oOGe the shift factor changes with temperature following equation ( 1 3) [20]: aT
T
-C(T - Ts )
=Ts = ---'---B + ( T - Ts)
( 1 3)
Ts is a reference temperature and e and B are constant factors. Williams, Landel and Ferry [20] found the values -1 7.4 and 51 .6 K for the parameters e and B suitable for the most polymers investigated. The WLF equation has also been applied to predict the temperature influence on viscosity of solid food materials by using Tg as a reference temperature [1 6,21]. log =
(11) = I1g
e(T - Tg) B + ( T - Tg)
(14)
Here I1 g is the viscosity in the glassy state and T the ambient temperature. Peleg found that the WLF constants depend on the substance investigated and the difference between T and Tg [22]. However, other authors obtained satisfying results with the published universal constants while predicting the state of dif ferent food powders [1 6,21]. It appears that, when approaching a certain tem perature, the relaxation time diverges against a finite value. This temperature is referred to as Vogel, Tammann and Fulcher (VTF) temperature Ts. Ts is sup posed to be 500e below the glass transition temperature. Using the VTF-tem perature Ts, the influence of temperature on viscosity can also be estimated using the law of Vogel, Fulcher and Thamann. o
( 1 5)
is a constant parameter. Since equations (14) and (1 5) include the glass transition temperature, the influence of moisture content on the viscosity is also considered in the calculation. Like the viscosity, the Young modulus depends on the time scale of the deformation, the temperature and the plasticizer (in most cases water) content [4]. Figure 5 illustrates how the Young modulus decreases with increasing temperature for amorphous, semi-amorphous and crystalline materials. As previously discussed a static stress leads to a creeping of the material. Alternatively, the food matrix can also be exposed to a dynamic stress or strain. For instance in the dynamic mechanical thermo analysis (DMTA) of materials a
604
S. Palzer
(log scale)
Young modulus
'-----+--;.-+ TemperatuTe T, Tm Fig. 5. Temperature dependence of the Young modulus for different molecular structures.
sinus-shaped strain profile y(t) is applied to test the mechanical material behaviour. I' = 1' 0 sin(wt) ( 1 6) where t is the time, w the frequency of rotation and 1'0 the amplitude of the strain. If the food matrix behaves more liquid-like, the following dynamic stress is ob tained : r = IJYo w cos(wt) ( 1 7) r is the resulting shear stress within the substance. For solids the following time/stress function is valid: = Gyo sin(wt) ( 1 8) G represents the shear modulus of the solid material. For visco-elastic solids, which show liquid- as weil as solid-like features, the shear and the normal stress can be calculated by combining equations ( 1 7) and (1 8): r = 1'0 ( G'yo sin(wt) + G" cos(wt)) withG" = IJ'Yo w or (J = 1'0 (E'1'0 sin(wt) + E" cos( wt») ( 1 9) G' is called the storage modulus and G" is referred to as the loss modulus. Thus the complex shear or Young modulus is composed of a real and an imaginary component. The storage modulus represents the elastic response on an applied stress, and thus includes the potential energy stored in the system. This energy is released when the applied stress disappears again. Large G' values are obtained r
605
Agglomeration of Dehydrated Consumer Foods
60 .-------�--�--�
9
'" Cl. -
W "5
50
8.5
o
"" Q)
'8
E Q) Cl
e!
0 u; Cl .Q
40
30 g> '"
8
7.5
7
6.5 -20
20 10
-10
0
10
temperat ure
20
O �------� -20
40
30
T / oe
o 20 temperature T / oe
40
Fig. 6. Temperature and frequency dependence of storage modulus and loss angle (dex trose syrup DE2 1 ) .
for glassy and brittle materials. 80th moduli are a funetion of temperature, mois ture eontent and strain rate. Signifieant temperature-related ehanges in these moduli can be used to detect Tg while increasing the temperature. The ratio between loss and storage modulus is called the loss tangent and the arctan of this ratio is referred to as loss angle b. tan i) = _
G"(w) G'(w)
(20)
The loss tangent represents the ability of the material to absorb shocks. While changing the temperature, a maximum value obtained for the loss angle indicates significant changes in molecular mobility. This approach can be used either to characterize the mechanical properties of the material or to measure the glass transition or crystallization temperature. However, the measured values strongly depend on the applied temperature gradient and on the used frequency of the strain variations (see Fig. 6). 2.4. Adhesion principles relevant for food agglomeration
Increasing adhesion forces between particles are essential for agglomeration. Adhesion is strongly depending on the physico-chemical material properties dis cussed in the previous subsections. The following adhesion mechanisms are relevant for food agglomeration: ( 1 ) Development of material bridges between particles, including: • Low-viscosity liquid bridges • High-viscosity amorphous bridges • Crystalline solid bridges.
606
S. Palzer
(2) Increasing Van der Waals forces due to increasing inter-particle contact area and decreasing distance between the particles. Possible mechanisms are: • Plastic deformation of the entire particle or a binder layer on the particle surface • Visco-elastic deformation of the particles • Fracturing of larger particles and thus increasing number of contact points. Since the stability of low-viscosity liquid bridges is limited, they must be trans formed into high-viscosity amorphous bridges or crystalline solid bridges by removal of water or cooling. Other mechanisms such as inter-Iocking or elec trostatic forces play only a minor role in food agglomeration. The tensile strength of an agglomerate built out of spheres with diameter a can be estimated according to Rumpf [23] using equation (21 ). F is the adhesion force between two spheres, t: the porosity of the agglomerate and K the coordination number. 1 - t: n 0'1 = KF K � (21 ) 2 t: na Using nlt: as a n approximate value for K and the equivalent diameter a of the primary particles it is possible to estimate the tensile strength of agglomerates built out of non-spherical particles [23]. --
2.4.1. Low-viscosity liquid bridges
Low-viscosity liquid bridges are often discussed in literature as one of the most important adhesion principles in agglomeration. In food agglomeration mostly pure water or a water-based binder solution is sprayed onto moving particles. Droplets colliding with particles can build liquid bridges between these particles. Alternatively, liquid bridges can be built between food particles, which are ex posed to condensing steam or humid air if enough water condenses on their surface. Some components of the particles may even dissolve in the liquid present on the particle surface. In parallel, liquid will either migrate into the solid matrix of the particles by diffusion or be sucked into the particle pores due to capillary pressure. Consequently, the concentration of solids in the liquid bridge and the concentration of water within the solid matrix increase with time. In case of amorphous polymers the viscosity of the bridge thus increases significantly. Successively, the liquid bridge is transformed into a stable viscous bridge. On the other hand, the viscosity of amorphous solids embedded into the particle matrix will decrease due to the adsorbed water according to equation (14). In conse quence, the outer particle layer is plastified. Crystalline low molecular weight substances absorb only minor amounts of water. The outer layer of the particles dissolves rather than become plastified. The low molecular weight substances dissolved in the liquid bridge lead only to a
607
Agglomeration of Dehydrated Consumer Foods
limited increase in viscosity. Thus, the strength of liquid bridges containing dis solved low molecular food substances or a low concentration of polymers mainly depends on capillary forces. A significant increase in adhesion forces can only be achieved by drying. In such low viscosity bridges, the capillary pressure is responsible for the adhesion of the particles. The capillary pressure p can be calculated based on the surface tension y , the radius r of the liquid bridge and the wetting angle 0. 2" cos 0 (22) P r_ Depending on the saturation of the resulting agglomerate, a pendular, a funi cular, a capillary and a droplet-like state can be defined. Assuming that the particles are spherical and in contact with each other, the tensile strength (}t of the agglomerate can be calculated according to Rumpf [24]: 1 8 2y (}t = SC -cos {j (23) a S is the saturation of the total void volume within the agglomerate, C a constant parameter (monosized spheres: C = 6 [24]), the porosity of the agglomerate, y the surface tension of the liquid, a the diameter of the primary particles and 8 the contact angle between the liquid and the solid substance. Due to the low vis cosity, such a liquid bridge can be formed in a very short time. =
-,-1 _
-
--
[;
[;
2.4.2. Solid bridges obtained by drying
If liquid bridges containing dissolved substances are drying out, a solid bridge is formed (see Fig. 7). Changes in the tensile strength (}t of the agglomerate due to drying of a liquid bridge can be estimated according to Rumpf [24] by using equation (24). Vd iss is the volume of dissolved solid within the agglomerate, Vagglo the volume of the agglomerate and (}s represents the tensile strength of the solid substance building
RH > RH,,".
Fig. 7. Dissolution of crystalline substance, building of liquid bridges and re-crystallization.
608
S. Palzer
the bridge after drying. (II
=
Vdiss ( 1 - 8)(Is Vagglo
(24)
-
A defined tensile strength of the solid can only be obtained for crystalline bridges. Amorphous substances are visco-elastic and thus their tensile strength depends also on the applied strain rate. 2.4.3. Sintering
Sintering is a process in which molecules or atoms move into the gap between two neighbouring particles. The process is driven by surface tension andjor an external force. While closing the gap between the particles. the free specific surface energy of the system is reduced. The required movement of the molecules into the gap depends on their mobility. which is linked to the viscosity of the material. Sintering metals or glass. the viscosity is commonly reduced by heating the particles. For water-soluble amorphous food matrixes the viscosity can be decreased according to equation (14) by increasing the moisture content andjor increasing the temperature. Sintering can happen during storage of food particles or while agglomerating powder particles containing amorphous components. Figure 8 iIIustrates the different stages of the sintering process. The different phases in sintering are: ( 1 ) Particles adhere and form bridges between each other (Fig. 9) (2) Bridge diameter and length increases while the open porosity decreases (Fig. 1 0) (3) Open pores disappear and only closed pores remain (Fig. 1 1 ). The kinetics of sintering can be calculated according to an equation pub lished by Frenkel [25] or using a similar equation from Rumpf etal. [26]. The ratio between the sinter bridge diameter x and the particle diameter a can be cal culated depending on the surface tension 'Y . the force Ft with which the particles
free-f1owing
adhering
Fig. 8. Sintering of spherical particles.
increase of bridge Ihickness and length
open pores disappear
609
Agglomeration of Dehydrated Consumer Foods
Fig. 9. Particles adhere to each other in an initial phase of the sintering process (dextrose syrup D E21 ).
Fig. 1 0 . Bridge diameter increasing during sintering (dextrose syrup DE21 ).
(�)2 a
(�l5 a + �) ! 511:a2
are pressed together, the particle diameter a, the time t and the viscosity 11 . =
11
(2 5 )
In case of non-spherical particles a is the radius of the surface curvature of the particle at the point of contact. The strength of the build sinter bridges mainly depends on the viscosity of the substance and the diameter of the bridge. According to Wallack and King [21 ] , a significant adhesion force F between particles should only be observed if the diameter ratio xja exceeds a value of 0.01 to 0. 1 .
610
S . Palzer
Fig. 1 1 . Disappearing of open pores in the final stage of the sintering process (dextrose syrup D E2 1 ).
As mentioned earlier, sintering of food substances is strongly dependent on the viscosity and, thus, on moisture and temperature. Combining the equations (14) and (25) and assuming that, due to sorption or desorption processes the humidity of the amorphous substance is changing permanently, equation (26) is obtained. X 2 4 y 2Ft -1 -C(T-Tg(t)) 1 0 B+(T-Tg (t)) dt + (26) a 1=0 5 a 5rca2 Yf9
( ) = lmox ( I
--
)
--
tmax is the time available for the sinter process. With equation (26) it is possible to predict the kinetics of sinter processes depending on temperature and moisture content. In addition, sintering might be accompanied by capillary condensation. If particles are close enough while they are compressed, a capillary condensation in the gap between the particles can occur (see equation (6)). Such a capillary condensation locally leads to an increasing moisture content at the contact point between the particles (see Fig. 1 2). Therefore, sintering at this contact point will be accelerated due to decreasing viscosity. 2.4.4. Solid bridges built by me/ting ot tat
Agglomeration of food powders containing fat can be achieved by melting the fat. To perform such a melt agglomeration, the powder has to be heated to a temperature close to the melting point of the tat. At least 50-80% of the tat material has to be in the liquid state (solid fat content less than 20%) to achieve a significant diameter of the liquid bridge between two particles. The liquid bridge constructed from melted fat is transformed later into a solid bridge due to re crystallization of the fat (Fig. 1 3).
61 1
Agglomeration of Dehydrated Consumer Foods
�
,../
H2
"
a
93
�2
/
amorphous
/ �
�z
-:;J \....;. H20
diffusion + plastification
crystalline ---...
capillary condensation
B HP _
amorphous substance sintering
_ H20
re-crystallisation
Fig. 12. Capillary condensation during compression facilitating sintering (amorphous sub stance) or dissolving the material locally (crystalline substance).
>S
-+
crystallisation of fat
melting of fat
Fig. 1 3. Solid bridges built by melting and re-crystallization of fat.
2.4.5. Increasing adhesion forces due to increasing contact area andjor distance between the partie/es
Adhesion between food particles can also be explained by increasing Van der Waals (electrostatic) forces. 8etween a sphere and a plate, these forces are approximately five times smaller than capillary forces. Knowing the diameter x of the created contact area, the distance 1 between the two particle surfaces and using the Lifshitz-Van der Waals constant hw ( 1 0- 1 8_1 0-20 J) or the Hamaker constant H ( 1 0-19_1 0-18 J) the resulting adhesion force Fad can be calculated according to the theory of Lifshitz or Hamaker [27,28]: Fvdw
=
Fvdw =
--3 X
hm 8nl H
2
2
Lifshitz
(27)
(28) 3 X Hamaker 61 80th equations are valid for distances smaller than 1 50 nm. Obviously, the Van der Waals forces strongly depend on the distance between the particles. In
612
s . Palzer
addition, they are proportional to the inter-partiele contact area. To increase the Van der Waals forces between food particles, their contact area has to be in creased andjor the distance between them has to be decreased. The required deformation of the partieIes can be plastic or visco-elastic. Plastic deformation. Particularly in pressure agglomeration of food partieles, sometimes plastie binders like fat are used. The plastie binder is either added in the form of a powder to the food partieIes or the food partieIes are eoated with fat prior to pressure agglomeration. Aeeording to Rumpf etat. [26] the adhesion force F between two spheres aehieved by plastie deformation is proportional to the force Ft with whieh the partieIes are pressed together and also proportional to the Van der Waals pressure PvdW . The Van der Waals pressure itself is proportional to the distanee t between the neighbouring surfaees. This distanee t is theoret ieally 0.4 nm for the ease where both surfaces are in eontaet with each other [26]. In addition, the adhesion forces generated by compression are depending on the yield pressure of the substanee Pp l . F
�
PvdW Ft Ppl
with
Pv dW
= nx2 = 8hwn2p Fvdw
(29)
The stability of the generated agglomerates depends on the adhesion of the deformed binder on the partieIe surfaee due to Van der Waals forces and as weil on the eohesion of the plastie binding substanee itself. Visco-etastic deformation. Some substanees deform viseo-elastieally. The viseo-elastie deformation leads to an inerease in Van der Waals forees due to a larger eontaet area and a deerease in distanee between single partieIes (see Fig. 1 4). The material partly relaxes if the stress is released. Equation (30), based on a simple Maxwell model, enables the ealeulation of the eontaet area between spherical partieIes ereated by a viseo-elastic flattening at
a:
�
...
...
t
a:
t
time �
Fig. 1 4. Visco-elastic deformation and relaxation of food partieIes.
Agglomeration of Dehydrated Consumer Foods
the contact points
[26].
2 = ( 3 :�r/3 G ir/3 G) 32 +
613
(30)
E is the Young modulus of the material.
3. AGGLOMERATION PROCESSES USED SY THE FOOD I NDUSTRY 3.1 . Agglomeration of food powders duri ng spray-drying
A number of dehydrated food products are produced by spray-drying or a com bination of spray- and belt-drying. It is desired to agglomerate such particles to improve their instant properties and the flowability of the powder. The finished powder can be agglomerated separately after the drying process in a pneumatically fluidized bed. However, the related additional handling and processing increases the manufacturing costs significantly. Alternatively or additionally, a limited ag glomeration can also be achieved during the spray-drying process. In most cases the drying droplets contain amorphous substances and depending on their tem perature and moisture content, they are in a sticky state. Sticky particles that collide with each other or with re-circulated fines adhere to form brittle agglomerates. Bhandari discussed the stickiness of powders during spray-drying. Werner et al. investigated the stickiness of maltodextrine solutions during drying by using a tack tester. A droplet of the solution was placed in a pan and a flat-headed probe was brought in contact with the solution. The whole installation was placed in a drying chamber. The force required to pull off the piston was measured at different moisture content. Both authors found a defined humidity level providing a maximum pull-off force. At low- and at high-moisture content the stickiness was significantly reduced. For spray-drying this means that at high moisture content the cohesion within the liquid bridge between two particles is low (cohesive failure). The droplets rather coalesce with each other or with dry particles than to form the desired porous agglomerate structure. Decreasing the moisture content of the droplet surface, the stickiness of the particles increases until a maximum is reached. Drying increases the viscosity, and, thus, the di ameter of the bridge between two colliding particles, which can be built within the short contact time decreases. Since inter-particle bridges are built by viscous flow, the adhesion kinetics should be predictable according to equation Further decreasing the water content, a point is reached at which adhesion is no longer possible (adhesive failure). According to these considerations re circulated fines should be brought in contact with droplets, which are within the state of maximum stickiness to achieve the best agglomeration result. However, it has to be considered that the state of maximal stickiness depends on the contact time of the particles.
[29,30] [31]
(26).
614
S. Palzer
Contact of sticky particles with the drier wall would lead to encrustation of the equipment. In addition, the majority of the particles falling into a fluid bed con nected to the drier outlet or integrated within a spray-drier should contain only a small amount of humidity to avoid a collapse of the fluid bed. ünce the temperaturejmoisture conditions for maximal stickiness are estimated according to equation (26) for a certain product composition, the region within the spray-drier where such conditions are given has to be identified by CFD modelling or by performing measurements. Agglomeration during spray-drying can be mod elled according to Blei and Sommerfeld [32] using a Langrangian approach. There are different technical approaches to achieve agglomeration in spray towers. üne possibility is to retain fine particles generated during atomization within the spray tower by using integrated bag-filters that are installed in the top part of the drier. Fine particles accumulating on the surface of the tissue of the filter bag fall back into the tower where they adhere to moist particles or droplets. Figure 1 5 shows a spray-drier equipped with integrated filter bags and a fluid bed at the boUom of the drier.
air
Feed Tanks Homogenizer Pump SSHEX LSI unit
Filter bags integrated into the drying chamber
Dehumidifi er Fig. 1 5. Integrated filter drier. (IFD-50-R/N; courtesy Gea Niro Soborg DK.)
Agglomeration of Dehydrated Consumer Foods
615
Another approach is to separate the fine particles from the exhaust air of the spray tower and the after-drier using a cyclone or an external bag filter. These fines are then re-circulated into the main drying zone of the tower. Sometimes the re cycled fine particles are also blown into the tower close to the spray nozzles [33]. A third possibility is to install an integrated fluid bed at the bottom of the drier. Agglomeration of partially dried droplets can happen due to the intensive contact between the particles in such a fluid bed. Sometimes also re-circulated fines removed from the exhaust air of the tower and the after drier are added into such a fluid bed. Figure 1 6 shows a spray-drier in which recycled fine particles are added back into the top part of the tower. In addition, this type of spray-drier is equipped with an integrated fluid bed. Such a system is referred to as multi-stage drier. The described spray-driers are mainly used for instant coffee, dairy powders like skim and whole milk powder, infant formulas, beverage powders, maltodex trines, dextrose syrup and powdered flavours. Figure 1 7 includes a picture of a whole milk powder agglomerated during spray-drying. Another system particularly suitable for spray-drying sticky or high fat powders is the so-called Filtermat-drier (Gea Niro), which is in fact a combination of spray and belt-drying (see Fig . 1 8). The liquid to be spray-dried is atomized into a short spray tower using a rotary atomizer or a spray nozzle. The particles that are often still in the sticky state fall on a moving belt where they agglomerate to a powder cake. This cake is dried by flushing it from the top with hot air. Carried by the
+-+<111� drying air
concentrate
fines fluidisation air
__-1-<"
-
finished product
Fig. 1 6. Multi-stage drying for food powders.
616
S. Palzer
Fig. 1 7 . Whoie milk powder agglomerated during spray drying.
liquid feed
sitter
exhaust air fines
Fig. 1 8. Seheme of a eombined sprayjbelt-drier. (Filtermat drier from Gea Niro Soborg DK.)
moving belt the powder cake advances to a cooling zone where cold, dry air is blown through the powder cake. During drying the exhaust air has to leave the system by passing the cake, which enables the fine partie/es contained in the exhaust air to agglomerate with the sticky partie/es of the cake. If a hard cake is obtained it is milled down to the desired agglomerate size. In case the adhesion
Agglomeration of Dehydrated Consumer Foods
61 7
forces between the particles are small (brittle cake), a final sieving step is sufficient to separate the lumps and the fines from the brittle agglomerates. The major advantage of this process is that stickiness of powder particles linked to glass transition or high amount of melted fat is not that problematic because the formed powder cake can later be grinded to a smaller particle size. Figure 1 8 shows a schematic drawing of a Filtermat drier. Filtermat driers are used for dairy blends, coffee whiteners, whey and whey protein, cheese powder, maltodextrines and glucose syrup, infant formulas, fruit and vegetable powders (e.g. tomate powder), soy sauce powder and instant coffee. Generally, spray-drying leads to highly porous, small and friable agglomerates. On the other hand, it is one of the most cost-efficient agglomeration technologies. 3.2. Steam jet agglomeration of food powders
Steam jet agglomeration has been used by the food industry for several years. During steam jet agglomeration a powder or a powder mix is first milled to a small particle size (below 1 00 Jlm). The milling step takes 1-2 s and is performed in rotor/stator mills (e.g. in a pin mill). After leaving the mill the powder has a tem perature of 25-35°C. The milled powder is then cooled down in double-jacketed pipes and by using cold air for pneumatic conveying to facilitate the condensation of steam on the particle surface. These particles are either blown into an ag glomeration tower or a fluid bed where they are exposed to steam. The steam condenses on the particle surface and the generated liquid forms liquid or viscous bridges (see Seetions 2.4 . 1 and 2.4.3). Different agglomeration equipment is used to perform steam jet agglomeration: Combined steam/powder nozzles integrated into spray-driers to agglomerate re circulated fines, stand alone agglomeration towers and fluid beds equipped with steam nozzles at the feeding of the bed. 3.2.1. Steam jet agglomeration systems integrated into spray-driers and stand-alone agglomeration towers
In spray-drying, steam jet agglomeration systems are used to agglomerate re cycled fine particles while they are added back into the spray tower. Similar systems are operated to agglomerate powder blends in stand-alone agglomer ation towers. In both applications, the particles to be agglomerated are first milled and then cooled during conveying to the steam jet nozzle installed on the top of the drier. The fine powder is then blown into the top part of the tower through a combi ned steam/powder nozzle or separate nozzles for powder and steam, which are
618
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installed close to each other. Steam is either applied centrally or laterally through the same nozzle or using separate steam nozzles. The central steam jet prevents the powder from sticking to the nozzle tip and accelerates the particles. Saturated steam applied laterally provides the necessary moisture required for adhesion of particles by condensation. In addition to condensation on the particle surface, droplets are also formed by condensation of water in the vapour phase. Approx imately 25-50% of the water contained in the steam condenses in the agglom eration zone while the powder moisture content increases from 0.1-2% up to 2-8%. The condensing steam heats the powder to a temperature of up to 80-90°C. The residence time of the particles within this agglomeration zone is about 1-5 seconds. While the particles fall further down the tower, they dry due to co- or counter-current airflow and their surface temperature drops from 80-90°C to the wet-bulb temperature, which typically is 50-60°C [34]. The particles collide with each other or with the droplets due to the different sedimentation velocity and acceleration by the steam jet. Larger particles falling down faster will collect smaller ones on their way through the agglomeration tower if they are still sticky. The main agglomeration zone ranges from the nozzle outlet to a distance of 0.5-1 m from the nozzle tip [34]. The presence of dry agglomerates (consisting of primary particles held together by Van der Waals forces) prior to entering the agglomerator is desired since the particles are al ready in close contact with each other. The following condensation of steam within the tower stabilizes such brittle agglomerates. Since the difference in velocity between single particles is lower than 0.2 m S-1 [43], the collision frequency and the stress on the particles is low. If, at the moment of collision, sufficient water is present at the contact points particles can adhere to each other. Agglomerating crystalline solids low-viscosity liquid bridges (see Sections 2.4. 1-2.4.2) are the main adhesion principle. If the particles are composed out of amorphous solids, a viscous layer is developed at the particle surface and viscous bridges are built between colliding particles. The increase in product temperature caused by the condensation of steam encour ag es the plastification of the particle surface. The agglomeration rate and the stability of the agglomerates obtained are high if the frequency of collisions is high and if the kinetic energy of the particles is dissipated upon collision. The frequency and the amount of condensed water can be influenced by the design of the nozzle and the orientation of the steam jets. A narrow powder jet resulting in a high concentration of powder particles leads to a higher shear force on the agglomerates and, therefore, to a higher amount of fines. The steam pressure of the different steam jets is important for the product quality. Increasing the velocity of the central steam jet accelerates the particles and, thus, leads to less contact time between the particles and the lateral saturated steam applied for humidifying the particle surface. Increasing the pres sure of the driving steam jet, thus, results in fragile agglomerates. Another in fluencing parameter is the temperature of the powder to be agglomerated.
Agglomeration of Dehydrated Consumer Foods
619
Decreasing the powder temperature before agglomeration leads to a more ef ficient condensation and, thus, to harder agglomerates. Co-current airflow is useful for temperature sensitive powders because the temperature at the drier outlet is lower than in case of a counter-current airflow. On the other hand, using a counter-current airflow, the drying is very efficient and the tower might be operated without an after-drier. The agglomerates leaving the agglomeration tower are often dried and cooled in a separate fluid bed. In the drying section of the after-drier the moisture content is reduced to less than 2%, while the powder temperature is about 50-60GC. In the cooling section of the after-drier the powder is cooled down to 20-30°C to avoid caking during storage. The average residence time of the particles in such an after-drier is around 1-3 min. 3.2.2. Steam jet agglomeration in a fluid bed
Steam jet agglomeration can also be performed in a fluid bed. A curtain of the milled and chilIed powder is subjected to a steam jet that moistens the powder by condensation. The wetted powder falls into the bed where it agglomerates fol lowed by drying in the first section of the bed and then cooling to their final temperature in the second section of the bed. Finally, the product is sieved and filled into storage containers. Agglomerates produced by steam jet agglomeration are highly porous and thus dissolve rapidly. The agglomerate sizes obtained vary typically between 0.5 and 4 mm. Besides the excellent instant properties of the agglomerated product, one of the major advantages of steam jet agglomeration is its short and narrow res idence time distribution. As a consequence, losses of volatile components and thermal degradation are minimized and the steady state of the plant can be reached quickly after start-up. 3.3. Fluid-bed agglomeration of food powders
Fluid-bed agglomeration is widely used in the chemical, food and pharmaceutical industries to improve powder products. There are different ways to fluidize a powder: flushing it with an air stream, moving it in a rotating device or stirring it mechanically. If the powder is fluidized by using air this is referred to in the following text as pneumatic fluidization. Mechanical fluidization refers to the case where the particles are fluidized by stirring. 3.3.1. Pneumatically fluidized bed
Pneumatic fluidization is often used by the food industry to produce highly porous agglomerates. The powder particles lay on a perforated plate while they are
620
s. Palzer
fluidized by air blown through holes in the plate. The air forced to flow through the powder bed exerts a drag force on the particles. At a certain velocity this drag force compensates gravity and the particles start to float. The air pressure at which the particles start to lose contact between each other can be calculated according to equation (31 ) [35]: I1p = h( 1 - 8) (Ps - Pa)g (3 1 ) where I1p is the pressure difference, Ps the density of the solid, Pa the density of the fluidization air, h the height and 8 the porosity of the powder bed. Setting the pressure difference required for separating the particles from each other equal to the pressure losses due to friction between air and particles and assuming a laminar flow through the bed, equation (32) is obtained. The air velocity u required for fluidization can be estimated according to the following equation [35]: u=
-
_1_ � ga�2
)
(
Ps - Pa (32) 1 50 1 8 VPa Pa where u is the kinematic viscosity of the air and 832 the equivalent diameter of the particles. u is the minimum air velocity within the empty bed required for fluid ization. At the air velocity u the drag forces exerted by the air are able to support the weight of the particle. The maximum air velocity is given at the point where the particles float. It can be estimated using equation (33) [35]:
(
) 0.67
8 w = f!. (Ps - Pa) (33) 9 PavO.5 The real velocity v while operating a fluid bed is thus smaller than w and larger than u. For food agglomeration in a fluid bed typically an air velocity between 0.5 and 1 m S- 1 is applied. In some equipment (e.g. the bottom spray system equipped with a Wurster tube) the particles do not move randomly, but circulate in a more or less controlled manner within the bed. The time 8 particle needs for one circulation within a spouted bed can be estimated according to equation (34) [35]: t
= 1.v-u67·h . ( 1 _ v-uus )
(34) UB = K1 . ( v - u) + 0.71 . 2 · ,Jl5 · )g . OB K 1 = 0.67 - 0.76 UB is the velocity of the bubble within the bed. The parameter K1 is depending on the design of the bottom plate. OB the diameter of the bubbles and 0 the diameter of the bed. While the particles are in motion, 2-20% of water or a water-based binder solution is sprayed on them. The particle temperature va ries between 35 and 50°C. The inlet air typically has a temperature between 70 and 1 00°C. The main influence on the final particle size appears to be the added binder quantity and the liquid flow rate per nozzle. In addition, the temperature of the drying air has an influence on the evaporation rate and thus on the final agglomerate size. During
621
Agglomeration of Oehydrated Consumer Foods
the agglomeration process the medium moisture content of the powder and the mean particle size increase steadily. Like shown in Fig. 1 9 the moisture content of the coarse particles is higher than the one of the fines. When spraying water on amorphous particles within a fluidized powder bed, the particles colliding with droplets become very sticky. If the relative humidity (RH) within the powder bed is too high, the entire bed can collapse due to sinter-like processes. Assuming a fixed value for the inter-particle contact time within a moving powder bed, moisture/temperature combinations leading to a blockage of the powder bed can be estimated using equation (14). Figure 20 shows a scan ning electron microscopic (SEM) picture of such a collapsed dextrose syrup powder bed. The agglomerates obtained by fluid-bed agglomeration are finally dried to a moisture content of 1-5% and cooled below their glass transition temperature to avoid caking during storage. The process can be performed in a batch or continuously operating fluid bed. Either single or double phase atomizers are used to inject liquid binder. The atomizers can be positioned above the bed (top-spray, see Fig. 21 ) or within the powder bed (bottom-spray, see Fig. 22). In ca se of bottom spray, a vertical tube can be installed within the powder bed just above the nozzle (Wurster tube) to facilitate a controlled circulation of particles within the bed.
100
90 30 80
Ö ;fl.
70
.'
60
20
III
'"
E Q) >
50
:; E
40
�
.
•
.
.
.
.
.
.
-
-
- - - - -. - - . . - .
.
- - - .. -
-
!c:
c: 0' <>
--- . 15
Ci; .,
;;
:0
Ü
25
. . . . . . . . . . . . . . . . .. . . . .
,.
-o- particle size at
30
1 5%
added wate r
particle size at 20% added water
10
-e- particle size at 30% added water
20
• •
10
.. . ...
• ••
water dislribution at
1 5%
added water
5
water distribution at 20% added water
water dislribution at 30% added water
O ���----,--�--r--.---�--+ O o
200
400
600
800
d
1 000
e
particle ia m ter
1 200 XSO,3 I
1 400
1 600
1800
2000
um
Fig. 1 9. Changes in particle size distribution and moisture content per particle class during the agglomeration of dextrose syrup (CPCG Glatt; top-spray system; dextrose syrup OE 21 agglomerated with a constant spray rate of 30 g waterjminjnozzle).
622
S. Palzer
Fig. 20. Scanning electron microscopic (SEM) picture of a collapsed dextrose syrup pow der bed.
o===� �
Fig. 21 . Batchwise operating top spray fluid bed.
Figure 23 shows a dextrose syrup agglomerate produced in a batch-wise op erating fluidized bed (top-spray). Obviously parts of the particle surface remain dry whereas others are clearly plastified by impacting droplets. These plastified areas provide potential adhesion points for other particles. Due to the strong adhesion forces generated by viscous bridges between the particles and the low shear forces, non-spherical agglomerates are obtained. For higher batch sizes continuous processes are applied. A continuous fluid-bed agglomerator is divided in different zones. In the first zone, the powder
Agglomeration of Dehydrated Consumer Foods
623
Fig. 22. Bottom spray (batch fluidized bed) with Wurster tube.
Fig. 23. Dextrose syrup agglomerate produced in a top-spray fluid bed (Glatt CPCG; 20% water; 60 g/min/nozzle, SEM picture).
is fluidized by using hot air and water is sprayed onto the moving particles. The particles are wetted, they stick to each other and simultaneously these agglo merates are dried. In the final section of the bed no liquid is injected and the powder is fluidized with cold air to cool it down to a temperature below its glass
624
S. Palzer
Drying or eooling air
Fig. 24. Continuous fluid-bed agglomerators. (Left: courtesy Glatt GmbH Binzen Weimar D; right: courtesy D M R Prozesstechnologie GmbH Kaiseraugst D.)
transition temperature. The movement of the power towards the outlet of the bed is linked to the direction of the air-jets leaving the holes in the boUom plate. Often the bed is vibrated by an exenter-motor, which helps to carry the product through the bed. At the outlet of the bed, a weir is sometimes installed to control the bed height and to adjust the residence time within the bed. In Fig. 24 two continuous fluid-bed agglomerators are shown. The agglomerator on the right side consists of an integrated system for spray-drying which can also be used for steam jet agglomeration. When operating a continuous fluid bed it is important to have an idea of the residence time distribution of the particles in the bed to be able to estimate the level of thermal degradation or crystallization of low molecular sugars during agglomeration. The residence time depends on the feeding rate, the weir height at the bed outlet, the air velocity, the orientation of the holes within the boUom plate and the vibration of the bed.
3.3.2. Mechanically f1uidized bed
In a mechanically fluidized bed the powder is fluidized by fast rotating stirrers while the binder liquid is sprayed on the moving particles. For agglomeration of powders in mechanical fluidized beds different types of equipment can be used: continuous and discontinuous paddle or ploughshare mixers (Figs. 25 and 28), vertical granulators with fast rotating blades on the boUom of the mixer (Fig. 26), mixers operating with turning drums and fast rotating blades and cont inuous mixers equipped with a flexible wall and fast rotating bl ades (see Fig. 27).
625
Agglomeration of Dehydrated Consumer Foods -'I!!!::::===> '--
binding liquid
moving particles
Fig. 25. Ploughshare mixer used for agglomeration. (Courtesy Lödige GmbH Paderborn 0.)
Fig. 26. Vertical granulator. (VG; courtesy Glatt GmbH Binzen/Weimar 0.)
Powders that are used for tabletting of confectionery, starch, bakery mixtures, proteins, sugar, instant beverages and feed products are agglomerated in mechanical fluidized beds. For agglomeration up to 1 5% water, water-based binder solution (e.g. con taining starch/sugar), lecithin, molasses or melted fat is sprayed onto the moving particles. In batch agglomeration systems, such as a high-shear paddle mixer, the process time varies between 1 0 and 1 00 min. The agglomerator is normally operated at a fill-level of 20-50% . In a first phase the liquid is injected at a high rotational speed of the mixing tools. In a second agglomeration phase usually the rotational speed of the mixer is reduced to form the agglomerates. Horizontal or vertical mixers with fast turning mixing tools (see Figs. 27 and 28) are used as continuous agglomeration systems. The residence time in such continuous agglomerators varies between 1 and 2 s and a fili level of 20-30% is applied. The
626
S. Palzer
Axis with mixer tools
Initial nn",rtA,'_
Flexible tube Pneumatic system for moving the tube system for moving the tube
•
Agglomerated powder
Fig. 27. Continuous high-shear mixer. (Sehugi Flexomix. eourtesy Hosokawa Mieron Doetinehem NL.)
BV
Fig. 2 8 . Continuous high-shear mixers. (Left: Turbulizer, eourtesy Hosokawa Mieron Doetinehem N L ; right: CB eourtesy, Gebrüder Lödige Paderborn 0.)
BV
mixing/cutting tools of a vertical agglomerator like the one shown in Fig. 27 are rotating with a speed of up to 3000 rpm in order to break lumps and distribute the liquid homogenously. So me continuous paddle mixers have a segmented mixer drum and each segment has a conical shape. Due to the reduced cross section the powder is densified towards the end of these sections, which should support the agglomeration process. After the agglomeration step the product is dried and cooled in a pneumatically fluidized bed to ensure its storage stability.
Agglomeration of Dehydrated Consumer Foods
627
The agglomerates produced in a mechanically fluidized bed typically have a diameter between 1 and 1 0 mm. They are more or less spherical, dense and mechanically more stable compared to agglomerates produced in a pneumat ically fluidized bed. 3.4. Press ure agglomeration of food powders
In steam jet or fluid-bed agglomeration, the particles adhere to each other upon collision if liquid or viscous bridges are generated between the particles. At low viscosities surface tension is the main driver responsible for developing liquid bridges. With increasing viscosity it is no Ion ger possible to build material bridges between the particles within the short contact time. However, at medium viscosities of the particles outer particle shell will still deform upon collision. The achieved deformation includes stronger Van der Waals forces due to a decreasing distance and an increasing contact area between the particles. Only if the viscosity at the point of contact is not too high, a significant and remaining deformation is obtained during collision. Increasing the pressure with which the particles are pressed together can compensate for the high resistance to de formation. Agglomeration processes in which the particles are subject to exter nal pressure are referred to as pressure agglomeration. Extrusion, tabletting and roller compaction are examples for such pressure agglomeration processes applied in the food industry. In extrusion of wet powder masses a low pressure is applied to form agglomerates. During roller compaction or tabletting the parti eies are subject to high pressure leading to dense and mechanically stable agglomerates. 3.4.1. Extrusion of wet powder masses
Extrusion is a process used for manufacturing various food products. In extru sion a paste like mass is pressed through a die with various holes. For example, for cereals and snack products extrusion is used to transform a starch- or flour-containing mix into swamp-like structures. Melt-extrusion applied in flavour encapsulation leads to a glassy structure in which the aroma droplets are em bedded. However, since the initial particles can no longer be. Such a process is by definition (see Chapter 1) not an agglomeration processes. A different case is the extrusion of wet powder masses known as "wet mass ing" or "sieve extrusion". A powder mix is wetted with 3-20% water in a kneader or powder mixer. In some equipment (as in Fig. 29) the wet mass is pressed through cylindrical holes by a piston or rotating blades. The obtained product string is then separated into individual agglomerates by cutting or due to forces like gravity or inertia (see Figs. 29 and 31).
628
s. Palzer
Fig. 29. Extruder for wet powder masses. (Bextruder; Courtesy Hosokawa Bepex GmbH Leingarten D . )
Fig. 3 0 . Extruder with two perforated rollers. (Courtesy Hosokawa Bepex GmbH Leingar ten D.)
Another equipment used for the extrusion of food and feed consists of two perforated rollers. The powder mass is pressed through holes in the roller wall while passing the gap between the roller pair. Cylindrical agglomerates (see Fig. 30), in which the original powder particles are still visible, are formed. Depending on the amount of added water, a subsequent drying step is required to stabilize the agglomerates. This drying can be performed either in a batch
629
Agglomeration of Dehydrated Consumer Foods
n��l' I
ROTATING PADDLES
---- ZONE 1 -----+· +-
ZONE
1 ,11 • •
2 · - - ZONE 3 - .Z0N E 4.
Fig. 31 . Extruder for wet or fatty masses. (Extrudo-mix; eourtesy Hosokawa Mieron B.V. Doetinehen NL.)
vacuum drier or a continuous or batch operating f1uidized bed. The final water content achieved after drying is normally in the range from 1 to 5%, depending on the drying temperature and the residence time within the bed. However, drying extruded agglomerates containing amorphous substances that are moisture and heat sensitive in a fluidized bed is difficult. In such a case, a low temperature and a low feeding rate has to be applied to avoid lumping or even a collapse of the bed. If fat is used as a binder, cooling (instead of drying) is required to stabilize the extrudates. Extrusion is applied for instant tea, sweet beverages, seasonings, culinary binders and various animal feed products. 3.4.2. Roller compaction
Roller compaction is a type of pressure agglomeration. A high pressure is exerted continuously on a moving powder stream while the powder particles are pressed into a gap between two synchronized counter-rotating rollers. Figure 32 includes a process scheme for roller compaction of food powders by using a vertical roller pair and a screw feeder. Figure 33 shows a roller compactor with flat rollers, whereas the compactor shown in Fig. 34 has roller surfaces with cavities forming briquettes. The powder is fed into the gap between the two rollers using a force feeder or sometimes just under gravity. The powder is then forced to pass the gap due to the pressure generated by the screw or gravity and to a great extend due to the wall friction between the powder and the roller surface. While passing the gap it is compacted into large flakes, briquettes or into an endless, dense ribbon. The two
630
s. Palzer base powder
+
coarse particles
sitter
g ri nde r lo:---� fine partie/es
Fig. 32.
Process scheme for roller compaction of powdered food materials.
Fig. 33. Roller compactor with vertical feeding. (Courtesy Hosokawa Bepex GmbH Le i ngarten 0.)
rollers turn at up to 20 rpm. Working with a flat roller surface, a thin flat ribbon sheet is obtained, whereas a roller surface with large cavities generates bri quettes. The compacting pressure is adjusted either by increasing the feed-rate or by adjusting the distance between the two rollers. According to Johanson [36], it is possible to increase the pressure generated within the roller gap by using rollers with rough surfaces.
Agglomeration of Dehydrated Consumer Foods
Fig. 34.
631
Roller compactor with teeth rollers. (Courtesy Hosokawa Bepex GmbH Leingarten 0.)
The compressed ribbons or briquettes can be grinded in a so-calied "gran ulator" which is a sieve basket in which a stirrer oscillates or rotates with 200-300 rpm (see Fig. 35). Alternatively, toothed crushers are used for crystalline materials. To optimize the particle size distribution of the final product the obtained coarse granules can be ground for a second time (see Fig. 36). The granules obtained after grinding are sifted into at least 2 fractions: the fines and the desired particle fraction. Oversize particles are normally not obtained by using the described granulator due to the installed sieve basket. The fines are added back into the feeding hopper of the compactor. In compactors, which consist of vertical roller pairs (see Figs. 32 and 36) the powder is fed from the side into the gap between the rollers. Compactors that have horizontal roller pairs (see Figs. 33 and 34) require a vertical feeding by using gravity or a vertical screw. For food materials, roller compactors with a throughput of up to 1 50 t/d are used. Food powders are typically agglomerated to a final particle size of 0.2-3 mm by applying a line pressure of up to 50 kN/cm. The resulting dense granules are sharp-edged, and compared to the porous agglomerates obtained by extrusion of wet masses their dissolution rate is lower. Several models to describe roller compaction have been published in the last 50 years. In some models, the gap between the two rollers can be divided into a slip and a nip region. In the zone outside the rollers the powder is exposed only to the minor principle stress generated by the feeder or by the weight of the powder
632
s. Palzer
g o
�
0
0 0
Fig. 35. Granulator used for grinding the ribbons into individual granules. (Courtesy Alexanderwerke, A.G. Remscheid, 0.)
Roller compactor with horizontal feeding and de-aeration funnel. (Courtesy AI exanderwerke, A.G. Remscheid, 0.)
Fig. 3 6 .
633
Agglomeration of Dehydrated Consumer Foods
-�
1
: -ir--
-
�
�7'""sl iP r�;
-
.----- Stress (J
length 1
Fig. 37.
Slip and nip region between the two rollers and resulting pressure profile.
itself. When the particles enter the gap between the two rollers a region whe the powder slips on the roller surfaee ean be identified (see Fig. 37). This regidn is ealled the slip region. For a steady state flow the yield eriterion aeeording to Jenike and Shield [ 1 8] ean be applied in order to deseribe the state of the powder in this region. While the particles move further into the gap between the two rollers they " nter the so-ealled nip region where the powder has no relative motion eompared ' the roller surfaee. The powder is eompaeted following a material-speeifie law. F lure 37 i1lustrates the nip and the slip region between the two rollers. Johanson [36] published a model for ealeulating the pressure generated in the powder depending on the position within the gap for these two regions. his model the pressure is predieted as a funetion of the flow properties of the po . der, the roller size, the width of the gap betwe�n the rollers, the surfaee propert" s of the rollers and the feeding pressure. In the slip region the powder slides on the surfaee of the roller and thE' e is signifieant movement of the particles within the powder bulk. Following the theory of Mohr/Coulomb the yielding of a bulk solid ean be approximated using a linear relation between normal stress and the resulting shear stress within the bulk [37]: • . '
'r
r
= (J tan (j + C
effeetive yield loeus
(35)
r is the shear stress, (J the normal stress within the powder and C represents the cohesivity. The slope of this straight line is given by the tangents of the so-ealled effeetive angle of internal frietion. This straight line represents normal and shear stress eombinations at whieh the powder starts yielding. Below the line the powder is not moving whereas any state above the Mohr-Coulomb line is not possible. It should be noted that eaeh powder density results in a different Mohr-Coulomb line. Beside particle movement within the powder bulk, the sliding of the powder particles on the surfaee of the rollers has to be eonsidered for modelling the
634
s. Palzer
system. This process can be described using the angle of wall friction ep. Multi plying the normal stress with the tangents of ep the shear stress required for sliding of particles on the roller surface is obtained: (36) r = (J tan ep wall yield locus All parameters in equations (35) and (36) describing the powder behaviour in the slip region can be determined by shear experiments using a Jenike shear tester or a ring shear cell. Considering the geometry of the gap between the two rollers and neglecting the cohesivity C, Johanson calculated the stress gradient d(Jjdx in the slip region according to the equations (37)-(39): 1 . sin ep = ep arcsln -.(37) 2 Sin D v
-
(1t
)
8h = 21t - V -
-
(38)
- e ) tan D 8( ) = � ( 1 � cos4(J (e�) (cot(A - cot(A with A � (� 8 ) and � � 4 2 2 2 d(J dx
-
+
=
+
v
-
-
+
J1 =
v
J1)
-
+ J1))
(39)
d is the diameter of the rollers, h the distance between the rollers and (J the normal stress. () is an angle describing the position of the particles within the slip region. eh, is the angle at which the particles enter the slip region. While e ap proaches 0h, the stress gradient d(J/dx decreases to O. For the nip region, in which the powder is compressed without relative move ment between the roller surface and the particles, Johanson assumed that the normal stress (pressure) within the powder mounts according to a simple tablet material law [36]:
(J2 (J1
=
(PP12) K P
(40)
K is the compressibility of the bulk solid, its density and (J the resulting stress. The indices 1 and 2 are defining different states of the powder. K has to be obtained experimentally. The powder density is depending only on the geometry of the system. Ac cordingly, the pressure within the nip region at a defined position in the gap (given by the angle can be calculated according to equation (41 ):
8)
d(J dx
- (0) = K
(J (2 cos 0 1 - �) tan e H� + ( 1 + � cos cos e) -
-
8)
(41 )
d is the roller diameter, h the distance between the two rollers and s the surface roughness of structured rollers. For = 0 or e�60° the stress gradient d(J/dx
8
635
Agglomeration of Dehydrated Consumer Foods
decreases to O. At the interface between slip and nip region both stress gradients are equal. The angle, at which the particles leave the slip region while entering the nip region, is ca lied angle of nip Thus, it is possible to identify by com bining equations (39) and (41 ). However, it has to be considered that in the slip region the density of the powder changes and thus, the effective angle of friction might change perma nently while the particles move through the slip zone. Johanson did not consider this fact. According to Dec et al. [38] the Johanson-model is useful for finding a theo retical value for the nip angle in compactors with gravity feeders. Furthermore, it enables to predict the pressure distribution in compactors with large smooth rollers (d> 500 mm). If rollers with structured sUrfaces are used, significant deviations between the model and the measurements are observed. The Johanson model leads to rea sonable results for granular materials having a high friction against the roller surface and a high compressibility K. If the powder is very compressible (small K value) or the applied compaction pressure is high, significant deviations between model and experiment can be expected [38]. Another modelling approach is the so-ca lied "slab method". This method was first applied by Katashinskii [39]. The zone between the two rollers is divided into trapezoidal slabs. Around these slabs a force balance is established. This force balance was combined with different material parameters that were obtained by shear tests or compression in an instrumented die. However, the nip angle has to be determined experimentally. According to Dec etal. [38] modelling by using the "slab-method" was in good agreement with experimental data in only a few of the investigated cases. Recently, the discrete element method has also been used to model roller compaction [38]. Knowing the pressure distribution within the roller gap and the material specific relation between pressure and the resulting compact strength, the achieved bri quette or ribbon hardness can be estimated. The obtained ribbons or briquettes should be stable enough to avoid a high amount of fines during the following grinding step but the obtained granules should also dissolve in a short time. Roller compaction is used for the agglomeration of various food products. Amongst them are sucrose, sodium chloride (bakery spread-salt), vitamins, fibres used as food ingredients, soup and seasoning powders, monosodium glutamate, encapsulated flavour powders and dairy powders. For crystalline food materials like sodium chloride a high pressure has to be applied to achieve stable agglomerates. Compacting soup and seasoning powders results in den se agglo merates with a reduced solubility. If fat is used as a binding substance, the solubi lity is good due to the lower pressure required for compaction. However, the IX .
IX
636
S. Palzer
dissolved product is often turbid due to a fine distribution of the fat. Compaction of spray-dried flavours is sometimes performed to encapsulate sensitive compo nents in a cost-efficient way. During compaction of flavour powders obtained by spray-drying of an emulsion, sometimes an oiling-out of the oiljaroma mix is observed. Fibres, cellulose, starches and other high molecular carbohydrates are compacted to reduce their transport volume and to improve their handling prop erties (e.g. their flowability). One of the major problems in roller compaction of food materials is de-aeration of the powder material. De-aeration of highly porous raw materials is crucial to reduce the elastic re-expansion of the compacted flakes or ribbons. Figure 38 shows a compactordesign facilitating de-aeration ofthe feed material. The airentrapped into the powder can escape via an additional funnel connected to the screw feeder. Within this funnel no high powder layer hinders the air to stream out of the system. Another major problem of roller compaction of food is the warming-up of the rollers due to friction between the particles themselves and friction between the particles and the roller surface. At increasing temperatures the fat can melt and amorphous components become sticky. Thus, the compressed powder can ad here to the roller surface after compression. By cooling the rollers (see Fig. 39) the warming up of the equipment can be minimized. The quality of the end product obtained by roller compaction depends on the homogeneity of the ribbons, since density variations within the ribbon sheet are often seen. Ribbon pieces with a low density lead to a high amount of fines Raw prod u e t
O e - d u s t i n g l ve n ting
U n d e r s i z e granule, dust l a nd overs i z e granule, addi tives)
S e p a r a t i o n of side seal leakages
Fig. 38. Roller compactor with de-aeration funnel and re-circulation of fines. (Courtesy Alexanderwerke, A.G. Remscheid, 0.)
637
Agglomeration of Dehydrated Consumer Foods [ ooUng c h onnels
[ 0 0 U n g wo f e r
i nlef
r;;;:::lt====;;;-J
Overprmure
I
[ooling w a f e r reservoi r
[ o oling water droin
Sue t i o n pump Overpressure
Fig. 39. Installation for water cooling of the rollers. (Courtesy Alexanderwerke, A.G. Remscheid, D.)
whereas dense ribbons may result in almost insoluble granules. Towards the border of the sheet the density decreases because a number of particles escape out of the roller gap. This problem is less important for compactors with long rollers than for machines with short roller pairs. Using a screw feeder, an os cillating density pattern is obtained due to the rotation of the screw's end. Some times the major amount of the powder is placed on the left side of the compactor and half a revolution later the major powder quantity is placed on the right side of the compactor gap. Installing two counter-rotating screws for feeding the powder into the gap can reduce density variations in the ribbon sheet. While compacting a food powder, which is sensitive to humidity, sticking is often observed on the roller surface. Specially structured roller surfaces tend to develop a crust if the feed is too humid. Most of such critical powders contain major amounts of amorphous substances that show glass transition. Thus, sticking in creases after running the compactor for some time due to the heating of the rollers. Adjusting the moisture content of the base powder, using rollers with a smooth surface and cooling the rollers themselves can help to avoid such problems. 3.4.3. Tabletting of food powders
Tabletting is a pressure agglomeration process which provides a pre-dose pow der quantity in a specific and easy recognizable shape. In addition, the high density achieved allows a slow dissolution of sweets and dextrose tablets within
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compression roller lablet
counter pressure plate
compression roller
Fig. 40. Double punch and single punch rotary tabtet presses used for food tabtets.
the mouth. Prior to tabletting the different powdered components are mixed within a typical powder mixer. In some applications this powder mix is agglomerated in a mechanical or pneumatic fluidized bed to improve the following tabletting process. Frequently, vertical granulators (see Section 3.3.2) are used for this first agglom eration step. The agglomerated moist powder is dried to avoid caking, chemical and enzymatic reactions and microbiological spoilage during the intermediate storage. The agglomerated powder is easier to compact and has an improved flowability compared to the initial powder mix. Finally, the agglomerated powder is compacted into tablets. However, sometimes the powder is also tabletted directly without any preceding fluidized-bed agglomeration to reduce costs. Tabletting is normally performed in rotary single or double-punch presses (see Fig. 40). The tabletting process can be divided in five different steps: ( 1 ) Filling of the powder into the dies (2) Pre-compression step air release and re-arrangement of particles (3) Main compression step deformation and breakage of particles; develop ment of adhesion forces (4) Pressure release elastic re-expansion of the tablet (5) Tablet ejection. -+
-+
-+
Figure 41 shows how the head of the piston is mounting on the compression roller. The resulting dwelling or loading time is dependent on the geometry of the system and the speed of the pistons.
Agglomeration of Dehydrated Consumer Foods
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Fig. 41 . Pistons and compression roller of a rotary tablet press.
r is the radius of the compression roller and d the diameter of the punch head. The time the pressure is applied (total cycle time) is called loading or dwelling time. The loading time t depends on the rotational speed n of the press (in revolutionImin), the diameter 0 of the rotating die table, the number of dies and the geometrical distances Sx 1 and Sx2 included in Fig. 41 . It can be calculated according to equation (42): t
= (Sx 1 + Sx2) rrnD
(42)
During the compression phase, the density of the mass increases while the head of the piston is in contact with the compression roller. With increasing density the axial stress (Jy acting in vertical direction increases as weil. The relation between density and axial stress (called the tablet law) is specific for each powder mass and has to be determined empirically. This relation can be described using a simple tablet law like the one given in equation (40). Due to the applied compression stress (Jy acting in axial direction, the stress (Jr acts on the die wall. The ratio between (Jr and (Jy is calied the pressure transmission coefficient A. For liquids A is 1 and for ideal stiff solid bodies O. Assuming a constant A over the tablet height, the ratio }o can be calculated according to Klasen [40]: 1 I\.
_
(J r
(Jy
0 F A = - In -b 4HJ1. Fu
(43)
where 0 is the diameter of the die, H the height of the tablet, J1. the coefficient of wall friction between tablet and die wall Fb the force acting on the lower piston and Fu the force acting on the upper piston. The coefficient of wall friction and the pressure transmission coefficient are both a function of the die material and the powder properties.
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Knowing the stress acting on the moving piston O"b , the coefficient of wall friction and the pressure transmission coefficient, the radial stress at a given position y in the die can be calculated according to equation (44): (44)
In opposition to the assumption made for deducing equation (44), it appears that the pressure transmission coefficient is neither constant over the tablet height nor constant during the compression process. Thus, a stress and density distribution Iike the one shown in Fig. 42 is resulting within the tablet. After compression the stress is released. During stress release the tablet shows a spring-back. Values for the elastic re-expansion are calculated by using the final height of the tablet hfinal and the minimal height hmin of the tablet during the compression process according to equation (45). Elastic re-expansion =
�� hmin
hfina
(45)
mm
The elastic re-expansion reduces the tablet strength because the distance between the particles increases and material bridges between single particles built during compression are disrupted again [1 8] . After pressure release and elastic re-expansion, the radial stress does not decrease to zero. The remaining remnant radial stress component increases with increasing plastic deformation. Thus, force is needed to overcome the resulting friction forces while pushing the
2.8 MN 1m2
6.1 M N l m 2
200 MNlm2 F i g . 4 2 . Density distribution (density expressed a s the value within a cylindrical tablet a t progressive densification [41 ] .
V=
1 00%-porosity
e
in % )
Agglomeration of Dehydrated Consumer Foods
641
tablet out of the die. Pauli [42] found a non-linear relation between the compres sion pressure and the remaining remnant stress for tabletting of maltodextrin at constant tablet height. The remnant stress causes an inhomogeneous stress distribution within the tablet during expulsion. Figure 43 illustrates stress profiles caused by remnant stress within a tablet [43]. The remnant stress is related to capping, a phenom enon in which the tablets break horizontally during expulsion. According to Ritschel and Bauer-Brandl [44] capping is more likely to occur at low radial stresses during compaction and high-remnant stress after pressure release. The mechanical properties of the powder mix used for tabletting, strongly de pend on the material used as binding substance within the tablet, the temperature and in the case of amorphous water-soluble substances also on the moisture content of the powder mass. Tabletting powders containing a significant amount of solid fat as binding substance plastic deformation of the fat is responsible for the final tablet hardness. Like mentioned in Section 2.4.5 the obtained tablet hardness mainly depends on the mechanical properties of the fat (which is a function of temperature) and the tabletting pressure. However, most tabletted food products contain amorphous substances that deform visco-elastically while exposed to stress. In this case the final tablet hardness depends on the pressure level, the time the pressure is applied (Ioading or dwelling time) and the mechanical prop erties of the substance, which are a function of temperature and moisture. As discussed in Sections 2.2 and 2.3, increasing moisture, increasing temperature and decreasing strain rate lead to a more plastic behaviour. Figure 44 shows the pressure/time profiles while compressing a single tablet using a dry and a moist powder at different tabletting speed on a rotary tablet press. The pressure first increases while the piston of the press mounts on the compression roller. After reaching the maximum pressure while passing the highest point of the compres sion roller the pressure decreases again until the tablet is released. Tabletting a dry powder fast (short loading time) the pressure/time profile is fairly symmetric because the material behaves elastically. Even after the piston has passed the highest point of the compression roller, the pressure does not drop immediately to zero due to the elastic re-expansion. Compressing the same amorphous material at higher moisture content or over a longer time a lower residual pressure is --------
Fig. 43. Pressure profiles within a tablet during expulsion leading to capping [43].
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25
dry powder (aw 0.19)
20 ro c.. ::2 c. � ::;) '" '"
� c. c 0 'iij '"
15 moist powder (aw 0.45 )
10
� c. E 0
-&- 80.000 tablets/hour dry -.!r- 50.000 tabletslhour dry -s-20.000 tablets/hour dry -+-80.000 tablets/hour moist -50.000 tablets/hour moist --20.000 tablets/hour moist
u
5
0 0.00
0.05
0.10
0.15
0.20
loading time t Is
Fig. 44. Pressure/time profile while tabletting dextrose syrup (DE2 1 ) at different speed (output/time) and different moisture content (aw = 0. 1 9 and aw = 0.45) on a double-punch rotary tablet press.
observed after passing the highest point of the compression roller due to the plastic deformation of the particles and the reduced elasticity [45]. In addition, it has to be considered that the temperature increase during com pression due to inter-particle friction and friction between the powder and the die wall can affect the tabletting of amorphous powders. Nürnberg and Hopp [46] found a temperature increase of up to 20°C with longer running time of the press. Several other authors reported an increase of the tablet temperature during tab letting [47--49]. While the density of the tablet increases during compression the particles de form plastic or visco-elastic. Thus, the distance between single particles de creases and the contact area between them increases. In addition, the particles break. Both deformation and particle breakage lead to increasing contact points between the particles. At these contact points amorphous materials might sinter together supported by capillary condensation and increasing temperature due to interparticle friction. Figure 45 shows scanning electron microscope pictures of different food tablets. In some tablets a significant deformation of primary particles is visible. In others the primary particles show nearly no deformation and, thus, there are only a few
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Agglomeration of Dehydrated Consumer Foods
Vitamin (ablet
tock tab let
Dextrose table!
Fig. 45. Photos of different food tablets (SEM pictures).
Pressure test
Bending test
�F Tensile strength
Fig. 46. Different ways to measure the hardness of food tablets. (Left: compression tests, middle: bending test, right: diametrical compression test.)
contact points between them. In such tablet structures sintering is likely to play a role in developing the final tablet hardness. The tablet hardness can be expressed as tensile strength, bending stability or breaking stress. The tensile strength is defined for round and homogenous tab lets with ideal brittle fracture, which have a line contact with the piston of the measurement apparatus ( see Fig. 46). The tensile strength can be calculated according to equation (46): 2F O"t = n
Dh
(46)
D is the diameter of the tablets, h their height and F the measured force required for breaking the tablets. For rectangular tablets, a crushing force is obtained while exposing the tablet to pressure or a bending stress is measured like shown in Fig. 46. The obtained value for the tablet hardness (expressed either as force or stress) depends on the geometry of the tablet and the measuring procedure.
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4. AGGLOMERATION TECHNOLOGIES FOR DIFFERENT PRO DUCT GROUPS
Various consumer foods are agglomerated. Amongst them are dairy powders, convenience foods, instant beverages, confectionery products and cereals. Ag glomeration is performed either for generating a distinctive shape or to improve application properties Iike dissolution time, flowability or shelf Iife. In the fOllowing, the technologies applied for different product groups are described. 4.1 . Dairy powders
The most important dairy powders are skim and whole milk powder. Besides these, several other powdered products are manufactured based on milk or milk powder. Infant formulas, for example, are composed of fresh milk, whole or skim milk powder, whey powder, micronutrients, carbohydrates, non-hydrogenated vegetable oil and sometimes also pro- or pre-biotic bacteria. Infant formulas are mainly manufactured by spray-drying. Another category of milk-based powders is the so-calied filled milk powder, which is used to replace pure milk powder. Filled milk powders are milk powders that are enriched with components Iike buttermilk powder, vegetable oils and micronutrients. Like other dairy powders, filled milk powder is mainly manufactured by spray-drying. Coffee creamers or whiteners are multi-component mixes made of casein, corn syrup, vegetable fat, emulsifiers and flavours. Furthermore, flow agents and col ours are added. Buttermilk, yoghurt, casein, caseinate, whey and hydrolysed whey powders are used by the food industry as ingredients. They are manufactured either by spray- or belt-drying. To improve dissolution of such dairy powders are often agglomerated. 4.1.1. Composition of dairy powders
Approximately 8 L of fresh milk are transformed into 1 kg of whole milk powder. Whole milk powder contains 38% lactose, which is amorphous or crystallized in its !X or ß form. Furthermore, whole milk powder is composed of 26% proteins, 26% fat, 7% minerals and less than 3% water. After the rapid spray-drying proc ess, the lactose is normally amorphous. Depending on moisture and temperature, it crystallizes into the !X- or ß-form. !X crystals are needles whereas ß crystals have the shape of a Tomahawk. Crystallization affects undesired and desired agglomeration processes because it Iiberates water. Furthermore, the crystalline state does not get sticky at higher temperature or moisture content. Thus, the presence of crystals on the particle surface might help to avoid caking of the powder.
Agglomeration of Dehydrated Consumer Foods
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The fat eontent of whole milk powder is present as fat globules that are em bedded in the spray-dried partieles or in form of a layer on the particle surfaee. These fat deposits melt at higher temperature. The melted fat ean eontribute to agglomeration by liquid bridges, whieh solidify upon ehilling. Conversely, fat present at the particle surfaee ean also reduee the adhesion between amorphous particles under humid eonditions. Figures 47 and 48 are images of agglomerated skim and whole milk powder partieles obtained by seanning eleetron mieroseopy.
Fig. 47. Agglomerated skim milk powder (SEM picture).
Fig. 48. Agglomerated whole milk powder (SEM picture).
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As for different milk-based powders a rapid dissolution in warm or hot water is desired, they are often agglomerated. Several agglomeration processes and technologies are applied to improve dissolution and flow properties of dairy pow ders: agglomeration in spray towers, agglomeration during spray-drying, ag glomeration in combined spray-jbelt-driers (e.g. Filtermat drier) or agglomeration in batch or continuous fluid beds. 4.1.2. Agglomeration of dairy powders during spray-drying
Most milk-based powders are manufactured by spray- or roller-drying. A limi ted agglomeration can already be achieved during spray-drying. One approach is to install a so-ca lied integrated fluidized bed at the boUom of the drier. The drying particles fall into this bed where they agglomerate (see Figs. 1 5 and 1 6). The agglomerated dairy powder flows over a weir outside the drier, and in an external fluid bed the powder is dried and cooled. Fines which are separated by cyclones or bag filters from the exhaust air coming from the drying tower and the external fluid bed are added to the fine fraction coming from the sifter. These fine particles can either be blown into the space above the internal fluid bed or they can be added into the internal or external fluid bed. Some spray-driers for dairy powders have integrated bag filters directly in stalled in the upper part of the tower. Fines accumulating on the tissue surface fall back into the humid drying zone of the tower where they agglomerate with other particles (see Fig. 1 5). Agglomeration during spray-drying can also be achieved by installing a steamf powder nozzle on top of the drier through which fine particles are added back into the tower by mixing them with steam while they are leaving the orifice. Figure 49 includes a steam jet agglomeration system, which is integrated into a spray tower for dairy products. fln�5
d•• 'ng
0
I
Fig. 49. Agglomeration of dairy powders using a steam jet agglomeration system, which is integrated into a spray tower.
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Agglomeration of Dehydrated Consumer Foods
4.1.3. Agglomeration of dairy powders during spray-jbelt-drying (filtermat drying)
Furthermore, a combination of spray- and belt-drying called Filtermat drying is used for dairy powders (see Fig. 1 8). This system is especially applied for high fat dairy powders with up to 80% fat content. The concentrated milk-based liquid is atomized into a short spray tower with co-current airflow. For the atomization a high pressure nozzle is used. The hot drying air passes an air disperser gen erating the desired flow pattern within the tower. In the tower the particles are pre dried while they fall down. These pre-dried particles fall onto a perforated belt where they sinter or melt together forming a particle cake. While the particle cake is transported by the belt towards the outlet of the drier, hot air streams through the powder cake. In a second zone the dairy powder cake is cooled using cold air. The product stays on the belt for several minutes before leaving the drier. A comparably low product temperature is applied for drying. Finally, the dried dairy powder is milled to a smaller particle size or directly sifted to obtain the desired agglomerate size. Filtermat driers with a throughput of up to 6-7 t/h are used for drying and agglomeration of different dairy powders. 4.1.4. Agglomeration of dairy powders in an external fluidized bed
Sometimes the spray-dried dairy powder is agglomerated in an external contin uous fluid bed by atomising water on the moving particles. Such a spray-drierl fluidized bed system can be combined with an addition of re-circulated fines into the middle part of the spray-drier (see Fig. 50). Smaller volumes of dairy powders are often also agglomerated in batch op erating fluid beds. 4.1.5. Lactose crystallization during agglomeration
Amorphous lactose generated during the rapid spray-drying is within a meta stable state. Depending on time, temperature and moisture content these amorphous
doclng
()
.;
fluldis&d bed agglom.rution p,..-hftot""
Fig. 50. Agglomeration of dairy powders in an external fluid bed.
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Fig. 5 1 . Agglomerated skim milk powder containing amorphous lactose (SEM picture).
lactose crystallizes more or less rapidly [1]. Upon crystallization, water is released because crystalline lactose is less hygroscopic than lactose in the amorphous form. Crystallization will increase the dissolution time of the powder. However, lactose crystals have the advantage that they are less hygroscopic compared to amorphous lactose. They also have a reduced risk of caking under higher tem perature and/or humidity and the flow properties of crystalline particles are im proved compared to an amorphous powder. Agglomerating milk powder in an external fluidized bed at higher tempera ture, and humidity provokes lactose crystallization. Lactose crystallization is also observed if the residence time of the particles within the spray-drier or in the after-drier is too long. If drying or agglomeration is performed rapidly by applying moderate temperatures, the lactose remains amorphous. Figure 51 shows an agglomerated skim milk powder particle containing lactose in the amorphous state. Figure 52 includes a scanning electron microscopic picture of a skim milk powder particle agglomerated under hot and humid conditions for a longer time. Needle-like lactose crystals are c1early visible on the particle surface.
4.2. Dehydrated convenience foods
The food industry manufactures various agglomerated dehydrated convenience foods. Amongst them is a wide range of dehydrated culinary kitchen aids Iike dehydrated sauces, stocks and seasonings. Beside these kitchen aids, there are
Agglomeration of Dehydrated Consumer Foods
649
Fig. 52. Agglomerated skim milk powder containing crystalline lactose (SEM picture).
also prepared dishes like instant soups, dehydrated mashed potatoes and pasta or rice containing dishes. 4.2.1. Composition of dehydrated convenience foods
Dehydrated culinary products are composed of starch, flour, vegetable- and yeast-extracts, meat powder, sodium chloride, sucrose and monosodium gluta mate, fat and oi! . In addition, such products typically contain spices, flavour powders, herbs and vegetable pieces. Crystalline ingredients like sodium chloride can be considered as inert during the agglomeration process. Only if a higher amount of water is present during agglomeration, such crystals dissolve partly and build solid bridges between each other upon drying. Spices and herbs also behave inert since they are mainly composed out of cellulose. A majority of the other ingredients are hygro-sensitive amorphous substances. Starch and flour, which are partly amorphous and partly crystalline have a high glass transition temperature (see Fig. 3). Thus, they only contribute to the adhesion forces at high humidity. Soups and sauce powders are mostly agglomerated for vending applications, to ensure an exact dosing by improving the flowability and to avoid caking of the powder within the vending machines. Sometimes seasonings are agglomerated in a fluidized bed to provide the flowability necessary for dosing out of a sprinkler. A desired side effect of such agglomeration is the increasing colour intensity due to the removal of fines. Some seasonings and stock powders are also structured by means of pressure agglomeration to provide them with a distinctive shape.
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Several agglomeration processes are used in the culinary industry. The most common processes are listed below: Growth agglomeration • •
Fluid-bed agglomeration of vending soups and seasonings Mixer agglomeration of sauce powders and seasonings Pressure agglomeration
• •
•
Tabletting of stock and seasoning tablets and cubes Roller compaction of seasonings, pure salt, glutamate and stock mixtures Extrusion of garnishes and seasonings
Growth agglomeration is used for improving the flowability and dissolution behaviour of dehydrated soups and sauces. Pressure agglomeration is mainly applied for structuring kitchen aids Iike stock or seasoning powders. Prior to agglomeration, the powdered components are blended batchwise in high-shear or ribbon mixers. These powder batches are then agglomerated batchwise in a second step. During mixing melted fat, oil, liquid flavours and for extrusion also water is added to the mix. Then the main agglomeration step is performed. Figure 53 shows the different agglomeration processes as applied to culinary powders. 4.2.2. Agglomeration of convenience food in mechanically or pneumatically fluidized beds
Culinary powders are sometimes agglomerated in fluid beds. The powder is flu idized either mechanically in powder mixers by fast rotating stirrers or pneumat ically by air flowing through the powder bed. Pure water is sprayed on the moving particles to increase the adhesion forces between them. Upon drying, such bridges are transformed into solid bridges with a high tensile strength. Droplets impinging on amorphous substances Iike meat-or yeast-extract generate a highly viscous solution on the particle surface providing adhesion points for other par ticles. However, it is essential not to exceed a critical RH of the air within the powder bed to avoid a collapse of the bed. Therefore, the glass transition tem perature and the collapse point (calculated using equation (26)) of the main ingredients within the powder mix have to be known to control the process. After water injection the powder is dried and cooled in a pneumatically fluidized bed. A number of ingredients used in dehydrated convenience foods have a very low glass transition temperature due to the presence of low molecular sugars or amino acids. These ingredients improve the strength of the agglomerates. Nevertheless, there is the risk of an increasing amount of oversize particles, encrustation of equipment and a collapse of the fluid bed since such substances get very sticky at high temperature or moisture.
651
Agglomeration of Dehydrated Consumer Foods
d051ng
()
Tablettlng scheme 01 a rolary lablet press
I
Rollor compactlon
Extruslon 01 wet powder massas
Wottlng and drylng
o L
Fig.
53.
In a batch or contlnou..
lIuldlzed bed
81g80g
.��t-. �
slorage'-L----'
conUnous mlver
Wettlng In contlnous
mixer an d drylng In a fluldlzed bed
ous ftuldi sed bed dryet condn
Agglomeration processes applied in the culinary industry.
Fluid-bed agglomeration of culinary powders is either performed batchwise for small volumes or continuously for higher tonnages. Figure 54 shows a typical line for a continuous agglomeration of culinary powders. For the agglomeration step a continuous mixer is used and drying is performed in a continuous pneumatically fluidized bed. When agglomerating the powder batchwise, agglomeration, drying and cooling are done in the same vessel. Figure 55 includes a sehe me of a batchwise operating pneumatically fluidized bed used for the agglomeration of instant soups. 4.2.3. Extrusion of wet powder masses
One agglomeration process used for dehydrated convenience foods is the ex trusion of wet powder masses. For such an extrusion process several powdered ingredients are mixed together. This mix is plasticized by addition of 2-1 0% water. Afterwards, the plasticized powder mass is pressed through a die with small holes. The resulting cylindrical particles are dried in a fluid bed or in a
652
s. Palzer powder dosing unit liquid dosing unit
fluid bed dryer
B;' Ba'
D
Fig. 54. Continuous line for the agglomeration of culinary powders in a mechanicaily fluidized bed (mixer agglomeration).
batchwise-operating vacuum drier. After drying in a vacuum drier, the resulting cake is broken in a grinder and then sifted. The fines are recycled by adding them to the powder mass during the initial wetting step. In case the product is dried in a fluid bed drier, no grinding and only sifting into a coarse, medium and fine fraction is required. Agglomerates obtained by extrusion of wet powder masses (see Fig. 56) have a diameter corresponding to the hole diameter of the extruder die. The length of the cylindrical agglomerates can vary between 2 and 4 mm. Agglomerates man ufactured by extrusion of wet masses are porous and thus dissolve rapidly. Figure 57 shows a continuous line for agglomeration of culinary powders by extrusion of wet powder masses.
4.2.4. Roller compaction of culinary powders
Another pressure agglomeration process applied for dehydrated convenience foods is roller compaction. Stock and seasoning powders and even pure sodium chloride or monosodium glutamate are first compressed between two rollers into
653
Agglomeration of Dehydrated Consumer Foods
Exhaust air Base powder
Fluidisation air
Spray nozzle --- ..J.Binder solution Cleaning nozzle
Product hopper Sitter Mill for oversize Finished product
Fig. 55. Pneumatically fluidized bed for instant soups. (Courtesy Aeromatic-Fielder AG CH.)
Fig. 56. Scanning electron microscopic (SEM) picture of an extruded seasoning agglom erate.
large flakes and then grinded into dense sharp-edged granules with a diameter of 1-3 mm. Fat and amorphous substances are sometimes added as binders to improve the cohesion of the granules. Such agglomerates manufactured by roller compaction are often difficult to dissolve and might lead to a turbid solution after
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Fig. 57. Une for manufacturing of agglomerated culinary products by extrusion of wet powder masses.
re-hydration if they contain fat as binder. For roller compaction of culinary pow ders a line pressure of up to 4 kN/cm roller length is needed. 4.2.5. Tabletting of culinary powders
Tabletting is applied for structuring kitchen aids Iike seasonings or stock powders. Fat or amorphous substances are used as binding agents. By applying pressure, the fat deforms plastically. The strength of the obtained tablet is, thus, mainly dependent on the applied pressure and the solid fat content. If amorphous substances are used as binding agents, these substances deform visco-elasti cally and the resulting tablet hardness strongly depends on compression time and the moisture content of the amorphous binder (see Section 2.4.5). Tabletting is performed using single-punch rotary tablet presses with an output of 200-1 200 tablets/min. The powder is dosed in a die, which is embedded in a rotating table. The bottom of this die is build by a piston, which moves up and down during the rotation of the die. While the piston is running over a compression roller, the tablet is formed by pressing it against a rotating counter-pressure plate. This system was specially developed for tabletting of culinary powder mixes containing fat, which would stick on an upper piston while using a double punch tablet press. Some tablet presses even consist of a pre-compression step, which should de-aerate the powder before it is pressed in the main compression step to the final tablet hardness. During the compression cycie the pressure mounts up to 30-1 00 M Pa. A full compression cycie takes about 30-200 ms depending on
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Agglomeration of Dehydrated Consumer Foods
the output and the press used. The produced tablets or cubes have a weight of 4-1 2 g. Figures 58 and 59 show two single-punch rotary tablet presses used for tab letting of culinary kitchen aids. Compared to agglomerates produced by fluid bed agglomeration, the manu factured culinary tablets are relatively dense. Figure 60 shows a tablet in which fat acts as a matrix binder. The powdered ingredients are embedded in the fat matrix which has been coloured black using Osmium-tetroxid. Figure 61 inciudes a scanning electron microscopic image of a culinary tablet in which big salt or sugar crystals are bound together by using fat and amorphous binding substances. feeding
feeding bowl :'.�____�'I
compression
ejeetion
release
rotating counter pressure plate
--'1 _
---,,.,.".. ,_ _ _
_ _ _
compression roler
Fig. 58. Scheme of a low-speed single-punch rotary tablet press with counter pressure plate used for kitchen aids. (Principle of a Fette Perfecta 4B or a Bonals BR12.)
2-.1 EJ(CT/ON
CJ.f.AJtHNG
DQS/S 2
Pß!COI/Pf?fSSION
CONPRfiS/ON
'" [J[CTION
Fig. 59. Scheme of a modern high-speed single-punch rotary tablet press used for culinary powders with pre- and main compression step. (BR680; Courtesy Bonals, S.A. Barcelona, E.)
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Fig. 60. Seasoning tablet with fat as matrix binder. (Light microseopie picture; fat coloured dark grey using Osmium-tetroxid.)
Fig. 6 1 . Scanning electron microseopie (SEM) picture of a seasoning tablet with low �at content.
4.3. Dehydrated beverage powders
For beverage powders, solubility is a key feature. Thus, the majority of beverage powders are agglomerated. Soluble coffee powder and different powdered coffee mixtures, coffee replacements, malted instant beverages, cocoa beverages, instant tea, isotonic beverage powders and sugar-based beverages are agglomerated to provide a beUer solubility in hot or cold water. Figure 62 shows soluble coffee particles agglomerated in a continuously operating pneumatically fluidized bed. 4.3.1. Composition of beverage powders
Soluble coffee must only contain coffee substances. No other additives are al lowed. Coffee mixes like cappuccino or milk coffee also contain milk powder,
Agglomeration of Dehydrated Consumer Foods
657
Fig. 62. Soluble coffee powder agglomerated in a continuous fluid bed.
flavours and sugar. Cocoa drinks are mainly composed of cocoa powder and sucrose. Malt-based beverages contain, beneath soluble malt powder, also sugar and micro-nutrients. Instant tea powders are a mix of ingredients like tea extract powder, dextrose, sucrose, maltodextrines, plant extracts, citric acid and fla vours. Sucrose, corn syrup, maltodextrine, f1avours and micro-nutrients are typi cal ingredients for various sugar-based beverage powders. Some of these sugar based beverages might also contain fruit powders, colours and citric acid. For Isotonic beverages also minerals and different salts are added. 4.3.2. Agglomeration of beverage powders during spray-drying
A limited agglomeration might already occur during the drying process. Agglom eration in a spray-drier can be achieved by adding fine particies, which have been separated from the exhaust air, back into the spray tower. These fines will stick to particies, which are still humid, and, thus, agglomeration is achieved. In addition, a limited agglomeration is observed in the after-drier, where the powder is dried to the desired final moisture content. The obtained fragile agglomerates have a medium particie diameter smaller than 1 50 �m. 4.3.3. Steam-jet agglomeration of beverage powders
For beverages, steam-jet agglomeration is the most common agglomeration process applied. The powder particies pass the agglomeration zone by free-fall or accelerated by a steam jet. While falling, the particies are subjected to saturated steam. The steam and the particles are often added through the same nozzle and the two streams mix with each other after leaving the orifice. The steam can either enter the nozzle centrally, laterally or by a combination of the two. The central steam-jet forces the powder through the agglomeration zone, whereas the
658
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lateral steam should support agglomeration by condensation on the particle sur face. A second possibility is to add the steam laterally through separate steam nozzles. To facilitate condensation, the beverage powder mix is cooled to a temperature below 30°C. Owing to the increasing moisture content, amorphous components become sticky while exceeding their glass transition temperature by 20-50°C. In the meantime, crystalline components partly dissolve. As a conse quence, colliding particles adhere to each other due to the formation of viscous or liquid bridges. The agglomeration process as such is rather fast and requires less than 1 s. Agglomerating a beverage powder containing also larger particles like sucrose crystals, it is advantageous to mill the powder prior to agglomeration to a smaller particle size [34]. Smaller particles adhere to each other more easily and the surface area available for steam condensation increases. Steam-jet agglom eration of beverage powders can be performed using a special steam/powder nozzle, which is integrated in a classical spray-drier (see Fig. 63). Alternatively, steam-jet agglomeration can be performed in a separate ag glomeration tower operating with co- or counter-current airflow (see Fig. 64). The agglomeration takes place in the upper part of the tower by mixing the powder with steam. While falling down through the tower, the built agglomerates undergo drying. Agglomeration towers for beverages operating with counter-current airflow tend to show a very efficient drying due to the turbulent airflow and due to the fact that the moisture and temperature gradient between the particle surface and the surrounding air is larger than in case of co-current airflow. In addition, no drying, but only cooling is required after the powder leaves the agglomeration tower. Co current airflow is suitable for heat-sensitive beverage formulations (e.g. recipes containing volatile aroma components) due to the lower temperature of the prod uct at the tower outlet. ftnes drying air
coffee or ma" axtract
Spray drya.
co-c.....nt
air fIow
aft.r dry." cooler pr.......t.r
Fig. 63. Agglomeration of beverage powders in a spray-drier equipped with a steam noz zle for agglomerating recycled fines.
b
Agglomeration of Dehydrated Consumer Foods doslng
659
I
mlil
Fig. 64. Agglomeration of beverage powders in a stand-alone steam jet agglomeration plant. (Agglomeration performed either in a pneumatically f1uidized bed or an agglomer ation tower.)
Another possibility for steam-jet agglomeration is to apply steam while the bev erage powder is falling into a fluid bed (see Fig. 64). In such a case the beverage powder is fed into a fluid bed drier using a vibrating conveyer. While the particles are falling in form of a powder curtain into the fluid bed, they are moistened with saturated steam. The obtained porous agglomerates are dried and cooled while they are passing through the different zones of the same or an additional fluid bed. Another approach is to dry the particles in a drum drier installed at the outlet of the fluid bed used for agglomeration. After steam-jet agglomeration, drying and cooling the agglomerated powder is sifted. The coarse fraction is either recycled to the grinder installed before the cooling step or it is grinded in a separate mill and then passed again through the sifter. The fines are added to the milled and cooled powder prior to agglomer ation. The final water content of the agglomerated beverage powder is between 0.5 and 2% depending on the product composition. Agglomerates produced by steam-jet agglomeration have a diameter of 1-3 mm, a high porosity and they are comparatively fragile. However, dissolution of such a beverage powder is very rapid. 4.3.4. Fluid-bed agglomeration of beverage powders
Beverage powders are sometimes also agglomerated in a continuous pneumat ically fluidized bed (see Fig. 65) which is attached to a spray-drier. The beverage powder is fluidized with air while it is Iying on a perforated plate. In the first part of
660
s. Palzer A
I
coffee or malt extract
Spray dryer counter CUlTent air flow
fluidhuld bad aaalomeration
Fig. 65. Agglomeration of spray-dried beverage powders in a continuous fluid bed.
the fluid bed, 2-1 5% of water is atomized on the moving powder particles. In the following zone, the agglomerates are dried at a temperature of 55-80°C to a moisture content below 3-5%. Finally, the agglomerated powder is cooled in a dedicated zone of the bed to a temperature of 20-25°C. A weir and the orien tation of the holes in the perforated plate on which the powder is Iying allows controlling the residence time within the bed. Compared to steam-jet agglomer ation the built agglomerates are more stable and dense. 4.4. Confectionery and sugar-based products
In the confectionery and sugar industry various products are agglomerated. Confectionery and sugar-based products are offen tabletted to give them an attractive shape and to provide them in a pre-dosed form. Some granular sugar products are agglomerated to improve their shelf life or to make them dispen sable more easily. Most of the mentioned confectionery products are manufac tured by tabletting of a powder mix in a double-punch rotary tablet press. Some of the formulations used for tabletting require a wet granulation step prior to tab letting. This accounts especially for formulations containing mainly crystalline sugars that are not easy to deform. Such sugar crystals are grinded and coated or agglomerated together with amorphous carbohydrates having a low or medium molecular weight. The resulting granules are deformable and the amorphous substances provide improved adhesion properties. 4.4.1. Composition of confectionery and sugar-based products
Compacted sweets based on sucrose are made by using dextrose and modified starches as binding substances. However, such sucrose sweets require an
Agglomeration of Dehydrated Consumer Foods
661
agglomeration step prior to tabletting. Some of these sucrose-based tablets are even made chewable. A wide range of confectionery tablets is mainly pro duced out of dextrose, which is directly compressible. These tablets mainly contain dextrose, dextrose syrup, citric acid, flavours and colourings. They are pressed into various shapes like hearts, Iipsticks, lollypops and round mini tablets. Pure dextrose tablets (see Fig. 45) serving as energy source are offered for sportsmen. Sugar-free confectionery tablets made to meet the consumer demand for more healthy products are based on sorbitol or isomalt, which are also directiy compressible. The confectionery industry also seils effervescing tablets that contain citric acid and calcium bicarbonate. The reaction of both generates carbon dioxide during dissolution. Sometimes food supplements like vitamins or minerals are incorporated into such effervescing tablets. Effervesc ing vitamin or mineral tablets are mainly based on dextrose, citric acid, sodium bicarbonate, flavours, sweeteners and different micro-nutrients. Sweetener tablets are made of saccharin, thaumatin, cyclamate and other sweetening substances. The amorphous low molecular carbohydrates and citric acid used in most of the mentioned products are easy to compact, but tend to stick on the surface of the piston of the tablet presses. In addition, they can increase the forces needed for the ejection of the tablets due to stickiness on the walls of the die. To avoid such problems, magnesium or calcium stearate is added as lubricants to the formu lations. The stearate is either mixed directly with the powder prior to tabletting or the dies and pistons of the tablet presses are coated with a thin stearate layer between two compression cycles. 4.4.2. Tabletting of confectionery
Tabletting of confectionery is similar to the tabletting of pharmaceutical products. For tabletting confectionery products double-punch presses (see Section 3.4.3) are used. The compression cycle in the press can be described as folIows: the bottom punch of the press descends to its lowest position by leaving a cavity. While the punches circulate in the turret of the press, cams control their vertical position. The powder is fed by gravity or by force-feeding into the dies and excess powder is scraped away while the dies are leaving the filling station. The powder is then compressed between an upper and a lower punch while both punches are moving over compression rollers. Some of the used rotary tablet presses consist of two compression stations: one pre-compression and one main compression roller. The aim of the pre-compression is to reduce the air entrapped between the particles. Air can cause problems during the main compression if it cannot es cape fast enough out of the die. During compression a pressure of up to 300 MPa is applied for up to 30-1 00 ms. After the compression phase, both punches are Iifted and the lower punch ejects the tablet out of the die. The tablet is then
662
S. Palzer
i
.-
--"
-�
main�compresSion ejection
filling
Fig. 66. Compression cycle of a double punch rotary tablet press. (Courtesy Courtoy, N .V. Halle, 8.)
knocked off the punch by a bar. Once again the emptied die moves to the filling station. Figure 66 shows a double-punch rotary tablet press. Common problems during tabletting of sugar confectionery are capping and lamination (see Section 3.4.3). In case of capping, the upper part of the tablet falls apart. Lamination results in a horizontal splitting of the tablet. Common reasons for both effects are the entrapment of air, low adhesion forces between the particles and highly elastic components within the formulation. Another common issue is the stickiness of the powder on the surface of the punches due to adhesion forces between the punch surface and the particles. Stickiness of powder on the punch surface is increasing with embossing or damage of the punch surface. Stickiness of confectionery powders on the punch surface is mostly linked to glass transition of amorphous components like dextrose or citric acid. 4.4.3. Manufacturing of compressed sucrose based sweets
Some compressed sweets are made using crystalline sucrose as the main com ponenl. Crystalline sucrose particles are not deformed easily and adhesion forces generated between single crystals during tabletting are limited. Thus, the crystal line sucrose is agglomerated before tabletting. To facilitate agglomeration, the sugar is grinded and sometimes mixed with 0.5-2% magnesium stearate that
Agglomeration of Dehydrated Consumer Foods
663
serves as lubricant during tabletting. While grinding the powder mix a narrow size distribution is desired. Very fine particles require a very high amount of binding substance in the following granulation step. Very coarse particles result in brittle granules, difficulties during tabletting and a poor mouth fee!. The sucrose/mag nesium stearate mix is then agglomerated by wet granulation in a high-shear mixer or kneader. For granulation, either pure water or a dextrose/starch solution is used as a binder. The obtained granules are dried to a final moisture content of 0.5-2% in ovens or continuously operating driers. The moisture content influences the flowability of the granules, which is reduced at higher water content. The hardness of the final tablet first increases with increasing moisture content before it softens again due to the plastification of amorphous substances. The dried granules are grinded and separated into different particle classes. The dried and sieved gran ules are mixed with powdered flavours and other heat-sensitive ingredients, which have to be added after the drying step to avoid aroma losses by evaporation or thermal degradation. Following this, the flavour/granules mix is tabletted in a rotary double-punch tablet press with an output of up to 4000 tabletsImin. 4.4.4. Agglomeration of sucrose-based products
Two main sugar qualities are offered by the sugar producing industry: Brown and white sugar. Brown sugar is composed of sucrose crystals which are coated with a thin molasses layer. The white sugar is composed of purified sucrose crystals in which the molasses has been removed before drying. Only molasses resulting from sugar cane processing is suitable for human consumption. Thus, brown sugar is either directly obtained by processing sugar cane or by coating of white sucrose crystals made out of sugar beet with sugar cane molasses. The mo lasses gives the brown sugar its distinctive colour and flavour. However, it con tains amino acids and carbohydrates, which are amorphous. These impurities are hygroscopic and can cause a caking of brown sugar particles. A strong caking might be observed already at a moisture content of 1 %. Both sugar types are offered to the consumer as cubes or different other shapes for application in coffee or tea. These shaped-sugar products are man ufactured by wetting the crystals with up to 5% water and pressing them into dies applying a low pressure. After this forming process the sugar cubes are dried to a moisture content below 1 %. White sugar is also compacted by roller compaction for decoration of bakery products and desserts. Brown sugar is hygroscopic and tends to cake during storage due to its molasses content. Thus, brown sugar is sometimes agglomerated in a mechan ically or pneumatically fluidized bed to increase the particle size. In addition, caking is reduced due to the decreasing amount of molasses present at the outer side of the granules. Prior to agglomeration, the brown sugar is milled to a particle diameter below 60 l1m and then agglomerated in a high-shear mixer or in an
664
S. Palzer
agglomeration tower. 4-5% of water is added to the sugar particles. The obtained granules are then dried to a water content below 1 %. Finally, the granules are sifted, the fines are recycled to the agglomeration step and the oversize particles are grinded in a mill or by using a roller refiner. Alternatively the milled sugar particles can be agglomerated by steam-jet agglomeration in an agglomeration tower. 4.5. Agg lomeration of breakfast cereals and manufacturing of cereal bars 4.5.1. Composition of cereal products
Cereals and cereal bars are composed out of various particles, which are ag glomerated together by applying a low pressure . Such bars are produced using cereal flakes, nuts, dried fruit pieces, chocolate flakes and various other ingre dients. In addition, cereal bars are often coated with chocolate or a milk powder/ fat mix. Extruded breakfast cereals, like corn flakes, are made for consumption after being mixed with milk. They are composed of a carbohydrate paste with various ingredients that are extruded to a defined shape. However, such an extrusion is often not considered as an agglomeration because the initial par ticles are no longer visible. An alternative process for manufacturing breakfast cereals is to granulate various ingredients like whole grains, extruded flakes, puffed rice and corn, dried fruits, chocolate pieces and nuts using a sugar-based binder. 4.5.2. Manufacturing of cereal bars
Cereal bars are made of cereal flakes, puffed corn and rice, dried fruit pieces, nuts and sometimes also chocolate flakes or pieces. These coarse particles are mixed with a sugar based binder solution. The binder solution is composed of various sugars like dextrose syrup, maltodextrine, invert sugar syrup, dextrose and fructose. The binder solution is cooked at 90-95°C. After cooking, flavours are added. The prepared binder solution is then mixed in a continuous mixer with the granular ingredients. After mixing, the sticky mass is compressed between two rollers into a layer of 0.5-3 cm thickness. This layer is then cooled down while it is passing a chilling tunnel. After chilling the layer is cut into strands, which are separated by a special transport band. These strands are cut into individual bars. In some processes the bar is cooled for up to 1 0-30 min with cold air of 1 0-20°C. Alternatively to the described continuous process forming, chilling and cutting can also be done manually. After cutting and cooling the bar is ready for coating with chocolate or a milk powder/fat based mixture. To solidify the coating a final chilling is applied prior to packaging.
Agglomeration of Dehydrated Consumer Foods
665
4.5.3. Extrusion of breakfast cereals
Since extrusion, starting with a paste and not with single particles, is not con sidered as an agglomeration process, this technology is only discussed briefly. Flour, fibres, sugar and other ingredients are mixed with water. Then this mix is exposed to increasing pressure and temperature in a cooking extruder. For this unit operation, often twin-screw extruders are used. Such extruders contain two screws which convey the product to the head of the extruder. Due to the specific geometry of the screws that changes towards the head of the extruder, the product gets compressed. The obtained plastified food mixture is then passed through holes with a defined shape. While leaving these holes, the product ex pands and solidifies. The resulting product string is cut into single particieE by a fast-moving rotating knife installed at the extruder outlet.
4.5.4. Granulation of breakfast cereals
Some granulated cereals are made by agglomeration of whole grain partides, cereals, nuts and dehydrated fruits. A sugar-based binder solution which some times also contains chocolate is sprayed on the granular solids which rotat0 in a drum or which are fluidized in a mixer with rotating tools. After agglomeratic the product is dried and cooled.
5. U NDESIRED AGGLOMERATION OF FOOD POWDERS
While manufacturing powdered food products, frequently undesired aggloP' �ra tion phenomena are observed: • • •
Caking of powder during storage Post-hardening of agglomerates (e.g. tablets) during storage Stickiness and lumping of powder during processing.
Undesired agglomeration of crystalline substances like salt or crystalline su crose can be explained with a partial dissolution of the crystalline material while exceeding the critical humidity. Liquid bridges are built due to the dissolution of the crystalline substance. These bridges solidify while they dry out (see Sections 2.4.1 and 2.4.2). Powder masses containing fat will show undesired agglomer ation if the powder temperature approach es the melting temperature of the fat (see Section 2.4.4). Undesired agglomeration of amorphous food powders like caking or stickiness is caused by sintering due to viscous flow of the plastified amorphous substance (see Section 2.4.3).
S. Palzer
666
5. 1 . Caking of amorphous food powders
Figure 67 shows SEM pictures of different caked amorphous food powders. Sev eral sinter bridges are clearly visible. Some of them are marked with white circles. Ca king is an undesired agglomeration of the powder during storage. In the initial stages the particles adhere to each other. Later they form brittle lumps and a powder cake is obtained. Finally, the particles lose their structure and shape and open pores disappear (see Section 2.4.3). Caking can be quantified by shear tests in combination with time consolidation experiments in a ring-shear tester or an annular-shear cell [50-52]. The degree of caking can be expressed by the unconfined yield strength of the powder cake [53]. Another possibility is to quan tify caking visually using a pre-defined scale. Each grade on this scale is linked to a specific appearance of the powder while emptying the storage container. One example for such a scale is given in Table 2. A caking grade of more than three is considered as a significant consolidation of the powder. The scale has been used for investigating the caking of dextrose syrup powder (DE 21 ) under different storage conditions [54]. Depending on the composition and the supra-molecular and microseopie structure of the food particles several mechanisms are responsible for the ob served caking during storage. In case of amorphous solids, sintering is the re sponsible mechanism. The kinetics of such undesired agglomeration processes should be predictable by applying equation (26). The measured unconfined yield strength obtained by storing powder under defined temperature/moisture conditions can be compared with the calculated theoretical diameter of the sinter bridge. In Fig. 68 the unconfined yield strength of a spray-dried tomate powder and hydrolysed whey permeate (vertical axis) is plotted against the diameter ratio (x/a)2 calculated according to equation (26). Obviously the unconfined yield strength increases significantly if the calculated ratio between the cross section of the sinter bridge and the particle exceeds a
dextrose syrup DE2 1
skim milk powder
tomato powder
Fig. 67. Caked dextrose syrup powder, skim milk powder and tomate powder. (SEM pic tures; sinter bridges are marked with a white circle.)
Agglomeration of Dehydrated Consumer Foods
667
Table 2. Scale for the visual assessment of caked powders
Caking grade 1 2 3 4 5 6 7 8 9
Observation Powder is free flowing Powder flowing out of the container with small clumps that dissipate easily upon slight vibrations Powder falls into fragile pieces when lifted Powder falls into pieces that can be dissipated applying low force Powder falls into pieces that can be dissipated applying moderate pressure Powder falls into pieces that can hardly be broken into larger hard pieces Powder particles stick together inseparably Powder particles form a sticky, rubbery mass. Surface is rough but flexible Powder particles form a sticky, rubbery mass. Surface is smooth and has little flexibility
value of 0. 1 5. This critical diameter ratio corresponds to the critical values pub lished by Wallack and King [20] and Aguilera et al. [16]. Although the measured yield strength values show a large variation, the theoretical area ratio (xja)2 seems to be suitable for predicting the intensity of time consolidation of amor phous particles. Furthermore, dextrose syrup powder (DE2 1 ) was stored at three different temperaturejmoisture combinations (30°Cj70% RH; 20°Cj65% RH; 20°Cj50% RH), which correspond to tropical, Mediterranean and Middle European climate conditions. After pre-defined time intervals the cups containing a thin powder layer were emptied and the state of the powder was judged using the scale given in Table 2. In Fig. 69 the experimental results are compared with the values obtained by calculating the diameter of the sinter bridge (expressed as the ratio (xja) 2). Owing to the ongoing water absorption during storage, the value for the glass transition temperature changes permanently. Thus, the ratio (xja)2 was obtained by numeric integration according to equation (26). Storing the dextrose syrup powder at 30°C and 70% RH, the powder starts to cake after 1 0 h (caking grade > 4). Simultaneously, the theoretical sinter bridge diameter increases dramatically. For the other two storage conditions only a minimal increase in the calculated sinter bridge diameter and the caking grade is obtained. Thus, again the kinetic of caking seems to be predictable by calculating the sinter bridge diameter applying equation (26). Consequently sintering seems to be indeed the process responsible for increasing the adhesion forces between
668
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amorphous particles. A value for (xja)2 larger than 0.01-0 . 1 indicates the risk of caking. 5.2. Post-hardening of agglomerates
Offen the hardness of agglomerates containing amorphous components in creases significantly during storage. Thus, theoretically, equation (26) should also enable to predict the kinetics of such post-hardening. The post-hardening of rectangular dextrose syrup tablets has been investigated by Palzer [54]. Rec tangular tablets composed of 1 5% dextrose syrup powder (DE2 1 ) and 85% so dium chloride were manufactured adding 1 .7 and 2.3% water during mixing of the powder mass prior to tabletting. The tablets were packed in sealed plastic pouches and stored at 23°C. The crushing force while compressing the tablet between two flat pistons (see Fig. 46) was measured depending on the storage time and the moisture content of the tablets. Furthermore, the area ratio (xja)2 was calculated using equation (26) for each storage time and each sampie while considering any changes in the produci's moisture content during the storage time. Figure 70 shows the development of the crushing force and the calculated
669
Agglomeration of Dehydrated Consumer Foods
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670
S. Palzer
sinter bridge radius (expressed as the ratio xja) with time. Included are also the measured differences between T- Tg. Only in tablets containing 2.3% added water the dextrose syrup used as binding substance is initially weil above its glass transition temperature. Ac cordingly, a strong increase in hardness is observed upon storage at 20-25°C. For those tablets, a significant increase of the sinter bridge diameter is meas ured. In the tablets containing only 1 .7% added, water the dextrose syrup is still below its glass transition temperature. Therefore, no increase in hardness is obtained and also the calculated sinter bridge diameter does not increase with storage time. Obviously, again the increase in the calculated sinter bridge di ameter indicates the risk of post-hardening of amorphous tablets. These exam pies show that undesired agglomeration of amorphous powders can be explained by sintering. A prediction of their kinetics is possible applying the equations included in Section 2. REFERENCES [ 1 ] Y. Roos, M . Karei, Differential scanning calorimetry study of phase transitions affecting the quality of dehydrated materials, Biotechnol. Prog. 6 ( 1 990) 1 59-1 63. [2] C . Kedward, W. McNaugthan, J . Blanshard, J . MitcheII, J . Food Sei. 63 ( 1 998) 1 92-1 97. [3] M. Avrami, J . Chem. Phys. 7 ( 1 939) 1 1 03. [4] L. Sperling, Introduction to Physical Polymer Science, Wiley, New York, 1 986. [5] T. Fox, P. Flory, J . Appl. Phys. 21 ( 1 950) 581 . [6] Y. Roos, M . Karei, J. Food Sei . 56 (6) ( 1 99 1 ) 1 676. [7] Y. Roos, Carbohydrate Res. 238 ( 1 993) 39-48. [8] K. Jouppila, Y. Roos, J. Dairy Sei . 77 ( 1 994) 2907-291 5. [9] Y. Roos, M . Karei, Biotechnol. Prog. 7 ( 1 99 1 ) 49-53. [ 1 0] G. Vuataz, Le lait 82 (2002) 485-500. [1 1 ] M. Sugisaki, M. Suga, S. Seki, Bull Chem. Soc. Jpn. 41 ( 1 968) 259 1 . [ 1 2] G. Johari, G. Ast!, E. Mayer, J. Chem. Phys. 92 ( 1 990) 809-8 1 0. [ 1 3] R. Hoseney, K. Zeleznak, C. Lai , Cereal Chem. 63 ( 1 986) 285-286. [ 1 4] L. Doescher, R. Hoseney, G. Milliken, Ce real Chem. 64 (3) ( 1 987) 1 58-1 63. [ 1 5] S. Palzer, U . Zürcher, Bedeutung und Berechnung des Glasübergangs komplexer amorpher Lebensmittelkomponenten Teil 1 + 1/; Lebensmitteltechnik; (2004b) 7 + 9. [ 1 6] J . Aguilera et a!. , Biotechnol. Prog . 9 ( 1 993) 651-654. [ 1 7] M. Gordon, J. Taylor, J. Appl. Chem. 2 ( 1 952) 493-500. [ 1 8] U. Caspar, Viskoelastische Phänomene während der Tablettierung. University of Bonn , Insitute for Pharmaceutical Technology, PhD thesis, 1 983. [1 9] J . Neuhaus, Viskoelastische Phänomene beim Tablettieren auf Rundläufer tablettenpressen . University of Bonn, Institute for Pharmaceutical Technology, PhD thesis, 1 985. [20] M . Williams, R. Landei, J. Ferry, J. Am. Chem. Soc. 77 ( 1 955) 3701 -3707. [21 ] D. Wallack, C. King, Biotechnol. Prog. 4 ( 1 ) ( 1 988) 3 1 -35. [22] M. Peleg, Crit. Rev. Food Sei. Nutr. 32 ( 1 ) ( 1 992) 59-66. [23] H. Rumpf, Chem.-Ing .-Techn. 42 (8) ( 1 970) 538-540. [24] H. Rumpf, Chem.-Ing .-Techn. 30 (3) ( 1 958) 1 44-1 58. [25] J. Frenkel, J . Phys. (USSR) 9 (5) (1 945) 385-391 . [26] H . Rumpf, K. Sommer, K. Steier, Chem.-Ing .-Tech. 48 (4) (1 976) 300-307.
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[27] E. Lifshitz, Soviet Phys. J ETP 2 ( 1 ) ( 1 956) 73-83. [28] H. Hamaker, Physica 4 ( 1 0) ( 1 937) 1 058-1072. [29] B. Bhandari, R. Crooks, T. Howes, S. Rigby, Drying Techno!. 1 5 ( 1 0) ( 1 997) 2509-2525. [30] B. Bhandari, T. Howes, J. Food Eng. 40 ( 1 999) 71 . [31 ] S. Werner, J. Jones, A. Paterson , Development of droplet stickiness during drying, Proc. 8th I nternational Symposium on Agglomeration , March, Bangkok/Thailand, pp. 87-1 06, 2005. [32] S. Blei, M. Sommerfeld, Lagrangian modelling of agglomeration during spray drying processes, Proc. ICLASS, Sorrento/ltaly, Paper No. 1 604, 2003. [33] G. Anderson, S. Gibson, Agglomeration with fluid-bed conditioning: three methods, PBE International 8/9 (2003) 28-33. [34] H . Schuchmann , Untersuchungen zur Strahlagglomeration pulverförmiger Lebensmittel, PhD thesis, Faculty for Chemical Engineering U niversity of Karlsruhe/G, 1 993. [35] H. U hlemann, L. Mörl, Wirbelschicht Sprühgranulation, Springer, Berlin, 2000. [36] J. Johanson, J. App! . Mech. , Transc. ASM E, 32 (4) ( 1 965) 842-848. [37] A. Jenike, R. Shield, J . App!. Mech. 26 (81 ) ( 1 959) 599-602. [38] R. Dec, A. Zavaliangos, J. Cunningham, Powder Techno!. 1 30 (2003) 265-271 . [39] V. Katashinsky, Soviet powder metal ceram 1 0 (6) ( 1 986) 765-772. [40] C .-J . Klasen, Die Agglomeration partikelförmiger Feststoffe in Matrizenpressen , Han nover, Fortschrittsberichte VDI (3), PhD thesis, 1 990. [41 ] W. Pietsch, Agglomeration Processes, Wiley VCH GmbH , Weinheim, 2002. [42] T. Pauli, Das Horizontallastverhältnis beim Kompaktieren von Pulver. Ü berprüfung und Inbetriebnahme zweier Sensoren zur Ermittlung der Radialspannung, Techical U niversity of München, Lehrstuhl für Maschinen- und Apparatekunde, Diploma thesis, 2003. [43] W.M. Long, Powder Metai!. 6 ( 1 960) 73-86. [44] WA Ritschel, A. Bauer-Brandl, Die Tablette, 2nd Edn, Editio cantor /Aulendorf, 2002. [45] R. Steendam, H W. Frijlink, C.F. Lerk, Eur. J. Pharmaceut. Sci. 14 (2001 ) 245-254. [46] E. Nürnberg, A. Hopp, Pharamaceut. Techno!. 9 ( 1 98 1 ) 8 1 -1 01 . [47] U . Bogs, E. Lenhardt, Pharmazeutische Industrie 33 ( 1 97 1 ) 850-854. [48] D. Wurster, C. Rowlings, J. Creekmore, Int. J. Pharm. 1 1 6 ( 1 995) 1 79. [49] E.J. Hanus, LD. King , J . Pharmaceut. Sci. 57 (4) ( 1 968) 677-684. [50] J. Schwedes, D. Schulze, Powder Techno!. 61 ( 1 990) 59-68. [51 ] E. Teunou, J. Fitzpatrick, E. Synnott, J. Food Eng. 39 ( 1 999) 3 1 -37. [52] E. Teunou, J. Fitzpatrick, J. Food Eng. 42 ( 1 999) 1 09-1 1 6. [53] S. Palzer, U . Zürcher, Chem. I ng.- Techn . 76 ( 1 0) (2004) 1 594-1 599. [54] S. Palzer, Desired and undesired agglomeration of amorphous powders, Proc. 8th International Symposium on Agglomeration, March, Bangkok/Thailand, pp. 251-264, 2005.
CHAPTER 1 4 Detergent G ra n u lation Renee Boerefijn , * Prasanna-Rao Dontula a n d Rei n hard Kohlus
Unilever R&D Vlaardingen, P.O. Box 1 14, 3130 AC Vlaardingen, The Netherlands Contents 1 . Introduction 2. Detergent powder ingredients 3. Detergent powder properties 3. 1 . I n-use properties 3.2. Detergent powder handling 3.3. Stability 4. Granulation technologies 4. 1 . Base powder 4.2. Adjuncts 5. Granules for tabletting 6. Structure of detergent powders 6 . 1 . Phases in a detergent granule 6.2. Granule design 6.2. 1 . Maximising liquid content 6.2.2. Retaining porosity 6.2.3. Example of structure effects on powder properties: granule dissolution 6.3. Techniques to measure granule structure 6.3. 1 . Scanning electron microscopy (SEM) 6.3.2. X-ray tomography 6.4. Quantification of particle structure 6.4. 1 . Amount 6.4.2. Sizes 7. Future directions Acknowledgements References
673 675 677 679 681 682 682 683 687 687 688 690 692 692 693 694 695 695 696 698 698 698 700 700 700
1 . I NTRODUCTION
The powder detergent market has a worldwide volume of about 1 4 million tons per annum, and about 50% of this global volume has traditionally been supplied by three large companies: Procter & Gamble, Unilever and Henkel, with furthermore Lion and Kao as strong regional contenders in Asia. It comes therefore as no surprise that three standard texts on powder detergents exist, each strongly rooted *Corresponding author. E-mail: [email protected]
( 2007
Granulation
Edited by A.D. Sa/man, Elsevier
BV
M.J. Houns/ow and J. P. K. All riqhts reserved
Seville
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in one of these companies [1-3]. The sheer volume of detergent powders and, as a consequence of an equally sizeable R&D effort, the conception and realisation of largely similar technologies by the main players of the industry with all kinds of inevitable complexities make it a suitable case for this handbook. Granulation gradually became of interest to the detergent market in the 1 960s in response to environmental pressure, and especially due to the following: • • • • • •
need to reduce chemicals usage, advent of heat-sensitive, weight-effective materials, strict air pollution regulation, pressure to reduce packaging (move towards higher bulk density powders), drive to lower water consumption and drive to lower energy consumption.
with respect to spray-drying. Only when Kao introduced true compact Attack powders in 1 987, did the larger companies follow swiftly and in force. Compact powders became synonymous with high quality and high efficacy, specifically suited to markets with high machine penetration, although here too the reduced dissolution propensity of densified powders manifested itself. This lasted until the mid-1 990s, when the advent of tablets under the convenience cloak broke the fresh dominance of compact powders, and this high-tech segment is now more and more taken over by Iiquids, often in capsules. High-shear granulation yielded products with bulk densities that were 50% higher than that of spray-dried pow ders. Consumer habits did not adjust to this very quickly, and as an intermediate position, several technology combinations and new technologies were devel oped, such as fluidised-bed granulation. As powder detergents are produced in large bulk volumes to serve markets requiring up to several million tons per year, each company has developed a specific technology base and its own terminology (Table 1 ). Typically, the powder detergent manufacture process requires drying, mixing and densification, though not necessarily in this order. Table 1 . Reference texts and terms Configuration (order of increasing density) Spray-drier - Mixer Mixer - (Mixer - ) Drier
Mixer - Drier Compactor
Unilever [1]
P&G [2]
Henkel [3]
Tower - Post-Tower (TPT) Non-tower route, Dry mixing Fluidised-bed g ranulation Granulation/ agglomeration Granulation, tabletting
Post-tower densification Dry neutralisation
Premix process
Compaction, pressure agglomeration
Compound process
Non-tower agglomeration
Detergent Granulation
675
This applies specifically to powders containing surfactants and builders, i.e. base powders, which make up typically between 30 and 90 wt% of the producl. In addition to this, there may be granular or spray-on admix components, e.g. en zyme, perfume and bleach. In contrast to other industries employing granulation, the amount of binder or liquid phase is not negligible in detergent manufacture. All components are func tional and are typically added for superior final application and not for a special purpose in the granulation process. One tries to incorporate as much liquid as possible in the granule, rather than trying to just bind the solids together with the least amount of liquid possible, making optimum use of two features of the ingredients: (i) the carrying capacity of the available solids, and (ii) the precursor state of liquid and solid ingredients to generate the desired components in situ. Furthermore , the "Iiquid-to-solid ratio" is a governing parameter of the granulation process and determines granulometry and granulation kinetics. This key differ ence between detergents granulation and conventional granulation invokes a different perspective on the role of the phase volume ratios that are a crucial part of the granule structure. The final section of this chapter will therefore mainly focus on the structure of detergent granules. Sections preceding this will address detergent powder ingredients, properties and granulation technol ogies. Given the large extent of available literature, e.g. in the above-mentioned texts and the plethora of patents, this chapter will mainly focus on recent additions. 2. DETERGENT POWDER INGREDIENTS
The wash process is a complex kinetic process and typically consists of the following steps that occur either sequentially or in parallel: water treatment, soaking andjor swelling of the cloth es in the detergent solution, physical andjor chemical dirt removal , stabilisation of the removed soils in the wash solution and the rinsing of soils and chemicals from the wash load. In addition, modern de tergents also include ingredients to deliver benefits such as softness and fresh ness. Given the numerous wash conditions, e.g. water hardness, water temperature, soak time, agitation level, product dosage, soil type and level and amount of clothes, laundry detergent formulations are complex and contain several different types of ingredients. These are typically classified into: surface active agents (or surfactants), builders and other additives, such as bleach sys tems, enzymes, polymers, foam regulators and fragrances. Detailed discussion of the various ingredients and their performance aspects can be found in various specialised books [1-4]. This section briefly summarises some of the common ingredients in detergent powders and their properties of relevance to the manu facture of free-flowing detergent powders via granulation.
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The main ingredients of fabric cleaning detergents are surfactants. The surfactants used in fabric cleaning detergents are mainly anionic and non-ionic surfactants and their mixtures. A small amount of cationic surfactants may aiso be included. The main anionic surfactant used is the sodium salt of linear alkyl benzene sulphonate (LAS). Other anionic surfactants include soaps (salts of fatty acids), primary alkyl sulphates (PAS), a-olefin sulphonates (AOS), alkyl ether sulphates (AES) and methyl ester sulphonates (MES). LAS acid is highly stable and upon neutralisation with an alkali source, such as an aqueous solution of caustic soda or sodium carbonate, will form a waxy solid. In spray-drying, LAS may be neutralised prior to slurry-making (neutralised LAS paste), or in the slurry itself. The spray-drying slurry is kept pumpable and stable against separation by manipulating the rheology of the mixtures of various phases of surfactant and water in the slurry with extra electrolytes, hydrotropes and water. In the so-ca lied "dry neutralisation", LAS acid is combined with an alkali source in high-shear mixers. LAS acid may be partly or fully neutralised in a loop reactor prior to introduction into the high-shear mixer [5]. This ensures that LAS acid is com pletely neutralised in the detergent powder and leads to improved powder quality because any residual acid can discolour the powder, degrade the perfume lead ing to bad odour or even make the granules and powder less resilient. Neutralised LAS, i .e. the sodium salt, is a waxy, hygroscopic solid phase, which at relatively high phase volumes may cause granules to lose their strength under compres sion and shear. Strengthening the surfactant phase in such situations by intimate mixing with finely divided solids or using other surfactants and polymers is rec ommended [6]. The principal non-ionic surfactants used in detergents are fatty alcohol ethoxylates with, typically, less than 1 0 ethoxylate groups. These surfact ants, though solid at temperatures below 20°C, have a pour point in the range of 25-40°C, above which they transform into a liquid with viscosity less than 1 00 mPa s. Such liquid-like surfactants are offen retained in granules by mixing them with anionic surfactants or granulating them with finely divided solids. In order to remain within flammability andjor (dust) explosivity limits, e.g. should fast rotating parts generate a spark, sizeable amounts of inert material need to be incorporated during high-shear granulation of high organic material (liquid, solid, acid) containing compositions. The other components in a fabric cleaning detergent include: •
So-ca lied "builders" whose role is to augment the surfactants in the wash. In addition to deactivation of calcium and magnesium ions in the water and thus preventing them from interacting with the surfactants and soils, builders may also provide alkalinity and also help to keep detached soil from redepositing onto the fabric. Common builders include sodium tripolyphosphate (STPP), various forms of zeolite, sodium silicate, nitrilotriacetic acid (NTA), layered sili cates and sodium citrate.
Detergent Granulation •
• •
• •
677
Sodium carbonate and sodium silicate whose role is to provide the necessary alkalinity and buffer capacity to maintain the pH at the desired value during the wash. Electrolytes including sodium carbonate and sodium sulphate that provide the necessary ionic strength. Organic non-surfactant additives are present in small amounts to serve one or more specific functions, such as to reduce redeposition of soil from the wash onto the fabric (e.g. sodium carboxymethylcellulose (SeMe)), to sequester heavy metal ions (e.g. phosphonates and sodium citrate), to reduce corrosion of machine parts and to maintain fabric whiteness (e.g. fluorescers and various blueing agents). Bleaching agents - such as sodium perborate and sodium percarbonate - and their activators - such as tetraacetyl ethylenediamine (TAED) - are widely used in Europe to provide effective bleaching at low water temperatures. Detergents for machine application may aiso include foam reg ulators to either augment the foam or reduce it depending on the application. Enzymes are also increasingly being used in detergents and specifically target proteinaceous stains (proteases), starches (amylases) and fatty esters and triglycerides (lipases). Fillers such as sodium chloride, clays and calcite. Fragrances.
Table 2 lists some common solid ingredients in detergent powders and their properties, as collated from various handbooks. Here, RH refers to relative hu midity at ambient pressure (closely related to water activity, 8w), and Lee refers to the liquid carrying capacity, i.e. the maximum liquid-to-solid ratio using a standard liquid such as linseed oil, 3EO non-ionic surfactant or dibutyl phthalate [7]. The Lee of various solids is an important parameter for detergents granu lation. The various hydrates indicate the ability of these solids to bind water and thus make them unavailable for carrying surfactants in the powder that can lead to poor powder properties. The combination of various surfactants with these ingredients to formulate detergents for fabric cleaning is treated by various authors, e.g. Ho [8] and Smulders [3].
3. DETERGENT POWDER PROPERTIES
Three types of powder properties are relevant, those which affect • • •
product performance in relation to consumer habits; product handle-ability in relation to manufacture, storage and transport; and physical stability in relation to climate.
Table 2. Typical solid ingredients found in detergent formulations and some of their properties relevant to detergent manufacture
Critical RH% at �25'C
Solubility in water (g/1 00 g)
Remarks on granulation
6 aq.
59 (phase I), 70 (phase 11)
Of 6 aq. 1 2.9 (20'C), 1 3.7 (40'C)
22.5 (1 aq.), 70 (7 aq.), 76 (10 aq.)
22.3 ( 1 0 aq. at 20'C), 38.4 ( 1 0 aq. at 30'C) 48.7 (40'C)
2165
10 aq. upto 32'C, 7 aq. 32-35'C, 1 aq. 35-1 00"C 7 aq. (below 24.4'C), 10 aq. (below 32.4'C) None
Encrustation in wet granulation, admix/granulate spray-dried or granular STPP High-shear (pre) granulation, layering High-shear (pre) granulation, layering Dry neutralisation, carrier, layering
75.3
Filler Additive, powder properties
2570 2112
None Not relevant
36 (20'C), 36.6 (40'C)
Not relevant
1 3 (O'C); 42 ( 1 00'C)
Additive, builder, dissolution aid Additive, dissolution aid Additive
1 665 1 665
1 aq.
�70%
1450
Melts at 58'C
Not relevant
Additive
2159
SCMC Sodium perborate
Additive Bleach
1 620
400 350
Decomposes > 50'C Not relevant 1 aq. above 40'C
Sodium percarbonate Clay
Bleach
700
Not relevant
Ingredient
Role
Density (kg m -3)
Particle size Ütm)
Hydrates
Sodium tripolyphosphate (STPP)
Builder, ionic strength
�2600
1 0-250
Zeolite 4A
Builder
2050
1-10
Zeolite A24
Builder
2220
1-3
Sodium carbonate
Buffer capacity, ionic strength
2532
1 50 (light), 500 (dense)
Sodium sulphate
lonic strength, filler
261 7
Sodium chloride
Filler
Calcite Sodium sesquicarbonate Sodium citrate, 2 aq. Citric acid Sodium acetate, 3 aq. Sodium bicarbonate
Lubricant, softener
2350
> 80
72 (25'C)
<10
76.2 (O'C) 9.6 (20'C), 1 2.7 (40'C)
44% (4 aq.)
Of 4 aq. 2.4 (20'C), 6.5 (40'C) 13.1 (20'C)
0) -..J 00
Admix, in situ generation Admix Carrier, admix Carrier, structurant generated in situ [9] Carrier [10] Hygroscopic, foam structure [1 1 ] Carrier, generate in situ [12] Carrier Binder, admix Admix Admix Carrier (perfume, non-ionic [13])
;:u
OJ 0 Cl>
CO
..., ...= :
m. � :::l
679
Detergent Granulation
Some properties have multiple relevancies; for example, the bulk density of a product is an important conversion factor for use in carton packaging machines, which typically are not weight but volume controlled, whereas the packs are sold on weight. At the same time, bulk density has an important impact on the per ceived quality of a product; high density is typically associated with premium quality. Table 3 lists properties, measurements and indications of their relevance, as will be discussed in following sections. 3.1 . I n-use properties
Handwash consumers, still 75-80% of the global market, demand rapid dis solution of the product, typically within 0.5-1 .5 min. Also in markets with high automatie washing machine penetration, robust dissolution behaviour of deter gents is growing increasingly important as environmental awareness and regu lation drive washing temperatures and water consumption down. Especially relevant for users of front-Ioader automatie machines is the dispensing behaviour, which is a complex interaction between the kinetics of dissolution and hydrody namics of the dispenser drawer, as shown in Fig. 1 . In most dispensers, water between 1 0De and ambient temperature emerges in the form of narrow streams of liquid onto the powder and along the edges of the dispenser drawer. Some water, drawn in by the action of capillary forces, penetrates into the loose powder bed and displaces the air within. The rest flows either over or around the powder in streams and into the drum of the washing machine (Fig. 1 ). Several processes then occur simultaneously: granule dissolutionjdisintegra tion , surfactant swelling, viscous phase formation and dissolution, electrolyte hydration and dissolution, granule agglomeration on account of the greater "sticking potential" conferred by partial granule dissolution and the convective transport of granules. If all of the above proceed as desired (to be defined), the powder is dispersed and dispensed into the drum within 30-60 s. Powders that dispense quickly, i.e. in 1 5-20 s or less, dispense in spurts during which (re latively) dry portions of the powder bed break away, are lifted up by water and dispensed. If the powder does not dispense as desired, dispenser residues result. Dispenser residues are chiefly of two types. The first is a soggy, often slimy, paste of partially dissolved granules, surfactant and water. The second is a hard lump, progressively less wet from the outside to the inside of the lump (but dry compared with the first type) in which the individual granules do not appear to have dissolved much. Figure 1 also shows the forces acting on particles inside the powder bed and on the surface. The greatest force acting in the dispenser is that of buoyancy: on the powder bed with air trapped in it as a whole or on each particle. However, it acts only when water has penetrated the powder bed. The impact of the water jet on the powder bed and its subsequent transmission into �
Table 3. Powder properties and their relevance, mostly from Ref. [1], apparatus drawings also to be found there
Range Property
AbbreviationjUnit Lo
Hi
Brief explanation
Depends strongly on
Relevance
Formulation, process (densification), internal porosity, partieIe size distribution Bulk density, fines level, attrition
Brand image, dispensing, packaging and transport consumption
Process, formulation (LjS)
Solubility, dispensing, dustiness, f10wability
Process, formulation (LjS)
As RRd
Process, formulation (LjS) Process, formulation (LjS) Process, formulation (LjS), shape
As RRd As RRd Dispensing, pneumatic conveying, dustiness [14,65]
Bulk density, partieIe size
Rate of dissolution, especially hand wash
PartieIe size distribution (fines level), formulation (salts, surfactants), granule structure Porosity, non-solidified ingredients, e.g. non-ionic surfactants Process temperatures, residence time, source quality and age Surfactant level, fines level, shape
Front loader drawer residues
Bulk density
BDjkg m�3
300
900
Fill a calibrated volume without tapping, measure weight
Dynamic flow rate
DFRjmL S�1
80
NA
Particle size
RRdj�m
500
710
Particle size distribution width Fines level Coarse level Spouted-bed test
RRnj-
2
4
Flow from a standpipe through a conical orifice Measure particle size distribution, calculate RosinRammler distribution parameters As RRd
< 1 80 �mj%wt > 1 400 �mj%wt SBTj%wt
0 0 0
10 10 15
Solubility
190js
0
90
Dispensing
Dispenser testj%wt
0
5
Bleeding
Ongj%wt
0
5
Colour
L,a,b
NA
NA
Caking propensity (unconfined compression test) Compression
UCTjkg Cj%vol
Measure weight increase of filter paper over time Measure colour space co-ordinates Measure strength of a pre-compacted cake
NA NA
Sieve at 1 8 0 �m Sieve at 1400 �m Fluidise powder with a jet, measure fines generation Measure conductivity of metered dose in water Operate dispenser, measure residues
25
Compress a powder in a standpipe, measure volume reduction
Surfactant level
Ol co 0
Flow in transport (silos) and packaging
Cohesivity of non-ionic containing products Product quality Storage
;:0
OJ 0 CD ...,
CD
...: :
Storage, especially in bags, solubility
� � :J
681
Detergent Granulation STRt:AM FROM A JET DIREcru AI:IOVE
DEF/J'.crEO STRt:AM
57'Rt:AM OF \VATER FROM ANOTII ER JET
Buoyancy or Drag Force
Forces on an internal granule
Forces on a surface or near-Ihe-surface granule
Fig. 1 . Schematic of water flow in and around the powder bed in a dispenser.
the bed is not shown. Interparticle forces are also not shown. EP0451 894 [6] gives an example of a well-dispensing detergent. Dispensing behaviour may be measured by mimicking the dispensing process itself and measuring the remaining residue after a given time of dispensing from a standardised commercial dispenser. The chief parameters are geometry of the dispenser, flow rate and temperature of the dispensing water and dispens ing time. 3.2. Detergent powder handl i ng
Granules require special care in handling, and as the technology grew more or less organically from post-tower operations, which include spray-drying as an early unit operation, to separate systems, the layout of granulation plants is often determined by existing systems and buildings. Through various handling steps, such as belt conveying, belt-belt and belt-hopper-belt transfer, screw feeding, etc., size reductions of up to 30% may occur. Hoppers are often emptied by belts running underneath at speeds up to 1 m S - 1 , and normal loads may be consid erable. Granules may experience tens of impacts at up to 1 0 m S - 1 , shear at normal loads in excess of 30 kPa, rates above 1 00 Hz and compression at loads
682
R. Boerefijn et a/.
# Locmion
of (he
I
Exil
2
Sieve unil
3 Tcm
ranulation
rar base
rocess
wder slOmge
4 Admix eo l leelor belt 5 Drum mixer and sieve unit
6 Mass tlow hopper. feedi ng packing unilS
Fig. 2. Typical post-process handling plant layout (bars indicate transfer belts).
above 50 kPa. Screw feeding and pneumatic conveying [14] may result in size reductions of up to 25%, each accompanied by large amounts of fines generated. This is why often bucket elevators are preferred for vertical transport. Figure 2 depicts a typical handling system, starting from the exit of the base powder production process, passing through a bucket elevator and a sieve unit via transfer belts to storage hoppers and finally through a loss-in-weight feeder onto an admix collector bell. Then the powder may be transferred via a second bucket elevator into a drum mixer that includes a perfume spray, through a final quality sieve (admix components are commonly not sieved before mixing) and then into a mass-flow hopper feeding storage bins or packing units. 3.3. Stability
Typically, highly soluble materials such as detergent powders also exhibit hygroscopicity, and "powdering" or dry-Iayering (e.g. with zeolite) is common practice to prevent caking. Layering may take place at any stage after the for mation of initial granules. A tight control over the zeolite dosage is required to prevent dustiness and lack of flowability while preserving ca king protection. 4. GRANU LATION TECHNOLOGIES
Extensive layout diagrams and specific operating parameters for most of the processes described below may be found in Ref. [1].
683
Detergent Granulation
4. 1 . Base powder
We recall that base powder commonly contains surfactant and builder, and consti tutes 30-90% wt of the total product. It is commonly made via the routes indicated in Table 1 . As surfactant often forms a soft or waxy solid phase within the granules, granule strength has to be obtained by an efficient construction of a solid network throughout the granule. This requires micromixing of liquids and solids, and is commonly performed in high-shear mixers. Perhaps counter-intuitively, while mix ing is on-going, granule growth has to be delayed as much as possible in order to maximise the liquid load [1 5]. As it arose out of post-tower densification, after elimination of the spray-dried powder, the granulation process used in the detergent industry is commonly termed the "non-tower process". Typical layouts are as shown in Fig. 3, and comprise a high-shear mixer, followed by another moderate to high shear mixer and then usually followed by a conditioning step (cooling, drying), e.g. in a flu idised bed. For non-tower granulation [1 6-1 8], equipment of choice commonly comprises a Lödige Recycler (eB-type) and Ploughshare (KM-type). Appel [1 9] lists a number of equipment manufacturers commonly found in the industry. In the process depicted in Fig. 3, the anionic feed can be partly or fully neu tralised. The second stage (ploughshare) serves mainly for densification, and distribution of the layering agent. It can also be replaced by a recycler unit. Liquids can be pumped or sprayed in. Typical residence times in the recycler are of the order of tens of seconds, whereas in the ploughshare it may be above 1 min. Residence time in the fluidised bed may amount to 30 min. For plant Salids
• •
zeolite
satts
Liquids
• •
nonionics anionics
�
�
\9:! e:;'�:1> .......
l�
,-------, fluidbed
hol air
hOl air
Fig. 3. Typical layout of a non-tower detergent granulation process.
cool air
684
R Boerefijn et al.
flexibility and better control of product quality, in the early days of non tower granulation, spray-dried base powders were used as carrier materials. Nowadays, admixtures of non-tower and spray-dried base powders may be used to achieve the same. Conversion kinetics of the surfactant precursor neutralisa tion depend largely on surface renewal, which occurs in the first mixer at high tip speeds, generating a crumbly dough of up to 20 vol% porosity. In the second mixer, this dough-like material is densified and spheronised and the resulting granules have at most 1 0 vol% porosity. Throughputs of several tens of tons per hour are common. Only recently have satisfactory scaling rules for high-shear granulation of LAS granules been published [20]: tip speed and apparent viscosity, which may be grouped in the typical Ennis and Tardos' critical Stokes number to constitute the balance between break-up and sticking force [21 ] as weil as the volumetric liquid to-solid ratio are indicated to be the essential parameters. This analysis has a limited scope to systems employing highly viscous binders and fine carrier solids, as is the case with LAS and zeolites. It clearly shows how closely the process passes by the wet-mass region in the Utster map of deformation vs. saturation [22] at which the entire hold-up turns into a single paste. If spray nozzles are fitted in the fluidised bed depicted in Fig. 3, a fluidised-bed granulation system arises. This may be used to advantage to obtain a better control over the particle size distribution and the bulk density in the intermediate range between spray-drying and non-tower granulation [23, 24]. A typical layout of this system is shown in Fig. 4. The surface area of the f1uidised bed is typically 1 0-40 m 2 and residence times of the order of tens of minutes are common. Equipment of choice includes those supplied by Ventilex and Niro. The fluidised bed is commonly operated in plug flow mode by suitable choice of distributor plate (gill orientation). The premixer before the fluidised bed can be run either in batch or continuous mode. Throughputs can be as above or much lower, e.g. several tons per hour in the semi-batch mode. Two-phase nozzles are typically used here.
Fig. 4. Typical layout of a fluidised-bed granulation process.
685
Detergent Granulation
Fluidised-bed granulation is a self-limiting growth process. The operating airflow yields a superficial gas velocity in the fluidised bed, which corresponds to the minimum fluidisation velocity to be calculated using the Ergun equation [25] of the largest granules; those larger will settle and be unavailable for futher growth. At the same time, the elutriation or terminal velocity sets the limit on the smallest particles or granules; any smaller will be blown out. The elutriation velocity can be calculated using drag correlations [26]. The premixer, commonly a Lödige recycler or ploughshare, is used to extend the particle size range to smaller, normally not fluidisable particle sizes, owing to elutriation and/or co hesivity, which exhibit high liquid carrying capacity. Extensive research has resulted in the quantification of the dominant controls for stable operation of fluidised-bed granulation to prevent wet-quenching [27], and to prevent granulation in the case of a coating process [28], as depicted in Fig. 5. The flux or Akkermans number expresses the balance of the binder spray flux and the solids recirculation rate through the spray-zone. ,
(1) 0.9 -+-- Ob (FN
2) kg/hr ----.- Ob (FN 3.5) kg/hr
0.8 I..
=
=
0.7
� N
E 0.6
� CI >< :I
0.5
Li: >«I
... c.. CI) ... CI) '0 s::::
0.4 0.3
äl 0.2
0.1
� -- � - - -
o
0.2
-----1
0.4
Superficial Gas Velocity (m S·1) Fig.
5.
Typical granulation regime map for f1uidised-bed operation.
1 .2
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The Akkermans number is also a useful tool for scale-up of fluidised-bed gran ulation systems [29]. Furthermore, the unique relation between the Akkermans number and the growth rate constant used in population balance modelling allows a priori determination of the growth rate constant [30]. Adequate description of granulation kinetics, in addition to reliable sensor technology, is the main chal lenge for online control [31 , 32], which can be in part alleviated with this approach. Fluidised-bed granulation is an intrinsically robust process with moderate shear, which allows for more controlled structure formation of granules. If the binder solidification can be boosted by chemical reaction and a fine crystal dis persion within it, strong and porous granules may arise as shown in Fig. 6, which allow a granule to break away from surface Iimited, slow shrinking core disso lution behaviour [33]. This is described further in Section 6.2. Figure 4 depicts the high-shear mixer, used to pregranulate a portion of the binder with the fine solid carrier to extend the carrying capacity, as a separate entity. The Schugi Flexomix is an example of a fluidised bed with integrated high shear impeller, as can be used to produce detergent base powders [34]. Some less common process routes for base powder production exist as weil: the Unilever VRV process [35-37], which employs a flash-drier with a thick rotor shaft and short bl ades with small wall clearance to produce granules containing weil in excess of 50 wt% anionic SUrfactant (Fig. 7) and • the Henkel Megaperls extrusion process, which employs a cooled twin screw extruder to mould a mixture of spray-dried base powder and other liquids and solids into highly spherical and uniform particles [3, 38, 39].
•
Particle Size (arb. units)
Fig. 6. Schematic influence of granule mesostructure on granule dissolution time.
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PRODUCT
Fig. 7. Layout of the VRV process capable of manufacturing high surfactant-containing granules.
4.2. Adjuncts
Adjuncts are commonly defined as granules containing high levels of minor in gredients, which may individually be added at levels between 0.2 and 20 wt%. Notable examples are enzymes, anti-redeposition polymers and bleach. In order to maintain good control over the bulk density of the final mixture, a simple mixing rule may be employed if the granule size distributions of the individual compo nents are reasonably similar (which in the absence of cohesion is a prerequisite to avoid segregation):
B� . = L BX�. mix
n
I
with
L Xi = 1
(2)
n
It appears that the non-tower process in its essentials, Le. a high-shear mixer and a fluidised bed, is the new standard not only for base powders, but also for adjuncts, such as • • • • •
TAED bleach precursor [40], which is often provided with an acid coating for stability; silicone antifoam [41 ] , which is processed anhydrously with a starch carrier; builder granules [42], which are typically bound with a surfactant or polymer; perfume granules [43], which are typically encapsulated; and enzyme granulation [44, 45], which may contain cellulosic fibres or film-forming polymers for increased resilience and solubility [46, 47].
5. GRANU LES FOR TABLETTING
Designing granules consisting of a mixture of materials with a complex mechan ical response, including elasto-viscoplastic, for incorporation of tablets of a few centimetres in size is weil beyond the scope of most of the available literature,
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which typically addresses small pharmaceutical pills made of virtually pure, highly elastic substances [48] , with exception of the work of Adams and co-workers [49, 50]. Existing techniques for quantification of compaction behaviour are still useful, as summarised by Celik [5 1 ]. Providing a unit dose for laundry applications requires compacting between 30 and 1 00 9 of powder into 1 or 2 tablets, resulting in a considerable size tablet, typically 2 cm in height and �4 cm in diameter, which affects both solubility and strength. Functionality of the tablet relies on a suitable trade-off between the two. Commonly a brick-and-mortar system is employed, with the mortar providing for the integrity and bricks for rapid dissolution. Henkel and P&G rely mainly on swelling cellulosic polymers respectively inside and around the tablets [52-54], Unilever to some extent on phosphates [55]. Tablet strength is commonly ex pressed as diametral fracture strength (DFS), a so-ca lied "Brazilian test" for tablets. Tablets of powder mixtures depend in a complex way on the constituent properties, as quantified by Van Veen [56]. DFS may be related to a composite yield strength (CYS) as folIows: CYS = a - b DFS (3) where 1 ""' Xi (4) CYS - � 'O , i �
with L: Xi = 1 and 'O, i the Kawakita yield strength as determined by bulk comn pression of single component beds [57]: bed compression tests using a mould of similar diameter to the rotary press and plotting stress P vs. strain 8 allows for the determination of '0 from In P = cx 8 + In
(�)
(5)
Repeating this measurement at different starting bed heights, plotting '0 as a function of initial bed height and extrapolation to the abscissa yields 'O,i' Param eter a is proportional to the maximum compaction force and b to the compaction speed. Knowing the formulation and the target DFS for a tablet and 'O, i of the remaining components, the target 'O, i of a new granule to be incorporated may now be specified. Evidently, design rules of a granule for a specified strength are next in order as part of granule structure formation. 6. STRUCTURE OF DETERGENT POWDE RS
A detergent granule consists of three major components: the primary particles (solid), the detergent (liquid or soft solid) and porosity (gas). The amount, size
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Detergent Granulation Table 4. Relation between basic powder properties and structure
Property Bulk density Attrition Compressibility Bleeding Solubility Dispensing
Relation to structure Intra- and infra-granular porosity Shape (asperities) Phase volume ratios Liquid retention in micro-/mesopore structure Shrinking core vs. disintegration, viscous phase formation (can be suppressed by ionic strength or hydrotropes), water ingress Drag and buoyancy (size, density) vs. phase formation and dissolution
and distribution of these three phases determine the granule structure. The granule structure is generated by the process route and conditions and is a free handle to optimise product properties (Table 4), within the limitations imposed by the formulation. The term "structure" is widely used but not weil defined and therefore needs further specification for technical use. The structure of a system is related to the manner in which the system is internally built up from its basic components. As agglomerates are multiple component systems, the structure of granules or ag glomerates will be defined as "the spatial arrangement of its basic components" [58]. Typically, a structure definition is combined with length scale information such as macro-, meso- and microstructure. In the case of particulate systems, this would be the powder bed structure, the granule structure and the structure of the basic components itself, e.g. crystal structure of primary particles. The quantification of structure has several aspects as depicted in Fig. 8: the amounts of various components, their sizes and the manner of their assembly. In particulate systems, the amounts of the basic building blocks are the most im portant variables that define the internal spatial arrangement (or granule struc ture). The granule porosity is of special importance because it is not predetermined by the formulation, but a parameter affected if not controlled by the formation process. At the next level of detail, the size of the spatial phases formed is of interest. And last but not least, the distribution of the phases through the system defines the homogeneity of the structure and its composite behaviour. All these measures just quantify the structure of an isotropic system. The granule shape or its outer morphology, as weil as radial gradients, is not taken into account here. Therefore, one would additionally use shape descriptors, which are weil known [61 ] , and radial distribution functions, which give the radial depend ence of the concentrations of the various phases.
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Type/Scale Macro
Powder bed I Tablet
Meso G ranule
Amount BD / Bed porosity
Size Particle Size Distribution
Distribution Pore size: tablet I powder bed
Phase volume I Particle
Chord length / Covariance
Covariance function / distance distribution I
porosity
function
radial distribution
function
Micro
Formulation
Raw Materials / molecular level
Raw material characteristics (e.g. PSD solid)
Spacings, crystal types
181 °1 o
0
Fig. 8. Definition and overview of granule structure parameters [59, 60].
6.1 . Phases in a detergent g ranule
A detergent base granule is chemically composed of inorganic salts, surfactants and some water. The behaviours of these groups of components are distinctly different and do not necessarily mix. The salts are typically solids, the surfactants are liquid-like or soff solids. A detergent granule therefore has at least two well-defined separate phases: a solid phase and a liquid phase. The liquid phase, typically consisting of surfactants and water, binds the solids during the granulation process; thus it is offen termed the "binder phase". Besides these two distinct phases, entrapped air or porosity forms the third phase in a detergent granule. Phase volumes have the largest impact on the granule properties. This is, for example, the well-known effects of the granule porosity on dissolution and bulk density, or that of the liquid-to-solid ratio (L/S) and granulation index on the granulation process [20]. The granulation index is defined as the ratio of L/S and the LCC of the solids. In granulation science, this has been captured in the so called capillary state of the granule. The different types of granule structures are schematically depicted in Fig. 9 and can be described as (a) solids that are just bound together by some binder (pendular state); (b) well-bound solids with interconnected porosity (funicular state);
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Detergent Granulation
Fig. 9. Granules i n varying capiliary state as defined by Rumpf [62]: (a) pendular state, (b) funicular state, (c) capiliary state and (d) droplet state.
a) Dense granule
b ) Porous granule
c) Aggl omerate
d) High porosity
Fig. 1 0 . Different types of detergent granules containing surfactant [58, 60]: (a) dense granule, (b) porous granule, (c) agglomerate and (d) high porosity.
(c) liquid-filled solid assembly bound by capillary forces at the boundary (capillary state) and (d) a droplet with some solids inclusions and no porosity (droplet state). All these types can be found in detergent granules. Figure 1 0 depicts generalised structures as described above. Examples of cross-sections of detergent granules are shown below the four schematic struc tures in the figure. The dense system depicted in Fig. 1 0(a) is typical for a high shear mixer granulation process, e.g. European non-tower detergent powder (Section 4.1). Almost no porosity is found and the coarse solids are not densely packed. Figure 1 0(b) shows a sodium LAS adjunct manufactured via dry neu tralisation and containing a lot of porosity generated by carbon dioxide released during the neutralisation process. Figure 1 0(c) shows an agglomerate of prima ries. The primaries may either be pre-granulated material or relatively coarse raw material solids. Here the porosity has become the predominantly continuous phase rather than the solids or the binder phase. Binding of the primaries is the main issue in this type of structure. The given example is a granule bound by a
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melting-type binder and produced in a fluidised bed [63]. The last type of granule structure depicted (Fig. 1 0(d)) is one where the porosity is entrapped by a shell formed by bridging particles, rather than porosity being an interstitial space be tween attached primary particles. This requires some "blowing action" as often found in non-disperse systems such as polymer foams, or products manufactured by the reactive foaming process such as bakery products produced using sodium or ammonium bicarbonate, or eitric aeid [1 1 , 34, 64]. Here binding between pri maries is crucial to retain the high amount of porosity and still form a mechanically strong granule. The low bulk density of the fluidised-bed granule based on sodium sulphate generated in situ is an example of such a granule that shows a high amount of porosity and rapid dissolution [33]. Looking at the variety of granulation processes on offer, it is clear that the granule structure can be va ried even further. Figure 1 0 also schematically depicts the variation in porosity in granules produced via different processes. The properties of a granule are a direct consequence of the granule structure and the characteristic of the used raw materials. Hence an optimisation process of granule properties needs a systematic approach based on an understanding of granule structure formation. 6.2. Granule design 6. 2. 1. Maximising liquid content
Design of a granulated powder typically starts with a formulation. This formulation determines the mass fraction of the powder ingredients. The so-ca lied process aids may be used if cost and formulation space and regulations permit. One would run through the following steps and decision points when faced with the task of designing a manufacturing process. The amounts of liquid and solid components are given when a formulation is specified. The volume fraction of each component can be calculated using the densities of the components. The volumes of the liquid and solid phases then follow by summing the volumes of all liquid component and solid components, respectively. The next question to be answered is "How to create a dry granular structure with the given amount of solid particles to accommodate the required amount of liquids?" Being the first dimension of the structure space, the amount axis is fixed; the other two dimensions are the free parameters. This means that the size and distribution of the phases need to be adjusted to design the granule. The most natural way to create a dry liquid-solid system is that of a liquid-filled particle packing wherein the solids are densely packed and touch each other to form a disperse but percolating solid network - a skeleton. The free room be tween the solid particles can then be filled with liquid without changing the spatial
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693
Fig. 1 1 . An example of a brick-and-mortar structure.
Fig. 1 2 . Sequential packing of primary structures.
arrangement of the solids. Such a structure would appear solid-like because the mechanical properties are governed by the percolating solid network. We call this a brick-and-mortar system (Fig. 1 1 ). The phase volumes here are determined by the packing behaviour of the solids, which can be roughly predicted by particie packing theory, e.g. using the Kerner equation. Filling the porosity of the packing only partially enables higher liquid contents. This has its limit in the binding capacity of the liquid, at least when the liquid is the binding material. Higher amounts of liquid can be realised by distributing the solids and liquids in a designed way. The brick-and-mortar system shown in Fig. 1 1 is a random homogeneous distribution of the solids and liquid. A se quential packing of granules from the first process that results in brick-and-mortar primaries is a straightforward route to obtain a structure with a higher liquid content or higher liquid-to-solid ratio (Fig. 1 2). 6. 2. 2. Retaining porosity
The air content or porosity can be approached in a manner similar to that de scribed for the liquid content. However, the desired level of porosity (C:gra nule) is not a specified formulation component, but is determined by the desired physical
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rel. porosity -, 90% change 80% -+-- 5% 70% ___ 1 0 % 60% 20 % 50% 30 % 40% -lI<- 50 % 30% -+- 1 00% 20% +----�--���-����-� 1 °% 0% 0.40 0.50 0.20 0.30 0.10 0.00 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
::::: � � ..c:
�
� al
!=;�i��=E:���:::��;;���� Particle porosity [-]
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properties, especially bulk density (BO) and speed of dissolution. The bulk den sity can be calculated as BO = Psolids (1 - cbed ) (1 - cgranule) (6)
The bed porosity (cbed) depends on particle shape and particle size distribution and cohesiveness of the powder. For a normal detergent powder, the bed porosity may be initially approximated to be 0.5. If the bed porosity remains constant and only the granule porosity varies, then the bulk density variation is as depicted in Fig. 1 3. This figure should be read as in the following example: suppose we have a powder with granules of 20% porosity, and we increase the porosity by 1 00%, then the bulk density is reduced by 25%. 6.2. 3. Example of structure effects on powder properties: granule dissolution
Granule dissolution speed is primarily determined by the granule size and its distribution. One would think that it is really the surface area of the powder that determines this dissolution speed. However, surface roughness and asperities are dissolved away quickly, so that it is really the granule size that determines the kinetics of the dissolution process. The speed of dissolution may aiso be viewed as the time required for an amount of material per disperse element to get into solution. This can again be altered by the granule porosity; the higher the granule porosity, the smaller the relative volume to dissolve per granule and hence, the quicker the dissolution. Promoting disintegration or crumbling of granules by manipulating the granule structure is an alternative method to influence the dissolution speed. A granule will disintegrate when the binding elements between the primary particles are
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695
either dissolved or broken. A bond between two primaries in a granule will dis solve before the prima ries if it is readily accessible to the surrounding water and of discrete size. A granule in funicular or pendular state demonstrates this be haviour when the binder is soluble. Breaking of the bonds is typically achieved by a swelling material (disintegrant) or by an effervescent action. The dissolution time of a granule in the ideal disintegration case is determined by the time needed for the disintegration process and the time needed to dissolve the primary parti eIes generated via disintegration. (7) tdissolution = tdisintegration + tdissolution of disintegration products Under the assumption that these disintegration products dissolve by a shrink ing core mechanism, the dissolution of the disintegration products is solely determined by their size. This is a relatively safe assumption for the granule structures typical to detergent powders. The size of the disintegration products is Iikely to follow from the size of primaries already in the granule and can be measured by X-ray tomography (Section 6.3) and used to estimate the disso lution time. The time taken to dissolve a collection of granules/primaries purely dissolving via the shrinking core mechanism varies as d2 under stagnant con ditions (external mass-transfer controlled process), whereas it varies as d1 . 1 8 if the same collection of granules is stirred (internal-diffusion controlled process). An example can show the order of change to be expected by disintegration. Combining the two effects of disintegration and dissolution, dissolution times of granules can be dramatically lowered. For example, a typical slow dissolution time of a 500 )lm fraction of granules would be 50 s (as measured by conductivity release indicative of 90 vol% dissolved, cf. Table 4). If the granules are composed of prima ries each about 1 50 )lm in diameter, the dissolution time measured in the same manner would be 1 2 s plus the time needed for the initial disintegration or crumbling process. This is exemplified in Fig. 6 (Section 4 . 1 ). 6.3. Techniq ues to measure g ranule structure
Before a structure can be quantified, a measurement is needed to provide quan titative data for a structure analysis. Since structure is defined in this artiele as the spatial arrangement of the basic components, the measurement technique should give a two- or three-dimensional image of the structure in every instance. These images will then be analysed to derive the quantitative information needed to predict the granule behaviour. 6. 3. 1. Scanning electron microscopy (SEM)
Electron microscopy has become a standard tool for the visualisation of micro structures [66, 67]. The advantages of this technique are its high spatial reso lution and good material contrast, both of which result in a good ability to
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Fig. 1 4. (Above) Scanning electron micrograph of two different granules in back scattering electron mode. (Below) Elemental mapping via EOX mode of the right-hand image [581.
distinguish and identify the phase of a granule or eomposite. As SEM is a two dimensional teehnique, the third dimension must be chosen representatively. This is done by earefully slicing granules near their meridian plane. Figure 14 shows two example granules. The main images are made in a back scattering electron mode. This technique already gives an element-dependent contrast, which can be analysed. Elemental scans of the right-hand image are also in cluded below these two images. Here, the concentration of a selected element is presented semi-quantitatively. These images allow for the composition of the identified phases to be qualitatively determined. The first example granule is a compact homogeneous granule with excellent mechanical properties. The sec ond example shows a very different open structure, although the eomponents per se are relatively homogeneously distributed. 6. 3. 2. X-ray tomography
Real three-dimensional techniques have the advantage of excellent statistical ba sis. This enables especially to check the assumption of isotropie strueture. The available three-dimensional techniques are non-destructive and based on compu ter tomography. For micro-tomography either X-ray absorption or magnetic res onance (Magnetic Resonance Imaging, MRI) is used. In the case of granules, the higher spatial resolution of the X-ray tomography, up to 1 J.!m pixel- 1 , is advan tageous. Figure 1 5 shows an image of a slice through a compact granule obtained by X-ray tomography. The right-hand part of Fig. 1 5 shows the image after seg-
Detergent Granulation
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Fig. 1 5. X-ray tomography slice through a granule, before and after segmentation [58].
mentation of the phases. The different phases could be separated using an al gorithm based on the greyscale histogram of the image. The contrast between the phases is sufficient to identify and analyse the structure of agglomerates. 6.4. Quantification of particle structure
Extensive quantification of granule structure requires the use of stereological methods as described by Kohlus [58, 60]. Stereology is the field of spatial statistics and especially useful to characterise composite materials. An excellent intraduction can be found in Underwood [68]. In this section, we focus on a simple quantitative description of granule structure. Granule structure has been introduced as a com bination of amount, size and distribution of the constitutive phases. The various phases in a detergent granule were identified as solids, binder and porosity (air). 6. 4. 1. Amount
The amounts of material that can be mixed to form a dispersed system are specified by the volume ratios of the materials and not their mass ratio. This is dictated by simple steric effects; the amount must pack together to fill the space. The feasible ratios are purely volume-based. Air and liquids cannot transfer forces without flow. Capillary forces are typically strang enough during granule formation but not during handling and storage. The achievable liquid-to-solid ratios are not changed by the indusion of air. 6. 4.2. Sizes
The size of the phases or primary structures within a granule directly affects the granule strength and dissolution behaviour. At present, extensive finite-element
R. Boerefijn et al.
698
studies and dissolution simulations are needed to theoreticaily assess these properties [69]. A much more direct approach is the comparison of the desired properties for various size fractions of the powder. The size of an object is easily described by the diameter of the sphere of equivalent projection area; however, reality is more complex. In order to obtain detailed, quantitative size information of multiple continuous phases, one needs to somehow separate the phases. A common technique would be to use the sizes of the biggest spheres that fit inside the phase. This needs a three-dimensional data space and is thus volume-centred. The use of linear analysis is an unbiased method to generate the size distribution of a continuous phase. This technique measures basically straight point distances, and gives thereby detailed size in formation. Figure 1 6 shows a typical profile of a granule structure starting at the highest value and decaying quickly to zero. This hyperbolic trend indicates a high probability of choosing a short chord. Weighting the number distribution with the chord length results in a distribution in which the occupied area of the chord is depicted, assuming a standard thickness of a chord [68]. The curve is typicaily skewed to the left. This measure can be interpreted directly as the free distances between two points of a given phase. The methods described above result in a set of distributions or functions, which allow generation of statisticaily similar structures. For use in property or process functions, scalar parameters are needed to avoid convolution operations. A set of key descriptors also enables an unambiguous comparison of different structures. These descriptors should capture the amounts of the phase volumes and their sizes as weil as a homogeneity measure. In summary, the phase volumes of the 0.30 ';"E
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699
Detergent Granulation
solid, binder and void phase are the descriptors on the amount axis. The sizes can be covered by mean diameter of the chord length distribution. These are generally defined as # 1 /(p- q)) qo(l) · IP. d/ ( Lp,q (8) ' P q Lmax ,10r qo(l)·lq. dl where qo(n denotes the number frequency distribution of the chord length distribution and I the chord length. The average length inside a phase would be given by L2, 1 , the length-weighted mean length. Inside a granule, the elements of each phase are typically closely packed. The nearest-neighbour distance of two elements of a phase is not of great interest as it is typically close to the elements size; wh at is of interest is the mean free distance between two elements of a phase. The mean free distance Aj between objects of phase i is given by - 1 -
Abstract The moist agglomeration process, i.e., the wet massing, screening and subsequent drying is often a critical unit operation. The correct amount of granulating liquid and the correct
*Corresponding author. E-mail: [email protected]
Granulation Edited by A.D. Salman, M.J. Hounslow and J. P. K. Seville D 2007 Elsevier B.V. All rights reserved
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monitoring and detection of the granulation kinetics are important issues. The method to monitor the kinetics needs to be robust and should be applicable for any batch size. In this context, the theory of scale-up and the monitoring of the moist agglomeration process are reviewed. It has to be kept in mind that the production of granules in the pharmaceutical industry is still based on a batch concept. This concept offers many advantages with respect to quality assurance as a batch can be accepted or rejected. From experience, it is weil known, however, that the scale-up of the batch size may lead to problems. This fact is due to the variety of the equipment involved and to the fact that there is a lack of well-known "scale up invariant" parameters. A survey of the granulation endpoint detection procedure shows that the majority of the equipment manufacturers offer mixerjkneaders for the moist ag glomeration process instrumented with a power consumption device. In the following chapter, this and other approaches are discussed and emphasis is put on how to best use the power consumption method. The question of robust formulations leads to the concJusion that, for a robust dosage form design, new concepts such as percolation theory have to be applied. A typical ex ample is presented, which illustrates the effect of a percolation phenomenon.
1 . I NTRODUCTION
New trends in the production of pharmaceutical granules: the classical batch concept and the problem of scale-up. What are the new trends? In the past, the batch concept was never seriously questioned. This situation has changed es pecially since production costs have become an issue. Thus, today the whole production process is analyzed to identify critical steps and to find out, whether there is a chance to save money and to increase productivity. It is evident that the scale-up process is a critical step leading to additional costs, especially when there are unforeseen problems. Thus, it is not surprising that the number of recent publications treating the scale-up process has considerably increased. In addition, scale-up problems are nowadays carefully analyzed by the registration authorities and in case of doubts about the quality of the production batch, ex pensive bioequivalence studies between small-scale and large-scale batches, i.e., manufactured with the small- and large-size equipment, have to be done. What are the reasons for the differences in quality between a small batch and a large batch? There are several possible explanations. In the early phase of the development, only a limited amount of the drug substance is available. Thus, small-sized production equipment is chosen for the small batch size. However, the most critical point is the following: the formulation and the process are opt imized using, in general, small-scale equipment. Subsequently, the formulation is "frozen," i.e., during the clinical studies it is no longer possible to change the process and/or the formulation. For this reason, the formulation needs to be robust and has to lead to the same quality of the product using small- and large scale equipment. Thus, the scale-up process is an extremely important step. Unfortunately, in many cases the variety of the equipment involved does not
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facilitate the task of scale-up. During the scale-up process, the quality of the granules may change. A change in the granule size distribution, final moisture content, friability, compressibility and compactability of the granules may strongly influence the properties of the final tablet, such as tablet hardness, tablet friability, disintegration time, dissolution rate of the active substance, etc. In order to iden tify critical steps of the batch granulation and the scale-up process the chapter is structured as folIows. Fundamental aspects of the classical batch-type moist agglomeration process and of the scale-up exercise are presented. However, other approaches and concepts are mentioned without elaborating the strengths and weaknesses. It is suggested that the reader of this chapter consults directly the original papers cited. It is important that the reader can make his own unbiased choice of his preferred approach. Thus, just the general ideas of the different types of approaches including important boundary conditions will be summarized. Without the intention of blame, it is also of interest to study the list of references of the individual research papers including the references that may have been omitted. For the better understanding of the subsequent sections, fundamental ap proaches on the micro- and macro-Ievel are reviewed in the following section.
2. FUNDAMENTALS
Fundamental research work in the area of the moist agglomeration process goes back to Newitt, Conway-Jones [ 1 ] , Rumpf [2] describing at the microscopic level the mathematical models for the liquid bridge forces [1 ,2] and Ennis et al. [3] for the dynamic viscous forces, which take place during the moist agglomeration process. The following equations describe the cohesive stress for the pendular liquid bridge force [1 ,4]: (Je Ani'/x( 1 + tg(8/2» (1 ) where A is the constant taking into account the packing and the shape of the particles, }' the interfacial tension between the granulating liquid and the particle, 8 the half center angle defining the extent of the liquid bridge between two spherical isometric particles of diameter x. The cohesive stress (Je for the force of the liquid bridge in the funicular state [2] reads as (Je
=
(2)
where S is the degree of saturation of the interparticulate void space with the granulating liquid and Pe the capillary pressure. The model of Ennis et al. [3] predicts that the collisions will result in coalescence when the viscous Stokes number Sty is less than some critical Stokes number Sr.; : Sty = 8pru/91] and Sr.; = ( 1 + 1 /e) ln(h/ha) (3)
708
H. Leuenberger and G. Betz
where p is the granule density, r the harmonie mean granule radius of the two spheres, u the half relative velocity of impact, IJ the viscosity of the granulating liquid, h the thickness of the liquid surface layer, ha the characteristic height of the surface asperities and e the coefficient of restitution [3]. Schubert [5] describes the relation between the tensile strength of moistened limestone and the degree of saturation S with water (see Fig. 1 ). Leuenberger was able to show the link (see Figs. 1 and 2) between the mi croscopic forces and the power consumption profile, measured during the con stant addition of granulating liquid to the powder bed [4,6] dN/d V = WIeK
(4)
where dN/dV is the volume specific energy consumption, J1. the apparent friction coefficient and K the shear rate. It has to be kept in mind that the moist agglomeration process is a superpo sition of different processes as described first by Sastry and Fuerstenau [7] and recently modified by Utster and Ennis (see, e.g., [8]). Among the fundamental approaches, the Population Balance Models have also to be addressed. ------------------� , 1 . 2 ------------------------� ,, • ...
i...... . Pk
1 .0 • Pk
N cm2
o
x
0 .8
-- --
P.
C>z .
Moisturization
C>z .
Demoisturization
,,/r
......
. +....t.
'+ ----�,-
.. .. ...
,,' I
bN " a.
0.6
0.4
0.2
o
.Q.
,�
- - ��
=
0
,.---=-----=-
(
./
••••
/
,
•
.. .. -1
�
..
f
Limestone. c . 0.4 1 5 x 1 .2 · 7 1 �m
0.2
"
JO
�
....•.
.
" .t-9-�-�- f····�... 0 . 05
I
· ··· L.·
'•
I f ii I
0.4
s
0.6
0. 8
Fig. 1 . Tensile strength of a moistened limestone powder bed according to Schubert [5].
709
Granulation Process Control
I
: I
; 51
U:
Stoges m
I
'Ss
I
Gronuloting l iquid [ % or kg l or time [ t I Fig. 2. Division of a power consumption curve according to Leuenberger [4].
Owing to the fact that today fast computation can be performed with personal computers, this discipline has evolved considerably and covers fluidized-bed ag glomeration, as weil as drum agitation and high-shear granulation [9-1 1] since the early work of Sastry. The goal of the Population Balance Models is to simulate real agglomeration processes from first principles. It is evident that such an ap proach is an ambitious one. Thus, in practice, the mathematical model needs to be adapted to the experimental findings. Another approach is not to improve the mathematical models but to adapt the experimental set-up to fit better an existing mathematical model. This point can lead to controversial discussions among people from industry and academia: a typical example is the use of glass ballotini, i.e., nicely spherical particles with a smooth surface as a starting material for moist agglomeration experiments. Both approaches have merits and demerits and will not be further discussed in this chapter. Another research area, which is not treated in this chapter, is related to the production of spherical granules by the extrusion process. A lot of excellent work has been done by Newton et al. [12]. The agglomeration processes including dry agglomeration techniques, such as tabletting and the roller compaction process are comprehensively reviewed in the books of Pietsch [1 3, 1 4]. The topics of the following chapters are dedicated to the classical batch gran ulation process in a bowl (planetary or high-shear mixer), to the questions related to the scale-up exercise and to the problem of robust and non-robust formula tions. Emphasis is put on the specific approach and on the underlying concept of the Basel research group. Questions related to the control of processes in the fluidized bed, i.e., the moist agglomeration and the drying process, are not treated.
710
H. Leuenberger and G . Setz
3. THE BATCH AGGLOMERATION PROCESS AND THE C HALLENGE OF SCALE-U P 3.1 . Monitoring a nd controlling the batch agglomeration process with respect to the scale-up exercise : approach and concept
The scale-up process of the batch-type moist agglomeration process is analyzed taking into account mathematical considerations of the scale-up theory [1 5-20], the search for scale-up invariants, the establishment of in-process control meth ods [20-23] based for example on the power consumption method as weil as the design of a robust dosage form. In this respect, new concepts such as the per colation theory [24] play an important role. In small-scale equipment, the use of torque measurement as an in-process control is often more sensitive than the measurement of the power consumption. The measurement of torque is also used to control the in situ production of pharmaceutical pellets in a rotary fluidized-bed system [25-27]. 80th the power consumption and the torque measurement method are today used in industry and by many research groups (see, e.g., [28-42]). 80th methods can also be suc cessfully applied to the melt agglomeration process [43,47]. It has to be kept in mi nd that in too many cases the focus for the in-process control of the moist agglomeration process was put on the "endpoint detection." In this respect it is important to realize that the measurement of the power consumption profile or the torque as a function of the amount of granulation liquid added can provide an earlier signal, such as the steepest ascent of the power consumption profile, which can be used to control very rigorously the wet agglomeration process (see, e.g., [4,20,21 ,42]). In practice, the "early signal" (power consumption threshold detection, turning point (TP) determination of s-shaped ascent in phase II or peak-detection) in dicates a well-defined and reproducible "cohesiveness" of the powder mass, which can be used to fine-tune the moist agglomeration process by adding from this "point of reference" a constant amount of granulation liquid. Thus minor changes in the particle-size distribution of the starting material and "seasonal effects" (different relative humidities in winter, summer) leading to differences in the moisture content of the starting material can be taken into account.
3.2. Theoretical considerations related to the scale-up process 3. 2. 1. The principle of similarity
The important concept for scale-up is the principle of similarity [1 5-20]. When scaling up any mixerjgranulator (e.g., planetary mixer, high-speed mixer, pellet izing dish, etc.) the following three types of similarity need to be considered:
71 1
Granulation Process Control
geometrie, kinematie and dynamie similarity. Two systems are geometrieally similar when the ratio of the linear dimensions of the small-seale and sealed-up system is eonstant. Two systems of different sizes are kinematieally similar when in addition to the systems being geometrieally similar, the ratio of veloeities between eorrespond ing points in the two systems are equal. Two systems of different sizes are dynamieally similar when in addition to the systems being geometrieally and kinematieally similar, the ratio of forees between eorresponding points in the two systems are equal. 3.2 . 1 . 1 . Similarity criteria
There are two general methods of arriving at similarity eriteria: 1 . When the differential equations or in general the equations, that govern the behavior of the system are known, they ean be transformed into dimensionless forms. 2. When differential equations or in general equations, that govern the behavior of a system, are not known, sueh similarity eriteria ean be derived by means of dimensional analysis. Both methods yield dimensionless groups, whieh eorrespond to dimensionless numbers [1 5], e.g. , • • • • •
Reynolds number Re Sherwood number Sh Froude number Fr Sehmidt number Sc, ete. [ 1 6] Nusselt number Nu
The classieal principle of similarity ean then be expressed by an equation of the form: (5) 7[ 1 = F(7[2 ][3 , . . . ) This equation may be a meehanistie (ease A) or an empirieal one (ease B): Case A: 7[ 1 = e-n2 with the dimensionless groups: P(X) = 7[ 1 P(O) where P(x) is the pressure at level x and P(O) the pressure above sea level (x = 0) E(x) (6) 7[2 = RT with E(x) = Mgx ,
712
H . Leuenberger and G. Betz
where E(x) is the molar potential energy, M the molecular weight, 9 the grav itational acceleration, x the height above sea level and R T the molar kinetic energy Case B: (7) The unknown parameters a, b and c are usually determined by non-linear regression calculus. 3.2. 1 .2 . Buckingham's theorem
For a correct dimensional analysis, it is necessary to consider Buckingham's theorem, which may be stated as follows [19,20]: The solution to every dimensionally homogeneous physical equation has the form F(n1 , n2, n3, . . . ) = 0, in which n 1 , n2 , n3, . . . represent a complete set of dimensionless groups of the variables and the dimensional constants of the equation. If an equation contains n separate variables and dimensional constants, and these are given dimensional formulas in terms of m primary quantities (dimen sions), the number of dimensionless groups in a complete set is (n-m) [60]. 3. 2. 2. Sca/e-up and monitoring of the wet granulation process
3.2.2. 1 . Dimensionless groups.
As the behavior of the wet granulation process cannot be described so far ad equately by mathematical equations, the dimensionless groups have to be de termined by a dimensional analysis. For this reason, the following idealized behavior of the granulation process in the high-speed mixer is assumed: • • • •
the particles are fluidized; the interacting particles have similar physical properties; there is only a short range particle-particle interaction; and there is no (macroscopic) system property equivalent to viscosity, i.e. (a) there are no long-range particle-particle interactions and (b) the viscosity of the dis persion medium air is negligible.
According to Buckingham's theorem the following dimensionless groups can be identified: Power number qt n2 = Vp
Specific amount of granulating liquid
713
Granulation Pracess Contral
Fraetion of volume loaded with particles Froude number (eentrifugaljgravitational energy)
n5 = dr
Geometrie number (ratio of eharaeteristie lengths)
-
where P is the power eonsumption; R the radius of the rotating blade (first ehara cteristic length of the mixer); the angular velocity; p the specific density of the particles; q the mass (kg) of granulating liquid added per unit time; t the process time; V the volume loaded with particles; V* the total volume of the vessel (mixer unit); 9 the gravitational acceleration; and d the diameter of the vessel (second characteristic length of the mixer). The following remark has to be made: if the viscous forces play an important role, i.e., in the case of highly viseous binders or in order to study properly the dynamie agglomeration events on the microscopic level, the Stokes number Sty [3] has to be introduced. The Stokes number describes the ratio of granule collisional energy to the viscous dissipation energy brought about by the inter stitial binder. In the case of high-viscosity binders, the (macroscopic) power consumption profile changes as the liquid bridges are no longer mobile [20]. On the basis of the above-defined boundary conditions using only low-viscosity granulating liquid, the following scale-up equation can be established: (8) n 1 a(n2)b . (n3)C . (n4)d . (n5)e In general, however, it may not be the primary goal to know exactly the empirieal parameters a, b, C, d and e of the process under investigation, but to check or monitor pragmatically the behavior of the dimensionless groups (proeess vari ables, dimensionless constant) in the small- and large-scale equipment. The ultimate goal would be to identify seale-up invariants. w
=
3 .3. The principle of the power consumption method 3. 3. 1. The power consumption method
The principle of the power consumption method was described in detail in the publications [5,20-23,42,61 ,62]. In the majority of our experiments in Basel, two different granulation equipments were used. A Diosna P 1 0 high-shear mixer with a volume of 1 0 1 and constant impeller speed kept at 452 rpm and chopper speed at 3000 rpm during the experiments and a Loedige M 5 high-shear mixer with a volume of 5 1, and constant impeller speed kept at 278 rpm during the experiments. However, there is no problem to use other types of high-shear mixers such as the Glatt-Powrex Vertical Granulator.
714
H . Leuenberger a n d G. Betz
If the goal is to study the agglomeration process in the bowl, it is important to measure the so-ca lied "native" granule size distributions as a function of the amount n of granulating liquid added. For this purpose the green, i.e., still moist, granules have to be dried very carefully. Thus, to reduce the possible side effects due to the friability of more or less already dried granules in a fluidized-bed equip ment andjor in order to prevent secondary agglomeration during the drying process in a dish dryer, on the granule size distribution the following process was adapted: ( 1 ) the granules are dried only for 3-5 min in a fluidized bed (Glatt Uniglatt) and (2) subsequently for 1 5-25 min in a dish dryer to obtain moisture equilibrium corre sponding to 50% relative humidity of the air at ambient temperature (20°C). The particle-size distributions were determined according to DIN 4188 using ISO-norm sieve sizes [23]. If the reader is interested in a literature study it is important to check, whether "native" granule size distributions have been measured or if the granule size distribution was measured after screening through a sieve. Nowadays, most of the mixerjgranulator types offered on the market are equipped or can be equipped with the option to measure the power consumption or torque profile during the moist agglomeration process. Concerning the meas urement of the power consumption profile or torque profiles different approaches are possible. It has to be kept in mi nd that power consumption profiles and torque measurement yield the same result [36,37]. Already the first attempts to monitor the granulation process were made by measuring the power consumption or torque of a planetary mixer [38,39]. In the case that the results were obtained with very small-scale equipment, such as mixers used in a kitchen, the signal-to-noise ratio has to be carefully analyzed. If the signal-to-noise ratio is low, the results have to be treated with caution. It is evident that the no-load power consumption has to be subtracted. It is not advised to simply measure the profile of the elec trical current of the motor, as this signal may not reflect the effective power consumption. If power consumption profiles are studied in the literature, it is important to note the type of mixer, the formulation and last but not least, whether the granulating liquid was added in the beginning as a bolus or continuously added with a pump. Also it has to be clarified, if after the addition of the granu lating liquid, the wet powder was still massed for a certain time or not. The Basel group has adopted the following concept to characterize a formulation: the power consumption is measured as a function of the low-viscosity granulating liquid added continuously with a pump to the dry powder mix containing the weil-soluble binder until a suspension is obtained. 3. 3. 2. Power consumption measurement using an Hin process" computer program
Recently, the Basel group developed an "in process" power consumption meas urement computer program [40,41 ,61]. In order to analyze the profile "in process"
715
Granulation Process Control
a new characteristic point, the TP of the power consumption profile in stage 1 1 is introduced (see Fig. 3). The TP is calculated by using a polynomial approximation of 3rd order and the simplex method. Using the configuration panel of the meas uring equipment produced by Pharmatronic Ud, CH-4143 Pratteln, Switzerland, the following settings can be made: x-axis y-axis Offset
Acquisition rate Play speed Measuring transducer Filter
Start of calculation Percentage of slope (ppm) (1 00-30,000 ppm) Granulation timer
time (min) 0-1 20 min voltage (V) 0-1 0 V, 1 V � 200 W Adjustable in the range of ± 5 V, offset was kept constant at 0 . 1 V (20 W) during all experiments in order to determine the filtered (smoothed) power consumption profile. Number of sampies measured per second, adjustable in the range of 5-1 00 was kept at 1 0 during all experiments. Reproduction of data in the Play modus. Range 0.5-20 (kW), was kept constant at 2 kW during all experiments. Number of sampies (5-200) to calculate the filtered power consumption profile. The filter was kept at 1 5 during all experiments in order to improve signal-to-noise ratio. The sampie number (1 00-1 0,000) from which on the data are used for the calculation of the TP. Mean of slope to indicate the start of stage II of the profile. Time in seconds (0-300) to stop the granulating liquid addition after having reached the TP.
Using the settings "Start of calculation" (sampie number) and "Percentage of slope" (ppm) stage II is selected in real time. The mean of the slope value indicates the start of stage II of the profile and the filter setting avoids that signal fluctuations (noise effect) caused by the mixer are wrongly recognized as the start of stage 11. Characteristic points of the power consumption profile obtained with the com puter program: In order to determine and compare the influences of formulation and process design on power consumption measurement the following two characteristic points were used: •
TP of the S-shaped ascent in stage II of the profile calculated by the polynomial approximation of 3rd order and the simplex method.
716 •
H . Leuenberger and G. Setz
Maximum point (MAX) equals to 1 00% saturation of the particulate system and is defined as the point at which maximum power is taken by the motor of the mixerjgranulator (see Fig. 3).
3. 3. 3. Tensile strength measurements
In order to measure the tensile strength of moist agglomerates a device was developed within the Basel group (see Fig. 4). The results of various granules with different water contents were compared with the power consumption meas urements. The constructed device can calculate the tensile strength by meas uring the total force used in the experimental set-up. The total weight (mtot) added is necessary to break the bonding forces within the powder bed. (J = mtot . 9 flo(0 . 5mf + mk)g (9) A -
1 000
!
900 800
c:
.2 700 C. 600 E :::l 500 '" c:
0 u
400
Gi 300 �
0 Q.
200 1 00 0
0
20
40
60
1 00 80 Saturation (%)
1 20
1 40
1 60
Fig. 3. Power consumption profiles of the high-shear mixers LoedigejDiosna.
5 Fig. 4. Tensile strength measurement device: (1) basic plate; (2) frame; (3) extended half cells Iimited by a frame which can be clamped together to fill in the wet granular material. The half-cell on the left-hand side is fixed and on the right-hand side is moveable; and (4) roll for the string with can (5) to load with weight and move the half-cell.
717
Granulation Proeess Control
where is the tensile strength in the powder bed (N m-2 ), mlol the total weight loaded (kg), g the acceleration due to gravity: 9.81 m S- 2 , Po the frictional resist ance, mf the weight of powder filled in the device, mk the tare weight of the moveable part of the device, and A the fraction plane (m 2 ). The testing procedure is performed as folIows: the two halves of the device are clamped together. The wet granular material to be tested is filled into the device and the bed height is adjusted to approximately 5.0 cm with two Plexiglas plates. Once the cell is filled and the granular bed is consolidated so that no air pockets are present in the material the clamps are removed. The force needed to fracture the sam pie is determined by measuring the total weight (mlol) loaded on the string. The tensile strength is obtained by inserting the total weight into equation (9). The sam pies were tested at different moisture contents corresponding to different saturation levels using purified water, ethanol 96% or mixtures of both as granulating liquid. Cf
3. 3. 4. Typical materials (example)
The physical characteristics of typical starting materials are compiled in Table 1 . Polyvinylpyrrolidone (PVP) was added in a dry state at a level of 4% (wjw) to the powder mix of lactose 200 mesh (86% wjw) with cornstarch ( 1 0% wjw) orte mannitol (96% wjw), respectively. Mannitol was used in two different polymorphie modifica tions, the ß and the 6 form. In addition, the influence of four lactose qualities, lactose 35j40 mesh, lactose 140 mesh, lactose 400 mesh, lactose anhydricum, on the power consumption profile was investigated. The physical properties of the various types of lactose are compiled in Table 2 (Chapter4. 1 ). For that purpose, 4% PVP (wjw) ofthe same lot were added to the different lactose types. Table 1. Physieal properties of lactose (L) and eornstareh (MS)
Lactose (L) 0.58
Bulk density (g cm - 3 ) Tapped density 0.84 (g cm - 3 ) True density 1 .54 3 (g cm ) Sm (mass specific 3055 surface) (cm 2 g - 1 ) Mean diameter 40 (�m) mod . , polymorphie modifieation.
Cornstarch (MS) 0.49
Mannitol: jJ-mod. 0.61
Mannitol: 6-mod. 0.50
0.65
0.70
0.64
1 .5
1 .53
1 .55
25
96.0
1 1 0.0
718
H . Leuenberger and G. Betz
Table 2. Physical properties of various types of lactose
Bulk density (g cm- 3) Tapped density (g cm - 3) True density (g cm - 3) Mean diameter (11m)
Lactose (L): 35/40 0.75
Lactose (L): 140 0.69
Lactose (L): 400 0.49
0.82
0.86
0.59
1 .28
1 .42
1 .73
535.8
71 .9
Lactose (L): anhydricum 1 .82 0.55
1 55.5
As a granulating liquid, demineralized water, ethanol 96% or mixtures of both were used and pumped onto the powder mix at constant rate of 1 5 9 min - 1 kg - 1 . It has to be kept in mind that the solubility of the components plays an important role and influences the power consumption profile. 4. EVI DENCE FOR SCALE-UP INVARIANTS BASED ON THE POWER CONSUMPTION 4.1 . How to monitor and control the moist agglomeration process
In the case of the wet granulation process in a mixer/kneader, the granulation process can be easily monitored by the determination of the power consumption [4,20-23,42] (Fig. 2) profile. The typical power profile consists of five different phases (Fig. 2), if water is added as granulating liquid. Uptake of the added amount of granulating liquid by the components to saturate the moisture content (equilibrium moisture content at 1 00% relative humidity of the air). Start of the formation of liquid bridges (pendular state) between the primary particles. Plateau phase, i.e., filling up the interparticulate void space with the granulating liquid (transition from the pendular to the funicular state). The liquid bridges are mobile. Funicular state with isolated three-dimensional clusters (snow balls) having already reached the capillary state. Transition from the capillary state (i.e., void space Phase V ( > S5): between the primary particles completely occupied by the granulating liquid) to a suspension.
719
Granulation Process Control
It is important to note that the power consumption profile is different if the moisture equilibration (water absorption) does not take place due to the use of an organic solvent as granulating liquid. If water or alcohol is used as the granulating liquid, it is important to check whether some of the components of the powder mix may form a hydrate or alcoholate, Le. , that certain molecules uptake some water or alcohol molecules in their crystalline structure. In such a case, the power consumption profile is different from the one plotted in Fig. 2. Usable granulates can be produced in a conventional way only within the plateau region $3-$4 according to the nomenclature in Fig. 2. It is important to realize that the liquid bridges of phase 1 1 1 are mobile and thus the granulation liquid needs to have a low viscosity. Figure 5 indicates that the change of the type of mixer changes the power consumption profile. The important increase in the power consumption of the Gien mixer for amounts of granulating liquid $> $4 can be related to the build-up of large snowballs in the planetary mixer between the wall and the impeller blade. However, the important plateau phase can be weil recognized in both cases. The power consumption profile generated "in process" with the computer pro gram, described in Section 3.3.2, using a Diosna P 1 0 with 2.5 kg of powder mix and Loedige M5 high-shear mixer with 1 .5 kg of powder mix, is shown in Fig. 3. A standard mixture containing lactose 200 mesh (86% wjw), cornstarch ( 1 0% w/w) and PVP (4% w/w) was granulated. The profiles indicate the Maximum (MAX) power consumption at 1 00% saturation of the particulate system independent of the high-shear mixer. The TP in phase 1 1 of the profile is calculated "in process"
POWER CONSUMPT ION
GLE N
-
Start
addItIon of graru1atoll9 lIquId
�"" '"" " '4:.�. ,�,:, _m� . � (·� MElu
i
S3
..
16
" t
"
S4
18
•
>0 % I
. �\
�
GRANUlATING lIOUlD ....
I
'
Fig. 5. Power consumption profiles of two types of a mixer/kneader.
720
H . Leuenberger and G. Betz
by the computer program and represents a reference point at an early stage. The position of TP takes into account the properties of the starting material. After having reached TP, the granulation timer can be used to add a fixed amount. An ideal power consumption profile is obtained with Diosna P1 0 (see also Fig. 2). The profile obtained with Loedige M5 differs particularly in phases II and 1 1 1 . Using Loedige M5, there is no sharp increase in power consumption during phase 1 1 , but a slow increase with a slight maximum at the end of phase 1 1 1 . The differences in the obtained power consumption profiles are due to construction design and working principles of the two different mixers. However, the computer program was able to determine the TP in phase 1 1 and the maximum at 1 00% saturation, using both equipments. It is evident that the signal-to-noise ratio can be improved if the amount of material to be granulated can be increased. However, the actual power consumption signal (absolute amount of power used) of mixers of different type, can differ greatly for a given granulate composition. The comparison of the power consumption profiles obtained with a test for mulation containing ß-mannitol (96% wjw) and PVP (4% wjw) with the standard mixture in a Loedige high-shear mixer (see Fig. 6) differed particularly in phase 1 1 1 of the profile. The profile obtained with the standard mixture showed a slow increase in phase II and 1 1 1 with a slight maximum at the end of phase 1 1 1 . Changing the formulation to ß-mannitol a straight plateau i s obtained in phase 1 1 1 and the slight maximum at the end of phase III was eliminated. The extension of the plateau in phase 1 1 1 is especially important because usable granulates can only be produced in a conventional way within the plateau region. The TP of the ß-mannitol profile occurred at lower amount of liquid present in the granular
1 000 900
�
= <:> -= CI.
E = '"
= <:>
'" ... ..
ce i:';
800 700 600 500 400 300 200 1 00 0
0
20
40
60 Saturation
80 (%)
1 00
Fig. 6. Power consumption profile of two different formulations.
1 20
1 40
721
Granulation Process Control
material (% saturation) than the standard mixture. This is due to the amount of cornstarch present in the standard mixture. Increasing amounts of cornstarch showed increasing amounts of granulating liquid requirement [41]. This is due to the high water absorption capacity of cornstarch and therefore freely moveable liquid bridges are formed at higher saturation levels. The test mixture containing 6-mannitol could not be granulated in both of the high-shear mixers. Using various lactose qualities (see Table 2) granulating liquid requirement at the characteristic points TP and MAX is increasing linearly with increasing total lactose surface, corresponding to decreasing particle diameter. The important point is now that the power consumption profile as defined by the parameters $3 , $4, $5 or TP and MAX is independent of the batch size. For this investigation, mixers of the planetary type (DOM INICI, GLEN, MOL TENI) were used in addition. The batch size ranged from 3.75 up to 60 kg. To obtain precise scale-up measurements the excipients that are used need to belong to identical lots of primary material 1 0% wjw cornstarch, 4% wjw PVP as binder, and 86% wjw lactose. As can be seen from Fig. 7, the amount of granulating liquid is linearly dependent on the batch size. During the scale-up exercise, the rate of addition of the granulation liquid was enhanced in proportion to the larger batch size. Thus, the power profile, which was plotted on the chart recorder showed the charac teristic $3 , $4 and $5 - values independent of batch size within the same amount of time since the start of the addition of granulation liquid. The same results were found for the characteristic points TP and MAX of the profile in a Diosna P 1 0 and
13 '1 C7I �
:E
9
::J
.2" 01 c
�
e
"3 c
(!)
7 5 3
20
30 batch size
Ikgl
40
50
Fig. 7. Scale-up precision measurements with identical charges [20].
722
H. Leuenberger and G. Setz
Loedige M5 high-shear mixer, which are calculated by the computer program. This fact is not surprising as in terms of scale-up theory, the functional depend encies of the dimensionless group numbers n 1 and n2 were measured: ( 1 0) The other numbers n3, n4 and n5, were kept essentially constant. From these findings, one can conclude that the chosen uncritical relative amount of granu lating liquid per amount of particles to be granulated is a constant [20-23]. It is evident that the first derivative of the power consumption curve is a scale-up invariant and can serve as an in-process control and for a fine-tuning of the correct amount of granulating liquid (see Fig. 7). These findings led to the con struction of a control device prototype [5,23] at Sandoz Ud. (today: Novartis Ud.) as a result of a fruitful cooperation between H. Leuenberger (Pharmaceutical Development Department), J. Werani (Pharmaceutical Manufacturing Depart ment) and M. Dürrenberger (Engineering Department) as early as 1 982 [5]. The control device was then successfully commercialized by Collette Ud., which instrumented at that time all the Collette Gral mixers used world wide by Sandoz Ud. in order to guarantee a higher homogeneity of the batch to batch quality (see Fig. 8) Le., between the sites of manufacture (Brazil, Spain,
Collette - gral 7 5 L
2.0 c
ä. g
Peak detection
15
E
:1 I/)
3
1.0 1------
.... GI
�
&
Level detection
0.5 0.2
0.8
I kg J
1.0
Granulahng hQUId
1.2
1.4
Fig. 8. Power consumption profile of a high-speed mixer (Collette-Gral 751 ) with peak and level detection [4].
Granulation Process Control
723
Switzerland, USA, etc.) as weil as a function of the time. In 1 985 Holm, Schaefer and Kristensen from the Danish School of Pharmacy in Copenhagen suggested also the use of power control profile as weil as its first derivative to determine the endpoint of the granulation process [28]. The Copenhagen group (see, e.g., [29,30]) and also the group in England with York, Cliff and Rowe et al. (see, e.g., [31 ,32]), have since that time invested a lot of research work in the area of process control and scale-up based on mixer torque rheometer andjor power consumption measurements. In 1 999, Landin et al. [31 ] published the results of a study using the dimensionless numbers of Power, Reynolds and Froude to anal yze the scale-up behavior of a dicalciumdihydrate formulation with pregelatinized starch as a binder in planetary mixers with a size capacity between 5 and 200 I. It is recommended that the power consumption profile be measured in parallel with the temperature of the moistened powder bed as an "in-process control" to avoid an excessive temperature increase (drug stability, undesired melting of components, formation of starch paste, etc.), however, the temperature profile may not be a very reliable or versatile enough parameter to detect the granulation endpoint [33]. In place of the already discussed power consumptionjtorque measurements other approaches were studied, e.g. , the frequency analysis of the power consumption [34], the use of fast Fourier transform technique [35] or sophisticated moisture sensors based on near infrared spectroscopy [48] during the moist agglomeration process. To the knowledge of the authors of this paper, none of these concepts have led so far to a control device, which proved to be the method of choice. The effort to look at alternatives to replace the method of measuring the power consumption profile indicates, quite clearly, that the power consumptionjtorque measurements are not always satisfactory. In many cases, the powerjtorque measurements are just used as a fingerprint for batch docu mentation and not for control purposes. For a successful application of the control device [4,20,23,40,42] based on the power consumption method, it is important to apply strictly the following rules: 1 . The formulation and the wet agglomeration process needs to show, if possible, an ideal power consumption profile (see Fig. 2). Such a profile can only be obtained if the components (drug substance, excipients) are not too soluble in the granulating liquid. It is important that the power consumption profile shows an increase before the endpoint, i.e., before the point of no return is reached. 2. In order to keep constant the amount of binder in the formulation, an easily water-soluble binder (PVP, pregelatinized starch, etc.) should be added to the dry premix. 3. As a granulating liquid, a low-viscosity solvent, preferably deionized water, should be used. 4. It is an absolute prerequisite not to add the granulating liquid at the begin ning as a bolus but to add the granulating liquid with a pump at a constant
H . Leuenberger and G. Betz
724
Table 3. Comparison between the manual and the automatie mode of controlling the
moist agglomeration process [23]
Type of mode Manual mode: n = 20 batches Automatie mode: n = 18 batches
Yield (% wjw): 90-71 0 f.lm 82.03 ± 2.42
% Undersize: < 90 f.lm 6.80 ± 0.51
% Undersize: < 71 0 f.lm 88.30 ± 2.05
91 .45 ± 0.36
5.40 ± 0.35
96.80 ± 0.31
speed to be able to "fine-tune" the necessary amount of granulating liquid on the basis of an early signal (not end point) as discussed in the previous chapters. 5. The validation of the moist agglomeration process with the control device needs to include the subsequent screening and drying process. 6. An excellent check is the higher homogeneity of the yield of the granule size distribution (see Table 3). Nevertheless, other granule properties such as the compression profile and the properties of the final tablets should be tested, too. With this method, the manufacturing department at Sandoz Ud. was able to increase the mean yield (see Table 1 ) of the granule size fraction between 90 and 7 1 0 ,um by 1 0% and, more importantly, could reduce the standard deviation of the mean yield by an order of magnitude [23].
4.2. Comparison of power consumption and tensile strength measurements
The influence of the amount of liquid present in the granular material (% sat uration) on power consumption and tensile strength measurements at different stops during the agglomeration process is shown in Fig. 9. The maxima of power consumption were determined at 1 00% saturation, whereas the maxima of tensile strength measurements occurs at 90% saturation as expected (see Ref. [44]). The tensile strength expresses the cohesiveness between the powder particles, which is dependent on saturation and capillary pressure. The measured tensile strength (J (N m -2 ) equals the volume specific cohesion (J m - 3). The obtained results proved that the power consumption measurement is an alternative, simple and inexpensive method to determine the cohesion of powder particles.
725
Granulation Process Control 1 000 ..,-------,--, 2200
�
1 800
800
c
,2 c.. Ei
1 400 600 1 000
'"
C 0 Tooo '"
&:
� ..<:
:I
U
1
400 600
::
200
Öl)
�
5
�c
�
200
0 +-----t-----1f---j--l--+--t---'- -200 1 18 1 03 80 . 9 92 47. 1 69.6 26.9
Saturation
(%)
___ Power Consumption ---*- Tensile St rength
Fig, 9, Comparison of power consumption and tensile strength measurements.
4.3. Effect of dosage form design on the power consumption and tensile strength measurements
The influence of the type of granulating liquid on tensile strength and power consumption was investigated using increasing amounts of ethanol addi tion to water and pure ethanol as granulating liquid, respectively. The results pre sented in Figs. 1 0 and 1 1 indicate that the values of tensile strength and power consumption declined with decreasing surface tension of the granulating liquid. The forces acting between the individual particles, such as van der Waals, capillary and electrostatic forces as weil as tensile strength are dependent on the surface tension of the granulating liquid. The mentioned forces decline with decreasing surface tension of the granulating liquid [45,46]. This is in agreement with the results obtained within the Basel group. Whereas independent of the type of granulating liquid the maxima of the tensile strength was constantly determined at 90% saturation and the maxima of power consumption at 1 00% saturation. In Fig. 1 0, the absolute value of the power consumption profile decreased with increasing ethanol additions to the granulating liquid, this is especially true for the values obtained at the maxima of power consumption (1 00%). In Fig. 1 1 , the tensile strength profiles at 90% saturation showed highest tensile strength with pure water and lowest with ethanol 96%. The ethanol/water mix tures in between showed no significant difference in tensile strength of the powder bed.
726
H. Leuenberger and G. Setz 300 �------�--, -+- water __ ethanol 24%
250
� .§ 200
ethanol 48% ethanol 96%
IL-------�
E � 1 50 +-----+-�--��-
n c; o u
�
1 00
o Q.
50 +-------��-o
1 2. 8
25.4
54.4
83.4
91 .7
1 00
1 1 2.4
Saturation (%) Fig. 1 0 . I nfluence of various ethanol mixtures as granulating liquid on power consumption measurements. 3000 Tr=======,----, -+- water 2500 c E
�
C, �
.t:
2000
-- ethanol 24% f------IIII\-------------------1 ethanol 48% ethanol 96%
1 500 +-------� c;; � '0 1 000 T------/-���-�--------����----�__I
c; GJ f-
.:: ----.:a_ ::. ---j 500 -l--«:r -------------------------....:., O +----,-----.--.--� 1 0.3 26 47. 9 87.5 1 24.4 1 1 2.8 1 00 Saturation (%)
Fig. 1 1 . Influence of various ethanol mixtures as granulating liquid on tensile strength measurements.
5. ROBUST FORMU LATIONS AND DOSAGE FORM DESIG N 5.1 . The use of power consumption method in dosage form design
Robust formulations are today an absolute prerequisite. Concerning the praduc tion of granules, the granule size distribution should not vary fram batch to bateh.
727
Granulation Process Control
The key factors are the correct amount and the type of granulating liquid. The interpretation of the power consumption method can be very important for an optimal selection of the type of granulating liquid. The possible variation of the initial particle-size distribution of the active substance andjor excipients can be compensated in the case of an intelligent in-process control method, e.g., based on the power consumption profile. However, the formulation may not be very robust if the volume-to-volume ratio of certain excipients such as maize starch and lactose correspond to a critical ratio or percolation threshold [24,49-53]. With dosage form design, it is often necessary to compare the performance of two different granule formulations. These two formulations differ in composition and consequently vary also in the amount of granulating liquid required. Thus, the following question arises: How can the quantity of granulating liquid be adjusted to achieve a correct comparison? The answer is not too difficult as it is based on identified physical principles. A correct comparison between two formulations is often a prerequisite as the dis solution process of the active substance in the final granulate or tablet can be affected both by the amount of granulating liquid and by the qualitative change (excipients) in the formulation. In order to calculate corresponding, i.e., similar amounts of granulating liquid in different compositions, it is necessary to intro duce a dimensionless amount of granulating liquid n . This amount n can be defined as the degree of saturation of the interparticulate void space between the solid material, according to Fig. 2. $ - $2 (1 1 ) $5 - $2 where $ is the amount of granulating liquid (in liters); $2 the amount of granulating liquid (in liters) necessary which corresponds to a moisture equilibrium at ap proximately 1 00% relative humidity; and $5 is the complete saturation of interp articulate void space before a slurry is formed (amount in liters). The validity of the dimensionless amount of granulating liquid n is also given for the charac teristic points TP and MAX and is calculated as folIows: n
=
-=------=c--
$ - TP n = MAX - TP
(12)
where $ is the amount of granulating liquid (in liters); TP the amount of granu lating liquid (in liters) necessary to reach the "in process" calculated turning point of the s-shaped ascent in phase 11 and MAX is the complete saturation of in terparticulate void space before a slurry is formed (amount in liters). Power consumption is used as an analytical tool to define $ values for different compositions. Thus, the granule formation and granule size distribution of a binary mixture of excipients are analyzed as a function of the dimensionless amount of
H . Leuenberger and G. Setz
728
granulating liquid n. This strategy allows an unbiased study of the growth kinetics of granules consisting of a single substance, or binary mixture of excipients. Thus, it is important to realize that the properties of the granule batches are analyzed as a function of the dimensionless amount of granulating liquid n [5,6]. Less dense and smaller granules are obtained with an amount of granulating liquid close to $3 ' Harder and denser granules can be produced with an amount of granulating liquid close to $4 ' It could be shown [52] that the growth of the mean granule diameter follows a first-order kinetics in the range between the saturation levels $3 and $4 (plateau), i.e., where the pendular state still dom inates. It could be shown that between $3 and $4 an exponential growth of the mean particle size occurs. For saturation levels exceeding $4 ($> ca. 60%) the system becomes overwetted. Thus, the measurement of the complete power consumption profile between $1 and $5 is important in order to determine the growth kinetics as a function of the dimensionless amount of granulating liquid n , i.e., as % liquid saturation $. It is evident that it is not possible that the granulating liquid can saturate the interparticulate pore space to an extent that exceeds $ = 1 00%, which was reported for the case of calcium hydrogen phosphate using different binders and a different approach [54]. The correct amount and type of granulating liquid are key factors in the pro duction of granules and therefore in the robust dosage form design. In a gran ulation process, the granule size distribution should not vary from batch to batch. Variation of the amount n resulted in a linear dependency of the log median granule size diameter with the amount of granulating liquid n added per unit time, dem onstrated in Fig. 1 1 . The dimensionless amount of granulating liquid was calcu lated using the equations ( 1 1 ) (Fig. 1 2, DA 1 ) and ( 1 2) (Fig. 1 2, DA 2). The results
�
E C1l
'ö Q) N
."S�
3.1 ,----. 2. 9 2.7 2.5
� 2.3
c:
.!!!
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E
Cl
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R2=O.9984 (DA2)
R2=O.9982 (DA1 )
2.1
1 .9
1 .7 +-----�----_+--�--+_--� -0.4 -0.2 0.8 o 0.6 0.2 0.4 dimensionless amount ( DA) of granulating liquid Fig. 12. Granule size analysis during moist agglomeration in a Loedige high-shear mixer. DA 1 , calculated by using equation (1 1 ); DA 2, calculated by using equation (1 2).
729
Granulation Process Control * *
e =. w => .....J <{ > z <{ 0 w ::E
*
1 1 94
*
*
754
* *
*
*
* 475
300
2.5
3.0
3.5
Nm 4.0
4.5
5.0
TORQUE
Fig. 1 3. Mean pellet size as a function of the torque measured [25].
of both equations show a linear dependency. Therefore, granule size design can be controlled by the amount of granulating liquid n in both cases DA 1 and DA 2. If excipients are used, which exhibit a high plasticity after being moistened such as microcrystalline cellulose spherical granules can be achieved for a liquid amount S elose to S4 in a high-shear mixer. If a rotary granulator [25,27] is used a direct pelletization of microcrystalline cellulose is possible with a rather narrow size distribution of the final pellets. It is recommended to equip such a rotary granulator in order to measure the torque exerted on the rotating bottom plate during the addition of granulating liquid. The mean size of the pellets is related to the torque value (see Fig. 1 3). An alternative approach is to characterize sep arately the rheological properties of the excipients used [55]. 5.2. The application of percolation theory
A percolation phenomenon can be best explained in the case of a binary mixture consisting of two substances with very different physical properties, such as an electrical conductive material and an electrical isolator. Thus, with a mixture between AI 2 0 3 (an electrically insulating material) and copper powder, electrical conductivity of the Al 20 3/copper tablet is only observed if the copper powder forms an electrical pathway between the electrodes at tached to the surface of the tablet produced. The critical ratio where conductivity is measured corresponds to the so-called percolation threshold Pe [24]. In the case of a fixed normalized amount n of granulating liquid (see Fig. 1 4), it is interesting to note that the granules obtained from a lactose/cornstarch powder mixture lead to granule size distributions equivalent either to the granule size distribution of lactose (L) or cornstarch (MS). This result can be interpreted based
730
H. Leuenberger and G. Betz y. ( W/I-D + .t + tI' C L ". Z 0 + 1 00 * a; o 75 25 • :§ 9.75 �o z 50 50 c o * 25 75 Zo "-B t 1 0 90 +� + jg 0 1 00 o ...z =*, 9.5 � '$ z. � 31 g; �z + �
A
�
__ _ _ _
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o
z
eZ
•
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+ * + fJf •
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+
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es)
In � 0')
es) csi csi
in ....:
1f) tn U")
N rri ";
CI)
N (D CS) - -N
normalized granule diameter
Fig. 1 4. Cumulative particle-size distribution of the agglomerates at a fixed normalized amount TC ( = 0.62) of granulating liquid for different ratios of the binary powder mixture consisting of lactose (L) and cornstarch (MS).
on percolation theory (Fig. 1 4), i.e., that the properties differ for compositions below or above a critical ratio Pe of components between lactose and cornstarch. This result can have a tremendous effect if, e.g., the particle-size distribution of the starting material changes and influences the exact percolation threshold Pe [57-59]. Thus, if the formulation is close to Pe concerning the ratio of the ex cipients lactose to cornstarch the resulting granule size distribution can exhibit a linear or an S-type shape (see Fig. 1 4) corresponding to a processing below or above Pe. In order to develop robust formulations it is important that the formu lation does not contain critical ratios or percolation thresholds [49-53,56], i.e., that the theory of percolation is taken into account. 5.3. The agglomeration process in the light of F DA's PAT initiative
Pharmaceutical formulations are complex systems and even nowadays are often developed empirically under a high time pressure on the basis of "trial-and-error" experiments. This procedure can easily lead to a non-robust formulation. Fur thermore, many pharmaceutical processes are poorly understood. Thus, the predictability of the manufacturing performance is low or even non-existent. The goal of FDA's PAT initiative is to achieve scientifically based decisions, i .e., to design the quality of the product and to "test-in" the quality by eliminating the bad items at the end of the production creating waste of time and money. The best solutions could be obtained if mechanistic models or even first principles in the
731
Granulation Process Control QuaUtvby Design
GMPfCMC FOCUS
Process Design
Yes, Umited to the Experimental Design Space
Design quallflcatlon
MECHANISTIC U N DERSTANDING
Focused; Critical Process Control Points (PA T)
Maybe, Difficult to Assess
Fig. 1 5 . Knowledge pyramid (courtesy: Dr. A Hussain, FDA).
knowledge pyramid (see Fig. 1 5) are known. The manufacturing process of granules or granulation process is still poorly understood especially in cases where the necessary boundary conditions for an optimal granulation process are not fulfilled [63]. The power consumption method presented in this chapter rep resents an in-line process control method where a reference point is calculated at early stage. Thus, taking into account the properties of the starting material and furthermore the possibility of a predefined quality of the granules. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [1 0] [1 1] [ 1 2]
D . M . Newitt, J . M . Conway-Jones, Trans. Inst. Chem. Eng. 36 ( 1 958) 422-442. H . Rumpf, Chem. Ing. Tech. 30 (1 958) 1 44-1 58. B.J. Ennis, G.J. Tardos, R. Pfeffer, Powder Techno!. 65 ( 1 99 1 ) 257-272. H . Leuenberger, Pharm. Acta Helv. 57/3 ( 1 982) 72-82. H. Schubert, Chem. Ing. Tech. 45 (1 973) 396-401 . H . Leuenberger, Pharmacy World Congress '93, Tokyo, Proc. 53rd Int. Cong. Pharmaceut. Sci. 1 993, D.J.S. Crommelin, K.K. Midha, T. Nagai (Eds.), Medpharm Scientific Publishers, Stuttgart, 1 994, pp. 493-5 1 1 . K.V.S. Sastry, D.W. Fuerstenau, Powder Techno!. 7 (1 973) 97-1 05. S.M. Iveson, J . D . Litster, K. Hapgood, B.J. Ennis, Powder Techno!. 1 1 7 (2001 ) 3-39. CA Biggs, C. Sanders, AC. Scott, AW. Willemse, AC. Hoffmann, T. Instone, M. J . Hounslow, 7th Int. Symp. Agglomerat. , Albi, France, May 29-31 , 200 1 , Preprints, Vo!. 1 , pp. 307-3 1 6 . S. Heinrich, M. Peglow, M. Ihlow, L . Morl, 7th Int. Symp. Agglomerat. , Albi, France, May 29-3 1 , 200 1 , Preprints, Vo!. 1 , pp. 295-305. AA. Adetayo, J.D. Litster, S.E. Pratsinis, B.J. Ennis, Powder Techno!. 82 ( 1 995) 37-49. J . M . Newton, S. BouteII , J. Chatchawalsaisin, 7th Int. Symp. Agglomerat. , Albi, France, May 29-3 1 , 200 1 , Preprints, Vo!. 1 , pp. 337-342.
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H. Leuenberger and G. Betz
[1 3] W. Pietsch, Wiley, Chichester, England, Otto Salle Verlag, Frankfurt/Main, Germany and Verlag Sauerländer Aarau, Switzerland, 1 99 1 . [14] W. Pietsch, Wiley-VCH , Weinheim, Germany, 200 1 . [1 5] M. Ziokarnik, Dimensional analysis, scale-up, i n : M . C. Flickinger, W . St. Drew (eds), Encyclopedia of Bioprocess Technology: Fermentation, Biocatalysis and Biosepaeration. [ 1 6] Dimensionless Groups, Handbook of Chemistry and Physics, 67th edition, 1 986-1987, pp. F307-324. [ 1 7] Pharmaceutical Manufacturers' Association 1 1 5 1 54th Street, N. W. Washington DC, 20005. Remington's Pharmaceutical Sciences, 1 5th edition Mack Publ. Co. , Easton PA, 1 975, p. 1 429. [ 1 8] RW. Johnstone, M W. Thring, Pilot Plants, McGraw-Hill, New York, 1 957, p. 1 2 . [ 1 9] H . Leuenberger, Bitte Hans fragen oder in der Bibliothek, Seminarraum nachschauen. Wir haben das Buch in IPL nicht. in: H. Sucker, P. Fuchs, P. Speiser (Eds.), Pharm. Technologie, G. Thieme Verlag, Stuttgart, 1 978, pp. 80-92. [20] H. Leuenberger, Acta Pharm. Technol. 29/4 ( 1 983) 274-280. [2 1 ] H. Leuenberger, Powder Technology and Pharmaceutical Processes, in: D. Chulia, M . Deleuil, Y. Pourcelot (Eds.), Handbook of Powder Technology, Vol. 9, Elsevier, Amsterdam, 1 994, pp. 377-389. [22] H. Leuenberger, Proc. 2nd World Congress Particle Technol ., Sept. 1 9-22, 1 990, Kyoto, Japan, Vol. 1 1 1 , pp. 3 1 7-328, Society of Powder Technology, Japan. [23] M. Dürrenberger, J . Werani, Proc. 4th I nt. Symp. Agglomerat. , Toronto, June 2-5, 1 985, C . E. Capes (Ed.), lron and Steel Society I nc., pp. 489-496. [24] H. Stauffer, I ntroduction to Percolation Theory, Taylor and Francis, London, 1 985. [25] H. Leuenberger, B. Luy, J . Studer, S.T.P. Pharma Sci 6 ( 1 990) 303-309. [26] J. Kristensen, T. Schaefer, P. Kleinebudde, Pharm Dev. Technol. 5 (2000) 247-256. [27] J. Kristensen, T. Schaefer, P. Kleinebudde, AAPS Pharmsci. 2/3 (2000) article 24. [28] P. Holm, T. Schaefer, H . G . Kristensen, Powder Technol. 43 (1 985) 21 3-223. [29] H.G. Kristensen, T. Schaefer, Drug Dev. Ind. Pharm. 13 ( 1 987) 803-872. [30] H.G. Kristensen, Powder Techn . 88 ( 1 996) 1 97-202. [31 ] M. Landin, P. York, M.C. Cliff, RC. Rowe, Pharm. Dev. Technol. 4 ( 1 999) 1 45-1 50. [32] A Faure, I.M. Grimsey, RC. Rowe, P. York, M.C. Cliff, Eur. J. Pharm. Sci. 8 (1 999) 85-93. [33] G.J.B. Horsthuis, J A H . Van Laarhoven, RC.B.M. von Rooij , H. Vromans, Int. J. Pharm. 92 ( 1 993) 1 43-1 50. [34] K. Terashita, S. Watano, K. Miyanami, Chem. Pharm. Bull. 38 ( 1 990) 31 20-3 1 23. [35] A Ohike, K. Ashihara, and R Ibuki, Chem. Pharm. Bull. 47 ( 1 999) 1 734-1 739. [36] H. Leuenberger, H . P. Bier, H. Sucker, Pharm. Tech. I nt. 3 (1 979) 6 1 -68. [37] H.P. Bier, H. Leuenberger, H. Sucker, Pharm. Ind. 41 ( 1 979) 375-380. [38] N.-O. Lindberg, L. Leander, L. Wenngren, H. Helgesen, R Reenstierna, Acta Pharm. Suec. 1 1 ( 1 974) 603. [39] D.N. Travers, AG. Rogerson, T. M . Jones, J. Pharm. Pharmacol. 27 (1 975) Suppl. 3P. [40] G. Betz, P. Junker Bürgin, H. Leuenberger, Int. J. Pharm. 252 (2003) 1 1 -25. [4 1 ] P. Junker, Ph.D. Thesis, Basel University, Switzerland, 1 998. [42] H . Leuenberger, A M unoz-Ruiz (Eds.), Date Acquisation and Measurement Tech niques, I nterpharm Press, Buffalo Grove, 1 998, pp. 1 4 1 -1 57. [43] A Johansen, T. Schaefer, H.G. Kristensen, I nt. J. Pharm. 1 83 ( 1 999) 1 55-164. [44] H. Rumpf, Grundlagen und Methoden des Granulierens. Chem. Ing. Tech. 30 ( 1 958) 1 44-1 58. [45] W. Pietsch, H. Rumpf, Chem. Ing. Tech. 39 ( 1 967) 885-893. [46] H. Schubert, Untersuchungen zur Ermittlung von Kapillardruck und Zugfestigkeit von feuchten Haufwerken aus körnigen Stoffen. Ph.D. Thesis, Karlsruhe University, Germany.
Granulation Pracess Control
733
[47] T. Schaefer, D. Pharm. Thesis, The Royal Danish School of Pharmacy, Copenhagen, 1 996, 98pp. [48] J . Ratanaen, O. Antikainen, J.-P. Mannermaa, J . Yliruusi, Pharm. Dev. Techno!. 5 (2000) 209-2 1 7. [49] H. Leuenberger, L. Holman, M . Usteri, S. Winzap, Pharm. Acta Helv. 64/2 (1 989) 34-39. [50] J.D. Bonny, H. Leuenberger, Pharm. Acta Helv. 68 (1 993) 25-33. [5 1 ] H. Leuenberger, Adv. Powder Techno!. 1 0 ( 1 999) 323-352. [52] H. Leuenberger, M . Usteri, G . Imanidis, S. Winzap, Bolletino Chimico Farmaceutico, Anno 1 28, 2 febbraio 1 989, pp. 54-6 1 [53] H . Leuenberger, Y. Jin, M. Kwauk, G. Jimbo, Y. Kousaka (Eds.), Powder Techno!. Proc. '96 China-Japanese Symp. Particuology, May 24/25, 1 996, Beijing, pp. 37-4 1 . [54] M . Ritala, P . Holm, 1 . Schaefer, H.G. Kristensen, Drug Dev. Ind. Pharm. 1 4 ( 1 988) 1 04 1 -1 060. [55] P. Luukkonen, T. Schaefer, L. Hellen, A.M. Juppo, J. Yliruusi, Int. J. Pharm. 1 88 (1 999) 1 8 1-1 92. [56] R. Luginbühl, H. Leuenberger, Pharm. Acta Helv. 69 (1 994) 1 27-1 34. [57] I. Caraballo, M. Millan, A.M. Rabasco, J. Contral. Release 69 (2000) 345-355. [58] I. Caraballo, M. Millan, A. Fini, L. Rodriguez, C. Cavallari, Pharm. Res. 1 3 (1 996) 387-390. [59] L.M. Melgoza, A. M . Rabasco, H. Sandoval, I. Caraballo, Eur. J. Pharm. Sci . 12 (200 1 ) 453-459. [60] H. Leuenberger, Eur. J. Pharm. Biopharm. 52 (2001 ) 279-288. [61 ] G. Betz, P. Junker Bürgin, H. Leuenberger, Int. J. Pharm. 272 (2004) 1 37-1 49. [62] G . Betz, P. Junker Bürgin, H. Leuenberger, Pharm. Dev. Technol. 8 (2003) 289-297. [63] H. Leuenberger, M . Lanz, Adv. Powder Technol. 1 6 ( 1 ) (2005) 3-25.
CHAPTER 1 6 Tabletti n g Kendal PiU * and Csaba S i n ka
Merck Sharp & Dohme, Hoddesdon, Herts, EN1 1 9BU, UK Contents
1 . Introduction 1 . 1 . Granule design 2. Compaction process 2. 1 . Granule flowjhopper 2.2. Die fill 2.3. Powder transfer 2.4. Compaction, ejection and post-compaction operations 3. Compaction mechanisms 3. 1 . Compaction background 3.2. Compaction equations 3.2. 1 . Walker equation 3.2.2. Cooper-Eaton equation 3.2.3. Kawakita equation 3.2.4. Heckel equation 3.3. General discussion of compaction equations 3.4. Work of compaction 3.5. Density distributions 3.6. Ejection and ejection profiles 3.7. The ejection stress 4. Compaction equipment 4. 1 . Single-station presses 4.2. Rotary press 4.3. Special tablet presses 4.4. Instrumentation 4.4. 1 . Production press instrumentation 4.4.2. Instrumentation for product and process design 5. Finished compact characteristics 5. 1 . Strength testing 5.2. Fracture mechanics 6. Compact problems and solutions 6. 1 . Cracking 6. 1 . 1 . Excessive elastic recovery 6 . 1 .2. Air entrapment
*Corresponding author. E-mail: [email protected]
Granulation Edited by A.D. Salman, M.J. Hounslow and J. P. K. Seville t: 2007 Elsevier B.V. All rights reserved
736 737 738 739 74 1 743 744 744 745 747 748 748 749 750 751 752 753 754 755 755 756 757 758 760 760 761 762 762 765 766 766 768 768
736 6 . 1 .3. Tool wear 6 . 1 .4. Lubrication 6.2. Picking 6.3. Pitted or fissured surface 6.4. Chipping 6.5. Binding in the die 6.6. Low tensile strength 6.7. Uneven weight control 6.8. Mottled appearance 6.9. Disintegration and dissolution 6.9. 1 . Porosity 6.9.2. Hydrophobicity of powder 6.9.3. Presence of disintegrant 7. New technologies 7. 1 . The structure of powder compacts 7.2. Triaxial testing 7.3. Compaction modeling 7.4. Quality control and compaction PAT References
K. Pitt and C. Sinka 769 769 769 770 770 770 771 771 772 772 772 772 772 773 773 774 775 775 776
1 . I NTRODUCTION
Powder pressing is a forming process used in a wide range of industries, such as powder metallurgy, industrial ceramics, pharmaceutical tablets, food, detergents, fertilisers, batteries, magnets, nuclear and hard metals. The process is fast, economic and lends itself to high-volume production. The production rate de pends on the complexity of the powder compact. Complex parts such as auto motive gearbox components can be pressed to near net shape at a rate of a tens or hundreds per hour, while modern pharmaceutical presses produce hundreds of thousands of tablets per hour. In spite of the broad range of powder materials and applications, powder pressing has common features in various industries. The operation consists of filling a die with powder, compressing using rigid punches followed by ejection from the die. During this process, the loose powder bed is transformed into a compact of given shape and microstructure. Depending on industry and appli cation, secondary operations such as sintering may be necessary to achieve the required properties of the final product. Powder metallurgy compacts are required to have sufficient strength to withstand handling and a dense, uniform and defect-free microstructure. Compaction is fol lowed by sintering to achieve near full density and maximum strength for structural applications. Sintering is also employed in producing ceramics, hard metal and other composite materials. Dimensional control is important during compaction and sintering in order to reduce the need for other additional operations such as sizing or additional machining. In other industries (pharmaceutical, food, detergents), the
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final strength and mechanical properties of the compacts is determined during the compaction step. These products must be strong enough to withstand subsequent operations, such as coating, packaging, transport and use, but weak enough to disintegrate upon administration (medicines) or use (detergents). The properties of a powder compact depend on the characteristics of the powder and the choice of process parameters during compaction. In order to achieve the desired compact properties, the powders are mixed with other in gredients having specific functions. For example, lubricants are added to reduce friction and wear of the tooling. Steel powders may be mixed with graphite, which acts as a lubricant during compaction and alloying material during sintering. Hard metal cutting tools are compressed by embedding the hard ceramic component into a soft metal matrix. In pharmaceutical tablets, the active ingredient is mixed with excipients, such as lubricants (to control friction between powder and tool ing), glidants (to improve flow), binders (to improve strength) and disintegrants (polymers that swell in contact with water). Fine partides in the micron and submicron range (ceramics, hard metals, pharmaceuticals, household goods, food) usually require granulation to improve flow and avoid segregation during the various powder handling processes prior to compaction. Pharmaceutical powders of low-drug loading (e.g. under 1 % by weight) are also agglomerated to ensure drug-content uniformity. 1 .1 . Granule design
The ideal properties of a granule for compaction are 1 . The granule should have binding properties and should confer physical strength and form to the compacts. In addition, if the compact is subsequently designed to disintegrate in fluid, e.g. a detergent or pharmaceutical tablet, then the granule should allow ingress of liquid. 2. The granules should be free flowing and hence should be as near spherical as possible with minimal surface roughness. The aim is to have rapid, reproduc ible flow of granules so that compact weight variation is kept to a minimum even at high production rates. 3. The granules should have a uniform distribution of all the ingredients across the partide size distribution and robust enough to withstand handling without breaking down. The granules should also be relatively dust free to minimise any containment concerns. 4. Segregation and agglomeration ("caking") during handling, transport and storage should be reduced. 5. The granules should not stick to the die or to the punches. Compaction forces the granule into very dose contact with the wall of the die. Adequate lubrication is required to reduce tool wear or damage to the compact.
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Items 1-4 are usually achieved both by the formulation and by controlling the process of the granule formation. Item 5 is normally achieved by extra-granular addition of a suitable lubricant after granule formation. Typical lubricants used in the food, ceramic and pharmaceutical industries are stearic acid-based metallic stearates, such as magnesium or calcium stearate. Other stearates (lithium, zinc), graphite or polymeric waxes can be used in other sectors and a range of proprietary lubricants have been developed for various applications.
2. COMPACTION PROCESS
In this section, a brief overview of tabletting science and technology from an industrial perspective is presented. Common issues in powder pressing using specific examples from various industries are discussed. More comprehensive presentation of industry-specific issues can be found in specialised textbooks published on powder metallurgy [1 ,2], ceramics [3] and pharmaceutical powder compaction [4]. Compaction is a mechanical process, where the state of the material is changed from powder into a compact of given porosity. Powder compaction can be classified broadly as •
• •
cold compaction, which includes die compaction isostatic pressing, roller com paction, powder extrusion and forging of prefabricated powder parts; warm or hot compaction, where the above operations are carried out at ele vated temperatures; powder injection molding, where a large amount of binder is mixed with the powder before injection molding and removed before sintering.
In the following sections, cold die compaction is only discussed. The compaction process is composed of the following steps: • • • • •
delivery of powder to the die die fill compaction ejection post-compaction operations.
Understanding the compaction process requires knowledge of the flow behav iour of powders, the densification mechanisms (which depend on the contact interactions between particles), the formation of bonds that give strength to compacts and the understanding of the response of a porous compact during
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unloading, ejection and post-compaction operations. These aspects of powder behaviour are discussed in the following sections in turn. 2.1 . Granule flow/hopper
The flow properties of a powder are important for the powder handling and pressing industries because the powder manufacturing processes (such as mix ing, granulation, drying, milling), powder pressing and powder transport involve flow in hoppers, pipes and chutes. The design of processing equipment is based on the flow properties of the powder and operating environment to ensure uniform flow patterns that reduce segregation and blockages. Powders flow because of body forces (gravity, centrifugal force) or extern al loads, which include air pressure and vibrations as weil as the constraints im posed by walls of the containers in which flow is ta king place. Powder flow is associated with dilation, contraction or can occur at constant volume. In order to describe powder flow, parameters such as dimensionless shear rate [5] were proposed. From this point of view, a number of flow regimes have been distin guished. Rapid flow, such as avalanches, is dominated by collisions between particles [6] while slow flow, such as in hoppers, is controlled by interparticle friction. During a given process, the different types of flow can occur concurrently. Under the applied loads and constraints the flow behaviour of powders is de termined by the fundamental powder characteristics (such as particle size and size distribution, morphology, material composition and density), operating con ditions (Le. moisture, temperature, static charge) and the current state of the powder (Le. tapped, consolidated, aerated, free flowing, etc.), which incorporates the effect of previous processes. The flow properties result from the combination of the factors listed above, which makes it difficult to characterise flow in a universal way for all applications and all industries, which in turn led to the development of a variety of testing methods. The flow characterisation techniques focus on specific aspects, such as measuring the flow rates through orifices of different size; the angle of repose; the energy to stir a powder bed; the cohesion and internal angle of friction of the powder; the bulk and tap densities; the formation of avalanches, etc. The effect of the initial condition of powder on the flow behaviour was recognised and devices such as a series of chutes, upstream funnels or special pre-conditioning cycles are employed to pre-condition the powder before the experiment in order to obtain repeatable results. There is a vast amount of literature, patents, standards, and specialised books and monographs dedicated to detailed descriptions of powder flow measurement methods, for example [7]. In the following section, the focus is on the issues specific to the flow of powders in hoppers.
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Hopper flow is important in industries, such as chemicals, plastics, pharma ceuticals, food, powder metallurgy, ceramics, mineral processing, etc. In compact formation, the delivery of powder to the die involves hopper flow. There are two main types of hopper flow, as presented in Fig. 1 . •
•
funnel flow, where some of the material is stationary. This may present prob lems for materials which cake, segregate or degrade. The most severe flow problems include arching and the formation of so-called rat holes. mass flow, where the entire powder mass is moving during discharge.
The uniform flow regime present in the mass flow hoppers eliminates some of the drawbacks of funnel flow hoppers; however, it requires taller hoppers with steep walls. In order to ensure mass flow, a number of designs were developed for the shape and size of the discharge zone. The calculation of the slope of the hopper walls requires Mohr-Coulomb type constitutive data [8], which are derived from techniques developed in soil mechanics, such as triaxial testing or shear-cell measurements. Shear cells work can work in translation [9] or by rotational shearing of the material. The rotational shear cells can be annular or full circle [ 1 0]. Shear cells can also be used to determine the friction coefficient between powder and a metal target to assist selection of container materials and surface finish to ensure that the powder flows along the walls. High friction can change the flow pattern from mass flow to funnel flow. An important consideration for the design of hoppers is to avoid formation of arches and rat holes. Arching occurs due to particle interlocking or material co hesion. A variety of flow meters based on powder flow through an orifice have been developed to measure quantities such as critical or minimal orifice size at which flow starts to occur [1 1 , 1 2] or the flow rate through a standard orifice [2]. The flow measurement techniques discussed above are based on different principles and it has been recognised that the choice of flow characterisation
stationary material
( a)
(b)
(c )
(d)
Fig. 1 . Flow regimes through hoppers: (a) funnel flow, (b) mass flow, (c) arching, and (d) rat hole formation.
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technique should be made in relation to the process under investigation [1 3]. In the following section, the specific features of powder flow into the die are reviewed. 2.2. Die fill
The flow behaviour of powders during die fill is different from the flow regimes discussed above because the discharge occurs into a c10sed cavity. The flow properties of powders have been studied extensively in relation to handling and hopper design as discussed above. On the other hand, only a limited number of studies concentrated On powder flow in constrained cavities under regimes sim ilar to die fill. As the powder is deposited in the die, a back-pressure is created, which reduces fill efficiency. Powder flow experiments carried out using metal, hard metal, ceramic and pharmaceutical powders [1 2] showed that flow meas ures, such as the Beverloo constant, are significantly altered when the powder is delivered into a c10sed container; this effect was found more pronounced for fine powders and for powders of low-density materials. The packing density of the powder in the die depends On powder properties, system geometry and process kinematics. The density variations can be ob served and quantified using non-invasive techniques such as X-ray computed tomography (CT) [14] for dies filled with metal powders. The initial density dis tribution is important because its effects propagate through the compaction cycle and subsequent operations. The density distribution after die fill is an input parameter for process models for compaction, which have been used in recent years. However, the results published in the literature to date are based On the assumption that the initial density in the die is uniform. The die fill systems on production presses are designed specifically to given powder materials, geometric complexity and production rates. Structural powder metallurgy parts employ high-capacity single-station hydraulic presses (see Sec tion 4. 1 ) where the powder is delivered from the hopper to the feed shoe through a series of hoses. The shoe travels linearly over the die opening and deposits the powder into the die through a sequence of motions under the effect of gravity. The shoe kinematics may include a number of shakes to facilitate the filling process. Additional mechanisms, such as fluidisation or vibration, are sometimes employed to loosen the arrangement of the powders, however, in most cases the shoes are simple rectangular boxes. In practice, the details of filling process are more complex. High-speed video observations [1 5] shows that rapid flow regimes, where particles interact by short collisions similar to gas dynamics, and slow flow, where the energy is dissipated through frictional interactions, occur simultaneously during die fill. The problem is further complicated when complex die geometries or complicated shoe kinematics
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is employed. The influence of air pressure was studied systematically for a wide range of powder materials, particies size and shape by performing die fill experi ments in air and vacuum [1 6]. Understanding these mechanisms is important in promoting strategies for maximising flow efficiency and packing uniformity to im prove product quality. Higher volume components (pharmaceutical tablets, magnets, detergents) are usuaily manufactured on high-speed rotary presses, which present further effects. Figure 2 presents a schematic diagram of a rotary press, where punches are mounted on a moving turret and pass through feeding, compression and ejection stations. The operation of the rotary tablet press is described in more detail in Section 4.2. Below the powder feed system of a rotary press using a Fette P 1 000 tablet press (Fette GMBH, Schwarzenbek, Germany) is examined as an example. The feeding system consists of a hopper connected to a feed frame. The feed frame consists of a box containing three paddle wheels driven by a motor. The powder is received from the hopper over the dispensing wheel and transferred to the feeding and metering wheels, which are located imme diately above the die table. The powder is deposited in the die while the die passes the die feed area seen in Fig. 2. A range of die fiil mechanisms can be identified. • • •
gravity feed; force feed, which represents the contribution from the paddle wheels; suction feed, where the power punch moves downwards in the feed cam while the die opening is exposed to powder;
Fig. 2. Schematic diagram of the feed frame of a rotary tablet press (top view).
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weight adjustment, which involves overfill and part ejection after the die passes over the feeding wheel; centrifugal effects and vibrations.
A detailed discussion of the mechanisms involved in die fill is presented else where [1 7]. The feed frames are geometrically and kinematically complex. Di mensional analysis [1 8] can be employed for quantitative evaluation of these effects for a given powder in order to improve feed frame design and selection of process parameters on a more rational basis. 2.3. Powder transfer
Powder transfer is an intermediary step between die fill and compaction, which is particularly important for the compression of complex multi-level parts (i.e. au tomotive gearbox components), which requires the use of a number of punches. The transfer operation is discussed below using the compression of an "H" shaped axi-symmetric component as example, as presented in Fig. 3. The tooling consists of a die, a centre rod and a set of three concentric lower and upper punches. The top surface of the powder is flat after the die fill. In the following step, the powder is transferred to a shape that is proportional to the compressed part. The punches are moved in a controlled manner so that they arrive at the
Upper punch set
Powder after die fill
Powder after transfer
Powder compact
Centre rod
Fig. 3. Powder transfer for manufacturing an "H"-shaped multi-level component.
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same time at the final position at the end of the transfer stage. Transfer is nec essary to avoid crack formation and the volume occupied by the powder is maintained constant during the transfer process. The compression step is normally designed so that columns of powder at different sections are compressed at the same strain rate. Optimum press con figuration is necessary during all stages in order to obtain a high-density crack free part with and mini mise the density variations in the compacL 2.4. Compaction, ejection and post-compaction operations
Compaction is one of the most important steps because physical properties of the compacts as weil as the pressing forces are determined not only by the properties of the powders constituting the powder mix (such as particle size distribution, shape, morphology, lubrication conditions) but also by the selection of the proc ess parameter. The stages of compaction and the mechanisms involved are described in Section 3. During compaction, the axial stress is transmitted in part to the rigid die wall. The sequence of removal of the axial loads for a complex part (see Fig. 3, for example) together with friction forces between the compacts and die wall (and punches) during unloading and ejection result in complex stress states which may lead to cracks and/or failure. Experiments using metal powders [1 9] indicated that the presence of lubricant has a significant effect on the ejection forces, while the type of lubricant was found to have a secondary importance. High-stress concentrations can also develop during ejection as the die wall constraint is progressively removed while the powder is being part ejected. One of the requirements of a powder compact is to withstand handling and loading during post-compaction operations. Parts made of metal, ceramic or hard metal powders are sintered to transform the mechanical bonds into metallurgical bonds. After sintering, secondary operations such as sizing, re-sintering or forging may be applied to achieve dimensional tolerances for ferrous structural parts. Control of tolerances after sintering is particularly important for hard metal compacts as grinding of cutting tool bits, for example, is expensive. Final finishing operations such as machining, heat treatments or plating may be necessary. Coating is largely used in pharmaceutical tablet manufacturing for functional purpose. All products though must withstand the loads during packaging, transport, storage and use. 3. COMPACTION MECHANISMS
In the following sections, details are given of compaction mechanisms and dis cussion of various equations to characterise the compaction processes are re viewed.
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3.1 . Compaction background
In 1 843, William Brackendon was granted patent number 9977 in London "for the shaping of pills lozenges and black lead by pressure in a die" [20]. In 1 884, Henry Wellcome registered the trade name "Tabloid" fram the words "tablet" and "al kaloid" to describe a small compressed item and manufactured and distributed a number of compressed items in Tabloid form including tea. By 1 895, the Pharmaceutical Journal in an editorial was commenting, "Un questionably, one of the greatest evils fram which legitimate Pharmacy and Medicine suffers lies in the indiscriminate use of the compressed tablet. We believe that tablets have had their day, or have reached the zenith of their pop ularity and like every other drug preparation that has preceded them, will pass away to make raom for something else" [21]. However, by 1 900 both single and ratary tablet presses were in routine use with Burraughs and Wellcome praducing 36,000 "Tabloids" an hour. However, measurement and understanding of compaction did not really com mence until the 1 950s when the advent of load cells and strain gauging instru mentation became more readily available. The pracess of compaction can be described as the route "whereby a loose natural or prepared powder is placed in some form of die and pressed between punches to form a coherent mass" [22]. Various densification mechanisms operate during powder compaction. The application of a pressure to the powder bed within the confines of the punches and die results in a reduction of the porosity. During these processes, adjacent particles are pressed together so that at the contact areas the action of the interfacial surface forces (atomic, molecular and electrostatic) will produce a stable and durable adhesive junction to give a potentially rigid and tough compact [23]. However, if too much energy is stored elastically when under compression, the elastic recovery during removal of the load may lead to adhesive failures and a soft, crumbly compact [24]. Hence the ability of a powder mass to reduce in volume when compressed does not however ensure the formation of a coherent compact. In general, powder compression progresses by • • •
rearrangement by particle sliding; reversible deformation (elastic deformation); irreversible deformation (plastic deformation and brittle fracture).
A number of stages can be identified during powder compaction, as illustrated in Fig. 4. After die fill, the powder is in a state of loose packing. The particles are able to translate and ratate with respect to one another to reach a state of dense packing, which is considered terminated where further rearrangement cannot
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poured powder
dense random packing
dense material
porous material
stage I I-roc---,....j isolated contacts
stage 1 1 isolated pores
increase in density the state of the material can be described by density Fig. 4. Stages of compaction.
take place. Next, densification takes place as a result of the contact interaction between neighbouring particles. In what is generally referred to as "stage 1 compaction" the contacts are isolated in the sense that the contact zones are not interacting. Some powder materials, such as ceramics, hard metals or pharma ceutical powders are granulated; these granules may deform and break down during the early stages of the process. As densification progresses, the contact zones between particles interact, the connections between particles are c10sed and isolated pores are formed, this is referred to as "stage 2 compaction". During this process the density of the material is increased and density is often used as a variable that defines the state of the material. Compaction occurs as a result of the interactions at the contacts between neighbouring particles. The relative contribution of these mechanisms changes as compression proceeds and varies from material to material. It should also be borne in mi nd that materials have a critical particle size below which they will exhibit plastic flow and above which they will fracture [25]. The critical particle size will also be influenced by compaction speed. The faster the compaction goes the more likely that the material is likely to fracture during compaction. The response of the material during compaction depends ultimately on the details of the interactions between neighbouring particles. At sufficiently small loads the interactions are elastic (recoverable). For ductile materials, such as metal powders, densification occurs as plastic deformation at the contacts. Ce ramic powders, owing to low fracture toughness, densify by particle splitting or crushing. These effects are iIIustrated diagrammatically in Fig. 5. The normal compaction process will never produce a compact that is totally free of pores. Pores, imperfect bonds and cracks within the particles, granules and compacts act as defects that may result in brittle failure initiation. The strength of the material increases as the porosity is reduced, hence structural components are compressed to near full density. However, it is not always
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Contact Mechanisms
8 8 ffi B
Elastic
Plastic
Splitting
Crushing
Fig. 5. Compaction mechanisms.
desirable to have a minimal percentage of pores especially when designing compacts that are required to disintegrate when in contact with water. In this case, it is crucial to have a balance between mechanical properties and disso lution characteristics, which are both related to the percentage porosity within the structure of the compact. Also, certain classes of compacts, such as sintered filters or catalysts, which are made of metallic, ceramic or composite materials, are designed to have certain porosity and pore structure rather than increased strength. The appearance of the microstructure and the development of residual stresses and density distributions are all influenced by the behaviour of the pow der and friction between powder and tooling as described in Section 7.3. In general, the lower the frictional forces the more even the pressure distribution and the more uniform the pore and density distribution within the compact. Graphic visualisation of the densification process is usually in the form of compaction curves. Compaction curves in the form of density-pressure relation ships can be used in the study of the compaction behaviour of powdered ma terials such as metals, pharmaceuticals and ceramics. Compaction curves have been used by various investigators, such as Lukasiewicz [26] and Briscoe and Rough [27], to identify the compaction mechanisms of powder masses. Figure 6 shows a representation of a compaction curve. When the density is plotted as a function of the logarithm of the compaction pressure used, the compaction curve shows a number of distinct regions. At the lower compaction pressures, as the particles rearrange, very little compaction occurs until a point is reached; in the literature this is referred to as the apparent yield point as shown in Fig. 6. The second yield pressure is referred to as the joining pressure and is interpreted as the point at which interagglomerate pores are removed. 3.2. Compaction equations
The relationship between compaction pressure and volume reduction or density increase has been extensively studied and several functions were proposed to fit
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"" . .
Jommg Pressure
Apparent Yield Point
Fig. 6. Schematic representation of compaction curve.
curves based on pressure and volume fraction. These equations often seek to provide an understanding of the basic mechanisms of the compaction process and also the magnitude of the resulting compact strength as weil as character ising the overall compaction process. The main equations extensively described in the literature are the Walker equation [28], the Cooper-Eaton equation [29], the Kawakita equation [30] and the Heckel equation [31 ,32]. 3. 2. 1. Walker equation
One of the earliest relationships was proposed by Walker in 1 923 [28] 1 00 V = K - Wa In PA (1 ) where V i s the volume of powder under applied pressure, K the constant, PA the applied pressure and Wa the constant equal to change in volume in percent of material volume when the pressure is increased by a factor of 1 0. Walker showed that the curves for this comparatively simple relationship fitted in a straight line for many sets of data. 3. 2. 2. Cooper- Eaton equation
Cooper and Eaton [29], when studying compaction of ceramics proposed that compaction occurs in two stages. Initially, the particles rearrange themselves and the large pores that are of similar size or larger than the particles within the powder bed are filled. In the second stage, the particles fragment or plastically or elastically deform and the smaller pores are filled. K K (2) V = a 1 exp - -1 + a2 exp - -2 P P I
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where V ' is the fractional volume compaction, 8 1 , 82 , K 1 , K2 are the fit constants and P the compaction pressure. The constants 8 1 and 82 indicate the fractional compaction associated with the different types of particle compaction: rearrangement (the filling of large pores) and fragmentation (the filling of smaller pores). When 8 1 + a2 = 1 , the compaction process can be completely described by the two processes, when the sum is less than one, other processes must be present. Constants K 1 and K2 indicate the pressures that correspond to the highest probability of one of the two compaction methods occurring. A Cooper-Eaton plot usually consists of two linear regions. A regression of these two lines enables the constants a 1 and a2 to be evaluated while the gra dient of the two linear regions allows the constants K 1 and K2 to be determined. The general suitability of using the Cooper-Eaton equation has been ques tioned. Studies have shown that when applied to relatively soft materials with polydispersed particles the two linear regions are not easily separated [33,34]. This could be due to the volume reduction occurring by several simultaneous compaction mechanisms. The Cooper-Eaton equation is, however, useful for understanding the mechanisms of volume reduction at initial stages of the com paction process (at low pressures) and as such information can be obtained regarding the effects of particle surface properties and shape and size of the densification of the powder columns. 3. 2. 3. Kawakita equation
Kawakita and Tsutsumi [30] showed that the relationship between compaction pressure and volume could be represented by 80 - ep e Va - V _ abP - 1 - Po _ (3) - � 1 bP Pp 1 - ep _
-
+
_
where e is the degree of volume reduction, Va the initial volume, V the volume of powder bed at pressure P, a, b the constants, P o the bulk density, Pp the apparent density at pressure P, 80 the porosity at the bulk state, 8p the porosity at pressure P and P the compaction pressure. The equation may be simply rewritten as [35] P 1 P (4) ab From a plot of Pie against the constants a (the reciprocal of the slope of the linear section of the graph) and b (obtained after evaluation of a and the value of the intercept obtained by extrapolation of the linear section) can be evaluated. Physically a is related to the initial bed porosity and b is related to the resistance force, although the meaningfulness of these parameters has been debated
C = + "8
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[35,36]. Also the value of C can differ depending on the experimental procedures. Sheikh-Salem and Fell [37] observed that both the die filling method and diameter of the die affect the value of C. The bulk and tapped density measurement technique provides information on powder flow and particle rearrangement at relatively small loads. Here, the pres sure can be replaced by the number of taps, N. 1 N N + -= (5) Ct at bt at The constant a is equal to the initial porosity and the constant b is considered to be related to the compressive resisting forces or cohesive forces of the powder particles. Alternatively N can be replaced by tapping time T. For agglomerates, Adams and McKeown [38] proposed a modified version of the Kawakita equation using a number of types of experimental agglomerates containing a fine inorganic particulate phase and a range of soft-binder phases, as their compressed sam pies. In P = In(ro' /r/) + + In(1 - e(-"'e») (6) -
r/ G
where P is the applied pressure, a' the constant related to friction, the strain and ro' the apparent single agglomerate fracture strength. G
3. 2. 4. Heckel equation
Heckel [31 ,32] examined the compaction of metal powders and developed an equation that regarded compression of metal powders as analogous to a first order kinetic process, where the pores are the reactant and the densification the product. This equation has since been applied to the compaction of pharmaceu tical and ceramic powders. 1 = kP + A In (7) 1 0 where 0 is the relative density at any given P, k and A are the constants and P the compaction pressure. A plot of In 1 /1-0 against P is usually referred to as a Heckel plot. The linear part of the plot can be fitted to a straight line. The intercept of the li ne will give the constant A. The value A can be related to the volume reduction of the powder bed by the process of die filling and particle rearrangement: 1 A In + (8) 1 00 B where 00 is the relative density of the powder bed at resting pressure and B the volume reduction caused by particle rearrangement. _
=
_
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At this stage no particle deformation has occurred. The relative density of the powder after die filling and rearrangement, DA, can be described by �=�+� 00 where Da is the relative density describing just the period of particle rearrange ment. DA can be found from 1 ( 1 0) A = In 1 DA The gradient of the Heckel plot, k, gives the plasticity of the material. The greater the slope the more plastic the material. Heckel showed experimentally for metals that the value k can also be related to the yield strength, Y, by the equation _
(1 1 ) Subsequently, the reciprocal of k has been defined as the mean yield pressure and has been used for comparison of properties between materials. The use of Heckel plots to describe the mechanism of powder compaction has been studied intensively. Heckel plots were analysed for pharmaceuticals by Hersey and Rees [39] concluded that the difference in shape of Heckel plots of a material with different initial particle sizes could be used to give information about the method of compaction for that material. Rue and Rees [40] and York [41 ] have published results on the limitations of the application. It has been noted that different particle sizes of the same material may compact with different mechanisms, which can involve transitions from brittle to ductile characteristics [25]. Other factors which should also be considered when evaluating the Heckel plots are the compaction time, die size, mode of die filling and dimension measurement techniques [42]. Die wall friction also affects the Heckel plots with Ragnarsson and Sjögren [43] concluding that parameters such as yield strength could be misinterpreted. How ever, they concluded if the mean compaction pressure of the upper and lower punches was used instead of the upper punch pressure the effect of lubrication, particle interactions and friction were minimised. 3.3. General d iscussion of compaction equations
The consensus is that Kawakita is most suited to low-compaction pressures and medium to high porosities. A mathematical analysis of the Heckel and Kawakita equations by Denny [44] has shown that when the compaction pressure is considerably lower than the yield strength of the compact, the two equations take the same form. Also when the Heckel equation is modified by introducing a
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pressure-dependent term into the yield strength, it is identical to the Kawakita equation over the full pressure range. It was therefore conciuded that the Kawa kita equation is a specific form of the more general Heckel equation [44]. Denny also concluded that compaction equations need further development to take into account the anisotropy in compacts made by uniaxial compression. A compli cation being that the Poisson's ratio of compacts will also increase with applied pressure that should be factored into any analysis. Hassanpour and Ghadiri [45] used the distinct element method (DEM) to sim ulate bulk deformation based on single-particie properties. They conciuded that there is a critical ratio of Young's modulus to the yield stress of individual particies above which the Heckel analysis does reflect the effect of the yield stress, but below which it in fact reflects the effects of Young's modulus. Therefore, the Heckel analysis does not have general validity and should be used with caution. Sonnergaard [46] has discussed the compression models given by Kawakita, Walker and Heckel who have suggested various interrelationships between the pressure and the density of the pressed sam pie and concluded that the simpler Walker equation [28] gave a beUer fit of the densityfpressure data in the low porosity region. An analysis specifically of agglomerates was undertaken by Niklasson and Alderborn [47] who took force and displacement data sampled during in-die compression of agglomerates to calculate compression parameters according to • • •
Heckel ((J Y) Kawakita (1fb and a) Adams (ro').
It was conciuded that 1fb and ro' may be interpreted as a measure of ag glomerate shear strength during uniaxial confined compression, and as such they may be used as indicators of the tableUing performance of the agglomerates. In summary, the best choice of pressure-volume relationship will depend on the experimental procedure and the use of bulk compression methods to infer single-particie properties should be made with caution [48]. All the main methods that have been discussed have advantages and limitations and no one relation ship is able to provide an adequate description for the whole compaction process. 3.4. Work of compaction
The three main deformation mechanisms that can occur to particies within the powder bed are elastic deformation, plastic deformation and fragmentation. Elastic deformation is reversible, Le. the work stored during loading is recovered during unloading. However, a material with time-dependent properties can store
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/ / / WORK OF /
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Fig. 7. Plot of upper punch force vs. upper punch dis placement.
elastic energy and may relax only after a period of time or after ejection from the die. The energy required to cause plastic deformation or fragmentation cannot be recovered, as these are permanent changes to the structure of the particle. In order to quantitatively evaluate the work required for compaction, force displacement measurements have been conducted by various authors [43J. A typical plot of the force exerted by the upper punch against the displacement of the upper punch is shown in Fig. 7. The compaction pracess can be split into two sections. The first section involves increasing the compaction pressure to a set amount: this is shown by the curve between A and B. The area under this curve, shown by E2 + E3 in Fig. 7, represents the total work of compaction. Some of the work required to compact the tablet will be recovered in the second section: represented by the curve between points B and D. Here the set pressure has been reached and decompression occurs. The material usually expands to relax at this stage. The area under this curve (E3) corresponds to the recovered or elastic work. The deduction of the elastic work fram the total work represents the unrecoverable work: this is represented by the area E2 .
3.5. Density distributions
Density distributions are thought to evolve during the compaction stage of pracessing. Early research conducted by Train [22J investigated the pressure response of powder under compaction. Manganin wire resistance gauges were
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K. Pitt and C. Sinka
employed and a complex pressure pattern within the powder bed was obtained. Train concluded that the resulting density distribution could be explained in terms of a varying pressure pattern, which evolved during compaction. The measurement of density distribution by both the coloured layer method [49] have shown that flat-faced compacts formed by uniaxial compaction typically are non-homogenous with high-density regions in the top corners of the compact adjacent to the moving punch and in the middle bottom half [50]. These are consistent with the patterns identified by Train [22]. A more detailed review of density distribution in powder compacts together with experimental characteri sation techniques is given in Section 7. 1 . 3.6. Ejection and ejection profiles
After compaction the compact is unloaded and ejected from the die. It is at this point that the compact can suffer mechanical failure because of the release of stored energy. Including a lubricant in a formulation to reduce friction at the die wall minimises the potential for failure of the compact structure during the ejection process. Various studies have been carried out in the past to observe the ejection behaviour of different materials. A study was carried out on the ejection behaviour of uranium dioxide compacts [51 ] . A schematic ejection profile of the ejection stress as a function of time is shown in Fig. 8. In Fig. 8, point A is known as the static ejection force and corresponds to the maximum point reached corresponding to the initial movement of the compact. After this initial movement of the compact, the force can be seen to decrease to a value that remains nearly constant throughout the ejection process until part of the compact is ejected from the die; this corresponds to point B shown in Fig. 8 A Breaking of die Wall adhesions
Static Ejection Force B Compact moving through the die Dynamic Ejection Force
p
C Compact emerging from the die
Fig. 8. Schematic profile of the ejection pressure as a function of time.
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and is known as the dynamic ejection force. The ejection force then falls gradually to point C, which corresponds to the complete removal of the compact from the die. The values of A, B and C are all dependent upon the compact aspect ratio, the state of the die wali lubrication and the compaction pressure used to form the compacl. While this is a typical profile, other, rather different profile shapes have been reported. Briscoe et 81. [52] studied the effects of aspect ratio, the effects of lubricants and the effects of applied compaction pressure with ceramic powders. The in vestigators showed that when the aspect ratio was increased, so too did the ejection pressure. Using lubricants also significantly reduced the ejection stresses observed and concluded that the higher the pressure the compact was formed at, the greater the force needed to eject the compact from the die. 3.7. The ejection stress
Briscoe and Evans [53] further investigated the effects of friction during the process of ejecting agglomerated alumina compacts from a die. They concluded that the ejection stress, Pe , required to eject a compact out of the die was con trolled by the interfacial shear strength, Te , whose value was governed by the die wall area and the radial stress, (J normal to the die wall. For a constant applied compaction pressure, the ejection pressure can be given by xx
(1 2) where H and 0 are the compact height and diameter respectively, and Te is the mean interface shear stress acting on the surface in contact with the die wall. The interfacial shear was considered to be sensitive to the contact conditions such as the compaction pressure, the ejection velocity, the temperature and the state of die wall lubrication. For pharmaceutical tablets and ceramic compacts the aspect ratio is often less than one. Hence the height of the compact is small compared to the diameter of the specimen and hence radial pressure can be regarded as being constant down the height of the side wall. Also the relatively short-column height means that the opportunity for frictional losses at the die wall is much reduced. Consequently, often the ratio of the upper punch pressure and the lower punch pressure (sometimes referred to as the force transmission ratio) is close to one.
4. COMPACTION EQUIPMENT
In this section, the defining features of powder compression presses and the latest technological developments are reviewed. As summarised in Section 2,
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powder can be compacted under a variety of conditions. Here only cold die compaction equipment is focused on, which can be classified as • • •
single station multi-station (rotary) special presses.
The same powder compact can be manufactured on a number of presses; the equipment is chosen depending on the volume and complexity of the pressed part. 4.1 . Single-station presses
Single-station presses are the equipment of choice for • •
low-volume production rates of simple geometry (i.e. pharmaceutical tablets); complex multi-level parts, such as presented in Section 2.3.
For the production of simple parts the punch movements are given by eccentric mechanisms driven by an electric motor. The cycle consists of die fill, compres sion and ejection, as illustrated in Fig. 9, for a typical press used for pharma ceutical tablet manufacturing. In single-station presses, the powder is fed into the die from a hopper and a feed shoe (Fig. 9). The bottom punch is stationary during filling. The feed shoe is moved above the die opening, executes a number of shakes and is withdrawn. The mechanisms executing shoe motion and die fill are usually mechanically interlinked and the shoe kinematics is dictated by the operating speed of the press. During compaction the top punch is driven by an eccentric while the bot tom punch is maintained stationary. Ejection is carried out by a mechanism that
Die table r punch Lower punch holder Collection end filling
Compression
Fig. 9. Operating cycle of a single-station tablet press.
Ejection
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operates the lower punch via a lifting block. The parameters that are adjusted by the operator are • • •
•
fill volume (tablet weight), which is the lowest position of the lower punch; ejection point (highest position of lower punch); tablet thickness, given by the maximum penetration of the top punch ; press speed.
More modern presses allow independent adjustments of a number of param eters. For example, depending on application, the powder movement in the feed shoe may be facilitated by a feeding mechanism (i.e. helical screws or rotating paddles). The compaction forces necessary for compressing relatively small simple components are of the order of tens of kilo newtons and eccentric presses can produce up to approximately 60 tablets per minute. In order to increase productivity, multi-tip tooling can be used, where a number of compacts are compressed simultaneously. More complex parts such as multi-level structural powder metallurgy compo nents are manufactured on single-station hydraulic presses, where control of punch movement is essential to prevent defects. Hydraulic computer numerical control (CNG) presses can apply hundreds of kilonewtons force on each of the punches. Owing to complex kinematics, the production rates are considerably reduced compared to the eccentric presses and depend on the complexity of the part. 4.2. Rotary press
Rotary presses are used for high-volume production (hundreds of thousands of tablets per hour) of relatively simple powder parts and are used mostly in the pharmaceutical, magnets, food, confectionery and detergent industries. The op erating diagram of a high-speed tablet press is presented in Fig. 1 0. The die and punches are mounted on a rotating turret and pass through the filling station, pre compression and main compression rollers and ejection station in succession. The feeding system, consisting of a mass flow hopper connected to a feed frame, was described in Section 2.2 in more detail. Compaction is carried out in two stages, as the punches travel through the pre compression and main compression stations. Pre-compression is necessary to prevent some of the practical problems described in Section 6, as the compaction step itself can be as short as a few milliseconds. The vertical movement of the punches is guided by cam mechanisms. Ejection is applied using a cam. On a standard rotary press, each toolset produces one tablet per revolution. The productivity of the press depends therefore on the speed of the press, which
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K. PiU and C. Sinka
Direction of Main Compression
j
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Rotation Material Feed
Q
from Hopper
.J
UlJ Pull
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Fig. 1 0. Diagram of high-speed tableUing press.
is limited by the die fill and compression behaviour of the material. Productivity can be increased by increasing the number of stations, which is dependent on the size of the turret and the size of the compact. On large presses it is possible to compress two tablets every revolution, by using double-sided configuration, as presented in Fig. 1 1 (a). For smaller tablets the productivity can be increased further by using multi-tip tooling. 4.3. Special tab let presses
Most rotary presses use die feed systems as described previously. An alternative centrifugal die-filling system [54] has been developed, where the powder is fed into the centre of the die table, which is connected by channels to the dies, the powder flows under the effect of centrifugal forces and enters a specially de signed die through a side opening. The die fill is facilitated by rapid separation of the punches, similar to the suction-feeding mechanism where both punches contribute to the suction effect. Then the powder is transferred to the lower, c10sed section of the die where compression takes place. The tablet is ejected at the lower opening of the die. The system is suitable for large-scale manufacturing as described by Catellani et al. [54]. The double-sided rotary presses have been adapted for the production of bi layer tablets. Here, the tablet is not ejected after the first compression step. I nstead, the die passes through the second feed-frame for filling the second layer
759
Tabletting Hopper I
Precomp I
.-----. Tabl et ej ection 2
Main comp 2 Tablet ej ection I
Precomp 2
(a)
Tablet ejection
Main comp
(b)
Precomp ( - 10-20% ofmain)
Fig. 1 1 . (a) Configuration of a double-sided rotary press and (b) configuration of a bi-Iayer press.
of the material. The fill depth of the second layer is dictated by the punch pen etration when compressing the first layer, although more modern presses allow further flexibility in terms of selecting the process parameters. A schematic di agram of a bi-Iayer press is presented in Fig. 1 1 (b). Tri-Iayer presses have also been developed using the same principles. Multi layer tablets are becoming more popular in the pharmaceutical industry, as they can be used for dosing two incompatible active compounds in one unit, or to releasing the active ingredients at different rates. Similarly, the detergent industry uses bi- and tri-Iayer compacts for dish washer and washing machine tablets. Low-volume bi-Iayer tablets can also be produced on single-station presses by increasing the number of feed shoes accordingly.
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K. PiU and C. Sinka
A special case of multi-Iayer tabletting is the compression coating process, also known as dry coating or powder coating, which involves the use of a bi-Iayer press. The compression rollers of the first layer are replaced by a unit that places a smaller core tablet on the powder bed. More powder is fed as the die set passes under the second feeding station, following which pre-compression, main compression and ejection occur in a standard way. The small core tablet is usually compressed on a separate rotary press running at the same speed as the main press. Commercial products may include up to three completely enclosed tablets. Smaller parts having a flat face can be manufactured on anvil presses, where instead of using an upper punch the parts are compacted against an anvil by the upward motion of the lower punch. The powder feed system, the anvil and a pick up mechanism are part of a single unit. The anvil press is mechanically simple and inexpensive to install/run, however, the compaction forces are relatively small (a few kilonewtons), and the production rate varies from tens to a few hundreds of units per minute. The system is suitable for metal, hard metal and ceramic powder compaction.
4.4. I nstrumentation
As described in the introduction, the formulation of a powder blend as weil as the choice of process parameters during manufacturing are essential for producing quality compacts, which requires controlling the process parameters on one hand and adequate characterisation of the behaviour of the powder during compaction on the other hand.
4.4. 1. Production press instrumentation
Measurement of forces and displacements is critical for the compression of complex parts on multi-axis presses in order to setup the die fill, transfer and compaction sequences. Modern production presses are instrumented with devices to measure the force applied by the punches during pre-compression, main compression and ejection. Weight and hardness are usually measured by devices downstream from the press. 80th types of measurement data can be fed back to the press for auto matic control of weight and compression parameters as a minimum. Tablet machine instrumentation is a subject on its own and textbooks have been published since the late 1 980s [55], which discusses the operating prin ciples of devices measuring force, displacement, temperature, weight, as weil as signal conditioning and data interpretation.
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4. 4. 2. Instrumentation for product and process design
The fundamental understanding of the mechanisms of compaction can assist in the formulation of powders. Experimental characterisation is however necessary because behaviours such as compactibility and compressibility are dependent on the processing conditions. The experimental data are generated using either small-scale production presses with additional instrumentation or specially in strumented presses. The instrumentation of small production presses follows the same general principles as for the larger presses described above. The instrumented presses vary in sophistication from general-purpose material testing machines to high-speed hydraulic systems, such as the compaction sim ulators used in the pharmaceutical industry, which is described in more detail below. A compaction simulator is presented in Fig. 1 2 (a ) . It consists of a le jing frame, die table and two independent servo-hydraulic systems controlled JY a computer, which operate the upper and lower punches as presented in Fig. ', 2 ( b ) . The displacement profiles of the punches can be programmed such that they mimic the compression schedule of any single-station press or rotary press used for tablet manufacturing. It is a distinct advantage that only a small amount of powder is necessary to generate a wealth of information that can be us=: d to optimise tablet formulation and selection of process parameters. Compaction simulator data for a simple compression sequence, wher : the bottom punch is maintained stationary, is presented in Fig. 1 3. The force ar, J!ied by the top punch is increased during compaction and is transmitted to the br,'tom punch and the die wall. Measurement of die wall stress is necessc)r'1 to
Upper valloadve,celactaccumul ul, punch ator,ator, punch andy Lholder, assembl VDT
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Lower valloadve,celactaccumul ul, punch ator, ator, holL der,assembl punch andy VDT
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( b)
Fig. 1 2. Compaction simulator: (a) general view and (b) schematic diagram.
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K. Pitt and C. Sinka
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characterise the behaviour of material during compaction and measure the fric tion coefficient between powder and die wall as described elsewhere [56]. For this purpose, dies have been instrumented with radial stress sensors, a typical output is presented in Fig. 1 3. 5. FINISHED COMPACT CHARACTERISTICS In this section, the various tests which can be performed on the finished com pacts are described. 5.1 . Strength testing The strength of a compact which can be defined simply in terms of the force is required to fracture a specimen across its diameter [57]. More complex shapes can also be crushed by opposed loads. However, the breaking load does not take into account either the dimensions and shape of the compact or the mode of failure. The conversion of a fracture load to tensile strength, wh ich takes these factors into account, allows for ready comparisons to be made between sam pies of different shapes or sizes. In industrial practice, the most commonly applied strength measurement for a compact is the diametral compression test. The procedure involves applying a load to a simple plane-face compact which is subjected to two diametrically opposed point loads. The test was developed independently at the same time by
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Carneiro and Barcellos [58] in Brazil, and by Akazawa [59] in Japan and is referred to as the "Brazilian" or "indirect" tensile test as a tensile fracture is induced by compressive loading. The test is simple and easy to perform and has been widely used to determine the tensile strength of a variety of brittle materials such as concrete [60], coal briquettes [61 ] , Gypsum [62] and lactose tablets [63]. A complete analytical so lution exists for the stress state induced by the loads [64]. The expression for tensile stress (0"1), determination in a flat-face compact is O"I =
2P � nOt
( 1 3)
where P is the applied pressure, 0 the compact diameter and t the compact thickness. This theory has also been developed for the determination of the tensile strength of convex-faced compacts by Pitt et al. [65]. 0"1
= n01 0P2 (2.84 0t - 0.1 26 t
W
W + 3.1 5 0 + 0.01
) -1
( 14)
where W is the central cylinder thickness. The positioning of the load has a big effect on the stress distribution and hence the fracture of the tablets. This is especially a concern when applying this method to brittle materials where the compact cannot deform and correct the misalign ment by plastic flow. The ideal situation involves applying a line load so the stress distribution is uniform through the centre diameter. In reality, this is impossible to achieve and the load will always be applied over an area. If the contact area is smalI, however, the stress distribution will only be affected near the ends of the loaded diameter and hence the equations still hold for the majority of the diam eter. Peltier [66] calculated that the tensile stress can be held uniform across the majority of the load diameter provided that the width of this contact area does not exceed one-tenth of the length of the diameter. A more detailed analysis of the diametrical compression tests, where the effects of contact flattening and plastic material behaviour were considered, was presented by Procopio et al. [67]. It was shown that the stress field in a plastically deforming material results in significant changes of the magnitudes and location of maximum principal stresses and a validity map of the Hertzian solution was proposed. The Brazilian method can only be applied to sampies which fail due to tensile stress. If the elastic moduli of the sampie and loading platens are too great then the tensile stress will not be constant over the loaded diameter and the maximum shear and compressive stresses will reach very high values. For some brittle materials, padding is required between the sampie and the load to assure adequate load distribution [63] and promote failure in tension [68]. The different failure modes were detailed by Mitchell [69] as presented in Fig. 1 4.
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K. Pitt and C. Sinka
Simple tensile Failure
"TripIe eleft" Tensile failure
Compressive Failure
Fig. 1 4. Failure modes i n diametral compression test.
If the loading is satisfactory then the specimen will fail diametrically in tension to give simple tensile failure. Another fracture mode, the tri pie cleft, was also identified [68] to be failure in tension. High compressive stresses around the loaded part will result in non-tensile failure due to shattering and cracking in the loading region. Hence the validity of the diametral compression test under a given set of con ditions to determine a tensile strength from a fracture load can be easily assessed by examining the specimen fragments after failure [62]. Strain rate sensitivity while conducting the tensile test should also be con sidered. Increasing the load rate of concrete cylinders has been reported [69] to result in higher observed tensile strengths. Rees et al. [70] recorded similar ob servation for lactose tablets and concluded that discrepancies in tensile strength values determined using different testing instruments may be partially attributed to differences in the loading rate of these machines. If the compact is elongated then flexural or beam testing can be applied. However, the stress distribution in the specimen is non-uniform, varying from zero at the neutral axis to a maximum at the outer edge surface. Canti lever methods for strength testing have been developed for beam or elongated specimens. The compact in the form of a parallel beam of rectangular section is subjected to three- or four-point bending. The modulus of rupture is calculated from the load at fracture [71]. The major drawback with the method of three-point bending is that there may be a large contribution from shear stresses at the failure force [72] and as such application of this method to several geometries is inappropriate. In addition, beam testing accentuates the effects of surface conditions on the measured strength and the test can give results considerably different from the true tensile strength [61 ] . The formulae are summarised in Stanley [72]. Stanley and Newton [73] have also published approximate relationships for three-point bending derived for capsule-shaped tablets using basic trigonometry. Their approximation of the tensile stress is given by 2a ] 2d [d+ 6A + bd
3 WI
(Jt � 2.
(1 5)
Tabletting
765
where W is the fracture load, 1 the distance between supports, A the area of curved segment, a the height of curved segment, b the capsule width and d the wall height. Four-point bending is generally considered the slightly superior test as it pro duces a region of constant bending moment between two inner loading points [72]. However, owing to the relatively small size of pharmaceutical compacts three-point bending is the more common choice. The size of the compact though can be quite smalI. Hancock et al. [74,75], investigated the use of three-point bending for the characterisation of very small powder compacts of approximately 20 mg. Elastic properties such as Young's modulus or Poisson's ratio of a material can be estimated from the linear regions of stress-strain curves. It has been shown, however, that the Young's modulus has no correlation with the fracture strength of materials [76], though obviously a high-fracture strength within one material would be an ideal situation. The testing methods for determining the strength and elastic properties of material are weil developed and form international standards. These behaviours are discussed in detail in materials engineering textbooks [77,78]. 5.2. F racture mechanics
The main fracture problems that affect compacts are cracking and lamination which are thought to be due to a combination of elastic strain release and die wall friction. Cracking can be induced at any stage of compaction of complex parts. For simpler geometries, cracking occurs particularly during decompression and during ejection. Early investigation concluded that compacts can fracture due to inhomogeneous density distribution creating weaker areas which can come apart [22]. Stored energy and bond strength play a major role in initiating cracking. Van der Voort Maarschalk et al. [79] showed that the amount of stored energy is the driving force for stress relaxation and hence cracking. If a material with a large amount of stored energy is coupled with low-bonding strength and low die wall friction the compact will readily expand resulting in a weak and porous structure. High-bonding strength and high die wall friction will prevent elastic relaxation and therefore the energy may be released by cracking of the compact. Research by Takeuchi et al. [80] concluded that the residual die wall force was related to the elastic and plastic properties of the material and the profile of die wall pressure for the materials they investigated was c10sely related to cracking and sticking prob lems during ejection. It has been shown with alumina compacts that the use of lubricants during the compaction process can improve the density distribution within the compacts by mducing the die wall friction [27,81 ] and can therefore help prevent fractures.
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Fractures occur by crack initiation and propagation. A crack will form when the applied stress reaches a critical value at a flaw for a given position and orien tation. Therefore, the statistical distribution of size and shape of flaws can lead to the calculation of the critical stress to cause a fracture. The original fracture mechanism postulated by Griffith [82] involved an energy balance analysis. In order for a fracture to occur, energy must be provided to create two new surfaces: if the stored elastic strain released by crack propagation exceeds the free-surface energy required to create the surfaces the material will fracture. It is assumed that the crack initiates from a defect in the material which acts as a stress concentrator. This phenomenon continues to concentrate the internal stresses and as such the crack grows. The Griffith equation is applied to brittle fractures, Le. one that occurs with little or no plastic deformation of the material. n(J2 a G 2y (16) E where G the energy release rate, (J the applied stress, a the half crack length, E Young's modulus and y the free-surface energy. When a ductile material fractures, plastic deformation will occur. This type of fracture usually corresponds to a higher tensile strength. An extension to this is the critical stress intensity factor, K,c. This value provides information about the stress distribution around the crack tip. The ratio of the maximum stress at the crack tip, (Jm , and the applied tensile stress, (Jo , is shown in the following equation: =
=
(1 7) where a is the crack length and rc the radius of crack tip. K,c is commonly used as an indication of the amount of stress required to propagate a crack, it is also an indication of the resistance of a material to cracking. Methods to determine K,c involve imposing a notch or crack into the sampie to induce a fracture in a specific position of the compact: methods include three- or four-point bending, double torsion and Vickers indentation [83]. 6. COMPACT PROBLEMS AND SOLUTIONS
In the following sections, a number of common compaction problems are iden tified and potential solutions discussed from an industrial point of view. 6. 1 . C racking
A major problem which can occur during or after compact manufacture is crack ing. This can manifest itself in a number of ways dependent upon the material
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properties of the feed material. It can range from surface cracking in metals through to "capping" in pharmaceutical tablets where the upper part of the tablet horizontally separates from the body during ejection (Fig. 1 5). Lamination can also occur which is where cracks form within the body of the compact resulting in the compact splitting apart into layers. The same factors may contribute to this problem. An example of a laminar crack through a microcrys talline cellulose tablet magnified using a scanning electron microscope (SEM) is shown in Fig. 1 6. Cracking can be caused by a number of factors. The principal material property leading to cracking is the viscoplastic-elastic behaviour of the powder materials comprising the compact. The elastic response during decompression is a major factor as non-dissipated stored elastic strain release is the source of the internal and disruptive forces. For complex shapes such as particularly compressed metals parts the effects of this strain release can be moderated by careful design and consideration of the powder flow and pressing sequence of the different regions of the component.
Fig. 15. Example of a pharmaceutical tablet that has "capped".
Fig. 1 6. SEM image showing a laminar crack developing through the centre of a tablet.
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K. PiU and C. Sinka
In addition the response is offen time dependent. As speed is increased, the relative elastic component of a given material also increases, giving rise to a higher incidence of cracking. Hence as compression speeds are further in creased, the occurrence of cracking and lamination of compacts tend to become more prevalent. Other than reducing compaction speed, a processing way of overcoming this and effectively increasing the relaxation time is to use pre-com pression prior to the main compression. Typically the pre-compression is at 1 0% of the main compression [84]. However, this is very much formulation dependent. Akande et al. [85] finding that optimal tensile strength was found by having a pre compression larger than the main one. Increasing speed will also reduce the time available for the air trapped between the granules to escape. Thereby leading to the potential for increased air pressure in the die to cause cracking and lamination particularly for high-porosity beds. Sticking of the compact to the die wall or punch components can also induce stresses resulting in failure. There are consequently a number of formulation and processing approach es, which can be used to address the causes of cracking and lamination. 6. 1. 1. Excessive elastic recovery
Elastic recovery itself will not necessarily result in lamination. Lamination will only occur if the interparticle bonding cannot accommodate this elastic recovery. Hence the formulation options are to either increase the binder level, or the type of binder in the granule. An alternative approach is to incorporate polymeric materials such as celluloses undergoing less-elastic recovery. For organic ma terial the moisture content can also be important as the level of residual moisture i n a polymer can affect its deformation properties. 6. 1 . 2. Air entrapment
The initial volume of granules may be several times that of the compact into which they are compressed particularly for low-apparent density materials such as de tergents, food and pharmaceuticals. During compression both particles and air will be compressed. The reduction in volume is due to removal of air. This air will need to escape from the compact otherwise there is the potential for this en trapped air pressure to blow apart the compact on ejection. Air removal can be facilitated by using dies that are tapered outwards towards the top of the die to allow the air to escape. Similarly, using punches with greater tolerances around the punch and die contact region will enable the air to escape [86]. Tapered dies also have the additional advantage of increasing the volume available for the tablet to expand radially into hence reducing residual die wall pressure. Pre compression is also a very important tool to reduce the effects of air entrapment.
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6. 1 . 3. Tool wear
Wear in the dies takes place usually about the point of compression, i .e. in the bore resulting in a circular depression within the die, which is usually referred to as banding in the context of high volume rotary presses. A compact compressed in this cavity has therefore to be forced out through the smaller aperture in the top of the die resulting in shear and lamination. Wear occurs an all tool surfaces in contact with the powder where sliding takes place and is accelerated when powder particles from hard materials, such as cera mies, are compressed. For a given material and compaction force, wear can be reduced by minimising friction using lubricant (see below) or coating the tool ing with wear-resistant materials. Tool wear occurs due to the contact interactions between various mechanical parts of the press, such as, for example, the contact between the compression roller and punch head on rotary presses, however, is present for all types of presses. Industries where product contamination is an issue require special measures for lubricating the mechanical parts.
6. 1.4. Lubrication
Lubricants will mini mise die wall friction and prevent the adhesion of the granules to the punch faces and hence can be manipulated to overcome cracking and lamination. Lubricants can be classified according to the way in which they are added to the granules. Internal lubricants are mixed with the dry powders prior to granulation, i.e. polyethylene glycol external lubricants are incorporated imme diately before compression by mixing in with the formed granules (e.g. stearates). An alternative approach is to spray in the lubricant into the punch and die cavity immediately before die filling and hence directly coating the surfaces of the tooling.
6.2. Picking
In some instances, a small amount of the compact material may stick to the tooling surfaces. As compacts are repeatedly made in this station of tooling, the problem gets worse as more and more material gets added to that already stuck to the punch face. The problem tends to be more prevalent on upper punches. The root cause is usually insufficient lubrication, although surface roughness of the tooling can also play a part. Sticking is more often observed for compacts with fine embossing, such as pharmaceutical tablets, where the design of such subtle geometrie details becomes important.
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6.3. Pitted or fissured surface
The most Iikely cause of a fissured surface, if it is not due to picking or sticking, is the presence of granules which are uniform in size and lack the sm aller particles to fill the voids. Generally, the problem can be resolved by broadening the particle size distribution of the granules provided that this does not lead to other problems such as cracking or segregation. High-speed compaction using tooling with deep curvatures, such as in pharmaceutical tablets, contributes to air entrapment at the top punch cavity, which is also thought to cause surface cracking. 6.4. C hi pping
Sometimes compacts after leaving the press, or during subsequent handling and coating operations, are found to have sm all chips missing from their edges. This fault is described as "chipping" and, in addition to the obvious formulation de ficiencies, may be caused by compaction conditions that make too soft or too brittle tablets. Incorrect machine settings, especially the ejection take-off plate and excessively harsh handling of compacts after they leave the press, may be the additional factors. Friability testing is employed as an indicator of an inherent tendency for a given batch of product to chip. In friability testing, the compacts are usually rotated in a defined drum at a set speed for a controlled number of revolutions. The amount of weight loss due from the compacts after the test is recorded as a percentage of their initial weight. The defects described above can be reduced by controlling the tablet micro structure. For example, by eliminating low-density regions where the local strength of the material is reduced. An understanding and control of microstruc ture evolution can be achieved using process modeling tools as described in Section 7.3. 6.5. Binding in the die
This is characterised by excessive side scraping of the die with the compact ejection forces being high with the resulting compact edges being rough and scored. The root cause results from high die wall friction. This in turn could be caused by poor lubrication or blemished and worn die or tooling. An alternative cause is too large a c1earance between the lower punch and die bore resulting in trapping of powder, which is compacted to form a hard film which hinders free movement of the lower punch. Binding is more frequent for materials with low-melting points or when tem perature sensitive lubricants are used. The plastic work during compaction is dissipated as heat, contributing to increasing compact temperature during the
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process. Selecting process parameters such as speed or using engineering methods such as cooling systems to reduce the temperature of the compaction equipment have been employed to reduce binding. 6.6. Low tensile strength
Structural engineering parts are pressed to near full density to maxi mise strength and control the microstructure better through post-compaction operations. Non structural compacts are designed for a variety of other requirements, for example a pharmaceutical tablet may be required to disintegrate as described in Section 6.8. In general, the higher the compaction pressure the denser the compact will be and hence the higher the resulting tensile strength of the compact. Conse quently, too low a compaction pressure will lead to low tensile strength or "soft" and crumbly compacts. Alternative reasons are excessive coverage of the gran ulation by a lubricant, such as a stearate, reducing the potential to form strong interparticle bonds. This can be caused by • • •
too high an initial level of the lubricant; excessive shear during the lubrication stage; excessive lubrication time.
An additional cause can be the weakening of the intergranular bonds by air entrapment, which is not sufficient though to cause capping. 6.7. Uneven weight control
Poor weight uniformity is usually due to poor die filling. This can be due to either poor flow characteristics of the granule or due to inadequate filling mechanisms on the compression machine. If it is due to poor granule flow then the addition of glidants such as silica or talc can be employed. A number of mechanisms have been proposed to account for glidant action. The flow properties of smooth, nearly spherical particles will be better than those of an irregular shape. Hence one mechanism proposed is that glidants fill the surface depressions and thereby reduce surface roughness. If the coefficient of friction of the glidant is less than that of the granules then the interparticle friction may be lowered. Alternatively the glidant may physically separate the solid particles so that the intermolecular at tractive forces such as van der Waals forces, or the capillary adhesion forces are reduced. So me particles may acquire a frictional electrostatic charge when handled and this mutual repulsion of the particles may be sufficient to impede die filling. Tale or
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sodium lauryl sulphate are approach es which have been used to reduce this charging [87]. Lubricants may or may not promote granule flow. 6.8. Mottled appearance
This is typicaily seen with coloured granules. This can be due to dye migration to either the smail or large granules during the granulation process. Alternatively, it can be an optical phenomenon due to the smailer particles providing a back ground of a slightly different hue whieh shows up the larger granules on the compaet surface. 6.9. Disintegration and d issolution
These are particularly applicable to pharmaceutical tablets although the concepts also apply to detergent tablets and food products. Disintegration is the time taken for the tablet to break apart into its primary particles in a fluid, normaily aqueous. Dissolution is a measure of the release of the active ingredient from the compact into solution. Disintegration and dissolution are dependent on a number of factors. 6. 9. 1. Porosity
Water can generaily only gain access to the inside of a compact via pores. Hence if the compact is compressed at high pressure then its porosity is likely to be too low to ailow water ingression. 6. 9. 2. Hydrophobicity of powder
Water will not readily penetrate hydrophobie powders. A potential issue therefore is the use of hydrophobic lubrieants sueh as the stearates, which in high con centrations can prevent penetration of water and ean decrease dissolution and disintegration. Addition of a wetting agent in the granule formulation ean assist in the penetration of water into the compact. 6. 9. 3. Presence of disintegrant
Disintegrants such as starches and modified ceiluloses may be included in a com paet formulation to assist disintegration. They ean act by two meehanisms. One is to act as a water- soluble path for the water to penetrate into the compaet. The other is by swelling up and applying pressure, which breaks apart the compact.
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7. NEW TECHNOLOG I ES
In this section, the latest developments in understanding powder compaction process and technology are reviewed. 7. 1 . The structure of powder compacts
Powder compacts are inherently non-homogeneous and anisotropie and present density variations, which are induced in powder compacts during die fill and compaction. Density variations affect the local properties of the compact, which in turn influence the behaviour after compaction, i .e. elastic rebound, ejection and post-compaction operations such as handling, packaging, coating, sintering, etc. The importance of density distributions in powder compacts has been recognised since the early 1 900s. Train [22] has described characterisation techniques based on differential machining, hardness tests or X-ray shadow of lead grids placed in the compaci. A less invasive technique for ceramic compacts present ing natural radioactivity was developed by Macleod and Marshall [51 ]. who related the density distribution patterns to die wall friction. More modern non-destructive techniques, such as X-ray CT, acoustic wave velocity measure ments and nuclear magnetic resonance (NMR) imaging, were summarised by Lannutti [88]. These techniques have been applied to a range of powder materials. Figure 1 7 illustrates the density variation after die fill [14] and in a pharmaceutical tablet [1 7]. The density gradients are induced during complex powder movements during powder fill and the pressing sequence and are affected by the interactions be tween the powder and tool surfaces. In most severe cases fractures occur. The tools and techniques described in the following sections can also assist in con trolling of the microstructure through fundamental understanding of material and process parameters.
Fig. 1 7. X-ray CT density variations in powder compacts: (a) after die fill with metal powder and (b) pharmaceutical tablet.
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7.2. Triaxial testing
The compression of a powder compact in a die involves uniaxial deformation, i.e. the movement of the powder in the plane normal to the compression direction is restricted. However, even for the simplest case (i.e. cylindrical compact with flat faces) the friction interaction between powder and tooling changes the strain path experienced by a small volume of material and the effects have been illustrated by Train in 1 957. In order to characterise the compaction behaviour of powder under the full range of loading conditions that occurs in practical situations, triaxial testing can be employed. Triaxial testing originates from the field of rock and soil mechanics as described in textbooks in the field [89] and has been adapted to examine the compaction behaviour of powders since the 1 970s [90]. A triaxial test specimen is presented in Fig. 1 8. The powder is placed in a rubber sleeve between two rigid platens. The specimen is introduced in a Hoek-type triaxial cell [89], where it is subjected to cell pressure and a superimposed axial load. The deformation of the specimen is measured in radial and axial direction using extensometry or other methods. Modern servo-hydraulic systems and computer control technology [91 ] allow investigating the high-pressure compaction response of powders along a variety of loading paths in stress or strain space and results for metals, hard metals and ceramics were presented in the literature [92]. Triaxial compression data are used for the development and calibration of constitutive models for powder com paction (as described in the following section) and probing of yield surfaces [93] of powder compacts in order to generate detailed information on the strength behaviour of powders.
I
Top platen Rubber jacket Radial displacement measurement canti lever device Powder specimen
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Fig. 1 8. Schematic representation of: (a) triaxial test specimen with a radial extensometer and (b) loading in radial and axial direction of a cylindrical powder aggregate in a triaxial Gell.
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7.3. Compaction modeling
Similar to modeling any other process, compaction modeling offers insight into the complex physical phenomena occurring during compaction, and allows sensitivity ranking of the contributing factors. The potential of numerical simulation has been recognised since the 1 980s [94]; however, systematic application to industrial problems became possible only in the 1 990s with the development of advanced computing technology. Initial compaction models have been developed for the powder metallurgy [95] and ceramic pressing applications and today the approach is being implemented by the magnets, hard metals and pharmaceutical industries. Constitutive models (such as the Cam-Clay [96] or Drucker-Prager cap [97] models) have been adapted from the rock and soil mechanics literature and cal ibrated using triaxial test data as described by Trasorras [95]. These constitutive models are based on continuum mechanics principles and describe the evolution of the material in terms of density or relative density. However, models using work quantities as state variables have been proposed recently [98]. Continuum models have been extended to low relative densities (Le. 0.3) [56]; however, detailed experimental data to ca Ii brate the yield surface and flow po tential evolution in regimes corresponding to partieIe rearrangement and early stage compaction are not available. To bridge the gap, discrete element ap proaches [99] or multi-partiele finite element models where each individual par tiele is made discrete, have been developed [1 00, 1 01 ] which allows the development of constitutive models from first principles across the compaction regimes and length scales. Compaction models are used in industry to optimise the formulation of the powders, the set-up of punch motion sequences, the tool design and to control the properties of the final products [95,1 02] and the dimensional tolerances after compression and sintering [1 03, 1 04].
7.4. Quality control and compaction PAT
Monitoring and controlling of the process parameters at every stage is an im portant way to ensure final product quality. The quality requirements are industry and application specific. The pharmaceutical industry employs batch processes and quality is ensured by inspection. Recently, however, companies and industry regulators have initiated the process analytical technology (PAT) programme whereby critical quality performance attributes are monitored at every stage of the process. If the processes are understood from first principles, then robust processes can be designed and implemented. For pharmaceutical processes where a distinct endpoint can be reached (such as dispensing, granulation, dry ing, milling, blending), PAT initiatives have been developed, which involve
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matching the "signature" of the process using spectroscopy techniques or acoustic wave emissions. In terms of pharmaceutical tablet compaction, product quality is essentially en sured by inspection and systems have been developed to perform quality measure checks on-line. The measurement data are used as feed-back signal to adjust the operating parameters on presses such as adjustment of fill depth (weight) or compression force, to achieve the desired properties (size, strength, friability, dis integration, etc.). To check content uniformity, techniques such as near infrared spectroscopy or light fluorescence-based monitoring systems have been devel oped for on-line (to all tablets) or off-li ne applications (for selected units). Near Infra-Red (NIR) can also be used as non-destructive strength testing tool [1 05]. REFERENCES [1] F. Skaupy, Principles of Powder Metallurgy, Philosophical Library, New York, 1 944. [2] R M . German, Powder Metallurgy Science, 2nd edition, Metal Powder Industries Federation, Princeton New Jersey, 1 994. [3] W. D . Kingery, HK Bowen, D . K. Uhlmann, I ntroduction to Ceramics, 2nd edition, Wiley, New York, 1 976. [4] G .Alderborn, C.Nystrom (Eds.), Pharmaceutical Powder Compaction Technology, Marcel Dekker, New York, 1 996. [5] G . 1 . Tardos, S. McNamara, I. Talu, Powder Technol . 1 31 (2003) 23. [6] S.B. Savage, Adv. Appl. Mech. 24 ( 1 984) 289. [7] S.A. Howard, J .W. Lai , Encyclopedia of Pharmaceutical Technology Volume 6, J. Swarbrick, J . C. Boylan (Eds.), Marcel Dekker, New York, 1 992, p. 141 (ISBN 08247-2805-X). [8] J.C. Jaeger, N .G .W. Cook, Fundamentals of Rock Mechanics, 3rd edition, Chapman & Hall, London, 1 979. [9] AW. Jenike, Storage and Flow of Solids. Bulletin 1 23, Engineering and Experiment Station, U niversity of Utah, USA, 1 964. [1 0] I .A.S.Z. Peschi , Powder Handling Process. 1 ( 1 989) 1 35. [1 1 ] RL. Carr, Chem . Eng. 72 ( 1 965) 1 63. [ 1 2] D. Guyoncourt, J . Tweed, Measurements for powder flow. Proc. Valencia Euro PM, Valencia, Spain, 2003. [ 1 3] Y.S.L. Lee, R Poynter, F. Podczeck, J . M . Newton, AAPS Pharm. Sci . Tech. 1 (2000) 2 1 . [ 1 4] S . F. Burch, J . H . Tweed, AC.F. Cocks, I .C. Sinka, C.Y. Wu , Proc. P M , Vienna, Austria, 2004. [ 1 5] C.Y. Wu, L. Dihoru, AC.F. Cocks, Powder Technol. 1 34 (2003) 24. [ 1 6] L.C.R Schneider, A.C.F. Cocks, A. Apostolopoulos, Powder Metall . 48 (2005) 77. [ 1 7] I .C . Sinka, L.C.R Schneider, AC.F. Cocks, I nt. J. Pharm. 280 (2004) 27. [ 1 8] L.C.R Schneider, I.C. Sinka, AC.F. Cocks, Powder Techno!. in press. [ 1 9] D.T. Gethin, D. Korachkin, J . H . Tweed, D . M . M . Guyoncourt, Proc. PM Vienna, Austria, 2004. [20] W. Brockendon, Patent number 9977. For the shaping of pills, lozenges and black lead by pressure in a die, 1 843. [21 ] The Passing of the Tablet Fad, Pharmaceutical Journal Editorial. February 1 2 , 1 895. [22] D . Train, Trans. I nst. Chem. Eng. 35 ( 1 957) 258. [23] J . M . Newton, D.J.w. Grant, Powder Technol. 9 ( 1 974) 295. [24] E . N . Hiestand, J.E. Wells, C.B. Peot, J.F. Ochs, J. Pharm. Sci . 66 ( 1 977) 5 1 0.
Tabletting [25] [26] [27] [28] [29] [30] [31 ] [32] [33] [34] [35] [36] [37] [38] [39] [40] [4 1 ] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51 ] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61 ] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71 ] [72] [73]
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RJ. Roberts, RC. Rowe, Int. J. Pharm. 36 ( 1 987) 205. S.J. Lukasiewicz, J.S. Reed, Am. Ceram. Soc. Bull. 57 ( 1 978) 798. B.J. Briscoe, S.L. Rough, Coll. Surf. 1 37 ( 1 998) 1 03. E.E. Walker, Trans. Faraday Soc. 19 ( 1 923) 73. JAR Cooper, L.E. Eaton, J . Am. Ceram. Soc. 45 ( 1 962) 97. K. Kawakita, Y. Tsutsumi, Bull. Chem. Soc. Jpn. 39 ( 1 966) 1 364. RW. Heckei, Trans. Metall. Soc. AlME 221 ( 1 96 1 ) 671 . RW. Heckei, Trans. Metall . Soc. AlME 221 ( 1 96 1 ) 1 00 1 . P. York, J . Pharm. Pharmacol. 2 5 ( 1 973) 1 P. T.RR Kurup, N . Pilpel, Powder Technol. 1 9 ( 1 978) 1 47. K. Kawakita, K.H. Ludde, Powder Technol. 4 ( 1 970/1 971 ) 6 1 . M . Yamashiro, Y . Yuasa, K . Kawakita, Powder Technol. 34 ( 1 983) 225. M. Sheikh-Salem, J.T. Fell, J. Pharm. Pharmacol. 33 ( 1 98 1 ) 491 . M.J. Adams, R McKeown, Powder Technol. 88 ( 1 996) 1 55. J A Hersey, J.E. Rees, Nature 230 ( 1 97 1 ) 96. P.J. Rue, J.E. Rees, J. Pharm. Pharmcol. 30 ( 1 978) 642. P. York, J . Pharm. Pharmacol. 31 ( 1 979) 244. F.X. Muller, L.L. Augsburger, J. Pharm. Pharmacol. 46 ( 1 994) 468. G. Ragnarsson, J. Sjögren, J. Pharm. Pharmacol. 37 ( 1 985) 1 45. P.J. Denny, Powder Technol. 1 27 (2002) 1 62. A Hassanpour, M . Ghadiri, Powder Technol. 1 41 (2002) 251 . J . M . Sonnergaard, Int. J. Pharm. 1 93 ( 1 999) 63. F. Niklasson, G. Alderborn, Pharm. Res. 17 (2000) 949. A Samimi, A Hassanpour, M. Ghadiri , Chem. Eng. Sci. 60 (2005) 3993. B. Eiliazadeh, B.J. Briscoe, K.G. Pitt, Y. Sheng , Part. Syst. Technol. 21 (2003) 303. B. Eiliazadeh, K.G. Pitt, B. Briscoe, Int. J. So lids Struct. 41 (2004) 5967. H . M . Macleod, K. MarshalI, Powder Technol. 16 ( 1 977) 1 07. B.J. Briscoe, N. ÖZkan, I. Aydin, Proc. Eighth Cimtech World Ceramics Congress, Florence, Italy, 1 994, p. 1 667. B.J. Briscoe, PD. Evans, Powder Technol. 65 ( 1 99 1 ) 7. P.L. Catellani, P. Santi, E . Gasperini, S. Ciceri , G. Dondi, P. Colombo, Int. J . Pharm. 88 ( 1 992) 285. P.R Watt, Tablet Machine Instrumentation in Pharmaceutics: Principles and Practice, Ellis Horwood Limited, Chichester, UK, 1 988. I . C . Sinka, J .C . Cunningham , A Zavaliangos, Powder Technol. 1 33 (2003) 33. J . E . Rees, E. Shotton, J . Pharm. Pharmacol. 22 ( 1 970) 1 7S. F.F.L. Carneiro, A Barcellos, R I .L.E.M. Bull. 18 ( 1 953) 99. T. Akazawa, R I .L.E.M. Bull. 16 ( 1 953) 1 1 . P.J.F. Wright, Mag. Concrete Res. 7 ( 1 955) 87. R Berenbaum, I. Brodie, Br. J. Appl. Phys. 1 0 ( 1 959) 281 . E . Addinall, P . Hackett, Civil Eng. Publ . Works Rev. 59 ( 1 964) 1 250. J .T. Fell, J . M . Newton, J . Pharm. Sci. 59 ( 1 970) 688. S. Timoshenko, J . N . Goodier, Theory of Elasticity, 2nd edition, McGraw-HiII, New York, 1 970. K.G. Pitt, J . M . Newton, R Richardson, P. Stanley, J. Pharm. Pharmacol. 41 ( 1 989) 289. R Peltier, R I .L.E.M. Bull . 1 9 ( 1 954) 33. A Procopio, A Zavaliangos, J . C. Cunningham, J. Mater. Sci. 38 (2003) 3629. A. Rudnick, AR Hunter, F.C. Holden, Mater. Res. Stand. 1 ( 1 963) 283. N . B . MitcheII, Mater. Res. Stand. 1 ( 1 96 1 ) 780s. J . E . Rees, JA Hersey, E.T. Cole, J. Pharm. Pharmacol. 22 ( 1 970) 64S. J . P . Den Hartog, Advanced Strength of Materials, MaGraw-Hill, New York, 1 952. P. Stanley, Int. J. Pharm . 227 (2001 ) 27. P. Stanley, J . M . Newton, J. Pharm. Pharmacol. 32 ( 1 980) 852.
778 [74] [75] [76] [77] [78] [79] [80] [81 ] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91 ] [92] [93] [94] [95] [96] [97] [98] [99] [ 1 00] [101] [1 02] [1 03] [1 04] [1 05]
K. Pitt and C. Sinka B.C. Hancock, S.O. Clas, K. Christensen, Int. J. Pharm. 209 (2000) 27. B.C. Hancock, S.o. Clas, K. Christensen, I nt. J. Pharm. 228 (2001 ) 1 39. M.S. Church, J .w. Kennerley, J . Pharm. Pharmacol. 35 ( 1 983) 43P. M . F. Ashby, D.R.H. Jones, Engineering Materials 1 : An I ntroduction to Properties, Applications and Design, 3rd edition, Elsevier Butterworth-Heinemann, Amsterdam, Boston, 2005. M.F. Ashby, D.R.H. Jones, Engineering Materials 2: An I ntroduction to Properties, Applications and Design, 3rd edition, Elsevier Butterworth-Heinemann, Amsterdam, Boston, 2005. K. Van der Voort Maarschalk, K. Zuurman, H. Vromans, G . K. Bolhuis, C.F. Lerk, Int. J . Pharm. 1 51 ( 1 997) 27. H. Takeuchi, S. Nagira, H. Yamamoto, Y. Kawashima, I nt. J . Pharm. 274 (2004) 131. B.J. Briscoe, S.L. Rough, Powder Technol. 9 9 ( 1 998) 228. AA. Griffith, Trans. R. Soc. A 221 ( 1 920) 1 63. R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 4th edition, Wiley, New York, 1 996. F.C. Masilungan, K.F. Kraas, Drug Dev. Ind. Pharm. 1 5 ( 1 989) 1 771 . O.F. Akande, M . H . Rubinstein, P.H. Rowe, J . L. Ford, I nt. J. Pharm. 1 57 ( 1 997) 1 27. S.C. Mann, D . B. Bowen, B.M. Hunter, R.J. Roberts, R.C. Rowe, R.H.T. Tracey, J . Pharm. Pharmacol. 33 ( 1 98 1 ) 25P. R. Chopra, F. Podczek, J . M . Newton, G . Alderboran, Eur. J. Pharm. Biopharm. 53 (2002) 327. J.J. Lannutti, M RS Bull. 22 ( 1 997) 38. D . M . Wood, Soil Behaviour and Critical State Soil Mechanics, Cambridge University Press, Cambridge, 1 990. R.M. Koerner, Ceramic Bull. 52 ( 1 973) 566. I .C . Sinka, AC.F. Cocks, C.J. Morrison, A. Lightfoot, Powder Metall . 43 (2000) 253. I .C. Sinka, AC.F. Cocks, J . H . Tweed, J. Eng. Mater. Technol. 1 23 (200 1 ) 1 76. L. Schneider, A.C.F. Cocks, Powder Metall. 45 (2002) 237. I . M . AI-Khattat, S.T. AI-Hassani, Chem. Eng. Sci. 42 ( 1 987) 702. J . R.L. Trasorras, R. Parameswaran, A.C.F. Cocks, ASM Handbook, Powder Metal Technologies and Applications, ASM I nternational, Vol. 7 1 998, p., 326 A.N. Schofield, C.P. Wroth, Critical State Soil Mechanics, McGraw-HiII, London, 1 968. D.C. Drucker, W. Prager, Q. Appl. Math. 10 ( 1 952) 1 57. A.C.F. Cocks, I .C. Sinka , Mech. Mater. in press. P. Redanz, NA Fleck, Acta Mater 49 (200 1 ) 4325. R.S. Ransing, R.W. Lewis, D.T. Gethin, Philos. Trans. R. Soc. Lond. A- Math. Phys. Eng. Sci. 362 (2004) 1 867. A Procopio, A. Zavaliangos, J . Mech. Phys. Solids 53 (2005) 1 523. K.G. Ewsuk (Ed.), Compaction science and technology, M RS Bull. 22 ( 1 997) 1 4 M . Reiterer, T . Kraft, U . Janosovits, H . Riedei , Ceram. I nt. i n Press T. Kraft, H. Riedle, O. Rosenfelder, I nt. J. Powder Metall. 39 (2003) 27. J . o . Kirsch, J . K. Drenne, J. Pharm. Biomed. Anal. 1 9 ( 1 999) 362.
CHAPTER 1 7 D i rect Pel letizat i o n of P ha rmace utical Pel lets i n F l u i d- Bed P rocesses Peter Kleinebudde * and Klaus Knop
Institute of Pharmaceutics and Biopharmaceutics, Heinrich-Heine-University Duesseldorf, Universitaetsstr. 1, 40225 Duesseldorf, Germany Contents
1. 2. 3. 4. 5. 6.
Fluid-bed equipment Granulation vs. pelletization Direct pelletization vs. layering of seeds Mechanisms of agglomeration/pelletization Response variables Wet pelletization 6. 1 . Process description 6.2. Pelletization aids 6.3. Equipment variables 6.3. 1 . Type of equipment 6.3.2. Diameter of rotor plate 6.3.3. Number, diameter and distance of spray nozzles 6.3.4. Surface of the rotor plate 6.3.5. PTFE lining, baffles and choppers 6.4. Process variables 6.4. 1 . Load 6.4.2. Spray rate 6.4.3. Rotor speed 6.4.4. Wet-massing time 6.4.5. Inlet air temperature 6.4.6. Air flow rate 6.4.7. Atomizing air pressure 6.4.8. Gap width/pressure difference 6.5. Formulation variables 6.5. 1 . Fraction of drug 6.5.2. Particle size and size distribution 6.5.3. Type and amount of binder 6.5.4. Solubility 6.5.5. Moisture content 6.6. Reproducibility
*Corresponding author. E-mail: [email protected]
Granulation Edited by A.D. Sa/man, MJ. Houns/ow and J. P. K. Seville " 2007 Elsevier SV All rights reserved
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7. Melt pelletization 7. 1 . Process description 7.2. Advantages of the process 7.3. Meltable binders 7.4. Mechanisms of pellet formation 7.5. Variables with influence on the process of melt agglomeration 7.5. 1 . Equipment variables 7.5.2. Process variables 7.5.3. Formulation variables 7.6. Process monitoring and control References
801 802 802 803 804 806 806 807 808 809 810
1 . FLUID-BED EQUIPMENT
Currently, there are two kinds of fluid-bed equipment available for direct pellet ization: the conventional fluid-bed granulator and the rotary fluid-bed processor. The schematic diagram of a conventional fluid-bed granulator is shown in Fig. 1 A. The product (first powder, later granules or pellets) is fluidized in the cylindrical product container by an airstream. The in/et air passes a screen or a perforated plate, fluidizes the particles and leaves the product container through a filter. This exhaust air filter prevents product losses and air pollution. The fluidizing air can be heated to the desired temperature to dry or melt the fluidized product. The binder solution or molten binder is sprayed onto the fluidized particles through a nozzle which has to be heated in case of molten binder. The spray nozzle is usually an air-atomising nozzle which uses pressurized air to produce droplets from a liquid. The droplet size can easily be controlled by the atomizing air pressure. The position of the nozzle is above the f1uidized product in most cases .
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Direct Pelletization of Pharmaceutical Pellets
781
A rotary fluid-bed processor (Fig. 1 B) has a rotating friction plate instead of a screen at the bottom of the product container. The inlet air passes through an air gap between the rotating plate and the wall of the product container. The movement of the particles in the equipment is helical and is the result of three forces: the centrifugal forces from the rotating plate, the fluidizing force from the airstream through the gap and the force of gravity. The nozzle or the nozzles in the rotary processor are often positioned tangentially in the wall of the container in the height of the fluidized product. A more detailed description of fluid-bed equipment is given in chapter "Equip ment" by Jacob. 2. G RANU LATION VS. PELLETIZATIO N
The term pellet is used i n many industries like food, animal feed, fertilizer, plas tics, mining, chemical and energy industry. Depending on the requirements of the intended use the pellet properties differ, e.g. in their size and mechanical strength. In some cases the pellets have diameters of several centimetres. Pharmaceutical pellets are agglomerates made from fine powder particles, characterized by nearly spherical or cylindrical shape, mean diameters of 0.2-2.0 mm and a narrow particle size distribution. The surface of pellets is typi cally smooth and of low porosity. The size range is typical for granules and pellets. Smaller particulate dosage forms are usually denoted as microparticles and larger particles are usually tab lets prepared by uniaxial compression. The defined shape, smooth surface and small particle size distribution distinguish pellets from conventional agglomerates or granules. Conventional granules usually have an irregular shape, a rough surface and a broader particle size distribution. Thus, pellets are a special type of granules. However, there is a smooth tran sition between granules and pellets and a lot of controversy and discussion ap pears in the literature about the identification of agglomerated particles as pellets or granules. One simple approach for the c1assification is based on shape pa rameters derived from image analysis. The surface structure and the particle size distribution are not taken into account by this approach. There is also controversy concerning suitable shape parameters. One parameter is the aspect ratio, de fined as the ratio of the longest Feret diameter and the Feret diameter perpen dicular to this diameter. Most image analysis systems allow the calculation of the aspect ratio. An ideal sphere should have an aspect ratio of 1 . With increasing aspect ratio the deviation from spherical shape increases. In practice, the value 1 for aspect ratio is usually not achieved due to unavoidable errors in image anal ysis systems. Therefore, a mean aspect ratio of 1 . 1 can be considered as prac tically spherical [1 ,2].
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P. Kleinebudde and K. Knop
Pellets can be manufactured in the same way as granules. In most cases some process parameters have to be fixed and controlled more strictly and at the same time changes in the formulation variables, e.g. the amount of granulation liquid, are required to obtain pellets instead of granules. In some cases special excipi ents are required for pelletization. In many cases pellets are coated in orderto obtain the desired release profile of the dosage form. In this case pellets are advantageous compared to conventional gran ules. The specific surface area of pellets having a defined particle size is smaller due to the spherical shape and smooth surface. This allows the use of less film forming polymer to achieve a required film thickness, simplifies the coating process and improves the reproducibility of the release profile, which is critical for drug products. The use of pellets is of relevance and importance, if the release profile relies on the intact body of the dosage form. Therefore, pellets are frequently used in gastric resistant and modified release dosage forms. In these cases multiple unit dosage forms (MUDF) like pellets have important biopharmaceutical advantages compared to single unit dosage forms (SUDF) like coated tablets. Usually, several hundred pellets filled into a capsule give one dose. The capsule shell dissolves rapidly after application. The passage time in the gastrointestinal (GI)-tract is more consistent for M UDF, which results in less variation concerning the plasma level-time profiles ofthe drug. Consequently, the reliability of the dosage form is higher in the case of MUDF. A coated SUDF can result in undesired release behaviour (time or place of release), if the coating film breaks during production, storage or application. This so called dose dumping, probably leading to severe unwanted effects of a drug product, is less likely to occur for MUDF like coated pellets. Owing to the dis tribution of the pellets in the GI-tract the risk of a local irritation is diminished. Furthermore, several pellets with varying release profiles can be combined within one dose allowing the adjustment of the final release profile. Compared to larger SUDF the specific surface area of pellets is much higher. This requires a higher amount of polymer per dose to achieve the desired film thickness and leads to longer coating process. The volume of the dosage form is higher for MUDF, which is a problem of swallowing, especially in case of high-dose drugs. Recently, coated pellets are compressed to rapidly disintegrating tablets [3]. For those purposes small pellets with mean diameters below 0.5 mm are most suitable. Such pellets can be produced by the direct pelletization methods described below. 3. DIRECT PELLETIZATION VS. LAYERIN G OF SEEDS
Owing to their internal structure homogeneous pellets can be distinguished from heterogeneous pellets. 80th types can be coated with a thin polymer film. Hetero geneous pellets consist of an inner core region and an outer shell region of a different composition. Homogeneous pellets have a macroscopically uniform structure without a core region.
783
Direct Pelletization of Pharmaceutical Pellets
The layering on seed material or starting core material leads to heterogeneous pellets. Usually, sugar spheres consisting of a sugar-starch mixture are used as seed material. Recently, spherical particles made of microcrystalline cellulose (MCC) gained more attention. In some cases, pure drug crystals or other ma terials like solid acids (e.g. tartaric acid) are used as seed material for the pel letization. Usually, a solution or suspension of the drug is sprayed on the seed materials. It is also possible to add the drug continuously as a fine powder and fix it on the seed material by the addition of a binder solution. The layering can be performed in many types of equipment: disc or pan agglomerators, conventional fluid-bed equipment, rotary fluid-bed equipment, etc. (Figs. 2 and 3). Owing to the simple process and equipment requirements layering processes are widely used for pelletization. However, there are some disadvantages. The
Ro llin g
statting germ
Powder
Binder droplets
DryinQ/ Solidifying
Liquid
bri d g e
Solid bridge
L.. y.r form.tion
First layer
P e l let
"Onion" structure
Fig. 2. Principle of the powder layering process (Souree: Glatt) .
Wettingl distribution
Soli dify i n g/Layer formation
Pe l let
t
Starti n g core
S u s p e n d e d a u x i l ia ry m atter a n d d i s s oilled b i n d e r
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Fig. 3. Principle of the suspension and solution layering process (Souree: Glatt).
784
P. Kleinebudde and K. Knop
Spr�ying
Powder Si n d e r droplets
Rolling
Liq u i d bridge
Drying/Solidifying
Pellet
S o l i d b ri d g e
Fig. 4. Principle of the direct pelletization process (Source: Glatt).
amount of drug loading is usually limited. Therefore, layering processes are not suitable for high-dose drugs. If a spray loss occurs, the composition of the final pellets can vary. This can have negative consequences for the drug content and the uniformity of content. In direct pelletization processes, the powdered starting materials are converted into homogeneous pellets in one process. The pelletization is facilitated by the addition of a binding liquid and allowing a suitable movement of the wetted pow ders. According to the nature of the liquid binder the process is described as wet pelletization or melt pelletization. In a wet pelletization process the binding liquid is liquid at room temperature. The solidification of the pellets is achieved by drying the liquid. The evaporation of the binding liquid leaves the drug and other excipients. Melt pelletization is performed at elevated temperatures at which the binder is molten. Solidification of the pellets is achieved by cooling so that the binding liquid solidifies. The pellets contain the drug, the solidified binding liquid and probably other excipients. The pellets are usually almost spherical. However, at the same time they are of a certain minimal size distribution. Direct pelletization processes are mainly performed in high shear mixers and fluid-bed equipment. Although the direct pelletization processes are known since a long time they have not been used widely for the production of spherical pellets ( Fig. 4). In this chapter, only direct pelletization processes are discussed but not lay ering processes. Furthermore, only fluid-bed processes are considered.
4. MECHANISMS OF AGGLOMERATION/PELLETIZATION
The mechanism of nucleation and particle growth in wet fluid-bed agglomeration is described in detail in "fluidized-bed spray granulation" by Mörl and Heinrich
Direct Pelletization of Pharmaceutical Pellets
785
and in "Fluidization of cohesive powders" by Seville. A comprehensive review of the mechanisms of agglomeration during wet granulation is given by Iverson et al. [4]. During fluid-bed granulation, the fluidized powder particles are wetted by the binder solution which is sprayed onto the particles. These wetted particles can stick together by random collision and form greater agglomerates. For the for mation of pellets it is necessary that the agglomerates remain in a sufficiently wet state to allow plastic deformation and densification. So the liquid saturation of the agglomerates during the granulation phase is one important factor in fluid-bed pelletization. The other one is the height of the shearing forces. Only if these forces are high enough to deform and densify the wet agglomerates pellets can be formed. In a conventional fluid-bed granulator, the shearing forces are rather low and pelletization is only possible under optimized conditions. In a rotary processor, the pellet formation is easier due to the higher shearing forces applied from the rotating friction plate. 5. RESPONSE VARIABLES
The response variables for pharmaceutical pellets are mainly related to the later use of these pellets. Thus, in most of the pharmaceutical literature the produced pellets are characterized with respect to several response variables. These are the same for wet and melt pelletization processes. Most important for the finished pellet product is the desired dissolution profile. Depending on the intended use, an immediate or modified dissolution of the incorporated drug is intended. Usually, immediate or fast releases rely on a fast disintegration or dissolution of the whole pellet after application. A modified dis solution can either be achieved by the uncoated pellet itself or by applying a coating polymer on the pellet. Since pellets are coated afterwards in many cases, the outer specific surface area should be constant from batch to batch resulting in a high product con formity. The thickness of the polymer film depends on the ratio of applied polymer to the surface area of the pellets. In order to achieve the conformity of the specific surface area, it is necessary to produce pellets of an equal mean particle size and particle size distribution, of an equal shape, porosity and surface texture. A de viation for one or more parameter will result in different specific surface area, leading to a change in film thickness and consequently in the intended dissolution profile [5]. Apart from the variables mentioned above, certain mechanical properties like the breaking force or the friability are of importance for further handling of the pellets. Further interesting response variables are the flow properties as weil as bulk and tapped density of the pellets.
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P. Kleinebudde and K. Knop
In order to evaluate the production process the yield is also used as a response variable. In some cases the total yield is determined. This includes the whole pellet batch. A loss in total yield can be attributed to material adhering to the wall or the friction plate or material, which has been transported to the filter or even leaving the equipment. The total yield can therefore be a useful response variable to describe the process performance. However, in many studies the usable yield is used as a response variable. For this purpose, a more or less broad range of particle sizes is arbitrarily defined as usable yield of the pellets. There are large differences for this definition depending on the intended use of the pellets, which makes a comparison of the usable yield values impossible. The definition for the undersized pellets (fines) or the oversized pellets (Iumps) also depends on the goals of the individual study and is somewhat arbitrary, making comparisons impossible. Sometimes the usable yield is used together with the mean particle size or a particle size distribution, but in other cases it is used instead. If the primary of the paper is to optimize a certain product the usable yield might be appropriate. However, if the primary focus of the paper is to understand the process, the usable yield does not help. For example, if authors find that a certain change of a process parameter results in a decrease of the usable yield, this finding does not contribute to the understanding of the process. Possibly the yield is decreased by an increase in particle size, because the fraction of oversized pellets is increased. An increase of undersized pellets due to a smaller particle size can also reduce the usable yield. Even a simultaneous increase of oversized and undersized fractions indicating a broadening of the particle size distribution or a change to a bi modal particle size distribution will lower the usable yield. It can be recom mended to use appropriate parameters for the mean particle size and the var iation in particle size or to give the whole particle size distribution instead of using the usable yield. In many cases experimental designs like full or fractionated factorial designs are used to investigate a certain pelletization process. From these experiments certain conclusions can be drawn from the investigated design space, but offen it is difficult to generalize these conclusions. Mechanistic approaches are rarely found in the pharmaceutical literature.
6. WET PELLETIZATION 6.1 . Process description
Direct wet pelletization can be performed in different types of fluid-bed equip ment. It can be described as a one pot process, because all process steps can be performed in the same type of equipment. A few studies are available using
Direct Pelletization of Pharmaceutical Pellets
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conventional fluid-bed equipment [6-8]. Most work is based on the use of rotary or centrifugal fluid-bed equipment. The rotor insert comprises a cylinder with a solid rotating disc at its base leaving a gap between the cylinder and the rotating disc for the fluidizing air. Thus, a rotary processor is a hybrid between a fluid bed and a spheronizer (see chapters "Equipment" and "ExtrusionjSpheronisation"). The further process description focuses on rotary processing. A review from Gu et al. on wet pelletization by rotary processing has been published recently [9]. Rotary granulation is similar to fluid-bed granulation with the exception that the rotating disk produces a denser, rounder, smoother surfaced granule due to the acting agitative forces. In rotary equipment, three forces are acting at the same time: the centrifugal force created by plate rotation, the vertical force created by slit air and the gravitational force allowing the product to fall towards the centre of the rotor plate. An ideal product movement is of high i mportance. This movement is described in terms of rope-like tumbling, twisted rope, spiral, spiralling helix and others. Especially in the beginning of the process having a dry or moderate wet powder this movement is difficult to achieve. However, at the end of the process the movement is of critical importance. Usually, different steps of the process can be distinguished: 1 . The first step is called setup or mixing andjor heating. During this step most process parameters are adjusted to their set values. At the same time mixing can occur and the inlet air temperature can be increased above room tem perature in order to avoid condensation of liquid during the following spraying phase. 2. During the second stage of the process, called spraying, moistening or liquid addition stage, the powder is moistened by spraying a liquid to the powder continuously. Usually, the spray nozzle is placed in the powder bed and a tangential spraying is chosen. This setup allows a very uniform distribution of the liquid in the powder bed with a minimal disturbance of the product move me nt. Homogeneous distribution of the liquid is a prerequisite to avoid adhe sion to the product chamber wall. The added liquid is partly removed by the fluidized air. The spray rate exceeds the drying rate giving rise to a steady increase in product moisture content. During the spraying stage the fluidization of the mass will become less effective, because the liquid addition and the agitating forces cause a densification of the mass. An induction period where nuciei agglomerates are consolidated but do not grow is followed by coales cence growth. Thus, the process can be described by an induction growth showing a delay period during which little growth occurs. After reaching a certain, probably desired moisture content of the liquid spraying is terminated. If a constant amount of liquid is applied to the powder, the final moisture content depends on many other variables like the amount, humidity and ve locity of the fluidizing air, the liquid spray rate, the rotor speed and the batch
788
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size. The moisture content of the mass at the end of the liquid addition is critical for the formation of pellets. At any time the moisture content of the granules depend on the extent of liquid addition and evaporation. Methods for end-point control are presented in Chapter 1 0 by S. Watano. 3. After spraying is stopped, usually the rotor plate continues to run at the same or a different speed as before. This stage is ca lied spheronization or wet massing. At latest during this phase the rope-like movement occurs and pellets are formed and will grow further. During this stage the pellets can initially grow further and the shape can be improved. However, due to evaporation the moisture content of the pellets starts to drop and a further growth is Iimited due to a decreasing deformability. 4. At the end of the process drying can take place usually at elevated inlet air temperature. However, due to the Iimited drying capacity of the single-wall rotary processors drying might be performed externally. It is highly important that the total load of powder is moved all the time and a loss of powder or wet mass does not occur due to pneumatic transport in the first stage before being wet enough, due to slipping through the gap between the rotor plate and the wall of the chamber or due to adhesion to the wall of the chamber or to the friction plate after being wetted. The remaining solid mass will be over wetted by applying a fixed amount of wetting liquid and the rope-Iike movement can be disturbed significantly. A uniformly moistened mass is essential for sphe roid formation and growth in a controlled manner to give pellets with a narrow size distribution [1 0]. Only a few papers give information about the evolution or kinetics of the proc ess parameters [1 2,1 3]. Figure 5 gives an example for a direct wet pelletization process [1 1 ]. After filling the powder mixture into the chamber the fluidizing air flow was initiated while the friction plate was elevated to adjust the air gap pres sure difference and then the rotation of the friction plate was turned on. Tem perature and fluidizing air flow rate were set to 40°C and 90 m 3 h - 1 , respectively. After the setup, the liquid addition started (first vertical line in Fig. 5). The initial decrease in the fluctuating torque values seemed to be related to the warming up of the rotary processor. During this period the water content of the powder in creased and the mass became denser. After a certain liquid addition time a rapid increase in torque was observed, accompanied by a further densification of the mass and a faster, rope-like movement of the mass. The increase in torque (�Tq) was computed as the difference between the minimum torque value (baseline) and a running mean of the last 1 00 torque values. The liquid addition was con tinued until the �Tq reached a desired value. After the liquid addition was stopped (second vertical line in Fig. 5) wet massing was continued for 6 min while the torque values started to decrease.
789
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Fig. 5. Process description of a direct pelletization experiment; development of different process parameters; (a) torque; (b) air gap pressure difference and f1uidizing air flow rate; (c) inlet air temperature (upper profile), product temperature (middle profile), outlet air temperature (lower profile); the vertical lines indicate start and stop of liquid addition [ 1 1 ] .
Direct wet pelletization is a multivariate process that demands a high level of control of all variables in order to achieve the desired product characteristics [14].
6.2. Pelletization aids
A suitable formulation for spheronization should possess a certain plasticity. In direct wet pelletization, the required plasticity is achieved by adding liquids,
790
P. Kleinebudde and K. Knop
especially water, to suitable powder mixtures. The fraction of liquid binder is critical for the success of the process. MCC is often used as a spheronization or pelletization aid in direct wet pelletization. MCC is weil known as a pelletization aid in extrusionjspheronization. The role of MCC has mainly been discussed with respect to extrusionjspheronization, but the proposed models can also be applied to direct pelletization [ 1 5]. On the basis of thermal studies about the interaction of water and MCC, Fiel den et 81. [ 1 6] have suggested that MCC can be described as a 'molecular sponge'. The material is capable of physically retaining a high percentage of water within itself, but allowing removal by evaporation to take place with great ease. The highly absorbent and moisture-retaining characteristics are physical in nature and unaffected by processing. The function of MCC is claimed to be twofold: it controls the movement of water through the wet powder mass during extrusion and modifies the rheological properties of the other ingredients in the mixture, conferring a degree of plasticity. The 'sponge' model has been explained further by Ek and Newton [1 7]. During extrusion, the 'sponges' are compressed until water is squeezed out and lubricates the particles flowing through the ex truder. Variations in water content will be needed for different types of extruders because different shear forces are involved. After extrusion, the volume of the 'sponges' will increase and the extrudate will be apparentiy 'dry' and brittle, allowing it to be chopped into short lengths in the spheronizer. Subjecting these cylinders to the forces of spheronization again compresses the 'sponges' and will allow deformation of the 'soft' structures. The 'sponge' model explains a number of observations and has been supported in the literature [1 8,1 9] . Another model has been proposed by Kleinebudde [20,21]: the 'crystallite-gel' model. He proposed that a 'gel' is formed during extrusion with MCC. In the presence of a liquid, especially of water, the MCC particles will break down into smaller subunits due to the application of shear forces during granulation and extrusion. With increasing shear stress this process will be more or less com plete, finally single crystallites of colloidal size may occur. These single particles are able to form a 'crystallite gel' and immobilize the liquid. The viscosity of the 'gel' depends on the particle size of the resulting components and the liquid content. Because the disruption into single crystallites is thought to be incom plete, the plastic, hydrated, semisolid mass of MCC is not a gel in the classical colloid chemical sense [22]. However, the resulting crystallites and porous par ticles form a coherent 'gel-like' network with a high fraction of insoluble solid phase and immobilize the granulation liquid. The inclusion of further components into the formulation leads to a two-phase model of a wet extrudate: a percolating 'crystallite-gel' phase formed by MCC and water during extrusion and a filler phase formed by the second component of the binary mixture. During 'gel' for mation the MCC particles are rearranged. The coherence of the solid network can be established by the formation of secondary valence bonds between the
Direct Pelletization of Pharmaceutical Pellets
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amorphous ends of the single crystallites or the crystallites on the surface of aggregates. The 'crystallite-gel' model is able to explain many observations and was applied also to other granulation processes [1 5,23,24]. Neither of the two models has been directly proved and there is some debate about the value of these models. While the 'crystallite-gel' model proposes a change in the particle structure during processing, the 'sponge' model implies that the original particles will stay intact. The breaking of the aggregates into individual particles was thought to be unlikely to occur by extrusion as the shear forces are relatively low [1 7]. The individual particles of MCC are very difficult to reduce further in size to colloidal dimensions by mechanical means. Individual particles and their agglomerates have been differentiated concerning particle size analysis of MCC [25]. During characterization of MCC, different degrees of de-agglom eration may be applied. Individual particles were separated from agglomerates by ultrasonic treatment of a water suspension of agglomerates. The median weight diameter of the individual particles was in the range of 20-30 11m for three types of MCC while the agglomerates were in the range of 80-1 20 11m. Brittain et 81. have shown that the mean particle size of an MCC suspension decreases with the energy input during the preparation of the suspension [26]. The blending step needed to affect the suspension of the material results in a disintegration of the MCC particles and a concomitant increase in the viscosity of the slurry. In wet extrusion as weil as in wet granulation it has been observed several times that the structure of the original MCC particles has changed deeply [20,23,24,27]. Dif ferent types of MCC produced colloidal particles after high-pressure homogen i zation [28]. In the same study it was confirmed that extrudates from the same types of MCC also contained colloidal particles. In the presence of water it is possible to decrease the particle size of MCC by applying mechanical energy. In a monograph about microcrystal polymer science, Battista has suggested as definition: systems of colloidal-size polymer microcrystals whose suspensoid properties are largely determined by the relative proportion of discrete unit par ticles in suspension vs. the proportion of the same particles present as aggre gates, each aggregate containing varying numbers of the same microcrystals clustered together [29]. One important example for microcrystal polymer science is MCC. Gels can be produced from MCC [30]. These gels are clearly composed of a highly polydisperse distribution of cellulose microcrystals and aggregates thereof. The microcrystals are released into a liquid medium by mechanical en ergy. Recovery of the smallest microcrystal unit component is highly dependent on the severity of the mechanical disintegration treatment. Mechanical agitation in a water slurry frees a fraction of the unhinged crystals. This fraction can be increased by improvement in mechanical energy input, preferably by high-shear action. The presence of a minimal concentration of single colloidal microcrystals in association with much larger colloidal particles comprising aggregations of the aforementioned basic unit microcrystal is a prerequisite for the formation of stable
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polymer microcrystal gel system. The microcrystals pervade the whole system at low concentrations without settling, the insoluble microcrystals touching each other. Their three-dimensional network has a certain rigidity and consequently they should be characterized as gels. Commercial pure MCC gels may have only 20-30% of individually dispersed microcrystals; the remainder are made up of aggregates of unhinged microcrys tals as large as 1 0-50 Jlm. It is important therefore to recognize this fact in interpreting data on the measured properties of MCC gels. The size and shape of the microcrystals, as weil as the properties of each cellulose suspensoid, de pends on the history of the precursor cellulose fibres. In general, an increase in the viscosity of a gel at a fixed solid concentration relates to the efficiency of microcrystal deaggregation. However, once a certain percentage of microcrystals have been freed and hydrated to develop maximum viscosity, it is difficult to produce further deaggregation of the remaining aggregated particles, probably because the brush-heap matrix of hydrated single crystals shields the remaining aggregates from direct shear-energy input. The general viscosity properties of MCC solutions are affected by the size of the microcrystals (which varies widely depending on the source), the polydispersity or size distribution (which is influ enced by the method and severity of mechanical attrition used), and the total concentration of particles. The amount of water or granulation liquid required for pelletization depends on the fraction of MCC in the formulation [1 5,31]. A linear relation between the amount of water (based on dry mass) and the fraction of MCC has been found (Fig. 6). Compared to extrusionj spheronization or high-shear granulation, the shear forces applied in fluid-bed processes including the rotor processes are rather low. This results in a lower slope of the straight line [1 5]. If the fraction of MCC is va ried in an experimental plan, the amount of liquid should be adapted. If the amount of liquid is kept constant, the results are not directly comparable. Table 1 gives an overview about the fraction and type of MCC used for direct pelletization. Depending on the individual process and the incorporated drug, 1 0-45% MCC are recommended for successful pelletization [1 5,31 ,32]. With 1 0% pelletization was possible, while other formulations required 20% or more of MCC [32]. Vecchio et al. [31 ] reported that 30-45% of MCC brought satisfactory results; a decrease led to an increased stickiness of the material and produced irregular large granules. With 1 5% of MCC they observed a bimodal size dis tribution. MCC not only confers plasticity to the wetted mass, but also imparts binding properties that are essential to obtain pellet strength and integrity. The type of MCC was found to be of less importance concerning the final pellet properties [33]. While some authors use a fixed level of MCC others study the importance of the fraction of MCC in the formulation. In some cases the studied range is rather smalI, e.g. 30-35% [14], while in other cases a wide range has been investigated, e.g. 1 0-1 00% [1 5,33].
793
Direct Pelletization of Pharmaceutical Pellets 100
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Source [6-8, 35] [13,32,36] [33] [1 5] [31 ] [37] [38] [ 1 0,39,40] [41 ] [34] [42] [43] [5,1 4,44] [45] [12] [46] [47] [48] [1 1 ] [49] [50] [51]
MCC type
MCC fraction
Avicel PH 1 02 Avicel PH 1 0 1 , 1 02, 200 Avicel PH 1 0 1 Avicel P H 1 0 1 Avicel PH 1 02 Emcocel 50M Avicel PH 1 0 1 Avicel P H 1 0 1 (bentonite, kaolin) Avicel PH 1 0 1 Avicel PH 1 01 Avicel PH 1 01 Avicel PH 1 01 Avicel PH 1 01 Emcocel Avicel PH 1 0 1 , PH 1 02, RC 591 Avicel RC 581 Avicel CL-6 1 1 or RC 581 Avicel PH 1 0 1 Avicel PH 1 01 Emcocel 90 M , 50 M, SM1 5, H D90 Emcocel 90M; 50M
1 0; 20; 30 1 0; 30; 50; 75; 1 00 1 0-1 00 1 5; 20; 30; 45 1 8; 47.5 24 25 25 (25) 25; 30; 35 30 30; 40; 50 30; 35 35 40; 1 00 42.5-1 00 50 50 50 50 50 + 50 (core and layering) 50 + 50 (core and layering)
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P. Kleinebudde and K. Knop
An increasing fraction of MCC resulted in smaller pellets for the same torque increase [1 5]. This might be attributed to a more pronounced shrinking of these pellets due to the high water content. Paterakis et al. have observed a smaller size distribution of the pellets with increasing fraction of MCC in the formulation [34]. Pellets based on MCC as a pelletization aid possess properties which can be in some cases disadvantageous. For instance, pellets containing MCC tend to swell but do not disintegrate during the application. As a consequence, they release the drug according to a matrix release profile [31 ]. According to the release equations derived by Higuchi, the release depends among other variables on the size of the pellet and the solubility of the drug. For drugs with low solubility, the dissolution rate can be too low. Identifying a pelletization aid that could substitute MCC and give rise to fast disintegrating pellets would be advantageous. Kristensen et al. have used water insoluble hydrated aluminium silicates, namely kaolin and bentonite, as alternative pelletization aids [41 ]. The fraction of kaolin or bentonite was set to 1 5-30%. Kaolin was found to be the most promising candidate for a pelletization aid, because it allowed the formulation of fast-disintegrating and fast-releasing pellets. However, the strength of the pellets from the kaolin for mulation was much lower. Gauthier and Aiache also present formulations without MCC [46]. 6.3. Equipment variables 6. 3. 1. Type of equipment
Different types of fluid-bed equipment can be used for direct pelletization: con ventional, rotary and tumblingjagitated equipment. Most of the work has been conducted in rotary equipment. Well-known rotary processors are made by the companies Glatt, FreundfVector and Niro-Aeromatic (see the chapter on 'Equip ment'). Principally, single-wall and double-wall rotary processors can be distin guished. The double-wall rotary processors have a higher drying capacity, because more air can pass the region between the inner and outer cylindrical wall. While in the rotary processors from Niro-Aeromatic and Glatt the nozzles are spraying tangentially in the bed, the CF-Granulator from FreundfVector uses a top spray system. Direct comparisons between different types of rotary equip me nt are, to the authors' knowledge, not published. Conventional fluidized-bed equipment has been used by Knop et al. [6-8]. The authors have not used microcrystalline cellulose or other pelletization aids but water soluble binder materials instead. In the first attempts the pellets did not show a satisfying strength and density. In a later paper a rotating motion of the material was created by the use of pneumatic nozzles, which were mounted tangentially in the chamber of a conventional fluidized-bed equipment. The
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rotating motion of the material resulted in a stronger densification and spheronization of the material. In a series of papers, Watano et al. used an agitated fluidized bed for gran ulation purposes [52-56]. An agitator is placed in the fluidized-bed chamber in stead of a rotor plate. The agitator is similar to those used in high-shear mixers and is used to control the movement of the particles in the product chamber. Most of the work has been performed in a rotary equipment with a rotor plate as main equipment detail. Studies have been performed in the equipment from Freund-Vector [47,48,50,51], Glatt [1 1 , 1 2 , 1 5,33,34,37,41-43,46,49,57] and Niro-Aeromatic [5, 1 0, 1 3, 1 4,31 ,32,36,38-40,44,45,58-63]. 6. 3. 2. Diameter of rotor plate
The diameter of the rotor plate is fixed for a given type of equipment. Most of the work has been published for laboratory equipment. Information about scale-up can be found in the chapter on 'Scale-up'. Chukwumezie et al. [48] have studied a scale-up in Flo-Coaters from Vector/Freund using rotor inserts of 9 (FLM 1 ) , 1 2 and 1 9 inch (both FLM 1 5) for batches of 1 , 5 , and 1 0 kg. The results are de scribed in Section 6.4. 1 . -
-
6. 3. 3. Number, diameter and distance of spray nozzles
The number and diameter of the nozzles has not been investigated. In the ma chines from Glatt and Niro/Aeromatic, the nozzles allow a tangential spraying directly in the rotating mass. The distance of spray nozzle between nozzle and rotor plate was studied by Rashid et al. using a CF-granulator [51]. which operates in top spray mode. Variation of the distance in the range 5-7 cm had no significant effects on the studied pellet characteristics. 6. 3. 4. Surface of the rotor plate
A smooth plate applies less energy than a textured plate [42,47], but is best in avoiding material adhesion. The most spherical pellets were achieved using a textured plate [42], which is able to transmit more mechanical energy to the wet mass. However, during drying an excess of mechanical energy can lead to at trition. There is a strong interaction with the rotor speed. A Teflon rotor plate resulted in a higher loss of drying compared to a stainless steel rotor plate [48]. This was attributed to a d ifference in heat conduction. The Teflon rotor plate tended to insulate the pellet bed from the drying medium,
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whereas the stainless-steel rotor plate allowed for a better heat conduction and consequently better heat transfer and drying.
6.3. 5. PTFE lining, baffles and choppers
In some studies a PTFE-lining of the product chamber has been used in order to reduce adhesion of the product to the container wall [ 1 3 , 14,32,36,45]. 8affles and choppers can be used in order to improve the material motion in a rotary processor [45]. Vertommen et al. [14,45] have not seen an effect of an additional chopper on the particle size distribution. The chopper did also not affect the amount of larger agglomerates. 6.4. P rocess variables 6. 4. 1. Load
Liew et al. [1 0] were able to optimize a pelletization process based on a load of 0.5 kg. Robinson and Hollenbeck [37] could show that a larger load improved yield as weil as size and shape characteristics of pellets (0.5 vs. 1 kg). In other studies, the load typically varies between 0.5 kg [39] and 6 kg [32], depending on the size of the rotor plate. Chukwumezie et al. [48] have studied a scale-up in Flo-Coaters from VectorJ Freund batch sizes of 1 , 5, and 1 0 kg. Scale-up was based on geometrie similarity using the radius of the rotor plate and the centrifugal force as similarity factors. The centrifugal force was kept constant by adapting the rotor speed. The particle size appeared to increase with larger batch size. The authors explained this by a greater attrition of the smaller sized batches. The drying efficiency was lower for the larger batch sizes. Therefore, the water content at a given time might be higher at a larger batch size resulting in larger pellets. 6. 4. 2. Spray rate
Together with other variables like the atomizing air pressure, the spray rate de termines the droplet size of the wetting liquid and the uniformity of liquid distri bution in the solid mass [40]. A low spray rate is associated with longer processing time resulting in a lower porosity of the pellets [36]. Higher spray rate results in a higher water content at the end of the spraying stage. The higher spray rates reduce the liquid addition period and during the shorter time less moisture will be evaporated. Thus, a higher spray rate will result in larger pellets, if all other factors are kept constant [31 ,34,39,40]. A higher spray rate was also found to lead to a broader size distribution [34].
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6. 4. 3. Rotor speed
The rotor speed affects mixing, liquid distribution [ 1 0], agitation, pellet growth and shaping. Holm found that the rotor speed was the dominating factor for the po rosity of pellets [36]. In a fractional factorial design, an increase in rotor speed from 1 80 to 280 rpm was the dominating factor for most response variables [51 ] . In this study, the pellets that were larger, showed a higher bulk density and an improved round ness with an increase in rotor speed. In other studies, the pellet size was smaller with an increase in speed, e.g. from 1 000 to 1 400 rpm [49]. The different findings might be explained by the different investigated ranges of rotor speeds, which can lead to different particle growth or particle reduction phenomena. Another explanation might be that the production methods differ from each other. In most studies the rotor speed was constant during mixing, liquid addition, wet-massing and drying. However, Liew et al. [ 1 0] suggested to use different speeds (low-high-Iow) during the different stages. A high rotor speed is useful during the liquid addition stage since it promotes a uniform liquid distribution, which is essential in the process. Furthermore, it reduces the material adhesion and enhances the break up of loose chunks of moist agglomerates. During wet massing, a high rotor speed can induce an excessive coalescence and growth due to stronger centrifugal forces particularly once the powder mass is ade quately wetted. This leads to a wider size distribution. Liew et al. suggest the use of a low rotor speed during mixing and early wet-massing stage until the mass is slightly wetted, which makes it more cohesive and less susceptible to be blown up out of the chamber. During the remaining liquid addition stage the rotor speed should be high but lowered again during the wet-massing stage. This rotor speed regime leads to a more controllable agglomeration process. A reduced rotor speed during the first stage [50] or the drying stage [46] was also recommended by other authors. Pisek et al. [42] reported that using a smooth rotor plate and a higher rotor speed during the wet-massing stage resulted in more spherical pellets with smoother surface. In contrast, using a textured rotor plate smaller and less spherical pellets with a rougher surface were obtained by increasing the rotor speed during the wet-massing stage. 6. 4.4. Wet-massing time
During the wet-massing time the product starts to dry, because no further liquid is added but the air flow leads to an evaporation of the granulation liquid. The drying can result in a change in deformability of the pellets and further drying will lead to an increasing abrasion of particles from the surface of the pellets. During the wet massing stage the pellets can be further spheronized, especially in the beginning at the initial liquid content.
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6. 4. 5. Inlet air temperature
Increasing inlet air temperature decreases the mean pellet size [34]. A higher inlet air temperature results in an evaporation of the moistening liquid. Thus, the moisture content of the wet mass is lower at the end of the liquid addition stage. If the other variables are kept constant, a lower moisture content of the wet mass results in the formation of sm aller pellets. 6. 4. 6. Air flow rate
The air flow rate is important for the drying capacity of the air and for the air velocity giving rise to the fluidization of the wet mass. 6. 4. 7. Atomizing air pressure
The atomizing air pressure is one determining factor for the drop size distribution of the wet-massing liquid. Together with the nozzle diameter, the spray rate and the physico-chemical properties of the liquid like surface tension, viscosity and density the atomizing air pressure controls the spray process. Depending on the range studied, the atomizing air pressure can be of minor importance [49,51]. 6. 4. 8. Gap widthjpressure difference
A positive pressure difference across the gap due to an air flow is necessary for the fluidization of the powder and wetted mass. If air passes through the gap, a slipping of the powder between the rotor plate and the chamber wall is avoided. The fluidizing air can also help to prevent the wet mass from adhering to the wall of the production chamber. If the powder is not completely available for pellet ization due to sticking to the wall or slipping through the gap, the wetting liquid is distributed to a smaller amount of solid material giving rise to a higher water content of the remaining load and thus to an undesired pellet size. Adhesion to the wall is crucial to the rope-like movement of the wet mass. Pellets with a much larger diameter were observed in spheronization experiments where substantial wall adhesion occurred [39]. The moisture content of wet pellets was found to decrease linearly with time after the complete addition of water (Fig. 5) [1 1 , 39]. With increasing pressure difference the decrease in water content was more pronounced [39]. This was attributed to the drying effect of the air passing the gap between rotor plate and process chamber. In case of a cylindrical chamber, the pressure difference is directly related to the amount of air passing the gap. In a conical chamber, the pressure difference can be adjusted independently from the air flow rate. At a given air flow rate giving a certain drying capacity the pressure difference across
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the gap giving the air velocity can be adjusted by raising or lowering the position of the plate giving rise to a wider or smaller gap width. During the drying phase an increased gap pressure difference can also result in increased attrition of the pellets [39]. Rashid et al. [51 ] have shown that an increase in the air flow rate from 1 40 to 240 I min- 1 resulted in significantly smaller pellets of a lower bulk density. 6.5. Form ulation variables 6.5. 1. Fraction of drug
Often it is aimed to incorporate a high fraction of drug into the pellets. With increasing fraction of drug, less pelletization aid is available. Depending on the physico-chemical properties of the drug the maximal fraction is limited. Si enkiewicz et al. [33] used formulations containing 0-90% of theophylline for direct pelletization. As the proportion of the drug increased, the process became more difficult to carry out to completion. A theophylline content of up to 50% resulted in spherical and elegant pellets, but 70 and 90% of theophylline gave more granular products. Vecchio et al. have incorporated 55-85% indobufen in pellet formu lations [31]. A fraction of 85% was not suitable for pelletization. 6. 5. 2. Partic/e size and size distribution
Sienkiewicz et al. tested three different particle sizes of theophylline for direct pelletization. Particle size of the drug was the most important factor in spheronizat ion. A large particle size was found to be most useful [33], while small theophylline particles showed a tendency to adhere to the wall. The adhesion prevented the rope-like movement of the wet mass required for the spheronization. Furthermore, the effects were more pronounced at a higher fraction of drug in the formulation. Drugs of a small particle size cause difficulties for direct pelletization in fluid bed equipment. Pisek et al. [42] tested ketoprofen of an average diameter of 7 J.lm. Using a textured disc it was not possible to produce pellets. Holm [32] found that the pellet size distributions for formulations with a coarse quality of dicalcium phosphate were less critical to the level of moisture content when compared with formulations containing lactose 450 mesh. The pelletization process was more critical for the formulations with the fine grade of dicalcium phosphate. 6. 5. 3. Type and amount of binder
A high amount of binding liquid results in more spherical particles and larger particle size [31 ,44,47,49]. Usually, water can be used alone as binding liquid, if a suitable pelletization aid like MCC is included in the dry formulation.
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PVP as an additional binder was found to be favourable compared to H PC due to less rapid particle agglomeration [46]. Other authors found that a binder dis solved in the aqueous phase caused the adhesion of the material to the product container and the disc [32], preventing a homogeneous flow. 6. 5. 4. Solubility
Soluble drugs need less water for pelletization than those with lower solubility [42]. The drug can partly dissolve in the wetting liquid, which increases the ratio of liquid to solid mass. 6. 5. 5. Moisture content
The moisture content at the end of the liquid addition stage is critical for the process. There is a sensitive relation between moisture content and particle size (Fig. 7). The process is extremely moisture sensitive and must be tightly controlled when trying to achieve a particular mean granule size [32,49]. The moisture sen sitivity depends strongly on the formulation, especially the fraction of pelletization aid. Owing to the multiple interactions between the different equipment, process and formulation variables the equipment and process variables have to be ad justed according to the physico-chemical properties of the drugs and the excipi ents in the formulation and the desired characteristics of the pellets, e.g. size. The moisture content is difficult to adjust, because direct pelletization is a multivariate process. Liquid is introduced by the moisture content of the starting materials, the moisture in the slit and spraying air and by the sprayed liquid. At the same time liquid is removed throughout the process by evaporation. The evap oration is affected by the amount, humidity and temperature of the spraying and
� 1200
Jo 1000 .� 800 '"
�
600
�
400
� c:
. dicalcium phosphate {coarse)/MCC (J0/30 w/w) " Lactose 450 mesh/MCC (70/30 w/w)
Ol
� 200 GI
E
moisture content, Itf.
Fig. 7. Relation between the moisture content (relative to dry material) after liquid addition and mean particle size of the final product for two formulations ([32], Fig. 6).
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slit air, the load and the rotor speed. Owing to the high importance of the moisture content many attempts have been made to control the moisture content of the wet mass. This can be used for end-point control of the liquid addition stage (see Chapter "Online Monitoring"). 6.6. Reproducibility
Holm has tested the reproducibility of the particle size distribution by con ducting the same experiment six times adding 2570 9 water at a spray rate of 200 9 min - 1 . The relative standard deviation of the mean granule size was 3.9% and the moisture content was kept within 0.3% [ 1 3]. For a formulation containing dicalcium phosphate, a suitable correlation between the power consumption of the rotor plate at the end of liquid addition and the mean granule size exist. This was not the case for a formulation containing lactose 450 mesh. Vertommen and Kinget reported differences in the geometrie mean diameter up to 60 I-lm and differences in the range d1 6%-d84% up to 35 1-lm. They classify the pelletization process in a rotor processor as a critical but nevertheless repro ducible one [14]. Kristensen et al. [1 1 ] achieved a mean particle size of 683 ± 40 I-lm in eight experiments. They used the increase in torque to control the end-point of the liquid addition stage. Although the end of the liquid addition stage varied between 28 and 44 min the pellets size could be kept within a small range. The variation in the time for liquid addition was explained by a varying spray rate.
7. MELT PELLETIZATION
An alternative way to obtain pellets by agglomeration in a fluidized bed is the process of melt pelletization. In this process, the powder particles are agglom erated in the fluidized state at a higher temperature by a molten binder, which solidifies during cooling. Melt granulation in a fluidized bed was first described by Heinemann and Rothe in a patent in the early 1 970s [64]. They granulated powdered drugs and excipi ents with powdered polyethylene glycol or a wax in a fluidized bed at temper atures above the melting point of the binders. Since this publication only little research has been done in that field. Most of the authors described the melt granulation process and the influence of variables on it. Only a few focused on the special properties of pellets concerning melt pelletization [65-67]. But like in the case of wet pelletization it is possible to transfer the knowledge of the melt granulation process to the melt pelletization process.
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7.1 . Process description
There are two approaches to melt pelletization in a fluidized bed, which differ in their methods of binder addition: •
Addition of powdered binder: The drug substance and all other high melting point solids are placed in a fluid bed granulator together with the powdered binder at room temperature. The powders are fluidized by hot fluidizing air and when the melting point of the binder is reached the fluidized particles begin to agglomerate. The agglomer ation phase is short because all of the molten binder is present at once. When the agglomeration is finished, cold air is used to fluidize and the binder solidifies or crystallizes. The granules or pellets are cooled in the same apparatus by this way. No spraying equipment is necessary for this process and it can be carried out in a conventional fluid-bed granulator or dryer [67-70] or in a rotary flu idized-bed processor when higher shearing forces are desired [65,71].
Addition as molten binder: The non-meltable ingredients are fluidized by hot air. The binder has to be heated above its melting point outside the apparatus, delivered through a heated tube to the heated nozzle and dispersed with hot pressured air into droplets of molten binder. When the desired temperature in the product chamber is reached, the molten binder is sprayed onto the fluidized particles. After all the molten binder was added and agglomeration was finished, the heater for the fluidizing air is turned off and cold air cools the agglomerates and the binder solidifies. This procedure is more similar to that of wet granulation in fluidized bed where a binder solution is sprayed onto the particles, but no drying step is necessary. So far, research in this field has only been done in conventional fluid bed equipment with additional heating supply for the molten binder [66,68,72]. A special case is the tumbling melt granulation (so ca lied by the authors) [73-78] where seed material is heated by hot air in a centrifugal fluidizing gran ulator and a powdered mixture of meltable and effectively non-meltable material is fed onto the preheated seeds which are moved by the centrifugal forces of the granulator. The meltable material melts and leads to an adherence of the powder mixture to the seeds, so acting as a binder. After cooling the powdered material forms a solidified layer around the seed material. This is rather a coating or layering process and will not be discussed here in detail. •
7.2. Advantages of the process
The melt pelletization in a fluidized bed has several advantages over the more common wet pelletization. There is no need of a solvent Iike water, alcohol or
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other organic solvents. So a drying step is no longer necessary. This reduces the supply of energy and the time of the process. Process times can be shortened to half an hour in the laboratory scale [67,69]. The renunciation of water makes it possible to agglomerate material, that undergoes hydrolysis in the presence of water or even to agglomerate effervescent mixtures containing anhydrous citric acid and sodium bicarbonate [69]. With the right choice of binder it is possible to produce fast-dissolving pellets (e.g. with polyethylene glycol) or pellets with prolonged release properties (e.g. with waxes). In comparison with the melt pelletization in a high-shear mixer, the process in the fluidized bed allows a better control of the product temperature. The product temperature is easily adjustable by heating or cooling the fluidizing air to the desired temperature. So the melting of the binder is achieved by hot air above the melting point of the binder and solidification occurs with cold fluidizing air. The fluidizing air (in a rotary processor together with the rotating friction plate) keeps the product in motion during the whole process, since heating and cooling is running in the same equipment. One disadvantage compared to the melt ag glomeration in a high shear mixer is that the shearing forces in the fluidized bed are significantly lower. This can be overcome to a certain degree by using a rotary processor with a rotating friction plate. Higher shearing forces lead to agglom erates, which show a denser and more spherical structure. The process of melt pelletization in a fluidized bed can be described as simple and easy to contro!. More specifically, when the binder is added in a powdered form there are only a few variables to be considered. 7.3. Meltable binders
The main factor is the choice of a suitable binder as it is in the process of wet granulation. The binder for melt agglomeration has to meet at least the following requirements: its melting point or range has to be above 30 or 40°C to ensure sufficient hardness at room temperature during storage. lf the binder is intended to act as a matrix substance for controlled release the melting point has to be above 3JOC. On the other hand, the melting point should not be too high because the product in the fluidized bed has to be heated above this temperature to form agglomerates. For practical and energetic reasons the temperature in a fluidized bed is Iimited to approximately 1 00°C and the thermal sensitivity of active and other ingredients has to be considered. Pharmacological and toxicological safe ness are further prerequisites for the use as a binder. Additionally, it has to be available in a pharmaceutical grade and defined quality in respect to crystal modification and other important properties. Two different kinds of substances were used in recent studies as meltable binders: substances with a good solubility in water like polyethylene glycol (of
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molecular weight 3000 to 20,000) which give rise to pellets with a rapid disso lution behaviour. On the other hand, hydrophobie material, such as fatty acids, glycerides and waxes result in pellets with a prolonged or sustained release or having taste masking properties. In a patent, Reo and Roche claimed that the binder in melt agglomeration in a fluidized bed can also be an active drug [71]. As mentioned above, the drug must have a melting point between 30 and 1 00°C in that special case and it must be ensured that no degradation takes place during melting. Ibuprofen with a melting point near 75°C seems to be a suitable drug which fulfils the requirements and is described as an example in the patent. 7.4. Mechanisms of pellet formation
The principle mechanisms of pellet formation in melt agglomeration in a fluidized bed are the same as in wet granulation. First, small agglomerates (nuclei) are built during nucleation, which grow by coalescence between the agglomerates or layering of fine particles onto the agglomerates. According to Abberger [68] and Abberger and Henck [79], the formation of agglomerates in fluidized-bed melt pelletization can be described by two mechanisms: on the one hand distribution and coalescence and on the other immersion and layering. 80th mechanisms were discussed earlier by Schaefer and Mathiesen [80] for the melt granulation in a high-shear mixer. •
•
Distribution and coalescence (Fig. 8): The molten binder comes into contact with the surface of a solid particle, the particle surface is wetted by the binder and the binder is distributed more or less evenly on it. The surface is now sticky and adhesive due to the molten binder. The nuclei are formed by random collisions of wetted particles. A nucleus is only built when the forces between the particles due to the liquid bridges of the molten binder are high enough. In contrast to wet granulation in a fluidized bed, no evaporation of solvent is possible and the liquid bridges or the liquid film remain between the particles until solidification takes place during the cooling phase. The nuclei grow by further collision to greater agglomerates. The ag glomerates may have air entrapped because of the unsaturated voids between the particles. When the shearing forces in the (rotary) fluidized bed are high enough , dens ification of the agglomerates is possible and the resulting granules may have a more spherical shape. Under these conditions pellets will be obtained. Immersion and layering (Fig. 9): The powder particles come in contact with a greater droplet of the molten binder by random collision; the particles stick onto the surface of the liquid droplet and
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Direct Pelletization of Pharmaceutical Pellets ..... + •• • • •• ••
:
powder particles
-
• •• • • • •• • • ••• • •• •• • • •• • •• ••
distribution
binder
coalescence
Fig. 8. Mechanism of distribution and coalescence (modified according to [80]).
-
+
powder particles
binder
immersion
layering
Fig. 9. Mechanism of immersion and layering (modified accordi ng to [80]).
form a droplet with a surface of wetted solid particles. The size of this nucleus mainly depends on the size of the binder droplet. The particles can be immersed in the liquid and the binder can move outwards due to capillary forces of the liquid. The surface of the nucleus is now partly covered by the molten binder again and more powder particles can adhere and form a layer. Therefore, this process is called layering. When more and more particles adhere to the surface and more binder is sucked out it is possible that a cavity is formed in the middle of the granule. This structure of a hollow pellet with a dense wall remains during melt pelletization in a fluidized bed due to the relatively low shearing forces. An example is shown in Fig. 1 0, similar pellets were shown by Abberger [68] and Haramiishi [81]. Of course, coalescence of nuclei or agglomerates is also possible as in the case of dis tribution. Which of the two mechanisms is dominant depends mainly on the relative size of the binder droplets to the solid powder particles. Distribution of the molten binder on the surface of the powder particles will be more likely when the droplets of the binder are small in comparison to the size of the solid powder particles. On the other hand, when the droplets are larger than the powder particles immersion will be the preferred mechanism. Other factors such as the viscosity of the molten binder, the amount of binder and the kind of shearing forces during the process may aIso influence the agglomeration mechanism.
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Fig. 1 0 . Cut through a hollow pellet obtained by f1uidized melt pelletization (SEM photo by Pauli and Matthee).
7.5. Variables with influence on the process of melt agglomeration 7. 5. 1. Equipment variables •
Rotary fluidized-bed processor: The use of a rotary fluidized-bed processor instead of a conventional one in creases the shearing forces during agglomeration. Higher shearing forces lead to a stronger densification of the growing agglomerates and to more spherical agglomerates. The advantage of the rotary fluidized-bed granulator for the for mation of pellets was investigated by several authors for the wet granulation (see the previous chapter), but only two publications deal with the melt agglomeration in a rotary processor [65,71].
•
Structure of the rotating friction plate: The friction plate of a rotary processor can have a smooth surface or can be grooved in a longitudinal or crosshatched way. It was shown [65] that this surface structure had a significant influence on the properties of the agglom erates. The grooved plates provided higher shearing forces and therefore the resulting agglomerates had a greater size and showed a more spherical shape.
•
Type and position of the spray nozzle: If the molten binder is sprayed onto the particles in a fluidized bed through a heated spray nozzle, the type, the temperature and the position of the spray nozzle in the granulation chamber may influence the agglomeration process.
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No systematic investigations have been published about this influence con cerning melt agglomeration. 7. 5. 2. Process variables •
Temperature of the fluidizing air: The temperature during agglomeration is one key factor in melt pelletization. The temperature of the product has to be high enough that the binder is sof tened or melted; otherwise no agglomeration will take place. The temperature of a fluidized air processor is usually controlled by the inlet air temperature. This temperature has to be higher than the desired product temperature due to heat loss to the environment. The heat loss is smaller than during wet granulation because no evaporation of solvent takes place. When the product temperature is above the melting point of the binder the influence of temperature is only smalI, regardless of the kind of addition of the binder (as powder particles or in a molten state) [68,72]. Because the viscosity of the molten binder is lower at higher temperatures, the agglomerates may be more deformable, greater and more spherical.
•
Fluidizing air flow: The air flow in a fluidized bed can only be varied within limits. A minimum fluidization velocity is necessary to fluidize the particles and filter clogging will take place at high air flow rates. Vilhelmsen et al. [65] showed that the fluidizing air flow rate within these limits had no significant influence on the properties of agglomerates produced in rotary fluidized-bed melt pelletization.
•
Process time: It is expected that the time during the process when the product temperature is above the melting point of the binder has an influence on the formation of agglomerates. When the particles, nuclei and agglomerates have more time to come into contact with each other it is more likely that particle growth will take place. A longer residence time during the agglomeration phase may additionally cause more densification of the agglomerates and give rise to higher liquid saturation (with the molten binder), which will lead to larger granules. But in vestigations showed that there was only a slight or no influence in the con ventional fluidized bed [69,72]. This can be explained by the relatively low shearing forces. The shearing forces in the rotary fluidized bed were higher and the agglomerate size increased with increasing process time as expected [65].
•
Rotor speed: The rotating disk in a rotary processor together with the fluidizing air flow is responsible for the movement of the particles in the rotary fluidized-bed
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granulator. A higher rotating speed causes higher shearing forces and therefore increased agglomerate size [65]. •
Atomizing air pressure and liquid addition rate: As mentioned above, the molten binder can be sprayed onto the fluidized par ticles. The size of the binder droplets has a major influence on the agglom eration process and agglomerate properties. The size of the droplets depends on the atomizing air pressure, the liquid addition rate and the viscosity of the molten binder which will be discussed later.
7. 5. 3. Formulation variables •
•
•
Amount of binder in the formulation: The influence of the amount of binder in the formulation was investigated for both ways of adding the binder: in a powdered form [65,67,69] and as droplets in the molten state [66,68,72]. In most cases, an increasing amount of binder led to larger agglomerates, which can be explained by a higher liquid saturation during the agglomeration phase. A higher liquid saturation results in more liquid bridges according to the mechanism of coalescence. In one case [67], the agglomerate size was reported to decrease with the increasing amount of binder. This may be explained by the mechanism of immersion when only a slight agglomerate growth (Iayering) occurs after the nucleation phase. The amount of binder can be varied only between limits. If there is only a small amount of binder, less agglomeration will take place and a lot of ungranulated material remains. If there is too much binder in the formulation the formation of large lumps will be the result and fluidization is no longer possible. This is similar to an over-wetted fluidized bed during wet granulation. The upper limit for the amount of binder was found to be around 28% for polyethylene glycol as a binder [65,72]. Size of the binder particles: When the binder is added as a solid material in a powdered form or as flakes its size influences the resulting agglomerate size. An increasing binder size leads to larger agglomerates [67,68]. Immersion was suggested to be the main ag glomeration mechanism in this case. The binder particles acted as seeds. Larger seed particles resulted in larger agglomerates. Layering seemed to be the only growth mechanism after the nucleation phase. Size of the binder spray droplets: The size of the binder droplets when sprayed through a nozzle is influenced by the atomizing air pressure, the liquid addition rate and the viscosity of the molten binder as stated above. The viscosity depends on the kind of binder
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(e.g. the molecular weight in the case of polyethylene glycol) and the temper ature of the melt. If the formulation and the liquid addition rate are given , the atomizing air pressure is the variable to control the droplet size of the sprayed binder. The mechanism of agglomerate formation is primarily dependent on the ratio of the sizes of binder droplets to solid particles. The melt agglomeration of fine powders with sprayed binder droplets often follows the immersion mech anism as nucleation and further agglomerate growth by coalescence between nuclei or agglomerates. The influence of droplet size on the size of the ag glomerates is difficult to interpret. Abberger [68] found larger agglomerates with larger droplets during the nucleation phase but no influence on the granule growth later. Seo et al. [72] reported only Iittle influence of droplet size on agglomerate size. •
Crystallization behaviour of the binder: Kidokoro et al. [82] investigated the crystallization behaviour of polyethylene gly col and found two different crystallization mechanisms. They showed that it is possible to reduce the amount of remaining fine particles after fluidized-bed melt agglomeration by using a polyethylene glycol with a slow crystallization behaviour.
7.6. Process monitoring and control
The monitoring and control of the melt pelletization process as weil as the de termination of the end point of pellet formation during the agglomeration phase are of great importance. But no systematic approach has been made until now. Some possible parameters for process monitoring are •
Product temperature: The product temperature in fluidized-bed melt pelletization is easy to control by the inlet air temperature as mentioned above. This was the only parameter, which was monitored or controlled in previous investigations.
•
Rheological behaviour of the fluidized particles: No systematic investigations have been published concerning the measurement andjor control of the rheological behaviour of the fluidized particles during hot melt agglomeration. It seems to be possible to measure the powder consumption of the rotor motor or the torque of the rotor shaft to get information about the behaviour of the particles in a rotary processor and the status of the process. This has been reported for wet granulation in a rotary processor [1 1 ,1 5].
•
Particle size: N IR-spectroscopic methods may be used to measure the particle size or other product properties on-line or in-line in the fluidized bed in future.
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Direct Pelletization of Pharmaceutical Pellets [44] [45] [46] [47] [48] [49] [50] [51 ] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61 ] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71 ] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81 ] [82]
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J . Vertommen, P . Rombaut, R . Kinget, Int. J . Pharm. 1 46 ( 1 997) 21 . J. Vertommen, B. Jaucot, P. Rombaut, R. Kinget, Pharm. Dev. Technol. 1 ( 1 996) 365. P. Gauthier, J.-M. Aiache, Pharm. Technol. Eur. 1 3 (2001 ) 22. B.N. Chukwumezie, M. Wojcik, P. Malak, F. D'Amico, M.C. Adeyeye, Pharm. Dev. Technol. 9 (2004) 49. B.N. Chukwumezie, M. Wojcik, P. Malak, M . C. Adeyeye, AAPS Pharm. Sci. Tech. 3 (2002) article 2. E.S. Korakianiti, D.M. Rekkas, P.P. Dallas, N.H. Choulis, STP Pharma Sci . 12 (2002) 1 91 . H A Rashid, J . Heinamaki, J . Yliruusi, STP Pharma Sci. 8 ( 1 998) 1 63. H A Rashid, J . Heinamaki, O. Antikainen, J. Yliruusi, Drug Dev. Ind. Pharm. 25 (1 999) 605. S. Watano, S. Yoshinobu, K. Miyanami, T. Murakami, Y. Ito, T.e.a. Kamata, Chem. Pharm. Bull. 43 ( 1 995) 1 2 1 2. S. Watano, S. Yoshinobu, K. Miyanami, T. Murakami , N. Nagami, Y.e.a. Ito, Chem. Pharm. Bull. 43 (1 995) 1 2 1 7. S. Watano, Y. Sato, K. Miyanami, Y. Ito, T. Kamata, N.e.a. Oda, Chem. Pharm. Bull. 43 ( 1 995) 1 224. S. Watano, Y. Sato, K. Miyanami, Chem. Pharm. Bull. 43 ( 1 995) 1 227. S. Watano, H. Takashima, K. Miyanami , Chem. Pharm. Bull. 45 (1 997) 7 1 0. E.S. Korakianiti, D . M . Rekkas, P.P. Dallas, N . H . Choulis, J. Drug Delivery Sci . Technol. 1 4 (2004) 207. P.W.S. Heng, C .v. Liew, L. Gu, I nt. J. Pharm. 241 (2002) 1 73. C .v. Liew, L. Gu, P.W.S. Heng, I nt. J . Pharm. 242 (2002) 345. C.v. Liew, L.S.C. Wan, P.W.S. Heng, STP Pharma Sci. 8 (1 998) 297. J. Vertommen, R. Kinget, J. Applied Ichthyol. 14 ( 1 998) 259. J. Vertommen, R. Kinget, STP Pharma Sci. 6 ( 1 996) 335. L.S.C. Wan, P.W.S. Heng, Y.T.F. Tan , STP Pharma Sci. 5 ( 1 995) 1 28. A. Heinemann, W. Rothe, Verfahren zur Granulierung von pulverförmigen Tablettenmassen. [DT 21 27683]. 1 975. T. Vilhelmsen, J. Kristensen, T. Schaefer, Int. J. Pharm. 275 (2004) 1 4 1 . T. Abberger, A. Seo, T. Schaefer, Int. J. Pharm. 249 (2002) 1 85. A. Pauli, K. Knop, B.C. Lippold, Fluidized bed melt pelletization: Effects of binder particle size, 2004, pp. 3 1 -32. T. Abberger, Pharmazie 56 (2001 ) 949. F . M . Yanze, C. Duru, M. Jacob, Drug Dev. Ind. Pharm. 26 (2000) 1 1 67. M . Kidokoro, Y. Haramiishi, S. Sagasaki, T. Shimizu , Y. Yamamoto, Drug Dev. Ind. Pharm. 28 (2002) 67. J.P. Reo, E.J. Roche, Dry granulation using a fluidized bed. [EP 0 582 380 B 1 ] . 1 996. A. Seo, P. Holm, T. Schaefer, Eur. J . Pharm. Sci. 16 (2002) 95. T. Maejima, T. Osawa, K. Nakajima, M. Kobayashi, Chem. Pharm. Bull. 45 (1 997) 5 1 8. T. Maejima, T. Osawa, K. Nakajima, M. Kobayashi, Chem. Pharm. Bull. 45 (1 997) 1 833. T. Maejima, T. Osawa, K. Nakajima, M. Kobayashi , Chem. Pharm. Bull. 45 ( 1 997) 904. T. Maejima, T. Osawa, K. Nakajima, M. Kobayashi, Chem. Pharm. Bull. 45 (1 997) 1 332. T. Maejima, T. Osawa, K. Nakajima, M. Kobayashi, Chem. Pharm. Bull. 46 ( 1 998) 531 . T. Maejima, M . Kubo, T. Osawa, K. Nakajima, M. Kobayashi, Chem. Pharm. Bull. 46 ( 1 998) 534. T. Abberger, J.O. Henck, Pharmazie 55 (2000) 521 . T. Schaefer, C. Mathiesen, I nt. J. Pharm. 1 39 ( 1 996) 1 39. Y. Haramiishi, Y. Kitazawa, M . Sakai, K. Kataoka, Yakugaku Zasshi-J. Pharm. Soc. Jpn. 1 1 1 ( 1 99 1 ) 5 1 5. M . Kidokoro, K. Sasaki, Y. Haramiishi, N . Matahira, Chem. Pharm. BuH. 51 (2003) 487.
CHAPTER 1 8 S hear-I n d u ced D is pers i o n of Particle Agg lomerates D . L . Feke *
Department of Ghemical Engineering, Gase Western Reserve University, Gleveland, OH, 44106-7217, USA Contents
1. 2. 3. 4.
Introduction Background Experimental Methods Experimental Results 4. 1 . Effect of packing density within the agglomerate 4.2. Effect of applied shear stress on the dispersion process 4.3. Effect of fluid viscosity on the dispersion process 4.4. Infiltration of processing liquids within agglomerates 4.5. Flow of fluid within the agglomerate 4.6. Transition between kinetic regimes 4.7. Dispersion of agglomerates containing binders 4.8. Investigation of the role of shear dynamics on dispersion 5. Gonclusions and synthesis of results - dispersion maps Acknowledgments References
815 818 820 822 822 823 824 825 827 828 834 836 848 851 851
1 . I NTRODUCTION
The breaking of agglomerates or assemblies of small (nanometer to micrometer) particles is frequently encountered in a wide range of industries including material processing, pharmaceuticals, mining, and food technologies. Often, the process ing goal is the dispersion into smaller clusters (or if possible, into its constituent particles) and distribution of these finely divided units throughout the suspending medium. Usually, the quality of the resulting product depends on the degree of dispersion achieved. Hence, a better understanding of the parameters that con trol the dispersion process can lead to advances in processing techniques or the design of efficient mixing equipment.
* Corresponding author. E-mail: [email protected]
G ranulation
Edited by A .D. Salman. M.J. Houns/ow and J. P. K. Seville C 2007 Elsevier s.v. All rights reserved
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This chapter presents a summary of the current state of understanding of agglomerate dispersion phenomena. 80th experimental approaches to elucidat ing the fundamental phenomena and modeling of these phenomena are de scribed. In practice, the dispersion operations described above are commonly achieved by suspending the agglomerates (or individual particles) within fluids and sub jecting them to agitation or shearing motions. In some cases, this step is preceded by some chemical treatment (e.g., intercalation of layered nano-solids, wetting of fine-particle agglomerates) to ease the dispersion. In industrial equipment, the shearing motions are inherently complex, and an understanding of the funda mental phenomena underlying dispersion operations is consequently difficult to glean. In order to surmount this obstacle, it is generally useful to study dispersion in well-defined, controlled-flow fields. In addition, we have found it useful to ob serve and analyze agglomerate dispersion phenomena in studies of single, well characterized spherical agglomerates subjected to hydrodynamic stress. In general, the dispersion of particle agglomerates into liquids is generally thought to consist of three steps, some of which may occur in parallel. A variety of chemical and physical effects govern the outcome of these processes. First, the agglomerates must be incorporated into the liquid medium. Para meters that control the wetting and spreading of the solid particles by the liquid medium, such as the interfacial tension and contact angle, determine the outcome and rate of the incorporation step. In addition, the size and surface texture (morphology) of the individual particles also play roles in the incorporation process. Since they are porous structures, fluid infiltration into agglomerated particles may aiso occur. Agglomerates that are well-wetted by the processing medium may experience extensive fluid infiltration. The presence of such processing fluid within agglomerates can have several effects. For example, the cohesive force between particles can be altered. Also, the additional capillary forces resulting from incorporated liquid may, in some cases, drive a rearrangement of the in ternal structure within the agglomerate. In addition, fluid within the pores of an agglomerate can be driven by external flows, and thereby affect the distribution of hydrodynamic stress on the agglomerate. The second step in particle processing is the application of hydrodynamic shearing motions to break apart the agglomerates and to distribute the fragments throughout the processing media. The process of breaking the agglomerates is known as dispersive mixing, while distributive mixing refers to the delocalization of the fragmented agglomerates throughout the processing medium. The best possible outcome of dispersive mixing operations is the complete breakdown of the agglomerate into its constituent particles. Creation of a completely homo geneous suspension of particles in the processing fluid is the usual goal for distributive mixing operations.
Shear-Induced Dispersion of Particle Agglomerates
817
The third aspect of particle processing has to do with the prevention of the reformation of particle clusters or assemblies once the original agglomerate has been broken. The naturally occurring interparticle forces can act to induce re agglomeration, and so strategies to prevent this from occurring, such as the use of stabilizing additives, which adsorb to and protect particle surfaces, may be employed. In this chapter, we focus attention solely on dispersive-mixing phenomena. Our goal is to provide fundamental insight from experimental studies that enables predictive modeling of dispersion behavior. In addition, a more thorough under standing of dispersion processing could enable the better design of practical mixing equipment, or interfacial engineering strategies for the particle agglom erates that could lead to a better control over dispersion operations. Many factors affect the outcome and rate of dispersive mixing. These include material properties such as the structure configuration and mechanical properties (e.g., cohesivity) of the agglomerates, the viscosity of the processing fluid and the various interfacial phenomena that govern the interaction between the processing fluid and particles. In addition, processing parameters such as flow-field geometry and shear rate history are important [1]. Our general approach is to study the response of individual, well-characterized agglomerates to controlled-flow fields. Agglomerate characteristics, such as the size, shape, and composition of the constituent particles, the size and the packing morphology within the agglomerate, and the presence (or absence) of infiltrated liquid within the agglomerate can be systematically controlled to elucidate differ ent aspects of the dispersion phenomena. Selection of the processing fluid de termines the wetting and infiltration interactions that govern the dispersion phenomena. Steady or time-varying flows, of controlled-strain rate are used to examine different dispersion regimes. In such experiments, we observe the crit ical shear stresses (at which dispersion commences), and analyze the relation ship between processing conditions and the modes and rate of dispersion, and the characteristics of the fragments produces by the dispersion process. Sub sequently, the results are interpreted in terms of the properties of agglomerate andjor fluid as weil as the processing history.
2. BACKGRO U N D
The manner and rate in which agglomerates disperse depends on the compe tition between those forces responsible for the cohesivity or rigidity of the ag glomerate and the hydrodynamic forces driving its fragmentation. The cohesive strength of agglomerates originates from three sourees: ( 1 ) interparticle forces such as van der Waals attractions and electrostatic effects between the solids; (2)
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interaction forces resulting from adsorbed surfactants or other secondary species such as binders; and (3) capillary forces from any liquid bridges present from infiltrated-processing liquid. Given detailed information (or assumptions) on the packing structure within the agglomerate, it is possible to quantify or predict the strength of an agglomerate. Most of these models correlate the tensile strength of the agglomerate to some lumped measure of the interparticle forces such as an effective Hamaker constant, which reflects the combination of forces that act within the agglomerate. The hydrodynamic forces, which act to disrupt the ag glomerate, depend on the details of the local flow field. Bulk fluid motions produce hydrodynamic stress on the periphery of the agglomerate. Also, additional shear stresses can act within the agglomerate structure since agglomerates are per meable to fluid flow, and for highly porous agglomerates, these internal stresses can significantly affect the dispersion process. Processing liquid, drawn into agglomerates through the capillary forces, can affect both the interparticle forces and the packing structure within the agglomerate itself. The complex interaction between all of these effects determines the rate and mechanism by which ag glomerates disperse. Several studies have been undertaken to characterize the dispersion process, to understand the various mechanisms and the principal factors affecting the outcome of dispersion [2-4]. For dry agglomerates (i.e., those in which no processing fluid is contained within the agglomerate structure), there are two c1assical dispersion modes; rupture and erosion [5,6]. Rupture occurs in those cases wherein the ratio of applied hydrodynamic stress to agglomerate cohesivity is large, and typically produces large fragments in a very short while following the application of shear. Erosion occurs at lower levels of stress, and typically pro duces smaller fragments over a longer period of shearing. Figure 1 contains images of the dispersion of silica agglomerates sheared within silicone oi!. Both dispersion modes are illustrated. These two c1assical-dispersion modes are cat egorized as cohesive-failure modes since they both result when cohesive forces between the fragment and neighboring particles are overcome. Also shown is the case of a different dispersion mode known as adhesive failure, which occurs when the wetted periphery of an agglomerate peels away from the core of the agglomerate. We have shown that this mode can occur under relatively low-shear stress conditions. Critical hydrodynamic conditions for dispersion are based, to a first approx imation, on a comparison of hydrodynamic forces exerted by the flow field and mechanical strength of the agglomerate. Manas-Zloczower et 81. [7,8] found that dispersion in simple shear flow could be correlated to a dimensionless quantity expressing the ratio of hydrodynamic stress and cohesive strength. Rwei et 81. [5] used the same concept to explain the extent of rupture observed in dispersion processes of carbon-black agglomerates of a range of packing density. Ottino and co-authors [9,1 0] labeled this ratio as the fragmentation number, Fa, and
Shear-Induced Dispersion of Particle Agglomerates
81 9
Dispersion Examples
Fig. 1 . Images showing the dispersion behavior of silica agglomerates sheared within silicone oil within the OSD device. The classical dispersion modes of rupture (occurring when the shear stress greatly exceed the cohesivity) or erosion (which occurs when the shear stress and the agglomerate cohesivity are of the same order of magnitude) are shown. Also shown is the mode of adhesive failure in which relatively large fragments peel from the surface of agglomerates under conditions of relatively low-shear stress.
related its value to the dispersion regime expected; erosion occurs at low fragmentation number, when hydrodynamic stresses are close to the cohesive strength while, at higher values of Fa, the dispersion process leads to rupture. During a practical dispersive-mixing operation, agglomerates may exhibit a combination of these dispersion mechanisms. As agglomerates are convected through mixing equipment, they may experience different flow conditions, and hence different values of Fa apply at different positions in the processing equip me nt. In addition, since the mechanical properties of agglomerates are often not homogeneous and the cohesivity of fragments may be different from that of the parent agglomerate, the value of Fa may change as dispersion proceeds, even when uniform stress conditions exists within the processing equipment. Kao and Mason [1 1 ] quantitatively related the initial stage of the erosion process of cohesionless agglomerates with a dimensionless quantity, yf indicating the effect of shear-rate magnitude on the dispersion process. Here y is the shear rate. Lee ef al. [1 2] and Rwei ef al. [6] used a similar model to analyze dispersion results obtained with titania and carbon black agglomerates, respectively. They found that for cohesive agglomerates the erosion rate depends on the fragmentation
820
D. L. Feke
number, and showed that both shear rate and shear stress play a fundamental role in dispersion kinetics. Lee et 81. [1 3] showed correlations between the erosion kinetics (and the consequent fragment size distribution) and the porosity of titania agglomerates. Yamada et 81. [14], studying the influence of matrix infiltration on the dispersibility of carbon black agglomerates, clearly distinguished different erosion regimes depending on the value of a dimensionless quantity that char acterizes the extent of fluid infiltration within the agglomerate. Levresse et 81. [1 5] studied this effect in more detail and analyzed the influence of fluid infiltration on the hydrodynamic stresses transmitted to an agglomerate with incorporated processing fluid. Bohin et 81. [ 1 6] developed a kinetic model for the erosion proc ess of sparse agglomerates, assuming the erosion rate to be proportional to the excess of hydrodynamic force to the cohesive force of the agglomerate. In the sections to follow, we elaborate on the experimental observations and modeling approaches found useful to quantify the dispersion phenomena.
3. EXPERIMENTAL METHODS
We have found it advantageous to use two types of tools in our experimental studies of dispersion. Figure 2 shows a schematic of the cone-and-plate (ep) shearing device in which single agglomerates suspended in a processing fluid can be subjected to a constant simple-shear flow. A camera, recording, and image analysis system allows monitoring of the dispersion process as a function of shearing conditions. Figure 3 shows a schematic of the oscillatory shear device (OSD), which employs a parallel-plate geometry. In this case, the rotation of the motor is converted into an oSciliatory translation of the plate. The dispersion of a single agglomerate placed in the gap between the moving plate and the station ary lower surface can be monitored with the video recording and analysis system. Operating variables include the rotation speed of the motor (which governs the Monitor
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Erosion Kinetics
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oscillation frequeney), the amplitude of the plate oscillation, and the gap between the moving and fixed surface (all of which determines the shear rate). Time resolved images of the dispersion of the agglomerates are recorded using a digital camera positioned in front of the transparent front wall of the chamber. Using these experimental tools, we have been able to observe dispersion modes, quantify dispersion kinetics as a function of processing conditions, and identify system parameters and processing histories that lead to dispersion. We can also study the effect of incorporated binder on the mechanieal behavior of agglomerates or of an interacting particle pair, and correlate this information with dispersion results. For the erosion mode, we have found it convenient to quantify dispersion kine ties by monitoring the change in size of the parent agglomerate as fragments are removed from its periphery. Typically, for applied shear fields that have non-zero vorticity, the rotational motion of the agglomerate helps it to retain spherical symmetry as dispersion proeeeds. Figure 4 depicts typieal dispersion kinetics results. The fractional reduction is shown in the size of the parent agglomerate as a function of shearing time. In this particular example, the agglomerate initially
822
D. L. Feke
disperses at a constant rate, but eventually dispersion slows and a relatively stable structure (approximately 40% of the original size of the agglomerate) re mains even upon prolonged shearing. The slopes of asymptotes to the short- and long-time data provide values of the fast- and slow-dispersion rate constants.
4. EXPERIMENTAL RE5ULT5
I n this section, experimental results that illustrate the range of erosion behaviors and the factors that affect erosion kinetics are presented. 4.1 . Effect of packing density within the agglomerate
Figure 5 shows results of shearing agglomerates of carbon black in silicone oil (polydimethyl siloxane, or PDMS) at a fixed shear rate. The agglomerates differ only slightly in terms of the volume fraction of solids within the agglomerate. Note the qualitative difference between the dispersion behaviors of the two types of agglomerates. The lower density agglomerate disperses in a relatively rapid way, and if shearing was to continue, the agglomerate would have eroded to com pletion (fractional-size reduction approaching 1 00%). In contrast, the higher den sity agglomerate disperses more slowly at the initial stages, but then dispersion 0.5
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Shearing time, mi n Fig. 5. Erosion kinetics for agglomerates of carbon black (Cabot Monarch 900) sheared i n P D M S fluid (30,000 cS) a t a shear rate o f 56.7 S- 1 . Results for two agglomerates of slightly different packing density are shown [5,6].
Shear-Induced Dispersion of Particle Agglomerates
823
stops when only about 7% of the agglomerate has been removed. Clearly, the packing density has a profound effect on the rate and ultimate outcome of the dispersion process. Typically, the higher the packing density in an agglomerate, the larger is its cohesivity. This is primarily due to the increased number of particle-particle contacts within the agglomerate, each of which contributes to the overall cohesivity. It is expected that in any batch of agglomerates used in a practical process, there will be some variation in the packing density between individual agglom erates. Particle scientist should be aware that such minor variations in density can lead to very different dispersion outcomes.
4.2. Effect of applied shear stress on the dispersion process
The pronounced effect of shear stress on the outcome of the dispersion process can be exemplified by the results shown in Fig. 6. Here, the dispersion kinetics of agglomerates of fumed silica (2.6 mm diameter and packing density of 0. 1 4 gjcm3) sheared in PDMS fluid (1 0.2 Pa s) are displayed. As in the previous plots, the fractional reduction in the size of the parent agglomerate is presented as a function of the shearing time. The plot shows that the initial rate of dispersion (given by the slope of the dispersion kinetic curve) increases with increasing shear rate. Note that two 1. 0
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0 23.3 S- I ; D 3 7.4 s-\ A 102.3 S-I ; -I -I -I -I o 1 10 S ; * 1 1 5.4 S ; • 124.3 S ; • 1 66.6 S Fig. 6. Dispersion kinetics for silica agglomerates (2.6 mm diameter, 0 . 1 4 g/cm3) are shown as a function of applied shear rate. The suspending fluid is 1 0.2 Pa s PDMS [ 1 6] .
O. L. Feke
824
distinct dispersion kinetic behaviors are observed. For an applied shear rate below a certain value (approximately 1 05 S - 1 in this example), the agglomerate initially disperses, but then dispersion stops. In these cases, note that the size of residual core decreases with increasing shear rate. For shear rates about the critical value, the agglomerate disperses to completion in the matter of a few seconds. For extremely high-shear rates (higher than those presented in Fig. 6), dispersion would go to completion very rapidly, which is a characteristic of the rupture mode of dispersion.
4.3. Effect of fluid viscosity on the dispersion process
As discussed above, the simplest models for dispersion behavior identify the ratio of the hydrodynamic stress to the cohesive strength of the agglomerate as the parameter that controls the dispersion process. For the case of Newtonian fluids, hydrodynamic stress is the product of shear rate and fluid viscosity. Thus, for dispersion experiments performed in different liquids, equivalent hydrodynamic stress profiles can be developed by compensating for differences in viscosity by adjusting the applied shear rate. Figure 7 shows a comparison of the dispersion results for carbon black ag glomerates of various packing densities sheared in silicone oil [1 7] . The second set of experiments was done using a fluid of twice the viscosity as that of the first set, but with one-half of the applied shear rate. Thus, the shear-stress profile is equivalent in the two cases. (Note that under the conditions of these experiments, the PDMS fluid behaves in the Newtonian regime.) Kinetics of erosion
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o
10
10 ShO.vW"O 'imo, "Mn
Fig. 7. Erosion kinetics for agglomerates of carbon black (Ca bot Monarch 900) sheared in 30,000 cS POMS at a shear rate of 56. 7 s- 1 or 60,000 cS POMS at 28.3 s- 1 . Results for agglomerates of different packing density are shown [ 1 7] .
Shear-Induced Dispersion of Particle Agglomerates
825
Consistent with the results shown in Fig. 5, agglomerates with lower packing density exhibit more rapid dispersion. Also, for agglomerates with relatively large packing density, dispersion ceases after some period of shearing. However, note the two curves identified by the arrows. These particular experiments involve agglomerates of identical packing density (and therefore identical cohesivity). Even though the hydrodynamic stress is identical in the two cases, the experi ment performed with the lower viscosity fluid (and higher shear rate) shows a qualitatively different dispersion result than its counterpart. In the case of the higher viscosity fluid, erosion can proceed to completion whereas it ceases in the case of the lower viscosity fluid. Clearly, under conditions of equivalent agglomerates and equivalent hydro dynamic stress, fluid viscosity plays a significant role in the dispersion outcome. Later, it will be shown that the infiltration of fluid within the agglomerate during dispersion (which occurs to a greater extent for the case of the lower viscosity fluid) also affect the dispersion process. 4.4. I nfiltration of processing liquids within agglomerates
Agglomerates are porous structures, and thus are subject to infiltration by the processing liquid. Figure 8 presents images that illustrate the phenomena. Shown
High density
time
-----
Low density
Fig. 8. I mages showing the process of infiltration of processing liquid (PDMS) into ag glomerates of fumed silica [ 1 8] .
826
D. L. Feke
are millimeter-scale silica agglomerates submerged within silicone oil. Since the refractive indices of silica and silicone oil are closely matched, it is possible to visualize directly the progress of infiltration. Since silica is favorabley wetted by silicone oil, infiltration readily occurs. The top pair of images shows the response of relatively high-density agglo merates at two immersion times. Note that the infiltration proceeds in a spher ically symmetric fashion, and that infiltration occurs at a faster rate for the lower density agglomerates. Analysis of the infiltration kinetics into powder beds is traditionally done using a Washburn analysis in which the driving force for infiltration (capillary pressure) is balanced against the viscous resistance to f10w within the pores. Under the con dition of a uniformly packed bed, and no influence of gravity, the Washburn analysis predicts that the infiltration depth is proportional to the half-power of the contact time. The same basic phenomenon applies to the infiltration within spherical ag glomerates, but the spherical geometry does influence the overall kinetic rates. In this case, the infiltration rate is given by [ 1 9] (1 ) where a is the radius of the agglomerate, R the radius of the uninfiltrated portion of the core, kw the permeability of the wetted region, Pe the capillary pressure driving infiltration, J.l the fluid viscosity, and t the infiltration time. The parameter C is an infiltration rate constant. This expression, which can be validated through experimental trials, can be used to predict the extent of infiltration within spherical agglomerates provided that the appropriate physical parameters can be obtained. One method for obtaining the infiltration kinetics within agglomerates is to measure the change in sedimentation rate of a single agglomerate. As fluid in filtration occurs, the effective density of the agglomerate (which includes the solid particles plus the incorporated fluid) will change. Thus, the sedimentation rate can be interpreted in terms of the extent of fluid infiltration. Indeed, our experiments confirm that the left-hand side of equation ( 1 ) increases linearly with infiltration time. The capillary pressure driving infiltration is proportional to YtvC0S 8 (where Ytv is the interfacial tension of the liquid and 8 the contact angle) and the physical details of the pore structure within the agglomerate. Thus, the infiltration rate constant can be viewed as containing two contributions. One is the contribution of the fluid (YtvCOS 8/11) and the second is the geometric details of the porous ag glomerate structure. For similar agglomerates, the structural details will be the same, and thus plots of C vs. the collection of fluid properties (Ytvcos 8/11) should be linear. Figure 9 shows typical results obtained from measurements of the infiltration of a variety of fluids within agglomerates of carbon black [20]. Note that
827
Shear-Induced Dispersion of Particle Agglomerates
0.01 ,------,
x PDMS 48000cS (high)
PDMS 48000cS (low) PBD 48000cS (high) PBD 48000cS (Iow) :l< PDMS 1 6400cS (high) PDMS 1 6400cS (low) + SB 1 6400cS (high) SB 1 6400cS (Iow) /::,. PDMS 4700cS (high) PDMS 4700cS (Iow) o PDMS 3400cS (high) PDMS 3400cS (Iow) o EP 4700cS (high) EP 4700cS (Iow) • PBD 3400cS (high) PBD 3400cS (low) x
o
0.008
o
•
_ �
I
0.006
•
'e
ü
+
0.004 0.002
o
A
D
:i: +
•
O +--.--,--�-�-� 12 10 6 8 4 o 2
•
YLvcos9//1 (mm/s) Fig. 9. Plot of the infiltration rate constant C for carbon black agglomerates as a function of fluid properties for a variety of liquids of different viscosity [20]. Note the linear relationship over a wide range of conditions. Key: PDMS - polydimethyl siloxane; PBD - poly butadiene; SB - styrene butadience; and EP - ethylene-propylene copolymer.
the linear relationship between the infiltration-rate constant and the collection of liquid properties strongly suggests that this model correctly captures infiltration kinetics. 4.5. F low of fluid within the agglomerate
The depth of fluid infiltration within the periphery of the agglomerate (b') provides one of two length scales relevant to the influence of the fluid on the dispersion process. Obviously, b' is a function of immersion time and the amount of material stripped off of the agglomerate through the erosion process. The second length scale comes from the notion that, since the agglomerate is a permeable structure, motions in the external fluid can drive fluid motion within the agglomerate itself. The characteristic depth through which fluid drains along the periphery of the agglomerate, denoted as L p , is taken as k;'}2. Agglomerate porosity (and hence L p) decreases with increasing packing density within the agglomerates. Values of L p can be inferred from measurements of the sedimentation speed of agglomerates that have been allowed to fully soak with processing fluids. Devi ation in the sedimentation speed from that provided by the Stokes settling velocity can be attributed to reduced hydrodynamic resistance of the fall of the agglo merate due to its permeability. Figure 1 0 shows typical results for carbon black
828
D. L. Feke 1 20 A
1 00
80 :1. ci. 60
-l
40 · · A
20 o · 0.25
�
��
0.45 0.35 Agglomerate density. gfcm3
•
Monarch 900 in POMS 30,000eS
A
Monarch 880 in POMS 30.000cS
o
Monarch 900 in POMS 60,000cS
x
Monarch 900 in PBD 3400cS
0.55
Fig. 1 0 . Typical values of Lp as a function of packing density for a variety of agglomerates of carbon black tested in various fluids (1 7].
agglomerates as a function of packing density within the agglomerate. Values of Lp on the order of tens of micrometers are typicaL
4.6. Transition between kinetic reg i mes
For a given agglomerate, Lp is fixed, and (5' can be determined as a function of the duration that the agglomerate has been in contact with the processing fluid. Plots of (5'/Lp reveal some interesting features. Figure 1 1 depicts typical results for carbon black agglomerates of various packing densities sheared in PDMSs of two different viscosities. I n some of the dispersion experiments, erosion proceeded only via a fast ero sion regime to complete dispersion. In these cases, the corresponding values of (5'/Lp always remained below a value of about 4. In other cases, the dispersion kinetics were seen to transition from a fast to a slow erosion regime. In all cases, the transition occurs whenever the value of (5'JLp was approximately 4-5. In no case did fast erosion occur when (5'/Lp was greater than about 5. Other results for carbon black agglomerates (not shown here) were consistent with these results. This result can be interpreted to mean that there exists a critical value of (5'JLp that demarcates the fast from the slow-erosion regime. (Note that the numerical value of this critical ratio will be different for other agglomerate-liquid systems.) As long as (5' is small enough , agglomerates can disperse via the fast rate. Experi mental observations have shown that during this fast-erosion process, relatively large fragments, with characteristic size comparable to (5', will be produced. Once
829
Shear-Induced Dispersion of Particle Agglomerates 1 5 �------� (b) .10)
10
o
o
o
o
'"
P =0.300
• P = 0. 3 3 5 0 p =0.344
h
1
5
10
T�====�------� (b) • P = 0. 3 3 5 P =0 . 3 44
o
,. p = 0 .378
,. p 0 1 78 =
5
o
0
o
=
.:
0 3%
,.
.
5 o
00 0 0
o �---+----+---�--� 40 20 30 10 o Shearing
time, min
O +-----+----..,I---t--I 30 10 20 40 o Shearing time, min
Fig. 1 1 . Plots of (j'/Lp as a function of shearing time for carbon black agglomerates of different packing density. The graph on the left applies for experiments performed in silicone oil of 30,000 cSt viscosity, while that on the right represents experiments using 60,000 cSt oil. I n all cases, data points appearing below the shaded area (4 < (j'/Lp < 5) are within the fast erosion regime, while the data points above this area correspond to the slow erosion regime [20] .
025 02
•
3 minutes soaking
j.
10 minutes soaking
X
60 minutes soa X Xx X X
:l
0 0.15
� 0.1
0.05
kfg x
X
X X
.. .. ! " .. ..••..• .. • • •
j.
•
•
0 0
200
400 Time (seconds)
600
800
0.45 • .. 300 minutes •• • 0.4 .. .. soaking time 0.35 .. .. .. .. .. .. .. 0.3 � • 390 minutes soaking time � 0.25 ;: • fully infiltrated ;r 0.2 0.15 agglomerate 0.1 0.05 • 0 800 600 400 200 ·0.05 Time (seconds)
Fig. 1 2. Dispersion kinetics of silica agglomerates sheared in silicone oil. The agglom erates were allowed to soak in the processing fluid for the various times listed prior to the application of shear [1 8].
the erosion process transitions to the slow-erosion regime, relatively small (or no) fragments are produced. When (jJ is small enough compared to Lp , the interface between the wetted and dry portions of the agglomerate is dose enough to the agglomerate periphery to be directly affected by the external f10w field. When (jJ becomes large, the whole of the wetted region can have a cohesivity that is enhanced by the presence of the interstitial liquid, thereby making it more resistant to produce large fragments. Additional evidence that fluid infiltration influences dispersion phenomena is provided in Fig. 12 above. The results of those experiments in which agglomerates
830
D. L. Feke
of fumed silica were sheared within high-viscosity silicone oil are shown here. In this case, the magnitude of the applied stress is of the same order as (but greater than) the cohesive strength of the agglomerate. Prior to the application of shear, the agglomerates were allowed to soak within the oil for the various times shown. Longer soaking time results in greater fluid infiltration. Note that for the relatively short soaking times (the graph on the top within Fig. 1 2), the duration of the fast erosion period increases with increased soaking time. This trend continues for extended presoaking times. However, beyond a certain presoaking time, the enhancement in dispersion kinetics reverses. For the particular example shown, for a presoak time of 390 min (the boUom graph within Fig. 1 2), the onset of dispersion is delayed for a several minutes (during which shear is applied), but then commences at a high rate. For even longer presoak times during which the agglomerate becomes fully infiltrated, no significant dis persion is seen at the same level of applied stress. Dispersion could be initiated, however, if higher stresses were applied. Note that in all of the experiments in which dispersion occurs, there is a transi tion to the slow-erosion regime, which for each of the trials shown in Fig. 1 2, the amount of material removed during the initial period of the fast-erosion kinetics can be determined as the intercept of the asymptote of the slow-kinetic regime with the vertical axis. Figure 1 3 shows a plot of the initial amount of material removed as a function of presoak time. Also shown in Fig. 1 3 is a curve that represents a plot of the expected infiltration depth ö normalized against the radius of the agglomerate as a function of the presoak time. Note that this curve is a pure prediction based on independently measured parameters as detailed by equation ( 1 ) above.
0 ...
iU Gi c -
0 ...
1: I
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Initial Erosion (Experimental)
•
--
0
200
400
600
800
lheoretical (Infiltration)
1 000
1 200
1 400
Infiltration Time (minutes) Fig. 1 3. Comparison of the amount of material removed during the initial erosion period and the depth of infiltration as a function of the time of presoaking prior to the application of shear for silica agglomerates in silicone oil. The results here are derived from the exper imental data shown in Fig. 1 2 [ 1 8].
831
Shear-lnduced Dispersion of Particle Agglomerates
The correspondence between the dispersion data and the infiltration depth is excellent. This result suggests that the initial fast erosion period is one in which the wetted periphery of the agglomerate is removed The two data points which fall off the curve represent the situation in which the depth of fluid infiltration has exceeded the critical value described above. The relationship between erosion kinetics and fluid infiltration suggest that there may be an optimum schedule of soaking that can be pursued to be nefit dispersion. To illustrate this possibility, please refer to the results shown in Fig. 14. Here, the dispersion behavior of agglomerates of fumed silica sheared within silicone oil were investigated further. In this case, periods of shearing approximately 1 min long were alternated with soaking periods of approximately 7 min duration. The symbols within Fig. 14 provide information on the size of the remaining parent agglomerate. Upon commencement of the shear, a relatively fast erosion period was observed. Had shear been continued beyond the end of these 1 min intervals, a transition to a slow-erosion regime would have occurred. The set of stepped curved in Fig. 1 3 represent the prediction of the depth of infiltration expected during each soaking period. In order to make this prediction for the second and subsequent steps (the dashed curves), it was assumed that the period of shearing successfully removed all of the periphery that had been wetted during the preceding soaking period. Thus, the residual core was presumed to be devoid of processing fluid, which allows infiltration to proceed rapidly in the initial portion of the soaking period.
0.25 0.2 0 0. 1 5 ;;0 'C c 0.1 ca 0 ...
'? 0.05 ...
,....
0 500
1 000
1 500
2000
2
0
-0.05
Time (seconds) Fig. 1 4. Dispersion results for agglomerates of fumed silica sheared in silicone oil. Ag glomerates were subjected to alternating periods of rest (�7 min) and shear (�1 min). The curves represent the independent prediction of the depth of fluid i nfiltration expected [1 8] .
D. L. Feke
832
Note that the amount of material removed during the fast erosion period weil matches the amount of infiltration that occurs during each period of soaking. This result corroborates the important role of fluid infiltration in determining dispersion kinetics, and points out that a carefully designed processing schedule involving periods of no shear may result in a better dispersion outcome than continuous shearing. Figure 1 5 provides a schematic that depicts the influence of infiltration on the dispersion process. For some agglomerate-liquid systems, the infiltration process can actually reduce the magnitude of the stress necessary to induce dispersion in comparison to the cohesive strength of the dry agglomerate. For example, con sider the case in which the capillary force associated with the wetting of the agglomerate by the processing fluid exceeds the cohesive forces binding the agglomerate together. Thus, the force that acts to dray the processing fluid into the agglomerate also pulls the particles within the periphery of the agglomerate away from its core. If the cohesivity of the agglomerate is low, then structural rearrangement will occur on account of the forces generated during the infiltration process. Thus, the interface between the wet periphery and dry core of the agglomerate is weakened. In such cases, the application of hydrodynamic shear can peel away the wetted peripheral region from the dry agglomerate core. In so me of our work involving the dispersion of fumed silica agglomerates in silicone oil we have found that disper sion can be initiated at applied stresses substantially below the strength of the fully infiltrated agglomerate. In this case, it was observed that the fragments produced have a thickness that it comparable to the depth of the fluid that infiltrates prior to the application of shear, as is depicted in Fig. 1 5. A comparison of the capillary Infiltrated Region -rearrangement of powder structure Dry
Core
----.>.,..�4.
Wet Dry Interface
o
Adhesive failure at wet-dry interface
Fig. 1 5 . Schematic representation of the formation of a structural discontinuity within an agglomerate at the wet-dry interface due to capillary pressure driven infiltration. Such a weakened interface leads to another mechanism of agglomerate dispersion known as adhesive failure [ 1 8].
Shear-Induced Dispersion of Particle Agglomerates
833
pressure in this case (�350 kPa) to the shear strength of the agglomerate (�1 50 kPa) confirms that the agglomerate structure may undergo changes as a result of fluid infiltration. The notion that the wetted periphery of the agglomerate is detached from the dry residual core leads to this type of dispersion being con sidered to result from an adhesive failure at the wet-dry interface [1 8]. The observation that the stress required to initiate adhesive failure can be lower than the wet strength of the agglomerate is rationalized in terms of the schematic representation as in Fig. 1 6. The upper portion of a partially infiltrated agglomerate is shown. In the case of a planar-fracture surface that passes through the wetted-peripheral region, both the hydrodynamic force (wh ich is proportional to the applied hydrodynamic stress and the surface area of the spherical cap which subtends the fragment) and the cohesive force (which is proportional to the cohesive strength and the area of the fracture plane) are both proportional to the square of the agglomerate radius. Thus condition for the onset of dispersion can be based on a comparison of the hydrodynamic stress to the cohesive strength of the agglomerate, and is independent of the position of the fracture plane provided that it passes only through the wetted periphery. However, in the case of fracture sUrfaces which pass along the wet-dry in terface (wh ich can be weaker than the cohesive strength of the wetted region), the situation is more complex. If, for example, the wet-dry interface is presumed to have zero strength, then the full burden of resisting the hydrodynamic force falls to the portions of the fracture plane that pass through the wetted periphery. Since the area that provides resistance to dispersion is sm aller than the corre sponding area of a planar fracture surface, the stress on this area is effectively amplified by this geometrie effecl. Thus, the dispersion process can appear to
(a) (b) (e)
Fig. 1 6. Depiction of the upper half of a partially infiltrated agglomerate. Various potential fracture surfaces (a-c) are shown. In the case of plane a, the applied hydrodynamic force would need to overcome the wet cohesive strength along plane 8. Fracture surfaces b and c include portions of the wet-dry interface, which are weak compared to the wet-strength of the agglomerate. In these cases, the portions of the fracture surface, which cut across the wetted periphery bear a disproportionate amount of the hydrodynamic force [20].
834
D. L. Feke
6 �------� 5
ö/Ro=0. 1
__-
4 � u c o
E
� 3 ca
� 2
0.2
(/)
�
O +------.---.--� o 0.2 0.6 0.8 0.4
Fig. 1 7. Stress amplification within the load-bearing portions of the agglomerate, assuming that the strength of the wet-dry interface is zero. Shown is the stress amplification factor as a function of the fragment size (the fragment area being the surface area of the spherical cap subtended by the fragment) and depth of fluid infiltration within the agglomerates. Note that substantial stress amplification can occur, especially for small depths of fluid i nfiltration [21 ] .
initiate at hydrodynamic stress levels that are lower than those that would be required to initiate dispersion across a planar fracture surface wholly contained within the wetted periphery. The amount of stress amplification within the portions of the agglomerate that bear the hydrodynamic force can be computed, provided that some basic as sumptions are made. In the most extreme case, one can assume that the wet-dry interface has zero strength, and thus does not contribute any resistance to the applied hydrodynamic force. Figure 1 7 depicts the resulting stress amplification within the portions of the wetted periphery that bear the hydrodynamic force [21 ] . The stress amplification is shown (the ratio of the actual stress to the stress that would be present if a planar fracture surface were present) as a function of fragment size and depth of fluid infiltration. Dispersion can be anticipated when the hydrodynamic stress is equal to the stress required to disperse a fully in filtrated agglomerate divided by the stress amplification factor. Note that for small infiltration depths, the thickness of the region withstanding the hydrodynamic force is smalI, and thus the effective stress amplification can be high.
4.7. Dispersion of agglomerates containing binders
In some cases, agglomerates are prepared in a manner that incorporates ad ditives (binders) that aid both the production of the agglomerates and its handling
Shear-Induced Dispersion of Particle Agglomerates
835
properties. The presence of interstitial liquid is expected to affect two things. First, the rate at which external processing fluid infiltrates within the agglomerate is expected to be affected by the presence of interstitial liquids. Binders that are chemicaily incompatible with the external fluid will retard infiltration, whereas compatible interstitial liquids may enhance infiltration. Second, the presence of interstitial liquids can augment the cohesivity of the agglomerate via liquid ridges. The higher the concentration of the interstitial liquid, the greater the enhancement of cohesivity that can be expected. Figure 1 8 shows dispersion results for CaC03 agglomerates (65% porosity) sheared in at a constant applied stress of 2 1 50 Pa. Note that both the binder liquid and shearing fluid are both PDMS liquids, and thus are chemicaily com patible. Note that the general trend is that the higher the concentration of incor porated liquid, the smailer is the ultimate dispersion level, which is consistent with the notion that additional liquid bridges result from the incorporated liquid. In contrast, Fig. 19 shows the result for identical CaC03 agglomerates sheared under identical conditions, but using glycerol as the interstitial fluid. Note that at low concentrations of glycerol, the erosion rate and ultimate level of erosion is higher than that for neat CaC03 agglomerates (no interstitial liquids present). However, for higher concentrations of glycerol, the erosion kinetics deciine below that for the neat agglomerates. The interpretation of these results can be based on the coun teracting effects provided by the incorporated glycerol. At low-glycerol concentra tions, there are not enough liquid bridges to lead to a significant enhancement of the agglomerate cohesivity. However, since glycerol is essentiaily insoluble with the background PDMS, external fluid infiltration is retarded, and a prolonged fast dispersion period is seen. However, at higher glycerol concentrations, the en hanced cohesivity of the agglomerate leads to lower overail dispersion rates. In Fig. 20 a direct comparison of experimental results is shown, all of which are obtained using the same type of CaC0 3 agglomerates (65% porosity) sheared at 0.25 0.2
;p 0. 1 5
�
�
0.1
0 �
..,
• ..,
0
•
10
... •
• 0
0.05
�
0
20 30 Time (mln)
0 0% . 0.1 % "' 1 .0% . 20% 0 1 0%
40
50
Fig. 1 8. Dispersion kinetics for CaC03 agglomerates with various concentrations of 1 0 cSt PDMS as interstitial liquid, sheared in 60,000 cSt PDMS [22].
836
D. L. Feke
0.5 0045 004 0.35
..
0.3 cf ct 0.25 0.2
..
, ....
•
0.15 0.1
0 X
!!!!!
0.05
10
..
..
•
•
.. 1 .0 wt%
•
•
0
0
0
0
X
X
X
i
X
20
30
I!!
�
0.1 wt% O wt% 5.0 wt% 1 0 wt% 20 wt%
40
50
Time (min) Fig. 1 9. Dispersion kinetics for CaC0 3 agglomerates with various concentrations of glyc erol as interstitial liquid, sheared i n 60,000 cSt PDMS [22].
0.5
l
I t: o
O.4 0.3
/11
�E � Ci
0.2 0.1
IF=======:;----, • Polyester Resin
PDMS .. Glycerol . . - . . No additive •
Ä . . _ _ . _ _ . .. . _ _ . _ _ . - . . •
_
. . _. .
_ _
.
•
_ _
.__. _-
•
Ä L. O �-------.----.I�: -� 0. 1 0.01 10 1 00 Concentratlon of Additive (wt %)
Fig. 20. Comparison of the effects of varying amounts of interstitial liquids that exhibit a range of compatibility with the background processing liquid (PDMS). All results pertain to CaC03 agglomerates (65% porosity) sheared at 21 50 Pa [22].
2 1 50 Pa. Significant variations in the ultimate extent of dispersion are seen. Clearly, the compatibility between the binder additive and the processing fluid strongly influences dispersion kinetics.
4.8. I nvestigation of the rote of shear dynamics on dispersion
There are significant differences in the results of dispersion experiments performed under steady shear and unsteady shear conditions, even when the hydrodynamic
Shear-Induced Dispersion of Particle Agglomerates
837 • OSD mean 600
0.4 0.35 0.3
� S 0.2 0:: c
�
0.25
0. 1 5 0. 1 0.05
• C&P
(jlllcan = 600 (jma. = 900 •
o OSD max 600
(j = 600
(jl11can = 400 (jmax = 600
•
o
1 .5
0.5
o
o
o
2
2.5
time (min)
Fig. 21 . Comparison of dispersion results for precipitated silica agglomerates in SBR. Data for the fractional reduction in size as a function of shearing time are shown for a cone and-plate (CP) experiment as weil as oscillatory flow experiments in which the mean or maximum stress matches that for the CP experiment [23].
eonditions in the two eases are similar. Figure 21 shows typieal result for agglom erates of preeipitated siliea sheared in POMS fluids [23]. Three sets of data are shown. In these experiments, the preeipitated siliea also had a 1 50 m2jg BET surfaee area, and the primary particles tended to be clustered into hard aggregates of 250 nm as determined by a light seattering teehnique. These aggregates were fashioned into 2.6 mm agglomerates (solids volume fraction of 0. 1 6) using the eompaction and shaping procedures deseribed in our previous reports. In addition to using POMS fluids as the dispersion media (viseosities of 1 0,000 cSt (�1 0 Pa s) or 30,000 eSt (�30 Pa s)), some experiments were performed using another liquid polymer, styrene-butadiene rubber (SBR) of viscosity 1 0 Pa s. The diamond symbols show the dispersion results for shearing in the CP deviee (steady shear) at an applied stress of 600 Pa. The filled eircles are the dispersion results for shearing in the oseillatory deviee for the case when the mean stress over a cycle is 600 Pa, while the open eircles eorrespond to the ease where the maximum stress over a cycie is 600 Pa. Note that the steady-shear results fall between the two eases for the OSO. Since the dispersion kinetics in the CP device are greater than the case where the peak stress in an OSO experiment is set to the same value, this suggests that the duration of the stress above a threshold value determines dispersion kinetics. However, since the OSO results for the case when the mean stress matches the stress in the CP experiment show a faster dispersion kinetic than that of the CP experiment, this indicates that the absolute magnitude of the applied stress also determines dispersion kineties.
838
D. L. Feke
To further iIIustrate the complex dependence of dispersion kinetics on hydro dynamic conditions, consider the OSO data shown in Fig. 22. Two sets of dis persion results for precipitated silica particles are shown; one for low-density (and hence weaker) agglomerates, and the other for higher density (stronger) ag glomerates. The mean stress in all experiments was set to an identical value (580 Pa). However, this hydrodynamic condition was accomplished by using ei ther a lower viscosity POMS fluid (1 0 Pa s) at a higher shear rate (red symbols) or a higher viscosity POMS fluid (30 Pa s) at a lower shear rate (blue symbols). As can be expected, the absolute magnitude of the dispersion rate is larger for the ca se of the lower density agglomerates. However, note that in both cases, dispersion proceeds at a faster rate for the cases when a higher shear rate was applied than when using a lower shear rate. Also note that there is a larger spread between the dispersion results for the case of the weaker agglomerates in comparison to the results for the stronger agglomerates. This result suggests that characterization of the hydrodynamic conditions through shear stress alone is not adequate for the prediction of dispersion kinetics. Furthermore, the ratio of shear stress to cohesivity is not an adequate predictor of dispersion kinetics as weil. In order to quantify these effects, it would be beneficial to devise a predictive model for dispersion kinetics of agglomerates that would be sensitive to the nature of the applied hydrodynamic stress field as weil as to the cohesivity of agglomerates. Based on consideration of the spectrum of our experimental
'10
" ( 1-1»
o
•
•
. o
o
., 0.2
..
0.1
0
cJ'
0
0.'
0.'
•
o
o
0
0.2
. 0
0.1
8
• 0
0.02
0.06
0.'"
0.1
I
u
�( I"") ' Visca.;ly
. Viscosily
0.184 · 1)-10 Pa s • 0.184 · 1)slO Pa s o 0 0.184 · 1)=30 Pas • 0. 1 84 · 1)=30 Pa s
0.'
0.'
OSO Device . (TIOeIll-S80 Pa
0
0 • S O • 0
0.02
o 0.
• o
•
O.191 - TF 30 P.lI$ O.191 - 1l"JO PlIIS
• •
0
O.191 - Tt- l 0 P U O.\91 - 1}=IO P u
o 0
0
o
•
• 0."
titnc(iS'IiiI)
0.06
0.08
0.1
Fig. 22. Comparison of dispersion kinetics for precipitated silica agglomerates. The lett graph shows results for the case of relatively low density (weak) agglomerates for which #(1 -4» is 0 . 1 84, while the graph on the right shows results for higher density (stronger) agglomerates for which #(1 -4» is 0. 1 91 . In both cases, the hydrodynamic conditions were such that a mean stress of 580 Pa was applied tho the agglomerates. However, this was accomplished by using a lower viscosity fluid and a higher shear rate, or a higher viscosity fluid and a lower shear rate [23].
839
Shear-Induced Dispersion of Particle Agglomerates
observations, a useful form for such a kinetic model is [23] dR - dt (Fh - Fe) "2Y for Fh > Fe
(2)
cx:
where R is the radius of the agglomerate, Fh the hydrodynamic force applied to the agglomerate, Fe the cohesivity of the agglomerate, y the shear rate, and K a scaling parameter that reflects the geometry of the flow field. This model can be interpreted as folIows. The left-hand side of this expression characterizes the rate of material removal from the parent agglomerate. Unless the hydrodynamic force exceeds the agglomerate cohesivity, no dispersion will take place. The dispersion rate is taken to be proportional to the hydrodynamic force applied in excess of the cohesive force (which determines whether fragments can be broken from the parent agglomerate) and the applied shear rate (wh ich determines the rate at which fragments can be removed from the vicinity of the parent agglomerate). The model expressed in equation (2) can be rewritten in terms of strain by rec ognizing that }' = yf as (3) Figure 23 shows dispersion results for precipitated silica agglomerates subjected to a mean hydrodynamic stress of 875 Pa, but under two different shearing con ditions. As was the case in Fig. 22, the absolute dispersion kinetics is faster in the case of higher shear rates. For this set of data, both the hydrodynamic force Fh and cohesive force are constant (since similar agglomerates are used in all cases). According to the kinetic model presented in equation (2), under these conditions, the dispersion rate is predicted to be higher for the case of the higher applied shear rate, as is observed experimentally. Shear Stress 875 Pa Real Time t
0.6 0.5 Q
�� ...
0.4 0.3
•
p25 · 1 0 Pa s
p26 - 1 0 Pa s p27 · 1 0 Pa s • - Model Prediction pl 0 - 30 Pa s •
silica <1>/(1-<1»
=
'h = 87.5 s- I J.l.1
•
•
0. 1 94
=
JO Pa· s
10 Pa s
Y2 = 2 9 s- I J.l.2 = 3 0 Pa · s
pl1 - 30 Pa s • - Model Prediction · 1 0 Pa s
0.2
I
0. 1
0.01
0.02
0.03
0.04
0.05 0.06 0.07 0.08
time (min)
Fig. 23. Dispersion results for dense agglomerates of precipitated silica (4)1( 1 -1;) = 0 . 1 94) as a function of shearing time for two shearing conditions but a fixed mean shear stress of 875 Pa [23].
840
D. L. Feke 0.6 0.5
o a:
0.4
S O.3 q:
�
• •
p1 0 · 30 Pa s
Shear Stress 875 Pa Dimensionless Time Scale r
pl I · 30 Pa s - - . Model Prediction - 1 0 Pa s • p25 · I O Pa s • p26 · I O Pa s p27 - I O Pa s • . Model Prediction • 1 0 Pa s
--
--
. -
- -
0.2 0.1 50
1 00
1 50
200
250
300
350
Strain 'Y Fig. 24. Dispersion results of Fig. 23 plotted as a function of strain rather than shearing time [23].
However, when these dispersion results are plotted according to strain as per equation (3), the two different sets of data collapse to a single curve as shown in Fig. 24. This result provides additional evidence that the scaling relationships provided in the proposed kinetic model are correct. Also, note that in both Figs. 23 and 24, the solid curves represent the prediction of the model. In order to make these predictions, we fit the value of K in the model to short-time dispersion data from an independent set of experiments. Then, the kinetic model presented in equation (2) (or equation (3)) is integrated over time to yield the predicted curves. The correspondence between the model predictions and the experimental ob servations are quite consistent. A second test for the kinetic model can be performed by analyzing dispersion under conditions involving fixed power input to the fluid, but where fluids with different viscosity are used. In this case both the shear rate and shear stress are different, and their relationship is summarized in the Table below. Considering the erosion 2 rate as expressed in equation (2), one can observe that if the hydro dynamic force applied is much larger than the maximum cohesive force of the agglomerate (Fh > > Fe), the erosion rate becomes proportional to the energy input of the system (4) However, for smaller hydrodynamic force (Fh � Fe ), this proportionality is lost. Experimental results confirmed the predictions. In Figs. 25 and 26, we present the erosion kinetics observed when disper sing identical agglomerates with a reduced solid-volume fraction of 0. 1 94 using
841
Shear-Induced Dispersion of Particle Agglomerates Erosion Kinetics for IdenticaI Power Input 3 P!V=50,OOO W/m
0.5
- <1>/(1 --$)=0. 194
�-�-�-�-�-�-�-�-�-��
- Model Prediction 1'1'== 1 0 Pa s ....
0.4
• •
�
Model Prediction 11=30 Pa s Experiments Tl=
10 Pa s
.. '
•
Experiments 11=30 Pa s
0.3
� �
..!. 0.2
0. 1
0.02
time (min)
0.04
0.08
0.06
0. 1
Fig. 25. OSD results at fixed power input, but with the applied stress comparable to the cohesive strength of the agglomerate [23].
Erosion Kinetics for Identical Power Inp ut J PN=90,OOO W/m • <1>/(1--$)=0. 1 94 - Model Prediction 11=10 Pa s .. -.
0.5
� S �
• •
.� .
Model Prediction 11=30 Pa s Experiments 11= 10 Pa s
..
Experiments 11=30 Pa s
..
.,
'
..'
0.4
•
0.3
0.2
0. 1
0.01
0.02
0.03
0.04
0.05
time (min)
Fig. 26. OSD results at fixed power input, but with the applied stress far in excess of the cohesive strength of the agglomerate [23].
polymers of different viscosity with a flow field set to have an energy input per unit volume of 50,000 or 90,000 W/m 3 . The specific mean stresses and shear rates applied in these experiments are summarized in Table 1 . I n the case of relatively low-energy input (Fig. 25), the high-molecular weight fluid leads to faster erosion kinetics due to the high-hydrodynamic stress applied by comparison with the case of low-molecular weight fluid. However, the erosion
D. L. Feke
842
.
Table 1 . OSD parameters used in the silica dispersion experiments at constant power i nput
Shear Viscosity (Pa · s)
Y 1,mean =
9.3 28 9.3 28
71 42 98 57
fj;/l;"Y' 2,mean(S- 1 )
0"1 mean = ,
670 1 1 80 914 1 580
/fi;.0"2 mean (Pa) /12
'
PjV (Jjm3) 50,000 50,000 90,000 90,000
kinetics becomes proportional to the power input at higher stress (see Fig. 26) and the erosion profiles are very similar, despite the fact that the high-viscosity fluid exerts a larger hydrodynamic stress than the low-viscosity fluid. Additional information can be obtained by examining the experimental results in the context of the model. The initial rate of agglomerate erosion, when cal culated with respect to strain imposed, can be calculated considering the orien tation of the spherical cap, which leads to the strongest hydrodynamic forces (8 = rt/2,
Shear-Induced Dispersion of Particle Agglomerates
010.t:91 1 0.02 I: 0.194
843
Comparison of Model with Experimental Data
/( 1-<�)
>"
:: � ::0
�
.5
0.01
I .....
.
.. . .
.'
.. . .. . '
:
. ...
1 000
0 0
..
.' . ..'
500
-
Mean OSD Hydrodynamic Stress (Pa)
1500
Fig. 27. Plot of initial erosion rates calculated with respect to mean stress for agglom erates of different solid volume fraction [23]. 7ÜO 600
� 5üO
."
"0
-= '"
] E-<
0: 0 '",
400 300
2 200
u.l
1 00
O. l 75
0. 1 80
0 . 1 85
Ü. 190
0 . 1 95
0.200
Reduced Solid Volume Fraction <1>/(1-<1» Fig. 28. Agglomerate cohesive stress extrapolated from Fig. 27 at the zero-erosion con dition [23].
To further investigate the influence of flow dynamics on dispersion phenomena, it is possible to perform experiments in the aSD wherein the frequency and amplitude of the shearing motion is adjusted to provide different dynamic con ditions, but with the same shear-stress range (over one cycle) . For example, it is possible to shear at a lower frequency and higher oscillation amplitude, or a higher frequency and lower amplitude, to produce unsteady shear stresses with identical ranges. However, dispersion results can be quite different in the two cases.
844
D. L. Feke Erosion Kinetics in osn <1>'(1-1>)=0,190 · F,=I.5 . SBR 11=18 r. (J�=600 Pa s ·
os •
•
•
0.4
• 0. •
0.2 -•
0, 1
•
•
•
,.
• • •
0,05
0,1
0,15
0,2
time (min)
Fig. 29. Comparison of the dispersion curves for silica agglomerates subjected to an oscillatory shear-flow field of mean stress 600 Pa, but applied with two different oscillation frequencies. The upper set of data was obtained using lower frequency, higher strain conditions [25].
Figure 29 provides an example for silica agglomerates subjected to a cycle mean stress of 600 Pa for two different frequency conditions [25]. Note that the dispersion experiment that utilized the larger amplitude of strain (gauged by the parameter A, which represents the amplitude of the oscillation of the driving plate) and correspondingly lower frequency resulted in faster dispersion than the ex periment in which a smaller strain (and higher frequency) was used. Recall that in simple-shear flow, the principle strain directions are along the ± 45° diagonals. These are the locations along the surface of the agglomerate where the production of dispersion fragments is most likely to occur. In the case of the higher strain experiments, a greater fraction of the agglomerate surface will rotate through these favorable positions than in the case of a low-strain flow field. Thus different dispersion kinetics may be expected. In order to analyze and provide a basis for the experimental results, one can resort to an analysis of the details of the shear stress profile acting upon the agglomerates within an OSO experiment. A summary of this analysis for dry agglomerates is presented here. Within an OSO experiment, different portions of the agglomerate experience compression, while other portions experience tensile stresses. If the tensile stress exceeds the local cohesivity, dispersion is expected to occur. Assuming that the agglomerates are dry (no infiltrated processing fluid), if the local frag mentation number Fa exceeds unity, then dispersion can occur, given that the duration of the stress at this value is adequate. As a measure of the likelihood of
Shear-Induced Dispersion of Particle Agglomerates
845
erosion at any given point on the surface of an agglomerate, we use the local value of (Fa - 1 ) which is a relative measure of the degree to which the applied stress exceeds cohesivity. Figure 30 provides a set of polar plots that give the likelihood of erosion for positions on the midplane of the agglomerate for different times within a half cycle. (See [26] for further details.) In this example, the cycle-averaged value of Fa is 2. The distance from the center of each polar plot gives the local value of (Fa -1 ), and the square inserts and depict the specific instance within the cycle. Progressing from the upper left plot to the lower right plot, we see that the likelihood of erosion starts off to be the greatest along the 1 35-3 1 5° axis, diminishes to zero in the center plot (which corresponds to the point of the
&; 90
24
120
-
1 ,. ,
180
:
.
_
)l
330
20
0
\
I
240
210
02
330 300
'0
U -2 I,' -t.20:1
120
ISO
180 f-!
210
.0
�''<'-, t: .
V: . "-, . t; -- -\ �
240
2�O
-
J...
210
04 03 02 01 300
)lO
210
�
°0
10
\0 I
330
.. � 03
/
f....
210
0.1
0
�
)l
- 1.2
.4
180
0.2
300
270
..� 03
..,-",,/
240
--- 1 ,6
I"
• �1
/' ______ .<
6()
2
2
_
210
'"
2••
120
60
....
0.1
00
.~
20
0.3
02 0.1
0
0
20
0'4 03
02 0.1
300
20
o
� 20
270
Fig. 30. Polar plots depicting the likelihood of erosion as a function of position , for five different instances within one half-cycle of oscillation. The square insets indicate the po sition within the shear cycle. The curves i ndicate the angular positions (on the midplane of the agglomerate) and the distance from the center of the polar plots gives the value of (Fa - 1 ) , which depicts the degree to which the local shear stress exceeds the agglomerate cohesivity. In this case, the mean value of Fa over one cycle is 2 [26].
846
D. L. Feke
oscillatory motion where the plate stops), and then increases along the 45-225° axis (when the plate crosses the center position of the cyele, moving rightward). Since the f10w field produced in the OSD has non-zero vorticity, individual locations on the surface of an agglomerate can experience alternating periods of tension and compression. The tendency to disperse can be expected to correlate with the duration that the particular location experiences tension, and the mag nitude of the tension during this period. Thus, it is possible to compute an inte grated measure of the expected extent of erosion by averaging the predictions of erosion likelihood, such as shown in Fig. 21 , over one cyele of the oscillatory flow. For unsteady flows with large oscillation amplitude, an individual position can rotate through multiple cyeles of tension and compression during one forward (or backward) stroke of the OSD. For flows with smalloscillation amplitudes, only a few locations on the agglomerate (e.g., those located near the boundaries be tween the compression and tensile quadrants) will pass between compression and tension (or vice versa) during one stroke. Figure 31 shows sampie results. A set of polar plots is shown that provide a relative measure of the tendency of an agglomerate to erode for three-different values of Fa. The polar plots represent initial positions on the midplane of the agglomerate, where the initial position is defined to the angular orientation of the agglomerate when the driving plate is centered within its stroke. The further the curves from the center of the polar plot the higher is the expected extent erosion. Note that as Fa goes up, so does the extent of erosion. At each fragmentation number, four different oscillation amplitudes are pro vided. Since each plot represents a fixed value of Fa, higher amplitudes corre spond to lower frequency oscillations. Note that the results show that for higher oscillation amplitudes, the erosion profiles are more uniform around the agglom erate. This stems from the notion that for large oscillation amplitudes, each 10cation on the agglomerate can feel multiple tension-compression cyeles. Note that in the limit of infinite amplitude (which corresponds to zero frequency, or equivalently steady shear flow), the erosion profile will become a perfect cirele. Note also that low-amplitude (high frequency) oscillations lead to an extent of erosion profile that is peaked around the ± 45° axes. This is consistent with the images presented in Fig. 1 , which show that eroded fragments are offen pro duced along these positions. This type of analysis can be used to interpret the experimental results shown in Figs. 21 and 29. Figure 32 presents the analysis for the three sets of experimental conditions depicted in Fig. 21 . Again, the expected extent of erosion is plotted as a function of initial position for the agglomerate midplane. The center curve (the ep experiment) has a circular profile, as is expected for a steady-shear exper iment. The inner and outer curves represent the peak and average stress matches, respectively. Note that this polar-plot representation of the expected
847
Shear-Induced Dispersion of Particle Agglomerates Fa = 1 . 5
90 120 / -0 5
60
90 - 0,8 -
60
ISO
180 210
330
/ 330
210
270
270
Flow Geomelly
Af(3=2.5/6
/
.-VG=5f6 AfG=I Of6 A G=::O 6
Agglomel'a1e Plane 6=7tI:!
120
Fa = 3
. ---....." 60
90
ISO � .
180 �-.-j 210 240
270
300
Fig. 31 . Strain-averaged extent of erosion as a function of starting position on the ag glomerate and the value of Fa [26].
extent of erosion clearly shows the ordering of the dispersion kinetics as pre sented in Fig. 21 . Similarly, Fig. 33 shows the analysis for the two experimental cases depicted in Fig. 29. Note that even though the peak stress is identical in these two exper iments, the case of the larger amplitude oscillation leads to a more uniform ero sion around the whole agglomerate. This evidently leads to the slightly higher overall erosion kinetics that is exhibited in Fig. 29. These analyses can also be used to make comparisons of the dispersion efficiencies of unsteady flows relative to steady flows at a fixed power input. As was discussed previously, at a fixed power input per volume of processing fluid, the peak stress applied to the agglomerate will depend on the shear rates used.
848
D. L. Feke
"
o�m
-
F
C'P - Fa=l " OSD - Fil=Q.95
Fig. 32. Representation of the expected extent of erosion for the three experimental con ditions depicted in Fig. 21 [26].
For a given value of Fa achieved in an OSO experiment, the power input per volume of fluid can be computed, and the shearing conditions necessary to achieve the same specific power input in a CP experiment can be determined. For both cases, the expected extent of erosion can be computed as described above. The ratio of the expected extent of erosion in the OSO experiment to that for a CP experi ment can be construed as a flow-efficiency metric. This analysis is presented in Fig. 34. Note that at values of Fa'"" 1 (applied stress just exceeding the cohesivity of the dry agglomerate), unsteady flows are much more efficient for dispersion compared to steady flows. However, for higher values of Fa, the difference in the dispersion outcomes for unsteady and steady-shear flows di minishes. This result is consistent with the conclusions reported previously that were drawn from experimental observations.
5. CONCLUSIONS AND SYNTHESIS OF RESULTS - DISPERSION MAPS
As detailed in this chapter, dispersion is affected by a number of factors asso ciated with the chemical and physical makeup of agglomerate as weil as the details of the flow applied to drive dispersion. Simple analyses, which compare the strength of the applied hydrodynamic stress to the strength of the agglomerate,
849
Shear-Induced Dispersion of Particle Agglomerates .-\geJomerilte Plane S-lt 2
"HccI of ,\nl 1lhlUdc
-
05D Fa-1 .5
I»
,I<
.-\. G:-I O 6 .-\:('-:" 6
Fig. 33. Representation of the expected extent of erosion for the three experimental con ditions depicted in Fig. 29 [26].
,...-----,---.---r---, O.08
1-
c
R.lio oso/cr 1
�
/
C; 0:: ;.... � 2.5 ;:)
-
/
/
,
/
/
,
/
,
, /
0.06
0.04
u
� W
�
�
..
,
spDI e -c 1 -
V
2 0.02 1.5
I
I FLOS!)
Fig. 34. Comparison of the dispersion efficiency of oscillatory flows to steady shear flows. The efficiency ratio (expected erosion kinetics in an unsteady simple-shear flow relative to a steady simple shear flow) and power dissipated per volume of fluid as a function of Fa [26].
850
D. L. Feke
provide the starting point for an advanced understanding of the conditions for the onset of dispersion. However, it is clear that varying degrees of fluid infiltration has a great influence on the outcome of dispersion attempts. In addition, there has been progress toward understanding the importance and role of unsteady shear ing conditions on the dispersion process. It is possible to form both a conceptual and mathematical model aimed at describing universal characteristics of agglomerate dispersion. To aid particle technologists, it would be useful to construct a type of schematic that could be used to predict the various types of dispersion according to readily accessible parameters. Figure 35 shows a one possible type of schematic that qualitatively depicts some of the dispersion behaviors we have seen. The vertical axis shows the value of Fa used in the dispersion attempt. The horizontal axis represents a characteristic measure of the agglomerate structure. In Fig. 35, the volume frac tion of solids within the agglomerate is used. With the exception of the dispersion mode of adhesive failure, dispersion will occur only if Fa > 1 . For relatively large values of Fa, very fast erosion or the limiting case of rupture will occur. The critical value of Fa for which rupture occurs will depend on the specific agglomerate, but as a rough rule of thumb, this critical value falls with the range of 5 < Fa < 1 0. For moderate and low-applied stress, dispersion kinetics are characterized by the type of model described earlier in this chapter. In addition , for relatively small values of agglomerate packing density, significant fluid infiltration within the agglomerate will significantly affect the dispersion process. When a significant amount of fluid infiltration does not occur during the time scale characterizing the dispersion process, the analysis for the dispersion kinetics of dry agglom erates applies. At the present time, there does not appear to be a proven model
Fa � l
Fig. 35. Semi-qualitative schematic depicting different agglomerate dispersion behaviors. The horizontal axis represents the volume fraction of solids within the agglomerate [26].
Shear-Indueed Dispersion of Particle Agglomerates
851
for the erosion kineties of agglomerates eontaining a signifieant amount of in filtrated liquid. It is also noted that most of the detailed analyses of dispersion kineties have assumed that the host liquid has Newtonian rheology. However, in many praetieal dispersion applieations, especially those involving polymerie fluids, the proeessing fluids are non-Newtonian in eharaeter. In the ease of viseoelastic fluids, the time scales associated with fluid relaxation can be comparable to the time scales for fluid infiltration and agglomerate dispersion kinetics. This, different complex and synergistic interactions may be expected for dispersion processes conducted in viscoelastic fluids. This area is also ripe for thorough investigation and analyses. ACKNOWLEDGME NTS
The work reported in this chapter would not have been possible without the hard work of many associates and the funding of several organizations, all of which is gratefully acknowledged. Most of the work reported in this chapter has been performed in a collaborative research effort with Prof. Ica Manas-Zloczower of the Department of Macromolecular Seience and Engineering at Gase Western Re serve University. This research formed part of the doctoral dissertation research of several students at Gase Western Reserve University, including John Boyle, Kuo Yuan Ghung, Philippe Levresse, Syang-Peng Rwei, Alberto Scurati, and Hiroshi Yamada. Funding agencies include I FPRI (International Fine-Particle Research Institute), the National Science Foundation, the Petroleum Research Fund of the American Ghemical Society, Pirelli Tire, Dow Gorning, and Ga bot Gorporation. REFERENCES [1] I. Manas-Zloezower, D.L. Feke, I nt. Poly. Proeess. 4 ( 1 989) 3. [2] G.D. Partitt, H. A. Barnes. in: N. Harnby, M . F . Edwards, A. W. Nienow (eds), Mixing in the Proeess Industries, 2nd edition, Oxford-Boston, BuUerworth Heinemann, 1 992, pp. 99-1 1 7. [3] D.L. Feke, I . Manas-Zloezower, J. Partieulate Sei. Teehnol. 5 ( 1 987) 383. [4] D.L. Feke, I. Manas-Zloezower, Chem. Eng. Sei. 46 ( 1 99 1 ) 21 53. [5] S . P. Rwei, D.L. Feke, I . Manas-Zloezower, Polym. Eng. Sei. 30 ( 1 990) 701 . [6] S . P. Rwei, D.L. Feke, I . Manas-Zloezower, Polym. Eng. Sei. 3 1 ( 1 99 1 ) 558. [7] I. Manas-Zloezower, A. Nir, Z. Tadmor, Rubber Chem. Techno!. 55 ( 1 982) 1 250. [8] I. Manas-Zloezower, A. Nir, Z. Tadmor, Polym. Composites 6 ( 1 985) 222. [9] J . M . OUino, P. de Rousell, S. Hansen, D. V. Khakhar, Adv. Chem. Eng. 25 ( 1 999) 1 05-204. [ 1 0] S. Hansen, D .v. Khakhar, J . M . Ottino, Chem. Eng. Sei. 53 ( 1 998) 1 803. [1 1 ] S.v. Kao, S.G. Mason, Nature 253 ( 1 975) 6 1 9. [ 1 2] Y.J. Lee, I. Manas-Zloezower, D.L. Feke, Polym. Eng. Sei. 35 ( 1 995) 1 037. [ 1 3] Y.J. Lee, D.L. Feke, I. Manas-Zloezower, Chem. Eng. Sei. 48 ( 1 993) 3363. [ 1 4] H. Yamada, I. Manas-Zloezower, D.L. Feke, Chem. Eng. Sei. 53 ( 1 998) 1 963.
852
D. L. Feke
[ 1 5] P. Levresse, D. L. Feke, I. Manas-Zloczower, ACS Rubber Division meeting, Dallas, Texas, 2000 (April). [ 1 6] F. Bohin, I . Manas-Zloczower, D.L. Feke, Chem. Eng. Sci. 5 1 ( 1 996) 5 1 93. [ 1 7] H. Yamada, I. Manas-Zloczower, D.L. Feke, Powder Technol . 92 ( 1 997) 1 63. [ 1 8] J. F. Boyle, PhD. Dissertation, Case Western Reserve University, Cleveland , O H , 2003. [ 1 9] F. Bohin, D.L. Feke, I. Manas-Zloczower, Powder Techno!. 83 ( 1 995) 1 59. [20] H. Yamada, I . Manas-Zloczower, D.L. Feke, Rubber Chem. Techno!. 71 ( 1 998) 1 . [21 ] J . F . Boyle, I . Manas-Zloczower, D.L. Feke, Powder Techno!. 1 53 (2005) 1 27. [22] K. Y. Chung, unpublished work, Case Western Reserve University, Cleveland, OH, 2004. [23] A. Scurati, D.L. Feke, I. Manas-Zloczower, Chem. Eng. Sei. 60 (2005) 6564. [24] H. Schubert, W. Herrman, H. Rumpf, Powder Technol . 1 1 ( 1 975) 1 2 1 . [25] P . Levresse, I . Manas-Zloczower, D.L. Feke, Rubber Chem. Techno!. 75 (2002) 1 1 9. [26] A. Scurati, PhD. Dissertation, Case Western Reserve University, Cleveland, O H , 2003.
CHAPTER 1 9 Scale-U p of H i g h-Shear B i n de r Agg l om e ratio n P rocesses Paul Mort *
Procter & Gamble Co., ITC, 5299 Spring Grove Ave., Cincinnati, OH 45217, USA Contents
1 . lntroduction 1 . 1 . Product design 1 .2. Transformations 1 .3. Process equipment/systems 1 .4. Scale of scrutiny 1 .5. Economy of scale 2. Product attributes - the micro-scale approach 2.1 . Dispersion, wetting, and binder coverage 2.2. l nterfacial reaction and drying 2.3. Granule structure - saturation 2.4. Nucleation 2.5. Granule g rowth - stokes criterion for viscous dissipation 2.6. Granule growth - coalescence 2.7. Growth limitation 2.8. Granule consolidation 2.9. Attrition, breakage 3. Scale up of process equipment - the macro-approach 3. 1 . Power-draw, torque 3.2. Specific energy (E/M) 3.3. Swept volume 3.4. Stress and flow fields 3.4. 1 . Granulation under gravitational flow 3.4.2. Granulation with centripetal flows 3.5. Delivery number 3.6. Spray flux 3.7. Process ancillaries 4. Multi-scale approach - linking micro- and macro-scale approaches 5. Summary and forward look 5. 1 . Flow patterns in mixers 5.2. Binder spray flux 5.3. Linkage of process parameters with material properties 5.4. Batch and continuous systems
* Corresponding author. E-mail : [email protected]
Granulation Edited by A . D. Salman, M.J. Houns/ow and J. P. K. Seville (' 2007 Elsevier B.V. All rights reserved
854 854 855 857 858 858 858 860 860 861 861 863 867 868 870 870 872 872 875 877 879 880 882 885 886 887 887 889 889 890 890 891
854 5.5. Productive use of recycle 5.6. Models 6. Conclusion Acknowledgments References
P. Mort 892 892 893 894 894
1 . I NTRODUCTION
This chapter describes scale-up of batch and continuous granulation processes where a liquid binder is added to fine powder in order to form a granular product. The technical goal of scale-up is to maintain similarity of critical product attributes as the production scale andjor throughput of a manufacturing process is in creased. This chapter provides a framework for scaling-up that considers critical process transformations in relation to the desired product attributes. A similar approach can be taken in developing process control strategies. In any agglom eration process, transformations can be used to describe how raw materials (typically fine powders and liquid binders) are converted into a granular product. While critical product attributes may be characterized on the scale of individual granules (e.g., size, shape, porosity, mechanical strength, etc.), industrial scale up requires predictive relations for the sizing, design and operation of larger-scale process equipment. Considering scale-up on the basis of transformations is one way to link the macro-scale equipment decisions with micro-scale product at tributes. This approach can be applied to the scale-up of batch andjor continuous granulation processes as weil as transitioning from small batch prototypes to continuous production circuits While much of the content of this chapter is taken from a recent review article [1], new material is also presented, mainly in the form of a proposed framework for the description and analysis of continuum flow and stress fields in mixer granulators (Section 3.4). The implications of flow and stress fields for scale-up of granulation processes are discussed throughout. The earlier review [ 1 ] was published as part of a topical issue of Powder Technology on Scale-up of Industrial Processes. This issue includes a collection of papers that were initially given as invited presentations at the 2002 Annual Meeting of the Particle Technology Forum ( PTF) j AIChE, including coating, heat transfer, crystallization, fluidization, etc.
1 . 1 . P roduct design
A current trend in the design of granular products is the move toward "engineered particles". Agglomerates are no longer simply random aggregates of powder and binder materials; rather, granular structures are being designed to perform
Scale-Up of High-Shear Binder-Agglomeration Processes
855
specific product functions. Examples of designed structure include surface char acteristics (e.g. , via coatings), porosity and other composite structural features. To improve product performance, it is first necessary to make the link between the desired performance of the product and the specific granular attributes that are associated with the performance benefit. Identifying the relationships be tween product performance and the physical-chemical attributes of the agglom erates is not necessarily an obvious step. Further, once the key attributes have been identified, the agglomeration process needs to maintain the desired at tributes on scale-up to full production. Often, key attributes depend on micro scale structural features. Process scale-up may depend on linking this micro scale understanding to bulk production on a macro-Ievel. With powders, it is rarely obvious how to bridge these scales. The scope of agglomeration processing includes many different materials over wide scales of production, from specialty materials and pharmaceuticals made in kg/day batches to continuous processes for detergents and fertilizers measured in tons/hour. Agglomeration adds value to the product, for example, by producing free-flowing, dust-free particles that are optimized for uses, such as tabletting, dispersion/dissolution and compact delivery (i.e., to increase the bulk density). There are a number of key physical attributes of agglomerates that are essential for product performance, such as granule size, size distribution, density, flow ability, mechanical integrity, compressibility and dispersion. An optimal agglom eration process will, in a controlled and reproducible way, produce granules with design attributes that are relevant to the desired product performance. Characterization of the important attributes may require investigation on several different scales of scrutiny. While specific single-particle attributes may require micro-scale scrutiny (e.g., particle size, intra-granular porosity), bulk or meso-scale characterization is more appropriate for inter-particle characteristics, such as flow, compressibility, packing and bulk dispersion. Modeling and sim ulation tools are becoming more and more important in this scheme of product evolution, both from a product design and process perspective. It is often easier and much more cost efficient to conduct experiments on a small scale, and then use models and/or simulation tools to scale up to larger production facilities. In terms of product engineering, modeling and simulation tools can be very useful in making functional linkages between material properties and product performance across various scales of scrutiny. 1 .2. Transformations
Transformations describe the many ways in which the raw materials are changed by the process to form the product [2,3]. Agglomeration includes a complicated collection of transformations, typically including the mixing of powder feeds,
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Agglomeration Transformations =f(Material Properties, Process Parameters)
Process parameters: o applied forces, rate of impact or shear, o residence time, Granular Product o energy, ° o fluidization, 00 0 o temperature . . . ° ° o
,
Material Properties Powders: o particle size viscosity, o elasticity, & distribution, o shape, o yield o surface area, stress, o surface roughness, porosity, tension Vapor: surface chemistry... o humidity o
o
o
I
Transformations: o atomization, dispersion, o wetting, o mixing, o reaction, o particle growth, o densification, o drying, attrition ... o
o
o ° 0 o
Product Attributes: o particle size and distribution, o shape, porosity & density (bulk, particle), o compositional homogeneity, yield stress, o fracture toughness, flowability, tabletability... o
o
o o
Fig. 1 . Linkage between material properties, process parameters, transformations and product attributes in a binder agglomeration process.
binder atomization, dispersion of binder in powders, wetting and spreading of binder on particle surfaces, chemical reactions between binder and powder (and sometimes vapor phase), particle growth by coalescence, consolidation, attrition and drying. This chapter reviews the recent agglomeration literature with the aim of summarizing transformations that typically have an important role in agglom eration processes. It also describes sets of process parameters and material properties that are critical to scale-up and process control (Fig. 1 ). In considering how to link the scale-up of agglomeration equipment with the need to maintain specific product attributes, one may find it helpful to separate the actions of the equipment (i.e., the process parameters) from the properties of the materials being processed. In a binder agglomeration process, both the solids and liquid binder properties are relevant, as are their interactions. Note that material properties may be especially relevant in intermediate states (i.e., a wet-mass) where the constitutive relations may change dramatically as a function of both composition (wet and dry) and consolidation. In addition, the properties of the gas phase can be very important to consider in scale-up, especially the moisture balance between the wet-mass product and the headspace or air-stream in the process. In identifying the key transformations, linkages between process parameters and the material properties are reconciled in the form of controlling groups. Wherever possible, it is recommended to separate (either temporally or spatially) the key transformations in a process. This is especially relevant in agglomeration processes where a large number of potentially conflicting transformations may be
Scale-Up of High-Shear Binder-Agglomeration Processes
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occurring simultaneously (e.g., wetting-drying, growth-breakage, mixing-segrega tion, etc.) Additionally, the separation of critical transformations can be very useful in moving toward single-variable process control strategies [4]. 1 .3. Process equipment/systems
This chapter is not intended to give a comprehensive review of agglomeration process equipment. For more discussion on agglomeration unit operations, there are several excellent references that are readily available [5,6]. The current discussion considers process equipment in terms of process parameters. There are various classes of agglomeration processes. For example, high-shear agglomerators typically operate with mechanical impellers at speeds sufficient to impose high impact and/or shear stresses on the wet mass. Roller compactors are also capable of high mechanical energy transfer from the process to the product. On the other hand, fluid-bed agglomerators are lower-shear devices with lower transfer of mechanical energy to the product. These various types of ag glomeration processes can be distinguished according to their process param eters (Fig. 1 ) and relative interaction between these parameters and the product (i.e., transformations). Many agglomeration devices have been developed as "black boxes" and do not allow the user to visually inspect the transformations as they occur. Exceptions include lab-scale equipment made with glass or trans parent polymer vessels (e.g., a fluid-bed agglomerator with a glass riser), or in some cases, pan agglomerators. The "black-box" unit operation has reinforced the view of agglomeration as an "art" rather than a "science". As a step toward a more scientific approach, transformations (i.e., transforming from raw materials into a product) are used to describe and quantify the changes that occur in materials as they are processed. In the case of binder agglomeration, we start with powders and binders that have a variety of distinct material properties, and these materials are transformed in a variety of ways to produce a product. The transformations are typically controlled by the process parameters and material properties. In regards to the equipment scope, engineers consider the overall plant system involved with the agglomeration process. There is often considerable complexity in ancillary equipment (e.g. , hoppers, feeders, transport, recycle loops, grinding, classification, etc.) beyond the unit operations that are most directly associated with agglomeration (e.g., mixer-agglomerators, drums, fluid beds, etc.). In many cases, these ancillary devices are tightly connected to the agglomeration process and have significant effects (both good and bad) on product quality as weil as overall system reliability. It is necessary to consider these ancillary operations in a successful scale-up strategy, especially given that process rate bottlenecks often occur in ancillary solids handling operations (hoppers, chutes, conveying lines, bucket elevators, etc.). Wherever possible, it is preferred to simplify the
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overall plant operation by reducing the number of steps in the process and es pecially to reduce or eliminate non-productive handling and transformations. 1 .4. Scale of scrutiny
Overall, the goal of scale-up is to maintain identical product attributes (micro-scale) across production scales (macro-scale). A successful scale-up depends on con sidering both scales of scrutiny. In an industrial scenario, a project team may include members whose specific focus and area of expertise is on one scale or the other. The success of the team depends on coordination of both levels of expertise. A typical macro-scale approach determines desired operating conditions over a range of dimensionally similar unit operations using dimensionless groups, such as Froude Number, Stokes Number, Reynolds Number, and Power Number. The concepts of dimensional similarity and controlling groups are discussed in more detail in the section on Scale-up of Process Equipment. According to the macro scale approach, a measurable process parameter, such as power draw in a vertical granulator, is used to determine the desired process residence time (e.g., endpoint in a batch mixer or fill ievel in a continuous mixer). This provides guidelines for scale-up of the equipment operation. Empirical adjustment of pa rameters is still required to achieve the desired product attributes. On the other hand, a micro-scale analysis is useful in characterizing important transformations and defining mechanistic Iinkages between transformations and desired product attributes on a particle scale. The challenge is to maintain the similarity of each transformation during scale-up. This approach helps in predicting the feasibility of scale-up around specific attributes, and also helps to guide em pirical adjustment of process parameters needed to achieve the desired results. 1 .5. Economy of scale
In the industrial production of a commercial product, an implicit goal of scale-up is to improve the economy of production. This economic analysis (e.g., a cost/value function) is critical to industrial applications, especially when considering tradeoffs in a scale-up execution. While this chapter includes some practical suggestions for scale up efficiency, a detailed economic analysis is beyond the scope of the current work.
2. PRO DUCT ATTRIBUTES - THE MICRO-SCALE APPROACH
The micro-scale approach to scale-up is based on defining the key transforma tions in an agglomeration process on the scale of individual granules. Earlier
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descriptions of granulation on the micro-scale involve complex collections of mechanisms using a population balance modeling approach [7]; while these mechanisms provide a useful micro-scale view, the complexity of the approach has proven to be excessive for practical scale-up applications. On the other hand, a more recent view has been to define granulation in terms of three sets of rate phenomena: nucleation: growth; and breakage [8]. The current review follows an intermediate approach, where the mechanisms are described in terms of key transformations (e.g., binder distribution, nucleation, growth, consolidation, and breakage), and selected based on their relevance to the desired product at tributes (e.g., chemical homogeneity, granular size, size distribution, and granule density). The challenge is then to maintain the similarity of each transformation during scale-up. This approach helps in scale-up of specific product attributes, and helps in the adjustment of parameters needed to achieve the desired results. Transformations describe the many ways in which the raw materials are changed by the process to form the product (Fig. 1 ). For example, atomization and binder droplet size can be a key to granule nucleation and growth. Dispersion of binder in the powder is often correlated to the breadth of distributed properties. Wetting refers to the micro-scale spreading of binder on powder surfaces. Reactions may occur between binder and powders. Particle growth is generally regarded as the primary transformation in the agglomeration process; however, it is very much affected by many of the other transformations. Granule consolidation is offen coupled with growth and coalescence. Moisture removal may be required to form a dry, flowable product from an aqueous binder system and drying has a very strong effect on other transformations if it is done concurrently in the process. Attrition, or particle breakage, is often regarded as a negative transformation; however, it can also be used advantageously in limiting the breadth of particle size distributions and in improving the chemical homogeneity of the product. Key powder properties include particle size, size distribution, shape, surface area, surface roughness, porosity and surface chemistry. Some of these, such as size distribution and surface area, can be characterized by fairly direct meas urements. Others, such as shape and roughness are more qualitative measure ments. Surface chemistry is a very important and often difficult area to characterize. Subtle changes in surface chemistry can have significant effects on the agglomeration process. Binder properties are most commonly character ized in terms of viscosity, although viscoelasticity and yield stress may aiso be relevant, especially in melt granulation and/or with binders that are used to deliver an active ingredient to the formulation. There are a variety of adjustable process parameters covering the combined collection of agglomeration unit operations. Here, these have been compressed into a short list of key parameter groups. Certainly, fluidization is a key to systems using binder sprays; shear rate is a key to binder dispersion and agglomerate consolidation; and impact velocity affects consolidation and breakage. Material
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properties, such as binder rheology, solubility of solids in the binder, reaction rates, and drying are sensitive to temperature. In the following discussion, intera ctions between material properties and process parameters are iIIustrated on a series of simple transformation maps. 2.1 . D ispersion, wetting, and binder coverage
For high-shear mixers, the dispersion of a binder in a powder depends both on the binder viscosity and the applied shear rate of the process [9]. A combination of high shear and low viscosity will disperse the binder evenly throughout the powder mass while a viscous binder with insufficient shear results in a heterogeneous mixture of over-wet globules and dry powder (Fig. 2a). In top-spray fluid-bed agglomeration, the dispersion of the binder depends on the spray coverage relative to the mass in mixer, as weil as the turnover of the powder mass (i.e., fluidization). Here, the best dispersion is achieved with a large area of spray coverage and aggressive flu idization (Fig. 2b). The effect of binder spray flux on dispersion (Fig. 2b) is weil illustrated in the series of papers by Watano et al. [1 0]. Wetting coverage refers to the local distribution of the binder on the particle surface. This depends on both the bulk dispersion of binder in the powder and the wetting chemistry between the binder and powder surface. Maximum binder coverage requires both good bulk dispersion and low binder-powder contact angle (Fig. 2c). The effect of heterogeneous binder distribution is often seen in the compositional assay of granules classified into a series of size cuts, i.e., a sieve-assay. Given that the binder loading contributes to growth, it is understandable that, within a granule size distribution, the finer particles are often found to have lower binder content [1 1 ]. 2.2. I nterfacial reaction and drying
Some granulation systems involve reactions between a binder and a powder. For instance, an aqueous binder will hydrate starch excipients in a pharmaceutical a) Dispersion-mechanical mixing 05 .q CI)
"
.S
8
.0 CI)
'S:
poor dispersion uniform dispersion shear rate
b) Dispersion -fluid bed spray uniform 5 dispersion g�
_
e� Q. �
poor dispersion
binder spray flux
c) Wetting coverage poor
� ai coverage %ö good �E coverage 8 B 05 .!!2
" 0>
dispersion
Fig. 2. Dispersion and wetting transformation maps for binder dispersion: (a) in a me chanical mixer; (b) spray-on in a f1uid-bed g ranulator; (c) coverage of binder on the particle surfaces.
Scale-Up of High-Shear Binder-Agglomeration Processes
861
Surface Reaction, Drying slow, incomplete reaction
fast, complete reaction
wetting coverage Fig. 3. Chemical reactions between the binder and the solid powders depend on disper sion and wetting coverage at the solid-liquid interface. In drying, the rate also depends on the liquid coverage over the solid surface; a higher coverage area provides more liquid vapor interface for drying.
granulation. In another example, granular detergents are made by an acid-base reaction between binder and powder. In such cases, reactions occur at the sur face interface between the binder and powder; thus, the extent and rate of the reaction depends on the wetting coverage. Drying is somewhat analogous to this, except that the drying rate increases with increasing liquid-gas surface area. This occurs when the binder is thinly distributed over a large powder surface area. Both reaction rate and drying are very important transformations because they can significantly affect binder properties (e.g . , viscosity, yield stress) and the effective binder loading (i.e., liquid saturation), which are key to the transforma tions of granule growth and consolidation (Fig. 3). 2.3. Granule structure - saturation
The primary factor controlling agglomerate growth is the relative binder loading level and degree of saturation in the granule structure (Fig. 4). The filling of the binder in the granule pores is expressed as the saturation ratio, relating the binder volume bridging between particles within the agglomerate to the total available pore and void space between particles [12-14] . The saturation ratio is increased by adding more binder andjor by consolidating agglomerates to reduce their internal porosity. The growth process depends on the success of particles stick ing together upon collision. More growth occurs with increasing binder saturation, especially as the saturation approach es 1 00%. In the (fully-saturated) capillary state, rapid growth occurs by coalescence. Beyond 1 00% saturation, the particles are suspended in a continuous liquid phase and a paste or over-wet mass results. 2.4. N ucleation
The nucleation stage of an agglomeration process is the initial phase where small agglomerates (nuclei) are formed. Two basic mechanisms can be considered
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Relative binder loading in liquid bridge structures a) Filling pores by binder addition: b) Pore space reduction by consolidation: pendular
funicular saturation
capillary I 1 00%
droplet ..
Fig. 4. The structure of granules evolves with increasing binder saturation. Saturation increases by: (a) additional binder loading andjor (b) granular consolidation.
a) Distribution Mechanism
• •-_ . solid particles
+
agglomerate growth
• dispersion � . -
�
wetted particles
binder
agglomerate, size and size distribution controlled by growth mechanism
b) Immersion Mechanism •
.
•
:
•
.
solid particles
+• binder
immersion agglomerate, size controlled size of binder "template"
Fig. 5. Agglomeration nucleation mechanisms: (a) distribution; (b) immersion. Granule properties typicaJly depend on the mode of nucleation and growth.
[ 1 5] . The distribution case assumes that the binder disperses as a film on the particle surfaces; nuclei are formed by successful collision and bridging of the particles (Fig. 5a). The immersion case considers a binder droplet or other binder mass as the core of the agglomerate, to which finer solid particles are attached and embedded (Fig. Sb). The results of the agglomeration, especially the size distribution of the agglomerates, can be related to the prevailing mechanism. The immersion mechanism is attractive because the binder droplet size can be used as a control parameter for the product agglomerate size [16] . Immersion is also very useful as a way to encapsulate a sticky binder in a dry shell. An example of experimental work on agglomerate nucleation by droplet immersion shows the effect of binder viscosity and powder-fluid interactions [1 7]. In this case, binder viscosity is a function of the solution concentration of
Scale-Up of High-Shear Binder-Agglomeration Processes
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Fig. 6. Binder droplet nucleation experiments from Hapgood [1 7] using an initial binder droplet diameter of �2 mm in lactose powder: (a) dyed water, d = 6.5 mm; (b) dyed solution of 3.5 wt% HPC, viscosity = 1 7 cP, d = 3.5 mm; (c) dyed solution of 7 wt% HPC, viscosity = 1 05 cP, d = 3.0 mm.
hydroxypropyl cellulose (HPC). Relatively large (�2 mm) individual binder drop lets with a dye tracer are contacted with a static bed of fine powder. The binder wets into the powder forming nuclei, which are recovered, dried and analyzed (Fig. 6). The lower viscosity binder (water) wets the hydrophilic excipient (lac tose) and spreads out from the core (dyed center, capillary structure) to form a looser network of extended pendular hydrate bonds. On the other hand, the water in the more viscous HPC solution is less available to spread and chem ically interact with the lactose and the agglomerate retains only a dense capillary core nucleus. This work shows the net effects of initial dispersion of binder in the powder (i.e., as discrete droplets), wetting-spreading interactions between the binder and the powder and chemical interactions between the binder and powder substrate. Schaafsma et 81. [1 8] proposed a quantitative nucleation ratio based on the volume ratio of the agglomerate nucleus relative to the binder droplet. It is in structive to notice that while the absolute size of nuclei formed using the simple single-droplet nucleation experiment (as shown in Fig. 6) can be an order of magnitude larger than nuclei formed in an actual granulation process with a spray atomizer, the nucleation ratio is reasonably consistent across scales. For exam pie, structural differentiation of lactose nuclei made with different binders (water vs. H PC solution) has been shown to be consistent for a wide range of droplet sizes [1 7] (Fig. 7). This suggests that the simple single-droplet experiment is a useful first step to investigate binder-powder interactions and their effects on the formation of nuclei structures [1 9].
2.5. Granule g rowth - stokes criterion tor viscous dissipation
Growth processes can be modeled using a force or energy balance that relates forces applied in the process to material properties. The relevant material prop erties depend on the growth mechanism (Fig. 8). In terms of process control
864
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1 0000
1 000 Nucleus size ( um)
Fig. 7. Nucleation ratio (K) for agglomerates formed with lactose powder and a binder (either water or an aqueous HPC solution), using both single droplet experiments with a syringe (as per Fig. 6) and nucleation experiments with a spray atomizer.
Agglomerate Growth:
"� '"
a) Viscous Stokes: 0 () '"
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c) Yield-breakage case: '" '"
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Fig. 8. Growth transformations analyzed in terms of force balances, where the extent of size growth is given by the mean particle size ( MPS) of the granular distribution: (a) viscous Stokes case describes growth limited by viscous dissipation in binder layer; it assumes good binder coverage and the formation of liquid bridges on contact. (b) In the yield-coalescence case, plastic deformation and binder flow must be activated to form bridges between particles andjor embed particles into a binder droplet. To activate binder flow, the stress at impact must exceed the yield stress of the material (either binder or granular composite). In this case, it is assumed that the energy dissipation in plastic deformation of the material is large compared to the impact energy; therefore, no rebound occurs. (c) The yield-deformation-breakage case describes an upper limit to growth based on granular breakage, where the shear stress increases with increasing granule size.
parameters and material praperties, the Stokes criteria (Fig. 8a) and the elas tic-plastic transformation maps for coalescence (Fig. 8b) appear to be in con tradiction. Obviously, it is of critical importance for scale-up and process contral that the mechanism of grawth is understood. The viscous Stokes criterion for granulation considers the force balance be tween colliding particles according to the dispersion mechanism (Fig. 5a) [20]. In this case, good binder coverage is assumed, and the success of collisions in
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Scale-Up of H igh-Shear Binder-Agglomeration Processes
producing larger agglomerates depends on whether the eollision energy is suffi ciently dissipated by the viseous binder to prevent the elastie rebound from breaking the binder bridge between the particles. Further, it is assumed that the binder rheology and surfaee tension permit the spontaneously formation of a liquid bridge on eontaet. The limitation to growth oeeurs when the viseous dis sipation in the binder is not sufficient to absorb the elastie rebound energy of the eollision, as with a low binder viseosity or high eollision velocity (Fig. 8a). The Stokes eriterion is expressed in the form of a viseous Stokes number (Stv), given as the ratio of the eollision energy to the energy of viseous dissipation equation (1 ), where ä is the harmonie mean particle size in a eollision of two particles equation (2), U the eollision velocity, P p the particle density and 11 the binder viseosity. The eritical Stokes number (S�) accounts for binder loading in a system equation (3) where it is assumed that particles possess a solid core. Here, e is the particle coefficient of restitution, h is the binder thickness at the collision surface and ha a charaeteristic length scale of surface asperities. For conditions in which Stv is less than the critical value, S�, collisions are successful and growth occurs. For Stv > Se;, viscous dissipation is insufficient and rebound occurs (Fig. 9). While it is difficult to measure the parameters in the critical Stokes number, it can be convenient, in practice, to correlate the ratio hjha to the degree of binder dispersion. For example, a poorly dispersed binder will result in some areas with thick binder eoverage and others with little to no binder. The result is a distribution
1) Particles on
collision course
2) Liquid bridge lorms on contact 3) Elastic collision 01 core particles, then rebound 4) Is viscous dissipation >
inertia?
rebound Stv > St'
/ , No
'- Yes
�
agglo meration Stv < St'
Fig. 9. Agglomeration sequence described by Stokes criteria.
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of critical Stokes numbers or even a bimodal distribution, leading to heteroge neous growth. 8pp Ua Stv = (1 ) 9 1] (2)
(3) Binder rheology is not necessarily confined to Newtonian fluids. In fact, many binder systems exhibit yield-stress behavior. Examples include binder solutions containing longer-chain polymers, especially when the local activity of the poly mer on the particle surface changes due to water evaporation, hydration andjor partial dissolution of the particulate solid. In such cases, small collision velocities andjor short collision times may be insufficient to allow for substantial binder flow and liquid bridge formation and more energetic particle collisions may be required to induce agglomerate growth. The combination of a high binder yield stress and a low collision velocity results in low growth while a low yield stress and higher collision velocity results in more growth (Fig. 8b), as long as the dissipation is sufficient to prevent rebound. Energy dissipation can be quantified in terms of viscosity or loss modulus. It is important to note that binder rheology at the time of collision is relevant to this analysis; this is not necessarily the same as the rheology of the starting binder material, measured before addition to the agglomeration process. One must consider other transformations that may alter the binder rheology after it is added to the granulation, such as thermal effects, drying and hydration. Kinetics of these transformations must be considered in processes where binder rheology changes simultaneously with agglomerate growth and consolidation. Other examples of yield-stress binder rheology are found in melt agglomer ation. Here, the binder is added as a powder or flake solid, mixed with the other powders, and then transformed into a binder by heating the entire mixture. In its transformation from solid to liquid the binder typically passes through a critical sem i-solid or glassy state where the yield-stress drops into the range of shear stress in the process, and growth occurs. Thermo-mechanical analysis can be used to quantify this growth onset [21]. In cases where the binder solids are larger in size than the other powders, melt-agglomeration may proceed according to an immersion mechanism, where the finer solids are embedded into the semi-solid binder particle.
Scale-Up of High-Shear Binder-Agglomeration Processes
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2.6. Granule g rowth - coalescence
Granular deformation leading to coalescence is a well-documented growth mechanism [22-24]. In coalescence, colliding granules stick together if the col lision force is sufficient to plastically deform the granules, increasing the zone of contact, and consolidate the granular microstructures to the extent that enough binder is expressed into the contact zone (Fig. 9). Iveson and Utster proposed a granular growth regime map that shows increasingly rapid growth with increasing deformation at relatively high binder loading [25]. Assuming that there is enough fluid binder within the granular microstructure to hold the deformed parts together and prevent fracture, then growth will occur. Although rebound will occur if the collision is not of sufficient energy to induce elastic to plastic deformation, once the plastic yield stress is exceeded, the energy absorbed is typically quite high compared to the collision energy, minimizing the chance of an elastic rebound to break the formed bridge. Thus, the key transformation is the deformation of the granular microstructure and the flow of capillary binder to the contact zone, where the coalescence bridge is formed. Iveson and Utster describe this deformation propensity in terms of a deformation number (Oe), where Yg is the granule dy namic yield stress, Pp the granule density and U a characteristic collision velocity for the granulator Oe =
2 Pp U Yg
(4)
The key material parameters relate to the deformation of the composite granular microstructure; typically, this is measured as an apparent plastic yield stress of the granular material (Fig. 8b). Note that the yield stress of the wet mass may depend on the deformation rate, which depends on the time scale of collisions and shear-induced consolidation associated with a given agglomeration process [26]. Figure 1 0 Returning to the apparent contradiction in the transformation maps for the Stokes' criterion vs. plastic coalescence (Fig. 8a and b), on closer anal ysis, the micro-scale models are not necessarily contradictory. In the case of elastic-plastic collisions leading to coalescence, consider that the critical Stokes number (S�) equation (3) accounts for binder loading in terms of the binder thickness at the zone of contact. During plastic deformation and microstructure consolidation, the binder thickness in the contact zone, h, may increase sub stantially as binder is expressed from the pore structure into the contact zone, thereby increasing the instantaneous value of S� at the relevant interface. Fur ther, the value of S� increases with a decrease in the coefficient of restitution (e), as in the transformation from elastic to plastic deformation. Thus, the force balance analyses remain consistent when one treats S� as a variable that can
868
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O"j < O"y
O"j
� elastic rebound
>
O"y
� plastic deformation of granules, flow of binder into contact zone, coalescence
Fig. 1 0. Agglomerate growth by plastic deformation and coalescence. Plastic deformation occurs when the collision impact stress (O"i) exceeds the plastic deformation yield stress of the composite granular material (O"y). Plastic deformation of the granules increases the contact zone area. If sufficient binder flows into the contact zone, coalescence occurs.
undergo instantaneous change during collisions involving micro-structural redis tribution of binder and/or change in restitution due to elastic-plastic transition. 2.7. Growth limitation
The yield-deformation-breakage case (Fig. 8c) considers the upper limit of growth in the process, beyond which breakage becomes dominant. The yield limit is expressed as a "Deformation-breakage Stokes number", Stdef [27]. This is the ratio between the kinetic energy of a collision to the energy required for breakage (equation (5)), where Tb is the shear stress required to deform and break the granule. Assuming that the local collision velocity is proportional to the shear rate and the particle size (equation (6)), and that the granule's yield strength is ap proximated by a power-Iaw rheology model (equation (7)), a power-Iaw relation ship is predicted between the limiting size, a* , and the shear rate in the mixer (equation (8)). This approach has been used to analyze the scale-up of agitated fluid-bed granulators [2, 1 0,27]. Ppu2 Stdef = -2Tb U�y x a Tb
=
kyn
a* = y« n/2)-1) + c
(5) (6) (7)
(8)
Scale-Up of High-Shear Binder-Agglomeration Processes
869
Growth is limited by the balance of the collision stress applied to the granule relative to the inherent fracture stress of the granular material. In theory, agglomerate strength can be considered on the basis of binder-bridge strength between particles [28]. In practice, it is observed that large agglomerates are more prone to fracture than smaller ones for two reasons: ( 1 ) for a given impact force, the larger the size of the agglomerate, the greater the moment and the larger the stress that will be exerted on a weak point in the micro structure; and (2) as a composite material, larger agglomerates are more likely to contain a larger number of flaws through which cracks can propagate and cause fracture. While the approach described above provides reasonable correlation with ex perimental data, it should be noted that it relies heavily on the approximate re lationshi p given in equation (8), where the shear rate is related to the impeller tip speed and a characteristic particle size. In actuality, the material will see a dis tribution of shear and impact stresses which could lead to breakage, and the distribution will typically depend on the pattern of flow in a mixer-granulator. Another approach is to experimentally measure the critical stress directly using a set of tracer particles [29]. Tracers with known yield stress and breakage be havior are added to the mixer; examination of their remains provides an exper imental basis for the in situ stress state in the mixer. Breakage of agglomerates also affects the homogeneity of the product [30]. The dynamic situation of granule growth and breakage leads to a continuous exchange of particles, which improves the homogeneity of the granules. When granule breakage is absent, any heterogeneity due to the non uniform distribution of the binder in the nucleation stage tends to remain in the final product. In terms of process control parameters and material properties, the elastic plastic transformation map for coalescence (Fig. 8b) and the yield-breakage map (Fig. 8c) appear to be in opposition. In the plastic coalescence case, more growth occurs with increased process energy. In the yield-breakage case, an increase in process energy causes more breakage, lowering the stable size limit. Although both cases are driven by mechanical interaction between the process and the granular materials, the product result is very different. In the elastic-plastic de formation case, the granule is able to absorb all of the impact energy and dis sipate it through plastic deformation and heat, resulting in coalescence. On the other hand, the material undergoing yield-breakage cannot absorb all the energy; it reaches a fracture point that limits its growth. The transition between plastic to breakage behavior can be strongly influenced by material properties such as moisture content and temperature [31]. Thus, the relevant transformation map may change during a typical agglomeration process, e.g., progression in tem perature and moisture level in a fluid-bed d ryer-agglomerator may move the process from case 8b-c or vice versa.
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2.8. Granule consolidation
Agglomerate consolidation requires the deformation of a granular structure into a dense-packed structure. Plastic deformation occurs when the localized impact force exceeds the composite yield stress of the granule (Fig. 1 1 ). Consolidation can increase the binder saturation ratio by reducing the intragranule void volume and can trigger coalescence when the saturation ratio reaches a critical point. Thus, the consolidation transformation is integral to the mechanism of growth coalescence by plastic deformation. If the yield stress occurs between an elastic and plastic regime, consolidation will occur. Below critical saturation, the granular strength tends to increase with consolidation, typically with an increase in res titution coefficient andjor yield stress. The linkage of consolidation and growth implies two potential feedback loops: ( 1 ) a negative feedback to offset growth - as growth proceeds by coalescence, granular densification may cause an increase in the apparent yield stress, thereby limiting further coalescence; and (2) positive feedback which can poten tially lead to runaway growth if consolidation increases binder saturation beyond a critical point (e.g., from capillary to droplet structure in Fig. 4b) or if the yield stress is reduced as the result of the internal heat produced by the work of plastic deformation. The dominant scenario is reflected in the value of the exponent "n" in equations (7) and (8). When n > 1 , we see a consolidation strengthening effect where the yield stress of the granule increases with consolidation. On the other hand, a value of n < 1 implies a softening of the material with increasing con solidation, which can lead to runaway growth. Obviously, the negative feedback scenario is preferred from the perspective of process control. 2.9. Attrition, breakage
As discussed earlier in the discussion of growth limitation, agglomerate breakage is a dynamic part of the process. It is essential to limit growth and to help improve Agglomerate Consolidation
density
� high density
impact stress
8
Fig. 1 1 . Consolidation of granular microstructure and the elimination of intra-granular po rosity.
871
Scale-Up of High-Shear Binder-Agglomeration Processes
the compositional homogeneity of the product. Beyond this, the details of granule attrition and breakage are quite complex. There are different mechanisms for surface breakage (i.e., erosion, abrasion) and particle breakage (fracture, shattering). These depend on material properties including elastic modulus, hardness and fracture toughness (i.e., the resistance to crack propagation), particle shape and impact conditions. In this illustration (Fig. 1 2), a tough particle may survive a high level of impacts before it finally shatters, while a particle with a lower toughness andjor more irregular shape may progressively break into smaller fragments with increasing impact stress andjor increasing number of impact events. Generally, one of the prime reasons for doing agglomeration is to avoid problems that are encountered with fine particles, e.g., hygiene, dust explo sively, or other product performance issues correlated with fines. Obviously, once having made the investment to make the agglomerates, it is paramount to avoid their attrition or abrasion in subsequent handling and conveying opera tions. Here, there is a balance in approach toward specifying more gentle han dling operations vs. the design and production of the agglomerates with increased resistance to attrition. There are a number of criteria for particle breakage, depending on the particle characteristics, material properties and the details of stress loading (compression, shear, stress rate, number of impacts, fatigue, etc.) [32,33].
Agglomerate Attrition a) Impact breakage
b) Compression / shear
c: 0 .Ci; CI) Q)
0. E
0 0
impact stress
�
0
breakage I
!JJ
0
� abrasion 0
0 0 0
shear stress
Fig. 12. Attrition of granules as a funcbon applied stress and material properties (com posite material toughness, flaw distribution, shape, etc.): (a) single particle impact mode tends to cause intermediate breakage and/or shattering depending on material properties and impact stress; (b) in multi-particle interactions (e.g. , shear and compression in bulk handling operations), abrasion can be a problem along with breakage. A more detailed discussion of breakage mechanisms and material property relations are cited in the lit erature.
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3. SCALE U P OF PROCESS EQUIPMENT - THE MACRO-APPROACH
Scale-up of agglomeration processes based on equipment parameters is referred to herein as the macro-scale approach. Typically, the macro-scale approach de termines desired operating conditions over a size range of unit operations using dimensionless groups, such as Froude number, Reynolds number, Power number, swept volume, delivery number and spray flux. While the actual unit operations may or may not be geometrically similar, it is generally sought to maintain the similarity of stress and powder flow fields across a set scales, especially for mixer granulators where the applied stress is critical to the micro-scale transformations. In order to control the stress and flow fields of the powder and granular ma terials, several other dimensioned parameters or parameter groups that are often used including mixer impeller tip speed, power draw and power draw derivatives. The effect of process time can be combined with power draw in a mixer to be expressed as the cumulative or specific energy dissipation. These operating parameters may typically affect multiple product transforma tions. It is a challenge to scale up equipment in a way that maintains key product attributes while also achieving an economical and industrially efficient operation. For example, impeller speed andjor the Froude number in a vertical granulator affect binder dispersion, consolidation, coalescence and breakage. Herein is a classic challenge for scale-up: one cannot increase the mixer diameter and keep both Froude number and tip speed constant. The suggested approach identifies the critical transformations based on product attributes and the selects appro priate scale-up criteria. If it is not possible to resolve the key transformations simultaneously, it is then advisable to separate the transformations, either tem porally or spatially. For example, by staged processing in a batch unit or adding additional unit operations in a continuous process.
3.1 . Power-draw, torque
A measurable process parameter, such as power draw in a high-shear vertical granulator, is often used to determine the desired process residence time (e.g., endpoint in a batch mixer or fili level in a continuous mixer). In the pharmaceutical and powder technology literature, there are numerous references on the use of power draw, torque or other similar indicator for endpoint control and scale-up of batch granulation processes [34-39]. While these provide guidelines for scale-up of the equipment operation, empirical adjustment of parameters may still be re quired to achieve the desired granular product attributes, such as granule size, size distribution and particle density. I n a classical scale-up approach [40], dimensionless groups relating process parameters and wet-mass material properties are applied over a series of vertical
Scale-Up of H igh-Shear Binder-Agglomeration Processes
873
mixer-granulators. The power number (Np) relates the net power draw (I1P) to mixer size (0), rotational speed of the agitator (N) and the instantaneous product bulk density (p) (equation (9)). A pseudo-Reynolds number (Re*) describes the kinematic flow in the mixer in terms of product bulk density (p), agitator tip speed (ND), characteristic shear dimension (0) and a pseudo-viscosity ( 11 *) (equation ( 1 0)). Here, 11* is a torque measurement obtained using a Mixer Torque Rheo meter (MTR). The MTR compares the measured torque to the applied shear in order to measure the consistency of the wet mass [41 ]. Other references provide rheological measurements based on compression of the wet mass [42]. Shear cells have also been used to measure the cohesivity or tensile strength of a wet mass sampie as a function of its compression state [43]. Each of these methods provide a reasonable correlation between a measured constitutive property and the power draw in the granulation process, where product sampies are collected intermittently at different residence times in a batch operation and measurements are made on their rheo-mechanical consistency. The MTR torque is assumed to relate to bulk flow behavior of the wet mass, in a way that is analogous to viscosity in a liquid system . The Froude number (Fr) is the ratio of centrifugal to gravitational forces, and describes the state of fluidization in the mixer (equa tion (1 1 )). The Fill number describes the relative loading level of the mixer (equation ( 1 2)). I1P Np = (9) 3 5 -
pN 0
Re* = Fr =
pN02
11* N20 9
�-
Fill # = � 0
( 1 0) (1 1 ) ( 1 2)
Analysis of data over a range of mixer scales collapse to an apparent power-Iaw relationship between Np and the product of Fr, Re* and fill numbers [40]. The strongest correlation appears between the power draw and the rate of energy dissipation (i.e., pseudo-viscosity) in the wet mass. The overlap of the data at different scales implies that there is a consistent scale-up relationship between the power draw of the mixer and the wet-mass consistency of the mixture; further, this relationship can be extended across mixers that are not necessarily geo metrically similar. This approach demonstrates the use of MTR to characterize sampies extracted from the process. It shows that the relevant rheo-mechanical properties of the wet-mass change as the bulk material is transformed during the agglomeration process. Although this approach does not directly address the
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scaling of micro-scale product attributes, the inclusion of product density and wet-mass viscosity in the dimensionless groups provide indirect linkages. Some correlation has been shown between the wet-mass properties and subsequent dry-granule product attributes [44]. The importance of the pseudo-Reynolds number underscores the interaction between the wet-mass rheo-mechanical properties (i.e., the transmission of stress through the material) and the tip speed (ND) of the mixer. Note that the collision velocity (U in equations ( 1 ), (4), (5), and (6), a key parameter in the micro-scale analysis, is dependent on the tip speed. This highlights the impor tance of tip speed in scaling up mixer-granulation devices. In another example from the pharmaceutical literature, lab scale tests were done to define an optimum power level for endpoint control in the scale up of a granulation process in a vertical mixer granulator [45]. The granulation process was followed by tabletting. The critical properties of granular flow, tablet weight variation and tablet disintegration time were optimized together at a single power-draw endpoint on the lab scale. On scale-up to a larger mixer, however, several product attribute issues were encountered. In maintaining similar mechanical fluidization for binder/powder dispersion (i.e., constant Fr), more granular densification occurred, which had a negative effect on tablet properties. Increased granular densification due to the higher impeller tip speed is often encountered when using a Froude Number scale-up to a larger diameter mixer. To adjust the density, the rotational speed can be reduced to approach tip speed (i.e., kinematic) similarity. To maintain equivalent binder distribution at the lower state of fluidization, a reduction of the binder spray flux (i.e., a longer batch time) may be required. It should be noted that the method of binder addition and its distribution in the powder typically becomes more and more critical at larger scales. Another approach to scale-up using power-measurement employs a small-scale batch mixer to estimate the optimal binder loading levels for a formulation to be produced at a larger scale (Fig. 1 3). In this example, an excess of a binder liquid is intentionally added to the batch mixer-agglomerator at a controlled feed rate, and the power-draw or torque is monitored. In a system where growth is driven by saturation coalescence, a sudden increase in the power draw indicates the onset of rapid agglomerate growth. The level of binder present in the mixer at the power draw onset point is defined as an empirical limit for binder addition in the given formulation. To avoid over-agglomeration on scale-up to a production system, the binder addition level is maintained at or below this limit. Note the increase in power consumption can also result in increased product heating due to shaft work (Fig. 1 3b). Additional examples showing the correlation between power consumption and temperature change are documented in the literature [46]. It should be noted that the binder content at the power draw onset in a small batch mixer is an empirical indicator, not an absolute measure of binder loading
875
Scale-Up of High-Shear Binder-Agglomeration Processes Add binder
Q) :l er
Q) :l er
t-
es
t-
;: �
�
es
es
....
E Q) t-
Q) a.
-0
Qj
"0
Q) ;: 0 a..
� 0 a..
(a)
es
� 2 �
Batch time
(b)
Batch time
Fig. 1 3 . Determination of formulation binder limit using analysis of power draw onset in a batch mixer: (a) link from power-onset to binder level; (b) increased power draw (i .e., post onset over-agglomeration) results in an increase in frictional heating of the product.
capacity. The more fundamental characteristic of wet agglomerate structure is the saturation [47], which is discussed in more detail earlier in this chapter. Ac celerated growth by coalescence and increased power draw typically occur at a critical state of capillary-filled saturation [48]. This structure depends not only on the binder loading level, but also on other scale-dependent process parameters and/or environmental conditions that can affect consolidation, e.g., the tip speed of the impeller, temperature, relative humidity. There is a nesting effect of interrelationships between binder loading, consol idation, saturation, granule growth and power draw. While feedback among these interrelationships may have a confounding effect, one can pose a rational se quence of cause and effect as folIows: ( 1 ) binder loading and/or consolidation causes an increase in the saturation of the granular structure; (2) increased sat uration causes an acceleration of the granular growth kinetics; (3) the combination of the increased particle size and surface-moist cohesion (due to higher saturation) can increase the shear stress transmission within the flow pattern, resulting in an increase in power draw. Further implications are discussed in Section 3.4.2.
3.2. Specific energy (E/M)
The net specific energy is a measure of the transformation work being done on the producl. Integrating the net power draw over the residence time gives the net energy consumed in the agglomeration process. In a batch process, the net energy divided by the mass holdup gives the net specific energy input, or E/M. In
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a continuous process, the specific energy can be obtained directly by dividing the net power draw by the feed rate. Specific energy is an appealing scale-up ap proach, with analogies in other process technologies, e.g., extrusion, kneading and milling. Recent work reports that process work can be effectively used to complement power draw analysis for more robust process control [49]. On the one hand, the advantage of specific energy is that it combines effects of net power, time and mass into a single group. On the other, the practical difficulty of the approach is determining the net power draw. The net power draw is that which is used to do productive work of agglomeration, i.e., to transform the product. Net power draw can be calculated as the difference between the gross power draw, which is easily measured, and the baseline power consumption. As a first approximation, the baseline can be measured by running the empty mixer. However, there are typically additional parts of the gross power consumption that are not directly related to the productive work of granulation. Examples include product fluidization, mixing, conveying, andjor drag caused by build up of product on mixer walls andjor impeller tools [50,51]. These effects may change from batch to batch, within a batch or during a continuous run and hence it can be difficult to pin down a constant value for the power draw baseline. Nevertheless, the specific energy approach offers some advantages. If care is taken to measure baseline power consumption, the resulting net energy can be shown to be a useful parameter for scale-up, especially in an agglomeration process that is driven by coalescence. With the coalescence mechanism, smaller agglomerates are fused together to make larger agglomerates by a mechanical consolidation process. If the energy of the process provides a force that is suffi cient to overcome the plastic yield stress of the agglomerates, then they will deform at their contact points and coalesce to a larger size. This energy balance can be expressed as a dimensionless group (see x-axis, Fig. 1 4b). This group is similar to the Stokes' deformation number described later in the micro-scale section, except that the energy in current expression is measured directly from the power draw consumption. The yield stress of the wet agglomerate (i.e., a binder-powder composite) is a critical material property that lumps together the composite effects of raw material properties (binder and solids) as weil as process and environmental factors, such as temperature and relative humidity. Yield stress is typically measured using a mechanical testing machine to collect load-displacement data on a small bed of granules (e.g., in a tablet die); these data can be analyzed by a number of different methods to determine a yield stress value [52-54]. Note that conventional load-displacement experiments are typically done at fairly low compression rates. While these data typically provide a useful and convenient basis for comparison, it should be noted that the in situ compression rates can be significantiy higher in the granulation device, especially for direct impact consolidation. On the other hand, in situ shear interactions are generally more gradual. Measuring energy dissipation
877
Seale-Up of High-Shear Binder-Agglomeration Proeesses
100
� 1 0 ::!---'-rI----i o
"0
(a)
1 00 ::r-------,
::r-------,
batch ti me
�
o
(b)
In(d/do) =
f(x)
10
x
=
(E.M) *p/Gy (
Gy = f(T,binder)
11
E = f( N )
1
Fig. 1 4. Scaling of agglomerate g rowth by eoaleseenee meehanism using speeifie energy
vs. yield stress of the wet-mass material. (a) The data in represent various binder loading
levels, operating temperatures (T) and operating speeds (N) in a horizontal-axis plough share mixer. The batehes are run for various bateh times and then eharaeterized for size growth, where the geometrie mean size on a mass basis (d) is eompared to the initial mean size (da) . (b) When resealed as speeifie energy (E/M) relative to yield stress (ay) , the data eoliapse to a master growth curve.
and deformation behavior at higher strain rates is a more difficult endeavor. Re sults of such experiments highlight the importance of viscous limitations in the kinetics of binder redistribution at high consolidation rates [55]. 3.3. Swept volume
Relative swept volume can be used to compare different mixing equipment de signs and size scales [56]. It considers the volume of product swept away by the impeller of mixing bl ade in a given period of time, combining the affects of product fill level, impeller speed and impeller design. This approach is valid as long as there is good mixing (i.e. , powder flow) throughout the filled volume of the mixer. The idea of swept volume analysis can be extended using a modeling ap proach to consider the probability, frequency and distribution of interactions be tween the active mixing elements (tools) and the product. Ideally, one seeks to have a tight distribution of interaction frequency such that transformations are uniform across the whole product. This approach can be useful in estimating relative impact velocities between product and active mixing elements or between a moving product and vessel wall. The velocity of impact and frequency thereof can be used as a way to scale physical transformations such as coalescence (growth) and consolidation (densification). As such, this approach can link equip ment parameters and micro-scale analyses of product transformations. Once again, the key to completing this link is an understanding of the constitutive properties of the wet-mass mixture.
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CFD Model Section �
mixing tools
V CFD results:
shovels
Appro ach' Measure or estimate residence time, RTD [C FD model used here]: Use geometry (tool design), shaft speed and fluidization (Fr#) to estimate product / tool interactions ( i . e . , swept volu me).
virtual particle injection
I
product
E
'Z
axial-position
Fig. 1 5. Model of product-tool interactions in a continuous high-shear mixer-agglomerator: the RTD is predicted based on the distribution of trajectory paths of particles added to the mixer in the coalescence section. The particle trajectories depend on the CFD solution of airflow in the mixer plus direct collisions with mixing tools.
An example of a swept-volume approach is presented for a continuous high shear mixer-agglomerator (Fig. 1 5). In this case, the shaft is running at a high speed, giving rise to an annular product flow (Le., a high Froude number). The interaction zone is primarily at the tips of the tools (Le., impact) or in the high shear zone between the tool ends and the wall of the mixer. One can consider the swept volume in terms of the probability of interaction between the product and the mixing element per axis rotation. Using a computational fluid dynamics (CFD) model to estimate the residence time distribution (RTD) is helpful in that it allows the process developer to do preliminary virtual experiments on tool design, tool configuration, operation speed, etc. Integrating this over the predicted RTD gives the net interaction in the process. As in the case of the specific energy discussion, the net interaction of shear and impact can be quantified using a force or energy balance to predict constitutive transformations in the process. The modeling ap proach can help to improve the efficiency of the scale-up process and minimize the need for costly full-scale experimentation. Another approach to quantify swept volume interactions in a batch mixer is experimental particle tracking to map out a distribution of interaction over the course of an agglomeration process [57]. Flow patterns in the mixer will typically change as fine starting powder is transformed into moist granules, and the
Scale-Up of High-Shear Binder-Agglomeration Processes
879
patterns of stress transmission and fluidization can change significantly. Thus, it is essential to consider swept volume in the context of the powder flow, i.e. , the powder's reaction to "being swept", and how this may change during the course of the granulation residence time. In regards to cohesive fine powder flow, problems with the swept-volume ap proach can arise in the scale-up of vertical axis batch mixers where "phase separation" in the flow of the fine powder is often observed in scaling up to larger volume mixers. In this case, some of the powder (on the bottom layer of a vertical granulator) is actively swept by the impeller element while the upper layer is in a dead zone with little mass exchange between the layers (Fig. 1 8a). This can be especially problematic when one considers that the binder is typically added to the top (unmixed) portion [1 6]. A more detailed analysis is given in the following section. 3.4. Stress and flow fields
The physical quantification of granular stress and flow fields is an emerging area of study, encompassing theoretical, simulation-based and experimental efforts. While this work is in its nascent stages, the application of continuum powder mechanics and granular dynamics to describe flow and stress fields within gran ulation unit operations may provide useful insight for scale-up, equipment design and process contro/. In the interest of furthering progress in this area, this section presents a hypothetical framework for analysis of flow regimes in mixer granulators followed by two examples: ( 1 ) a cohesive powder mechanics ap proach to the analysis of scale limitations in a mixer with gravitational flows; and (2) a continuum analysis of centripetal flow patterns in vertical axis high-shear granulators. A tentative regime map of granular flow (Fig. 1 6) is proposed as a way to elucidate the state of flow in a mixer-granulator [58,59]. Three regimes are iden tified depending on a dimensionless shear rate (y*) which is the shear rate (y) made dimensionless using a characteristic particle size (dp) and gravitational acceleration (g) [60]. In dry granular flows, the shear rate is calculated based on a particle velocity (Vp) and a characteristic dimension such as the particle size (dp) or a relatively narrow shear-band of particles (i.e., 6-1 0 particle diameters). In a mixer-granulator, particle velocity is often scaled using the impeller tip speed (Vi), even though it may be only a fraction thereof. In a cohesive binder-powder mix ture (i.e., a wet-mass), the characteristic dimension for the relaxation of shear may be significantly larger than in dry flows. In Fig. 1 6, physical phenomena that are characteristic of each flow regime are shown at various scales of scrutiny, ranging from continuum approximations to cluster interactions and single particle interactions. The following examples focus
880
P. Mort
CD
-= ..:a::
,Q
T: *
I
� e�0 co:l �
'"
0 .. (J
·s
f(y)
T:
_
yn
n
Granular Temp. (gas conlinuum)
�I
Do m a i n interactions (coherence length scale)
Spalial and temporal distribution or
Part i c l c
ombined interaetion (fTietionaVrolling! collisional), m ul ti p le contacts
't
eontacts
0.2
Di mension l ess shear rate,
_
1'2
Transi nt clusters?
coherence, stress ehains
packing
0
@)
®
Fluid-like continuull1 (N.S. analogy)
Frictional eo nt i nuu m
ßinary eol l i ion
'ffg
3
»
r-y
Fig. 1 6. A schematic representation of different regimes in powder and granular flows, following Tardos et al. , where the flow regime depends on a gravity-based dimensionless shear rate [58,60]. Regimes include: (i) slow-frictional or quasi-static; (ii) intermediate, fluid-like or dense-inertial; (iii) free collisional or granular temperature regime.
on the continuum scale. To develop scaling criteria for particle attributes, much more work needs to be done to link continuum models with micro-scale phenomena. In addition, please note the boundaries on both sides of the inter mediate regime are not as clear-cut as shown in the figure, and much more work is needed before these boundaries are better defined. 3.4. 1 . Granulation under gravitational flow
In some granulation equipment, bulk flow of the material is driven by gravity, for example, drum-granulators, V-blenders and other tumbling blenders. While the powder is typically moving at the point where binder is dispersed into the powder, there are periodic stops and starts in the bulk flow. In moving from the static to the flowing condition, the material must pass through a stage of incipient flow in the slow-frictional regime, i.e., the LHS boundary of the Slow-frictional regime (Fig. 1 6i). While there is a significant body of work dealing the use of shear cells to measure and analyze incipient flow behavior for application in hopper and bin design [61 ,62], there has been relatively Iittle attempt to apply these methods and analyses to the scale-up of binder-granulation processes. This hypothetical ex ample considers the application of continuum powder mechanics to scale-up of a formulation over a scaled-up series of granulation equipment. The theory inc\udes the material properties (i.e., flow function) of the in situ wet-mass granulate as weil as the features of the mixer design (geometry) and mixer-prod uct interactions (wall friction) that are described in a hypothetical flow factor.
881
Scale-Up of High-Shear Binder-Agglomeration Processes
Many powders and granular materials exhibit downward curving flow functions over the range of relevant pressures in bin flow - in this case, there is no "upper limit" to the bin design problem, only a lower limit for the bin opening. On the other hand, it should be noted that some materials exhibit upward curving flow fune tions, as iIIustrated by Jenike [61]. In the upward eurving ease, there is an upper limit to the bin diameter, above which whole bulk mass of material in the hopper is in a no-flow condition. An example of an upward-curving flow function for a wet granular material is eontrasted with that of a free-flowing dried granule in Fig. 1 7, where the unconfined failure stress (fe) is plotted as a function of the principal eonsolidation stress (0" 1 )' The unconfined failure stress eorresponds to the onset of inci pient bulk flow under gravity. While there is little published information on flow functions of wet-mass ag glomerates, it is likely that a signifieant proportion of wet-mass granular materials may exhibit upward-curving flow funetions, especially at higher wet-binder con eentration. The upward eurving flow funetion is eharaeteristic of plastie materials that may significantly inerease in strength as they are eompressed. A practitioner of granulation might eompare this to the familiar "squeeze test" in whieh the wet granulate is squeezed by hand to form a "ball" and the processability of the product is judged based on how easily the ball crumbles. When the material gains significant strength with eompression, there may be difficulty in sealing up,
12
non tlowing
10
--*- Dried agglomerates
very cohesivc
8
--<>-- Wet-mas agglomerates
� 6 "......
«l
- - Mixer Flow Factor (hypothetical)
'-"
�
4
easy tlow
2 0
free tlow 0
5
10 0' , (kPa)
15
20
t,.
Stress limit (A), minimum discharge opening
o
Stress limit (8), maximum cale-up
25
Fig. 1 7 . Flow functions for wet (ex-granulator) and post-dried granulations along with a hypothetical f10w factor for the mixer, plotted at the boundary of the cohesive and very cohesive regions. Point (A) is the lower intersection of the wet-granulate f10w function and the flow factor - it defines the minimum opening required to discharge the wet mass. At point (B), the upward-curving flow function crosses back over into the no-flow condition this represents the hypothetical maximum mixer size limit for scale-up of the wet-mass formulation.
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especially in mixer geometries where the principal consolidation stress increases with the process scale. Crossing into a no-flow condition in a larger scale mixer (e.g. , Fig. 1 78) may cause build-up in the mixer and an increased incidence of oversize producl. The hypothetical flow factor for a mixer granulator is analogous to that for a bin, except that contributing factors are dynamic in the mixer. For example, wall angles constantly change with a rotation (e.g., in a V-blender) or with the angle of rotation in a drum. The wall friction in a mixer-granulator increased as binder and wet-mass material smears and/or accumulates on walls or tool surfaces. While it may be unwieldy to calculate instantaneous, localized flow factors and integrate over the full mixer, it may be useful to consider a critical flow factor at the point in the process that is most prone to product smearing or build-up due to a potential no-flow condition. 3. 4. 2. Granulation with centripetal flows
On scale-up, it is advantageous to maintain similar patterns of granular flow and inter-granular stress. This is especially relevant in high shear mixer-granulators where inter-particle stress is critical to micro-scale transformations including co alescence, consolidation and breakage. In a collisional flow, the stress depends primarily on the collision velocity, which scales with impeller tip speed. In a more dense flow, the collisional impact of a mixing blade within a slower-moving wet mass is relevant, along with the contact or consolidation time and boundary conditions, especially in compressive flows. In either case, the magnitude of fluctuations in the flow and stress fields may be even more critical to the micro scale transformations, and much work remains to be done in this area. In the current analysis, however, we consider flow regimes broadly based only on conti nuum averages of flow fields. A regime analysis of granular flow (Fig. 1 6) is helpful to elucidate the state of flow in a mixer-granulator. Empirically, many practitioners observe an operational "sweet spot", corresponding to a stable or resonant flow condition in the mixer. In the current analysis, we hypothesize that this stable flow falls within the "fluid-like continuum" or intermediate flow regime (Fig. 1 6ii). For example, in a vertical-axis granulator, a material in this flow pattern may be observed to follow a spiral "roping" flow, i.e., a toroidal flow with a helical spin, where the entire batch of material is uniformly participating in the flow field (Fig. 1 8b). In some cases, this type of flow may induce an audible resonance or "ringing" in the mixer. This type of flow provides a relatively uniform stress field throughout the product mixture and may result in a product with a narrow distribution of granular attributes (a narrow particle size distribution, uniform particle porosity, compositional homogeneity, etc.). Detailed simulations of centripetal flows further elucidate the shear gradients in such flows [63].
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Fig. 1 8. A vertical section of a flow patterns in a vertical-axis mixer-granulator. In case (a), the shear stress from the impeller decays over a short distance (3) relative to the mixer scale (R), net, the flow above the impeller may remain in frictional regime (i) even though the flow in volume swept by the impeller may be highly agitated or cOllisional (iii). In case (b), the shear stress is substantially transmitted into the granular mass, resulting in a spiral flow pattern (ii).
To place the centripetal spiral flow on the regime map, we use a modified the definition of the dimensionless shear rate. For mixers operating at high particle Froude number, Le., in substantial excess of unity, it is relevant to use centripetal acceleration instead of gravity. Further, we notice that in a binder-granulation process, the shear-induced flow may extend substantially across the ring-width of the spiral flow. As such, the characteristic length scale (<5) used to calculate the shear rate may be significantly larger that the particle size (dp). In the presence of cohesive binders, <5 may even approach the full width of the spiral flow. Lastly, the shear rate should reflect the actual granular particle velocity rather than the im peiler tip speed. Combining these adjustments, one can re-write the dimension less shear rate for a vertical-axis mixer-granulator in terms of two other dimensionless quantities: K1 is the ratio of the average particle velocity (Vp ) to the impeller tip velocity (Vi); and K2 the ratio of the shear stress decay length scale (6) relative to the mixer radius (R) (equations (1 3-1 5)). (1 3) (1 4) ( 1 5) K1 is the ratio of the average tangential particle velocity relative to the impeller tip speed. It represents the normal transfer of momentum from the impeller to the granular material, Le., in the direction tangential to the impeller rotation. The value of K1 may depend on the design of the impeller and its angular velocity, the
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constitutive properties of the material and the fill ievel. Two sorts of analyses have been published for vertical axis machines: ( 1 ) bulk flow at the free surface, using high-speed image processing [1 7,63,64]; and (2) tracer particle tracking using positron emission particle tracking (PEPT) to elucidate distributions of particle translation and velocity based on tracking individual particles within the bulk flow [57,65,66]. The former shows have shown typical values for K1 on the order of � 1 0-1 5% with pharmaceutical-grade excipient powders in an industrial mixer granulator while the latter, using mm-scale glass beads in a customized flat-blade mixer, shows a skewed velocity distribution with the a well-defined mode at �60% [65]. PEPT studies in a horizontal axis mixer at moderate Froude numbers show K1 values ranging from 2 to 25% for an agglomeration system of PEG solution binder and calcite powder, depending on the position in the mixer and the amount of binder addition [57]. Note that the instantaneous velocity of a particle may fluctuate substantially from the mean particle velocity. Indeed, the magni tude of the velocity and stress f1uctuations may be more relevant to micro-scale transformations such as coalescence, consolidation and breakage. K2 is the ratio of the shear stress decay length scale relative to the mixer scale; it also depends on the constitutive properties of the powder or granular material as weil as the fill level and mixer scale. For a wet-mass granulation in a lab-scale granulator, one might estimate typical values of K2 in the range of �1 0%. On the other hand, a larger-scale granulator will tend to see smaller values of K2 be cause 1J does not necessarily scale with the mixer radius. This is especially critical at the start of a batch as binder is initially added to the dry powder. In a dry powder, shear stress decays substantially on the order of a few particle (or cohesive cluster) diameters and 1J may be very small compared to R. Indeed, scaling-up to a larger mixer diameter may cause flow bifurcation (Fig. 1 8a) [1 6]. It is only after the binder is distributed throughout the powder mass that 1J increases due to bulk cohesion and the intermediate flow pattern is achieved. Using the modified version of the dimensionless shear rate (equation ( 1 5)), the flow behavior of powder or granules in the mixer-granulator can be mapped as a function of the tangential and shear flow components, K1 and K2 (Fig. 1 9). The intermediate or "fluid-like" regime is shown in the middle of the diagram (Region ii). At higher K1 and lower K2 values, the flow may become more excited and collisional (Region iii). On the other hand, lower relative particle velocities com bined with more cohesive interactions may result in slow-frictional flow (Region i). Generally it is preferable to operate mixer granulators in a more uniform flow and stress field (Region ii). It is fortunate that this region appears to be large com pa red to the range of reasonable parameter values on the diagram. In this example of the centripetal mixer-granulator, a key result of the analysis is that the angular velocity (w) drops out of the dimensionless shear rate. In other words, the flow regime hypothesis predicts that is not necessary to maintain the exact value of the Froude Number on scale-up, only that the Froude number is
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Scale-Up of High-Shear Binder-Agglomeration Processes 1 00%
� 11
-r----r--""l-----,
10%
'"
�
1 % +--.-,-,--.-.TTTr-�____,_.__TT"rrrl 1%
1 00%
Fig. 1 9. Hypothetical flow regime map for a mixer-granulator operating at high Froude Number. The dimensionless shear rate, defined according to equation ( 1 5), is used to define flow regions: (i) frictional , y' < 0.2; (ii) intermediate, f1uid-like; and (iii) rapid collis ional, y' > 3. K1 represents the transfer of tangential momentum from the impeller to the powder or granular material; K2 represents momentum transfer by shear along the axial direction.
high enough to assure that centripetal acceleration exceeds gravity. This means that the impeller tip speed is the more relevant parameter for scale-up, as it relates directly to the inter-particle stress in the bed. This theoretical result is consistent with many experimental and empirical findings where tip speed (or a tip-speed favored compromise with Froude number) is used as a basis for scale up for high-shear mixer granulators.
3.5. Delivery number
The delivery number is a measurement of throughput capacity in a continuous agglomeration system (equation (1 6)). It relates the size of the mixer (0) to the speed of the mixing bl ades (N) and the volumetric throughput rate of the product (Q). delivery # =
Q ND
3
(1 6)
On scaling up, the delivery number can be used as starting point calculation of the physical throughput capacity in a continuous mixer-agglomerator system ; however, similarity of the delivery number does not guarantee similarity of other parameters which may have more important effects on the transformations oc curring in the process. For this reason, it is recommended to consider details of
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the swept volume interactions along with the delivery number, specifically in regards to potential differences in the direct interaction between the mixing tools and the product (i.e., impact) vs. shear interactions where the product is not directly impinging on the tools. 3.6. Spray flux
The spray flux is related to the dispersion of an atomized binder in the powder, and it is related to the homogeneity of the product on a micro-scale. A dimen sionless spray flux for drop-templated nucleation is defined as a measure of droplet density on the surface of a moving powder bed (equation ( 1 7» , expressed in terms of the volumetrie liquid spray rate ( V'), average droplet size (dd) and the speed of the powder bed surface traversing the spray zone (A') [1 9,67]. spray flux =
'Pa = 2A'3 V'dd
(1 7)
Other aspects of the spray (e.g., conventional spray flux, number of droplets/ particle) are relevant to dispersion and coating. Additional discussion of the spray flux, nucleation and product homogeneity is provided in the micro-scale section. There are many advantages that a binder spray system can afford to a granulation process; however, there can be diffi culties both in scaling-up and in scaling-down equipment on the basis of the dimensionless spray flux [64]. From an equipment scale-up perspective, it may be necessary, from a micro seale perspective, to maintain the size of the droplet diameter (dd). And the range of adjustment in the volumetrie liquid flow rate ( V') may be narrow based on formulation and throughput rate requirements. Therefore, to maintain similarity of the spray flux, one is required to maintain the flux of powder traversing the spray zone (A'). In most industrial mixer-granulators, the bed depth increases on scale up, making the above requirement unfeasible unless the powder in the spray zone can be actively refreshed by a more rapid turnover of the powder bed surface. To an extent, this laUer approach can be achieved by increasing the level of fluidization of the powder in the spray zone, i.e., by operating at a higher Froude number; however, this may introduce other complications, e.g., by in creasing consolidation or breakage. In this case, agitated fluid-bed mixers may be advantageous [ 1 0]. There are also practical limitations in scaling down a spray-on system. It may be desirable to scale down to the smallest practical size for development work. However, in a system that involves spray-nozzles, especially single-fluid atomizers, there is typically a minimum working distance for atomization to occur, i.e., for the breakup of the fluid sheet and/or ligaments to form discrete droplets.
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3.7. Process ancillaries
In industrial installations, ancillary powder-handling infrastructure is also critical to scale-up. The stability of a continuous operation depends on the precision of feeders and flow controls. Conveying, handling and, in some cases, climate control of sensitive raw materials can be critical to processing. Care in conveying and handling of the finished product is important in preventing attrition or other degradation of the finished granular material. Transport of intermediate material between unit operations can be especially critical to process reliability. In scaling up continuous agglomeration processes from pilot to full scale, it is common to see an increase in the ratio of product/air flux in ancillary chutes, bucket elevators, classification screens, etc. On the pilot scale, the average product rate is intentionally low relative to the instantaneous handling capacity of chutes and other transport operations. On the other hand, the economic objective of the full-scale plant is to maximize the production rate relative to the equipment capacity. This can create issues for moist products in chutes and other conveying systems between unit operations. If the product/air ratio becomes too high, then the air-stream can become saturated and condensate will form on cooler sur faces, leading to product build-up and potential blockages. The analysis of instantaneous VS. mean rates is especially relevant to the sizing of recycle handling systems. In some cases, the instantaneous recycle in an agglomeration plant can be very substantial compared to the mean recycle rate. Instantaneous surges in recycle can clog conveyors, overload bucket el evators, etc. Design of product handling systems based on mean product rates can fail in cases of startup, shutdown or other process disturbance where the instantaneous rates may be substantially higher than the mean. The value of process control is amplified when considering opportunities for capital avoidance in handling systems. A more robust control strategy can minimize surges and reduce the need for over-sized handling equipment. This is a good example of how linkages between macro-scale process design and micro-scale analysis and control strategies for specific product attributes can be very cost effective.
4. M U LTI-SCALE APPROACH - LlN KI N G MICRO- AND MACRO SCALE APPROACHES
The transformation approach provides an overall framework for considering how scale-up decisions on a macro-scale may influence micro-scale particle attributes. Conversely, if specific product attributes are known to be very impor tant to the performance of a granular product, then the scale-up decisions can be focused on maintaining similarity of these specific attributes. Beyond this framework, however, the transformation approach does not give explicit linkages
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between the micro and macro scales. More recently, the linkage of micro and macro scales, i.e., in the form of a multi-scale approach, has evolved into the current state-of-the-art in granulation research. It may be convenient to develop meso-scale linkages using a collection of models (Fig. 20) [68]. Combining the micro and macro approach is important to achieve a practical scale-up and control strategy. The two approaches offen overlap at a constitutive level (e.g., case 3 in Fig. 20), where the physical response of the raw materials to process energy and power is defined [24-27]. Given the degree of complexity posed by the agglomeration process (i.e., both powder and liquid material prop erties, where the distribution of the two change during the process), it may not be practical to attempt to model the full system in a purely fundamental way. On the other hand, an empirical or phenomenological understanding of the rheo-mechan ical properties of the in situ wet-mass materials is very helpful in building models that link the micro and macro scales. For this reason, it is offen convenient to define a meso-scale based on constitutive interactions in the agglomeration process. Another key area where multi-scale modeling may ofter breakthroughs is in the understanding and manipulation of powder and granular flows in agitated mixer granulators. The flow of the material inside of the unit operation is a direct result
Seale:
Partiele produetion / handling:
Maero / system
Plant
Maero / Unit-op
Proeess equipment
Meso
Many partiele eonstitutive relations
Miero
Single particle
Miero
Partiele surfaee
Fig. 20. A multi-scale diagram for a particle production. Examples of models that span scales: ( 1 ) Optimize arrangements of unit-operations within a production system, e.g., a dynamic process model used to optimize the throughput and reliability of a continuous manufacturing process with recycle streams; (2) Visualization of flow patterns in process equipment and the interaction between product transformations and flow patterns; (3) Constitutive models linking equipment operating parameters with material properties to predict product transformations; (4) Design of micro-scale granular features to improve meso-scale constitutive behavior, for example, surface modification of granules for im proved flow and dispersion; and (5) Design of granular structures based on simulation of desired performance attributes; for example, the use of coating layers with various me chanical properties to provide attrition-resistant granules.
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of the interaction between the mechanical mixing elements and the product in the mixer, as discussed in earlier sections: swept volume, stress and flow fields. The resultant flow patterns depend on the rheo-mechanical properties of the powder/ granules and the stress transmission therein. Inversely, the flow patterns can influence many of the transformations in the process, as the powder is converted to a granular form. As such, the characterization of transitional flows is a prom ising area of work that may help advance the subject of granulation scale-up. Progress is being made in both modeling and experimental investigation of tran sitional flow phenomena [39,57] as weil as in sensors that can detect changes in flow patterns [69].
5. SUMMARY AND FORWARD LOOK
This chapter is primarily focused on reviewing the considerable body of work that is relevant to scale up of binder agglomeration processes, much of which has been published over the past decade. Over this time has evolved the realization that binder granulation is both a sequential and interconnected set of complex sub-processes that can be categorized into binder wetting and spreading, granule growth and consolidation, and granule attrition and breakage. A more detailed progression of the product through these sub-process categories can be con veniently analyzed using the concept of transformations. Several key advances complement this view of agglomeration, including the analysis of flow patterns in mixer-granulators, the effect of spray flux on binder dispersion and granule nu cleation, and the linkage of process parameters with material properties to de velop controlling groups for product transformations. The linkage between mixer flow patterns and the deformation of wet-mass materials is especially apt for scaling of mechanically agitated mixer granulators [70]. 5.1 . Flow patterns in m ixers
On a macro-scale, there have been significant advancements in understanding flow patterns within granulation equipment and the importance of distributed flow patterns to critical transformations. Flow patterns are relevant to the binder dis persion, shear and impact interactions within the product. For batch processes, one often finds significant changes in the flow patterns inside of the mixer on scaling-up to a larger volume. An appreciation for the bulk flow patterns may affect the operating strategy relative to the introduction of a liquid binder. For example, a strategy to temporally separate the dispersion and growth transfor mations suggests that it may be more efficient to start the addition of binder in a more highly-fluidized mixer (e.g . , following a Froude number scale-up), but then
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reduce the speed to a constant tip-speed basis as the saturation increases and the shear stress is more effectively transmitted through the bulk bed. Continuous processes offer the option to spatially separate flow-dependent transformations across multiple mixers or multiple zones in a mixer. Flow patterns in mixers are important for both of the following discussion points. 5.2. Binder spray flux
On a micro-scale, the effect of spray flux on the nucleation of granules is an important concept for both scale-up and control applications. Maintaining a con stant spray flux from small to large-scale process equipment is typically a chal lenge. A rigorous scale-up strategy based on dimensionless spray flux may compromise the economy of the larger scale. Given the economic objectives of scale-up, it is common to see an increase in the spray flux as material flow rates and/or batch sizes increase. Increasing the spray flux typically results in a broadening of distributed product characteristics, e.g., a broader agglomerate size distribution. The spray-flux concept underscores the balance between binder atomization (i.e., droplet size) and the location of the spray zone relative to the powder flow in the mixer. In a mechanical mixer, a weil-mixed powder flow can be used to effectively compensate for a higher binder spray flux. 5.3. Linkage of process parameters with material properties
In the case of mechanically agitated granulators, the development of controlling groups that link process parameters with material properties has been an im portant advancement. 8alancing the force and energy acting on the wetted par ticles with wet-mass constitutive properties provides a more fundamental basis for understanding the importance of tip-speed as a primary scale-up parameter. In a mixer granulator, the motion of the impeller creates a distributed range of shear and collisional impacts within the product, where the maximum shear and impact events are related to the impeller tip-speed. These forces are linked directly to consolidation and coalescence of the wet-mass materials. 80th av erage and maximum forces are relevant to product transformations, where the distribution of the applied stress and net energy may be significantly related to the flow patterns in the mixer. 80th force and energy balances are applicable to the analysis. The force bal ance considers single shear or impact events. Energy balance can be applied to discrete deformation events as weil as the cumulative energy obtained by integrating power draw over the RTD. While the latter approach is attractive
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because of the convenience of measuring power draw, challenges remain on how to partition the gross power consumption into net power associated with critical transformations vs. other power that is lost in the process. The material characteristics of the wet mass are the other part in the consti tutive balance. Linking the applied forces (e.g., via tip speed of the mixer) with material properties (e.g. , via binder loading and/or temperature) expands the palette of design options in scaling-up an agglomeration process. For example, an empirical understanding of how wet-mass material properties change with raw material or seasonal variations (e.g., alternate suppliers, lot to lot variation, tem perature, humidity, etc.) can be used as a basis for specifying an adjustable range of process parameters that can be used to compensate for the material variations. Empirical characterization of lumped properties can be a useful way to quan tifying parameters in controlling groups. For example, an apparent yield stress of a granule or wet-mass mixture can be a useful indicator of the constitutive re sponse of the composite material. A yield stress measurement includes the lumped effects of raw material properties (powder and binder), the interaction of these properties in the mixture and the structure of the composite mixture. An other example of this practical, if not elegant, lumped-approach include the droplet penetration time measurement developed in conjunction with the inves tigation of binder spray-flux [8, 1 7]. which considers the effect of powder surface chemistry as weil as the surface tension and the viscosity of the liquid binder. Another more recent example is the use of in situ sensor particles to measure the net physical effect over a distribution of shear and impact stresses within an agitated granular flow inside a mixer-granulator [29]. During scale-up, it may be advantageous to include process control features that enable product attribute adjustments by adjusting characteristics or proper ti es of the raw material inputs. This approach requires a model that links fun damental material properties to a product transformation. For example, a process adjustment for binder viscosity has been used to control particle density accord ing the Stokes criteria for consolidation [4]. More broadly speaking, however, the use of constitutive models based on fundamental raw material properties remains as a practical challenge for both scale up and contral applications. 5.4. Batch and continuous systems
Batch and continuous processes each have advantages and disadvantages. On the one hand, batch processes are best suited to small production quantities and/or when frequent product changeovers are required in a set of production equipment. While product changeovers and equipment cleanouts are never efficient usages of capital, cleanout is considerably simpler in a batch process
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vessels compared to cleanout of transport and recycle streams associated with continuous processes. Batch processing also provides a basis for mass balance closure between raw material inputs and the product assay. On the other, continuous processes are much more efficient for production of large product quantities, and offer increased capability for on-line process contro!. In addition, scaling-up the production rate by moving from a small-scale batch prototype system to a continuous production system with similar critical dimen sions is typically more robust than scaling from small to large batch vessels because the pattern of flow within the similarly sized mixers can be more easily maintained. 5.5. P roductive use of recycle
The effect of recycle can be significant in a scale-up strategy. Continuous sys tems typically include integrated or downstream classifying steps. The center-cut product is consistently high in quality, and the outlying cuts (e.g. , fines and over size) can be recycled back to the granulation unit. The oversize material is usually reduced in size (e.g. , by a grinder) before it is re-introduced to the granulator. The recycle stream can be very useful in stabilizing the granulation process, espe cially when recycle streams are metered back to the process in a controlled way (e.g . , from a surge bin). A controlled recycle stream in a continuous operation can improve product quality and process control, e.g., by increasing product homo geneity, seeding growth and providing a means to implement feed-forward con trol strategies. Adding a fractional amount of recycled material in a batch process can also provide an operational advantage. Recycle material is typically coarser in size and has a higher bulk density than the raw materials which are offen cohesive fine powders. In this case, the effect of the recycle can be to "seed" or ignite the bulk flow of powder inside the mixer, providing a more consistent pattern of powder flow during the binder addition stage of the process. 5.6. Models
The development of population balance models has seen considerable academic progress over the past decade and there has been progress toward the formu lation of models with growth kerneis based on physical mechanisms [71 ]. The population balance has been applied to process simulators and to feed-forward control of continuous systems with recycle streams [72]. However, the practical use of such models for many scale-up applications remains on the technical frontier [73]. Recent work using multi-dimensional population balances is moving
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toward the capability to model multiple granule attributes [74]. Multivariate mode ling promises to become a useful way to formalize knowledge of critical trans formations as interdependent kernel functions, e.g., coalescence and breakage functions that are dynamically dependent on binder distribution (dispersion) and granule structure (consolidation) functions. Stochastic population balances and simulation methods are becoming attractive for multivariate analyses. Constitutive models can be used to describe physical transformations in terms of force or energy balances. The ability to quantify applied force or energy relative to material properties is vital to the utility of these models. For initial scale-up estimates, it may be sufficient to calculate applied energy based on tip speed of an impeller, and to use a simple lumped-property measurement (e.g., yield stress) as an estimate of the complex rheo-mechanical interactions in the wet mass material. Moving forward, more sophisticated modeling techniques (e.g. , CFD, DEM, and quasi-continuum models) are anticipated to predict particle flow patterns, shear distributions and collision velocities for mixer-granulators of different scales. 6. CONCLUSION
Scale-up is complicated by the many product transformations that may occur si multaneously in agglomeration processes. Although transformations may overlap and feedback among each other, they can be modeled discretely on a micro-Ievel. Deeper understanding of discrete transformations lends insight to the fundamental mechanisms affecting the product attributes. Ideally, scale-up based on product attributes would maintain similarity across all transformations that effect key product attributes. However, when it is not possible to maintain similarity across all transformations within a given unit operation, it may be advisable to separate the transformations, for example, by staged processing in a batch unit or adding ad ditional unit operations for specific transformations in a continuous process. Transformations depend on interactions between the process and material properties. Scale-up is often complicated because process parameters may effect more than one transformation. Additional complexity is introduced by the require ment to consider material properties in all relevant states, including intermediate binder-powder mixtures and local temperature and humidity conditions. It is often the case that the relevant material properties are based on a mixture of powder and binder that is changing depending on the degree of saturation. To move ahead, we need to continue to link micro-scale analysis with key product trans formations. Sorting out the complexities of in situ material property transforma tions requires continued progress in on-line monitoring of process-parameters and material properties. This expanded capability of materials characterization is im portant for both micro-scale and macro-scale approaches.
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ACKNOWLEDGME NTS
I would like to acknowledge my extensive collaboration with Prof. Gabriel Tardos as weil at the fruitful discussions on granulation and multi-scale modeling projects supported by the International Fine Particle Research Institute (IFPRI), especially Prof. Peter York, Prof. Jim Utster and Or. Karen Hapgood. In addition, I would like to acknowledge my colleagues at the Procter & Gamble Co., especially Or. Hasan Eroglu for his contributions on CFO modeling, Larry Genskow, George Kaminsky, Wayne Beimesch and Scott Capeci for their insight on the efficient and practical scale-up of industrial granulation processes. REFERENCES [1] P. Mort, Powder Technol . 1 50 (2005) 86-1 03. [2] P. Mort, G . 1 . Tardos, Kona 17 (1 999) 64-75. [3] P. Mort, Dimensional analysis of agglomeration: scale-up using transformations, Proceedings of the World Congress on Particle Technology, Vol. 3, 1 998. [4] P. Mort, S. Capeci, J. Holder, Powder Technol . 1 1 7 (200 1 ) 1 73-1 76. [5] B.J. Ennis, J.D. Utster, Size reduction and size enlargement, in: D . Green , (Ed.), Perry's Chemical Engineer's Handbook, McGraw-HiII, , 1 997, Section 20, pp.56-89. [6] W. Pietsch , Agglomeration Processes: Phenomena, Technologies, Equipment, Wiley-VCH, Weinheim, 2002. [7] K.V.S. Sastry, DW. Fuerstenau, Powder Technol. 7 (1 973) 97-1 05. [8] S.M. Iveson, J.D. Utster, K. Hapgood, B.J. Ennis, Powder Technol . 1 1 7 (2001 ) 3-39. [9] T. Schaefer, C. Mathiesen , Int. J. Pharm. 1 39 ( 1 996) 1 25. [ 1 0] S. Watano, Y. Sato, K. Miyanami, T. Murakami, Chem. Pharm. Bull. 43 (7) (1 995) 1 2 1 2-1 220. [1 1 ] P.C. Knight, T. Instone, J . M.K. Pearson , M.J. Hounslow, Powder Technol. 97 ( 1 998) 246-257. [1 2] D . M . Newitt, J . M . Conway-Jones, Trans. Inst. Chem. Eng. 36 (1 958) 422-441 . [1 3] H.G. Kristensen, Particle Agglomeration, in: D . Ganderton, T. Jones, J . McGinty (eds), Advances in Pharmaceutical Sciences, Academic Press, London, 1 995. [14] S.H. Schaafsma, P. Vonk, P. Segers, NW.F. Kossen, Powder Technol . 97 ( 1 998) 1 83-1 90. [ 1 5] T. Schaefer, C. Mathiesen, Int. J . Pharm. 1 39 ( 1 996) 1 25-1 38. [1 6] J . D . Utster, K.P. Hapgood, J . N . Michaels, A. Sims, M. Roberts, S . K. Kaminini, Pow der Technol. 1 24 (2002) 272-280. [ 1 7] K.P. Hapgood, Nucleation and Binder Dispersion in Wet Granulation, The University of Queensland, Ph. D . Thesis, 2000. [1 8] S . H . Schaafsma, P. Vonk, NW.F. Kossen, Int. J. Pharm. 1 93 (2000) 1 75-1 87. [ 1 9] K.P. Hapgood, J . D . Utster, E .T. White, P. Mort, D.G. Jones, Powder Technol. 1 4 1 (2004) 20-30. [20] B.J. Ennis, G . 1 . Tardos, R. Pfeffer, Powder Technol. 65 ( 1 99 1 ) 257-272. [21 ] P. Mort, R.E. Riman, Kona 1 2 (1 994) 1 1 1-1 1 7. [22] N . Ouchiyama, T. Tanaka, I&EC Process Des. Dev. 1 4 ( 1 975) 286-289. [23] H.G. Kristensen, P . Holm , T. Schaefer, Powder Technol . 43 ( 1 985) 225. [24] S . M . Iveson, J . D . Utster, B.J. Ennis, Powder Technol . 88 (1 996) 1 5 . [25] S.M. Iveson, J.D. Utster, AIChE J . 44 (7) ( 1 998) 1 51 0-1 5 1 8. [26] S.M. Iveson, N.W. Page, J . D. Utster, Powder Techno!. 1 30 (2003) 97-1 0 1 . [27] G . 1 . Tardos, M. Kahn, P. Mort, Powder Techno!. 94 ( 1 997) 245-258.
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[28] H. Rumpf, The strength of g ranules and agglomerates, in: WA Knepper, (Ed.), AlME, Agglomeration, Interscience, New York, 1 962, pp. 379-41 8. [29] G . I . Tardos, K.P. Hapgood, 0.0. Ipadeola, J.N. Michaels, Powder Techno!. 140 (2004) 2 1 7-227. [30] K. van den Dries, O . M . de Vegt, V. Girard, H. Vromans, Powder Techno!. 1 33 (2003) 228-236. [31 ] D. Verkoeijen, G . M . H . Meesters, P.H.W. Vercoulen, B. Scarlett, Powder Techno!. 1 24 (2002) 1 95-200. [32] W.J. Beekman, G. Meesters, T. Becker, A. Gaertner, M. Gebert, B. Scarlett, Powder Techno!. 1 30 (2003) 367-376. [33] M. Samimi, R Ghadiri, A Boerefijn , R Groot, Kohlus, Powder Techno!. 1 30 (2003) 428-435. [34] T. Schaefer, P. Holm, H . G . Kristensen, Acta Pharm. Nord. 4 ( 1 992) . [35] P. Holm, T. Schaefer, H . G . Kristensen, Powder Techno!. 43 ( 1 985) 225-233. [36] H. Kristensen , T. Schaefer, Drug Dev. I nd. Pharm. 1 3 ( 1 987) 803-872. [37] H. Leuenberger, Eur. J. Pharm . Biopharm. 52 (2001 ) 279-288. [38] Faure, P. York, RC. Rowe, Eur. J. Pharm. Biopharm. 52 (200 1 ) 269-277. [39] Talu, G. Tardos, J .T. van Ommen, Powder Techno!. 1 1 7 (2001 ) 1 49-1 62. [40] M . Landin, P. York, M.J. Cliff, RC. Rowe, AJ. Wigmore, Int. J . Pharm. 1 33 ( 1 996) 1 27-1 31 . [41 ] Hancock, P. York, RC. Rowe, I nt. J. Pharm. 83 ( 1 992) 1 47-153. [42] M. Delalone, G. Baylac, B. Bataille, M. Jacob, A Puech, I nt. J. Pharm. 1 30 ( 1 996) 1 47-1 51 . [43] G . Betz, P.J. Bürgin, H . Leuenberger, I nt. J. Pharm. 252 (2003) 1 1 -25. [44] Faure, I . M . Grimsey, P. York, M.J. Cliff, RC. Rowe, Mixer torque rheometry: rela tionships between wet mass consistency in pharmaceutical wet granulation proc esses and subsequent dry granule properties, Proceedings of the World Congress on Particle Technology 3, 1 998. [45] M.J. Cliff, Pharm. Tech. 4 ( 1 990) 1 1 2-1 32. [46] P. Holm, T. Schaefer, H . Kristensen, Powder Techno!. 43 ( 1 985) 2 1 3-223. [47] H.G. Kristensen , Powder Tech. 88 ( 1 996) 1 97-202. [48] P.C. Knight, Powder Techno!. 77 ( 1 993) 1 59-1 69. [49] M . Bardin, P.C. Knight, J.P.K. Seville, Powder Techno!. 140 (2004) 1 69-1 75. [50] M. Mackaplow, L. Rosen, J. Michaels, Powder Techno!. 1 08 (2000) 32-45. [51] N . Somerville-Roberts, P. Mort, Product build-up in high-shear agglomeration sys tems, Proceedings of the AIChE Particle Technology Forum Topical Conference, Engineered Particle Systems: Synthesis, Processes & Applications, 2003. [52] M.J. Adams, R McKeown, Powder Techno!. 88 ( 1 996) 1 55-1 63. [53] P. Mort, Analysis and application of powder compaction diagrams, in: A Levy, H. Kaiman (Eds.), Handbook of Conveying and Handling of Particulate Solids, Elsevier Science, Amsterdam , 2001 . [54] M . Naito, K. Nakahira, T. Hotta, A Ito, T. Yokoyama, H . Kamiya, Powder Techno!. 95 ( 1 998) 2 1 4-21 9. [55] S.M. Iveson, J A Beathe, N.w. Page, Powder Techno!. 1 27 (2002) 149-16 1 . [56] T. Schaefer, H . H . Bak, A Jaegerskou, A Kristensen, J . R Svensson, P . Holm, H . G . Kristensen, Pharm. I n d . 4 9 ( 1 987) 297-304. [57] S. Forrest, J. Bridgwater, P. Mort, J. Utster, D. Parker, Powder Techno!. 1 30 (2003) 9 1 -96. [58] P. Mort, I ntermediate powder flow - An industrial perspective, IFPRI Powder Flow Workshop, International Fine Powder Research Institute Annual Meeting, Bremen, 2003. [59] G . I . Tardos, P. Mort, Dry Powder Flows, in: C. Crowe, (Ed.), Multiphase Flow Hand book, CRC Press, , 2006 , Chapter 9. [60] G . ! . Tardos, S. McNamara, I. Talu, Powder Techno!. 1 31 (2003) 23-39.
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[61 ] A.W. Jenike, Storage and flow of solids, Bulletin No. 1 23, Utah Engineering Experi ment Station, Vol 53, No 26, ( 1 964). [62] R.M. Nedderman, Statics and Kinematics of Granular Materials, Cambridge University Press, Cambridge, U K, 1 992. [63] Y. Muguruma, T. Tanaka, Y. Tsuji, Powder Technol. 1 09 (2000) 49-57. [64] R. Plank, B. Diehl, H. Grinstead, J. Zega, Powder Technol. 1 34 (2003) 223-234. [65] R.L. Stewart, J. Bridgwater, D.J. Parker, Chem. Eng. Sci. 56 (20 0 1 ) 4257-4271 . [66] B.F.C. Laurent, J. Bridgwater, Chem. Eng. Sci. 57 (2002) 3781-3793. [67] J.D. Litster, K.P. Hapgood, J.N. Michaels, A. Sims, M. Roberts, S.K. Kameneni, T. Hsu, Powder Technol. 1 1 4 (200 1 ) 32-39. [68] P. Mort, A multi-scale approach to modeling and simulation of particie formation and handling processes, Proceedings of the 4th International Conference for Conveying and Handling of Particulate Solids, 2003. [69] H. Tsujimoto, T. Yokoyama, C.C. Huang, I. Sekiguchi, Powder Technol. 1 1 3 (2000) 88-96. [70] P. Knight, Powder Technol. 1 40 (2004) 1 56-162. [71 ] L.X. Liu, J.D. Litster, Chem. Eng. Sci. 57 (2002) 21 83-2 1 9 1 . [72] F .Y. Wang, ! .T. Cameron, Powder Techno! . 1 24 (2002) 238-253. [73] S.M. Iveson, Powder Techno!. 1 24 (2002) 21 9-229. [74] A. Biggs, C. Sanders, A.C. Scott, A.w. Willemse, A.C. Hoffman, T. I nstone, A.D. Salman, M.J. Hounslow, Powder Technol. 1 30 (2003) 1 62-1 68.
CHAPTER 20 G ra n u lation Rate P rocesses K . P . H a pg oo d , a S . M . Iveso n , b J . D . Litsterc, * and L.X. Liuc
aOepartment ofChemica/ Engineering, Monash University, P o. Box 36, V/C 3800, Australia bcjo 7 Long/and St, C/eve/and QLO 4163, Australia cSchoo/ of Engineering, The University of Queens/ami, St Lucia, Q/d 4072, Austra/ia Contents
1 . I ntroduction 2. Wetting and nucleation 2. 1 . Wetting and nucleation regi mes for granulation 2 . 1 . 1 . Drop penetration times 2.1 .2. Experimental measurement of drop penetration time 2.1 .3. Dimensionless spray flux 2.1 .4. Practical application of 'Pa and 'Pn 2.2. A nucleation regime map 2.3. Other nucleus formation modes 2.3. 1 . Hydrophobie nucleation 2.3.2. Porous particles 2.3.3. Nucleus structures 2.4. Summary 3. Growth and consolidation 3. 1 . Background 3.2. Granule growth regimes 3.3. Granule consolidation 3.3. 1 . Consolidation models 3.3.2. Experimental studies of consolidation 3.3.3. Particle size and binder viscosity 3.3.4. Binder surface tension 3.3.5. I mplications for granule growth and induction time 3.4. Granule coalescence models 3.4. 1 . The ennis coalescence model for non-deformable granules 3.4.2. The liu et al. model of deformable g ranule coalescence 3.4.3. Limitations of both coalescence models 3.5. Bond formation between granules 3.5. 1 . Theory 3.5.2. Experiment 3.6. Summary comments on granule growth and consolidation 4. Wet granule breakage 4. 1 . Experimental observations * Corresponding author. E-mail: [email protected]
Granulation Edited byA.D. Sa/man, M.J. Houns/ow and J. P.K. Seviffe .c Elsevier SV All rights reserved
2007
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4.2. Predicting conditions for breakage 4.3. Mechanical properties of semi-brittle wet agglomerates 4.4. Concluding comments on wet granule breakage 5. Concluding comments: where to from here in the field of granulation? Uncited References References
1 . INTRODUCTION
Wet granulation is a complex process with several competing physical phenom ena occurring in the granulator, which ultimately leads to the formation of the granules. We will divide these phenomena into three groups of rate processes (Fig. 1 ): 1 . wetting, nucleation and binder distribution; 2. consolidation and growth; and 3. attrition and breakage. (i) Wetting & Nucleation
. .. . .. .. ..
.
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•
..
• • •• • •
.
.. •
•
.
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(iii) Attrition & Breakage
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.-
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.
.
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.-
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Fig. 1 . Rate processes i n granulation (i) wetting and nucleation; (ii) consolidation and g rowth; (iii) breakage and attrition [1].
G ranulation Rate Processes
899
The physical phenomena that contral these processes are the same, inde pendent of the type of granulation used. Granule size, size distribution and po rosity, as weil as many other key product attributes, are controlled by the balance of the rate processes that occur in the granulator. The first stage of granulation is the addition and distribution of the binder to give nuclei granules. This occurs within the liquid spray zone in the granulator. The liquid binder is usually sprayed onto the moving powder bed. Ideally, each drop will imbibe into the powder bed, engulfing particles to form a single granule nucleus. If the drop does not easily wet the powder, or the rate of imbibition is slow, large wet agglomerates will form at the powder surface. Sometimes shear forces within the powder bed are large enough to break up these clumps of wet material to further distribute the liquid. Nucleation gives a distribution of loosely packed granule nuclei. Granule nuclei will consolidate through collisions with other granules, and granulator. The extent of consolidation depends on the intensity of agitation in the granulator and re sistance of the granule to deformation. Granule consolidation controls the final granule porosity which influences many other granule properties. When two granules collide they may stick together to form a single large granule. This is growth by coalescence. For successful coalescence (a) the en ergy of impact must be absorbed during collision so that the granules do not rebound; and (b) a strong bond must form at the contact between the colliding granules. The presence of liquid at the surface of the granule is important for growth by coalescence and coalescence rate is very sensitive to liquid content. Consolidation and coalescence are closely related and are considered together in this chapter. Breakage of wet granules will influence and may control the final granule size distribution, especially in high-shear granulators. In some circumstances, breakage can be used to limit the maximum granule size or to help distribute a viscous binder. These rate processes are at the heart of the granulation process and determine the final granule properties. It is important to know which rate processes dom inate in any particular application. For example, if nucleation is the dominant rate process, adjusting the liquid spray nozzles will have a prafound effect on granule size distribution. If coalescence rates are high, granule size will be very sensitive to liquid content and granule residence time. In this chapter, we will: • • • •
examine the underlying physics behind each rate process; define the controlling formulation properties and process parameters for each rate process; use regime maps to establish the operating regime for the granulator; and provide quantitative relationships to predict the effect of changing operating parameters and formulation properties.
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This chapter focuses on developments in the last decade where substantial advances in our quantitative understanding of granulation rate processes have been made with an emphasis on work done by our group at The University of Queensland and The University of Newcastle. We have drawn on recent reviews and monographs in this area [1-3] and current ongoing research. The philosophy of this chapter is to characterise process parameters in generic terms that are equipment independent (collision velocity, powder surface flux, etc.). For a more detailed guide to applying the rate process analysis to specific granulator types (fluidized beds, tumbling granulators, mixer granulators) see Utster and Ennis [2]. 2. WETTING AND NUCLEATION
The first stage in any wet granulation process is the distribution of the liquid through the feed powder, also called solution delivery and binder addition. The initial wetting and liquid distribution to produce nuclei or wetted particles is im portant for a variety of reasons: •
•
•
•
poor wetting leads to very broad nuclei size distributions and in extreme cases a mixture of over wet and ungranulated material; the granulation often retains a "memory" of the nucleation stage, with broad nuclei size distributions leading to broad granule size distributions; preferential distribution of liquid between individual ingredients can cause com ponent segregation with granule size; and Wetting phenomena also influence downstream granule processes, such as drying and redispersion in fluids.
Most experimental data in the literature is difficult to interpret because nucle ation, growth and perhaps breakage are occurring simultaneously. However, they generally agree that poor liquid distribution can change the granule mean size, the breadth of the granule size distribution, cause defluidisation and create large clumps or agglomerates. In some cases, changes in process variables, such as drop size and flow rate, were shown to be responsible for liquid dispersion prob lems. In other cases, changes in the material properties (e.g. contact angles of the powders or solution properties, such as viscosity), were shown to affect the granulation fluid dispersion. In many combinations, it was an unknown combi nation of both. When the drop size is larger than the particle size, wetting the powder with the liquid gives a distribution of seed granules or nuclei. When the drop size is small compared to the unit particle size, the liquid will coat the particles. The coating is produced by collision between the drop and the particle followed by spreading of the liquid over the particle surface. If the particle is porous, then liquid will also
901
Granulation Rate Processes
suck into the pores by capillary action [4]. The wetting dynamics control the distribution of coating material which has a strong influence on the later stages of growth. For these systems, the nucleus is the wetted primary particle. There are two conceptual nucleation mechanisms based on the relative size of the droplet to primary powder particles (see Fig. 2) that are particularly relevant for fluidized-bed granulation. If the drop is large compared to the particles, nu cleation will occur by immersion of the smaller particles into the larger drop. This produces nuclei with saturated pores. Nucleation with relatively small drops will occur by distribution of the drops on the surface of the particles, which will allow the wet particle to coalesce with other dry particles that it collides with. This will produce nuclei which may have air trapped inside and hence the granule will not be fully saturated (8< 1 00%). Although these mechanisms were originally proposed for melt agglomeration, they have been extended to cover wet granulation by Scott et al. [5], and have been directly observed by Si mons and Fairbrother [4]. The underlying assumption of the immersion-distribution hypothesis is that the thermodynamics of the wet ting are favourable and that the binder will always spread over the powder sur face. This is not necessarily true as the thermodynamic spreading coefficients AL S and ASL may be negative. Experimental observations support this [4,6]. In addition, the possibility of the solid spreading over the liquid must be included. This has been observed experimentally by Simons and Fairbrother [4]. Figure 2
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----.
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000
ogo
Solid (a)
/
�
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No spreading
�
Coalescence
<0 0 & (98
Limited coalescence
Solid spreading Fig. 2. Nucleation formation mechanisms when (a) the liquid drops are smalier than the solid and (b) when the solid particles are smalier than the liquid droplets. Adapted from Ennis and Litster [7], Rowe [8] and Tardos et al. [9].
902
K.P. Hapgood et al.
summaries all the possible formation mechanisms described in this section as a function of the ratio of particle to drop size and spreading coefficients. Each nucleation mechanism produces different nuclei morphologies, but ultimately they all depend on the same thermodynamic properties of the feed formulation during the nuclei formation stage - contact angle e and spreading coefficient. Utster and Ennis [2] discuss definitions of these properties and measurement techniques for typical granulation formulations in detail.
2. 1 . Wetting and nucleation regimes for granulation
The nucleation process can be divided into four stages (see Fig. 3): 1 . Droplets are formed at the spray nozzle at some size distribution and fre quency. 2. Binder droplets impact on the powder surface. Drops may coalesce at the powder bed surface and increase the effective drop size. 3. Each drop spreads across the bed surface and penetrates into the bed by capillary action to produce a loosely packed nucleus. 4. Shear forces within the bed may break up large wet clumps and nUcieate into smaller entities. These processes combine to define the nuclei size distribution produced as the powder passes through the spray zone of the granulator. The nucleus is the initial wetted aggregate that forms when the liquid hits the surface or is distributed through the powder by shear forces. The nuclei sizes depend strongly on the size of the drop and local amount of liquid present in the nuclei - the size of the primary particles has a multiplying effect, but does not control nuclea tion size. Droplet formation
Droplet coalescence & overlap
Binder dispersion by wetting & capillary penetration
Powder bed
Fig. 3. The tour stages of nucleation in fine powders [ 1 0].
Binder dispersion by mechanlcal mixing
Granulation Rate Processes
903
For the case where the droplets are larger than the particles, we define three nucleation regimes: 1 . Drop/et controlled: Each individual drop wets completely and quickly into the powder bed to form a single nuclei granule. The nuclei size distribution is essentially controlled by the drop size distribution. 2. Shear controlled: Liquid pooling or caking occurs where the spray meets the bed. Binder distribution occurs only by breakage of lumps or granules due to shear forces within the powder bed and the "nuclei" size distribution is inde pendent of the drop size distribution. 3. /ntermediate: This regime is intermediate between droplet controlled and shear controlled. Some agglomeration does occur in or near the spray zone without complete caking or pooling. The nuclei size distribution will be sensitive to many formulation properties and operating parameters. Wetting thermodynamics, wetting kinetics and the ratio of powder to liquid fluxes in the spray zone will all influence the nucleation regime. Operation in the drop controlled regime is ideal as it is easier to control the size (and size dis tribution) of drops from a spray nozzle than it is to mechanically disperse the liquid through the bed. However, it is possible to operate successfully in the mechanical dispersion regime, as is common in mixer granulators. To achieve drop controlled nucleation, two conditions are required: 1 . Drops penetrate into the bed quickly and do not roll on the bed surface and contact other drops. 2. Drop density and overlap on the powder surface is low. Drop penetration rate is set by wetting thermodynamics and kinetics and pri marily influenced by formulation properties. Drop overlap is related to the flux of drops hitting the powder surface and is set by operating parameters. We will consider each of these phenomena below. 2.1.1. Drop penetration times
The powder bed can be considered as a porous surface consisting of a series of capillary pores. For a drop to penetrate the pores, the contact angle between the liquid and the powder must be less than 90° (wetting thermodynamics). If this is so, drop penetration is driven by capillary suction and the rate at which liquid penetrates the pore is given by the Washburn equation. Consider a drop of volume Vd hitting the powder surface. The drop will have a circular footprint on the surface of radius: (1 )
904
K.P. Hapgood et al.
The rate at which the liquid flows from the drop is (2)
where "b is the powder bed voidage. The average velocity in the pore by the differential form of the Washburn equation: RYlv cos B 8flt
ii
is given
(3)
Combining equations (1 )-(3) and integrating gives the penetration time, i.e. the time for the total volume of drop to penetrate the bed: V2/3 fl tp = 1 .35 + -'---__ --- _=_ "b R Ylv cos B
(4)
This equation was derived separately by Middleman [1 1 ] and Denesuk et al. [1 2]. There are many assumptions made in this derivation but the key one is assuming the total voidage of the loosely packed powder bed is present as uniform cylindrical pores. With this assumption, the pore radius can be expressed as a function of the bed voidage and the specific surface mean particle size: d R =
(5)
-
This Kozeny model for the bed voidage is reasonable for random close pack ing, where the powder is weil packed and has a relatively constant porosity throughout. However, loosely packed powder have very heterogeneous voidage distribution, and recent X-ray tomography of granules [1 3-1 5] has confirmed that the internal void structure of individual granules is also heterogeneous (see Fig. 4). Hapgood et al. [1 0] divided the voidage into two parts: micropores and mac rovoids (see Fig. 5). Liquid will flow through the micropores, but there is no capillary driving force for the liquid to flow into the expanding macrovoids. In effect, the liquid does not see the macrovoids. Clarke etal. [1 6] describe this as a fractal-like wetting front which reduces the permeability and effective porosity. I n addition, if the powder is loosely packed, the capillary forces in the moving liquid front may rearrange the powder particles to create new macrovoids in the powder structure. Using the Kozeny approach will overestimate both the void age and the pore size seen by the penetrating fluid. Hapgood introduced an effective voidage "eft. If we assume all the voidage above the tapped bed
Granulation Rate Processes
905
Fig. 4. Granule structures showing large macropores: (a) low shear granule side view X ray image; (b) vertical cross-sectional 80 11m slice; (c) cross-section of granule from a high shear mixer granulator [14].
Fig. 5. Liquid will penetrate the micropores by capillary action but stops where the pore
expands into a macrovoid [1 0].
906
K.P. Hapgood et al.
voidage is present as macrovoids, then the effective bed voidage for capillary driven flow is (6) eeff = etap (1 eb + etap) The effective pore size seen by the liquid is the average micropore size: -
d
Reff = tp 32 � 3 1 ee -
and the drop penetration time is tp
=
V2/3
1 . 3 5 -2-d
ff
I-t
eeffReff Ylv COS f) -
--__=_ --'-
(7)
(8)
From equations (6) to (8), the drop penetration time is calculated from the measurable properties of the powder and liquid. 2.1.2. Experimental measurement of drop penetration time
Hapgood etal. [ 1 0] did an extensive study of drop penetration into loosely packed powder beds. It is a relatively easy experiment to perform, similar to the contact angle goniometry. A carefully metered single drop is placed on a carefully pre pared powder surface and the time for complete penetration of the drop is measured (see Fig. 6). Figure 7 shows the effect of liquid properties on drop penetration time. For a range of different powder beds, the penetration time varies linearly with the group jlIYlv COSf) as predicted by equation (8). Penetration time is proportional to liquid viscosity and inversely proportional to adhesion tension. This emphasizes the importance of both wetting thermodynamics and kinetics. The contact angle needs to be less than 90° to ensure penetration. Provided this is the case, the dominant liquid parameter is the viscosity, which can vary at least two orders of magnitude for typical liquid binders used in granulation.
(a) impact
(b) 2 seconds
Fig. 6. Drop penetration time measurement: A single drop of polyethyleneglycol solution
(PEG200) penetrates into a bed of glass baliotini [ 1 0].
907
Granulation Rate Processes 1 40 1 20
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4
6
8
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12
14
Fig. 7. Effect of liquid properties on drop penetration time in a range of powder beds [1 0].
1 00 -r-------i
ü
PEG 200
(J)
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E
(J)
---.- Water, fractionated lactose --0-- PEG 200, fractionated lactose � Water, unfractionated lactose ----'V- PE G200, unfractionated lactose
10
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e 0
o
20
80 60 40 Surface mean particle size d32 (�m)
1 00
Fig. 8. Effect of particle size on the penetration time of water and PEG200 drops into
lactose powder beds [1 0].
Figure 8 shows an example of the effect of powder properties. The penetration time decreases sharply as the specific surface mean particle size is increased. Note also that penetration time is different for broad size distribution powders because the bed voidage is a function of the spread of the size distribution.
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I::.
AI Ballotini AE Ballotini AI Ballotini Zinc Oxide Titanium Dioxide UQ Lactose Fine Lactose Medium Lactose Coarse Lactose Merck Lactose
tii C
.�cD 0.1 cD
0.. X W
0.01 T-���,___��.,..,...,.,-��,..,.,.���rrrl 0.01 0.1 10 1 00 Theoretical penetration time 'tCDA (sec) Fig. 9. Experimental drop penetration times compared theoretical predictions. Solid line is the equality line and the dashed Iines show ± 1 s [1 0].
Figure 9 compares the predictions from equation (8) with experimentally measured penetration times for several different powders and fluids. Data are scattered around the equality line and within ± 1 s of the penetration time. Pen etration times on loosely packed powders can be predicted within an order of magnitude for all powders. Equations (5) and (8) are crude estimates of effective porosity and pore size in loosely packed beds. Nevertheless, this relatively simple model is very useful for estimating drop penetration time, and the effect of liquid and powder properties for all but the finest powders. 2.1.3. Dimensionless spray flux
The second parameter describing nucleation is the dimensionless spray flux [ 1 7, 1 8], which considers the granulator spray zone and the flux of drops landing on the surface. The derivation of spray flux is straightforward. Powder surface is traversing through a spray zone with a velocity v underneath a flat spray of width W. The powder flux A through the spray zone is simply given by (see Fig. 1 0): A = vW
(9) Each drop hitting the powder surface will leave a footprint as it wets into the powder. If a second drop overlaps this footprint, a doublet will form. The number of drops hitting the powder surface per unit time is
. (-)
. nd = V
6 3 ndd
( 1 0)
909
Granulation Rate Processes .. - - - - - - - - - - - - - - - - - Spray n07.l.Ic
.-- --- - --- Binder liquid �"p",y Q. �. �. C1., ,,.. - ... - .. _ - - - - - - -
�.: �-.!'"-�.� - -,7- �;",I�.� -::�.�- -� x,4
,/
, ,/ / ,:;" ' , r,7"'-',7I'..,,. ','"
+--
Moving po",'der bed
w
Fig. 1 0 . An idealized spray zone in a granulator using a flat spray [ 1 8],
V n�� n:�
( )( )
Thus, the rate of production of covered area in the spray zone is a=
=
��
(1 1 )
Let us define the dimensionless spray flux as the ratio of the rate at which wetted area is covered by the droplets to the area flux of powder through the spray zone: a
\l'a = --;- =
A
3V' -
( 1 2)
-
2Add
The dimensionless spray flux is a measure of the density of drops falling on the powder surface. At low spray flux (\I' < < 1 ) drop footprints will not overlap and each drop will form a separate nucleus granule. At high spray flux (\I' � 1 ) there will significant overlap of drops hitting the powder bed. Nuclei granules formed will be much larger and bear little relationship to original drop size. The process is illustrated schematically in Fig. 1 1 . Dimensionless spray flux parameter is intended to capture the major effects of drop overlap in the spray zone on the nuclei distribution as simply as possible, to encourage its use as a scale-up parameter. Equation ( 1 2) contains two major simplifying assumptions. First, the spray is assumed to be uniformly distributed over the entire width of the spray. This is rarely true in industrial applications. Secondly, since nucleus size is always larger than the drop size, nuclei granules may overlap and coalesce even when the spray drops do not. For most industrial applications, the total flow rate, average drop size and average powder velocity are sufficient. However, by discretizing the spray zone and calculating spray flux for each section, variations in spray rate and drop size across the spray zone and radial velocity variation can be accounted for. a
a
910
K.P. Hapgood et al.
••
I.
�,
:. ,.
..
'• • • ... . .. . .. .J
.1
-. .
(a )
(b )
(c)
Fig. 1 1 . Monte-Carlo simulations of drop on the powder bed after the spray zone: (a) 50 discs 'Pa 0.29, fcovered 0.26; (b) 1 00 discs 'Pa = 0.59, fcovered = 0.45; (c ) 400 discs 'Pa 2.4, fcovered 0.91 [19].
= =
=
=
Wauters et al. [20] show detailed spray flux values across the width of the spray in a rotating drum. This level of accuraey may be important for some modelling applieations. Wildeboer et al. [1 8] recently extended the spray flux to include non-uniform sprays, and aceounted for the effeets of nucleus spreading by defining a nuele ation area ratio Ka, as folIows: ( 1 3) where a is the projeeted area of the nucleus (an) and drop (ad)' The probability of a single drop forming a single nucleus is therefore related to the dimensionless nueleation number,\f'n: 3 11 (14) \f'n Ka 2 Wvdd Wildeboer etal. [ 1 8] modelled the nuclei distributions in the spray zone over a range of \f'n (Fig. 1 2), accounting for non-uniform sprays and nucleus spreading and eoaleseence. Simulation results of nuelei eoverage in the spray zone are shown in Fig. 1 3. It is important to note that at a given value of the dimensionless nuclei funetion, the density of the nuclei at the surfaee is eonstant, regardless of the individual drop size, flow rate ete values. Assuming complete spatial randomness, spatial statisties ean be used to derive an analytieal solution for both the fraetion surfaee eoverage and fraetion ag glomerates. Under these eonditions, the drops landing randomly on the target area are deseribed by a Poisson distribution. The fraetion surfaee eoverage is given by Hapgood et al [1 9] : ( 1 5) fcovered 1 - exp(-\f'a )
=
=
Granulation Rate Processes
91 1
6 �-------r--,---�--, 8--"::] '1', (Q=71 mJ/mlll) A-·t:J. '1' , (Q-95 m nun)
� - � 'I', {Q=1 1 9 m1/min) G- - -() '1'. (Q-1 43 ml/min)
Diameter (mm)
Fig. 1 2. Simulated nuclei size distributions as a function of liquid flowrate. 1J'1 1J'2 = 0.48, 1J'3 = 0 .64, 1J'4 = 1 .2 [1 8].
( Dircction of powder motion)
(a)
(bI
(C)
(dl
(c)
( f)
(g)
(h)
(i)
Fig. 1 3. Simulations of nuclei coverage in the spray zone [1 8].
(j)
(l;)
(I)
=
0.8,
912
K.P. Hapgood e t al.
The fraction of nuclei formed from n drops is given by ( 1 6) Thus, we can calculate the number of single drops, not overlapping with any other drops, and by difference, the number of agglomerates: fsingle = exp(-4qt ) (1 7a) a
fsingle = 1 - exp( -4qt ) (1 7b) Figure 1 4 shows the nuclei distributions predicted by equation ( 1 6) at a range of spray flux values. As shown in Fig. 1 4, the higher the spray flux value, the wider the nuclei size distribution. The impact of qta on nuclei formation can be studied in ex-granulator nucleation experiments where the nuclei size distribution is analysed after a single pass of the powder through the spray zone [ 1 7]. Figure 1 5 iIIustrates the dramatic effect of qt on the nuclei size distribution. At low spray flux (v = 1 .36 m/s; qta = 0.22) the nuclei size distribution is quite narrow. As spray flux increases, the distribution broadens as agglomerates begin to form. At the highest spray flux (v = 0.25 m/s; qt = 1 .2) the spray zone has become a continuous cake and the nuclei distri bution bears no resemblance to the drop distribution. However, when the spray flux is low and it is in the drop controlled regime, changes to the spray drop distribution are directly mapped onto the nuclei size distribution (see Fig. 1 6). fagglom
=
1
-
a
a
a
0.7 0.6
,
ß t: 0
� (j)
E
0.5 0.4 0.3
::J
0
>
0.2 0.1 0.0 0
200
400
600
800
1 000
Nuclei size (microns)
Fig. 1 4. Nuclei size distributions predicted by equation ( 1 6) at a range of spray flux values assuming 1 00 J.lm mono-sized drops.
913
Granulation Rate Processes 1 .4
�------�--�
----
1 .36 m/s 1 .20 m/s � . 0.96 m/s --'\j- . 0.56 m/s - 0.25 m/s -0-
1 .2 1 .0 x-
0.8
c =
- 0.6 0.4 0.2 .lII ==o{'}o='-"--....----____j 0.0 +-------jIl----------.� 0.1 10 Nuclei size ( m m)
Fig. 1 5. Effect of powder velocity o n nuclei size distribution i n ex-granulator nucleation experiments: lactose powder with water spray [2 1 ] . 1 .6
Cj\ 0.066 mm drop
/
1 .4
1 .0 c
=
0.8 0.6 0.4 0.2 0.0
---. - Water 31 0 kPa -0- Water 620 kPa ---T- HPC 620 kPa
\ � 0 . 1 00 mm drop I j\ If S I \ 11 "«: 0.25 mm drop 11 r � 111
1 .2 x-
----�---�
�-
JI
\
\ �� \ C\\ '" '" �
-� ��=< � �-�� ��---� I_�ä------��
+
0.1
10
Mean size (mm) Fig. 1 6. Effect of spray drop size distribution on nuclei size distribution (v = 1 .36 mjs; o/a = 0.22). Data for water and H PC solutions varying nozzle pressure [21 ] .
The dimensionless spray flux characterises the equipment operating param eters with respect to nucleation in a single dimensionless group. Figure 1 6 shows that the fraction of agglomerates formed in ex-granulator and in-granulator ex periments is predicted extremely weil by equation ( 1 7) with spray flux as the only parameter. The dimensionless spray flux provides a good basis for equipment scale up to maintain good nucleation.
914
K . P . Hapgood et al.
1 .0 i-------=====j �
:::- 0.8 u :::l C
"* 05
E
g C\l o c o
�
_
LL
J
•
o o
0.6
Riffler • Water 310 kPa cutsize 294 11m � Water 620 kPa cutsize = 215 11m 0.4 • HPC 620 kPa cutsize = 556 11m Granulator o Water 310 kPa cutsize 294 11m 0.2 'V Water 620 kPa cutsize 215 11m o HPC 620 kPa cutsize = 556 11m - fagglom = 1 -exp (-4'l'al: 0.0 +----,------,---I----'=c;------,.:-----1 0.4 1 .2 0.6 0.0 0.2 1 .0 0.8 Spray Flux =
= =
'Pa ( )
Fig. 1 7. Agglomerate formation as a function of spray flux for in-granulator and ex-gran ulator nucleation experiments using lactose powder with water and H PC solution binders [1 9].
2.1.4. Practical application of 'Pa and 'Pn
Practical application of dimensionless spray flux requires measurements of the drop size distribution and powder velocity, and spray distribution for 'Pn . Spray distribution is the easiest of the three parameters to measure (e.g. Wauters etal. [20]), and laser diffraction andjor doppler analysis of spray nozzles is widely available for drop size characterisation. Currently, the most challenging parameter in 'Pa to measure in real granulators is the powder velocity. This can be iIIustrated with reference to high-shear mixer granulators. Measurement of powder velocity requires high speed video cameras with sophisticated image analysis software, or positron emission particle tracking (PEPT) technology. Powder flow is covered in detail in chapter Modelling in this handbook. In all observed powder flows in mixer granulators, the powder velocity is at least one order of magnitude lower than the impeller tip speed [21 -24]. When the powder is in the roping flow regime, the surface velocity is independent of impeller speed [22,25]. To support the use of 'Pa as a scale-up tool in pharmaceutical granulation, Plank et al. [23] measured surface velocities at a range of impeller speeds in commercial 25, 65 and 300 L Fielder mixers (see Figs. 1 8 and 1 9). As the liquid content of the powder increased, the velocities shifted upwards. They found that mixer scale had little effect at a set tip speed, but even a small increase in fill level could significantly decrease the powder velocity. At 300 L scale, they dis covered that the powder surface was stagnant approximately 1 j3 of each impeller
915
Granulation Rate Processes 1 .2
------�
l 1 .0
'g �
�
0.8
2l 0.6
ca "t: :::J
�
Cl
� �
.-/
� /"
/
0.4 0.2 0.0
Standard Low Setti g
o
V
� / V /
Ci)
1 00
50
I -- 7% water I I ....... 1 8% water I
r;,.. vlC1I1UF"U
High fetting 250
200
1 50
Impeller RPM
300
Fig. 1 8. Surface velocities as a function of impeller scale and liquid level for a 300 L Fielder mixer [23].
1 .2
�� 1 .0 f- ....... 65 L
---
- 25 L
'(3
0 Qi > Q)
0.8
-
u 0.6 ca
"t: :::J
(f) 0.4 Q) Cl
� 0.2 Q)
> «
0.0 0.0
....... 300 L
;::;/ � /
2.0
/
Stardard Low Speed 4.0
/
/
-
6.0
8.0
------
....
.....
Impeller Tip Speed ( m/s)
1 0.0
�Stancard High peed 12.0
14.0
Fig. 1 9. Surface velocities as a function of i mpeller tip speed and granulator scale [23].
revolution, even though the impeller was running at 1 80 rpm, the standard "Iow" speed setting. Stagnation of the bed during solution delivery is clearly undesir able, but Plank et al. [23] demonstrated that it was not an unusual occurrence. Maintaining constant spray flux on scale-up is actually challenging. The sim plest method is to maintain the same flowrate through the nozzle, but this extends the total granulation time in proportion to the scale-up ratio. If the saturation exceeds the nucleation regime limit (see Section 3), then the growth and con solidation will be affected. This is usually undesirable. In mixer granulators, the powder surface velocity often decreases as the granulator scale increases, and the spray width and drop sizes do not usually compensate for this. Increasing the
916
K.P. Hapgood e t al.
impeller speed to maintain equivalent surface velocity at full scale may signifi cantly affect the forces experienced by the granules, and again change the con solidation rate and Stdef growth regime. Alternatively, the total granulation time can be maintained during scale-up, and the solution flow rate increases proportionally. This is the more common ap proach in pharmaceutical granulation, and results in a significant increase in the spray f1ux. Table 1 below gives an example of scale-up from a 1 5 kg batch to a 70 kg batch. Initially, the calculated spray flux 'Pa = 0.36, which is in the inter mediate nucleation regime. Powder velocity data is taken from Fig. 1 9. In the first case, the spray rate is maintained constant, but there is still an increase in spray flux. The second case considers if the spray rate is adjusted to maintain constant granulation time. In both cases, the spray flux increases and moves firmly into the mechanical dispersion regime. Note that the example above implicitly assumes that the fan spray is orientated perpendicularly to the direction of powder flow. This is often overlooked in in dustrial granulation in mixers, particularly is the powder flow direction changes on scale-up due to the usually lower mixing intensity. In the examples in Table 1 , 'Pa increases at least 1 0-fold if the powder runs through the fan length ways, as the spray width decreases to less than 5 cm for most nozzles. A conical nozzle eliminates the orientation effects, but often creates new problems due to wet patches and buildup on the granulator walls. Alternatively, the spray nozzle can be placed directly over the chopper, where the turbulent powder flow and strong localised shear forces ensure minimal effect of nozzle orientation and minimal effect of high spray flux. Figure 20, shows the size distribution of granules formed in a 300 L mixer using a single nozzle. Owing to the turbulent flow, the powder direction through the spray could not be determined. However, by taking the best and worst possible cases, the spray flux is not less than 1 .6 and could exceed 'Pa = 1 2. This is the mechanical dispersion regime and the chopper is able to Table 1 . The effect of scale-up on spray flux 'I'a in a mixer granulator
Mixer size
65 L mixer
300 L mixer
Scale-up approach Base case Constant spray rate Constant granulation time 70 kg 1 5 kg 70 kg Batch size 1 kg/min 1 kg/min 4.7 kg/min Flowrate 1 000 Jlm 400 Jlm 400 Jlm Drop size 0.40 m 0.25 m 0.25 m Spray width 1 08 rpm 1 08 rpm 21 6 rpm Im peiler speed 0.35 m/s 0.35 m/s 0.7 m/s Powder velocity Spray flux 'Pa
0.35
0.71
0.84
917
Granulation Rate Processes 30% �======�----� � Single noule. parallel to powdcr flow
25%
____ Single nozzlc. perpcndicular to powder tlow
20% "ö
';a 1 5 % " .. � 1 0%
o
45
63
90
1 25 1 80 250 500 Sieve size (microns)
1 000 2800 6300 1 2500
Fig. 20. Mechanical dispersion in the chopper of a mixer granulator effectively eliminates significant changes in spray flux due to nozzle orientation.
sufficiently disperse the fluid such that regardless of the nozzle orientation, the granule size distribution is unaffected [26]. The judicious selection of nozzle placement over the highest shear zone is an alternative method to minimize the effect of changing \f However, multiple nozzles are the only way to maintain spray flux independ ently of granule growth and consolidation rates. This is weil known in fluid-bed granulation scale-up [27-29] but has not been applied to commercial mixer granulators. A four nozzle spray manifold was designed for a 300 L mixer gran ulator [30]. The manifold attaches to a normal spray lance (Fig. 2 1 a) and the four nozzle apparatus is attached underneath the lid (Fig. 21 b) through the centre nozzle port. The four nozzle tips are at the same radial distance as the standard single nozzle port. The liquid is now distributed over four times the area, and flow rate through each nozzle is reduced. The multi-nozzle spray manifold shown in Figs. 21 a and 21 b was applied to the scale-up of two granulated pharmaceutical products in the final stages of devel opment. Table 2 summarizes the starting parameters at 65 L scale, the "stand ard" parameters at 300 L scale using a single nozzle, and the spray flux when the multi-nozzle spray manifold was used to maintain approximately equal spray flux. Note that this is an example of scale-up in the mechanical dispersion regime, where mixing forces dominate the liquid dispersion. Analysis of the granule size distributions showed that there was no effect of spray flux on the size distribution of granules less than 2 mm in size. However, the fraction of coarse granules greater than 6.3 mm (the coarsest sieve aperture used) was a strong function of spray flux. These coarse granules were undesirable as they required an extended drying cycle and necessitated the a.
K.P. Hapgood e t al.
918
( a)
( b)
Fig. 2 1 . (a)Multiple nozzle manifold [30] (b)installed in 300 L mixer granulator [30].
Granulation Rate Processes
919
Table 2. Scale-up in a mixer granulator using multiple nozzles [30]
65 L mixer Single Base case nozzle
Mixer size Scale-up approach
Batch size (kg) 1 5 Flowrate (kgl 3.3 min) Drop size (11m) 750 Spray width (m) 0. 1 9 I mpeller speed 21 6 (rpm) Powder 0.7 velocity (m/s) Calculated 0.83 spray flux 'Pa
65 1 4.3
300 L mixer Four Siow Fast nozzles spray impeller 65 4 x 3.6
65 7. 1
65 14.3
1 370 0.38 1 08
750 0.37 1 08
1 000 0.38 1 08
1 370 0.38 216
0.37
0.37
0.37
0.37
1 .9
0.85
1 .3
0.86
25 �====�----� o 65L control E • One nozzle 1 4 Umin E Four nozzles 1 4 Umin � 20 c Eil! Siow sprayrate 7 Umin <11 -S � High impeller speed Q5 ca 1 5 �
Cl (ij
�E
� 'E eh a: rf.
10
'C
5
o -I-
..L -'--
__
55 retaw %
65 retaw %
Fig. 22. Effect of spray flux and multiple nozzles on the proportion of coarse granules [30].
installation of a wet mill prior to drying, a significant capital cost. Figure 22 plots the % coarse granules as a function of spray flux at two different binder con centrations. The use of four nozzles reduced the proportion of coarse granules. The most significant reduction occurred at the highest fluid level. Figure 22
920
K.P. Hapgood et al.
illustrates that the most effective way to scale-up liquid distribution in the me chanical dispersion regime is to use mixing and shear forces. Doubling the impeller speed or doubling the granulation time matched the level of coarse granules that occurred at the 65 L scale. 2.2. A nucleation reg ime map
We have defined three regimes for nucleation: drop controlled, intermediate and shear controlled, and analyzed the factors, which dictate the operating regime in any particular system. It is useful to try and summarize this information in a nu cleation regime map. Drop controlled nucleation should occur when there is both • •
Low \{Ia relatively few drops overlap, and Fast tp the drop must wet into the bed completely before bed mixing brings it into contact with another partially absorbed drop on the bed surface. -
-
If either criterion is not met, powder mixing characteristics will dominate: this is the mechanical dispersion regime. Viscous or poorly wetting binders are slow to flow through the powder pores and form nuclei. Drop coalescence on the powder sur face (also known as "po?ling") may occur and create a very broad nuclei size distribution. In the mechanical dispersion regime, nucleation and binder dispersion can only occur by mechanical mixing and agitation, and the solution delivery method (drop size, nozzle height, etc.) has a minimal effect on the nuclei properties. Figure 23 summarizes these concepts in a regime map for nucleation. The map centres around the drop controlled regime, where one drop makes one nuclei, provided the drop penetrates fast enough and the drops are weil separated from each other. The regime limit lines are indications only. The horizontal axis is the dimensionless spray flux \{Ia , which describes the spray pattern and multiple drop behaviour. On the vertical axis is dimensionless drop penetration time Tp : ( 1 8) where tp is the penetration time of the spray drops and tc the circulation time, which is the time taken for a packet of powder to return to the spray zone. The circulation time is a function of powder flow patterns and the amount of material in the granulator and is equipment dependent. However, typical values in industrial granulators will be the order of seconds implying the drop penetration time needs to be of order 0.1 s to ensure drop controlled behaviour. We can validate the regime map by carrying out granulation experiments var ying both equipment parameters and formulation conditions and observing the changes to the granule size distribution [31 ]. Figures 24 and 25 show examples of such tests in a 25 L batch mixer granulator. Drop penetration time is varied by
921
Granulation Rate Processes 10
..
Mechanical Dispersion regime
no change in distribution
1 .0 I ntermediate narrower nuclei size distribution
0.1 Drop controlled
Caking
0.01
0.1
1 .0
10
Fig. 23. Proposed nucleation regime map for ideal nucleation i n the drop controlled re gime, it must have (i) low 'I'a and (ii) low tp. I n the mechanical dispersion regime, one or both of these conditions are not met, and good binder dispersion requires good mechanical mixing [26].
0'
:
§:
•
�
00'
Pl;GWO ..,..s 160 .... WOIo,_ W*"" po&.l'.-d . V PEG200_ - . ---- -
.�
ii
W""f9J'.Y'ld 310 kP� W_ _ 820 1oP'o
, . ::::-'::';:0":"...
1I �*
-"
Q.
0001
O�I +_----�--- -�l�--�+_--�--00
Fig. 24. Nucleation regime map in 6 L mixer after 1 0 s. Breadth of the distribution indicated by 0 values at each data point. Lactose with water and PEG200 [26].
changing formulation properties (the viscosity of the binder liquid). Spray flux is varied by changing operating parameters (the spray rate through a single nozzle). Figure 24 shows the data after a very short granulation time. Results should be dominated by nucleation only. The spread of the granule size distribution
922
K.P. Hapgood et al. 1 0 �------�====�--� • Water sprayed
,.
31 0 kPa
Water sprayed 620 kPa • Water pumped & HPC pumped • HPC sprayed 620 kPa
12 •
9.5
�
c.
a;
,§
§ 0.1
12
e a;
c CD c..
0.01 3.6 •
11 ,. 0.001 f----.-----,---,L---.--i 0.2 0.0 0.4 0.8 1 .0 0.6
Spray flux 'Pa ( ) -
Fig. 25. Nucleation regime map in 25 L mixer at 1 5% liquid content. Lactose with water and PEG200 [26].
(represented by the parameter <5) increases with both ! p and 'Pa. The narrowest granule size distributions occur only in the bottom left hand corner of the map the drop controlled regime. A similar effect is seen at longer spray times and higher liquid contents (Fig. 25) even though nuclei rewetting and granule growth will now also influence the granule size distribution. The regime map is a helpful tool to focus trouble shooting of wetting and nucleation problems, for example, if the drop penetration time is large, then making adjustments to spray rates and nozzle positioning will not lead to nar rower granule size distributions because the system will remain in the mechanical dispersion regime (see Fig. 23). Significant changes to wetting and nucleation will only occur if changes take the system across a regime boundary. This can occur but is undesirable if processes are not scaled with due attention to remaining in the drop controlled regime [32]. 2.3. Other n ucleus formation modes 2.3.1. Hydrophobie nueleation
There are very few clear studies of poorly wetting systems, even though this is a common problem in pharmaceutical, minerals and fertilizer granulation. Many
923
Granulation Rate Proeesses 200 11m
200 11m Fig. 26. Side view X-ray transmission image of a hydrophobie fine powder nucleus (Iett), formed by powder spreading over the drop surfaee. Dotted line on a side view image indieates position of the eross-section (shown on right)[33].
papers eontain a statement to the effeet that good wetting is a prerequisite for good nucleation. Although this is usually true, robust granulations with poor wet ting are possible. Figure 26 shows the strueture of a granule made from a hydro phobie material formed by the solid-spreading nucleation meehanism (see Fig. 2), where the powder has spread around the drop. After drying, a hollow eore re mains in the eentre of the granule. Nuclei formed by powder spreading over the liquid ean produee some highly desirable granule properties, such as highly porous granules. If the powder shell is strong enough, or there are enough fines in the granulator, liquid ean be eontained in the interior of the granule for an extended time. The granules in this state are quite strong, as their shear strength is dominated by the fluid, and ean survive vigorous agitation. This allows good granulation eontrol in the nucleation regime. However, onee the liquid ruptures the powder shell, the granule growth oeeurs extremely rapidly and ean be diffieult to eontrol. Sinee teehniques to study internal nuclei struetures are very new and only reeently applied to granulation, this nueleus strueture is likely to be reported more frequently in the future. The response of this type of system to ehanges in granulation operating para meters is often the opposite of the "normal" response. If the nucleation meeha nism of a hydrophobie formulation is not reeognized, it is highly likely that the proeess troubleshooting will be unsueeessful! 2.3.2. Porous partie/es
The vast majority of papers use non-porous particles, so that the amount of liquid available for granulation is unaffeeted by the adsorption state of the powders.
K.P. Hapgood et al.
924
However, many eommon industrial granulation proeesses eontain large propor tions of porous particles. If the particle is porous, then liquid will also suek into the pores by eapillary aetion (see Fig. 27) [34]. In the ease of iron ore granulation, the amount of water added needs to be minimized, to minimize the energy eosts of drying, transport and smelting the ores. For a non-porous granulation system, the best way to minimize liquid usage is to optimize the wetting eonditions using surfaetants ete. However, Iveson et al. [34] showed theoretieally that for porous partieles, sueh as iron ore, the lowest eontaet angle does not neeessarily equate to the best nucleation. The small eapillaries within the porous particles draw liquid into the interior of the partiele, leaving less surfaee liquid available to form liquid bridge bonds with other partieles. Figure 28 shows a perfectly wetting fluid will be Liquid Drop
...
Liquid Absorbtion into Pores Porous Surface Fig. 27. The amount of liquid available on a porous particle depends on the wetting dy na mies and rate of water adsorption into the particle pores [34] .
� G) E t...
:::I GI - CJ o ca
> "t: 0. :::1 0 111
o e 0
1 00
. . . . . . . . . • . . . . . . . . . . . . . . . . . . . .
80 .0
60
D'
_
0
Cl e e 0 _ e
ti m � E u.. !!! 20
40 : :
0
.0
.
0
'
.
.
..
Cf '
•
5
•
t;, '
•
. .
0·
<::f . . .
. .'
0·'
30
' O' . '
0 .. .
'
.
.
0
.-
..
Porosity
0% 1% 0 1 0% -- 20% 0 30% . ----... . . .
.
45
' .
(t
•
o'
'
,
,D
.'
'
60
. .
• • •
• • •
• • •
• • •
75
90
Contact Angle (0) Fig. 28. Effeet of eontaet angle of the liquid volume remaining above a porous surfaee [34].
925
Granulation Rate Processes
drawn entirely into the pores of the particle preventing nucleation until the pores are completely full. Microcrystalline cellulose (MCC) is in porous particle form that can absorb several times its own weight in water, and is commonly used as an ingredient in pharmaceutical granulations. Initially, the nuclei formed contain no MCC, as the liquid bridge that initially bonds the nucleus together is absorbed into the pores of the MCC and the nucleus disintegrates. Once sufficient fluid has been added to the granulator to saturate the MCC particles, or at least allow them to become surface wet, the MCC is incorporated into the granules. This has been shown experimentally across a wide range of granulation conditions by Plank et al. [35] (Figure 29).They determined the composition of granules > 1 25 Ilm (avoiding ungranulated material) and plotted the normalized percentage of each compo ne nt against the fraction of material greater than 1 25 Ilm. The extent of gran ulation is an important variable but is difficult to define and measure. In Fig. 29, the fraction of granules larger than 1 25 Ilm is a measure of the extent of gran ulation. Since only a very low percentage of starting excipient particles were larger than 1 25 Ilm, we have a clean comparison of the composition of the gran ules only. Each data point in Fig. 29 summarizes the three compositions at a particular liquid level and different sets of processing conditions. The distribution of the components is complex but can be explained by a combination of competition for the available granulating fluid and preferential granulation of the finest particles. Initially, at low liquid levels, liquid bridges hold the particles together. However, liquid that contacts the MCC particles can be absorbed into the MCC internal pores. If the MCC manages to (briefly) form a liquid bridge, it will absorb the fluid, fall off the granule and return to the excipient 1 80%
�
1 60%
�
1 40%
E
1 20%
.-------1.�H�PC�-, - - - - - . - - - - - - - - -. - - - - - - - - - - - - - - - - - -
10 C\J
�
� u
.!:
'(ij o Qi 1 00% e>
�
?f.
80%
-
. - - - - - - - - - - - - - - - - -•- - - - - - -
--•
•
--
JL
• -- •
Avicel Lactose
.- - - - - - - - - - - - - - - - - - - - - _ _
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
•
+------'�r.,,�--� - - - - - - - - - - - -.- -.- - - - - - - - - - - - - - - - .
..
--------- -----
. -----.�----
60% +---.---�--�--����---,0% 1 0% 20% 30% 40% 50% 60% 70% 80% 90% 1 00% % Milled Granulation > 1 25 um
Fig. 29. Effect of porous MCC particles on granule composition [35].
926
K.P. Hapgood et al.
size fractions. This creates granules initially depleted in MCC, and therefore preferentially composed of lactose and H PC as shown in Fig. 29. When approx imately 40% of the material is > 1 25 f.lm, the MCC and lactose curves cross indicating a switch in granulation behaviour. At this point, enough water has been added to hydrate the HPC and at least partially saturate the MCC particles and/or form a liquid layer at the surface. The MCC particles are generally smaller than the lactose and is now capable of forming liquid bridges. The granules compo sitions now become enriched with lactose and HPC. 2.3.3. Nucleus structures
Once the drop has imbibed into the powder, the structure of the nucleus depends on the properties of the formulation, as weil as the kinetics of consolidation and further re-wetting in the granulator. Several theoretical relationships between drop size and nuclei size have been proposed [36-38]. The simplest description of nucleus structure is to compare the drop diameter or volume to the nucleus diameter or volume. Waldie [39] was the first to recognize that each spray drop formed an individual nuclei. A known number of droplets were introduced into a fluidized bed and retrieved a short time later. He found a correlation between the nucleus diameter and droplet diameter, that held over three orders of magnitude: ( 1 9) dg cx d� where dg is the granule diameter, dd the drop diameter and n a correlation co efficient found to range between 0.8and 0.85. More recently, Schaafsma etal [37] recognised that peaks in their product size distribution were caused by two or more drops coalescing in the spray or on the surface to form larger agglomerates: (20) where Nd is the number of drops used to form the agglomerate and K the nu cleation ratio. The nucleation ratio is a constant, which is expected to depend on material properties including contact angle, granule porosity, particle size distri bution and others. Physically, the nucleation ratio represents the structure of the nuclei: (21 ) where s i s the wetting saturation [37,40]. The nuclei distribution of lactose formed is shown in Fig. 30. The nucleation ratio has been found to vary widely, values between 2.9 and 1 6 have been reported [40,41 ] , depending on the powder and binder combination
927
Granulation Rate Processes � E c -
6. :·03
��
3. E·Ol
� � g- � .;: .Q Ö � > ..,
�
..J
..5- C�
4. ::-03
E C�
g � J
2.E-Ol 1
: · 03 200
300
'00
500
auo
700
equiv granule diamc:t.. , (mieron)
�
0,
03 02
�
,,4 4
'U
o e>(·) +-'z:o..,.� .. ........ .. � ... _�;::;:t:j.
(a)
(.6
5. : 0)
2
droe>lel 'ILB
. 225 mlc,o� . ,lSS mlcr
0 1
1 :l.O .f-AI""-o._�,--, C 0 ('2 0 0-1 0 rw: 0.08 ( b) bi nder liquid volume {JIL)
I
(I
Fig. 30. (a) Lactose g ranules formed after spraying with mono-sized drops dd = 226 fim. (b) A linear relationship exists between the peaks of the volume frequency and the number of drops required to form it. The nucleation ratio K is given by the slope (6.58) [37].
Fig. 3 1 . Nuclei formed from lactose and (Ieft to right) water, 1 7cP H PC solution, and 1 05cP H PC solution. Actual nucleus diameters are 6.5, 3.5, 3.0 mm respectively [ 1 9] .
used. Figure 31 shows lactose powder nucleated with three fluids with different viscosities. Red dye was added to the fluids to indicate spreading. The most viscous 1 05cP HPC solution formed nuclei shaped like stubby cylinders. As the viscosity decreases to a 1 7cP H PC solution, the base of the stubby cylinder begins to spread forming a mushroom shape. For the water nuclei extensive fluid spreading beneath the powder surface gives a white, spherical, crumbly shell of lactose encompassing a dark pink 'stalk' where the drop imbibition occurred. Nuclei morphology is therefore a complex balance of several factors including: • • • •
particle size; the rate of drop penetration; the rate of secondary spreading; and the rate of drying.
Very fine powders undergo particle rearrangement and shrinkage and can be clearly separated from the dry feed powder. For coarser powders, liquid spreading,
928
K.P. Hapgood et al. 70 60
• \l
11
• o
� 50
� c 0 :;:; as
40
...
:::J
-
as
111 'a; 13 :::J z
30
&
Ballotini UQ Lactose Merck lactose ZnO Ti02 AI
•
Q
��.
Q
20 10 �
!\'l!
!\'l!
o +-----.-----,---� o 10 20 30 40 50 60 70
Nucleation ratio K
=
Vn I Vo ( ) -
Fig. 32. Nuclei saturation at different nucleation ratios for different materials [31 ] .
evaporation and nuclei attrition will affect the nuclei size and liquid distribution in a granulator. The difference in nuclei size and saturation between the water- and H PC based nuclei is due to balance between the rate of drying compared to the rate of liquid spreading. In nuclei formed from low viscosity fluids such as water, the drop penetration and secondary spreading stages occur at a similar or faster rate than the drying stage, and spherical nuclei are generally formed. For nuclei formed from high-viscosity fluids, the rate of drying becomes com parable or faster than the fluid spreading and only a highly saturated core is formed. The nuclei saturation is closely related to the nucleation ratio K (Fig. 32). Large nuclei mean that the fluid has spread some distance from the original core, causing the total overall nuclei saturation to be quite low. Some nuclei are more than 50 times the volume of the original drop [31 ] , with the nuclei saturation as low as 3%.
2.4. Summary
In any granulation process the first aim should be to ensure good wetting and nucleation, thus removing binder distribution problems from the picture and allow the engineer to concentrate on other issues. In this respect, wetting thermody namics, wetting kinetics and spray flux considerations are important. The two di mensionless groups 'I' and 'p capture the impact of the key formulation properties a
Granulation Rate Processes
929
and process parameters on wetting and nucleation. The regime analysis presented in this section provides the tools for quantitative analysis and design. 3. GROWTH AND CONSOLI DATION 3. 1 . Background
The last decade has seen a rapid advancement in the understanding of growth and consolidation in agitated wet granulation processes. A major turning point in this field was the publication of the land mark paper by Ennis and co-workers [42], in which they proposed a physically based model for predicting the growth be haviour of granules. The beauty of the Ennis model is that it is physically based and, in theory at least, the variables in the model are measurable and the el egance of the model was its simplicity. However, such simplicity inevitably brings with it many assumptions, and the accuracy of these was immediately the subject of much debate within the granulation research community. This debate served to trigger an explosion of interest in quantifying growth mechanisms, and challenged researchers to attempt to develop more advanced coalescence models to include some of the important effects neglected in Ennis's version. In this section we begin by describing granule growth regimes and present a regime map that captures many of the of the complex granule growth mechanisms in a relatively simple way that is immediately useful for scale up and operational trouble shooting. We then look critically at recent detailed studies attempting to model accurately different aspects of granule growth and consolidation. 3.2. Granule growth reg imes
There are two main forms of granule growth. In some systems, granules grow, more or less steadily with time. Figure 33 shows the median granule size versus time for sand granulated in a tumbling drum. The rate of growth is approximately constant. We term this behaviour "steady growth". However, in other systems, there can be a long period of time in which no growth occurs at all. During this period of time, the granules consolidate. This phase has been variously referred to as the "nuclei", "no growth", "induction" or "compaction" phase [43-46]. Eventually, if a time is reached where granules have consolidated sufficiently for liquid binder to be squeezed to their surface, rapid growth can follow. Figure 34 shows an example of this type of growth behaviour. We term this an "induction-growth" system. There are also several other distinct regimes of granulation behaviour. Nucle ation only behaviour occurs when granule nuclei form during the binder-addition phase, but no further growth occurs after that (e.g. Butensky and Hyman [36],
930
K.P. Hapgood et al. 3 �
E � (J) N
U)
Liquid Content (%VN)
2.5 2
tJ.
(J)
"3 1 .5
72.2%
:.: 70.8%
� (!)
. 68.5%
::a: 0.5
X 64.3%
c
c <1l (J)
<> 66.0%
. 62.5% Number of Drum Revolutions (revs.)
Fig. 33. Granule size vs. n umber of drum revolutions for the drum granulation of 67 )lm silica sand with varying moisture contents [48].
E 900 2: 1 000
Cii a; E <1l '5 c <1l
(J)
E
(J) (J) <1l
800
600 500 400
E
300
(J)
200
"3
� c
(!)
3
700
1 00 0
20
0
40
-.- 1 7.8 wt.% liquid 1 9.8 wt.% liquid
""*"""
60 80 Time (min)
1 00
1 20
1 40
--- 1 8.4 wt.% liquid .....- 1 9. 1 wt.% liquid -+- 20.4 wt.% liquid
Fig. 34. Effect of liquid content on the growth behaviour of sodium sulphate and cellulose mixtures during batch granulation in a Lödige high-shear mixer: 1 . Nucleation only; 2-4. Induction time followed by rapid g rowth; 5. rapid growth fol lowed by breakage [46].
see curve 1 in Fig. 34, Sherrington [38]). Crumb behaviour occurs when the formulation is too weak to form permanent granules, but instead forms a loose crumb material which cushions a few larger granules constantly breaking and reforming [47]. Overwetting occurs when excess binder has been added and the system forms an oversaturated slush or slurry.
Granulation Rate Processes
931
Steady growth is most frequently seen in systems with relatively coarse particles, non-viscous binders and/or a high agitation intensity i.e. systems in which a large amount of deformation occurs during collisions between granules (Fig. 35a). Induction growth is typically seen in systems with fine powders, vis cous binders and/or relatively low levels of agitation intensity, i.e. systems in which little deformation occurs during granule collisions (Fig. 35b). Hence, the two basic parameters that determine which type of growth behav iour occurs are the maximum pore liquid saturation attained and the typical amount of granule deformation during impact [49-50]. Granule pore liquid sat uration will vary during batch granulation as the granules consolidate and any soluble components gradually dissolve. Therefore, the maximum granule pore saturation (smax) is used as the measure of liquid content: (22) where w is the mass ratio of liquid to solid, Ps the density of the solid particles, P I the liquid density and amin the minimum porosity the formulation reaches for that particular set of operating conditions. The liquid saturation term must include any extra liquid volume due to solids dissolution, but should not include liquid, which is absorbed into porous particles. If this maximum saturation is greater than 1 00%, then it indicates that if left long enough, the granules will consolidate sufficiently to become surface wet, and hence Steady Growth Behaviour
lnduction Behaviour •......
O ·
0··
Granulation Time
Granulation Time
High Deformation System
Low Deformation System
• • m-;+ . coalescence growth (a)
surface wet
. . , :- .�"= , consolidation
growth
(h)
Fig. 35. Schematic of the two main different types of granule growth and the way that they depend on the deformability of the granules.
932
K.P. Hapgood et al.
that induction type growth can occur. Of course, if the granules are sufficiently deformable, then steady growth will have occurred before the surfaces become wet. The typical amount of deformation during granule collisions can be character ized by a Stokes deformation number, Stdef [9]: (23) where Uc is the representative collision velocity in the granulator and Pg and Yd the granule density and dynamic yield stress, respectively. 80th Yd and Pg will vary with the formulation properties and granule porosity and should be meas ured at the characteristic porosity reached by the granules in the granulator, cmin (equation (26» , (see Section 3.3. 1 ). Estimates of Uc for different types of process equipment are given in Table 3. The Stokes deformation number is a measure of the ratio of impact kinetic energy to the plastic energy absorbed per unit strain. It takes into account both the process agitation intensity and the granule mechanical properties. The way that these two parameters influence the type of granule growth be haviour is shown in Fig. 36, the granule growth regime [49,50]. At low liquid contents, the mass behaves as a dry powder. At slightly higher liquid contents, granule nuclei will form, but there is insufficient moisture for further growth. AI ternatively, for coarse powders that result in weak granules, a crumb will form with a few granules that continually break and reform. At high liquid contents, a weak system will form a slurry, an intermediate strength system will display steady growth, and a strong system (Iow Stdef) will exhibit induction time behav iour. Note that at extremely high liquid saturations the distinction between steady growth and induction-growth systems disappears, because an induction-growth system with zero induction time grows quickly just Iike a fast steady-growth sys tem (this is in some ways analogous to how the distinction between liquid and gas disappears in the supercritical fluid region). Table 3. Estimates of Uc for different granulation processes [2]
Type of Granulator Fluidized beds Tumbling granulators Mixer granulators
Average Uc
Maximum Uc
Granulation Rate Processes
933
i "Crumb" " Dry" i . � . "" Free- , .. .... L . Flowing j ,' . ., Powder! "'.
I
. ....
..
.
Siurry
"
Increasing
Steady Growth Inc reas ing Growth
. \\\ ••
Nucleation Only
Stdef 2 pgUc 12Yd Number,
• . ..... .
!
Rate
-+\
..•................
•
=
f'
............•.......
' ' .::. .: .../ " ,' ./
Deformation
. .' ':' .'. ,
Rapid Growth
•..... .•
Induction
10ecreasing Induction Time ! . • .... ..... _ �
!
.
1 00%
o
Max i m u m Pore Saturation,
smax = wPs(1-&min)IP/&min
Fig. 36. Granule growth regi me map as given in Iveson et al. [50] (an adaptation from the one originally proposed by Iveson and Litster [49]).
. Induction
>-
1 .0E·1
<::<.1 ..J'CI)Q;
1 .0E·2
� '" :::;,
•
Steady Growth
I
Rapid Growth
Iron Ore in Drum
x
/
Nucleation Region x
x
1 .0E-3
Rapid Growth
o
•
o .
•
� Ballotini
•
,. '"Chalcopyrile j in Drum � Ballotini
& Water in Drum
•
&
Glycerol in Drum
1 .0E·4 0.700
0.800
Induction
0.900
1 .000
1 .1 00
1 .200
Pore Saturation (-)
Drum granulation results plotted on regime map using wet tapped porosity to calculate liquid saturation [50].
Fig. 37.
Figure 37 shows a range of drum granulation data covering different formu lations and different drum sizes and speeds. The data fall neatly into the regime map frame work [50]. The growth regime map can be used to explain the majority of the commonly observed effects of parameters such as binder content, particle size, and binder
934
K.P. Hapgood et al.
I
"Dry" Free Flowing j Powder ! / :'
Increasing
.
Deformation
Stdef = 2 PgUc 12Yd
/ /
Number,
...
..
.. •. .•
�/
o
Siurry
"Crumb"
..
}f: '
Steady
..• •
Decreasing Binder Surface Tension
.
....
,
\
'-;
i
Nucleation Only /I
. . .. . .. ......
......-....:. . ..............................l....................,......... . .... ....... ..... :: . ..... ..... Increasing ..
..
.
Agitation Intensity
Increasing Binder ·········· ... . . Content ..
Increasing Binder Viscosity or Decreasing ParticIe Size
Rapid Growth
Induction
1 00% Maxim u m Pore Saturation,
smax = wps(1-Smin)IP/E;min
Fig. 38. The effect of different variables on a formulation's position on the growth regime map.
viscosity and surface tension on the growth behaviour of granules (Fig. 38). Namely: •
•
•
•
Decreasing binder surface tension andjor increasing particle size weakens granules (decreases Yd and hence increases Stdef) and makes them more likely to form a crumb material [47]. Increasing process intensity (increasing Uc and hence increasing Sfdef) makes granules grow faster, but may cause the formation of crumb or an over-wet slurry. Systems with fine particles andjor viscous binders often display induction time behaviour. Increasing liquid content (increasing smax) increases granule growth rate (e.g. see Fig. 38).
This granule growth regime map enables one to make sensible predictions about the likely effect of changes in a system parameter. It also hel ps to explain why scale-up has often proved to be so hit-and-miss. A system might be in the induction-growth regime in the gentle environment of a laboratory-scale tumbling drum, but then shift into the steady-growth regime in a full-scale drum where the granules fall further and experience greater impact forces. Conversely, the intense environment inside a smali laboratory scale high-shear mixer might result in a system displaying steady-growth behaviour, but when scaled up, the intensity may drop to such an extent that the system shifts to induction-growth behaviour. From an operational point of view, if the objective is to obtain relatively smalI, uniformly sized granules, then the ideal region of operation is in the nucleation
Granulation Rate Processes
935
regime, or else in the induction-growth regime provided that the residence time of granules in the granulator is kept less than the induction time. In these two cases, the size distribution of the granules depends only on the size distribution of the initial nuclei formed. Hence, if the binder-addition process can be controlled to obtain uniformly sized nuclei, then a uniformly sized product can be obtained (see Section 2 above on wetting and nucleation). However, if the objective is to obtain relatively large granules, then the steady-growth regime is preferable, as this minimises the residence time needed and the final size can be controlled through varying the binder content and/or the residence time. Operating in the rapid growth regime is generally undesirable as the granules grow too quickly to obtain a weil controlled final size, and also because layering of the material on the granulator walls and inserts starts to become a major problem. Although successful at qualitatively explaining the observed effects of different parameters, this regime map has its limitations. Firstly, it can not as yet be used predicatively because the two parameters, smax and Sfdef, require a priori knowl edge of the maximum extent of consolidation (Emi n ) since this affects both granule yield stress and pore saturation. Unfortunately, we have as yet no way of pre dicting how much a given formulation will consolidate under a given set of op erating conditions (see section below on consolidation). Different types of granulation equipment cannot be easily compared. Iveson et al. [50] attempted to compare granulation data from drums and mixers on the same regime map. While all the data from different drums were mutually con sistent, the data for mixer granulators did not agree with the drum data, nor between different geometry mixers, with several having values of Sfdef that were orders of magnitude too high. This difficulty is presumed to be because of the uncertainty of the correct characteristic impact velocity to be used in calculating the Stoke's deformation number for a mixer. This velocity represents some sort of average collision ve locity. We used the impeller tip speed as an estimate. However, a mixer may have more than one impeller spinning at different speeds, and the mass of ma terial usually circulates much slower than the im peiler, and within this body of material, the relative collision velocity between granules is slower again. There is still much work to be done to measure and predict the flow patterns and collision velocities of granules inside granulators. This limits our ability to use the regime map to compare different types of granulators. However, once the location of the regime boundaries are determined experimentally for a particular type of gran ulator operating at a given speed and loading, the behaviour of other formulations in the same machine should be predictable. This is useful for industrialists who often have only one machine at their disposal, but are needing to regularly vary formulations. Another limitation of the regime map is the very simplistic rheological model used to describe the mechanical properties of the granules. It is assumed that the
936
K.P. Hapgood et al. 1 40,000 1 20,000
AH ballotini
A
0 . 1 53 glg 60 Pa.s Oil 35% Porosity 70% Saturation
ro � 1 00,000 <J) <J)
U5 80,000 Q) >
<J) Q)
60,000
Ci E 40,000 0
D: 30 mm/s
- E: 1 0 mm/s - F: 1 mm/s - G: 0 . 1 mm/s - H: 0.01 mmls
�
'(ij
- A: 1 50 mm/s - B: 1 50 mm/s - C : 1 00 mm/s
D
ü
20,000 0.0
0.1
0.2
0.5
0.3 0.4 Natural Strain ( -)
0.6
Fig. 39. Flow stress vs. strain for pellets bound with 60 Pa · s silicone oil at impact speeds varying from 0.01 to 1 50 mm{s [51 ] .
granules are rigid-plastic materials with a strain-rate independent yield stress, Yd. However, wet granular materials are actually complex visco-elastic-plastic ma terials with strain-rate and history-dependent behaviours. For instance, Fig. 39 shows how the flow stress varies with strain when a granular pellet is crushed at varying speeds. Rather than a steady plastic flow stress, instead there is a rapid rise to a peak value, and then a drop off to a level value after about 30% strain. Hence, the "average flow stress" during any col lision will depend on wh at extent of deformation occurs. In addition, from Fig. 39 it can be seen that the granule flow stress is strain rate dependent. Figure 40 shows how the dimensionless peak flow stress, Str* = (JP dp/ycos8 , va ries with the capillary number, Ca dp p,ej(y cos 8), where dp is the average particle size, y the binder surface tension, e the contact angle ande the bulk strain-rate (deformation velocity divided by instantaneous pellet length). Str* the ratio of peak flow stress to capillary (or surface tension) forces and Ca the ratio of viscous to capillary forces. The data are weil described by the Herschel-Bulkley model: k
=
(24) with the best-fit values of the three parameters being k1 = 5.3 ± 004, k2 = 280 ± 40 and n = 0.58 ± 0.04. There are two regions of behaviour. At low Ca, the granule flow stress is independent of strain rate, so in this region viscous forces in the binder phase must be negligible. At high Ca, viscous forces become significant and the flow stress becomes dependent on Ca. This transition coincides with a change in the
Granulation Rate Processes
937
Cä°·58
1 .0E+3 .,-------, Best Fit: SIr' = 5.3 + 280 cn cn
U5 �
1 .0E+2
�
Li:
cn cn
� �
o '00
E
Ci
1 .0E+1 X
Region 11
Region I
1 .OE+O -!-....I-L..J....I..l.i.LIj!---J..L..U.J.J..Lf-----1.-'-l.LLJ"t-..I-.L...J.J.llJ.I--J...J..I.JJJ.j 1 .0E+O 1 .0E-4 1 .0E-2 1 .0E-6 1 .0E-1 0 1 .0E-8 Bulk Capillary Number, Ca ( ) -
x
Water
0 0.1 Pa.s Oil
• Glycerol
o 0.01 Pa.s Oil
ß 1 Pa.s 0iI
0 60 Pa.s Oil
Fig. 40. The dimensionless flow stress Str* vs. capillary number Ca with added sche matics of deformed pellets shown above selected points. Pellets: 35% porosity, 70% saturation, 35 �m glass ballotini. Une shows best fit of equation (24) [51 ,52] .
mechanism of deformation. At low Ca, strain occurs in distinct failure planes, resulting in bulk cracking. However, as viscous forces become important, shear band widening occurs which results in plastic flow without cracking [52]. So the parameter that best represents the average effective yield stress Yd in a granulator is not clear. It will be a function of both how much strain occurs, and the strain rate at which deformation happens. Two dimensionless groups are also unlikely to be sufficient to adequately ex plain all observed granulation behaviour. For instance, in the coalescence model of Liu et al. [53] outlined below, the following additional dimensionless groups emerge: • •
Yd/E * - the ratio of plastic yield stress to elastic modulus. Stv the viscous Stokes number. -
The effect of binder viscosity (as measured by Stv) needs to be included be cause a coarse formulation with a viscous binder, and a fine formulation with a non-viscous binder, may both have the same yield stress and hence deform to the same extent, and yet the one with the viscous binder will grow much more easily because of the greater bond strength formed [54]. Similarly, for non viscous binders, the magnitude of the binder surface tension forces will need to
938
K.P. Hapgood et al.
be accounted for, perhaps via the capillary number Ca, the ratio of viscous to surface tension forces. Lastly, the regime map only teils us about the type of granule growth. It does not supply any rate information, which is usually of major importance in designing and sizing granulation systems. Hence, the semi-quantitative understanding gained from this regime map needs to be combined with rate information obtained from population balance modelling (see Chapter---Modelling in this handbook). Theoretical models that may be useful for predicting the location of some of the regime boundaries are discussed in the sections on coalescence modelling below and in more detail in Iveson et al. [54]. I n the induction-growth region, growth occurs by the collision of essentially non deformable granules with a layer of liquid binder at their surfaces. Liquid binder is squeezed to granule surfaces by the process of consolidation. In the steady growth region, growth occurs by the coalescence of deformable granules with the formation of a bond between them. Hence, the four important aspects that need to be understood in order to model granule growth are: 1. 2. 3. 4.
Granule consolidation, Coalescence of non-deformable granules, Coalescence of deformable granules, and Granule bond formation.
These four topics will now be discussed in turn. 3.3. Granule consolidation
As granules collide with other granules and equipment surfaces they gradually consolidate. This reduces their size and porosity, squeezes out entrapped air and may even squeeze liquid binder to their surface. Porosity affects granule strength. Granules with high porosity are weak and friable. These granules will break and generate dust during handling which is undesirable in most cases. However, for many products it is also desirable that the granules be porous in order to facilitate fast dispersion and dissolution. Hence granule porosity is an important product property to control and optimise. Granule consolidation also influences granule growth mechanisms. This is clearest in induction-growth systems, where the length of the induction period depends on the rate of consolidation. However, even in steady-growth systems, consolidation is likely to have a significant influence. Granule yield stress gen erally increases as granules consolidate [55]. This decreases the amount of de formation when two granules collide which decreases the likelihood of coalescence. However, consolidation also increases the pore saturation, which
939
Granulation Rate Processes
in turn increases granule plasticity [56] and the availability of liquid at the granule surface. 80th of these effects will aid coalescence. Hence, the net effect of consolidation in the steady-growth region is uncertain and will probably depend strongly on the formulation and binder properties. As a rule of thumb, the granules formed in fluidised beds have porosities ranging from 30 to 50%, in tumbling drums and pans from 30 to 40%, and in mixer type granulators from about 20 to 30%. However, understanding granule growth requires a much more detailed knowledge of how granules consolidate. 3.3.1. Consolidation models
There are only two theoretical treatments of granule consolidation in the liter ature, both of which are quite limited. Ouchiyama and Tanaka [57] assumed the particles in a granule were held together by the capillary pressure of the binder. This pressure generates a normal force causing friction at inter-particle contacts. They considered how the coordination number of particles in the granular as sembly increased when forces were applied on the granules as they tumbled inside a rotating drum. They ignored any particle detachment that might occur due to dilation of the assembly and did not consider viscous effects. They found that the rate of granule consolidation was: n d e :::,: (1 _ e)3 1(25) dr - e.K,
{
}
where e is the granule porosity, r the "dimensionless compaction time" which depends on the frequency of granule collisions, K" the "dimensionless granule compaction rate", which depends on the impact forces between granules and the capillary and friction forces within granule, and n a parameter describing distri bution of granule impact energies. The dimensionless compaction rate, 1<" in creases with decreasing liquid surface tension, increasing particle size and increasing "process intensity". Setting de/dr = 0, the minimum porosity the system reaches, em in , after an infinite time is emin (26) K, (1 - emin )3 - Hence this model predicts that the dimensionless compaction rate and mini mum porosity are linked. Increasing the compaction rate will decrease the mini mum porosity (i.e. increase the amount of consolidation). The second theoretical treatment of granule consolidation was a brief consid eration by Ennis et al. [42] of the effect of binder viscosity. Using an adaptation of their coalescence model, they suggested that the amount of consolidation per
940
K.P. Hapgood et al.
collision would increase with increasing viscous Stokes number, Stv (equation (32)) according to (27) where LlX = reduction in inter-particle gap distance h per collision. In this case, the size and mass used to calculate the viscous Stokes' number are those of the constituent particles, not of the granule as a whole. Hence increasing binder viscosity and decreasing particle size should both decrease the amount of con solidation and increasing the process intensity (impact energy) should increase the amount of consolidation. 80th these models predict that factors which make granules stronger (in creasing surface tension, increasing viscosity, decreasing particle size) will cause a decrease in the rate of consolidation and that increasing the process intensity (energy and frequency of impacts) will increase the rate of consolidation. They also predict that the rate of consolidation will slow down as granules densify. However, there was little detailed experimental evidence at the time to quanti tatively validate these predictions. 3.3.2. Experimental studies of consolidation
Until the mid-1 990s, effectively all that was known experimentally about consol idation was that porosity initially decreased quickly and then levelled off to a stable equilibrium value. The effect of different parameters on the process was uncertain (e.g. [43,48,58]). Iveson and co-workers performed a series of experiments measuring the effect of different variables on consolidation behaviour [59,60]. Granules were made with glass ballotini of various size fractions bound with water, glycerol or surfact ant solutions. Figure 41 shows a plot of granule porosity versus the number of drum rev olutions for a batch granulation in the nucleation regime. The porosity initially drops quickly and then levels off to a stable value. This trend suggests a first order rate process, where the driving force for the decrease of porosity is pro portional to the difference between the present state and the final equilibrium state. Expressed mathematically, (28a) d c/d t = - k(c - cmin ) Integrating gives c - cmin = (cQ - cmin ) eXp( -kt) (28b) where k is termed the consolidation rate constant (with units S-1 ), co the initial porosity of the batch and cmin the minimum porosity reached. Equation (28b) was fitted to all of the batch consolidation data to extract the three parameters, k co
Granulation Rate Processes
941
0.38 ,-----,----,--, 0.41 7 ml Glycerol/ml Solid • 1 0 iJm Glass Ballotini 1 9 iJm Glass Ballotini 'V • 37 iJm Glass Ballotini
0.37 �
� 'üj e 0 c.. 0.36
� 0
0.35
0.34
Fig.
41 . 8VS.
L-___"'--___-L-___--"--___-'-___-..l
o
1 000
3000 2000 Number of Drum Revolutions
4000
5000
time for different sized glass ballotini with glycerol binder.
and emin. eo is a function of the initial mixing of the particles and binder, so k and are the two parameters of most interest. The consolidation rate constant, k, is postulated to be proportional to the fre quency and energy of collisions between granules (the "process intensity"), and inversely proportional to the resistance of the granules to consolidation, which in some way is related to the dynamic strength of the granules; k process in tensityjgranule dynamic strength For a batch granulation process in the nucleation regime with relatively little change in granule size, we may assume that the process intensity remains con stant throughout the process. Hence, k should depend solely on the dynamic strength of the formulation i .e. k should increase with increasing particle size and decreasing surface tension and binder viscosity. From the work measuring gran ule dynamic strength, we expect that surface tension will only be significant for small Ca and viscosity will only become significant for large Ca [52]. According to the model of Ouchiyama and Tanaka (equation (25)), factors which increase the rate of consolidation should also increase the extent of consolidation i.e. reduce emin' Hence, we expect emin to be decreased with increasing particle size and decreasing surface tension and binder viscosity. emin
oc
3.3.3. Partic/e size and binder viscosity
Figure 41 shows that, as expected, increasing particle size does indeed decrease the minimum porosity. Figure 42 shows that increasing binder viscosity and de creasing particle size both decrease the consolidation rate constant.
942
K.P. Hapgood et al. 0.007 '� 0.006
�
,-----.-------,---,---,.------,---,--,.-/ --,-----,
Variable Binder Contents • Water Binder o Glycerol Binder
�
.lc
/
5
/
/
/
/
20 15 10 30 25 Surface Mean Particle Size. x3,2 (11m)
35
40
Fig. 42. k vs. particle size for water and glycerol binders at various liquid levels [60].
Figures 43a and 43b show the effect of varying binder content on granule consolidation for water and glycerol binders respectively. Figure 43a shows that when the amount of water (a low viscosity binder) is increased, the granules consolidate to a greater extent. However, Fig. 43b, shows that when the amount of glycerol (a high-viscosity binder) is increased, the granules consolidate to less of an extent. Figure 44 summarizes the effect of binder content on the minimum porosity, cmin , for a range of water-glycerol solutions with different viscosities. The increase in the extent of consolidation with increasing water content (Fig. 44) is counter to the prediction of the consolidation models above. There are two possibly explanations: ( 1 ) In the sub-saturated state, increasing liquid saturation usually increases the tensile strength of granules made from relatively coarse particles [55]. This increased tensile strength may actually aid consolidation as it hel ps resist granule dilation and provides an increased force that is seeking to pull the particles of the granule together. (2) Alternatively, increasing water content may serve to lubricate the inter-particle contacts and thus reduce the frictional resistance to consolidation. The reversal of this trend for the high-viscosity glycerol binder (Fig. 44) sug gests that inter-particle capillary and frictional forces are no longer important. Instead, increasing the amount of a viscous binder increases the viscous resist ance to consolidation and thus reduces the extent of consolidation. Figure 44 suggests that there is an intermediate binder viscosity at which the effect of
943
Granulation Rate Processes 0.39
,
rr-----,-----,
�
0.38
Z'00 e 0 0.37 a.
:;c � <.9
�
1 9 IJm Glass Ballotini (AI#2) 0 OA 1 7 mI/mi Water .A. OA41 mI/mi Water 0 OA66 mi/mi Water • OA90 mi/mi Water
� � ' G-
� \ .A.
. ---0-
\
<1>
..� . • I
----
___
0.35
(a)
0
0
Q ---8
_ . _ .
� .A.
••�t:J� . '"
0.36
. 0
-----... o
.
_ .A._
--- - -Q - -ld
:;c � <.9
o - TI
1 000
500
1 500
Number of Drum Revolutions
2000
Glycerol Content e OA 1 7 mi/mi
/:). 0.441 mi/mi
0.38 ,
•
_ _
0
0.39
Z·00 e 0 a. <1>
-.A.- ---&- -
e OA66 mi/mi
e 0.37
0.36
0.35
'!::s .
ii ' i:J."
"
h.
"
'A
0.34 +-----1-----1 o 3000 2000 4000 1 000 5000
(b) Fig. 43.
!;
Drum Revolutions (Revs.)
vs. time for different liquid binders (a) water and (b) glycerol [59].
binder content has no effect on the extent of consolidation as the decrease in frictional resistance is matched by an increase in viscous resistance. One im portant lesson to be leamt from Fig. 44 is that it is impossible to make a priori predictions about granule consolidation behaviour, even qualitatively, unless one has some knowledge of the relative importance of viscous and frictional forces. However, whilst the effect of binder content on k may be unclear, the effect of viscosity is unambiguous. Figure 45 shows that increasing the binder viscosity decreases the rate of consolidation, which agrees with the predictions of the
944
K.P. Hapgood et aJ.
0.38
r----,---,---;-
0.37 � ijj e o Il.. E '
0.36
L-r
E 0.35
�
'c
0.34
-
1 9 m Ballotini (AI#2) • Water D 50wt% Glycerol V 85wt% Glycerol A Glycerol
-'-___-'-___'---___'---__---.J
0.33 L0.40
___
0.42 0.48 0.46 0.44 Binder Content (mi Binder/mi Solid)
0.50
Fig. 44. 6min VS. binder content for different binders [59].
0.01 ui
1
� >
� �
-E
->::
Ci) c: 0 Ü
�
0.001
�. . +
j
... .......
a:
�
c: o
:Q
gc: o
ü
1 9 11m Ballotini (AI#2) Variable Binder Contents
t
-' . "-'.
0.0001 L-_'--__'_L....C--L.-_-'-_--'-----'_�_--'-__'__'_--'-.J 0.1 0.01 0.001 Binder Viscosity, (Pa.s)
Fig. 45. k VS. binder viscosity [59].
consolidation model of Ennis et a/. [42]. The combined effect of decreasing par tiele size (dp ) (above) and increasing binder viscosity (11) on the consolidation rate constant (k) may be summarized according to the equation (60):
dp
k cx: 8 11
(29)
Granulation Rate Processes
945
where a = 0.26 ( ± 0. 1 3) for these experiments conducted with 1 9 J.lm ballotini granulated in a 30 cm drum at 30 rpm. The value of a is lower than the expected value of about 0.6 that might be expected based on measurements of granule dynamic strength (see equation (24)). This may be because the data in Fig. 45 does not extend fully into Region II where viscous effects dominate. Hence a is biased towards a lower value. 3.3.4. Binder surface tension
Figures 46 and 47 show how Cmin and k respectively varied with surface tension, for different particle sizes and binder content. The Ouchiyama and Tanaka model predicts that lowering surface tension will result in granules that consolidate more quickly and to a greater extent, because lowering surface tension makes granules weaker. With the exception of some of the data for pure water (surface tension 72 N/m), it appears fram Fig. 47 that the consolidation rate constant did indeed increase as binder surface tension was lowered. However, in spite of this increase in k, lowering binder surface tension had the unexpected effect of decreasing the maximum extent of consolidation, Le. increasing cmin (Fig. 46). One possible explanation for this behaviour is that the minimum granule po rasity is not a static final state, but rather represents a dynamic equilibrium be tween the tendency of granules to both densify and dilate during collisions. If this is the case, then lowering the binder surface tension, which makes granules weaker and consolidate more easily, would also lower a granule's resistance to 0.40
r------,--""T'"--,..---.
0.39
":�
.5
�
0.37
§
0.35
o
.: ..!!
0.38
i!! f 0.36 C .§
�
1 0 pm Ballotini • 0.441 mVmI Binder 19 pm BalIotini (AI#3) o 0.466 mVmI Binder o 0.441 mVmI Binder Cl. 0.417 mVmI Binder
=
0.34 0.33
'---_--'-____-'-____...L.-___....I.-. ...J --.J
30
40
50
Binder Surface Tension
60 (mN/rn)
Fig. 46. Minimum porosity VS. binder surface tension [60].
70
946
K.P. Hapgood et 81. ( 1 9 �m Ballotini AI#3) o 0.466 mi/mi Binder o 0.441 mi/mi Binder D. j 0 41 7 m,ml rn'M'
0.008 CJi
0.007
� 0.006 >
�
-E
\
0.005
Ci) c 0 0 0.004
. , /' -��;-; /' /.
�
"
CI: c 0.003 0
�
:2 0.002 -0 CI) c 0 0 0.001
0.000 30
/'
"
1 0 �m Ballotini T 0.441 mI/mi Binder 40
50
(60
./
70
Binder Surface Tension mN/m) Fig. 47. Consolidation rate constant VS. binder surface tension [60].
dilating during impacts. Depending on the relative change in the ease of con solidation versus the ease of dilation, this might then shift the dynamic equilibrium to a higher minimum porosity value. It should be recalled that the Ouchiyama and Tanaka model of consolidation does not consider the possible occurrence of dilation, and so this would explain why it fails to predict this trend. 3.3.5. Implications for granule growth and induction time
In summary, we now have a good knowledge of the effects of particle size and binder viscosity on the consolidation process, although there still remains some ambiguity about the effect of surface tension that needs to be resolved by further experimentation. The effect of binder content depends on whether viscous or frictionaljsurface tension forces dominate. Because of these complexities, there are currently no models that correctly predict either the rate or extent of con solidation a priori of a particular formulation under a given set of operating con ditions. Any such model will need to include the inter-related effects of capillary, viscous and frictional forces, and the fact that consolidation may be a dynamic process involving an equilibrium with dilation. This is important as we want to predict whether granules will become 1 00% saturated or not during a granulation process, in order to predict whether the formulation is in the nucleation only, or in the induction-growth regime. Nevertheless, it is possible to develop a consolidation-Iayering model for in duction regime growth based on our understanding of the consolidation-Iayering mechanism [1 8]. The model proposes that a layer of fines is gradually built up as
Granulation Rate Processes
. . . . . .- .. . ' .. • • .•. .... . . . . . .. . . .
:
..
. . . .. " •
•
.' . " ,-
••
.'
•
: ' :.. .
:
. . . . .. . ' . .1
• •,
.
: .:• ... . . .. . . . . ..' .. .... . .... . . .
. . . �� . !" : " . . ' ' ' . : : . ... . ' . . ' , " .' ' . " . . ., . . .' . '
'�/.
Wet spot
.
.
,
(b)
(a)
947
-
-
• • '-. / Liquid film
D
.. Ce)
Fig. 48. Schematic of the mechanism for consolidation and layered growth in the presence of fines.
granule consolidation squeezes liquid to the granule surface (see Fig. 48). This will occur during the induction or consolidation phase. Once all fines have been layered, surface wet granules will grow by coalescence. The layering growth rate is, therefore, directly related to consolidation rate of the granule, which is a func tion of Stokes deformation number (granule strength): c - cmin G(v) = _ kv c
(30)
(31 ) Where G(V) if the growth rate of granule with size v, k is the consolidation rate. The model predicts the length of the consolidation (induction) stage, the rate of fines layering and granule size distribution during the consolidation stage. Batch drum granulation experimental results using chalcopyrite and limestone were compared to the model output using the consolidation rate constant as the single fitting parameter. Good agreement was observed between the experi mentally measured and simulated mass mean diameters, size distributions and rates of fines disappearance (see Fig. 49). The fitted rate constants for chalco pyrite was 1 0 times larger than that for limestone, which matched weil with their dynamic yield stress and know consolidation behaviour. 3.4. Granule coalescence models
If we survey the existing coalescence models from a range of applications, we see that they fall into two classes (Table 4). Class I models only consider what happens during the initial collision - do the colliding entities stick or rebound? If all of the kinetic energy of impact is dissipated, then they are assumed to have coalesced. If not, then they rebound. Class 11 models assume that the collided granules remain in contact for some fixed average period of time (i.e. it is implicitly assumed that all the initial kinetic
948
K.P. Hapgood et al.
0. 8
� O ln'$ 0 7 2 I'C\'$ (Clp) 0 O I 17 1'(\'$ «(xp) 0 70 I'C\" (rmd) --- l ::n 1'(\'$ (moo) -
::::: JS.
�
0. 6
0.4
0. 2
0 0, 1
Oiamelef (mm) 1,0
1 0,0
Fig. 49. Comparison between simulated and experimental granule size distributions during the consolidation phase (- 1 80 �m chalcopyrite powder) [ 1 8].
energy of impact is dissipated). During this time a bond strengthening process of some type occurs. The strength of this bond is then compared with the average separating force applied to the joined pair of entities. This difference in approach is shown schematically in Fig. 50. 80th c1asses of coalescence models include important elements of what ac tually happens. Clearly, granules must "stick" during their initial contact. But in order to survive, their bond must become strong enough to resist subsequent separation. So both aspects need to be included in any complete model of gran ule coalescence. This requires both an understanding of the rate of strengthening of granule bonds and the frequency and magnitude of separating forces that granules experience. Unfortunately, neither of these aspects of granulation is currently weil understood. In spite of these limitations, we can gain some useful insight into granulation behaviour by considering some of the existing models in more detail.
3.4.1. The ennis coalescence model for non-deformable granules
Figure 51 illustrates schematically the coalescence model proposed by Ennis et al. [42]. The colliding granules are considered to be elastic spheres (not nec essarily of equal size) with surface protrusions that are covered with a uniform layer of viscous liquid binder. The granules initially approach each other head-on at a certain relative velocity. lf the initial kinetic energy is entirely dissipated
949
Granulation Rate Processes
Table 4. Summary of some of the coalescencejaggregation models available in the literature
Authors Ouchiyama and Tanaka [57]
Typea Class 11
Ennis et al. [42]
Class I
Moseley and O'Brien [61 ]
Class I
Simons et al. [4] Adams et al. [62]
Class II Class I
Seville et al. [63]
Class I1
Thornton and Ning [64]
Class I
Liu et al. [53]
Class
Hounslow et al. [65]
Class II
a According
I
Comments Distinct compression and separation zones in drum granulator; plastic deformation; adhesive force; force balance. Head on collisions; viscous fluid layer; coefficient of restitution; energy balance. Collisions at an angle; elastic deformation; adhesion energy; energy balance. Capillary bridge rupture energy. DEM simulations of agglomerate collisions including friction, viscous and capillary forces, pendular bridge rupture and partieIe elastic deformation. Balance between partieIe contact time and visco-plastic sinter neck growth time. Head on collisions; elastic-plastic deformation; adhesion energy; energy balance. Head on collisions; elastic-plastic deformation; viscous fluid layer; energy balance. Balance between growth rate of crystal contacts vs. time between eddies causing separation.
to classification of Iveson [66].
through viscous and elastic losses, then the granules will remain stuck together and are considered to have coalesced. Otherwise they will rebound. Viscous losses were calculated using the results for Stokes flow between two approaching spheres completely submerged in a liquid medium. This is justified on the basis that the majority of the viscous force was generated only in the immediate gap region between the two surfaces. Granules were assumed only to approach as elose as 2ha , the height of their surface asperities. This assumption is needed to avoid the viscous force approaching infinity for zero gap
950
K.P. Hapgood et al.
Class 1 1 : Survive or Separate during the First Major Impact?
Class I: Rebound or Stick?
o o
�: C6 Cö ;::otC6 ; 8 O 00 S"N;"
,,,,,.
""d
M=T eN" between major separation events during which bond strengthens.
O
Fig. 50. Illustration of class l and ciass 1 1 coalescence models [66].
Fig. 5 1 . Schematic of the Ennis et al. [42] coalescence model.
distance. So me dissipation of energy within the solid phase is included by use of a coefficient of restitution, e, which may be less than unity. During re bound, the liquid bridge between the two spheres was assumed to rupture at a distance of 2h (i.e. the same distance at which the liquid layers first touched), even though in reality once formed, the bridge might rupture at some greater distance. The resultant calculations predict that collisions will result in coalescence when the viscous Stokes number (Stv) is less than some critical viscous Stokes number (S(). For equi-sized granules, these are defined as folIows: Sty
=
4puoD
9/1
(32) (33)
951
Granulation Rate Processes
where p is the granule density, Ua half the initial relative velocity of impact, D is the granule diameter, J1 the liquid viscosity, e the coefficient of restitution, h the thickness of the liquid surface layer and ha the characteristic height of surface asperities (Fig. 5 1 ). Stv is the ratio of initial kinetic energy to the energy dissipated by viscous effects. During batch granulation, Stv increases as granules grow in size. This enables three stages of a batch granulation process to be identified. The non inertial regime occurs when Stv < < St:. All collisions are successful regardless of the size of the colliding granules. As the granules grow larger, the system enters the inertial regime when Stv St:. The likelihood of coalescence now depends on the size of the colliding granules. Collisions between two small or one small and one large granule have a low Stv and hence are more likely to succeed than collisions between two large granules. Eventually, the system enters the coating regime when Stv � St;. Here, all collisions between granules are un successful and all that is possible is to coat added powder onto the surface of pre existing granules. These three regimes of growth have been observed experi mentally in many granulators [42]. According to this model, agglomerate growth is promoted by a low Stv and a high value of St;. For instance, increasing binder content will increase the binder layer thickness, h, which will increase St; and hence increase the growth rate a commonly observed behaviour in many systems. Likewise, since increasing binder viscosity and decreasing impact velocity both reduce Stv , it might appear that these two changes will always increase the growth rate. However, these two variables also indirectly influence St;. Increasing binder viscosity decreases the rate of granule consolidation. This will reduce the thickness of the liquid layer squeezed to the granule surface, which inhibits coalescence by decreasing St;. Hence, a high-viscosity binder might initially inhibit growth by preventing liquid being squeezed to a granule's surface, but once the liquid is there, the higher binder viscosity will aid granule growth. Similarly, increasing the impact speed will increase the rate of consolidation, which increases the liquid layer thickness, aiding coalescence. Therefore, the effects of variables such as collision speed and binder content on granule growth rate will depend on their net effect on the ratio of Stv:St; , which may be time dependent and not easy to determine be forehand [67]. The model of Ennis et al. [42] is significant because it was the first physically based model in which the parameters could potentially be measured, and it was also the first model to consider dynamic viscous effects. However, the model assumes the granules are elastic, liquid is present as a distinct layer at the granule surfaces and viscous forces dominate over capillary ones. Hence the Ennis model only applies to the initial nucleation phase where granules consist of individual particles covered by a layer of liquid binder, or else to induction-growth systems, in which granules are essentially non-deformable and only grow when �
952
K.P. Hapgood et al.
they become surface wet. It cannot be applied to the steady-growth region, nor does it apply in systems with low-viscosity binders where capillary forces are important. There are many practical systems in which these restrictions are satisfied namely induction-growth systems with viscous binders. For instance, in the granulation of many pharmaceuticals and detergents, the powders used are fine and the binders are viscous (either deliberately so, or because of partial disso lution of the solid). In such cases, viscous forces could be expected to dominate over surface tension ones and the granules are often quite strong and deform little during collisions. One prediction of the Ennis model is that low velocity collisions are more likely to result in granule coalescence than high energy ones. This is because there is less kinetic energy to be dissipated in such collisions. However, this prediction is incorrect for surface-dry granules that require a significant amount of deformation in order to become bonded together. The model of Liu et al. [53] below accounts for this effect.
3.4.2. The liu et al model of deformable granule coalescence
Liu et al. [53] extended the Ennis model to inciude the effects of granule defor mation. Granules were assumed to have a strain-rate independent elastic mod ulus (E) and plastic yield stress ( Yd ). Two cases were considered: surface wet granules (Fig. 52) and also surface-dry granules where liquid is squeezed to the granule surfaces by the impact (Fig. 53). Again, coalescence is assumed to occur when the kinetic energy of impact is all dissipated, which in this case inciudes plastic deformation of the granule matrix. During approach, the viscous force between the two spheres is only propor tional to the square of sphere radius, R2. However, during rebound the viscous dissipation that occurs between the two flattened portions of the surface is pro portional to the radius of the flattened area to the fourth power, a4 . Hence, the retarding viscous force acting on the spheres during rebound is very sensitive to the amount of permanent plastic deformation that has occurred. This important influence of granule deformation was not accounted for in the Ennis model. Liu et al. [53] described two types of coalescence, termed types I and type 1 1 . Type I coalescence occurs when all the initial kinetic energy i s dissipated i n the surface liquid layer before the granule surfaces have touched. This occurs when Stv < In
G�)
(34)
Type 1 1 coalescence occurs when granules are slowed to a halt during rebound, after their surfaces have made contact. The critical condition for Type 1 1
953
Granulation Rate Processes
:(e)
:(a)
"0
Fig. 52. Schematic diagram of the model used to predict coalescence of surface wet, deformable granules. (a) Approach stage. (b) Deformation stage. (c) Initial separation stage. (d) Final separation stage [53]. (b)
(a)
141 = 110
L1 1
l
t
U2
t
142
143
(e)
1/3
Fig. 53. Schematic of the Liu et al. [53] model for the case of the collision of surface-dry deformable granules.
coalescence is given by the following result:
K.P. Hapgood ef 8/.
954
Stv is the viscous Stokes number, and Stdef the Stokes deformation
where number:
Stv = 38nmupD_o2
mu2 Stdef = � 20 Yd
(36) (37)
= (38n) 1 /2(Stder )1 /2Ö[1 - S:v In G�) ] 1 1 - 7.36 (��) (Stdef)-1 /4 ( 1 - S:v In G�) ) - /2]
(38)
Ö
where and m are the harmonie mean granule diameter and mass, respectively, and [)" the extent of permanent plastic deformation given by [) "
[
The predictions of these equations for set values of Yd/E*, ho/ha and Ö/ho are for the surface-wet and shown in Figs. 54 and 55 as functions of versus surface-dry cases, respectively. There are aetually 4 types of differenee behaviour that can be identified. Region A is the region in which granules
Stv
1 00
Stdef
r----...,..---,
System: Y / E*
d
NO cJ
ho/ha D/ho
�
�
1
E �
� CI)
0.01
==
=
==
10
10
10 X
In (ho/ha)
C. Coalescence with Plastic Deformation
B. Coalescence with Elastic Collisions A. Coalescence without Surface Contact 1 1 . E-6
1 . E-5
1 . E-4
1 . E-3
1 . E-2
St dei == (O.5mU 02)/(03 yd )
1 . E-1
1 . E+0
Fig. 54. Stv vs. Sfdef showing regions of rebound and coalescence for surface wet de formable granules [53].
955
Granulation Rate Processes
1 00 ,-------�--_. 10 __
't:!=L "
0:
8
�
0.1
E �
0.01
Ci)
0.001
11 ...:
--
Rebound
h = o" h = ho
. . . . 8"/0 =
0.1
C: Coalescence with Permanent System: 0.01 10 10
Y dlE* = h olha
0.0001
Dlh o
0.00001 L...1 .E-5
=
=
__-'-----L__ '---__--"---__ __ __-'--'____-----'
__
1 .E-4
1 .E-3
1 . E-2
1 .E-1
Fig. 55. Coalescence criteria for collision of surface-dry granules [53].
coalesce without their surfaces even touching (Type I coalescence above). This implies that the binder is extremely viscous and/or that the collision velocity is very low. The Type 1 1 coalescence defined above can be further sub-divided into two regions. Region B, is the region in which coalescence occurs without any permanent plastic deformation. In this region Sfdef is low and the collisions are all fully elastic (e = 1 ). The boundary between coalescence and rebound depends only on the critical Stokes number, Sfv1s= (1 + 1 /e)ln(ho/ha ) as per the original model of Ennis ef al. [42]. As Sfdef increases, we enter Region C to the right of the line e = 1 . In this region permanent plastic deformation occurs and the range of Slvis for coalescence becomes wider with increasing amounts of deformation (higher values of Sfdef). This is because permanent granule deformation occurs which aids coalescence in two ways: (i) it dissipates some of the impact energy, and (ii) it creates a flat surface between the two granules, which creates a greater viscous dissipation force during rebound. In Region D, the granules rebound without coalescing. A series of arrows shows the effect of increasing impact velocity. At low Sfdef, increasing U causes a shift from Region B to Region D i.e. the probability of coalescence decreases because of the greater kinetic energies involved. However, unlike the model of Ennis ef al. [42], this model predicts that when plastic deformation becomes significant, increasing impact velocity may shift the formulation into Region C, a coalescence region. This is because of the large viscous forces required to separate two flattened areas.
956
K.P. Hapgood et al.
Figure 55 shows the predictions of the model for the case where the granules are initially surface dry. Two cases were considered. Either the liquid layer formed was assumed to be of a constant thickness ho regardless 0 f how much deformation occurred, or else it was assumed the liquid layer had the same thickness as the amount of permanent plastic deformation (5" (probably the latter is more realistic). In the low Stdef region, no permanent plastic deformation occurs and hence no liquid binder is squeezed to the surface to prevent granule rebound . Above a critical value of Stdef, the probability of coalescence becomes a function of Stvis and Stdef in a similar way to the surface-wet case.
3.4.3. Limitations of both coalescence models
Both these models predict the maximum size of granules which can coalesce for a given impact speed. They say nothing about the rate of granule growth - this will be a function of the frequency of collisions between granules. In any granulator, there is no one single granule collision velocity. Rather there is a range of collision velocities and hence a range of Stv. Hence, as the average Stv increases, there is not a sudden transition from growth to non-growth. Rather the proportion of collisions which satisfy the criteria of Stv < St: will decrease and hence the observed growth rate will also decrease. The model of Liu et al. [53] is an improvement on the model of Ennis et al. [42] because of the inclusion of granule deformation. However, both models still suffer many Iimitations. Capillary forces have been neglected. Hence the models only applies to systems where viscous forces dominant over capillary forces Le. sys tems in which Ca � 1 . Ennis et al. [42] argued that surface tension forces add energy during approach and absorb energy during separation and so these ef fects roughly cancel out. However, this does not agree with experimental obser vations that surface tension is indeed an important variable in low-viscosity systems. Two possible reasons for this discrepancy are that ( 1 ) liquid bridges may rupture at a greater length than they were formed at, and (2) because some of the energy added during approach is dissipated by elastic and plastic losses in the solid phase. Neither model accounts for additional bond strength due to particle interlocking at the interface between the two granules. The Liu et al. model attempts to con sider the collision of surface-dry granules, but has not proper basis on which to assume how much binder is present in the bond zone during rebound. The complex strain-rate dependent mechanical properties of wet granular ma terial are not adequately described in either model. Neither model considers the possibility of granule breakage during collisions (Section 4). And finally, neither model considers the possible effect of subsequent collisions, a limitation of Class I models.
Granulation Rate Processes
957
3.5. Bond formation between granules
One important aspect of granule coalescence that has received scant attention in the literature is the strength of the bond formed between the deformed surfaces of two granules when they collide. Clearly if this bond is weak, then the granules will easily be separated by a subsequent collision, and permanent coalescence will not occur. However, if the two surfaces are strongly bound, then coalescence is more likely. 3.5.1. Theory
The models of Ennis et al. [42] and Liu et al. [53] assume that this bond strength is the same as that of a viscous liquid bridge. The model of Ouchiyama and Tanaka [57] assumes that the bond had the same tensile strength as the bulk gran ules. Models of coalescence between particles and fibres in the field of filtration often assume there is a contact energy or van de Waal force that needs to be overcome. The factors controlling the strength of the bond formed between two granules during collision should be no different to those which control the strength of the bulk granules (see Section 4). However, the particle packing and liquid distribu tion in the contact zone may differ significantly fram that in the bulk of the gran ules. We expect that the bond zone will have a higher porosity and a lower liquid content than the bulk, and hence will be weaker. The bond zone will only develop significant strength if there is a re-distribution of liquid and re-arrangement of particles. As deformation occurs, the bond plane will be stretched and disrupted, and binder-rich material from the granule bulk will flow into the contact zone. Using an analogy with the cold-welding process, Iveson and Page [54] derived a semi-empirical model for the predicted bond strength. 3.5.2. Experiment
Cylindrical pellets were made from 37 flm glass ballotini with water and silicone oils as the binders. The pellets were then mounted vertically facing one another in a load frame and braught into contact at a rate of 0.05 mm/s for a period of 1 00-200 s. The two pellets were then left in contact for 1 00 s before the lower one was pulled away at a displacement rate of 0.05 mm/s (the tension stage). Figure 56 shows the typical load and displacement curves fram pushing to gether two water-bound pellets and then pulling them apart after a rest of 1 00 s. The compressive (negative) load initially increases more-or-Iess linearly with displacement, reaches a peak, and then levels off to a lower magnitude stable value. When the displacement is stopped, the load relaxes quickly to a lower
958
K.P. Hapgood et al.
stable value. Upon reversal of the strain, the load drops back to zero and then goes into tension for a short while until the bond eventually ruptures and the load returns to zero. For the water-bound pellets there was little elastic recovery of the bond. The granules tend to deform by localized "barrelling" along planes of slip (visible in Fig. 57). 0.2
B-
0
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0
....J
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-8
-4 -6 Displacement ( mm )
..
-2
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Fig_ 57. Photo of two pellets compressed together before tension is applied to the bond [54] .
959
Granulation Rate Processes
0.3 .------------------. . .' . 70% Pore
-S 0.2
Saturation . 73% Pore Saturation
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Radial Strain (") Fig. 58. Bond rupture energy vs. loeal radial strain for water-bound 1 9 11m glass ballotini pellets of 40% porosity eompressed at 0.05 mmjs [54].
Figure 58 is a plot of the bond rupture energy calculated from the area under the tensile portion of the load-displacement curve vs. the local radial strain measured at the bond contact plane. The bond rupture energy is linearly pro portional to the radial strain at the bond. The more saturated pellets had slightly higher bond rupture energies. This is consistent with the general finding that granule tensile strength is proportional to liquid saturation for systems with rel atively coarse particles (e.g. Rumpf [55]). Figure 59 shows the typical load versus displacement curves for experiments using water and each of the three different viscosity silicone oils. The water bound pellets had a compressive strength approximately three times higher than that of the silicone-oil-bound pellets. This can be attributed to the fact that the surface tension of water is approximately 3 times higher than that of the silicone oils. For the three silicone oils, the rate of increase of load with displacement declines with increasing oil viscosity. Only the 1 0 mPa s oil reached a peak load, with the other two still increasing in load at the end of the compression stage. During unloading and tension, Fig. 59 shows that the bond between the water bound pellets was brittle and failed at low tensile strains. In contrast, the bonds between silicone oi! bound pellets were ductile, with the extent of strain recovery increasing with oil viscosity. The surfaces were also observed to slowly "peei" apart, rather than by simultaneous failure across the whole rupture surface. For the 60 Pa s oil, the pellets barrelied over their whole length under compression and then returned back to over 60% of their original length before failure oc curred. This transition from brittle to ductile behaviour is similar to what was observed in the measurements of dynamic granule strength reported above
K.P. Hapgood et al.
960
0.5
60,000 mPas
0 -0.5 -1
�
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-2 -2.5
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-3 -3.5
-6
-5
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0.7 60,000 mPas + 1 000 mPas D 1 0 mPas )!( Water /::,. SE
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;: 0.5 �
(i) c w
/::,. /'
./
/::,.
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./
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./
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./
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/::,.
./
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)!( - - - - - - -- -- - --- - - - - -
0.06 0.04 Radial Strain at Contact ( )
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-
Fig. 60. Contact rupture energy vs. radial strain for water at 70% saturation and the three silicone oils at 80% pore saturation.
(Section 3.2). The large influence of binder viscosity is surprising given the rel atively low strain rates used, and serves to i1lustrate just how complex the whole phenomena of granule deformation iso Because of the greater strain recovery of the silicone oil-bound pellets, the bond rupture energy calculated from the area under the tensile part of the load-displacement curve was much higher, even though the peak tensile stress was approximately the same in both cases (Fig. 60).
96 1
Granulation Rate Processes
_ - 8. �
>Cl Cl c LU
0.1
"5
Cl. c
ß
�.
.A.
0.01
>-
[?
Cl c LU "0 c 0 (J)
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0.001
0.0001 0
0.1 0.05 Radial Strain ( )
0.1 5
-
Fig. 61 . Ratio of bond rupture to bond formation energy for pellets made from the four different binders as a function of radial strain i n the bond zone.
This difference is highlighted in Fig. 6 1 , which shows the ratio of the com pressive work done to form the bond versus the energy required to rupture it, as a function of radial strain in the bond region. Compared on this basis, the 60 Pa s silicone oil produced bonds that were approximately two orders of magnitude "stronger" than the bonds between granules bound with water. To a first ap proximation, the ratio of bond rupture to formation energy was approximately independent of the amount of strain (Fig. 61 ). Hence knowing how this ratio varies with granule properties and strain rate may prove useful in modelling granule coalescence. The experimental work discussed was preliminary and limited in extent. Nev ertheless, it is clear that the bonding process between collided granules is a complex phenomena. Much more experimental and theoretical work is needed, particularly to include dynamic viscous effects, which through their influence on the bulk deformation behaviour have a large influence on how much energy is actually needed to rupture a bond.
3.6. Summary comments on granule growth and consolidation
The key formulation properties and process parameters that impact on granule growth and consolidation are identified and captured in a series of important dimensionless groups smax, Sfdef, Stv and Ca. A regime map is presented which defines the different growth regimes and is a useful tool for scale up, design and trouble shooting.
962
K.P. Hapgood et al.
There are now several physical based models for coalescence and consoli dation, which can be used in quantitative frameworks such as population bal ances to track the generation of granule attribute distributions. None of these models are completely predictive, nor does any model completely capture the very complex physics involved. Nevertheless, they are powerful tools when used cautiously with some experimental validation. Further improvement to the validity and application of the models is reliant on ( 1 ) more complete information o n velocity and stress distributions i n granulators; and (2) more comprehensive constitutive models for granule mechanical properties. 4. WET GRANU LE BREAKAGE
This section considers the last of the three classes of granulation processes that control granule attributes - breakage and attrition. There are really two separate phenomena to consider: 1 . Breakage of wel granules in the granulator; and 2. Attrition or fracture of dried granules in the granulator, drier or in subsequent handling.
Breakage of wet granules will influence and may control the final granule size distribution, especially in high-shear granulators. In some circumstances, break age can be used to limit the maximum granule size or to help distribute a viscous binder. Wet granule breakage in granulators is less weil understood than either nucleation or growth. It remains an active research area. In this section we will review some of the current research and attempt to define key formulation and granule properties for developing the controlling groups or equations for the breakage processes. Attrition of dry granules leads to the generation of dusty fines. This phenomena is important in fluid bed granulation (where granulation and drying occur simul taneously) and in downstream handling of dried granules from any granulation process. A study of dry granule attrition is beyond the scope of this chapter. For more information see chapter Single granule in this handbook, Litster and Ennis [2] and Bika el al. [68]. 4. 1 . Experimental observations
Few investigators have described or studied wet granule breakage in granulation processes. Some preferential growth mechanisms in tumbling granulation may involve attrition or breakage of weak granules (crushing and layering, abrasion transfer) [69]. However, breakage is much more likely in higher intensity mixer
963
Granulation Rate Processes
and hybrid granulators. The limited work on wet granule breakage focuses on these processes. Several studies show an increase in agitation intensity (increased impeller speed) reduces the final granule mean size in granulation experiments [56,70,71]. For example, Fig. 62 shows median granule size from three scales of agitated fluid bed granulator decreases with increasing agitator tip speed [9]. However, reduction in product size with increased agitation could also be ex plained by a reduction in the maximum granule size for coalescence. So changes to granule size distribution, on theirown, are insufficient evidence for wet granule breakage as a key mechanism for controlling granule properties. However, wet granule breakage has been identified clearly in high-shear mixer experiments by other means. Ramaker and co-workers [22], Vonk et al. [41 ] and Pearson e t al. [72] both used coloured tracer granules or liquid to identify breakage of wet granules. Pearson et al. added narrow size fractions of weil formed tracer granules part way through a batch high-shear granulation. Some of the tracer granules were broken, leaving coloured tracer fragments in smaller granule size fractions. Large tracer granules ( > 1 mm) were more likely to be broken than smaller granules (Fig. 63). Knight et al. [70] showed that mean granule size decreased after impeller speed was suddenly increased part way through a batch high-shear mixer experiment. This was attributed to granule breakage. Vonk and co-workers added a coloured liquid at the start of the granulation process and observed the dispersion of the dye through a process of "destructive 800
...... o 10
o
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•
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O 5 D / D = 1 / x .2 50 O 1 00 1
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964
K.P. Hapgood et al. 1.0
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>196 J4I11 >550 J4I11 > 1 090 J4I11 ----I 1 800 1600
_ _ _
TIme (sec)
Fig. 63. Breakage of tracer granules in high-shear mixers: Effect of tracer granule size on mass fraction of unbroken granules [72].
nucleation" where loosely bonded nuclei are broken down into smaller fragments via attrition or fragmentation (Fig. 64). The initial weak nuclei were quite large in these experiments (5 mm diameter). We can view this destructive nucleation process as simply a subset of all the breakage processes occurring in the gran ulator. In fact, all binder distribution in the "mechanical dispersion" (Section 2) is essentially a breakage process and should be treated as such. In summary, wet granule breakage is potentially an important process affecting binder distribution and granule size in high intensity processes. Therefore it is important to establish the conditions under which breakage will occur.
4.2. Predicting conditions for breakage
There is very little quantitative theory or modelling available to predict conditions for breakage, or the effect of formulation properties on wet granule breakage. Tardos ef al. [9] considered that a granule will break if the applied kinetic energy during an impact exceeds the energy required for breakage. This analysis leads to a Stokes deformation number criteria for breakage: (39) wh ere Sfdef is the Stokes deformation number as defined by equation (23) and Sfdef the critical value of Stokes number that must be exceeded for breakage to occur. There are strong analogies to the development of the Stokes deformation
965
Granulation Rate Processes
0° % °0 0 0 0 ... .... 0 o 0 o 0 0 00 0
Fig. 64. The destructive nucleation mechanism proposed by the Groningen group [41 ) .
number for granule deformation and growth (equation (23)). It is Iikely the critical value for breakage will be greater than that for coalescence as granules may deform plastically at the impact point without breakage of the granule. Note that the original work of Tardos et al. [9] proposed a more general char acteristic stress than the dynamic yield stress in equation (23) and considered breakage of granules by shear rather than impact. They postulate the granule will behave under shear as a Herschel-Buckley fluid, which is also what has been observed in measurements of granule dynamic yield stress (Iveson et al. [51], equation (24) and Fig. 40 above), i.e. (40) where r(Y) is the characteristic stress in the granule, ry the yield strength and y the average shear rate. Two simplifications were considered, neglecting either the apparent viscosity (r(y) = ry) or the yield stress (r(y) = kyn ) . In either case,
966
K.P. Hapgood et 8/. 1 00%
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•
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500/0 40% 30%
• •
•
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20% 1 0% 0% 0.0001
0.001
0. 0 1
0.1
10
Stdef Fig. 65. The relationship between the Stokes deformation number and the determined breakage numbers. The vertical line represents the experimentally determined boundary between breakage and no breakage [73].
the model predicts granules above a maximum size will break and this size is decreased with increasing shear rate. Tardos and co-workers measured granule deformation and break up under shear in a novel constant shear fluidized-bed granulator. Granules first elongated under shear and then broke at a Stokes deformation number of approximately 0.2. Van der Dries et al. [73] also used equation (39) as a criteria for breakage. However, they estimated the dynamic yield stress by assuming a Rumpf style expression for the granule strength and assumed the bond strength was due solely to viscous forces. In experiments using a laboratory high-shear mixer granulator, Stokes deformation number was varied by changing impeller speed and there was a sharp change in the number of unbroken granules at Stdef = 0.05 (see Fig. 65). Qualitatively, these results are consistent with those of Tardos et 81. [9]. Quantitatively, it is not possible to do a direct comparison because of the different methods of estimating granule strength and effective collision velocity. Kenningly et 81. [74] used a similar approach to predict a "crumb" region and a controlled growth region in mixer granulators. This general approach to predicting a breakage regime is a good starting point, but there remain a number of questions to be answered before a general break age regime map is available: 1 . It is not c1ear whether breakage of wet granules is predominately due to high velocity impacts or to shear within the powder bed. In fact, the mode of breakage may be a strong function of powder flow field and the design of impeller bl ades and choppers. 2. There is very Iimited experimental data to test the models at present. Stokes number is generally varied by changing the impeller speed or shear rate. There
Granulation Rate Processes
967
has been no systematic study of breakage of a wide range of formulations with very different mechanical properties. 3. The models equate granule breakage with plastic yield. A granule may deform plastically without breaking. A purely plastic granule will smear rather than break when its yield stress is exceeded. At high impeller speeds such ma terials may coat the granulator wall or form a paste. Semi-brittle granules will break at high impact velocity giving a maximum stable granule size or a weak crumb. Thus, considerable information about the granule mechanical proper ties is needed to predict their behaviour. Note this yield behaviour should be measured at strain rates similar to those during impact in the granulator, not in static mechanical tests. 4.3. Mechanical properties of semi-brittle wet agglomerates
The brittle nature of some wet agglomerates can be demonstrated using dynamic measurements of granule mechanical properties. In Section 3.5.2, uniaxial com pression test were performed to measure a peak flow stress or "yield" stress of granules as a function of strain rate. Iveson and Page [54] noted that in so me cases failure was by macroscopic crack formation and in others by plastic, almost paste like flow. However, uniaxial tests are not the best way to examine brittle behaviour. Smith [75] examined the failure behaviour of a wide range of formulations using diametrical compression tests using the same Instron dynamite testing machine as Iveson's earlier work. Three different modes of failure were observed: 1 . Brittle failure along a central crack (Fig. 66). In this case there is a clearly defined yield stress corresponding to crack formation and propagation at low strain (0.01-0.03). 2. Cone formation and diagonal cracking (Fig. 67). In this intermediate behaviour, a significant failure cone forms at the point of contact with cracking along the edge of the cone. There is still a clear peak stress but at much higher strains (0.07-0 . 1 0). 3. Squeeze flow (Fig. 68). The formulation behaves as a paste with completely plastic deformation. There is no macroscopic crack formation and no peak stress is observed. Smith's experiments were conducted at intermediate strain rates (0.005-1 0/s). Salman et al. [76] conducted ballistic studies at much higher velocities and strain rates (of order 1 5 ms 1 and 1 03/s). These experiments showed that there was a critical velocity above, which cracks propagated through the granules and fracture occurred. The critical velocity was a function of formulation properties and there was considerable plastic deformation before any cracking occurred.
968
K.P. HaPQood et 8/.
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3500 3000 2500 2000 1 500 1 000 500
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(b)
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0.2
0.3
0.4
0.6
0.5
0.7
0.8
0.9
Natural Strain ( ) -
Fig. 66. Diametrical compression tests - 45-90 11m lactose powder with 1 0 mPa.s silicone oil binder (a) briUle failure along a single crack (0.001 m/s, 1 0% strain), (b) stress strain relationships at different platen speeds.
This wide variety of behaviours reinforces the need for a more substantive inclusion of granule mechanical properties in breakage criteria. This remains an area of current research. 4.4. Concluding comments on wet granule breakage
Breakage is the least studied of the three classes of granule rate processes. Although, the fundamental basis for predicting breakage is incomplete, we
969
Granulation Rate Processes
(a) 6000 200 mm/s -1 00 mmps
5000
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- 1 mmps
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0.6
0.7
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Fig. 67. Diametrical compression tests - 45-63 flm glass ballotini powder with water binder (a) cone formation and diagonal cracking (0.001 m/s, 20% strain), (b) stress strain relationships at different platen speeds.
can still use our limited knowledge for scale up based on equation (39). For breakage, the appropriate velocity for the Stokes deformation number is the maximum collision velocity a granule can experience with another granule or with part of the granulator equipment. For mixer granulators, this is clearly the impeller tip speed. Equations (39) and (40) suggest breakage will increase with increasing tip speed. Figure 62 shows that the relationship between tip speed and granule mean size was the same for three different scales of agitated
970
K.P. Hapgood et al.
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0.3
0.4
0.5
0.6
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Fig. 68. Diametrical compression tests - 45-63 11m glass ballotini powder with 1 Pa.s silicone oi! binder (a) completely plastic deformation (0.2 m/s, 40% strain), (b) stress strain relationships at different platen speeds.
fluidised bed granulators, as we would expect if granule size were controlled by breakage processes. Controlling wet granule breakage gives the opportunity to give a narrow gran ule size distribution by growing granules up to a breakage limit [9,22,771. This has been the driving force in the development of some newer granulator designs [71 ,781. It is important to note that size distribution control will also depend on the impact velocity distribution and turnover of granules through the high impact
971
Granulation Rate Processes
region (impeiler or chopper). Granulators with broad impact velocity distributions and smalI, uncontrolled turnover through the high impact region are unlikely to ever yield narrow granule size distributions. 5. CONCLUDING COMMENTS : WHERE TO FROM H ERE IN THE FIELD OF GRANU LATION?
Analysis of granulation rate processes over the last decade has been very fruitful . We now know the key formulation properties and process parameters that control the rate processes of ( 1 ) nucleation and wetting, and (2) consolidation and growth. For both these rate processes, regime maps have been developed and validated based on the controlling dimensionless groups: Stv, Stdef, S, \f' and 'p. We are close to a similar understanding of wet granule breakage. This under standing is already reflected in the quality of research with the quantitative anal ysis in most recently published papers, a far cry from the qualitative descriptions of 1 0-1 5 years ago. This understanding is now at the point where it can be directly used in scaling granulation processes (e.g. keeping dimensionless spray flux constant to main tain nucleation conditions) and characterizing formulations for their granulation behaviour (e.g. measuring the dynamic yield stress of a new formulation) [3]. This quantitative understanding is already being built into population balance models to predict the generation of granule size distribution and density (see Chapter -Mode/ling in this handbook). Our improved knowledge also challenges us to improve our granulator designs, moving to regime separated granulators to simplify scale up and give better control of granule attributes. However, there are still important needs and opportunities for research and development in this field. We can characterise these in terms of the scale of observation (see Fig. 69): Particle to granule scale: We are yet to reach the point where we can quan titatively predict the behaviour of a granule by scaling up from measurements or models of particle-particle and particle-fluid interactions within the granule. Iveson's work on a non-dimensional correlation for granule strength, following the earlier work of Ennis and Tardos shows that we are making progress. DEM approaches provide great promise for predicting granule behaviour if the infor mation can be captured in terms of constitutive models at the granule level. This approach mimics that used for some time in thermodynamics where molecular modelling is used in lieu of experiments to predict bulk thermodynamic properties. Importantly we have a much improved suite of tools to provide particle level input to these simulations (AFM, nanoindentation and other micromechanical meas urements) and to help "scale up" to granule scale through detailed measurement of granule structure (X-ray microtomography). Subgranule scale modeling and a
972
K.P. Hapgood et 8/.
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Fig. 69. A summary of the status of wet granulation research using the scale of obser vation as a frame of reference.
characterization are discussed in detail in Chapter- Sub granule scale modelling in this handbook. Granule to granule bed scale: We have reasonable models for the granulation rate processes that incorporate granule properties. Our constitutive models for granule mechanics are still simplistic representation of a very complex three-phase system. There remains a need for improved characterization and models for granule mechanical behaviour. The current model - that of an elas tic-plastic material with strain rate dependent yield stress is a reasonable starting point only. Our quantitative understanding of granulation rate processes is now being used to create more predictive population balance models for a bed of granules to describe distributions of granule properties. The challenge is that one-dimen sional population balances looking only at the distribution of granule size n(x) or n(v) cannot effectively include the necessary information on granule porosity and liquid content needed to predict rate constants. Multidimensional population bal ances are needed which consider the distributions of volume of solid, liquid and gas in the granules ie. n(vs v" vg). Granule size, porosity and liquid saturation can all be calculated from this base distribution. For these multidimensional models, effective and efficient solution techniques remain an important research area. Multidimensional population balances are addressed in Chapter-Modelling of this handbook. ,
Granulation Rate Processes
973
Granule bed to vessel scale: The key issue here is the ability to model powder flow behaviour and mixing in the granulator and link this information effectively to our population balance models. Powder flow is not a solved problem, particularly in the "intermediate flow regime" experienced in many granulators. There are a number of possible approaches to quantifying powder flow in granulators: 1 . The use of macroscopic momentum balance equations with appropriate con stitutive equation to model the flow of powder as a continuum. This is anal ogous to traditional CFD models for fluid flow. 2. Application of DEM where each granule is tracked and its interactions with all other granules in the granulator simulated. 3. Use of flow characterization measurements such as PEPT to provide empirical models or correlations for velocity distributions and mixing. One approach is to characterize powder flow and use this information in com partmentalised models of a granulator. A population balance is written for each compartment and the transfer rates of material between compartments are mode led with the help of data from powder flow measurements. While this approach is still quite crude, it is more sophisticated than a single whole granulator model. Vessel to granulation circuit scale: Granulation plants include dryers, screens, crushers and solids handling that also impact on the quality of the product gran ules. Dynamic simulations of whole granulation circuits exist and are especially valuable where there is significant recycie of off spec granules. The current challenge is to incorporate more predictive models, especially of the granulator, into these simulations. As our models becomes more physically realistic, the way is opened for more sophisticated use of the models for plant optimization and in different types of model based control schemes. This is a natural transition al ready seen for fluid processing plants for which good predictive models of the unit operations have been available for several decades. Finally, integration of models across different length scale is a key to granulation design and modeling. However, such integration may lead to enor mous and unwieldy models and simulations. We need to develop effective and efficient modeling frameworks for this integration. This is a current area of re search in the modelling community and we need to take advantage of current developments in this area, not just in granulation, but more broadly in all par ticulate processes. Nomenclature EI
Ä
area flux of drops hitting powder surface (m2/s) area flux of powder through the spray zone (m2/s)
974
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Ca db dd d32 dp d32
dg , D Ddru m E*
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h, hb ha Ka Ke Ib
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u
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K.P. Hapgood et al.
initial area of the sampie (m2) the deformed contact area after impact (m2) Capillary number (-) bubble size (m) liquid drop size (m) specific surface mean particle size (m) particle diameter (m) Sauter mean size of particles (m) granule size (m) Drum granulator diameter (m) Young's modulus (Pa) coefficient of restitution (-) fraction of overlapping drops on powder surface (-) fraction of powder surface covered by drops (-) fraction of single drops on powder surface (-) gravitational acceleration (m/s2) liquid layer thickness (m) height of surface asperities (m) nucleation area ratio (m) compaction rate (-) spacing between two bubbles (m) particle mass (kg) number of drops hitting the powder surface per unit time (no./s ) flow rate of liquid into powder bed (m 3/s) Drop circular radius (m) particle radius (m) effective pore radius (m) pore radius (m) liquid saturation of pores (-) critical Stokes deformation number (-) critical Stokes deformation number (-) viscous Stokes number critical Stokes number time (s) powder circulation time (s) drop penetration time (s) velocity (m/s) collision velocity (mjs) bubble velocity (mjs) liquid flow rate (m3/s) drop volume (m 3) liquid penetration velocity (m/s) volumetrie spray rate (m 3/s) drop volume (m3) flat spray width (m)
Granulation Rate Processes
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975
granule dynamic yield stress ((Njm2 ) minimum granule porosity (-) bed voidage ( - ) granule porosity ( - ) surface tension (N m) granule deformation (m) granule density (kgjm 3) liquid density (kgjm 3) particie density (kgjm 3) liquid-vapour interfacial energy (Njm) effective powder bed voidage ( - ) tapped powder bed voidage ( - ) contact angle ( ) dimensionless spray flux ( - ) sphericity ( - ) dimensionless penetration time ( - ) viscosity (Pa s) impeller and chopper speed 0
REFERENCES [1] S.M. Iveson, JA Beathe, N.W. Page, Powder Techno!. 1 27 (2002) 1 49-1 6 1 . [2] J . D. Litster, B.J. Ennis, The Science and Engineering of Granulation Processes, Kluwer Academic Publishers, Dordrecht, 2004. [3] Y. He, L.X. Liu, J . D . Litster, Scale-Up Considerations in Granulation, in: D . M . Parikh, (Ed.), Handbook of Pharmaceutical Granulation Technology(2nd edition), Taylor & Francis, Boca Raton, 2005, pp. 459-489, Chapter 1 6 . [4] S.J . R Simons, R J . Fairbrother, Powder Techno!. 1 1 0 ( 1 -2) (2000) 44-58. [5] AC. Scott, M.J. Hounslow, T. Instone, Powder Techno!. 1 1 3 ( 1 -2) (2000) 205-2 1 3. [6] !. Krycer, D.G. Pope, Powder Techno! . 34 (1 983) 39-51 . [7] B.J. Ennis, J.D. Litster, Granulation and coating technologies for high value added industries, Client in-house short course, E&G Associates: Section 3(1 996). [8] RC. Rowe, Int. J. Pharm . 52 ( 1 989) 1 49-1 54. [9] G.!. Tardos, M . Irfan-Khan, P . R Mort, Powder Techno!. 94 (1 997) 245-258. [ 1 0] K.P. Hapgood, J . D. Litster, S.R Biggs, T. Howes, J. Colioid Int. Sci . 253 (2002) 353-366. [1 1 ] S. M iddleman, Modeliing Axisymmetric Flow: Dynamics of Films, Jets and Drops, Academic Press, San Diego, 1 995. [ 1 2] M . Denesul, G.L. Smith , B.J.J. Zelinski, N.J. Kreidl, D.R Uhlmann, Colioid Int. Sci . 1 58 ( 1 ) (1 993) 1 1 4-1 20. [ 1 3] D.J. Golchert, J.D. Litster, L.x. Liu, The use of X-ray micro-tomography to charac terize agglomerate structure, World Congress on Particle Technology 4, July 2 1 -25, 2002, Sydney. [ 1 4] L. Farber, G. Tardos, J . N . Michaels, Powder Techno!. 1 32 (2003) 57-63. [1 5] R Kohlus, Quantitative descriptors for granule structure characteristion, World Con gress of Particle Technology 4, IChemE , Sydney, Australia, 2002. [ 1 6] A Clarke, T.D. Blake, K. Carruthers, A. Woodward, Langmuir 1 8 (2002) 2980-2984. [ 1 7] J.D. Litster, K.P. Hapgood, J.N. Michaels, A Sims, M . Roberts, S.K. Kameneni, Powder Techno!. 1 1 4 (2001 ) 32-39.
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[ 1 8] w.J. Wildeboer, J.D. Litster, I .T. Cameron, Chem. Eng. Sci. 60 (2005) 3751-376 1 . [ 1 9] K.P. Hapgood, J.D. Litster, E.T. White, P.R. Mort, D.G. Jones, Powder Technol. 1 4 1 (1-2) (2004) 20-30. [20] PAL. Wauters, R.B. Jakobsen, J . D. Litster, G.M.H. Meesters, B. Scarlett, Powder Technol. 1 23 (2002) 1 66-1 77. [21 ] J.D. Litster, K.P. Hapgood, J.N. Michaels, A. Sims, M. Roberts, S.K. Kameneni, Powder Technol. 1 24 (2002) 272-280. [22] J.S. Ramaker, MA Jelgersma, P. Vonk, N.w.F. Kossen, Int. J. Pharm. 1 66 ( 1 ) ( 1 998) 89-97. [23] R. Plank, B. Diehl, H. Grinstead, J. Zega, . Powder Technol . 1 34 (3) (2003) 223-234. [24] Y. Mugumara, T. Tanaka, Y. Tsuji, Powder Technol. 1 09 (2000) 49-57. [25] J . D . Litster, K.P. Hapgood, S.K. Kamineni, T. Hsu, A. Sims, M. Roberts, J. Michaels, Scale-up of mixer granulators for effective liquid distribution, Proceedings AIChE Annual Meeting, Oct 3 1 -Nov. 5, 1 999, Dallas, TX, USA. [26] K.P. Hapgood, J.D. Litster, R. Smith, AIChE J 49 (2) (2003) 350-361 . [27] C.E. Capes, Particle Size Enlargement, Elsevier, Amsterdam; New York, 1 980. [28] M.E. Aulton, M. Banks, Fluidised bed granulation - factors influencing the quality of the product, Int. J . Pharm. Technol. and Prod. Manuf. 2 (4) ( 1 981 ) 24-29. [29] B. Rambali, L. Baert, L. Massart, I nt. J. Pharm. 252 ( 1 -2) (2003) 1 97-206. [30] K.P. Hapgood, R. Plank, S. Jain, J. Zega, World Congress Particle Technology 4, Sydney, Australia, 2002. [31 ] K.P. Hapgood, Nucleation and Binder Dispersion in Wet Granulation, PhD Thesis, The University of Queensland, 2000. [32] K.P. Hapgood, Case study: liquid distribution on scale-up, AAPS Summer Confer ence, Advances in Wet Granualtion Technologies, Lansdowne, VA, June 2003. [33] L. Farber, K.P. Hapgood, J.N. Michaels, World Congress Particle Technology Vol. 5, Orlando, FL, USA, 2006. [34] S.M. Iveson , S.Holt, S. Rapmond, C.E. Loo, S.R. Biggs, AIChE Annual Meeting, AIChE, 1 998. [35] R. Plank, J. Zega, L. Wei , Granule content as a function of size studied for wet granulation of a 3-component system. Paper presented at the AIChE Annual Meeting, Reno, NV, 2001 . [36] M . Butensky, D. Hyman, Ind. Eng. Chem. 1 0 (2) ( 1 97 1 ) 2 1 2-21 9. [37] S.H. Schaafsma, P. Vonk, N.w.F. Kossen , Int. J. Pharm. 1 93 (2) (2000) 1 75-1 87. [38] P.J. Sherrington, Chemical Eng. JulyjAugust ( 1 968) CE201 -CE2 1 5 . [39] B. Waldie, Chem. Eng. Sci. 4 6 ( 1 1 ) ( 1 99 1 ) 2781-2785. [40] S.H. Schaafsma, N.w.F. Kossen, M .T. Mos, L. Blauw, A.C. Hoffman , AIChE J 45 ( 1 998) 1 202-1 21 0. [41 ] P. Vonk, C.P.F. Guillaume, J.S. Ramaker, H . Vromans, N .W.F. Kossen, Int. J . Pharm. 1 57 (1 997) 93-1 02. [42] B.J. Ennis, G. Tardos, R. Pfeffer, Powder Technol. 65 ( 1 99 1 ) 257-272. [43] P.C. Kapur, D .w. Fuerstenau, I&EC Proc. Des. Dev. 8 ( 1 968) 56. [44] P.G. Smith, A.w. Nienow, Chem. Eng. Sci. 38 (8) ( 1 983) 1 223-1 231 . [45] C.C. Hung, H.O. Kono, Powder Technol. 55 ( 1 ) ( 1 988) 1 9-34. [46] F. Hoornaert, P.A.L. Wauters, G.M.H. Meesters, S.E. Pratsinis, B. Scarlett, Powder Technol. 96 (2) (1 998) 1 1 6-1 28. [47] C.E. Capes, P.V. Danckwerts, Trans. I. Chem. Eng. 43 (1 965) 1 1 6. [48] D.M. Newitt, J.M. Conway-Jones, Trans. I . Chem. Eng. 36 ( 1 958) 422. [49] S.M. Iveson, J . D. Litster, AIChE J 44 (1 998) 1 5 1 0-1 5 1 8. [50] S.M. Iveson, PAL. Wauters, S. Forrest, J.D. Litster, G.M.H. Meesters, B. Scarlett, Powder Technol. 1 1 7 (2001 ) 83-97. [51 ] S.M. Iveson, JA Beathe, N.W. Page, Powder Technol. 1 27 (2) (2002) 1 49-1 6 1 . [52] S.M. Iveson, N.W. Page, J . Appl . Mech. 7 1 (2004) 470-475. [53] L.X. Liu, S.M. Iveson , J.D. Litster, B.J. Ennis, AIChE J 46 (2000) 529-539.
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[54] S.M. Iveson, N.W Page, Powder Techno!. 1 1 7 (200 1 ) 1 1 3-1 22. [55] H. Rumpf, The Strength of Granules, and Agglomerates, in: WA. Knepper, ( Ed.), Agglomeration, Interscience, New York, 1 962, p. 379. [56] P. Holm, O. Jungersen, T. Schalfer, H . G . Kristensen , Pharm. Ind. 45 (8) ( 1 983) 806-81 1 . [57] N . Ouchiyama, T. Tanaka, I&EC process Des. Dev. 1 4 ( 1 975) 86. [58] K.V.S. Sastry, S.C. Panigraphy, DW. Fuerstenau , Trans. Soc. Mining Eng. 262 ( 1 977) 325. [59] S.M. Iveson , JD. Litster, B.J. Ennis, Powder Techno!. 88 ( 1 996) 1 5-20. [60] S.M. Iveson , JD. Litster, Powder Techno!. 99 ( 1 998) 243-250. [6 1 ] J.L. Moseley, T.J. O'Brien, Chem. Eng. Sei. 48 ( 1 993) 3043-3050. [62] M .J . Adams, C. Thornton, G. Lian, 1 st Int. Part. Tech. Forum, Vol 1 , Denver, Aug. 1 7-19, 1 994 pp. 220-224. [63] J.P.K. Seville, H . Silomon-Pflug, P.C. Knight, Powder Techno!. 97 ( 1 998) 1 60-1 69. [64] C . Thornton, Z. Ning, Powder Techno! . 99 ( 1 998) 1 54-1 62. [65] M .J. Hounslow, H.S. Mumtaz, A. P. Collier, J.P. Barrick, A.S. Bramley, Chem. Eng. Sei . 56 (7) (200 1 ) 2543-2552. [66] S . M . Iveson, Chem. Eng. Sei. 56 (2001 ) 221 5-2220. [67] T. Schalfer, C. Mathiesen, Int. J. Phamaceut. 1 39 ( 1 996) 1 39-148. [68] D.G. Bika, M. Gentzier, J.N. Michaels, Powder Techno!. 1 1 7 ( 1 -2) (200 1 ) 98-1 1 2 . [69] K.v.S. Sastry, D . W Feurstenau , Int. J . M iner. Process 2 (1 975) 1 87. [70] P.C. Knight, A. Johansen, H . G . Kristensen, T. Schaefer, J.P.K. Seville, Powder Techno!. 1 1 0 (2000) 204-209. [7 1 ] S. Watano, Y. Sato, K. Miyanami, T. Murakami, Chem. Pharm. Bull. 43 (7) ( 1 995) 1 2 1 2-1216. [72] J . M . K. Pearson , M .J . Hounslow, T. Instone, P.C. Knight, Proc. 3rd World Congress on Particle Technology, Vo!. 3, 1 998, paper 86. [73] K. Van den Dries, O.M. de Vegt, V. Girard, H. Vromans, Powder Techno!. 1 33 ( 1 -3) (2003) 228-236. [74] S.T. Keningley, P.C. Knight, A.D. Marson, Powder Techno!. 91 (1 997) 95-1 03. [75] R.M. Smith, Wet granule breakage in high shear mixers, PhD thesis, The University of Queensland, 2006. [76] AD. Salman, J. Fu, DA Gorham, M .J . Hounslow, Powder Techno!. 1 30 (2003) 359-366. [77] P.R. Mort, G . ! . Tardos, Kona 1 7 ( 1 999) 64. [78] B. Denes, Z. Ormos, H u ngarian J. Ind. Chem. 21 (3) ( 1 993) 225-23 1 .
CHAPTER 21 Breakage in G ra n u l at i o n Ag ba D . Salman * , Gavin K . Reynolds, Hong S i ng Tan , l a n Gabbott, and M ichael J. Hou nslow
Depattment of Chemical & Process Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK Contents
1 . I ntroduction 2. Breakage at the process scale 2. 1 . Observations of the breakage process 2.2. Measurement of the breakage process 2.3. Role of variables on breakage behaviour 2.3. 1 . Binder viscosity 2.3.2. Binder surface tension 2.3.3. Contact angle between binder and primary particle 2.3.4. Primary particle size and shape 2.3.5. Equipment-related variables 2.3.6. Binder content 2.3.7. Binder addition method 2.3.8. Agitation intensity 2.3.9. Granulation time 3. Breakage at the granule scale 3. 1 . Bonding forces in granules 3 . 1 . 1 . Rumpf's theory 3 . 1 .2. Kendall's theory 3.2. Measuring granule strength 3.2. 1 . Tensile strength 3.2.2. Dynamic-yield strength 3.2.3. Shear strength 3.2.4. Bending strength 3.2.5. Hardness 3.2.6. Summary 3.3. Dynamic strength of granules 3.3. 1 . M ulti-particle impact tests 3.3.2. Single-particle impact tests 3.3.3. Breakage patterns 3.3.4. Extent of breakage 3.4. Variables affecting granule strength 3.4. 1 . Binder viscosity * Corresponding author. E-mail: [email protected]
Granulation Edited by A.D. Salman, M.J. Hounslow and J. P. K. Seville f: 2007 Elsevier B.v. All riQhts reserved
980 982 982 984 987 988 989 990 990 990 991 991 992 993 994 994 997 999 1 000 1 000 1 002 1 003 1 004 1 005 1 006 1 006 1 007 1 008 1010 1013 1016 1016
980 3.4.2. Binder surface tension 3.4.3. Contact angle between binder and primary particle 3.4.4. Primary particle size and shape 3.4.5. Porosity and structure 3.4.6. Binder content 4. Modelling of Breakage 4. 1 . Predict the conditions for breakage 4.2. Process scale: population balance modelling 4.3. Micro scale: discrete modelling 4.4. M icro scale: continuum modelling 5. Conclusions References
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1017 1017 1019 1019 1 020 1 021 1 021 1 024 1 030 1 034 1 035 1 036
1 . I NTRODUCTION
The process of granulation is used in a wide range of industries, including mineral processing, agricultural products, detergents, pharmaceuticals, foodstuffs and speciality chemicals. Typically, fine powders are agglomerated together to form larger particles, or granules. In wet granulation, for example, liquid is used to stick the constituent particles together. Granules generally have a variety of advan tages over fine powders in that they flow weil, pose lower environmental hazards, and dissolve or disperse better. The process of granulation still remains relatively poorly understood. However, it is generally accepted that granulation is a combination of three rate processes, namely wetting and nucleation, consolidation and growth, and attrition and breakage [1]. In addition to the obvious growth retardation, attrition and breakage help to improve granule homogeneity [2] and granule strength by promoting consolidation. The importance of the study of granule breakage is in two principal areas. First, understanding breakage as a rate process and part of the granu lation process allows improved process design and specification. More specif ically, due to the importance of breakage in homogenising a batch of granules, improved knowledge of this process can lead to more controlled product quality. Second, study of the breakage of granules as products of the process can inform the behaviour of granules under further processing, handling and transporting conditions. In addition, deformation and breakage of granules can be used as a product quality tool to assess the granule properties. For example, it has been shown by Fu et al. [3] that the coefficient of restitution is very sensitive to var iability in granule composition and structure. This chapter discusses breakage in granulation from a number of different length scale perspectives. At the process scale, breakage is important in en hancing the material distribution and eventual strength of the product granules. Knowledge of how operating parameters and equipment design influence the breakage process can help to improve the properties of the granular products.
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Knowledge of the true rates of breakage can improve modelling and prediction of granulation behaviour. At the single-granule scale, extensive studies have been made to characterise granule strength and behaviour under static and dynamic conditions. Understanding how different variables affect the strength of granular materials again will assist in improving the properties of granular products. Also, knowledge of breakage behaviour at the single-particle scale can inform our understanding of breakage at the process scale. Sub-granule scale experimental studies can provide an understanding of how different variables and components contribute to the apparent granule strength, giving a physical basis for how to improve granule properties. In reviewing the modelling of granule breakage, a similar scale approach is adopted. Population balances are a powerful tool for modelling the influence of various rate processes on the properties of large groups of granules. Micro-mechanical modelling of granules allows further insight into the breakage behaviour of granules. Granulation in itself is a broad topic. In this case a granule, or an agglomerate, refers to a body that consists of constituent particles held together. Here, we define three-generic types of granule that will be discussed. First, a binderless granule is as described, whereby the constituent particles are held together by micro-scale forces, typically van der Waals forces. Second, a solid granule refers to a granule where the constituent particles are held together by solid bonds. Third, a wet granule is described as a granule which contains interstitial liquid. Although these three generic cases could all be described as granules, it is expected that they will exhibit different breakage behaviour due to the different nature of the constituent particle bonding forces. Figure 1 illustrates the typical fragmentation of the three types of granule under moderate impact conditions. In addition to different granule classifications, there are a wide range of prac tical processes to create granules, and a wide range of techniques to charac terise the breakage of granules. It is not the aim of this chapter to be completely exhaustive in reporting all of these. At the process scale, studies using high-shear mixer granulators and fluidised-bed granulators are reviewed. This is due to the
(a)
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(b)
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Fig. 1 . Example of the typical impact fracture of the three generic types of granules under moderate impact conditions. These granules are between 4 and 5 mm i n diameter.
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increased perceived importance of the breakage process in these granulators and the focus of the literature on investigating breakage in this type of equipment, rather than any attempt at excluding other processes.
2. BREAKAGE AT THE PROCESS SCALE
Some of the early studies of attrition and breakage in the granulation process were carried out by Capes and Danckwerts [4] and Sastry et al. [5]. They pro posed that the mechanisms by which granules grow in tumbling drum granulators involved crushing and layering. This mechanism is now generaily considered as attrition and breakage [6], and describes the breakage of wet or dried granules due to impact, wear or compaction in the granulator or during subsequent product handling. In reviewing the experimental studies of breakage during granulation proc esses, two broad groupings of research can be found. These are firstly studies of the process, where breakage is inferred from observation of some ensemble property such as the temporal granule mean size. Second, are studies where the extent of breakage is identified directly during granulation, offen through addition of coloured dyes to create tracer granules, providing data from which breakage kinetics can be extracted. 2. 1 . Observations of the b reakage process
Knight et al. [7] examined size enlargement of melt granules with time and im peiler speed in a vertical axis high-shear mixer. They found great variation in agglomeration behaviour with impeiler speed. In particular, it was found that an increase in impeiler speed exhibited an increase in the extent of granule growth. However, this pattern did not continue indefinitely, and at high-impeiler speeds, there was a noticeable reduction in the extent of granule growth (see Fig. 2). They found that granule size distributions were bi modal throughout the granulation process. It was argued that the bimodal distribution persisted at long times due to the breakage of large granules into smail fragments. In addition, it was found that there was a considerable reduction in the fraction of relatively large granules above 1 mm at high-impeiler speeds. They deduced that these observations were evidence of a breakage process. They also observed a reduction in the size of the granules when increasing the mixer speed from 800 to 1 500 rpm for 1 min at the end of an 800 rpm batch (shown in Fig. 2). However, Iveson and Utster [8] argue that changes to the granule-size distribution, on their own, are insufficient ev idence for wet-granule breakage. For example, an increase in impeiler speed could contribute to an increase in rebound of coiliding granules due to the in-
983
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creased impact velocities. This would lead to a reduction in the coalescence probability, although an increase in collision rates would also be likely. Knight et al. [7] support their deduction through further analysis of the granule mor phology. They found that low-impeller speed granules exhibited high sphericity, whereas those from high-im peiler speed experiments has a more irregular shape, again consistent with a breakage process. Vonk et al. [9] highlighted the importance of breakage process in granulation and proposed a destructive nucleation-growth mechanism based on their high shear pelletisation experiments. They proposed that granulation starts with the formation of large primary nuclei, and small secondary nuclei are subsequently formed by the break-up of the primary nuclei (see Fig. 3). Break-up of the nuclei proceeds according to two mechanisms: attrition and fragmentation. The weak nuclei break due to the nucleijnuclei and nucleijwall collisions (attrition) and re duce into fragments as a consequence of the action of the impeller and chopper (fragmentation). Both mechanisms result in the formation of small secondary nuclei, which is then responsible for the subsequent growth. Granule growth then commences once the solid mass is sufficiently wetted and densification of the secondary nuclei occurs. Owing to the consolidation process, the stronger pellets can survive further impacts and in addition, the liquid squeezed to the pellet surface would also increase the coalescence probability. Granule breakage also occurs in low-impact fluidised-bed granulation. Biggs et al. [ 1 0] investigated the extent of granule breakage in fluidised-bed melt gran ulation using a "spray on-spray off" experiment. The results show that the mean granule size increases with binder spraying and subsequently decreases when
984
A. D. Salman et al.
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the binder spray is turned off (Fig. 4). Their results clearly iIIustrate that granules experience breakage even in a low-shear environment. 2.2. Measurement of the breakage process
Breakage during the granulation process has been identified more clearly through the addition of dyed tracer granules or binder. Ramaker et al. [1 1 ] used tracer pellets to investigate equilibrium between growth and breakage processes in two high-shear mixers: a coffee grinder (sm all scale, 0.25 1) and a Gral 1 0 (Iarge scale, 8 1). Amaranth was used to colour a fraction of the small pellets in an experiment. The dye concentration with processing time for different sieve frac tions was then measured. It was found that the dye distribution became more
985
Breakage in Granulation
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homogeneous with time, and they found an exponential relationship for the dye concentration in a sieve cut. The exponential rate constant was termed the con version-rate constant. The smallest pellets were found to give higher conversion rate constants compared to larger ones, indicating fast growth of small pellets and fast formation of small pellets by break-up of larger pellets. An increase in the conversion-rate constants was also found at increasing impeller speeds, indicat ing faster break-up of pellets. They also concluded that the conversion-rate con stants were independent of the scale of the equipment used. Pearson et al. [12] carried out similar experiments to that of Ramaker [1 1 ] to investigate the breakage of granules in a vertical axis 30 L pilot-scale high-shear mixer. Detailed tracer experiments using tracers of different sizes and different processing times (ages) were used to study size and age effects on the breakage kinetics. Tracer granules were created under the same conditions as the stand ard batch, but with the addition of a blue dye, Patent V80. Tracer granules of different narrow sieve cuts were taken at different processing times, and sampies of these added to standard placebo batches at a specific operating time. The dye concentration with size was measured at different times after addition of the tracer granules. They quantified the tracer redistribution as X , the mass fraction of tracer smaller than the initial tracer size. Generally it was found that there was a fast movement of dye to smaller granule sizes, followed by a steady movement to larger sizes. For example, Fig. 5 shows the movement of dye for 1 090 11m tracer granules of different ages. An initial rapid redistribution of dye to smaller sizes followed by a slow increase can be seen in all cases. In addition, the extent of the initial movement to sm aller sizes is c1early a function of age, showing that younger granules exhibit a much greater breakage rate. They also present similar results for different age tracer particles of the same age. These show that larger tracer granules redistribute dye to smaller-size fractions to a much greater extent than smaller tracer granules. This is consistent with the general understanding that larger particles tend to be weaker than nominally identical smaller particles.
986
A. D. Salman et al. ...
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The observation of a reduction in breakage with increasing age is also consistent with the process of consolidation (see Section 2.3.9). Van den Dries et al. [2] attempted the addition of tracer granules into a high shear granulator to investigate the influence of breakage mechanism on granule homogeneity. Similar to Pearson et al. [12], tracer granules were added into the reference batch manufactured under similar conditions. They introduced a break age number to quantify the fraction of broken tracer granules, which is 1 00% minus the ratio of the tracer content present in the tracer granules in a particular size-class divided by the total amount of tracer in all the granules. To describe the extent of homogeneity, the excipient distribution in the granules is measured, expressed as the relative standard deviation (RSD) of the excipient concentration in the sieve fractions. A higher RSD therefore indicates poorer distribution. Figure 6 shows the relation between the breakage number and granule homogeneity, as it clearly demonstrates the higher degree of uniformity with increasing granule breakage. Tan et al. [1 3] carried out almost identical experiments to Pearson et al. [1 2] , but for a small-scale fluidised-bed melt granulator. Their tracer results suggested that larger granules were more prone to breakage than smaller granules during granulation. However, they performed an additional experiment where they added tracer granules, but did not add any further binder to promote aggregation. From this they observed tracer breakage without the complication of simultane ous aggregation and found the breakage rate to be independent of granule size. This apparent paradox was resolved by suggesting the actual aggregation rate to be faster for smaller granules than larger during the granulation process. They also found the breakage rate to be independent of granule age. This is
987
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(a)
0 0%
•
•
20%
40%
80%
60%
Breakage [%]
100%
SO x 40
x
x •
� 30
•
� 2O Q
o
10
0
(h)
•
o
0%
20%
60% 40"10 Breakage [%]
80%
100%
Fig. 6. Relationship between percentage of breakage and the distribution of various ex cipients (0 corn starchflactose 200 M; • estradiolfiactose 450 M; • H PCflactose 200 M; *estradiolflactose 200 M ; A estradiolflactose 1 00 M). The distribution is expressed as RSD. All components were added as powder, except for H PC, which was added as an aqueous solution. (a) Process time of 1 min, (b) process time of 1 5 min [2].
contradictory to the result of Pearson et al. [1 2] in high-shear granulation, but can be explained due to the lack of granule consolidation in the low-shear fluidising environment. It has been shown that detailed data from such tracer experiments can provide valuable insight into the kinetics of the breakage process useful for modelling purposes, such as that shown in Hounslow et al. [14] and Tan et al. [1 5] for high shear and fluidised-bed granulation, respectively (Section 4.1). The technique of adding tracer granules, if designed with care, can also be used to probe the in fluence of operating conditions on granulation mechanisms and granule properties. 2.3. Role of variables on breakage behaviour
This section discusses the roles that different variables play in the behaviour of the breakage process. In particular, the perspective is from the granulation
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process, and observations on breakage inferred from this scale. Specifically characterisation of single granule strength is not discussed here, but rather in Section 3.4. 2. 3. 1. Binder viscosity
Binder viscosity acts to affect wet-granule strength by determining viscous forces in liquid bridges between primary particles during relative movement under im pact conditions. The dynamic liquid-bridge strength within a wet granule is dom inated by viscous forces [1 6] and is additionally affected by capillary forces from the surface tension of the binder [ 1 7, 1 8]. This explains the results by Eliasen et al. [1 9] who investigated the effect of binder viscosity on the granulation of lactose monohydrate in a high-shear mixer. They found that a low-viscosity binder re duces the strength of the granules and makes them more susceptible to com minution during the granulation process. Knight [20] presented a brief review about the effect of binder viscosity on the granulation process in high-shear mixers. They summarise that in a high-shear mixer binder viscosity dominates the consolidation process above a critical vis cosity (1 Pa s), below which surface tension forces dominate. Similar to Keningley et 81. [21], they found that a critical minimum binder viscosity is required for a given size of constituent particles to form granules and this critical value in creases with increasing primary particle size. This is essentially due to the need of the higher viscous force to prevent granules formed from larger partic!es from breaking during the shearing process. !veson et 81. [22] studied the effects of binder viscosity and binder content on the granule consolidation process. They found that granule consolidation was a complex process controlled by a balance between the two mechanisms of in terparticle friction and viscous dissipation, which resist granule deformation. In creasing binder viscosity reduces the deformability of granules, hence reducing the consolidation rate. This is also shown by other studies that in general an increasing of binder viscosity reduces binder mobility in granules, limiting com paction by resisting binder migration to the granule surface [1 7,21 ,23,24]. Schaefer and Mathiesen [23] and Johansen and Schaefer [25] found that the initial growth rate was lower for higher viscosity binders, but that the subsequent growth rate was higher. It was also found that lower binder viscosity led to more spherical granules and an improved binder distribution. The laUer observation was also made by van den Dries et al. [2], who investigated the effect of binder viscosity on the granule-breakage mechanism. They defined a breakage number to quantify the fraction of broken tracer granules, which is 1 00% minus the ratio of the tracer content present in the tracer granules in a particular size class d ivided by the total amount of tracer in all the granules. Their results show that the binder viscosity had a very large influence on granule breakage and the
Breakage in G ranulation 1 00% 90% � 80% Q; 70% ..Q E 60% => c 50% (]) Cl 40% co -'" co 30% � III 20% 1 0% 0%
0
989
2 3 Viscosity (Pa.s)
4
5
Fig. 7. Influence of the binder viscosity on the g ranule breakage behaviour of lactose 200 M granules [2].
extent of granule breakage in turn greatly influenced the granule homogeneity. A high-viscosity binder results in stronger granules, less breakage and therefore low homogeneity (Fig. 7). Some other researchers also found that a high binder viscosity will result in larger granules with a wider size distribution [26,27]. Many works [28-30] were performed using aqueous-binder solution to inves tigate the effect of binder viscosity on the performance of fluidised-bed granu lation. The results are consistent; the increased binder viscosity produces stronger granules with a larger average size. This was attributed to the increase in adhesiveness and binder tackiness that promotes successful agglomeration. A different observation was, however, made by Ormos et al. [31 ] , who examined this effect to a high-viscosity range by increasing the binder concentration. They found the final average granule size and wear resistance to increase with higher binder concentration (hence viscosity) to an optimum, beyond which it will drop. The subsequent decrease in size and strength at higher binder viscosities has been attributed to the poor wetting of the more viscous binder on the powder, which induces weak adhesion between the particles.
2. 3. 2. Binder surface tension
Binder surface tension plays an important role in determining granule strength by causing capillary forces between primary particles at the initial stage of granu lation. This is confirmed by one of the earlier works by Capes and Danckwerts [4], who found that a minimum surface tension is required to form granules from particles of a given size. Iveson and Litster [32] and Iveson et al. [33] investigated the effects of binder surface tension on the dynamic-yield strength and intra-granular porosity. They
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found that decreases in binder surface tension decreased the dynamic-yield strength of granules and increased the minimum intra-granular porosity reached over the duration of the granulation experiment. 2. 3. 3. Contact angle between binder and primary particle
Contact angle of the liquid binder to solid partieIes affects the wetting behaviour of binder on the powder surface when it is first introduced into the granulator. It is worth noting here that the change in contact angle of a particular binder-solid system can also be affected by a change in binder surface tension and viscosity. It was mentioned by Simons and Pepin [34] that the influence of contact angle, together with other physiochemical parameters such as powder surface area, powder density and binder surface tension will determine the frictional forces between particles. Combining this with the capillary and viscous forces acting between constituent partieIes in the granule, the granule yield strength can be determined. Knight [35] reported that binder-wetting abilities, which were strongly related to binder contact angle, became a critical parameter to influence the granulation process when contact angle of liquid binder was elose to a critical value of above 90°. For contact angles above the critical angle, product granules tend to have wider-size distributions and lower strength. 2. 3. 4. Primary particle size and shape
It is generally assumed that high-granule strength is associated with small partieIe size, and Van den Dries et al. [2] have confirmed this to a certain extent. On the basis of his tracer experiments, it was found that a decrease in the starting primary partieIe size leads to a decrease in granule breakage. It was also ob served by Johansen and Schaefer [25] that highly spherical primary partieIes and a narrow primary particle-size distribution will dramatically decrease the granule strength because of a reduction in primary-particle interlocking. 2. 3. 5. Equipment-related variables
Schaefer et al. [36] pointed out that the effects of mixer construction on granule properties were rather complex. Furthermore, the effect of granulator capacity is more related to the issue of scaling-up the granulation process. Generally it has been found that larger mixers will produce rounder and smoother granules with a narrow size distribution [36], and lower porosity [37]. More work has been conducted on the construction effects of moving parts in a high-shear mixer, such as the impeller and chopper, on the granulation process.
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Schaefer et al. [38] studied the effect of impeller shape on the granulation proc ess. They found that curved impeller bl ades gave rise to smooth granules of spherical shape, whereas plane impeller bl ades caused product granules with irregular shapes. Holm [39] also investigated the effect of impeller and shopper design in a high shear mixer. The effects of blade inclination and impeller rotation speed, which was equivalent to the relative volume swept out by the impeller, were described. It was found that a high-swept-out volume gave rise to low porosity and narrow granule size distributions. The chopper size and rotation speed was found to determine granule strength. The proportion of large granules reduced with in creasing chopper speed due to a comminuting effect in the case where granule strength was low, while the size of the chopper had no effect on the granule size distribution. It was concluded that the chopper continuously cut the mass into smaller fragments and promoted densification, although in the case of small particles it aided fluidisation of the mass. The breaking effect of chopper was also observed by other workers [26,40], who recorded a reduction in the amount of large granules with the use of chopper. 2.3. 6. Binder Gontent
Sherington and Oliver [41 ] state that the amount of binder is a principal parameter in controlling granulation. It is generally acknowledged that granulation rate and the mean size of the granule product increases with increasing binder content up to a certain extent. In addition, it has been shown that the porosity decreases with increasing binder content, due to pores being filled with binder [22,24,42]. Typi cally a reduction in porosity leads to an increase in granule strength, and hence a higher resistance to breakage. 2. 3. 7. Binder addition method
It is generally assumed that the method of binder addition will impose a consid erable effect on the granulation process and properties of the granules [20,43,44]. There are three main categories of binder addition: pouring, melting and spraying. Holm et al. [44] found that binder atomisation improved binder distribution, while binder addition without atomisation resulted in inhomogeneous liquid dis tribution, in particular at low impeller and chopper speeds. Knight et al. [20] studied the three binder addition methods in a high-shear mixer. They found that in spite of the binder addition method used, binder distribution was granule size dependent initially, but tended towards a uniform distribution with longer granulation time.
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2.3. 8. Agitation intensity
A higher impeller speed would lead to an increase in both the frequency and energy of collisions, thereby promoting both the granule consolidation and break age rate. Detailed results about the effects of impeller speed on granule-growth behaviours have been reported in the literature. A high-impeller speed was found to cause a higher granule growth rate [40,42] up to a certain limit, beyond which the growing significance of granule breakage will reduce the overall granule growth [7]. The former observation is most probable due to an increase in granule densification rate and consequently increases both the granule saturation, and hence probability of successful coalescence. The laUer observation is also Iikely to be caused by a loss in aggregation efficiency when the granule i mpact energy becomes too high. Since the consolidation process promotes granule growth while the breakage opposes granule growth, the net effect of impeller speeds on granule growth depends on the balance between these two competing processes [20 ,45]. In such cases, the effect of binder viscosity becomes important, as it will determine whether the wet granule formed is sufficiently strong to resist the shearing forces of the impeller. Schaefer et al. [38] found that variations of the impeller speed had liUle effect on porosity of the product granules. In contrast, Eliasen et al. [19,46] reported that granule porosity could increase with increasing impeller speed due to increased comminution. The laUer observation coincides with VialaUe [24] who reported that an increase in impeller speed gave rise to a faster compaction rate. There are some reports on the influence of impeller speed on the shapes of the granules. At higher impeller speeds, the smoothness and sphericity of the gran ules decreases due to increased granule breakage caused by the intensive im pact load of the impeller [7,46]. Here, granule spheronisation was counteracted due to continuous granule formation and breakage. An increase in chopper speed was found to reduce granule mean size [42], and the width of the granules size distribution [40,46], but liUle effect on granule porosity [42]. Although Schaefer et al. [42] reported that the chopper reduced the mean granule size, they concluded that its effect was inappreciable compared with the effects of other process variables. It was also reported by Hoornaert et al. [26] that increasing the chopper speed promoted the consolidation process, de pending on the shape of the chopper. The effects of impeller and chopper speeds on granule homogeneity were studied by van den Dries et al. [2]. It was found that an increase in impeller speed improved granule homogeneity by increasing the extent of granule breakage for cases where the granule strength was low compared with the impact forces generated by the impeller. In the case of fluidised-bed granulation, the intensity of fluidisation determines the uniformity of binder dispersion. It is commonly observed that increasing the
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fluidising air velocity decreases the final granule size and the width of the size distribution [47,48]. This is mainly due to the increased powder flux through the spray zone that essentially decreases the amount of binder picked up per unit time. The increased agitation also reduces the probability of successful aggre gation, and the combination of two factors will effectively lead to a more uniform distribution of binder and subsequently results in a slower growth rate. 2. 3. 9. Granulation time
Schaefer [45] reports that granule strength increases by gradual densification as the granulation process time is extended. The densification process leads to a reduction in the granule porosity, an increase in primary particle packing and transport of the binder to the granule surface. This is in agreement with the work of Fu et al. [49]. They show that wet-granule porosity reduces with granulation time and also explain that this is due to the consolidation, or densification proc ess. Such a result is illustrated in Fig. 8 for two different experimental protocols (optimised and non-optimised operating conditions). For details of the operating conditions, refer to Fu et al. [49]. Additionally, Fu et al. [50] studied the impact breakage of wet granules of different granulation times. They found that the critical impact velocity required for breakage increased, approximately, linearly with increasing granulation time (Fig. 9). In their work, the measured critical velocity is defined as the minimum impact velocity required to form one or more visible cracks on the granule surface. 0.05 __ Optimised
'E (11 '0 c
---- Non-oplimised
0.04
.!!!
(/)
'0 c e (11 0
0.03
>, :.::t :t= (tS (/) .-
> 0 (I) 0 '0 a. (I) Cl � (I) > « �
0.02
0.01
0
10
20
30
40
50
Granulation time. minute
Fig. 8. Comparison of the standard deviation in the porosity for granules (size 4.35-4.75 mm) produced by the optimised and the non-optimised operating conditions. Durcal 40 is the powder material, PEG 400 is the binder and the binder ratio is 0 . 1 5 (Adapted from F u e t al. [49]).
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et 8/.
1 6 �------� • •
4 +---�----�--� 20 60 40 1 20 o 80 1 00 Granulation time (min) Fig. 9. The variation of the critical impact velocity with the granulation time for granules with a mean diameter of 4.5 m prepared with PEG 400 and Durcal 40 [50].
3. BREAKAGE AT THE GRANU L E SCALE
In Section 2, granule breakage was examined from a process perspective. Breakage was studied based on the properties of a batch of granules (macro scale) or a sam pie (mesoscale). In this section, studies of granule breakage at the microscale are reviewed in which single or small numbers of granules are examined. Interest in granule breakage at this scale is manifested in two main areas. First, the resistance or propensity to breakage of a granule as a product is important depending on the use of the granules. Second, understanding the properties of single granules that determine their strength can be linked with meso- and macro-scale studies allowing better understanding of the granulation process and control of granule properties. In particular with respect to breakage we are interested in some property or properties of the granule that can describe how easy or difficult it is to break. This concept of granule 'strength' would initially appear to be something that could be measured and perhaps predicted. 3. 1 . Bonding forces in g ranules
The strength of a material can be interpreted as the resistance of the material to permanent deformation and fracture during a stressing event. It is normal to attribute material strength to be a maximum allowable stress value before frac ture occurs. Hence, the stress distribution arising when a material is loaded plays a significant role in determining the fracture behaviour of the material. For a homogeneous elastic sphere (the proverbial particle) in contact with external bodies, c1assical theories of Hertz [51 ] and Lurje [52] can be superposed to the
Breakage i n Granulation
995
overall stress distribution within the sphere Kienzier and Schmitt [53]. More re cently, Shipway and Hutchings [54] derived numerical values for elastic stress fields developed in spheres under uniaxial compression and free impact against a platen. If the sphere is deformed inelastically, it is expected that there is dramatic departure of the resulting stress field fram the elastic case. Catastraphic failure of solid particles will take place once the maximum allowable stress of the material is exceeded. The failure modes can be c1assified into three categories viz. brittle, semi-brittle and ductile failures depending on the extent of plastic deformation experienced by the material during fracture. Brittle failure occurs without signif icant plastic deformation whereas substantial plastic deformation can be found in material fails in a ductile manner. An intermediate case where brittle fracture occurs at the boundaries of a small plastically deformed region is termed semi brittle failure [55]. However, while these descriptions are suitable for homogene ous continuum solid particles where local stresses can be transmitted throughout the entire volume of material, they are insufficient to describe the failure of gran ular solids. Granular material is a cluster of small particles held together by interparticle bonds. The interparticle bonds within a granular solid may be rup tured causing the particles at the point of load application to be sheared apart before the load can be transmitted thraughout the solid as in a homogenous elastic system [56]. Fram this it can be concluded that the strength of a granular medium is governed by interparticle bonding mechanisms rather than the strength of individual constituent particles. Furthermore, the load transmission in a granular medium is affected by its internal particle packing. It is c1ear that the perceived strength of a granule will be a function of the nature and concentration of its internal bonds. Before looking in more detail at granule strength, it is worth reviewing the interparticle forces that are Iikely to be contributing to a granule's strength. These inter-particle adhesive or bonding forces have been reviewed by Rumpf [57], Schubert [58] and Sherington [41 ] . The different types of bonds that may exist within a granule can be c1assified as folIows. Forces due to immobile films. A thin immobile liquid layer can be formed on the surface of primary particles due to reasons such as granule reaching a critical level of compaction or excess binder removal thraugh evaporation. Overlapping of the immobile liquid layer between primary particles praduces this bonding force. The strength of these bonds is dependent on contact area and the prap erties of the binder such as the tensile strength of the liquid layer. Forces due to mobile-liquid bridges. With increasing liquid content in the granule, the liquid between primary particles tends to be mobile, forming liquid bridges. In this case, adhesion forces arise fram surface tension forces at the liquid/air interface- and hydrostatic-suction pressure in the liquid bridge. Typically it is found that wet-granule strength increases with increasing liquid content up to the point at which the granule is saturated and the liquid bridges no longer exist.
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Forees due to solid bridges. Solid bridges ean be formed, for example, through ehemieal reaetions, erystallisation, binder solidifieation and sintering. If these types of bonds exist, they will typieally be the primary strength determining bonds. Forees due to attraetive effeets between solid partieles. Attraetive forees be tween solid particles ean take many different forms, sueh as van der Waals forees, magnetie and eleetrostatie. These are typieally short-range forees and are only signifieant for very small partieles sizes (less than 1 )lm), or eases where the particles have been brought close together by high eompression forees. Forees due to meehanieal interloeking between solid particles. Irregular shaped particles ean eontribute signifieantly to granule strength if they are paeked tightly, due to interloeking effeets. The relative importanee of these bonding forees in determining the strength of a granule will vary from ease to ease. In some types of granules, some of these forees will not exist and it is unlikely that all these forees will be aeting. For example, in a dry granule there will be no interstitial liquid and so there will be no internal forees due to immobile or mobile liquid films. In addition, these forees will also interaet with eaeh other. For example a liquid layer on a solid particle will reduee interparticle frietion and interloeking forees by aeting as a lubrieant. The relative magnitudes of the different bonds are also a strong funetion of particle size (see Fig. 1 0). In the ease of wet granules, it has been shown by Rumpf [57] that eontributions to wet granule strength by van der Waals forees, and forees from thin films on l� �------,
100
]
N
�
6
10
1
0.1
0.01 +-----.,----'''r-''--'l 1� 100 1 10 0.01 0.1
d, f1m Fig. 1 0 . Theoretical tensile strength, Rumpf [57]).
(Jt,
of agglomerates as a function of size, d (after
997
Breakage in Granulation
particle surfaces are usually very small. In addition, formation of solid bridges between primary particles is usually not applicable in the case of wet granules. It is also then assumed that the interlocking effect is only significant in a few specific cases. It is therefore widely accepted that the static strength of wet granules is determined principally by liquid-bridge forces between primary particles. It is due to the complicated interactions of these forces that it is difficult to define granule strength. As a result of trying to understand the failure of granular materials, prin cipally two theoretical paradigms have developed [35]. The first is attributed to Rumpf [57] and considers that a granule fails by simultaneous rupture of all the bonds along a fracture plane. Alternatively, Kendall [59] argued that a granule failed through crack nucleation and propagation, and adopted fracture mechanics to describe this. 3. 1. 1. Rumpf's theory
Rumpf [57] developed a classical model for predicting the static-tensile strength of granules. Considering a granule under the action of applied loads, he pointed out that fracture of the granule is mainly caused by the tensile stress generated within the assembly. The theoretical tensile strength of a granule is suggested to be the summation of all the interparticle bond strengths across the fracture sur face. The implicit assumption in this analysis is all the interparticle bonds across the fracture surface ruptured simultaneously during the fracture process. This leads to the derivation of the following expression for theoretical granule-tensile strength, (Jt, in its general form. (J t nF (1) where n is the average number of interparticle contacts per unit area across the granule cross-section and F the mean force required to separate them. It is found that n scales with granule-solid fraction and size of the constituent particles with a uniform primary particle size distribution. Therefore, equation can be rewritten as follows (Rumpf [57]): ( 1 8) � (Jt 1.1 (2) 8 02 where 8 and 0 are the intra-granular void fraction and constituent-particle diam eter, respectively. Nevertheless, the constituent particles of real granules are often poly-disperse and non-spherical. In respect to this problem, it is proposed that 0 in the foregoing should be substituted with the mean diameter, for instance the surface-volume mean diameter, of the real constituent particles [35]. Equa tions ( 1 ) and (3) are applicable to granules with different internal bonding mech anisms, which results in different expression for F. For wet granules, where =
-
=
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primary particles are held together with liquid bridges, the model is given as: - 8 Yt (Jt = CS - cos e (3) 8 dp where C is a material constant (for uniform spheres C = 6), S the liquid satu ration, 8 the intra granular void fraction, dp the surface average diameter of pri mary particles, YI the liquid surface tension, and e the liquid-solid contact angle. In this case, the liquid saturation of a wet granule is defined as - 8 Ps S=H (4) 8 Pt where H is the moisture content, which can be calculated as the ratio between liquid mass and dry-solid mass. The powder and liquid densities are expressed as Ps and Pt, respectively. The model shows that wet granule-tensile strength is determined by starting material properties (C, dp, e and YI) and parameters that express granule structure (8 and S). It indicates that granule strength is propor tional to liquid surface tension and saturation, increases with decreasing porosity and is inversely proportional to primary particle size. In the case of binderless granules, the main bonding mechanism can be considered to be van der Waals interparticle attraction. In this case, can be expressed by the following well established relationship: AD (5) 24a2 where A is the Hamaker constant and a the separation between the surfaces of the constituent particles and where the remaining symbols have the same des ignation as before. However, there are a number of deficiencies in the model of Rumpf [57]. The model assumption that all the interparticle contacts in the fracture plane fail sud denly is contested by Kendall [59]. He argues that simultaneous failures do not usually occur in practice, where the real-failure mode is by cracking due to con tacting primary particles in a granule separating sequentially (see Section 3.1 .2, for more details on this argument). The assumption that a granule consists of mono-sized spheres is also not generally realistic. Kapur [60] shows that con stituent particles exhibit size variation and the content of the fines plays a dom inant role in determining the granule strength. Cheng [61 ] also showed that the shape of primary particles has a significant effect upon the strength of wet gran ules. The model also does not take account of interparticle friction forces. Chan et al. [62] found that reduction in porosity would increase friction forces between particles by reducing separation distances between substrate particles. Fu et al. [3] show that the critical impact velocity (the impact velocity above which a granule breaks) increases consistently with granulation time even though the binder content and air fraction remain relatively constant after a long period of
1
--
1
F
F=
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Breakage in Granulation
granulation. They argue that this is contradictory to the model of Rumpf [57], and suggest that this consistent increase in apparent granule strength is due to a densification of the interparticle contacts, and hence an increase in inter-primary particle friction which is not included in the model. In addition, the use of static capillary force in Rumpfs model is not ideal for describing the impact strength of granules. Inside a high-shear granulator, gran ules experience high impact strain rates with impact velocities as high as 1 0 ms - 1 . Under such conditions, the dynamic effects, such as viscous dissipation and liquefaction, may become significant [17]. Van den Dries et al. [2] highlighted the importance of the viscous forces in high-shear granulation, and modified the Rumpf model by considering the viscous forces using the Reynolds lubrication equation. The modified equation describes the tensile strength of a granule under dynamic conditions 9 (1 - Ei 91t,LWp (6) 8 � [',2 1 6d3,2 where up is the relative velocity of moving particles, f1 the binder viscosity and d 3 .2 is the surface mean diameter. This model assumes that the tensile strength is independent of the liquid saturation and only depends on the number of contact points between particles, which is consistent with the viscous force of a single liquid bridge between two moving particles. (Jt = -
-
3. 1 . 2. Kendal/'s theory
Kendall [59] argued that Rumpfs theory (Section 3. 1 . 1 ) failed to account for the actual failure mechanism found in granular materials and the theory led to over estimation of granule strength. According to Kendall [59), fracture of granule is a consequence of crack nucleation at flaws leading to subsequent crack propa gation through the granular structure. Thus, the failure mechanism in this case is sequential separation of interparticle bonds in contrast to the simultaneous bond rupture proposal of Rumpf [57]. The propagation of cracks through a granular solid consumes the amount of energy needed to create new surfaces along the crack planes. Griffith [63] initially developed fracture mechanics for linear elastic materials, the basis of which is an energy balance in which the strain energy released at the crack tip provides the driving force to create new surfaces. Kendall [59] applied these concepts to derive the following expression of fracture strength of granules, (Jf: (7) where
1 000
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dependence of granule strength on solid fraction and weaker correlation with constituent particle size in comparison with Rumpfs theory. This fracture strength can be compared directly with the tensile strength predicted by Rumpf [57] owing to the fact that crack propagation is a result of tensile separation of particles perpendicular to the propagation direction ahead of the crack tip. Bika et 81. [64] state that given the inherent heterogeneity of agglomerates, it is not obvious that their mechanical properties can be described by such continuum descriptions. However, they note that agglomerate deformation is fundamentally similar to other solids. 3.2. Measuring g ranule strength
Mullier et 81. [65] states that granule strength is not weil defined in the literature, and measured strength is heavily dependent on the particular experimental technique used. Granule strength is usually taken to include its resistance to breakage (of any kind) during its formation, handling and subsequent processing. A more precise definition is given by Bika et 81. [64], who suggest that granule strength is the stress at which a material either begins to deform plastically or develops macroscopic damage. A number of different terms and techniques are used to describe and char acterise granule strength and these are now described. 3. 2. 1. Tensile strength
Tensile strength is arguably the most frequently used term to describe granule strength. Rumpf [57] simply describes granule tensile strength as the tensile force at failure divided by the cross-section of the agglomerate. Rumpf [57] measured the tensile strength of limestone powder and water agglomerates by cutting the original pellets into cylinders, bonding adaptors to the ends and applying a uni axial tensile force using a conventional testing instrument. The reported results were in good agreement with his theory. Schubert [58] suggested that this suc cess was due to the ability of wet granules to demonstrate slight 'plastic' defor mation. They give a more complex definition for this strength, as the unidirectional, maximum tensile force per unit of the plane cross-sectional area of the bulk material at right angles to the direction of the tension force when a locally constant, purely tensile stress prevails in the fracture cross-section of the material regarded as a continuum. Bika et 81. [64] summarise that the tensile test of Rumpf [57] is one of the few tensile measurements on agglomerates reported in the literature. This is because it is not practical for most agglomerates, which are too weak to be tested in this way. They state that most tensile methods produce shear and tension simultaneously in different directions within the solid,
Breakage in Granulation
1 00 1
requiring careful microscopic inspection to differentiate between the tensile- and shear-failure modes. They recommend that tensile strength can be more easily measured using unconfined uniaxial compression tests. The quasi-static diametrical compression test has been a popular technique to study the crushing strength of single granules [64,66-69]. It provides a means of measuring the indirect tensile strength of a granule. During crushing a tensile hoop stress is generated, and it is actually this stress required to split the granule apart that is reported as the granule-tensile stress. It is generally considered that this type of test is more representative of granule strength over tests requiring special preparation of the granules. For example, the bending test (Section 3.2.4) requires preparation of an ensemble test bar, rather than testing the individual granules. The energy utilised to fracture the granule can be estimated from load displacement data. However, it is argued by Bika et al. [64] that the granule crushing strength measured in this case must be interpreted with great care as it was only representative for highly brittle and isotropic materials. Kapur and Fuerstenau [56] investigated the quasi-static behaviour of dry binderless granules by compressing limestone pellets of 8to 20 mm in diameter. At the instant of fracture, a cone of material was generated at the poles of a spherical pellet opposite to each other. These poles corresponded to the contact points between the pellet and the upper and lower plates of the Instron machine. The general fracture pattern was splitting along a vertical plane creating two hemispherical halves. As suggested by Kapur and Fuerstenau [56], fracture of the pellet was initiated once the separation between the interparticle bonds along a potential fracture plane exceeded a critical value. Since it was assumed that no prefer ential fracture plane existed, they proposed that all the interparticle bonds were subjected to the same horizontal tensile force. By equating the total compressive work experienced by the cones at the poles until fracture to the tensile strength across the fracture plane, the crushing strength was related to the pellet size and limestone powder surface area. This relationship reflected the divergence of the strength of dry, porous pellet from that of homogenous, elastic body. A later quasi-static compression test conducted by Arbiter et al. [70] using large sand cement spheres (up to 1 20 mm in diameter) yielded fracture pattern similar to that obtained by Kapur and Fuerstenau [56]. Their inspection of the contact area of the sphere just below the fracturing load revealed that minute cracks were densely distributed along the periphery of the contact area. The periphery was indicated by the sharp change in radius of curvature, which was expected to be heavily stressed. The breakage efficiency for diametrical compression to produce fragment of a specific size was deduced and was compared with that for free-fall impact. It was found that the energy input necessary to initiate fracture in free-fall impact was twice that required by quasi-static compression. Besides that, their work indicated that slow compression and low-velocity impact ind uced geomet rically similar stress field in spherical sand-cement spheres.
1 002
A. D. Salman
et 81.
In addition to strength testing, diametrical compression has been used as a complimentary test to visualise the sequence of crack formation in fertiliser granule under impact loading [71 ] . In this investigation, the load application was continued after fracture to examine the subsequent crack formation. Primary fracture of fertiliser granules into two hemispheres was observed in these com pression tests followed by secondary fracture of the hemispheres into quadrants and segments. Consequently, Salman et al. [71 ] concluded that the fertiliser quadrants collected from low-velocity impacts against a platen were the conse quence of secondary fracture preceded by primary fracture. Adams et al. [72] discuss two disadvantages of single-particle compression tests. First, in any batch of particles formed under nominally identical conditions, there always exists a wide variation in the measured-fracture loads, requiring a large sampie size from which a reliable average can be calculated. Second, single particle fracture loads are usually smalI, typically of the order of a Newton, thereby reducing the accuracy with which they can be measured. They present an alternative method consisting of replacing the single particle with a confined bed of similar particles, essentially using a piston in a cylinder type of arrange ment. By treating the system as purely dissipative and applying Mohr-Coulomb macroscopic failure criterion, they develop a simple first-order lumped-parameter analysis enabling average single agglomerate strengths to be deduced from the initial deformation behaviour of the bed under relatively low loads. In testing a range of agglomerates, they found that the deduced single-particle fracture loads were approximately proportional to experimentally determined single-particle compression loads. 3. 2. 2. Dynamic-yield strength
Iveson and Utster [32] introduce dynamic-yield strength as a measure of defor mation capability of granular material under impact conditions. The dynamic-yield strength is the stress at which the granule begins to deform plastically. They measured the deformed contact area of cylindrical agglomerate pellets dropped from several heights. They then used the model of Hawkyard [73] to calculate the dynamic yield stress of the pellets. The model states that for a cylinder of initial area dynamic yield stress Y, impact velocity and density p the deformed contact area will satisfy 1 Q 1 + In (8) =Y
Aa, A1
2 P Uo [AA1o
-
Ua, (A1Ao)]
Further work by Iveson et al. [74] and Iveson and Page [75] shows that there is a critical strain rate (which was binder dependent) below which the dynamic flow stress, (Jpk, was independent of the strain rate, i;. Above this critical strain rate, the flow stress increases with increasing strain rate (see Fig. 1 1 ). They investigated
1 003
Breakage in Granulation 1 .0E+3 "...-----, Based on d 32 mean size. Sfr
::!:
* =
Ca 0.58
5.3 + 280
1 .0E+2
.
•
� CI)
1 .0E+1 0
x
•
1 .0E+O 1 .0E-10
Region II
Region I
1 .0E-8
1 .0E-6
1 .0E-4
1 .0E-2
Ca (-) x o
0.1
Pas Oil
- Equation
1 Pas Oil 0.01 Pas LUB
Glycerol
Water
(9)
ß •
0 0 •
1 .0E+0
0.01 Pas Oil 60 Pas Oil 60 Pas LUB
Fig. 1 1 . Dimensionless pellet flow strength vs. capillary nuber (Adapted from Iveson
et 81. [74]).
the influence of particle size [75], strain rate, binder viscosity and binder surface tension on the dynamic-flow stress of liquid bound granular materials and found that the results at low- and high-flow stress collapse on to a single curve when plotted in terms of two dimensionless groups (9) where Str* = ((JP!P3,2IYLV) is the dimensionless peak-flow stress and Ca = (8f1d3,2/YLvr is the dimensionless capillary number defined as the ratio of vis cous to capillary forces. d3,2 is the surface-mean particle size, YLV the Iiquid-va pour surface tension, i; the strain rate, (Jpk the peak-flow stress and f1 the viscosity. The best-fit values of the parameters were k1 = 5.3 ± 0.4, k2 = 280 ± 40 and n = O.58 ± O.04. This work is highly significant in the area of high impact gran ulation where granule collision occurs at a very high -strain rate. This work sug gests that the traditional methods of measuring granule strength at static conditions are not realistic by any means when used to predict the granule de formation behaviour upon collision. 3. 2.3. Shear strength
The shear testing of bulk solids has originated from soi! mechanics and handling bulk solids. Of the various types of shear-testing device available, Ghadiri et al. [76] states that the annular-shear cell test has become a widely used method. Paramanathan and Bridgwater [77,78] pioneered the use of the annular shear cell for the evaluation of the attrition propensity of particulate solids. Figure 1 2 shows
1 004
A. D. Salman
et al.
Radial saw-tooth - grooves
1 60 mm Fig. 12. The annular attrition shear cell of Paramanathan and Bridgwater [77,80].
a diagram of their shear cell. Ouwerkerk [79] has shown that compression alone does not produce as much damage as when accompanied by shear. However, it should be noted that these tests are static and the behaviour of granules under dynamic conditions can be very different, such as that shown by Iveson et al. [74]. Specifically in impact testing of granular materials, it has been shown by Salman et al. [71 ] that impact under normal angles produces much more damage than at more acute angles in which shear-forces become important. 3. 2.4. Bending strength
Bending strength of agglomerates is based on a fracture mechanics understand ing of granule breakage, whereby breakage occurs due to the propagation of a crack under an applied stress, rather than simultaneous rupture of all bonds [59]. Figure 1 3 shows the arrangement of a typical three-point bending test. In this case, a test bar agglomerate is prepared with a notch and supported on two rollers. The test bar is then broken by a blunt-ended wedge applied to the top of the bar. The force-deflection data are recorded during the test. Bika et al. [64] discussed some of the problems with this measurement approach. The most important problem with this method lies in the preparation of the agglomerate. In the case of studying granule breakage, typically the test bar will be formed by
1 005
Breakage in Granulation F
\.••.
:L,eryy- K(2nr)
-U2
+...
"='r Sc · . . . . . ' 0.
er_
__ er
Fig. 1 3. The three-point bending test [81 ] .
consolidating the subject granules together into the appropriate shape. To elim inate the boundaries between the granules without deformation or fracture of the original agglomerate is perhaps a particular problem. The aim is to ensure the tablet is macroscopically homogeneous and contains the same internal structure as its constituent granules. Scoring of the notch will also typically produce a localised region of lower porosity, and any cracking from the bar formation cannot be easily controlled. These difficulties make it hard to determine whether the fracture behaviour is representative of the constituent granules, or is simply a measure of how weil the constituent granules have been consolidated together to form the test bar. Iveson et a/. [64] summarise that despite the difficulties with this technique its value lies in the study of the fundamentals of granule fracture as weil as process troubleshooting. 3. 2. 5. Hardness
Typically the hardness of a material is measured by indentation. In an indentation test, a load is applied to an indenter at right angles to the sampie surface, causing it to penetrate the surface. A variety of shapes are available for the indenter tip, inciuding a sphere, square diamond pyramid, rhombohedral dia mond pyramid and dia mond cone with spherical tip. The hardness can then be defined as the load divided by the indentation area projected onto the plane of the surface. Bika et a/. [64] summarise that in general the hardness is a function of tensile-yield strength, elastic modulus, Poisson's ratio and total strain (for work-hardening materials), whose functional form depends on the type of material ranging from rigid-plastic to elastic-plastic with and without work hardening. A principal ad vantage of indentation tests is that they can easily be applied to the surface of agglomerate compacts when the indenter is large enough with respect to any characteristic length scale of the solid such as primary particie size or pore size. However, measuring the hardness of small particies using this technique can
1 006
A. D. Salman
et al.
cause problems, in particular trying to image small indentations with sufficient contrast using a scanning electron microscope. This has led to the development of a nanoindentation technique [82]. Rather than measure the indentation area directly, this technique requires measurement of the penetration depth and load of the indenter during loading and unloading. Pepin et al. [83] consider that from a global point of view, plastic agglomerates deform against hard surfaces with a hardness which is the ratio between the applied load and the contact area of the agglomerate with the hard surfaces between, which it is compressed. They state that for wet agglomerates, the hardness is related to three factors: the liquid-binder surface tension, viscosity and the interparticle friction. Simons and Pepin [34] develop a model allowing prediction of wet-granule hardness including these factors. They point out that the model is only valid for particles which can be considered independent from one another during deformation and when the liquid bridge volume ensures that pendular liquid bridges can exist between touching particles. In addition, if con stituent particles have a shape that deviates significantly from a sphere, or if they tend to aggregate, the model will fail. 3. 2. 6. Summary
It has been noted, for example by Schubert [58] and Pietsch [84], that a theory and a transformation of these measured results to other stress conditions is more or less impossible, since it is difficult to identify which stress component causes the granule to fail. Therefore experimental results reporting granule strength, but measured by different techniques, cannot be compared with each other. 3.3. Dynamic strength of granules
In general, the definitions of granule strength described in Section 3.2 in fact refer to static strength. Despite the large amount of work on characterising static granule strength, it is really the dynamic-breakage behaviour, in particular the granule deformation under impact that is critical in determining granule-growth behaviour [21 ,32,85-87]. Iveson et al. [88] conclude that when it has been high lighted in recent years that viscous effects are significant in granulation proc esses, it has not been appreciated that the mechanical properties of granules are strain-rate dependent. They state that strength tests performed at pseudo-static conditions give no indication, even qualitatively, of how materials will behave at high-strain rates, and hence are actually misleading when used to model-granule coalescence. Impact load can be induced by various collisions within a granula tor, such as granule/granule, granule/wall collision. In addition granule collisions with moving parts, such as the impeller and chopper in a high-shear mixer, will
1 007
Breakage in Granulation
impose impact loading. As a consequence of these collisions, granules can un dergo rebounds, deformation, coalescence and breakage. Impact velocities of as high as 1 -1 0 mjs are typical in many types of granulating equipments, and par ticularly high-shear mixers. Dynamic forces may become significant, especially where binders are used. Deformation of granules leads to a reduction in granule porosity. This causes more binder to be squeezed to the granule surface, sub sequently promoting consolidation and coalescence. Adams and Edmondson [89] developed a model that can be used to approx imate viscous forces, Fy , raised from a liquid bridge between two spherical sur faces that are relatively moving 31Lf.1r2 dh Fy = (1 0) 2h dt where r is the characteristic particle size or radius and h the gap distance be tween the spheres. This equation has been verified experimentally by Mazzone et al. [1 6] and Ennis et al. [90]. Their work highlighted the fact that dynamic-bridge strength could exceed static-bridge strength by several orders of magnitude un der industrially relevant conditions. However, it has also been found that increasing-strain rate for low-viscosity binders (such as water) exhibit a reduction in bond strength due to limited-liquid movement over the particles surface resulting in a rapid narrowing of the bridge. For liquid bridges of low viscosity, capillary forces dominate over viscous forces. Under high rates of strain, the decrease in capillary strength of the bridge is more significant than increase in viscous forces. The effect of strain rate is then de termined by competition between the increase in viscous forces and the decrease in capillary forces [88]. Viscous, capillary and frictional forces can all be important in determining the dynamic strength of granules [32]. The deformation of wet granules can also be characterised by the coefficient of restitution [32,49]. The coefficient of restitution is related to the energies asso ciated with impact and rebound . This has been measured experimentally as the ratio of rebound to initial-dropping height [32] and rebound to incident velocity [49]. The reported restitution coefficients for wet granules are typically less than 0.2. In general, studies on the dynamic strength and behaviour of granules have used single and multi-particle impact techniques. These are now discussed.
( )
3. 3. 1. Multi-partic/e impact tests
Bemrose and Bridgwater [80] concluded in their general review on attrition and attrition test methods that multi-particle impact tests were more closely related to realistic applications. In multi-particle impact tests, the extent of damage due to impact can be expressed using the term damage ratio, which is defined as the
A. D. Salman
1 008
et al.
mass ratio of the debris produced due to impact on the mother granules [91 ,92]. Verkoeijen et al. [93] measured the size distribution and shape of granules after impact in a repeat-impact testing unit (see Fig. 1 4). From this analysis, they were able to differentiate between attrition and a fragmentation breakage mechanism. However, to study the detailed granule behaviour and breakage mechanisms under impact, single particle studies are required. Pitchumani et al. [94] used a similar arrangement to Verkoeijen et al. [93] in order to characterise the breakage behaviour of enzyme granules. They summarise that this type of test is suitable for quantifying the effects of granule breakage due to the normal forces of attrition (Iow magnitude) and fragmentation (high magnitude). They found high repro ducibility in the measurement of the change in particle size distribution . They argue that granules are generaily complex structures made from many different materials, and that this type of repeat impact testing can characterise the strength of successive 'Iayers' of a granule. Samimi et al. [95] used a system whereby a large number of granules (3000-4000) were impacted successively on a target. The extent of breakage was then characterised by the ratio of mass above (mother particles) and below (debris) a specific sieve size. Multiple impact tests were also made whereby the impacted material was fed through the apparatus successive times. Figure 1 5 shows a schematic diagram of this apparatus. 3. 3. 2. Single-particle impact tests
The failure patterns of granular materials have been investigated in a number of studies. For example, Salman and Gorham [96] have investigated the effect of resonating plate counter-weight
vibrating plate
amplitude regulator
Fig. 1 4. Schematic drawing of repeated impact test unit for multi-particie impact analysis [93] .
1 009
Breakage in Granulation Air eductor
Image tmalysls computer
Rotamele1'-
Photodiodes
�
High speed digillJl camera -----'
compressor
Chamber
/
Collection
VIlCUIlm
Pump
Fig. 15. Schematic drawing of the impact test apparatus used by Samimi et al. [95].
Velodty
ElectromagneUc valve
Gas cyllnder (Pressurised gas)
Fig. 1 6. Single particle impact apparatus used by Salman and Gorham [96).
impact velocity and Subero and Ghadiri [76] and Samimi et al. [95] have inves tigated the effect of structure. The deformation of granular material under impact conditions has been investigated by Iveson and Utster [32] and Fu et al. [49,50]. Typically high-speed single granule impact studies will use compressed air to fire granules at a solid target, such as the arrangement shown in Fig. 1 6. The in fluence of different impact velocities on the extent of granule impact deformation can be seen in Fig. 1 7. For low-velocity measurements, such as those used for wet-granule deformation and rebound studies, free-fall apparatus is commonly used (Fig. 1 8). Generally, high-speed imaging of the impact will be made to study the impact behaviour, and the fragments will be collected in order to measure the fragment-size distribution.
1010
A . D . Salman e t al.
(al 0
0.049
0.098
0. 1 4
0
0.098
0.17
0. 1 9
(cl 0
0.05
0.07
(dl 0
0.07
0. 1 5
(bl
0. 1 7
0.27
1 .75
3.16
0.24
1.1 1
1 .85
0.27
0.5 1
1 .76
0.5 1
0.76
0.27
1 .26
Fig. 1 7 . I mages of the impact of granules made from PEG 400 and Durcal 40 with a binder ratio of 0. 1 5, air voidage of 0.009, diameter range of 4.00-4.75 mm and mass range of 0. 1 2-0. 1 6 g. They correspond to impact velocities of (a) 1 2 , (b) 1 6, (c) 20 and (d) 28 ms- 1 ; the times (ms) for each frame are also given in the figure where 0 ms refers to first contact of a granule with the target (From Fu et al. [50]).
3. 3. 3. Breakage patterns
The breakage patterns of continuum solids can be described as brittle, semi-brittle or ductile. The brittle mode describes when the solid material fractures without noticeable plastic deformation. In contrast, the ductile mode describes fracture with considerable plastic deformation in the solid. The semi-brittle fracture mode occurs where brittle fracture takes place at the boundaries of a region of Iimited plastic deformation, and as such is an intermediate case between brittle and ductile failure modes. It has been argued that these modes cannot be used to describe structured materials such as porous solids and granular materials [55,97]. Mishra and Thornton [98] identified four different failure modes based on the extent of damage observed in a systematic study of impact behaviour of a gran ule using discrete element method (DEM) simulations: •
This failure pattern occurs where visible cracks can be identified. It can also be used when two or more large daughter fragments are formed in addition to some fines adjacent to the impact site. Fracture
-
1 01 1
Breakage in Granulation 2
8
o
--
3.
I . Anti-vibration mounts. 2. Vertical optical beneh. Horizontal optical bcnch, 4. Nozzlc,
5 . Granule,
6. Target. 7. High�peed camera, 8. Vacuum pump, 9. pe.
Fig. 1 8. Schematic diagram of free-fall rig used for single impact wet granule studies [49].
•
•
•
Shattering - This occurs at increased impact velocities, where larger fragments can themselves be broken into small clusters of primary particles. Disintegration Here, one large cluster is centered on the upper part of the agglomerate with the remainder of the agglomerate reduced to small clusters of 1-1 0 primary particles. Total disintegration This describes the case where there is no 'Iarge' surviving cluster after impact at very high velocity. -
-
Mishra and Thornton [98] and Ciomocos [99] have found that granular particles will break in different modes at the same impact velocity if they have different contact density and solid fraction. Denser granules will favour the fracture mode, whereas looser granules will tend to fail in the disintegration mode. Subero et al. [1 00] studied experimentally and numerically the effect of inter facial energy, described as the strength of bonds holding together primary par ticles, on the impact strength. They found that interfacial energy has a greater effect on breakage behaviour at low-impact velocities. It has also been found that the failure mode is strongly dependent on the impact velocity. However, different descriptions of the failure modes have been
1 01 2
A. D . Salman et al.
made by different researchers. In the simulation work by Thornton et al. [ 1 0 1 ] and Mishra and Thornton [98], they describe the failure mode of granular particles to vary from fracture, shattering, disintegration and total disintegration with increas ing impact velocity. Subero and Ghadiri [55] classified the failure of agglomerates into two main types: localised disintegration and fragmentation. Here, localised disintegration occurs at relatively low-impact velocities where the damage due to impact is limited to the impact site with some production of fines. Fragmentation occurs at higher relative impact velocities where the granule undergoes both localised disintegration on the impact site, with propagation of large cracks into the granule body. Alternatively, Salman et al. [1 02] present three failure regimes into which a wide range of materials can be classified. The failure regimes are described by low-, intermediate- and high-relative impact velocities. They ob serve that the failure forms of particulate materials are significantly different and material dependent in the low- and intermediate-velocity regimes, whereas many materials exhibit similar failure modes in the high-impact velocity regime. Figure 1 9 shows the typical failure patterns of solid, wet and binderless gran ules at increasing impact velocity. For solid granules, Salman et al. [1 02] report that at low-impact velocities, there is local cracking with the development of a flat region over the contact area accompanied by some localised disintegration. In addition, one or more fractures propagate from the apex of the conical zone through the specimen on meridian planes, which pass through the centre of the particle. At intermediate-impact velocities, the number of fracture segm ents is observed to increase. At high-impact velocities, a cone of crushed and
(a)
�)
m 0 (W)
, , 0 ill
� &�p
Fig. 1 9. Failure forms of solid, wet and binderless granules from the side view with impact region at the boUom. Failure forms change with increasing impact velocity from left to right (after Salman et al. [1 02]): (a) solid granule, (b) wet granule and (c) binderless granule.
Breakage in Granulation
1013
compacted material is formed on the impact site, with several oblique cracks propagating through the granules. In particular, a large characteristic cone shaped fragment is formed, which becomes narrower and shorter with increasing impact velocity. It should be noted that the impact breakage forms of large spherical concrete agglomerates tested by Tomas et al. [1 03] exhibited similar patterns at low and intermediate velocities even though they were using spheres of 1 50 mm compared with the 5 mm granules discussed by Salman et al. [1 02]. Figure 1 9(b) shows the changing failure forms of a relatively large (5 mm) wet granule made from calcium carbonate and polyethylene glycol 400 at increasing impact velocities. Salman et al. [1 02] report that plastic deformation was ob served for low-impact velocities below 8 ms- 1 . This deformation resulted in a flattening of the impact region leading to a relatively large contact area without the appearance of cracks. Slight elevation of the impact velocity from this point re sults in a number of small cracks propagating from the deformed contact area, parallel to the impact axis. The length and number of these cracks increase with increasing impact velocity, although the integrity of the granule is maintained. They describe this failure form as the low-velocity regime mode. At increased impact velocities above 1 2 ms - 1 , a distinct cone-shaped fragment is formed at the contact region with the residue of the granule forming a mushroom-cup shape. Above 1 6 ms - 1 the mushroom-cup residue tends to fragment into several equal-sized pieces. This shape is described as the intermediate-velocity regime mode. Finally at very high-impact velocities, greater than 20 ms - 1 , they found a significant size reduction due to fragmentation. Here, the contact area of the compacted cone increases with increasing impact velocity, which they attribute to plastic deformation. Salman et al. [1 02] also present the impact breakage form of binderless granules (Fig. 1 9c). It was found that at relatively low-impact veloc ities, cracks propagate from the impact zone towards the upper hemisphere of the granule. Some flattening of the impact area, accompanied with some material detachment was also observed. Increasing impact velocity leads to more oblique cracks developing with further localised damage around the contact area. At higher impact velocities, a compacted cone is left on the target, with the remain der of the granule splitting into several equally sized segmental fragments. The number of these fragments with smaller sizes increases at high-impact velocities, with growth in the size of the compacted cone. Finally, at very high-impact ve locities, the whole granule is transformed into a single-compacted zone sticking to the target. 3.3.4. Extent of breakage
The extent of breakage is usually described as 'damage ratio' in computer sim ulations of granular breakage. Damage ratio is defined as the ratio of the number of contacts broken upon impact to the total number of initial contacts
1 01 4
A. D. Salman e t al.
[ 1 00, 1 04, 1 05]. This parameter reflects the extent of the internal breakage by accounting for the total contact separations. However, it cannot be measured experimentally, as it is impossible to characterise the internal damage of a gran ule by counting the number of contacts. Alternative experimental measures have been used to characterise the extent of breakage, including mass loss per impact [92,95,1 06], and fragment size distribution [55,70, 1 00]. Generally, the failure extent of a granule at a given impact velocity, �, can be determined by gravimetric analysis based on the fractional-mass loss per impact �
= Mdebris
(1 1 ) Mf wh ere Mdebris is the mass of debris produced after impact and Mf the total mass of particles before impact. The extent of fracture can be assessed quantitatively by modelling the frag ment size distribution. In comminution, the Rosin-Rammler model has been widely used to describe skewed particle size distributions [1 07]. This two-para meter model is characterised by the mean size and width of the distribution. An alternative two-parameter equation is presented by Schuh mann [1 08], which is defined by distribution and size parameters. However, there is no significance to the size parameter in Schuhmann's model [1 09]. Gilvarry and Bergstrom [1 1 0] proposed an idealised three-parameter distribution function to describe the frag ment size distribution of brittle solids. This function was in good agreement with experimental results in the fine size region from 1 to 1 00 /lm, although it gave poor performance outside of this region . Similarly, Arbiter et al. [70] found only reasonable agreement in the fine sizes when the Gaudin-Schuhmann double logarithmic plot was used to describe the overall size distribution of glass fragments produced in double impact and slow-compression tests. Ryu and Saito [1 09] found a relatively good fit to both fine and course fragments when reviewing the Gaudin-Meloy-Harris equation, which states that the volume fraction, y', passing fragment size of x takes the following form: (1 2) where a, ß and Xo are the empirical parameters. However, this equation is not particularly favourable due to the large number of parameters required. Cheong et al. [1 1 1] used a two-parameter Weibull distribution equation to characterise the fragment-size distribution of impacted-glass spheres. The Weibull distribution was found to satisfactorily fit the fragment-size distributions and the fitted pa rameters were interpreted and able to distinguish between failure modes. Sim ilarly, Salman et al. [71 , 1 1 2] used Weibull distribution functions to characterise breakage of aluminium oxide and fertiliser granules, respectively. Rather than fitting the fragment-size distribution they characterised the extent of breakage as
1015
Breakage in Granulation
the number of damaged particles out of a hundred that were fired individually at a target using an experimental arrangement similar to that shown in Fig. 1 6. They plotted the number of unbroken particles, No, against impact velocity, v and fitted the following two-parameter Weibull distribution to the data: ( 1 3)
where c and m are the fitting parameters. A typical plot showing the fitted function to some experimental data is shown in Fig. 20. In equation (1 3), the parameter c corresponds to the velocity at which the failure probability is e- 1 ( = 0.368). This can be considered a measure of strength for the batch under the given loading conditions. The parameter m is related to the slope of the curve, and hence the distribution of strengths for the population of granules. It was found by Salman et al. [71] that m remained roughly constant over all angles (1 0°-90°) and granule sizes (3.2, 5, 7.2 mm) of fertiliser granules tested. In addition, they showed that m varied little for several other particles, including aluminium oxide and polystyrene. On the other hand c was found to be a good indicator of relative particle strength. Samimi et al. [1 1 3] also investigated the effect of impact angle on the extent of damage to agglomerates. In this case the agglomerates were from a synthetic detergent formulation and exhibited ductile failure rather than brittle failure in the case of the fertiliser granules of Salman et al. [71 ] . Here, a converse relationship between breakage and impact angle was found in that reducing the impact angle from 90° to 30° increased the extent of breakage. Samimi et al. [1 1 3] argue that this difference is due to the difference in the failure mode of their tested ag glomerates to those of other workers. In their case the predominant failure mode 1 00 t/J GI
1:: ("Il
U
a. c:::
�
0 ...
.c c::: :::J ....
0
...
GI .c
E
:::J z
90 80
70 60 50 40 30 20 10 0
0
5
10
15
20
25
im pact velocity m/s
30
35
Fig. 20. The n umber of u nbroken fertiliser granules (7.2 mm) out of each batch of 1 00 plotted against impact speed for impact angles from 90° (normal) to 1 0°. The data are fitted to a Weibull distribution function (equation 1 6) [71 ] .
1016
A . D. Salman e t al.
is ductile failure, which is sensitive to shearing, hence the more acute the impact angle, the greater the extent of breakage. 3.4. Variables affecting granule strength 3. 4. 1. Binder viscosity
Fu et al. [3] investigated the impact deformation and rebound of wet granules. The effect of binder viscosity on the coefficient of restitution is shown in Fig. 21 . This shows a monotonie decrease in the coefficient with increasing viscosity. They also found the contact ratio increased with increasing viscosity. The contact ratio is defined as the ratio of the maximum radius of the deformed contact region to the granule radius. For explanation they refer to the model of Lian et al. [1 1 4] in which the dependence of the coefficient of restitution on impact velocity, V, was expressed in terms of the Stokes number St, which is defined as follows for a sphere impacting a rigid flat plate: St = � 6rr.J1�
(1 4)
where m is the mass of the granule, J1 the viscosity of the binder and R the granule radius. They argue that given the Stokes number is the dominant pa rameter, the energy dissipated will increase with the viscosity of the liquid junc tion, and hence the coefficient of restitution will decrease with increasing binder viscosity. Fu et al. [50] measured the critical impact velocity as a source of estimating the granule strength, using granules made of Durcal 40 with glycerol of different 0.25 .....-----, 1:
0.2
CI)
=8() 0.15 '
c: o
2 �
0.1
CI)
Il: 0.05
500
1000
Binder viscosity. mPa s
1 500
Fig. 2 1 . Relationship between binder viscosity on the restitution coefficient at an impact velocity of 5.86 ms- 1 made from Durcal 1 5 (calcite) and a binder ratio of 0. 1 5 [3].
1017
Breakage in Granulation 20 ,-------,
� E 16
O! .!al ·E u
4 O +-----�r_----�--_.--� 1 600 1200 o 400 800 Binder viscosity (mPa s)
Fig. 22. The critical impact velocity as a function of the binder viscosity [50].
viscosity. The results (Fig. 22) show that the critical-impact velocity increases with binder viscosity, suggesting the granules made by higher viscosity binder to be stronger. This is most probably due to the ability of the more viscous binder to dissipate more kinetic energy upon impact. 3.4.2. Binder surface tension
Iveson and Utster [32] measured the dynamic-yield strength and coefficient of restitution of cylindrical agglomerates. They found that lowering the surface ten sion decreased the dynamic-yield stress of agglomerates (Fig. 23). They explain that this is due to a reduction in the capillary forces holding the primary particles together. However, they also found that the viscous effects will dominate over capillary forces in determining the strength of agglomerates. 3. 4. 3. Contact angle between binder and primary partic/e
Using a novel micro-force apparatus, depicted in Fig. 24, Simons et al. [1 1 5] investigated the primary particle and liquid interaction. They measured bridge geometry, contact angles and the forces exerted by axially strained liquid bridges of hydroxypropyl methylcellulose (HPMC) and polyvinylpyrrolidone (PVP) formed between two paracetamol crystals. They found that the formation of liquid bridges and their ability to bond the particles together depends on the wetting behaviour of the liquid on the particles. In particular, binders that de-wet the solid surfaces during separation were found to produce weaker adhesion forces. They note, however, that the effect of primary particle's geometry contributes some uncer tainty to the measurements. This is due to the geometry complicating contact
1018
A. D. Salman et al. 1 000 Sl&e. 8Inder . 31 11m. Watet 0 31 Ilm. Gly. 0 31 11m. NOSS • 19 11m, Water A 1 9 11m. NOSS
';:;) Q.
� � CI)
.t:; (J) �
">
CI)
1 00
'E
u
/Il C >.
0
'0 0.38
0.42
0.46 B l ndor Contenl
(mVmi)
0.50
0.54
Fig. 23. The dynamic yield stress VS. binder content or pellets made from two different sized ballotini with water, glycerol (Gly.) or NDBS surfactant solutions (adapted from [32]).
PEC input LVDT output
Optical folIower
(attachcd to control system incorporating a PEC and LVOT)
Fig. 24. Schematic of micro-force apparatus used to examine liquid bridges taken from Si mons et al. [1 1 51. (PEC, piezo-electric crystal ; LVDT, linear variable differential trans ducer).
angle measurements and measurements of the bridge contact perimeters, which are used to normalise the force measurements. Willett et 81. [1 1 6] investigated the effects of wetting hysteresis on the behav iour of liquid bridges. They argues that this contributes important complications that have largely been ignored in studies of liquid-solid contact angle. This effect describes the cases where the contact angle is greater than equilibrium when the liquid is advancing, but is smaller when the liquid is retracted. This typically arises when the wetted solid is not perfectly smooth or chemically heterogeneous. The effects of wetting hysteresis can lead to extended bridge rupture distances, and imply that capillary interactions are dissipative rather than conservative as is typically assumed.
1019
Breakage in Granulation
3. 4. 4. Primary particle size and shape
Fu et al. [3] investigated the impact deformation and rebound of wet granules. They found that the coefficient of restitution decreased with increasing primary particle size. Although it was acknowledged that the distribution of primary particle sizes can complicate experimental results, this effect was concluded to be due to an increase in interparticle contacts, and hence the density of interparticle forces, with reducing primary particle size. Similarly, Iveson and Utster [32] found a decrease in dynamic yield stress of agglomerates with an increase in primary particle size, when water is used as a binder (dark symbols in Fig. 25). They explained that decreasing particle size decreases the average pore size between particles and increases the volume density of interparticle contacts. This increases both capillary and interparticle fric tion forces, and thus explains why the yield stress increases when water is used as the binder. However, they also explained why there is no significant influence of particle size on the dynamic-yield stress when a more viscous glycerol was used as the binder (open symbols in Fig. 25). They explained the observation on the basis of the lubrication theory (equation (9)), which predicts the viscous force to dominate as interparticle space increases, thus increases the yield stress. 3. 4. 5. Porosity and structure
Subero et al. [1 1 7] developed a technique to produce agglomerates with con trolled bond properties and void distributions. Subero and Ghadiri [55] investi gated the breakage pattern of these agglomerates. They found that a high, local macro-void density results in a weak local structure. Impact near this region causes extensive local disintegration. However, the disintegrated zone spreads out, producing a 'cushioning' effect that reduces the level of stresses transmitted to the remainder of the material. This leads to a breakage pattern where the 1000 �
�
�
� ..
�
(1)
�
�
+
��
�, ��w..
..
& 0.4110 """f wat.
1 00
0 0.441 """f Glycerol
> .1<
A 0.490 """f Glyeerol
�
�
��r
10
0
10 20 30 40 60 Specific Surface Uoen ParticIQ SIZ8 (mtcron!O)
Fig. 25. Dynamic yield stress vs. surface-mean particle size for glass ballotini with water and glycerol binders (adapted from Iveson and Litster [32]).
A. D. Salman et al.
1 020
agglomerate largely remains intact apart from the localised impact zone. Con versely, if the macro-void number and size are low, the local structure is strong. This structure can transmit loads into the bulk of the agglomerate, increasing the possibility of crack propagation. Samimi et al. [95] studied the impact breakage of two types of detergent gran ules from different processes and exhibiting different structures. One type was more spherical and denser, and the other type had a more cauliflower-type structure and was more porous. In general, it was found that the former exhibited less breakage than the laUer. Golchert [1 1 8] also studied the compression fracture of two granules with dif ferent structures experimentally and using DEM [1 1 9]. The first had a spherical structure and the second was somewhat irregular. They found that the irregular granule shaUered under low-compression displacement, whereas the spherical granule remained intact, with fracture along particular planes. They found that the irregular granule exhibited much more non-uniform loading than the spherical granule that prevented breakage from proceeding along fracture planes. Fu et al. [50] found that the critical-impact velocity decreases with increased fractional interstitial voidage, suggesting that the granule strength decreases with higher porosity. 3. 4. 6. Binder content
Schubert [58] investigated the relationship between tensile strength and wet-gran ule saturation. He argued that the relationship between saturation and tensile strength would change, depending on the granule state as described by Kapur [60]. The characteristic relationship is shown in Fig. 26. In this case, Sp denotes the end of the pendular state, and Sc the start of the capillary state. The pendular state describes where the binder forms discrete lens-Iike rings (liquid bridges) at the point of contact between particles, leaving air as a continuous medium. The capillary state describes the completely saturated granule. Tensile strength is expected to increase consistently with increasing saturation in the furnicular state (Sp < S< Sc)
1
o
•
Sc
1
Saturation, S
Fig. 26. Relationship between tensile strength, Schubert [58]).
(I/,
and wet granule saturation, S (after
Breakage in Granulation
1 02 1
as both bridge bonding and bonding caused by regions filled with liquid contribute to the tensile strength. This is consistent with the theory of Rumpf [57] (see Section 3. 1 . 1 ). In addition, the tensile strength is then expected to decrease at high levels of saturation as the material becomes a paste. Schubert [58] found reasonably good agreement between experimental observations and this hypothesis. More recently, Fu et al. [3] investigated the impact deformation and rebound of wet granules. They found that increasing binder content of granules made fram calcite and polyethylene glycol 400 resulted in kinetic energy dissipation on im pact, leading to a reduction in the coefficient of restitution. In addition , the Young's modulus is likely to decrease with increasing binder ratio. In the work of Iveson and Litster [32], they examined the dynamic-yield strength of cylindrical pellets made fram either 1 9 or 3 1 11m ballotini with water, glyceral or surfactant binders. They found that with glycerol as the binder, increasing binder viscosity fram 0.001 to 1 Pa s greatly decreased the amount of pellet deformation. They also explain that this is due to an increase in viscous dissipation. However, they also suggest that the effect of binder content is complex. With water as a binder, at low-mois ture contents, increasing the amount of water increased the yield strength. How ever, at higher moisture contents, increase in the amount of water resulted in a reduction of the yield strength. Whereas, with glyceral as a binder they found that increasing binder content always resulted in yield strength increase thraugh the range of conditions studied. They argue that this complex behaviour is a result of a balance between the three forces of interparticle friction and capillary and viscous forces. As discussed in Section 3. 1 , these forces all resist granule deformation. However, Iveson and Litster [32] discuss that increasing-binder content can in fluence the contribution of these forces. For example, increasing-binder content can reduce interparticle friction by lubrication, whereas capillary forces are in creased up to the saturation point. In addition viscous forces should be increased as more binder is required to be squeezed from between primary particles. They suggest that for low-viscosity binders, an increase in binder content will increase the capillary forces and hence the yield strength of the agglomerate. However, lubrication effects eventually dominate, resulting in a decrease in strength at high binder contents. For higher viscosity binders, the viscous forces dominate, and hence an increase in binder content will increase the agglomerate-yield strength (up to a point, at wh ich the agglomerate becomes a slurry).
4. MODELLING OF B REAKAGE 4. 1 . Predict the conditions for breakage
Little has been done to predict the conditions for granule breakage, or the in fluence of operating and formulation praperties on wet-granule breakage. The
1 022
A. D. Salman et al.
work by Tardos et al. [1 8] is one of the first to estimate the physical conditions at which wet granules will break during granulation. Tardos et al. [ 1 8] consider that in order for the granules to break in the shear fields, the collisional kinetic energy of the granules must exceed the internal energy of the granules required for breakage. A dimensionless Stokes number has derived to describe this breakage condition where
Stdef _ -
externally applied kinetic energy . energy reqUIre d for d eformat·Ion mp u� Stdef = 2 VpT(Y)
( 1 5)
where mp is the granule mass, Vp the granule volume and Uo the relative granule velocity. St�ef is the critical value of Stokes number, which must be exceeded for breakage to occur. T(Y) is defined as the characteristic stress in the granule, which they assume which can be postulated according to Herschel-Bulkley model (1 6) where Ty is the yield strength, k an apparent viscosity and n the flow index. The model assumes a wet granule is complex system possessing both yield strength and some non-Newtonian behaviours. Assuming both simplified ca ses in which the apparent viscosity (T(Y) = Ty) and yield strength (T(Y) = Ty + kyn) are neg ligible, the model predicts that the granules will break after it reaches a critical size during granulation and this critical size will decrease with increasing shear rate. They measured granule deformation and breakup under shear in an agitated fluidised-bed granulator, which they found that granules first elongated under shear and then broke at a Stokes deformation number of 0.2. This model as sumes that granule breakup is mainly induced by shear, but it was argued by Iveson et al. [8] that in the case of mixer granulation, the granules may break upon impact with the impeller and chopper rather than in shear. They expect that the 'critical stress' for granule breakage is to be determined by the dynamic yield stress measured under high-strain rate conditions. Iveson et al. [8] then derived a similar Stokes deformation number, except that the shear stress is being replaced by the dynamic-yield stress as discussed in Section 3.4.4. They also established the relationship between growth behaviour and pore saturation and deformation number on a growth regime map as shown in Fig. 27. This regime map is useful when used to compare the behaviours of materials with similar binders in the same granulator, but not for comparing materials formu lations with dramatically different binder viscosities or materials in different types
1 023
Breakage in Granulation
1
"Dry"
F�O�g ;
0.1
Powder;'
Increasing Deformation Number,
Slunyl Over-Wet Mau
"Crumb"
. . . • . . .
:..........•...
Steady Growth Incre88lng Growth Rate
Nucleatlon Only
Stdef = 2 pgUc 12Yg
'� f(StJ
:.- - . . L
_ _ _ _ . _ _
Inductlon
: Decreasmg )nducti)n Time ,
o
1 00%
Maximum Pore Saturation,
smax = Wps(1-EmlrJlP/Emln
Fig. 27. Proposed modified regime map. The n ucleation-to-steady g rowth boundary and steady-growth-to-induction-growth boundaries are functions of 8t and there is no distinct rapid g rowth regime.
of granulators. This is demonstrated in Iveson et al. [8] when they tried to compare the high shear and drum granulators. Despite this, the regime map technique is pioneering and looks promising in predicting granulation behaviours if the required physical properties on the regime map can be pre-measured with confidence. Keningley et al. [21 ] also developed a strain criterion, which describes whether a wet granule will break or survive in high-shear granulation, depending on the amount of strain resulted from the compression during the impact. Assuming that granule deformation depends on the pressure loss through the flowing viscous fluid between particles upon impact, the collisional kinetic energy can be equated to the plastic deformation energy of the granule to obtain the following: 1 c3 PDuo d3,2 2 (1 7) cm 540 1 2 J1 c -
-
where Cm is the maximum compressive strain, c the granule porosity, P the gran ule density, Uo the granule impact velocity, d3, 2 the sauter mean diameter and J1 the binder viscosity. They mentioned that the granules will break when the maxi mum strain, Cm , exceeds 0. 1 . This model allows a plausible interpretation of the effect of binder viscosity and primary particle size on the ability to form granules during high-shear granulation (Fig. 28) and the predicted boundary by the model is shown to be reasonably consistent with the experimental data. These two approaches have certainly looked promising to be used for pre dicting purposes. However, the nature of these models means that a significant amount of effort is required to accurately measure the physical properties of the granules, which can be heterogeneous in nature.
1 024
A. D. Salman et al.
�
UI
.. E
Q..
1 .000
..
CI 'C C
10
CD
1� o
__����
�
__ __
50
�______�__� �__��
__ __
1 00
1 50
200
250
Median Size ( microns ) of the C on stitu ent P.rtioles Fig. 28. Binder viscosity vs. median particie size showing regions i n which granules did and did not form for agglomeration of glass baliotini with silicone oils in a high-shear mixer. Line shows prediction of equation (adapted from Kenningley et al. [21 ]).
4.2. P rocess scale: population balance modelling
Population balance equations (PBEs) have been used in many branches of sci ence and engineering to relate observed distributions of properties to the rates of the underlying processes that change those distributions [1 20-1 23]. It is o!f no surprise, therefore, that they have been used in granulation studies for many years. A PBE is an expression of number continuity and can be expressed as [1 22] an(v, f) =B_D at
( 1 8)
where B and 0 are the sources of creation and destruction, and v the size of the granules. In general, the use of PBEs to study granulation systems has been to reduce the mass of experimental size distribution data into an empirical rate con stant describing the net-aggregation rate. In such a case, the PBE can be written as [14] an(v f) m
'-
1
100
1 v d 2 0 ß(v - e, e)n(t, v - e)n(t, e) u - n(v, f) 0 ß(t, v, e)n(t, e)du
=-
( 1 9)
where ß is the aggregation kernel or rate constant. ß is also time-dependent, and dependent on the sizes of the colliding granules, v and e. ß can be decomposed into a size-dependent and time-dependent parts [5] ß(V, e, t) = ßo(f) · ß*(V, e)
(20)
1 025
Breakage in Granulation
Given a size-dependent aggregation kernei, ß, the aggregation rate constant, ß, can be found using experimental granule size distribution data by solving the inverse PBE [121 , 1 24]. A number of size-dependent aggregation kerneis that have been used are shown in Table 1 . The selection of the size-dependent aggregation kernel can be informed from a physical understanding of the process, although typically a 'best fit' approach is adopted. Adetayo and Ennis [125] argue that even if a good fit is found, there is no certainty that it is the best fit or has any physical basis. There is a large volume of experimental evidence showing that aggregation is not the only mechanism at work during the granulation process. Therefore, a PBE that only considers aggregation rate, and only dependent growth will ulti mately have a tenuous physical basis. Breakage rates can be incorporated into the PBE by adding breakage source and sink terms to equation ( 1 9)
(OO
an(v t) 1 r ß(v - s, s)n(t, v - s)n(t, s)du - n(v, t) o = 2. ----iJ Jo
+ 100 b(v, ß)S(t, s)n(t, s)ds - S(t, u)n(t, v)
ß(t, v, s)n(t, s)du (21 )
where S i s the selection rate constant, which describes the rate of breakage of particles of a given size, and can also be considered time-dependent. This time dependence can incorporate the expected densification of granules with extended granulation time, which will lead to stronger granules, and hence a Table 1 . Summary of physical aggregation kemels [1 26]
Kernel ß (v,v) 1 v+v 1 /3 + v1ß (v 1 /3 + V1 /3 ) (v - v 3 + V- 1 /3 ) (v 1 /3 + V1 /3 )2 tJ
V(� +�) (v 1 /3 + V1 /3 f VG + �)
Name Size independent Sum Orthokinetic Perikinetic EME EKE
Basis Size independent
Reference
Coagulation of rain drops Shear RandomjBrownian motion Equipartition of momentum Kinetic theory of gases Equipartition of kinetic energy
[148] [1 47] [147] [1 23] [14]
1 026
o Fig. 29. Bimodal breakage model [ 1 4].
A. D. Salman et al.
0 0 0 00 ° 0 000 o
0 0 o
Fine fragments,
mode 1
Coarse fragments mode 2
reduction in breakage (see Section 2.3.9). The breakage function, b, describes the sizes of the fragments from the breaking particle. Hounslow et a/. [14] point out that time is an unsatisfactory correlating variable for modelling at any rate process, as the fact that any rate constant seems to depend on time is evidence that some physical property of the system is also varying with time. Salman et a/. [71 ] discuss that the breakage rate should be a function of a number of granule properties that affect granule strength. As shown in this review, a number of granule properties that affect strength typically change with granulation time, such as porosity. Inclusion of these additional properties into the PBE increases the difficulty of solving in addition to the increased quantity of experimental data required for validation and fitting, as discussed by Reynolds et a/. [1 26]. However, the use of a one-dimensional PBE with aggregation and breakage terms in order to find breakage rates in a high-shear granulator has been pre sented by Hounslow et a/. [14] . A multiphase-discretised population balance model was constructed in order to extract breakage rates from tracer experi mental data presented in Pearson et a/. [ 1 2]. Examining the distribution of dye 1 min after adding a tracer sampie, they deduced a bimodal breakage model as shown in Fig. 29. The model describes a breaking granule producing many fine fragments of the small size, and a few fragments of the large size. By fitting two truncated log-normal distributions to the tracer mass distribution after 1 min, they obtained b, the breakage function. For the aggregation size-dependence they used the EKE kernel (Table 1 ) . They admiUed that, in part, that this selection was based on improved fitting. However, they argued that it was significant that this choice of kernel was capable of describing not only the granule-size distribution but also the tracer mass distribution, in particular when the tracer was added in narrow-size ranges. They also found with this selection of aggregation kernel that the aggregation rate constant was only very weakly time-dependent. They pro posed that this selection of aggregation kernel may have been a suitable choice because small-Iarge aggregation events are preferred in this system. However,
1 027
Breakage in Granulation
verification of this was left open for further analysis. From this model, they ob tained the following rate constants. Se t, f)
= 0.025 exp (- t -2�80) S-1
ßo (t) = 1 .30
x
1 0 -9 - 6
x
(22a)
-
1 0 - 1 3 (t 480) kg S - 1
(22b)
The selection rate constant was found to be very strongly time-dependent, starting high and rapidly becoming negligible. Hounslow et al. [14] suggest that this must be a consequence of the changing properties of the granules, and propose a 'heterogeneous strength' hypothesis. This argued that within any size class there exists a distribution of strengths. When tracer granules are added, the weaker granules rapidly break leaving only a strong, non-breaking residue. Sanders et al. [1 27] use a DPB to model the size distribution of a pharma ceutical high-shear granulation experiment. In this case, an aggregation only model was used with the EKE kernel used for the size dependence (Table 1 ). They determined the aggregation rate constant for experiments conducted at several different impeller speeds. A summary of their results is shown in Fig. 30. This shows an increase in the aggregation rate constant with impeller speed up to 350 rpm, followed by a reduction. This is similar in a sense to the change in mean granule size with impeller speed observed by Knight et al. [7] (Fig. 2). Again, following the argument that at high-impeller speeds the granule breakage mech anism becomes increasingly important, it can be expected that a drop in mean 12 ,------, •
10 • •
•
2 O �������-L� 200 250 350 300 400 450 500 impeller speed (rpm)
Fig. 30. Relationship between fiUed aggregation rate constant and impelier speed in an aggregation only PBM [ 1 27].
A. D. Salman et al.
1 028
granule size will be observed. Because the model of Sanders et al. [1 27] only includes aggregation, any effects of breakage will be absorbed into the aggre gation rate constant and appear to suppress the true rate constant. Essentially the reported aggregation constant is actually a net rate constant, and so the increasing role of breakage exhibits as a reduction in the fitted rate constant. A similar approach to Hounslow et al. [14] to determine breakage rates in fluidised-bed melt granulation has recently been presented by Tan et al. [1 5]. They developed a refined breakage function that describes the breakage event to form two large fragments and some primary particles. The fraction of the breaking granule that forms primary particles is fitted as the parameter z, or the attrition constant. The remaining mass fraction is then determined by random binary breakage. The breakage function is given as 6x2 f3 (23) b(x, l) = zfo(xL -2 + (1 - Z) 7 2 '0 (10 + 3 0"0 ) where 0"0 is the standard deviation of the primary particle size distribution. The basis for the proposed breakage function was photographic evidence of tracer granules and the tracer mass distribution taken from the tracer experiment. They found the presence of both large tracer fragments and tracer primary particles in product granules after the addition of a tracer sampie. Using this breakage model and an EKE aggregation kernei, they were able to successfully predict the gran ules size distributions and tracer mass distributions. They found the selection rate constant, So, to be independent of size and time. The modelling techniques are subsequently used to model a series of fluidised bed melt granulation conducted at various operating conditions. A series of se0.010
1 .2
1 .0
'", '"
b
�
0.6
0.4
�
0.2
0.0 (a )
I �
0.8
24
28
32
0.008
CI) Cl c:
�
Cl c: ""
,
a; E
�
�
N
0
i
36
2
E 40
44
0.006 0.004 0.002
48
CI) Cl c:
0.000
24
�
i
28
Cl
�
! 32
a; E
� 0
36
40
44
48
(b)
Fig. 31 . Influence of bed temperature on the breakage selection rate constant, So" and attrition constant, Z [1 28].
1 029
Breakage in Granulation
lection rate constants, attrition constants and aggregation rate constants were extracted and expressed as a function of individual operating conditions, forming a series of rate constant plot. The results look promising in revealing the de pendence of breakage rate on operating conditions, with two of the examples presented in Fig. 31 . It can be clearly seen that breakage selection rate (So) and the attrition constant (z) decreases with increasing bed temperature. This is at tributed to the stronger granules formed at higher bed temperature due to the slower binder solidification rate which allows the particles to move and pack closer as the binder remains molten for a longer period. This work clearly sug gests that the granule breakage rate can be quantified with sound physical basis and can be used to enhance the understanding of operating conditions on granule breakage during granulation. Biggs e t al. [1 0] present an alternative method of including breakage in a population balance model. They used a fluidised-bed granulator configuration where melted polyethylene glycol 1 500 was sprayed onto cool glass ballotini. They measured the mean granule size change with time during and after spraying (see Fig. 32). After spraying they noticed a decrease in mean granule size. They found that the relationship between the granule mean size and distribution standard deviation was the same during and after spraying, and hypothesised that the observed breakage process was the reverse of the growth process. This argument suggests that the granules break into the granules that were used to form them. They used a PBE of the form of equation (14), but included two aggregation rate constants as folIows: t � tspray off
(24)
t> tspray off
During spraying the aggregation rate constant was modified by the negative rate constant, and after spraying only the negative rate constant was used. They observed an exponential decrease in mean size after spraying (see Fig. 32) and so used an exponential model with characteristic time constant, in this part of the process. They used the EKE size-dependent aggregation kernel (see Table 1 ). The PBE was solved using the discretised population balance model of c,
0. 8 ,.-_ _ _ _ _ _ .---,
0.8 ,.-----�--...__,
'[ 0
0.6
;;;: .. Cl
0.2
,/'
�/ o
tJ. , � , .
0.6
0. 4 �.-�Jk�·A·lI;X-� � ...
250 500 750 1 000 1 250 1 500 Time(s)
�
o
0. 2
i
' �.fj.
f>., 4 -" ..- ....�.
,.
.
500
1000 1500 Time (s)
2000
o
500 1 000 1500 2000 2500 3000 Tlme (s)
Fig. 32. Comparison between model ( - ) and experimental ( . ) results of the mean granule size during ( 6 ) and after spraying (.) in a fluidised-bed granulator for liquid to solid ratios of (a) 0.05, (b) 0. 1 , and (c) 0.2 [ 1 0].
1 030
A. D. Salman et al.
Hounslow et al. [1 29]. Their modelling results presented in Fig. 32 show good agreement with the experimental results during the spraying of binder. However, discrepancies are found in the 'spray off' breakage regime. This approach rep resents a fairly straightforward way of including breakage in a PBE of a gran ulation process. However, there are problems with this approach as aggregation is a second-order rate process, and breakage is a first-order rate process. Therefore, trying to model breakage as a negative aggregation rate process is fundamentally flawed and will not succeed with any physical basis.
4.3. Micro scale : d iscrete modelling
Recently, computer simulation has been used to study the evolution of impact breakage for particulate systems. This is because the same granules can be tested repeatedly and information about different impact parameters at any in stant of time can be retrieved as required. Furthermore, computer simulation offers the advantage of revealing information, such as different energy dissipation or load transmission paths within a granule under impact that is not accessible through physical experiments. One example of the force transmission paths is shown in Fig. 33 [1 30], which iIIustrates the force transmission through the ag glomerate when the wall force is 6.5 mN. The lines show the location and ori entation of the (resultant) contact forces and its thickness indicates the
Fig. 33. Force IransmISSIon mrougn me granUles upon ImpaCl wnn me wall l l "UJ.
1 031
Breakage in Granulation
magnitude of the force, scaled to the current maximum. It is c1ear from this graph that larger forces are generated at the impact point near the wall . Unlike homogenous materials such a s steel, the granular medium exhibits discontinuous material structure with interaction occurring at interparticle con tacts only [ 1 3 1 ] . Hence, DEM is a suitable tool to study the macroscopic response of a particulate system, which depends on the discrete behaviour of its constit uent primary particles. Impact breakage of granules is one of the examples of application of DEM simulation. The evolution of granule impact is mode lied as a dynamic process by tracing the motion of the granule's constituent particles throughout the impact event using Newton's law of motion. The resulting particle motion is influenced by the interaction at the interparticle contacts. The simulation is advanced over a large number of small-time steps and the particle motion is updated continually. This methodology was initially proposed by Cundall and Strack [1 32]. Attempts to study granule impact breakage were initiated at Aston University by incorporating well-established particle interaction laws into the methodology of Cundall and Strack [1 32]. The DEM code at Aston code is capable of simulating the interactions between elastic, spherical, frictional and auto-adhesive particles. The earlier version of the code by Thornton and Yin [1 33] considered only elastic deformation at the interparticle contacts. Plastic yield was accounted for in the subsequent version developed by Thornton and Ning [1 34]. There are two types of force-displacement relationships according to the model in the Aston code namely normal and tangential interactions. For auto adhesive particle, the normal force-displacement relationship due to the pres ence of surface energy is determined using the theory of Johnson et al. [1 35]. This is an extension of Hertzian elastic contact mechanics that predicts the nor mal force increment, AP, as a result of an increase in the relative approach between two elastic spheres, Aa, as folIows: AP =
2E*a
[
]
3 jP' - 3 vPc 3 jP' - vPc
Aa
(25)
where E* is the effective elastic modulus, a the radius of the contact area, pr the effective Hertzian force and Pe the pu li-off force. The model for the tangential interaction is a combination of the theories of Mindlin and Deresiewicz [1 36] and Savkoor and Briggs [1 37]. According to Thornton and Yin [1 33], sliding between two contacting spheres must be preceded by a 'peeling' action, which causes a reduction in the contact areas of the spheres. Several researchers have used the Aston code to perform computer simulation of granule impact breakage against a target wall [91 , 1 00, 1 01 ,1 38, 1 39]. The recent review of Mishra and Thornton [98] reported that there were five factors governing the breakage behaviour of granules under impact. These factors were impact
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A. D . Salman et al. 0.5 rn/sec
•
1 .5 m/see
Fig. 34. Fracture pattern at different impact velocities; solid tractions = 0.602. On the right-hand side, the top two images show views below the agglomerate, while the lower two images show views trom above (Adapted trom Mishra and Thornton [98]).
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Breakage i n Granulation
velocity, bond strength (interface energy), granule porosity, particle contact density and the local structural arrangement of particles near the impact region. Inves tigating the combined effects of impact velocity and porosity, significant breakage was found to occur when the impact velocity exceeded a certain threshold value. Figure 34 shows a set of snapshots taken after the impact of the densest ag glomerate 4Y = 0.602 with the wall at different impact velocities. The upper two snapshots shown on the left-hand side of the figure shows that little breakage is observed up to an impact velocity of 1 ms� \ while the agglomerate exhibit clear evidence of fracture planes at impact velocities of 1 .5 and 2.0 ms� 1 . Once break age took place, dense granules always fractured while loose granules disinte grated. Granules with intermediate porosity exhibited mixed-mode failure where both fracture and disintegration were possible. Furthermore, they compared the breakage behaviours between similar granules, one with more particle contact density than the other. The granule with higher contact density fractured in contrast to disintegration shown by the granule with lower contact density. It was postulated that significant amount of stresses were transmitted through the bulk of the granule with higher contact density storing sufficient elastic energy for fracture. One of their findings suggested that different breakage patterns could be obtained when dif ferent granule surface was subjected to impact. This was due to the difference in local particle arrangement near the impact location. collisional contact with wall
collisional contact between particles
Fig. 35. A collision between two macroscopic particles showing the division of the particles i nto elementary triangles and examples of collisional and glued contact (adapted from Potapov and Campbell [ 1 4 1 ]).
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A. D. Salman et al.
Using the same code, Kafui and Thornton [140] simulated the collision between a pair of similar granules in order to understand the fragmentation process due to this impact arrangement. They proposed that the number of broken bonds within the granules and the amount of fines generated were proportional to a dimen sionless group, which accounted for the system properties. A slightly different approach was adopted by Potapov and Campbell [141] to represent an elastic solid by glueing polyhedral elements together. A particle in this case is viewed as a composite material glued together by many elements of known stiffness. An example of two contacting particles is shown in Fig. 35. The glue at the interface between two elements in a particle could withstand certain tensile stresses before it breaks, and the point of joint separation represents the formation of a crack. The corresponding energy released is then equivalent to the potential energy stored in that portion of the joint. For particle collision, the con tacting forces are accounted for by the normal and the tangential elastic force characterised by a normal and tangential stiffness. Using this modified technique, correlation between the breakage patterns of an elastic solid and different frac ture mechanism was established. 4.4. Micro scale: continuum modelling
A key problem with DEMmodelling of granule deformation and failure (see Sec tion 4.3) is the inclusion of the effect of binder. An alternate modelling approach considers granules as continuous bodies that can be specified in terms of a material model, representing the bulk deformation behaviour, and boundary con ditions that define the frictional and adhesive interactions [142]. Elastic materials exhibit restitution coefficients approaching unity, whereas wet granules typically exhibit restitution coefficients below 0.2 [3]. In this case, granules are generally considered to deform elastoplastically. Johnson [143] presented a theoretical model for the contact of an elastic-perfectly plastic sphere with a rigid wall . His model was based on fully developed plastic loading and perfectly elastic unload ing. Thornton et al. [144] refined this approach by defining a limiting contact pressure and approximating the evolution of the normal contact pressure distri bution by an elastic phase during which the pressure distribution was described by a truncated Hertzian pressure distribution. Unloading was considered to be elastic, but with a reduced contact curvature as a result of the irrecoverable plastic deformation. However, neither of these models considers the curvature a variable during loading. Li et al. [145, 1 46] used finite element analysis to examine the impact of non-adhesive elastic-perfectly plastic spherical particles. They found that the computed coefficients of restitution as a function of the impact velocity were intermediate between those predicted by the models of Johnson [1 43] and Thornton [144], although the differences were relatively small. Adams
Breakage in Granulation
1 035
et al. [142] suggests that this is probably because the cases investigated did not exhibit substantial elastic strains. Of particular interest in the modelling of granule interactions is the effect of binder at the interface of two colliding particles/granules. An attempt to model the influence of viscous liquid on particle collisions has been presented by Lian et al. [1 1 4]. Here, they developed an approximation to the elastohydrodynamic collision between two spherical solids with an interstitial incompressible Newtonian fluid of constant viscosity. They assumed a Hertzian-like profile for the elastic deforma tion, and developed a c1osed-form solution capable of predicting the evolution of relative particle velocity, force and restitution coefficient.
5. CONCLUSIONS
Experimental studies at the process scale have been able to investigate granule breakage using tracer particles. However, analysis of these results invariably requires removal of sampies for analysis, which can alter the properties of the granules in addition to increasing the quantity of work required to characterise a given set of conditions. Further work in this area in the future should concentrate on online sampling and analysis. By measuring particle size, shape and tracer concentration online, more detailed information about the breakage process can be obtained. At the single granule scale, characterisations of pre-product granules are re quired. A lot of the reviewed experimental work is based on measuring the strength, for example, of granules as products. These tend to be large, with well consolidated structures. It is unlikely that this type of granule is representative of the granules that are undergoing breakage during the process. In order to using single granule scale observations to inform our understanding of the breakage rate process, this needs to be addressed. The size of sampled granules needs to be reduced from, for example 5 mm, down to something more representative of the early stage of granulation. The work of Hounslow et al. [14] (see equation (21 )) shows that the breakage rate is highest in the early stage of granulation, and granules from this stage of the process should be characterised. In addition to this, there is a lot of characterisation of individual granule breakage against solid surfaces. It is expected that granule/granule interactions are an important part of the breakage process, and the resulting breakage behaviour from these types of interactions deserves more investigation. Already, interesting micro-mechanical work is being conducted to characterise the strength and breakage of sub-granule components, such as liquid bridges. This can be extended to characterise other types of bonds and to relate these to the bulk granule properties.
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From the modelling perspective, more rigorous inclusion of breakage rates in PBM will require multi-dimensional models capable describing breakage de pendence by relevant granule properties, such as binder composition, rather than only size and time. Time-dependent breakage rates can implicitly include other breakage dependent properties, that happen to also change with time, such as porosity, but more physically based breakage rates will require these properties to be included in the PBM. Modelling of the single granule and sub-granule scale requires the key weaknesses to be addressed. In particular, DEM fails to ad equately model realistic interparticle bonds, and there is the need for incorpo ration of interstitial liquid. Overall, the importance of breakage during the granulation process has in creased in its perceived importance. Understanding in more detail, the role that breakage plays in the granulation process to distribute components and structure granules will allow better control and design of granular product properties in the future. REFERENCES [ 1 ] S . M . Iveson, Chem. Eng. Sci. 56 (200 1 ) 21 75-2220. [2] K. van den Dries, O . M . de Vegt, V. Girard, H. Vromans, Powder Techno! . 1 33 ( 1 -3) (2003) 228-236. [3] J . Fu, M . J . Adams, G . K. Reynolds, AD. Salman, M.J. Hounslow, Powder Techno!. 1 40 (3) (2004) 248-257. [4] C. Capes, P. Danckwerts, Trans. ! . Chem. Eng. 43 ( 1 965) T1 1 6-T1 24. [5] K. Sastry, S. Panigraphy, D . Fuerstenau, Trans. Soc. Min. Eng. 262 ( 1 977) 325-330. [6] B. Ennis, J. Utster, Particle Size Enlargement. Perry's Chemical Engineers' Hand book, in R. Perry, D. Green (Eds.), McGraw-Hill, 7th edition, New York, 1 997, pp. 20-89. [7] P.C. Knight, A Johansen, H . G . Kristensen, T. Schaefer, J . P . K. Seville, Powder Techno!. 1 1 0 (3) (2000) 204-209. [8] S . M . Iveson, J . D . Utster, K. Hapgood, B.J. Ennis, Powder Techno!. 1 1 7 ( 1 -2) (2001 ) 3-39. [9] P. Vonk, G. CPF, J.S. Ramaker, H . Vromans, N .W.F. Kossen, Int. J. Pharm. 1 57 ( 1 997) 93-1 02. [ 1 0] C . Biggs, R. Boerefijn , M . Buscan, A Salman, M . Hounslow, World Congress on Particle Technology, Sydney, Australia, 2002. [1 1 ] J.S. Ramaker, MA Jelgersma, P. Vonk, NW.F. Kossen, Int. J . Pharm. 1 66 ( 1 998) 89-97. [ 1 2] J . M.K. Pearson, M.J. Hounslow, T. Instone, AIChE J 47 (9) (2001 ) 1 978-1 983. [ 1 3] H . S . Tan, A D . Salman, M . J . Hounslow, Chem. Eng. Sci. 60 ( 1 4) (2005) 3835-3845. [ 1 4] M . J . Hounslow, J . M .K. Pearson, T. Instone, AIChE J 47 (9) (2001 ) 1 984-1 999. [1 5] H . S . Tan, A D . Salman, M . J . Hounslow, Powder Techno!. 1 43-144 (2004) 65-83. [1 6] DN Mazzone, G . ! . Tardos, R. Pfeffer, Powder Techno! . 51 ( 1 ) ( 1 987) 71-83. [1 7] B.J. Ennis, G. Tardos, R. Pfeffer, Powder Techno!. 65 ( 1 -3) ( 1 99 1 ) 257-272. [ 1 8] G . ! . Tardos, M . Irfan-Kahn, PR. Mort, Powder Techno! . 94 ( 1 997) 245-258. [ 1 9] H . Eliasen, T. Schaefer, H . Gjelstrup Kristensen, Int. J. Pharm. 1 76 ( 1 ) ( 1 998) 73-83.
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[ 1 37] A.R. Savkoor, G.A. D . Briggs, Proc. R. Soc. London Sero A 356 ( 1 684) ( 1 977) 1 03-1 1 4. [1 38] C. Thornton, K.K. Yin , M.J. Adams, J. Phys. D (App!. Phys.) 29 (2) ( 1 996) 424-435. [1 39] K.D. Kafui, C. Thornton, Powder Techno! . 1 09 ( 1 -3) (2000) 1 1 3-1 32. [ 1 40] K. Kafui, C . Thornton, Fifth World Congress of Chemical Engineering, San Diego, California, USA, 1 996. [ 1 4 1 ] AV. Potapov, C.S. Campbell, Powder Techno!. 8 1 (3) ( 1 994) 207-2 1 6 . [1 42] M . J . Adams, C . J . Lawrence, M . E . D . Urso, J . Rance, Powder Technoi. 140 (3) (2004) 268-279. [1 43] K. Johnson, Contact Mechanics, Cambridge U niversity Press, Cambridge, 1 985. [1 44] C . Thornton, J . Appi. Mech. Trans. ASM E 64 (2) ( 1 997) 383-386. [1 45] L. Li, C. Thornton, C. Wu, Proc. Inst. Mech. Eng . , Part C J. Mech. Eng. Sci. 2 1 4 (8) (2000) 1 1 07-1 1 1 4. [1 46] L.-Y. Li, C.-Y. Wu, C . Thornton, Proc. Inst. Mech. Eng . , Part C J . Mech. Eng . Sci. 2 1 6 (C4) (2002) 421-43 1 . [1 47] M . Smoluchowski , Mathematical Theory of the Kinetics of the Coagulation of Colloidal Solutions. Zeitschrift für Physikalische Chemie 92 ( 1 9 1 7) 1 29. [1 48] A Golovin, Soviet Physics-Doklady 8 ( 1 963) 1 91 -1 93.
CHAPTER 22 F l u i d isat i o n of Co hes ive Particles J onathan P . K. Sevi lle *
Gentre for Formulation Engineering, Department of Ghemical Engineering, University of Birmingham, Birmingham B15 2TT, UK Contents 1 . Basic aspects of fluidisation 1 . 1 . Introduction 1 .2. Pressure drop through packed beds 1 .3 . Minimum fluidisation velocity 1 .4. Particle and fluid properties 1 .5. Slugging 1 .6. Distributor design 1 .7. Bubbling and solids circulation 2. Types of fluidisation 2. 1 . General description of group behaviour 2. 1 . 1 . Group B 2.1 .2. Group A 2 . 1 .3. Group G 2.1 .4. Group D 3. I nterparticle forces 3.1 . Van der Waals forces 3.2. Liquid bridges 3.3. Sintering 4. The effects of cohesive forces 4. 1 . Effects of "natural" cohesion - Van der Waals forces 4.2. Effects of liquid bridges 4.3. Sintering 5. Conclusions Acknowledgements References
1 04 1 1 04 1 1 043 1 044 1 046 1 047 1 048 1 049 1 05 1 1 056 1 056 1 057 1 057 1 058 1 058 1 058 1 059 1 06 1 1 062 1 062 1 063 1 065 1 067 1 068 1 068
1 . BASIC ASPECTS OF FLUIDISATIO N 1 . 1 . I ntroduction
A fluidised bed is formed by passing a fluid, usually a gas, upward through a bed of particles supported on a distributor (Fig. 1 ). As the fluid velocity is increased, *Corresponding author. E-mail:
J . P. [email protected]
Granulation
Edited by A.D. Sa/man, '
M.J.
Hounslow and J. P. K. Seville
(' 2007 Elsevier B.V All rioht� ",�"rv"rl
1 042
J. Seville
Bed weight per unit area, W/A Minimum fluidisation velocity , Umf
Pressure difference across bed, M' U
Fig. 1 . A basic fluidised bed and determination of the minimum fluidising velocity.
the pressure drop aeross the bed also inereases until it equals the weight per unit area of the bed. At this point (the point of ineipient or minimum fluidisation) the bed is said to be fluidised. In gas-fluidised beds, at gas veloeities in exeess of the minimum fluidisation velocity, Umf, some of the fluidising gas passes through the bed in the form of moving voids, whieh resemble (in some respeets) bubbles in a viseous liquid. At mueh higher gas velocities still, these clearly identifiable bubbles are no longer seen, and the predominant struetures are par tiele clusters. In general, a fluidised bed exhibits the following useful properties: (a) It behaves like a liquid of the same bulk density - particles ean be added or withdrawn freely, the pressure varies linearly with depth, heavy objeets will sink and light ones float. (b) Particle motion is rapid, leading to good solids mixing - henee little or no variation in bed temperature with position. (e) A very large-surfaee area is available for reaetion and mass and heat transfer - 1 m 3 of 1 00 l!m partieles has a surfaee area of about 30,000 m 2 . There are, however, some disadvantages, whieh should be eonsidered in any application. In the context of fluidised-bed agglomeration, these include the following: (a) Gas and solids motion may not scale easily, so that seale-up ean be difficult. (b) Particle entrainment can oceur, espeeially with wide size distributions, prefer entially removing fine particles from the bed. (c) Particle attrition andjor surfaee erosion ean occur. The favourable properties listed above have given rise to many applications of fluidised beds in industry, some of which are listed in Table 1 [1]. Gas-fluidised
1 043
Fluidisation of Cohesive Particles
Table 1 . Classification of fluidised bed applications according to predominating mecha
nisms [ 1 ]
Industrial processes
Heat and/ar mass
Heat and mass
Heat transfer
Gas/gas reactions
transfer bctween
transfer between
between
in which solid
in which so lids are
ga�/particles
particle/particle
bedisurface
aets as catalyst or
transformed
heat sink
or partie leIsurface
'Solids drying -Absorption 01' solvents -Cooling of fertilizer prills -Pood freezing
•
Plastic coating
of surfaces
·Coal combustion -Heut treatment of textile fibrcs, wire, rubber,
-Coating of
glass. metal
pharmaceutical
components
tablets -Granulation eMixing 01'
Gas/solid reactions
·Constant temperature baths
solids -Dust filtration
Oil cracking, reforming
-Caal gasification eRoasting of nickel
Manufacture of:
and zinc sulphides
eAcrylonitrile
elncineration of
'Phthalic
liquid and solid waste
anhydride
·Production of
'Polyethylene
titanium terachJoride
'Chlorinated
·Catalyst regeneration
hydrocarbons
·Decomposition 01' l imestone ·Production uf UFo' AlF, ·Production of UO:!, uo,
beds are in wide use for agglomeration and also for drying of agglomerates made in other types of equipment. As indicated earlier, most industrial uses are for gas-fluidised beds, although liquid-fluidised beds are also found, particularly in biochemical engineering separation processes. The remainder of this chapter refers to beds which are fluidised by gas,
1 .2. Pressu re d rop through packed beds
When a fluid passes through a fixed bed of solid partie/es, a pressure drop results, It is best to describe this in terms of the manometrie pressure drop: the manometrie pressure difference between two points is the total pressure differ ence minus the hydrostatic pressure difference arising when a stagnant fluid is present between the two pOints, 1 1 In other words, the manometrie pressure differenee is the pressure differenee whieh results solely from the motion of the fluid. The distinetion between total and manometrie pressure differenee is only of praetieal importanee if the density of the fluid is signifieant, Le, in liquid-fluidised beds but not usually in gas-fluidised beds,
1 044
J. Seville
The most popular result used to estimate pressure drop in paeked beds is that due to Ergun [2f (1 ) where I1P is the manometrie pressure differenee between two points in the bed, a distanee H apart in the direetion of flow and U the superfieial fluid veloeity (the total fluid flow rate divided by the eross-seetional area of the bed). The void fraction in the bed is denoted by 8. This includes interstitial voids (i.e. voids between the particles) but not interparticle voids (i.e. voids within the particles). A typieal value of 8 for closely sized particles of near-spherieal shape at the point of minimum fluidisation might be in the range 0.40-0.45; dp is the particle diameter. Note that the form of equation ( 1 ) indieates that in general the fixed bed pressure drop rises non-linearly with inereasing gas veloeity. (Figure 1 shows a linear inerease, whieh is the ease only for fine particles - see below.) Fluid flow is often deseribed in terms of dimensionless groups, the most eom mon of whieh is the Reynolds number, pUd/ll, where p is the fluid density and 11 its viseosity. The value of the Reynolds number provides a simple indieation of whether flow behaviour is dominated by fluid viseosity or density - that is by viseous or inertial effeets. In the eontext of fluidised beds, the form of the Reynolds number to be used is the particle Reynolds number, Rep or pUdp/ll, where dp is the particle diameter. The first term on the right of equation ( 1 ) dominates in ereeping flow, i.e. when the particle Reynolds number, Rep, is small so that drag is dominated by fluid viseosity and not affeeted by its density; thus I1Poc U. The seeond term dominates at relatively high Rep, i.e. when drag is dominated by the inertia of the fluid and is therefore affeeted by p but not 11 ; thus, at high Rep, I1Poc U2 . 1 .3. Minimum fluidisation velocity
When a fluid passes upwards through a paeked bed, the manometrie pres sure gradient inereases as U inereases. When the pressure drop is just sufficient to support the immersed weight of the particles, then the partieles are sup ported by the fluid and not by resting on neighbouring particles. Therefore, at this point, the particles beeome free to move around in the fluid, and are said 2 At low Reynolds numbers, the second term in the Ergun equation disappears and the equation then becomes virtually the same as the well-known "Carman-Kozeny equation". The simple result that the pressure gradient is proportional to the flow rate (which is only true at low Reynolds numbers) is generally credited to Darcy ( 1 846). For a more extensive explanation ofthe basics of particies in fluids, see Seville et al. [3], Chapters 2 and 6.
1 045
Fluidisation of Cohesive Particles
to be "fluidised" (see Fig. 1 ). ApjH = ( 1 - Gmf)(Pp - p)g
(2)
where the subscript "mf" is used to denote minimum fluidisation conditions. Using equation (1 ) to evaluate APjH leads to an equation for the minimum fluidisation velocity, Umf, which rearranges to - p)g _ 1 50(1 - Gmf) pd 1 .75 p2 cP p cF (pp 0---'-; -Umf + -3- - 2- u2mf 3 Gmf G mf fl 112 fl -
(3)
Each individual term in equation (3) is dimensionless. It is therefore convenient to rewrite it in terms of a dimensionless diameter, d*, and the particle Reynolds number at minimum fluidisation, Remf (4) In these terms, and combining the numerical constants with the voidage terms as suggested by Wen and Yu [4] , equation (3) becomes (d*)3 = 1 650 Remf + 24.5 Re�f
(5)
which is widely used for estimation of minimum fluidisation velocities. For low d*, such that the viscous term in equation (5) dominates (6) For high d* , where the inertial term dominates
[
]
_ d(Pp _ P)g
Umf -
24.5p
1 /2
(7)
The different dependencies on particle size and fluid praperties should be noted. Figure 2 shows some numerical values, calculated fram equation (5), to illustrate these effects. In the context of batch-type fluidised-bed agglomeration, where the particle size may increase fram < 1 00 to �1 000 Ilm, the implication is clear: the operating velocity must remain weil above Umf at all times. However, too high an operating velocity at the start of the process may cause excessive elutriation. The form of the pressure drop curve with increasing gas velocity is affected by size distribution, pre-preparation of the powder bed and other factors, as in dicated in Fig. 3.
1 046
J. Seville
Umf
m/s 0.1
0.01
1 00 d 1 m 1 000 c 1 Fig. 2. Superficial gas velocity of air at minimum fluidisation, for spherical particles of density 2500 kgjm3 [ 1 ] , continuous line 25°C and 1 bar, - - - line 1 00o-C and 1 bar, chainline 1 000°C and 1 0 bar.
Pressure difference across bed, �P
'Overshoot' due to fluidisation in a narrow tube or of a compacted bed ,�
- - - - �J/- �X� ; " � \
....
Narrow range, weIl mixed bed
-
I ;I � I "', Ir'" Same mean
" I I /
I /
t. '/
size, increasing spread
: Umf I
Fixed bed
Fig. 3. Varieties of pressure drop i ncrease as a function of gas velocity (after [1 ]).
1 .4. Particle and flu id properties
As regards fluidisation behaviour, the most important particle properties are den sity, size, and size distribution. The density of interest is the true solids density, Pp, for whieh a range of pyenometers is available. For beds eontaining a range of sizes, the question arises of whieh mean dia meter to use to eharaeterise the partieles. For purposes of eomparison between different materials, the appropriate diameter to use is the surface- vo/urne rnean,
1 047
Fluidisation of Cohesive Particles
also known as the "Sauter mean" or the weight-harmonic mean: (8)
where the particles contain a mass fraction f; in size range i, the mean particle size in this range being di . If the size analysis is carried out by sieving with the usual logarithmic progression of sieve sizes, the di should be taken as the geo metrie mean of the sieve opening which retains cut i and the next larger sieve. The significance of dsv is that it gives the particle size whose surface area per unit mass or per unit solids volume is the average value for the whole particulate. It is therefore the best single measure of particle size for processes controlled by the interfacial area between gas and solids; this includes mass transfer proc esses and, to a first approximation, fluidjparticle drag at low particle Reynolds numbers. The relevant properties of the gas in a fluidised bed are its density p and viscosity f.1 . For virtually all practical purposes, the density of a gas or gas mixture can be estimated from the ideal gas laws; it is proportional to absolute pressure and inversely proportional to absolute temperature. To a good first approximation, the viscosity of a gas or gas mixture is independent of pressure but increases with increasing temperature: the variation is as T1 j2 according to elementary kinetic theory, and is usually somewhat stronger in practice. The effects of temperature and pressure on gas properties explain most of the effects of T and P on the behaviour of fluidised beds in Geldart's groups B and D (see Section 2. 1 ). How ever, as shown later, the behaviour of finer particles is influenced by cohesive interparticle forces; in their case, therefore, the effects of temperature and pres sure cannot be predicted solely in simple hydrodynamic terms. -
1 .5. Slugging
If the bed diameter is relatively small and the bubbles grow sufficiently to fill the column, then the bed will be in eontinuous slug f1ow, as shown schematically in Fig. 4. Bubbles formed at the distributor grow by coalescence until they form slugs. In this flow regime, which is usually regarded as undesirable, the bed surface fluctuates widely, collapsing sharply with each slug eruption. A bed will show slug flow if (a) the bubble diameter exceeds about 60% of the column diameter; (b) the gas velocity is high enough; (c) the bed is sufficiently deep.
1 048
J . Seville
A ..... -�..,...,,,.J- _ , A I I I I I I I
I
I I I I I I I B
L_
I I I I I I I
tt t
_ -1 8
Fig. 4. Bubble and slug growth [ 1 ] .
Condition (a) depends on the gas and particle properties. Conditions (b) and (c) are combined in a criterion developed by Baeyens and Geldart [5], which gives the minimum superficial velocity for slugging as Umsl = Umf + 0. 1 6(1 . 340°· 1 75 Hmf)2 + 0.07(gO)0.5 (9) -
where Hmf is the bed depth at minimum fluidisation. The second term on the right, which allows for the fact that the bed must be sufficiently deep for slugs to develop, is omitted if Hmf > 1 .340°. 1 75 , and equation (9) then becomes identical to a result derived for deep beds by Stewart [6]. 1 .6. Distributor design
Many types of gas distributor are in common use, including woven or sintered polymers and metals, simple drilled plates and complex directional pressings. Considerations which apply when designing a distributor include: •
•
•
•
pressure drop (must be above a certain minimum value necessary to fluidise the bed uniformly, but not so great as to give rise to excessive gas compression costs); the height of the region of high gas and particle velocities adjacent to the distributor (this region is associated with both attrition and erosion of in-bed surfaces); mechanical strength (which must be sufficient to support the bed weight when the bed is not fluidised); orifice size (which must be small enough to prevent the particles running back into the wind-box).
1 049
Fluidisation of Cohesive Particles
The fractional free-area of a multi-orifice distributor is given by F = najA (1 0) where n is the total number of orifices, a the area of each orifice and A the total area of the distributor. The pressure drop across the multi-orifice distributor is then f...PD = p 2 d.d F2
U2
(1 1 )
where Cd is the orifice discharge coefficient. (This derivation, and other aspects of distributor design are considered in detail by Geldart and Baeyens [7].) Qureshi and Creasy [8] concluded, from a review of published data, that the minimum distributor pressure drop required for satisfactory operation is
�lJ.PpDs = 0.01
+
0.2[1
-
exp( - 0j2H)]
(1 2)
where f...po is the pressure drop across the bed. Thus, the minimum distributor pressure drop depends on the aspect ratio, the ratio of bed diameter, 0, to bed height, H. For large beds, f...P o/f...Ps must be at least 0.2 and up to 0.3 is rec ommended if the bed is "sticky". This is an aspect which is insufficiently con sidered in some fluidised-bed agglomerators, which tend to suffer from gas maldistribution because the particles are cohesive. 1 .7. Bubbling and solids circulation
Solids motion in fluidised beds is strongly associated with bubble flow, since the bubbles transport solids in their wakes and drifts (Fig. 5). The bubble flow rate in a fluidised bed, Ob, is defined as the rate at which bubble volume crosses any level in the bed. A first estimate for Ob is given by the "two-phase theory of fluidisation" [1 ], which conceives the bed as consisting of two "phases": (a) a dense "phase" in which the gas flow rate is equal to the flow rate at incipient f1uidisation, i.e. the 0.3 r------, 0.25 0.2
Wake
0. 1 5 0.1 0.05
0.05
0.1
0. 1 5
Fig. 5. Bubble wake and drift; particle motion driven by rising bubbles. Left - schematic;
right - discrete element simulation.
1 050
J. Seville
voidage is constant at the minimum fluidisation value and (b) a bubble "phase" that carries the additional flow of fluidising gas. The bubble flow rate is then estimated as (1 3) where U is the superficial fluidising velocity and Umf the value at minimum flu idisation. In words, the simple two-phase theory can be stated as: "the excess gas flow above that which is necessary for minimum fluidisation passes through the bed in the form of bubbles". Many features of fluidisation, notably the partieIe circulation time and the mixing rate, depend on the "excess gas velocity", U - Umf. When a bed of partieIes is fluidised at a gas velocity above the minimum bubbling point, bubbles form continuously and rise through the bed, which is said to be "freely bubbling". Bubbles coalesce as they rise, so that the average bubble size increases with distance above the distributor (see, for example [9]) until the bubbles approach the maximum stable size. Thereafter, splitting and re-coalescence cause the average bubble size to equilibrate at a value elose to the maximum stable value. For large particles ( ;G 1 mm), the maximum stable bubble size may be many metres, so that bubbles can grow to occupy the entire bed cross-section. For partieIes of 20-1 00 11m, however, the maximum stable size at ambient conditions is in the range 1-20 cm, so that bubbles in beds of sub-1 00 11m particles are typically constant in size over much of the bed height. Bubble coalescence can also have an influence on circulation of the dense phase. The effect is shown schematically in Fig. 6(a). Bubbles usually coalesce by overtaking a bubble in front (Fig. 6(b)(i)) and may move sideways into the track of a leading bubble (Fig. 6(b)(ii)). Thus coalescence can cause lateral motion of bubbles. Bubbles near a bed wall can only move inwards, while bubbles weil away from the walls are equally likely to move in any horizontal direction. As a result of this preferential migration of bubbles away from the wall, an "active" zone of enhanced bubble flow rate forms at a small distance from the wall. In this zone, coalescence is more frequent so that the bubbles become larger than at other positions on the same horizontal plane. Because the region between the "active" zone and the wall is depleted of bubbles, coalescence continues to cause preferential migration towards the bed axis. Eventually, if the bed is deep enough, the "active" zone comes together to form a "bubble track" along which the lean phase rises as a stream of large bubbles. On the other hand, if the bed is wide and shallow, it may divide into several mixing "cells", with relatively little exchange between them (Fig. 7). Because of the transport of partieIes by the bubbles, the solids tend to move up in regions of high-bubble activity and down elsewhere. In the upper levels, the motion is up near the bubble tracks and down near the walls. At lower levels, the partieIe motion is down near the axis and outwards across the distributor; this motion can in turn enhance bubble activity near the walls elose to the distributor.
1 05 1
Fluidisalion of Cohesive Particles
( a ) Overall bubbl ing pattern circulation Sol ids
_ .
-.- . _
A
1 f f t t
(b) ( i )
0
6
( ii )
0
o
Fig. 6. (a) Bubble and solids flow patterns (b) bubble coalescence modes in fluidised beds
[1].
All of the comments above apply regardless of the shape of the bed. In many agglomeration applications, the bed walls are conical for at least some of the bed height This serves to enhance the concentration of bubble flow towards the centre of the bed, and therefore to increase the overall solids circulation, up in the centre and down at the walls.
2. TYPES OF FLUI DISATIO N
As the fluid flow upwards through a settled bed of particles is increased, the pressure drop across the bed also increases, but a simple force balance shows that it is not possible for this pressure drop to exceed the buoyant weight of the
1 052
J. Seville 35
35
30
30
25
25
20
20
15
15
10
10
/�__ 'I ?�
1W:\�IJJ�� ____ \
5
o , 0
5
,
10
15
5
5
10
15
Fig. 7. So lids circulation i n beds of different heights (DEM simulation).
particles. At higher fluid velocities, therefore, either the bed voidage must increase so as to maintain the pressure drop at or below this level, or not all the fluid can flow interstitially. The following types of behaviour are now possible (see Fig. 8): • •
• •
•
bubbling and slugging; uniform expansion, which is found over a certain range of gas flows for "group A" particles (see below); jetting (where gas jets from the distributor penetrate significantly into the bed); spouting (where the gas is deliberately added over a limited central area of the distributor and a lean "spout" penetrates the entire bed height to the free board [ 1 0]); channelling ("rat-holing").
All of these types of behaviour, with the exceptions of spouting and channel ling, can be described as fluidisation, because both the bed and the individual particles within it are wholly supported by the pressure drop. Spouting and chan nelling cannot, because, in general, the pressure drop during these types of behaviour is less than that required to support the bed. There have been several attempts to devise theoretical and empirical classi fications of these behavioural types. Of these, the most widely used is the empirical
1 053
Fluidisation of Cohesive Particles A
8
0
0
D 0
Cl C
° D O 0 " •
0
. _ _
0 . .. • •
'!_ _ '!.
u
Bvbbltng
0
D
0°
p C:>
u
SllI9ging
(
o
c::I
� ""
u
u
u
Ä##ing
Fig. 8. Types of fluidisation [ 1 ] .
c1assification of Geldart [1 1 ], who divides fluidisation behaviour according to mean particle size and density difference between the solids and the fluidising gas (Fig. 9). Geldart recognises four behavioural groups, designated A, B, C and D. Typical fluidisation behaviour of groups A-C is illustrated in Fig. 1 0. Group B particles fluidise easily, with bubbles forming at or only slightly above the minimum fluidisation velocity. Group C particles are cohesive and tend to lift as a plug or channel badly; conventional fluidisation is usually difficult or impossible to achieve. Group A particles are intermediate in particle size and in behaviour between groups B and C, and are distinguished from group B by the fact that appreciable (apparently homogeneous) bed expansion occurs above the minimum fluidisation velocity but before bubbling is observed. There is now much experimental evi dence (see Section 3) that group A particles are also intermediate in cohesive ness between groups B and C, their interparticle cohesive forces being of the same order as the single particle weight. Group 0 particles are those that are "Iarge" andjor abnormally dense. Such particles show a tendency to "spout", rather than fluidise. Other properties of the groups are summarised in Table 2 and are discussed further below. It should be emphasised that the Geldart diagram (Fig. 9) is applicable only to particles fluidised by air under ambient conditions, and in the
1 054
J. Seville 7 6 5 4
r-..
3
"'e u
2
Q.Q.
Aerotoble
/ I
......
.!? � .
A
J
I
i\
ß
0.5 f- C
Cohesive
/
i
I
1\ \
B 1\
f\
Sond - like
�
"
iJ utoble
0
\
1\ � \
"'
I IJ
"1\
� \
",
20
100
50
5
\
\
1,000
Fig. 9. Geldart diagram for classifying powders according to their fluidisation behaviour in air at ambient conditions [1 1 ].
6P
AP
H
H
�A .
uf
AP
H
1-----:,
: �u�t..!.t«;. _
.... I ....
u
f
BEHAVIOUR ERRA Tl C AND IRREPRODU5,l8lE
I , EXPANDING I I
u
u
Fig. 1 0. Typical f1uidisation behaviour in Geldart's groups B, A and C (from left to right). Note that the scales are different for each group [24].
1 055
Fluidisation of Cohesive Particles
Table 2. Charaeteristie features of Geldart's ( 1 973) classifieation of fluidisation behaviour
(after Geldart [1]).
Typieal examples
Flour, eement
Craeking eatalyst
Building sand, table salt
Crushed limestone, eoffee beans
Bed expansion
Low when bed ehannels; ean be high when fluidised Can be very slow Channels
H ig h
Moderate
Low
Siow
Fast
Fast
Splitting and eoaleseenee predominate Maximum size Large wake H igh H ig h Axi-symmetrie; breakdown to turbulent fluidisation Shallow beds only
No limit on size
No known upper size Small wake
Moderate Moderate Asymmetrie
Low Low Horizontal voids Solid Slugs Wall Slugs Yes, even in deep beds
De-aeration rate Bubble properties
Solids mixing Gas baek-mixing Slug properties
Very low Very low Solid slugs
Spouting
No, exeept in very shallow beds
Shallow beds only
absence of artificially enhanced cohesive interparticle forces, due to the presence of liquid layers on the particles, for example. A more recent c1assification due to Grace [12] is shown in Fig. 1 1 . This uses the dimensionless particle diameter introduced in equation (4) and dimensionless gas velocity, U* , where U* _
U -
[_p'-2_--- p ] )g I1(Pp
1 /3
(14)
-
Figure 1 1 also shows the various processing options which might be con sidered for particles of various sizes and gases of different properties. Grace's classification successfully accounts for the effects of variation in gas properties due to operation at elevated temperature and pressure but there is, as yet, no satisfactory c1assification that also takes into account interparticle forces, which in many practical situations may be of considerable importance.
1 056
J. Seville Group C powder
I I i i
j 1( / /
,
bed I �\Spouted .
,'
i.
Movlng
bed
I
Fixed bed
10
{
}1I3
Dimensionless porticle diameter 2 113 1/3 (3,44 � Re I :Ar : d g ( pp -PQII/
Fig. 1 1 . Regime/processing-mode diagram for grouping systems according to type of powder and u pward gas velocity used [12].
2.1 . General description of g roup behaviour 2. 1. 1. Group B
Many commonly encountered experimental particles lie in group B, which, for a particle density of about 3000 kgjm 3 , encompasses the particle size range from about 75 to 600 11m. In group B, as mentioned above, bubbles form at about the minimum fluidisation velocity. Bed expansion is smalI, and the bed col lapses rapidly when the gas supply is cut off. Bubble rise velocity depends on bubble size, but most bubbles travel faster than the interstitial gas velocity, Umt/8mf, so that gas tends to circulate within the bubble, except during coales cence and splitting. There is no evidence of a maximum bubble size (so that bubbles will continue to grow by coalescence until their size is limited by the size of the apparatus) .
1 057
Fluidisation of Cohesive Particles
2. 1 . 2. Group A
As mentioned earlier, group A particles are those which exhibit a region of non bubbling expansion for gas velocities above the minimum fluidisation velocity. (In earlier literature, non-bubbling expansion is known as "particulate" fluidisation, by contrast with "aggregative" bubbling fluidisation.) Geldart [1 1 ] defines a minimum bubbling velocity, Umb , and designates group A particles as those for which Umb/ Umf > 1 . The non-bubbling expansion of a group A bed can be characterised in terms of the Richardson and Zaki [1 3] equation. U - = cn Ut
( 1 5)
where UI is the particle terminal velocity in an infinite medium and n a function of the particle Reynolds number at the terminal velocity, normally taking values between 2.4 and 4.65. As the superficial gas velocity exceeds the minimum bubbling velocity, the pas sage of bubbles breaks up the expanded structure, causing a decrease in bed height (Fig. 1 0) as the dense phase voidage is reduced to somewhere between C mf and C mb ' When the gas supply is suddenly cut off, the bed initially collapses rapidly as the bubbles leave and then continues much more slowly, at a rate which is similar to the superficial velocity of the gas in the dense phase. This property of slow deaeration is responsible for the ease with which fluidised group A solids are maintained in a fluidised state, but is also responsible for their tendency to "flood" on discharge from hoppers [14]. In bubbling group A beds, all bubbles travel faster than the interstitial gas, but a tendency towards bubble splitting limits the size to which they can grow by coalescence. Circulation and mixing are rapid, bed-to-surface heat transfer is favourable, and gas exchange between the bubbles and the dense phase is high due to frequent splitting and coalescence. All of these factors, together with a larger solid surface area per bed volume than for groups B and D, favours the use of group A particles in many applications. 2. 1 . 3. Group C
Group C powders will readily form stable channels from the distributor to the surface, and may aiso litt as a cohesive plug, particularly if the apparatus is small. The pressure drop across the bed usually remains below the bed weight per unit area, and mixing and heat transfer are poor. Fluidisation can sometimes be made possible by increasing the gas velocity to break up the cohesive struc ture, or by mechanical stirring or vibration. Fluidisation can also sometimes be promoted by adding a small proportion of fumed silica or some other sub-micron powder; these reduce the interparticle forces by modifying the contact geometry.
1 058
J. Seville
2. 1.4. Group D
The distinction between groups B and D concerns the rise velocity of the bubbles, which is, in general, less than the interstitial gas velocity in group D beds, so that gas flows into the base of the bubble and out of the top. Because of the size and density of the particles, the permeability of the bed is high, so that the minimum fluidi sation velocity is also high. Gas and solids mixing is low, but cohesive solids can be fluidised because the greater momentum of the particles on impact and fewer particle-particle contacts per unit area reduce the tendency towards agglomeration. Introduction of a liquid spray may then lead to coating rather than agglomeration. If gas is introduced over a small part of the distributor, group D particles can be made to spout [1 0] . In practice, it is often advantageous to exploit this tendency and to use a spouted bed rather than a fluidised bed when processing or handling them.
3. INTERPARTICLE FORC ES
By definition, a state of fluidisation exists when the force of gravity on a set of particles is balanced by the drag arising from the flow of the fluidising gas. It folIows, therefore, that small interparticle forces, which may not be noticeable in other circumstances, may have observable consequences at the point of fluid isation and beyond. Interparticle forces can occur due to a variety of causes; those of interest here are van der Waals interactions, liquid bridges and sintering. 3.1 . Van der Waals forces
"Van der Waals forces" is a collective term taken to include the dipole/dipole, dipole/non-polar and non-polar/non-polar ("dispersion") forces arising between molecules [1 5]. Though other intermolecular forces can occur, such as hydrogen bonding, these are related to the specific chemical nature of the materials; van der Waals forces always exist. Although intermolecular forces decay with mo lecular separation, a, as a-7 , when the pair potentials are integrated between macroscopic bodies, such as spherical particles, the resulting force is much less sensitive to separation, decaying as a-2 in the case of sphere-sphere interaction.
AR Fvw = 1 2 a 2
( 1 6)
where R is the sphere radius, A the Hamaker (materials-related) constant and a the surface separation, which takes a minimum value of the order of the inter-molecular spacing. Suitable values for the variables give the lines plotted in Fig. 1 2. It will be apparent that intermolecular forces depend more on the particle
1 059
Fluidisation of Cohesive Particles
1 0-5
g GI () ... 0 u.. GI
1 0-6
U 1:
111 Q. ... GI
�
Force - ----ra:�:e�:��::e Capillary
(Max)
------------
--
a l
1 0-8
--------
a=4_ A
---0 ---10
----100
1 000
Particle Diameter (11m)
Fig. 1 2. Comparison of the magnitude of sphere-to-sphere cohesive forces (dashed lines indicate asperity-to-plane contact) _ Quartz/water system [30].
surface properties than on the bulk, so that it may be more plausible to assume (or measure) a surface roughness and use this to determine the curvature. The van der Waals force then depends on this local curvature and is independent of R. This result is also plotted in Fig. 1 2, and suggests, for the set of variables chosen here, that spherical particles of diameter of order 1 00 �m should exhibit interparticle van der Waals force to equal their single particle weight. If the gross particle radius is taken as the controlling factor, as in equation ( 1 6), the corre sponding diameter is 1 mm, which is less plausible. Particles of 1 00 �m are commonly found adhering to surfaces and resisting the force of gravity; 1 mm particles are not! 3.2. Liquid bridges
Liquid bridges are more interesting than van der Waals forces from a practical point-of-view, since their magnitude can be adjusted by altering the amount of
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J. Seville
free liquid and its properties, particularly surface tension and viscosity. They are of practical importance in agglomeration processes, driers, and in some types of reactors and bioreactors. They are also more complex than van der Waals forces in that they exhibit both dynamic and static forces and are dissipative of energy. Their behaviour is considered in detail in Chapter 28; only a brief summary will be given here. The static liquid bridge force arises from the sum of the surface tension force and the force arising from the pressure deficit in the liquid bridge [3] (Fig. 1 3).
!:lP
(17) where is the reduction in pressure within the bridge with respect to the sur rounding pressure and y the surface tension. The magnitude of this force is difficult to compute exactiy, even for spheres, because the bridge forms a gas-liquid interface of constant curvature in order to satisfy the Laplace equation.
!:lP = Y [�r1 - �r2]
(1 8)
This results in a bridge shape (Fig. 1 3(a)) in which r1 is a variable for a given bridge volume, so that r2 must also be a variable. However, the toroidal approximation (2 ), in which r1 is taken as constant, enables a simple and rea sonably accurate result to be obtained. At contact, the maximum static liquid bridge force is ( 1 9) F[s,max = 2nRy which is plotted in Fig. 1 2 and again compared with the force which would arise if the contact were dominated by surface asperities of dimensions independent of gross particle diameter. For water, the static liquid bridge force is rather larger than the maximum van der Waals force. It is generally assumed that the static (or low-relative velocity) liquid bridge force is conservative, but Willett et al. [1 6] have shown, both experimentally and theoretically, that this is not the case. If the contact angle is non-zero and the surface is "rough", both of which are often true, the contact line may be "pinned"
Fig. 1 3. (a) Liquid bridge between two spheres, (b) sinter bridge between two spheres.
1 06 1
Fluidisation of Cohesive Particles
and the force/separation curves on approach and departure follow different paths, leading to hysteresis and energy dissipation. The liquid bridge also dissipates energy by viscous flow, away from the contact area on approach and vice versa. The viscous force always opposes relative movement, unlike the surface tension force. During separation, the reduction in pressure around the point of e/osest approach may easily lead to cavitation in the liquid [1 7]. The force is given, to a first approximation, by Reynolds' lubrication equation [1 8, 1 9]. (20) where v is the separation velocity, J1 the viscosity and a the separation distance. This equation implies a singularity at contact; in practice, the surfaces are rough , so that there exists a non-zero minimum separation, ao, and/or they deform. In practice, therefore, the interpartie/e force due to the viscous contribution (equa tion (20)) will exceed the static force at higher relative velocities. For the partie/es of interest for fluidisation, this velocity is in the approximate range 1 cm/s to 1 m/s [3]. To a first approximation it is permissible to superimpose the static and the dynamic forces, since the former depends mainly on the shape of the gas-liquid interface while the laUer depends mainly on fluid motion near the point of e/osest approach. A third energy dissipation mechanism is the stretching and eventual rupture of the bridge; in a wet-fluidised bed, bridges can be imagined to be continually rupturing and reforming. The energy thus dissipated depends on the rupture distance, which takes the very simple form [20]. 13 a a x = (0.5 + 0.25
where V is the liquid bridge volume and
The forces arising from sintering are quite different in kind from those discussed above. Sintering is a time-dependent process in which material migrates, due to diffusion, viscous flow or some other mechanism or combination of mechanisms, to the region of contact to form a "neck" (Fig. 1 3(b)). The size of the neck increases with time according to an equation of the form (xjR)2 = kr
(22)
where x is the neck radius at time r . In the Frenkel equation for viscous sintering [22], for example, k = 3y/2RJ1, where y is the surface energy of the bridge material
1 062
J. Seville
and 11 its viscosity. Migration is driven by surface energy minimisation (which is relatively independent of temperature) and (in viscous sintering) opposed by viscosity, which is an Arrhenius function of temperature T: 11 = 110 exp(EjRT)
(23)
where E is the activation energy for sintering and R the gas constant. The result is that sintering occurs much faster at higher temperatures. It may be noted that the effect of temperature on sintering is therefore quite different from its effect on dynamic liquid bridge forces, where higher temperatures and reduced viscosity leads to lower forces (equation (20)), lower energy dissipation in collision and therefore lower probability of agglomeration (provided that the fractional liquid loading remains constant). 4. THE EFFECTS OF COHESIVE FORCES 4.1 . Effects of "natural" cohesion - Van der Waals forces
The central reference point for much discussion on the effect of particle size on fluidisation is Geldart's famous c1assification [1 1 ]. The "Geldart diagram" (Fig. 9) has been of great value in allowing easy prediction of fluidisation properties in terms of particle size and density, but the reasons for the different types of behaviour have remained controversial, particularly the transition from group B type (bubbling at minimum fluidisation) to group A type ("uniform" bed expansion with separation of the points of minimum fluidisation and minimum bubbling). It is worth noting that Geldart never intended this diagram to be used for other than dry hard materials in the Earth's gravitational field. Molerus [23] was the first to suggest in print that there was another way of viewing this diagram, as a competition between cohesion and weight, so that the behavioural boundaries between groups A-to-C and (more controversially) B-to-A should be given by Single particle weightjcohesive force = constant
(24)
He suggested that in group A the interparticle cohesive force and particle weight are of comparable magnitude, whereas in group B the interparticle forces are insignificant by comparison with weight. Molerus's explanation fits the observations, particularly since a number of workers (see below) have shown how enhancing the interparticle forces can move the observed behaviour from B to A to C. Molerus attempted to obtain a value for the ratio of interparticle cohesive force to particle weight at the transition from group B to group A, from equation ( 1 6) and literature values of Hamaker constants; this resulted in an estimate of about 6.
Fluidisation of Cohesive Particles
1 063
However, as noted above, van der Waals forces are in practice determined by surface properties and a more realistic value, taking into account experimental measurements for interparticle forces [24] might fall in the range 0.3-0.5. (Rhodes et al. [25], using Discrete Element modelling, also came to the conclu sion that the critical ratio of cohesive force to particle weight was of order one at the B-A boundary.) It is probably uncontroversial that the A-to-C transition should be expressed in the form of equation (24), since the effects of cohesion are very apparent clumping, plugging and rat-holing when fluidisation is attempted. It may be ar gued that if cohesion is important here then the chemical nature of the solids should affect whether or not they can be fluidised, because the Hamaker constant is a material parameter. There is not much systematic data on this, but the very different fluidisation behaviour of aerogels of similar size but different chemical composition [26] provides some evidence that this is true. A further piece of evidence that the balance of forces is important in determining group C behaviour is provided by work on fluidised beds in which the gravity forces are replaced by centrifugal ones [27]; increasing the latter can make fluidisation possible for particles which do not normally fluidise. The B-to-A transition is much more controversial. The principal feature of group A solids is expansion without bubbling and the main question is therefore how the expanded non-bubbling bed is stabilised. Some have argued (e.g. [28]) that the observations can be explained by hydrodynamics alone. The problem with a purely hydrodynamic interpretation is this: it is generally predicted that all fluidised beds should be unstable to voidage perturbations, liquid- and gas-fluidised beds differing only in the rate at which disturbances grow [29]. Disturbances in a gas-fluidised bed should grow approximately one-hundred times as fast as in a Iiquid-fluidised bed. This explains why gas-fluidised beds generally exhibit bub bling behaviour while Iiquid-fluidised beds do not, but it is at variance with the observed stability region in group A. Both hydrodynamic and mechanical expla nations for this stability are summarised by Seville [30]. 4.2. Effects of liquid bridges
Small amounts of free surface liquid on particles can give rise to cohesive forces which can be much larger than those arising from van der Waals forces alone (Fig. 1 2), and the effect on fluidisation can be very great. The large number of studies in this area is reviewed by Seville [24]. These studies are very diverse, but three general conclusions can be drawn. •
Increase in cohesion can stabilise a settled bed at a higher void fraction than would be the case in the absence of cohesion. If the voidage at minimum
1 064
•
•
J. Seville
fluidisation, 8mb, is increased, then the minimum fluidisation velocity, Umf, must necessarily increase also, since a higher flow rate is then required to produce enough pressure difference to support the bed weight. (Some authors have erroneously introduced a cohesive term into the force balance at minimum fluidisation in order to explain the observed increase in Umf for cohesive ma terials, in contravention of Newton's Second Law.) Small increases in cohesion can result in a separation between Umf and Umb, just as for group A powders. Seville and Clitt [31 ] showed this for glass ballotini as large as 600 11m, when coated with very thin liquid layers. They subsequently measured the cohesive force necessary to cause this behaviour and found that it occurred at a ratio of cohesive force to particle weight of about 0.43, which lends further support to Molerus's arguments about the B-to-A transition. Similar conclusions were reached by McLaughlin and Rhodes [32]. Further increase in liquid loading can lead to defluidisation, either through the effects of static liquid bridge forces or dynamic ones. The effects of dynamic forces are considered further below.
Particles within a fluidised bed are in frequent collision with their neighbours; if the particles have surface liquid, some of these collisions may lead to bonding, which may in turn lead to defluidisation. Barnocky and Davis [1 7] have considered in detail the conditions under which particles impacting on a thin-liquid layer will be captured, using equation (20) to estimate the forces during the impaction process. They showed that whether capture occurs depends on the value of an impaction Stokes number, mvj6n/lf?'2, where v is the velocity and m is the particle mass. This approach was also used by Ennis et 81. [33] in developing a predictive approach to deciding whether surface-wet particles will coalesce in agglomer ation processes, including fluidised beds. In summary, defluidisation is predicted to occur when the particles within the bed no longer have enough kinetic energy to escape capture on impact with their neighbours. Leaving aside the question of whether a fluidised bed can be adequately described in terms of independent particles in free-flight between collisions, this approach predicts defluidisation when (25) where St* is the critical value of the Stokes number, e the coefficient of restitution for the particles, 80 is the two-thirds of the liquid layer thickness and 81 is the characteristic roughness dimension of the particles. In general 8 1 is unknown, but it can in principle be obtained by carrying out experiments with different liquid layer thicknesses and plotting St* against In 80' A further difficulty with use of this equation to predict defluidisation is that it requires a measurement of the collision velocity, v, which is not generally known.
1 065
Fluidisation of Cohesive Particles
Ennis et al. [33] assumed, quite reasonably, that the collision velocity is given by v = Ci( U - Umf) (26) where is a constant of proportionality, which depends principally on the parti cle size. They tested this approach by plotting a modified Stokes number, m(U - Umf)/6npR2 , against the logarithm of the layer thickness for a series of experiments performed by Gluckman et al. [34], where liquid loading but not viscosity was varied. Good agreement was reported, although this has not been confirmed by other workers in the field. In cases where the liquid viscosity was varied [35], the result was not consistent with equation (26), so that this approach to predicting the conditions leading to "wet" defluidisation remains controversial. Ci
4.3. Sintering
If particles which are prone to sintering are fluidised at too high a temperature, defluidisation by sintering will readily occur. Figure 14 shows an example of the minimum fluidising velocity required to prevent defluidisation, as a function of temperature. Sintering is qualitatively different from the other cohesive effects discussed above in that it is time-dependent: for an effect to be observed, par ticles must remain in contact long enough for a sinter neck to form. It is Iikely that some liquid bridge effects will also show such time-dependent behaviour at high viscosities or with non-Newtonian liquids. Seville et al. [36] have modelIed particle sintering in fluidised beds using two assumptions: (a) sintering occurs in the quiescent zones in which interparticle motion is limited; the time spent in the quiescent zones is a function of the excess
1 .5 ,---c�
....
o
E
�
Fluidised bed temperature eC) Fig. 14. The effect of temperature on the minimum fluidising velocity of low-density po
lyethylene granules of particle size 2 mm (melting point 1 00-1 25 °C) [36].
1 066
J . Seville
fluidising velocity; (b) the force applied to sintered agglomerates by the bubble movement is independent of the excess fluidising velocity. Therefore for a given bed, the critical size of sinter neck, which is just sufficient to remain permanent will be independent of the fluidising velocity. They argued that there are two possible measures of the quiescent time (Fig. 1 5): the time Tbo for which particles are able to move down in the bed in close proximity and relatively undisturbed, which is related to the overall circulation time; and the time Tbb for which particles are undisturbed by passage of bubbles past a point in the bed. 80th are of the form (distance)j(U - Umf). The critical time Ts for sintering, to the extent (xjR) which is sufficiently large for the agglomerate not to be broken by the passage of bubbles, depends on the mode of sintering. For viscous sintering, for example, equation (22) gives _
(�) 2 2rJi3
(27) ")1 If now the time for sintering is equated with one of the characteristic times for bed movement, an expression is obtained relating the critical excess fluidising velocity to the surface viscosity, and hence the temperature Ts - R
K1 K2 (Umfs - Umf) = Jio exp(EjRT)
(28)
where K1 and K2 are constants, the laUer characterising the critical size of the sinter neck. Equation (28) is a predictive expression for the temperature de pendence of the minimum fluidising velocity under sintering conditions. The sur face viscosity can be measured independently and hence the equation provides predictive capability. (A similar analysis can be applied for the case of sintering by diffusional processes [37].)
w
w W Q
Q
Q
wtTbb
Q
Q
Q
W
W W
Q
W W Q
Q Q Q Q
Fig. 1 5. Characteristic quiescent times - two alternatives.
Q
1 067
Fluidisation of Cohesive Particles
1 . 1 ,------, 0.9
•
0.7 �
E 0.5
�E
0.3
2. 0.1 :E �
-0. 1 -0.3 -0.5 +--,----.---,--...,--,--1 2.49 2 .5 2.51 2 .52 2.53 2 .54 2.55 2.56 2 .57 2.58 2 .59 1 000rr (K-1)
Fig. 1 6_ Dependence of minimum excess gas velocity on operating temperature - poly ethylene.
Figure 1 6 shows a test of equation (28) in the case of low-density polyethylene. The gradient of the line gives a value for the activation energy for sintering of polyethylene. In general, good agreement has been found with equation (28) for many materials, from polymers [36] to iron [37]. Furthermore, independ ently obtained values for activation energy agree with those obtained from plots similar to Fig. 1 6.
5. CONCLUSIONS
The basic behaviour of a fluidised bed is weil understood and predictable using well-tested approaches. This understanding is less complete where cohesive behaviour is concerned. Cohesion between particles in a fluidised bed may arise through the natural effects of van der Waals forces or through artificially en hanced effects due to the presence of surface liquid or material migration due to sintering. The force, which arise will have static and (in the case of liquid layers) dynamic components. In addition, there may be time-dependent bond formation in the case of sintering and (though not considered here) surface reactions. There is now widespread agreement that cohesive forces, however caused, of the same order as the single particle weight, will give rise to fluidisation char acteristics which are similar to those observed in Geldart's "group A". Much larger ratios of cohesive force to particle weight will prevent fluidisation unless mechanical agitation is provided. The mechanism by which cohesion allows a degree of expansion without bubbling remains unclear in detail but the formation
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J. Seville
and expansion of cavities in the expanded structure seems likely and their breakdown will occur at the minimum bubbling point. Prediction of the conditions for defluidisation remains difficult in the case of free surface liquid, where a model for energy exchange in collision is not entirely consistent with the observation of defluidisation effects when the liquid viscosity is varied. A "critical time" approach to prediction of defluidisation under sintering conditions has been successful for a wide range of materials.
ACKNOWLEDGEMENTS
Part of this chapter first appeared at "Fluidization XI" [30]. The author is indebted to a variety of sponsors, including the Engineering and Physical Sciences Re search Council , the Biology and Biological Sciences Research Council , Unilever Research, BP and NEDO for support of parts of this work; to a number of ex cellent research students: Matthias Stein, Roland Schiftner, Heike Silomon-Pflug, Michael Kemmerich, Aidan McCormack, Mark Leaper, Amran Salleh; and to his collaborators Professors Roland Clift, Peter Knight, Masayuki Horio and Hidehiro Kamiya. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [ 1 0] [1 1 ] [ 1 2] [ 1 3] [ 1 4] [ 1 5] [ 1 6] [ 1 7] [ 1 8] [1 9] [20] [21 ]
D.Geldart (Ed.), Gas Fluidisation Technology, Wiley, New York, 1 986. S. Ergun, Chem. Eng. Prog 48 ( 1 952) 89. J . P.K. Seville, U . Tüzün, R Clift, Proc. Particu!. Solids, Kluwer, Amsterdam, 1 997. C.Y. Wen, Y.H. Yu, AIChEJ. 12 ( 1 966) 6 1 0. J . Baeyens, D. Geldart, Chem. Eng. Sci. 27 ( 1 974) 2309. P.S.B. Stewart, Trans. Inst. Chem. Eng. 46 ( 1 968) 60. D . Geldart, J . Baeyens, Powder Techno!. 42 ( 1 985) 67. A.E. Qureshi, D . E . Creasy, Powder Techno! . 22 ( 1 979) 1 1 3 . R C . Darton, R D . LaNauze, J . F . Davidson, D. Harrison, Trans. I . Chem. E. 55 ( 1 977) 274. K.B. Mathur, N. Epstein, Spouted Beds, Academic Press, New York, 1 974. D. Geldart, Powder Techno!. 7 ( 1 973) 285. J . R Grace, J. Can. Chem. Eng. 64 ( 1 986) 353. J . F . Richardson, W.N. Zaki, Trans. I nst. Chem. Eng. 32 ( 1 954) 35. D . Geldart, J . C. Williams, Powder Techno!. 43 ( 1 985) 1 8 1 . J . N . IsraelachviIi, Intermolecular & Surface Forces, Academic Press, London, 1 99 1 . C.D. Willett, M.J. Adams, S.A. Johnson, J . P.K. Seville, Powder Techno! . 1 30 (2003) 63. G. Barnocky, R M . Davis, Phys. Fluids 31 (6) ( 1 988) 1 324. A. Cameron, Basic Lubrication Theory, Ellis Harwood, Chichester, 1 98 1 . M . J . Adams, B. Edmondson, in Tribology in Particulate Technology. In: B.J. Briscoe, M . J . Adams (Eds.), Adam Hilger, Bristol, 1 987. G . Lian, C. Thornton, M . J . Adams, J . Colloid Interf. Sei. 1 6 1 (1 993) 1 38. S.J.R Si mons, J . P.K. Seville, M.J. Adams, Chem. Eng. Sci . 49 ( 1 994) 233 1 .
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[22] W.D . Kingery, HK Bowen, D.R. Uhlmann, in Introduction to Ceramics, Wiley, New York, 1 976, p. 492. [23] O. Molerus, Powder Techno!. 33 ( 1 982) 8 1 . [24] J.P.K. Seville, i n Tribology i n Particulate Technology, B.J. Briscoe, M .J . Adams (Eds.), Adam Hilger, Bristol, 1 987. [25] M.J. Rhodes, X.S. Wang, M. Nguyen, P. Stewart, K. Liffman, Chem. Eng. Sei . 56 (2001 ) 69. [26] C . Lauga, J . Chaouki, D . Klavana, C . Chavarie, Powder Techno!. 65 ( 1 99 1 ) 461 . [27] S. Watano, Y. Imada, K. Hamada, Y. Wakamatsu, T. Tanabe, R N . Dave, R Pfeffer, Powder Techno!. 1 31 (2003) 250. [28] P . U . Foscolo, L.G. Gibilaro, Chem. Eng. Sei. 39 (1 984) 1 667. [29] R Jackson, Fluidization, 2nd edition, J . F . Davidson, R Clitt, D . Harrison (Eds.) , Academic Press, London, 1 985, p. 47. [30] J.P.K. Seville, Proc. Fluidization XI, ECI, New York, 2004, pp. 37-50. [31 ] J . P.K. Seville, R Clitt, Powder Techno!. 37 ( 1 984) 1 1 7. [32] L.J. McLaughlin, M.J. Rhodes, Powder Techno! . 1 1 4 (200 1 ) 2 1 3. [33] B.J. Ennis, G . ! . Tardos, R Pfeffer, Powder Techno!. 65 ( 1 99 1 ) 257. [34] M.J. Gluckman , J. Yerushalmi, A.M. Squires, Fluidization Technology, Hemisphere, New York, 1 975. [35] M. Kemmerich, J . P. K. Seville, u npublished work. [36] J . P. K. Seville, H . Silomon-Pflug, P.C. Knight, Powder Techno!. 97 ( 1 998) 1 60. [37] P.C. Knight, J . P.K. Seville, H . Kamiya, M . Horio, Chem. Eng. Sci . 55 (2000) 4783.
CHAPTER 23 M u lti-Leve l Com p utat i o n a l F l u id Dyna m i cs M od e l s for the Descri pti o n of Particle M ix i n g a n d G ra n u lation i n F l u i d ized Beds M . van S i n t An naland * , N . G . Deen and J .A. M . Kuipers
Faculty of Science and Technology, University of Twente, P.O. Box 217, NL-7500 AE Enschede, The Netherlands. Contents 1 . Introduction 2. Discrete element model (DEM) 2. 1 . Model description 2. 1 . 1 . The discrete elements 2 . 1 .2. The gas phase 2 . 1 .3. The collision model 2 . 1 .4. Numerical implementation 2.2. Hydrodynamics in spout fluidized beds 2.3. Example of a simulation of a granulation process 2.4. Conclusions 3. Multi-fluid model 3 . 1 . I ntroduction 3.2. Kinetic theory of granular flow (KTGF) of multi-component mixtures 3.2. 1 . Definitions 3.2.2. Conservation equations 3.2.3. Particle velocity distribution function 3.2.4. Radial distribution function and chemical potential 3 .2.5. Constitutive equations 3 .2.6. Numerical solution method 3.3. Bubble size and induced particle drift in a mono-disperse fluidized bed: comparison of tfm and dem simulations with experiments 3.3. 1 . Bubble size and shape 3.3.2. I nduced particle drift 3.4. Particle segregation rates in a freely bubbling bi-disperse fluidized bed 3.5. Conclusions 4. Outlook Acknowledgments References
* Corresponding author. E-mail: [email protected]
Granulation
Edited by AD. Salman, M.J. Houns/ow and J. P. K. Seville {" 2007 Elsevier BV All riahts reserved
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1 . I NTRODUCTION
In many industrial granulation processes involving dense gas-fluidized bed, mixtures of particles differing in size andjor density are encountered. In these processes, particle mixing and segregation phenomena play a very important role and determine the product quality to a large extent. Moreover, the continuous change in the particle size (andjor density) distribution due to granulation, affects the fluidization behaviour of the bed. Bubbles are known to play an intricate and ambiguous role [1]. On the one hand, rising bubbles can increase the particle segregation rates by carrying a mixture of particles to the top of the bed disturbing the local packing state of the bed, which might result in segregation of the larger or heavier particles. On the other hand, bubbles induce large-scale mixing in the bed equalizing the particle sizejdensity distribution. Accurate prediction of segregation dynamics is required to improve the design, operation and scale-up of gas fluidized-bed granulation processes. With better understanding and quantitative descriptive tools for particle mixing and segregation phenomena, the growth rate and segregation dynamics can be better tuned to improve the product quality. To model gas-fluidized-bed granulation processes a multi-level modelling approach is adopted, which is illustrated in Fig. 1 (see also [2]). The idea of this approach is to use different levels of modelling, each level developed to study
LatticeBoltzmann Model
Fluid-particle i nteraction
Discrete Particle Model
Pal1icle-particle inleraclion
Continuum Model
Particle-particle interaction; Bubble behav i o ur
Larg er scale phenomena
Fig. 1 . Multi-level modelling scheme for dense gas-fluidized beds.
Discrele Bubble Model
Large scale motion I ndu stri al size
Multi-Level Computational Fluid Dynamics Models
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Table 1 . Overview of the (dis)advantages and length scales of gas-solid hydrodynamic
models
Model
Advantages
Lattice Boltzmann model (LBM)
Fully resolved flow field; no closure needed at all
Discrete element model (DEM)
Particle interaction fully resolved
Continuum model
No limitation on number of particles
Discrete bubble model
Can handle very large systems
Empirical engineering models
Can handle very large systems, simple, fast
Disadvantages Only 0(1 02) particles can be treated. Computationally rather expensive Only 0( 1 06) particles can be treated. Closure required for gas-particle interaction Closure required for gas-particle and particle-particle interaction Closure required on bubble-bubble interaction and emulsion properties Depend on nonuniversal closure information
System size 1O-6_10- 5 m 3
References
10-4_1 0-2 m 3
[5 , 6]
1 0- 3-1 0- 1 m 3
[7 ,8]
10- 1_1 0 1 m 3
[9-12]
1 0 1 _1 02 m 3
[1 3]
[3,4]
phenomena that occur at a certain length scale. Information obtained at the level of small length scales can be used to provide closure information at the level of larger length scales. The merits of each of the models along with the corresponding length scale that can be studied are summarized in Table 1 . As indicated in Fig. 1 , discrete bubble models can be used to describe the large-scale circulation patterns of the emulsion phase prevailing in large, industrial scale systems. In this model the large gas bubbles are treated in a discrete mann er, whereas the emulsion phase (the particles plus the interstitial gas) is described as a continuous phase. The discrete bubble model relies on appropriate closure models for the description of the bubble rise velocity, the bubble-bubble interaction (i.e. coalescence) and the hydrodynamic properties of the emulsion phase (i.e. the density and viscosity). In this model the effect of bubble coalescence on the macro-scale circulation patterns can be incorporated. It is quite difficult to obtain information about bubble-bubble interaction experimentally, due to the lack of visual access. For this reason numerical models, such as the continuum model, can be used to acquire the required closure information. In the continuum model, both the gas and particulate phases are described as interpenetrating fluids. Continuum models often use the kinetic theory of granular flow (KTGF) to provide closure equations for the internal momentum transport in the particulate phase. Although these Euler-Euler models have been developed and studied extensively in the literature [7, 1 4-1 6], these models still lack the capability of describing quantitatively mixing and segregation rates in poly-disperse fluidized beds.
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M. van Sint Annaland et al.
Direct experimental validation of the continuum models in large-scale systems is difficult and cumbersome, since only macroscopic phenomena are accessible, such as macroscopic velocity profiles, bubble size distributions, etc., which result, however, indirectly from microscopic interactions between the particles and the particles with the gas phase. In discrete element models (DEM), where each particle is tracked individually, detailed collision models can be incorporated, rendering the DEM a valuable research tool to validate the underlying assumptions in the KTGF concerning the particle-particle interactions and the particle velocity distribution functions (see a.O. [ 1 6]). The interaction between the gas and the particles is another important aspect in the continuum and the DEM, which requires closures. There are a number of semi-empirical closure relations available, which despite their widespread application contain a large uncertainty, rendering accurate prediction of the overall bed behaviour difficult. Techniques, such as the lattice Boltzmann model (LBM) can be used to validate and eventually improve these closure relations. In LBM the flow around small ensembles of particles can be modelIed, without making prior assumptions, so the gas-particle interaction can be quantified [4]. In this work, we will focus on the levels of the DEM and the continuum model. A detailed theoretical description of these models will be given and the predictive capabilities of these models will be iIIustrated with a few examples. 2. D1SCRETE ELEMENT MODEL (DEM)
In the DEM, the behaviour of the gas phase and individual particles and/or droplets is described in detail. The DEM takes into account the interactions between individual elements and between the elements and the gas phase. The gas phase is described by volume-averaged Navier-Stokes equations, whereas the motion of each individual element is described by Newton's laws of motion. Two approaches are generally used for the description of collisions between the elements: a hard sphere approach, which was first used to model fluidized beds by Hoomans et al. [6], and a soft sphere approach, which was first used to model fluidized beds by Tsuji et al. [5]. In this chapter we only present the former approach. 2.1 . Model description 2. 1. 1. The discrete elements
The motion of every individual element i (particle or droplet) in the system is calculated from Newton's second law: dü Vi - + mig- + F-ipp + F-ipw mi Cft; = - ViVP + ß (Ug (1 ) - Ui) a; 11
Multi-Level Computational Fluid Dynamics Models
1 075
where the forces on the right-hand side are respectively due to the pressure gradient, drag, gravity, particle-particle interaction and particle-wall interaction. The inter-phase momentum transfer coefficient ß is frequently modelIed by combining the Ergun equation [1 7] for dense regimes (8g < 0.8): ßdp2 82s + 1 758s Re = 1 50 (2) 8g 11 and the correlation proposed by Wen and Yu [1 8] for the more dilute regimes (8g > 0.8): . ßdp2 24( 1 + 0.1 5Re ·687 ) / Re If Re < 1 03 �4 cD Re 8S 8g-2.65 . CD (3) 11 0 .44 if Re > 1 03 -
_ _ -
.
_
-
,
{
O
where Re = 8gPg J Üg - üp J dp /llg is the particle Reynolds number. The particle Reynolds number is usually much larger than unity, which gives rise to an unrealistic jump in the drag curve at eg = 0.8. This problem can be circumvented by using the minimum of equations (2) and (3) for the calculation of ß. Recently, Koch and Hili derived a new drag relation [3], obtained from simulations using the Lattice Boltzmann approach: ß d�
- = 1 8eg2 es[Fo(es) + 0.5F3 (es)Re] 11
1 /2 + ( 1 35/64)es In es + 1 6. 1 4es _ 1 + 3(es/2) 1 + 0.681 es 8 48e� + 8.1 6e�
Fo ( es) -
- . 0.0232 F3(es) = 0.0673 + 0.21 2es + -eg5
(4)
2. 1 . 2. The gas phase
The gas phase flow field is calculated from the volume-averaged Navier-Stokes equations: a
at ( egPgUg) + _
_
_
-
V(egPgUg Ug) = - egVpg - V(egTg) - Sp + egPgg -
_
(6)
The gas-phase stress tensor is given by (7) where the bulk viscosity Ag can be set to zero for gasses. The two-way coupling between the gas phase and the particles is enforced via the sink term Sp in the
M. van Sint Annaland et al.
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-J -
momentum equations of the gas phase, which is computed from: i ug - Vi- ) 0(r- - -ri)d 1 � � V ß (S-P = v. V cell
i=O es
(8)
The distribution function 0 distributes the reaction force acting on the gas phase to the Eulerian grid. When the volume of the smallest computational cell for the fluid is much larger than the volume of a particle, the mapping of properties from the Lagrangian particle positions to the Eulerian computational grid and vice versa can be done in a straightforward manner through volume-weighing techniques [6,1 0]. On the other hand, when a high-spatial resolution is required for the solution of the gas flow field, the computational grid can become smaller than the particle size. In that case, other distribution functions are needed. One of these functions is introduced in Section 2. 1 .4. 2. 1 . 3. The collision model
The collision model used in this work is based on the hard-sphere model developed by Hoomans et al. [6, 1 9,20]. In this model, it is assumed that the interaction forces are impulsive and therefore all other finite forces are negligible during a collision. Consider two colliding spheres a and b with position vectors Ta and h and radii Ra and Rb ' The particle velocities prior-to-collision are indicated by the subscript 0 and the relative velocity at the contact point c is defined as Uab ua,c - Ub,c = (ua - Ub) - ( Rawa + Rbwb) x ii. For a binary collision of these spheres the following equations can be derived by applying Newton's second and third law: (9) ma( Ua - ua,o ) = -mb (ub - Ub,O) = J ==
la ( - - Wb,O - ) = - n- x JW- - W- a,O ) = - h (Wb Ra a Rb
where the moment of inertia of a particle is given by 2 1 = - mR'2 5 Equations (9) and (1 0) can be rearranged to obtain: 7J - 5ii(Jii) Uab - Uab'O = 2 mab where mab is the reduced mass given by 1 1 mab = - + _
_
(
ma
mb
)-1
( 1 0) (1 1 )
( 1 2)
( 1 3)
In order to calculate the post-collision velocities, a closure model consisting of three parameters is used to describe the impulse vector J. The parameters are the coefficient of normal restitution (0 :::; e :::; 1 ), the coefficient of dynamic friction
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Multi-Level Computational Fluid Dynamics Models
(f.1 ?: 0) and the coefficient of tangential restitution (0 � ßo � 1 ), defined by: uabn -e( uab,On) In JI = -f.1(n.J) =
x
(14) (1 5)
Uabt -{5o (Uab,Ot) -
-
(1 6) Combining equations (12) and (14) yields the following expression for the normal component of the impulse vector: (1 7) Jn -(1 + e)mab(Uab,On) For the tangential component, two types of collisions can be distinguished, Le. sticking or sliding collisions. If the tangential component of the relative velocity is sufficiently high in comparison to the coefficients of friction and tangential restitution, gross sliding occurs throughout the whole duration of the contact and the collision is of the sliding type. The non-sliding collisions are of the sticking type. When ßo is equal to zero, the tangential component of the relative velocity becomes zero during a sticking collision. When ßo is greater than zero in such a collision, reversal of the tangential component of the relative velocity will occur. The criterion to determine the type of collision on basis of pre-collision information is as folIows: if Jn + ß )m (1 8) Jt = -�(1 + ßO )mab(Uab,of) f.1 ?�(1 O ab(Uab,of) -f.1Jn otherwise =
=
{
where the two equations respectively describe collisions of the sticking and sliding type. Given the definition of J in equations ( 1 7) and ( 1 8), the post-collision velocities can now be calculated from equations (9) and (1 0). There are two special types of collisions, i.e. a collision between a particle and a wall and a collision between a particle and a droplet. In particle-wall collisions the mass of particle b (i.e. the wall) is taken infinitely large, which makes all terms containing 11mb equal to zero. The collisions between particles and droplets are generally considered as perfectly inelastic (i.e. e 0, ßo 0 and f.1 = 0) leading to a coalescence of the particle and the droplet. When such a collision occurs, the post collision velocities are given by =
=
=
Wa wa,o 2. 1.4. Numerical implementation
(1 9)
(20)
The equations for the gas phase are coupled with those of the particle phase through the porosity and the inter-phase momentum exchange. All relevant
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M. van Sint Annaland et al.
quantities should be averaged over a volume, which is large compared to the size of the particles, and in such a way that they are independent of the Eulerian grid size. A straightforward method for the calculation of the porosity was given by Hoomans et al. [6]. In their work, the porosity in an Eulerian cell is calculated as folIows: 1 " . . (21 ) cg,cell = 1 - v.- � f�ell V� cell ViEcell
where f;ell is the fractional volume of particle i residing in the cell under consideration. This method works weil when the size of the grid cells is much larger than that of the particles (i.e. Vcell > > Vp). From a numerical point of view however it is sometimes desirable to use small computational cells in order to resolve all relevant details of the gas flow field and to obtain a grid-independent solution. Unfortunately, the method by Hoomans et al. [6] generates problems once Vcell approaches Vp . That is, computational cells can be fully occupied by a particle, which leads to numerical problems. In order to overcome these problems, we suggest a new method to calculate the porosity. In this revised method the particles are represented as porous cubes. The diameter of the cube depends on the particle diameter and a constant factor a, which defines the ratio between the cube and particle diameter and consequently the volume, where interaction between the fluid and the particle under consideration occurs: (22) dcube = adp The volume of the cube should be larger than or equal to the volume of the particle, resulting in 1 /3 (23) a � 6" � 0.8
(n)
The porosity of a porous cube representing a particle can now easily be calculated as ccube
=
\I, = 6n3
Vp cube
a
(24)
Finally, the porous cube representation can be used to calculate the gas fraction in a computational cell in a manner analogous to equation (21 ): (25) cg,cell = 1 - ccube L f;ell 'tiEcel!
where f;ell is the volume fraction of the cell under consideration that is occupied by cube i. Contrary to the real particles, the cubes representing the particles are allowed to overlap. By representing the particle as a porous cube, its presence is feit only relatively weakly in a larger portion of the flow domain. Consequently, grid refinement will
Multi-Level Computational Fluid Dynamics Models
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not lead to local extremes in the gas-fraction around the centre of mass of the particle. The force balance for a single particle, wh ich is used in our model to calculate the acceleration of the particle, is given by equation ( 1 ). Most of the variables in this equation are only available at distinct positions in space (i.e. the Eulerian grid). The acceleration of the particle should however be available on the Lagrangian position of the particle. In order to calculate the acceleration of the particle, these variables need to be mapped to the position of the particle. In order to satisfy Newton's third law, a consistent mapping technique should be used for the calculation of the momentum exchange coefficient ß. Hoomans et al. [6] used a volume-weighing technique for the mapping. Unfortunately, this technique yields a porosity that depends on the numerical grid size. Since the momentum exchange coefficient is non-linear with respect to porosity, the overall calculated momentum exchange is also grid-dependent. Furthermore, numerical problems should be prevented, by circumventing that the local porosity becomes close to zero in case the size of the computational cells approaches the volume of the particles. For a proper treatment of the drag force, the control volume used in the calculations should match the control volume for which the drag relation was derived. Generally, the control volume will be much larger than the particle size (i.e. a = 3-5). For the calculation of the acceleration of the particle, we suggest a method similar to the one presented for porosity mapping. A general variable
=
_1 _ �
� fcube V J
cube VjEcube
(26)
where �cube is the volume fraction of cell j occupied by the cube. On the other hand, a general variable
'Vcell
=
�
� 'deli
(27)
where ':ell is the volume fraction of the cell under consideration that is occupied by cube i. 2.2. Hydrodynamics in spout fluidized beds
The DEM that was introduced in the previous section was used to model the gas and particle dynamics in a spout fluid bed. In order to investigate the validity of the model, the results were compared with the characteristics of the pressure drop
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M. van Sint Annaland et al.
fluctuations and particle flux profiles, which were measured experimentally. Two typical operating conditions were selected from the flow regime map, which is shown in Fig. 2. This map was obtained by [21 ] in a 3D-spout fluid bed, with the spout positioned at the front wall. The different flow regimes were identified on basis of high-speed camera observations combined with measurements of the pressure drop fluctuations. In this section the spout-fluidization regime and the jet-in-fluidized-bed regime are investigated. The spout-fluidization regime is
Spout with Aeration
J et in
Fluidized Bed
Fig. 2. Regime map with example snapshots of the flow in a 3D spout-fluid bed. The background velocity (Ubg) was varied from 0 to 3.5 mjs with increments of 0.5 mjs and the spout velocity (usp) was set to 0 and varied from 40 to 95 mjs with increments of 5 mjs. All gas velocities were normalized by the minimum fluidization velocity (Umf)'
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Multi-Level Gomputational Fluid Dynamics Models
characterized by a steady spout channel, which is periodically blocked by particles moving into the spout channel from the annulus. In the jet-in-fluidized bed regime the particle dynamics are dominated by the relatively high background velocity. In the annulus surrounding the spout channel, bubbles are formed continuously. Similar to the spout-fluidization regime the spout channel is periodically blocked. This generally occurs at a low position in the bed involving a large number of particles. Removal of the blocking particles from the spout channel consumes more time and consequently leads to a lower dominant frequency compared to the spout-fluidization regime. The physical properties of the phases, along with the numerical settings used in the simulations are presented in Table 2. A schematic representation of the mode lied spout-fluid bed can be found in Fig. 3. The particle collision characteristics play an important role in the overall system behaviour as was shown by Hoomans et al. [6] and Goldschmidt et al. [22]. For this reason realistic collision properties of the particles are supplied to the model, i.e. the coefficients of normal and tangential restitution are respectively set to e 0.97 and ßo = 0.33, and the coefficient of friction is set to J1 0. 1 . In order to investigate what drag model is most appropriate to describe the gas-particle interaction, the following drag models were applied: =
=
• • •
Conventional model: the relation of Wen and Yu [1 8] is used when 8g < 0.8 (equation (2)), and the equation of Ergun [1 7] (equation (3)) when 8g > 0.8. Minimum model: the minimum of the relations by Wen and Yu [1 8], and Ergun [1 7] is used. Koch and Hili model: equation (4) is used.
Table 2. Physical properties and numerical settings for the granulation simulation
Parameter
Symbol
Gase 1
Gase 2
Gase 3
Unit
I nitial particle diameter Particle density Number of particles Droplet diameter Droplet density Droplet flow rate Gas density Gas viscosity Background gas velocity Gas velocity in the spout Number of celis in the X-direction Number of cells in the Y-direction Number of celis in the Z-direction Time step particles Time step droplets Time step gas
dp Pp Np dd Pd Fd Pg f.i.g Ubg Ujet NX NY NZ
4.0 2526 44,800 n.a. n.a. n.a. 1 .2 1 x 1 0�3 1 .5 30 15 1 200 1 x 1 0�4 n.a. 1 X 1 0�4
4.0 2526 44,800 n.a. n.a. n.a. 1 .2 1 x 1 0�3 3.0 20 15 1 200 1 x 1 0�4 n.a. 1 x 1 0�4
3.0 ± 0.2 2526 39,667 200 2526 2.2 x 1 0�6 1 .2 1 X 1 0�3 3.5 40 30 1 240 1 X 1 0�4 1 .6 x 1 0�5 1 X 1 0�4
mm kg/m3
Li tp Li td Li tg
pm kgjm 3 m /s kg/m 3 kg/(m s) m/s m/s
s s S
1 082
M . van Si nt Annaland et al.
/
/
2000
.�
/
x
/
.�
YL 70 10 70 x
Fig. 3. Schematic representation of the geometry of the pseudo-2D bed, dimensions are given in millimeters.
3� r-----, - Exp.
3500
,-----------
3000
Cii'
�
- Kochand
- mln(Ergun. Wen and Yu)
- Koch 800 Hili
3000
2500
--,
__ __ __ __ __
-ErgurvWen and Vu
- ErgunIWen and Yu
Hili
-mln(Ergun, Wen and Yu)
� 2500
2000 1�
1�
�--�
1� � -1 1 .0
�
__ __ � __ � __
1 1 .2
1 1 .4
1 1 .6
1 1 .8
I [sJ
Case 1 ,
spollt-tlllidization
12.0
----�----�
__ � ____ �
1�� 18.0
18.5
19.0
1 [8J
19.5
20.0
Case 2. jel-in-f1uidized-bed
Fig. 4. Measured and computed pressure drop fluctuations over the entire bed for two different regimes using several drag c1osures.
For spout-fluidization (Gase 1 in Fig. 4) a periodically fluctuating pressure drop is obtained for the model of Koch and Hili, the minimum model and the experiments, while the conventional model displays a less regular pattern. These results are also reflected in the power spectra for Gase 1 , which are presented in Fig. 5. That is to say that, except for the conventional model, a dominant frequency between 5 and 6 Hz is found. The jet-in-fluidized-bed case (Gase 2 in Fig. 4) shows that the differences between the drag models are less pronounced resulting in similar frequency spectra for Gase 2, which are given in Fig. 5. Each of the drag closures predicts a randomly meandering spout, which leads to an irregular pressure drop signal.
1 083
Multi-Level Computational Fluid Dynamics Models 100,000
, ,000, 000,--, -Koch and H ili - Exp.
100.000
_
�
';
""
[
!!:.
1 ,000
c.
- ErgurvWen and Yu
- mln(Ergun, Wen and Yu) - - Koch and Hili
10,000
N� 10,000 "
,::-....,.,.,-,-:-:----,
�
'00
1 ,000
1 00
10
6
9
12
frequency (Hz]
12
15
15
frequency [Hz]
Case I, spout-nuidization
Case 2, jet-in-nuidized-bed
Fig. 5. Measured and computed pressure drop fluctuations over the entire bed for two different regimes using several drag c1osures.
�E
'ä;
900
600 ,------,
600
400
e
=:
-600
-900 0.00
,�
., ,
=��(g;�� X'edn��d Yu) , •
200
=;; -200
0
� -300
�
Ni
300
Exp.
0
•
' -400
- -Koch and Hili
0.05
x [m]
0.10
Case I, spoul-fluidization
0.15
Exp.
- ErgunIWen and Yu - min(Ergun, Wen and Yu) - - Koch and Hili
-800 .J..:-----� 0.15 0.10 0.05 0.00 x [m] Case2, jet-in-fluidized-bed
Fig. 6. Frequency spectra of the measured and computed pressure drop fluctuations over the entire bed for two different regimes using several drag c1osures.
In Fig. 6, Gase 1 displays a relatively narrow peak in the vertical time-averaged particle flux profile, which is captured rather weil by both the Koch and Hili model and the minimum model. The conventional model however, produces a broader peak. The deviating results obtained from the conventional model can be attributed to the discontinuity in the drag relation at = 0.8. In this case, the relation of Wen and Yu [1 8] is used in the spout region, whereas the relation of Ergun [1 7] is used in the annulus. The system will therefore display behaviour, which resembles the situation with a higher background velocity and a lower spout velocity, and will consequently resemble the results for Gase 2. Figure 6 shows that for Gase 2 all drag models predict similar particle flux profiles. The agreement with the experimental results is very good. The conventional drag model is less suitable for modelling fluid beds with stable high-velocity jets, as encountered in spout(-fluid) beds. The minimum of the relations of Ergun [1 7], and Wen and Yu [1 8], as weil as the relation proposed by Koch and Hili [3] are more suitable, although the computed frequency of the pressure drop fluctuations is somewhat too high. 39
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M . van Sint Annaland et al.
2.3. Example of a simulation of a g ranulation process
With the use of the DEM the interaction between droplets and particles and the evolution of the particle size distribution as encountered in granulation processes, can be modelIed in a deterministic fashion. Results of a sam pie calculation are discussed in this section. In this example a pseudo-2D flat bed was filled with particles with a size distribution around 3 mm. A schematic representation of the bed can be found in Fig. 3. The particles in the bed are fluidized through background fluidization gas streams, which enter the bed alongside the spout. The droplets are introduced to the bed through the spout. The interaction between the droplets and the gas phase is handled through one-way coupling. That is to say that the droplets are assumed to enter the bed at their terminal velocity and thereafter follow the gas stream. The effect of the droplets on the phase fractions and the feedback effects from the droplets to the gas phase are neglected. The properties of all the phases, along with the numerical settings are presented in Table 2. An impression of the particles dynamics can be obtained from Fig. 7, which shows an instantaneous snapshot of the particle velocity field along with the particle positions and their sizes. The air originating from the spout moves through the bed in a meandering fashion. It can be seen that particles are entrained in the spout stream from both si des of the bed. Most particles move down along the side walls and return to the spout region. When the particles enter the spout stream, they impact with droplets and grow accordingly. Figure 7c shows that most particle-droplet collisions take place in a very small region just above the spout mouth. It is stressed that the DEM can be used to deduce growth kerneis for the particle phase or alternatively sink terms for droplet transport equations, which can be used in higher level models, such as the multi-fluid model (MFM) or the discrete bubble model. In order to investigate the particle growth rate as a function of the particle size, the particles were split into four particle size groups. Figure 8 shows the partial density functions of the growth rate of each of the different particle c1asses during a simulation period of four seconds. The particles outside the spout region hardly come in contact with droplets. It is these particles that show a large peak in the partial density function around zero growth. A second peak is observed for each of the particle c1asses around 0.1 5-0.25 mm 3/s. This peak results from the particles that have travelled through the spout region and have been hit by droplets. It is seen that the position of this peak on the x-axis (i.e. the growth rate) scales with the mean surface area of the particles. Furthermore it is observed that the fraction of particles that grows in the spout region is larger for small particles than for large particles. That means that the number of encounters with droplets is relatively larger for small particles as compared to large particles. This can be explained from the fact that small particles that return to the spout region are able
Multi-Level Computational Fluid Dynamics Models
1 085
... 2.0 mI!l
( a)
Fig. 7. Close-ups of the instantaneous particle velocity field (a), instantaneous snapshot of
particle positions and sizes (b), and cumulative density function of the number of deposited droplets for a period of 4 s (c) predicted by the DEM.
to move closer to the bottom plate, due to their smaller size. Consequently, they have a higher probability to be hit by droplets as compared with the larger particles, which are partly blocked by the small particles. 2.4. Conclusions A hard-sphere DEM was developed, which takes into account all relevant
interfacial interactions in a deterministic manner. It was shown that for systems with relatively large particles subject to high velocities as experienced in spout fluid beds the conventional drag model (the equation of Ergun [1 7] when <-g < 0.8 and the equation of Wen and Yu [18] when <-g > 0.8) performs worse than the minimum of the two equations and the new drag model derived by Koch and Hili [3] based on lattice Boltzmann simulations. Furthermore, it was demonstrated how the DEM can be used to obtain information about the interaction of the discrete phases, i.e. the growth zone in a spout-fluid bed. This kind of information can be used to obtain closure information required in higher level models.
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M. van Sint Annaland et al.
0.03 . Class 1 ; dp 2.70 - 2.85 mm Class 2; dp = 2.85 - 3.00 mm • Class 3; dp = 3.00 - 3.15 mm • Class 4; dp = 3. 1 5 - 3.30 mm =
•
..!.. t/l t/l IU
(j l!l
(j t
0.02
'iii CI)
IU Co
-
0 c:
.2 Ü
0.01
IU ..
LI..
0.00 L-�-�---r---�-���� 0.00 0.05 0.10 0. 1 5 0.20 0.25 0.30 0.35 0 . 40 Growth rateper particle [mm3/s] Fig. 8. Probability density function of the growth rate for four different particle size classes during 4 s of simulation time. The symbols are actual simulation results. The lines are fits to the simulated data and are merely intended for visualization.
3. M U LTI-FLUID MODEL 3. 1 . Introduction
In order to gain more insight in how the operating conditions affect the particle mixing and segregation rates and to elucidate the role of the bubbles, fundamental hydrodynamic models are required. To enable a quantitative description of particle mixing and segregation phenomena, it is essential that the bubbles and the bubble behaviour (bubble break-up and bubble coalescence) is resolved with sufficient accuracy. This entails that a sufficiently large part of the fluidized bed is modelIed in order to capture the macro scale particle motion in the fluidized bed, while still completely resolving the phenomena occurring at the scale of a single bubble. Due to the required size of the computational domain to study particle mixing and segregation phenomena, a continuum modelling approach is needed. Smaller systems could be simulated with more detailed DEMs, which can (or even should) be used to validate assumptions required in the continuum approach (a.o. [1 6, 1 9,20,23]). However, for systems at engineer ing scale, which capture the macro scale circulation patterns, the required number of particles and the corresponding calculation times would definitely become prohibitive. With discrete element simulations the importance of particle-particle collision parameters on the bubble dynamics and consequent segregation rates has been demonstrated.
Multi-Level Computational Fluid Dynamics Models
1 087
In the continuum approach both the gas and particulate phases are described as interpenetrating continua. In the continuum approach only the ensemble averaged behaviour of a group of particles is considered, which should be sufficiently large in number to allow for a statistical description of the particle-particle interactions, but also sufficiently small to still resolve all the prevailing local phenomena. Poly-disperse particle mixtures can be described with multi-fluid continuum models, which divide the particle mixture in a discrete number of classes, for which different physical properties may be specified. The conservation equations employed are a generalization of the Navier-Stokes equations for interpenetrating continua. Owing to the continuum representation of the particle mixture, multi-fluid continuum models require additional closure laws for the description of the rheology of the particulate suspension. Since accurate modelling of bubble dynamics is of crucial importance to capture segregation dynamies, and bubble behaviour strongly depends on the amount of energy dissipated in particle-particle collisions, the closure laws should account for the effect of energy dissipation due to non-ideal particle-particle encounters. Closure laws derived from the KTGF have significantly improved the description of the bubble behaviour of mono-disperse gas-fluidized beds (see for a critical comparison [24,25]). A MFM with a novel set of closures was derived, extending the classical kinetic theory for dense gas multi-component mixtures to account for non-ideal particle-particle collisions as weil as for gas-particle drag. The Chapman-Enskog solution method of successive approximations is used [26], following the work by L6pez de Haro et al. [27] and Jenkins and Mancini [28,29]. In this section, firstly, the MFM is described. Subsequently, the bubble size and shape and induced particle-drift are studied for an idealized mono-disperse system, where a single bubble is injected with a jet into the centre of a pseudo two-dimensional fluidized bed at incipient fluidization conditions. Simulation results obtained with the continuum model are compared with discrete particle simulations and dedicated experimental results. Finally, simulation results on the segregation rates in bi-disperse freely bubbling beds are compared with experimental results, demonstrating the capabilities of the MFM. 3.2. Kinetic theory of gra nular flow (KTGF) of multi-component mixtures 3. 2. 1. Definitions
The KTGF of multi-component mixtures describes the mean and fluctuating motion of particles of all species (1 . . Np) based on the assumption that the velocity distribution fn(cn , r, t) of individual particles of species n, among a large number nndr of particles within an ensemble of volume dr, can be represented by the distribution of their velocity points cn in the velocity space. The number of .
1 088
M. van Sint Annaland et al.
particles of species n per unit volume and the ensemble average of a particie quantity
J fn(cn, r, t) dCn (
=
(28)
(29)
Defining the mean velocity ün of particie species n as (cn), the mass average mixture velocity Üs is given by
(30) where the particie number density ns, total solids volume fraction es and the mixture density Ps are defined as
(31 ) (32) 63 1 Np n with = mn (33) n Pn L: e Ps = P es n=1 R(Jn The actual particie velocity cn is decomposed into the local mass average mixture velocity Üs and the peculiar velocity Cn :
(34)
Associated with the random motion of the particies, the granular temperature and the diffusion velocity of species n are defined as
1 en = 3 mn ( � )
(35)
Vn = (Cn) = ün - Üs
(36)
from which the mixture granular temperature is obtained by
1
Np
es = - L: nnen ns n=1
(37)
and the diffusion velocities naturally satisfies Np
L: en Pn Vn = Ö n=1
(38)
The kinetic theory accounts for two different transport mechanisms of particie properties. On the one hand, particies can transport a property by carrying it
1 089
Multi-Level Computational Fluid Dynamics Models
during free flight between collisions (kinetic transport), on the other, particle quantities can be transferred during a collision (collisional transport). Modelling these transport mechanisms for a particulate mixture results in a set of coupled integral-differential equations, referred to as the generalized Boltzmann equation, describing the rate of change of the velocity distribution fn of species n, moving under influence of an external force Fn and colliding with particles of all species present in the particle mixture, as iJtt + cn �:? + at (�� fn ) = I: JJ [f,;;l (c; n , r; c�p , r + (Jnp k; t)
p
]
(C12np k:>:O)
(39) - f,;;) (c;n' r; c�p ' r + (Jnp k; t) (J�p ( C12ni) d k dC2 where fn(cn , r; t) dr dCn represents the probable number of particles present at time t in a volume dr at position r possessing a velocity between cn and cn + dCn , while the pair-distribution function f,;;J is defined in such a way that fn�) (C1 n ' r1 ; C2p ' r2 ; t) dr1 dr2 dC1 n dC2p represents the probability of finding a pair of
particles in volumes dr1 and dr2 centred around points r1 and r2 having velocities within the ranges C1 n and C1 n + dC1n and C2p and C2p + dC2p respectively. In this equation (Jnp = « (Jn + (Jp) /2 is the inter-particle distance, C12np C1 n - C2p th � impact velocity between particle 1 of species n and particle 2 of species p and k the unit vector directed from the centre of particle 1 to the centre of particle 2 at contact. Furthermore, c; n and c�p denote the particle velocities after collision, which can be related to the velocities prior to collision according to =
(40)
c-,2p
mn
=
--
C2p + mn + mp (1 + enp)(c- 1 2np k)k
(41 )
where enp represents the coefficient of normal restitution for collisions between particles of species n and p, defined by the following relation between the impact and rebound velocity: (42) ( C'12np k) = -enp(c12np k) 3. 2. 2. Conservation equations
The ensemble average transport equation for particle property CPn, referred to as the Maxwell transport equation, can be obtained by multiplying the generalized Boltzmann equation with CP n dCn and integrating over the entire velocity space, which yields:
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M. van Sint Annaland et al.
where nn Ap4>n represents the rate of change of property 4>n due to collisions with particles of species p, which is decomposed in a collisional source Xnp(4)n) and collisional flux 8np(4)n) term:
nnAp4> n = Xnp(4)n) - 8,ßnp(4)n) 8
(44)
(46) The conservation equations for mass, momentum and fluctuating kinetic energy for each species n can be obtained from the Maxwell transport equation by substituting for the particle property 4>n: mn , mncn and �mn� respectively. The mixture conservation equations are obtained by summing over all species n and are listed in Table 3 . The external forces acting on the particles that are relevant for gas-fluidized beds are gravity, buoyancy and drag exerted by the gas phase: 1 ßng Fn (47) 9 - - VPg + -- (cg - cn)
mn
- =
-
nnmn
Pn
-
In the mixture granular temperature equation the correlation between the fluctuating velocities of the gas and particulate phases (CgCn) (turbulence Table 3. Conservation equations
Species continuity equations: Mixture continuity equation: Mixture momentum equations:
ft (önPn) + v pn + 8nPnusl where Jn
önPn(Cn)
ft(ösPs) + V(ösPsus) =
0
ft (ösPsus) + V(ös Psusus)
0
-
-ös VPg - VPs - VTs + L ßng(Ug un) + ösPs9 Np
=
n�1
t (nnmn(Cn Cn) + p�1t Onp(mncn») 1 - (Psi"0 + es= ) .. VUs - Vqs l; 3 ßng On [c(nsos) 2 --;;r- + V(nsOsus)
where psi + Ts Mixture granular temperature equation:
=
=
3
where Cis and Ys
=
Np
-
=
=
(
-
n�1
-
=
_
� � nnmn(�Cn) + n
L L Xnp G mn c;) Np
Np
n�1 p�1
-
-
;E OnpG mn�)) Np
Np
mn
-
,
Ys
1 09 1
Multi-Level Computational Fluid Dynamics Models
modulation) has been neglected, which is allowed when modelling dense fluidized beds. For the evaluation of the transport coefficients defined in Table 3 explicit functions for the individual particle velocity distribution function fn and the pair distribution function fnp(2) are required. 3. 2. 3. Particle velocity distribution function
In order to determine the collisional terms in the balance laws, the pair distribution functions at contact �� (C1 n ' (1 ; C2p' (2 ; t) d(1 d(2 dC1 n dC2p are needed. Following Enskog, assuming binary interactions and 'molecular' chaos, i.e. information on the particle velocity of a certain particle is lost after only a few collisions, the pair distribution function can be approximated by the product of two single-particle velocity distribution functions and the radial distribution function gnp (( - �O"npk, r + �O"npk) that corrects the probability of a collision for the volume occupied by the particles: ( - 1 -. - - 1 - _ - 1 - 1 fnp2) C1 nJ - "2 O"npk, C2pJ + "2 O"npk,. t - gnp r - "2 O"npkJ + "2 O"np k fn
(
(
-
C1 n , r -
; O"npk; t) fp (
C2 , ( + p
)
; O"npk; t)
(
)
(48)
In order to avoid conflicts with irreversible thermodynamics that arise for multi-size particle mixtures when the radial distribution function is evaluated at a specific point on the line joining the midpoints of the two colliding particles at contact, Van Beijeren and Ernst proposed the so-called Revised Enskog Theory (RET) [30]. According to this theory a non-Iocal functional of the particle density field is taken for the radial distribution function, which give rise to gradients of the chemical potential of all species n present in the particle mixture instead of the gradient of the radial distribution function that appears in the standard Enskog theory. The RET was also employed by L6pez de Haro et al. [27] and Jenkins and Mancini [29], whose results have been used to derive detailed expressions for the particle velocity distribution functions for multi-component mixtures of inelastic spheres. The particle velocity distribution function for particles of species n can now be obtained by solving the generalized Boltzmann equation. Here the Chapman -Enskog solution method of successive approximations is applied [26]: fn = f�O ) + f� 1 ) + f�2 ) + . . . (49) where in this work terms up to the second approximation fn( 1 ) have been included. The first approximation to the velocity distribution is the velocity distribution of a non-dissipative system at equilibrium. The effects of energy dissipation in particle-particle collisions and spatial gradients in the state variables are taken into account in the second approximation by the coefficients of normal restitution
1 092
M. van Sint Annaland et al.
enp and a perturbation function
(50) The solution of the generalized Boltzmann equation for species n has been summarized in Tables 4 and 5 . Explicit expressions for the bracket integrals for hard spheres up to the third order Enskog approximation, appearing in Table 5, have been given by Ferziger and Kaper [31 ] and L6pez de Haro et 81. [27], and can also be found in Goldschmidt [22]. It is important to note that in the Enskog solution procedure the first order approximation corresponds to the situation that the particulate suspension is in steady state and at equilibrium, Le. the particles are not subjected to external forces, the particles are uniformly suspended (no gradients in solids volume fraction and velocity and granular energy) and that no kinetic energy is dissipated in the particle-particle collisions (enp = 1 ). Thus, the first order approximation requires that the particle velocities of all particle species are distributed around the
t(O)
Table 4. Particle velocity distribution function
First-order approximation (Maxwellian velocity distribution): Second order approximation: First order perturbation function:
n
=
(
--'I!.rL) nn 21[Os
3/2
exp (
_
.
20s
-
2
mn(Cn -Us)
)
mn N b(n) S(r) 1[2 ) H Bn = 28 "" 6 r 5/2( n ' -1
n
s (=0
where the Sonine polynomials have been defined as: S�\x) and denotes the product of the q factors 1 -q dimensionless peculiar velocity: Cn ji;Cn rq
Diffusion force:
External forces based on averaged velocities: First-order approximation for the particulate phase pressure:
an
=
['Vp�O) t ( [ 4" --
)] 1 'V r, r-
=
... r
+
_
S
-1 N"" Hn) (r) (1[2 ) L r S1/2 n (=0
=
cnpn Fu,n cp pp Fu,p + � espsnsBs mp mn p= 1 N N nn p mn np 3 + - L ,)np + 3 n s + nnI) Lp1 mn + mp (Jnp9np I e ns p= ns p=1 -
-
1
n
L (-x)P (;��;)F ,
p�O ,
having used the
(apan) p
n OS,nkolP
'Vnp
1 093
Multi-Level Computational Fluid Dynamics Models Table 5. Sonine coefficients
Sonine coefficients a/n ):
Np N-1 p= 1 r=O n r Np ( n)
'\"' '\"' A. qrp alP) 6 6
L !:nPn a0 = 0
n=1 i:sPs
= 15 '2a ns Kn 1:5q1
-
1)
( n = 1 ; q = 0)
b/n):
Np N- 1 2n n Kn' 1:5qO '" '" Hqr HP) = L L np r 0 n p=1 r=O
Sonine coefficients
(n = 1 , 2, . . . , Np; q = 0, 1 , . . . , N
-
(n = 1 , 2, . . . , Np; q = 0, 1 , . . . , N - 1 )
S
S
Sonine coefficients h?):
Np N-1 '" rqnpr h(P) = nn Kn" 1:5q1 (n = 1 , 2, . . . , Np; q = 0, 1 , . . . , N - 1 ) n p=1 r=O Np L 9;: h;n) = O (n = 1 ; q = 1 ) n=1
'" LL
r
S
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M. van Sint Annaland et al.
Table 5. Continued
(n = 1 , 2 , . . . , Np; q = 0, 1 , . . . , N Np
'\"' L..
n=1
'nPn 'sPs
-
1 ; i = 1 , 2 , . . , Np) .
cf/) n.O = 0 (n = 1 ; q = O ; I' = 1 , 2 , . . . , Np)
same mean velocity (the mixture velocity) with the same granular temperature (the mixture temperature). This is in contrast with the equations derived by Manger [32], Mathiesen [33], Huilin et al. [34] and Ramahan et al. [35], who assumed that the first order approximation to the particle velocity distribution is Maxwellian distributed around different mean velocities and different granular temperatures for all particle species involved. Hence, in this work differences in the granular temperatures for the different particle species and particle segregation are higher order effects arising from the first order perturbation function. 3. 2.4. Radial distribution function and chemical potential
In order to arrive at a consistent set of equations, where the sum of the diffusion forces over all species present in the particle mixture equals 0, the chemical potential and the radial distribution function should result from the same equation of state. The equation of state for a multi-component hard-sphere particle mixture has been derived from the compressibility of a single-component hard-sphere system, applying the recipe proposed by Santos et al. [36]. The results have been summarized in Table 6. 3. 2. 5. Constitutive equations
Explicit expressions for the transport properties, i.e. the diffusion fluxes, normal and shear stress tensor, granular energy flux and granular energy dissipation rate, defined in the conservation equations listed in Table 3 can be obtained via substitution of the derived particle velocity distribution function and performing the ensemble averaging. The resulting constitutive equations are given in Table 7. For the gas-particle momentum transfer coefficient ßnp the combination of the equations of Ergun [ 1 7] and Wen and Yu [ 1 8] was used. 3. 2. 6. Numerical solution method
The MFM for a multi-disperse suspension consists of the total continuity and Navier-Stokes equations for the continuous gas phase and the species and
Multi-Level Computational Fluid Dynamics Models
1 095
Radial distribution function and chemical potential for multi-component hard sphere systems
Table 6.
Radial distribution function for multi component hard sphere particle mixtures:
where ((JU) ) I: ii; dn Np
Radial distribution function for a mono-disperse hard-sphere fluid:
(1 )(,:1 ) ") " n= 1
'L cjI!s 8
gO( Es)
=
-
,
where in this work the coefficients derived by Song used:
et 81. [37]
have been
= 0.6435, 8 = 1 , b = 0.76, Co = 1 , C1 = 1 .3 1 92, C2 = 1 .4 1 872, C3 = 0.94208, C4 0 . 1 381 376, C5 = -0.3659776, C6 = -2.336768, Cl = - 1 .9857408, Cs = -7.5431936 fln = Os In nn + Os In A� + !l�x Esmax
=
Chemical potential of species n in a hard sphere mixture: Excess chemical potential of species
, [1
] ( Yn 1 - 2yn31 ) ] Os lS
Where An represents the De Broglie wavelength for granular materials ex ) '( 1 Pn = { sYn3
n:
+
'2 (m
1 + m2)4 ösgO + ( 1 + m 1 - 2m2)
- [ 1 + m1 (Yn1 l + Yn2)
where
-
� [m1 (Yn1 1 + yn21 - y;l ) + m - Yn3 1 )
2
3 2
2 m2 (3yn2 )
1
ES _
ös
4g0 ( E�) dE�
- 2Yn3 ))] Os In(1
- Es)
mixture continuity equations, mixture Navier-Stokes equations and the mixture granular temperature equation for the solids phase. Standard prescribed pressure, inflow, no slip and zero gradient boundary conditions were assumed in this work (see also [38]), since particle-wall collisions play a minor role in dense gas-fluidized beds. For dilute multi-disperse systems the boundary conditions proposed by Sinclair and Jackson [39] could be extended. A numerically advantageous feature of this MFM is that only the mixture Navier-Stokes equations and mixture granular temperature equation need to be solved, since explicit expressions have been derived for all the transport properties of the particulate phases in terms of the mixture velocity and the mixture granular temperature. This is in strong contrast to other MFMs proposed in the literature [32-35], where Navier-Stokes equations and a granular temperature equation needs to be solved for every particle species present in the particulate mixture. The granular temperature and diffusion velocity of particle phase n can be directly computed from the mixture granular temperature (see Table 8). As a consequence of the first order perturbation function, particle
1 096 Table
M. van Sint Annaland et 81.
7. Constitutive equations for particulate phase n
Diffusion flux:
Solid phase pressure:
Solids phase stress tensor: Solids phase shear viscosity:
Solids phase bulk viscosity:
Granular energy dissipation: Granular energy flux:
phases of different diameter or density will in general possess different granular temperatures, which is in correspondence with experimental data by Zhang et al. [40] for dilute gas-solid riser flow. Due to the tendency of inelastic particles to contract into high-density clusters and the strong non-linearity of the particle pressure near the maximum packing density, special care is required in the numerical implementation of the MFM conservation equations. The implementation is based on a finite difference technique employing a staggered grid and the numerical algorithm strongly resembles the Semi-implicit method for pressure-linked equations (SIMPLE) described by Patankar and Spalding [41 ] . A detailed discussion on the application of this numerical technique to two-fluid models (TFM) for gas-solid fluidized beds has been presented by
Multi-Level Computational Fluid Dynamics Models
1 097
8. Constitutive equations for the granular temperature and diffusion velocity of phase n (up to second order approximation)
Table
Granular temperature:
Diffusion velocity:
_
_
_
�1)
Vn = Un - Us = -8n P n
Kuipers et al. [42]. Basically, this method is a prajection-correction method, which involves the solution of a Poisson equation for the gas phase pressure field to annihilate the mass residuals fram the total gas phase continuity equation. In principle this numerical solution method can be applied straightforwardly to the MFM equations. However, due to the strong non-linear dependency of the solids phase pressure on the solids volume fraction, unacceptably small time steps are required in the order of magnitude of 1 0 - 5-1 0-6 s. Therefore, this numerical algorithm has been extended (see [22]) to directly take the compressibility of the particulate phase into account in the calculation of the particle volume fractions. In this numerical algorithm, referred to as the P-8s algorithm, an additional Poisson equation is solved (sequentially) for the total solids volume fraction field to minimize the mass residuals fram the mixture solids phase continuity equation. Due to the enhanced numerical stability larger time steps can be handled (10- 5-1 0-4 s) with this method, even for strangly dissipative systems. In the next sections, simulation results obtained with the MFM will be presented and discussed, focusing first on the bubble size and shape and the induced particle drift by a single injected bubble passing through a mono-disperse fluidized bed at incipient fluidization conditions and subsequently on the particle segregation rates in a freely bubbling bi-disperse fluidized bed. 3.3. Bubble size and induced particle drift in a mono-disperse fl uidized bed : comparison of tfm and dem simulations with experiments
Since bubble dynamics play a very important role in particle segregation phenomena, it has been studied first whether continuum models can accurately resolve the bubbles in gas-solid mono-disperse fluidized beds. The computed bubble size and shape are compared with DEM simulations and dedicated experiments for an idealized case, where a single bubble is injected with a jet into the centre of a pseudo two-dimensional mono-disperse fluidized bed at incipient
M. van Sint Annaland et 81.
1 098
fluidization conditions. Subsequently, the extent of particle mixing is studied caused by the passage of a single injected bubble through a fluidized bed at incipient fluidization conditions, where the bed consists of two layers of identical particles only differing in colour. 3. 3. 1. Bubble size and shape
The evolution of the bubble size and shape in time of a single bubble injected with a central jet into a fluidized bed, kept at minimum fluidization conditions via a porous plate distributor, was recorded with a high-speed digital camera (LaVision ImagerPro HS, frame rate: 625 Hz; exposure time: 0.5 ms; resolution: 1 280 H x 1 024 V). Experiments were performed in two separate flat beds: (0. 1 5 m x 0.01 5 m 1 .00 m; 0.01 m jet width) and (0.30 m x 0.0 1 5 m 1 .00 m; 0.0 1 5 m jet width), with spherical glass beads of 2.5 mm diameter (2526 kgjm 3), fluidized with humidified air (70%). The initial bed height was 0.22 m, the background velocity was set at 1 .25 mjs and the jet velocity and pulse duration were 20 mjs and 1 50 ms. Further details about the experimental set-up can be found in [1 1]. In Figs. 9 and 1 0 the pictures of the bed at different moments in time after bubble injection have been compared with simulation results obtained with the DEM using a 1 5 45 and a 40 x 80 grid for the large bed and the small bed respectively (handling the particle dynamics fully 3D, while approximating the gas phase as 20) and the TFM using a 30 90 and a 60 x 1 20 grid, employing a time step of 1 0-5 s in the flow solver. The restitution coefficient for particle-particle collisions was 0.97. Both models capture the interaction of the particles with the jet: particles in the wake of the bubble are dragged into the centre of the bubble, although this effect seems to be slightly overestimated by the TFM. Additionally, the raining of the particles through the roof of the bubble is predicted by the simulations. Clearly, the wall effects on the shape of the injected bubble are much less pronounced in the wider bed, which results in a rounder bubble shape. Both the DEM and TFM predict a slightly larger bubble size compared to the experiments for both beds, which can be attributed to the implemented equations for gas-particle drag (Ergun [1 7] and Wen and Yu [1 8] drag closures). A somewhat better correspondence with experiments was obtained (see [43]) with new gas-particle drag closures derived from Lattice-Boltzmann simulations (Koch and Hili [3,4]). Similar results were obtained for systems with different particle diameters and fluidization velocities. Concluding, the bubble size and shape for a single bubble injected into a bed at minimum fluidization conditions can be weil described with the DEM and TFM. x
x
x
x
3. 3. 2. Induced partic/e drift
Subsequently, the extent of particle mixing induced by a single bubble passing through a mono-disperse fluidized bed at incipient fluidization conditions has
Multi-Level Computational Fluid Dynamics Models
1 099
1 = 0.4 5 Exp.
DEM
TFM
Fig. 9. Injection of a single bubble into the centre of a mono-disperse f1uidized bed (bed width: 0 . 1 5 m), consisting of spherical glass beads of 2.5 mm diameter at incipient fluidization conditions. Comparison of experimental data with DEM and TFM simulation results for 0 . 1 , 0.2, 0 . 3 , 0.4 and 0.5 s after bubble injection.
been studied with the DEM and TFM and compared with experiments (see Fig. 1 1 ). To visualize the particle mixing in the experiment and in the DEM two layers of particles have been used, differing only in colour. In the TFM simulations fictitious marker particles, initially positioned at a regular spacing, were used to visualize the induced particle mixing. The figure shows that the DEM can weil describe the extent of particle mixing, especially when keeping in mi nd the large impact of the background velocity on the particle drift profile in the centre of the bed [43]. However, the TFM grossly overpredicts the extent of particle mixing induced by a single bubble, which can largely be attributed to the neglect of
1 1 00
M . van Sint Annaland et al. t = 0.4
s
Exp.
DEM
TF M
Fig. 1 0. Injection of a single bubble into the centre of a mono-disperse fluidized bed (bed width: 0.30 m), consisting of spherical glass beads of 2 . 5 mm diameter at incipient fluidization conditions. Comparison of experimental data with DEM and TFM simulation results for 0 . 1 , 0.2, and 0.4 s after bubble injection.
1 1 01
Multi-Level Computational Fluid Dynamics Models (J= 2.5
(J= 1 . 5
mrn
mrn
Experiment
DEM
TFM
DEM
TFM
(a)
(h)
(e)
(d)
(e)
Fig. 1 1 . Induced particle mixing due to passage of a single injected bubble i njected into the centre of a pseudo two-dimensional mono-disperse fluidized bed at incipient fluidization conditions. The bed consisted of two layers of particles with identical properties differing only in colour. Comparison between experimental results with DEM and TFM simulation results for two different particle diameters.
frietional stresses assoeiated with long-term multiple particle-partiele contacts. When accounting for frictional stresses in the TFM, the emulsion phase mobility is suppressed, whieh reduces the extent of the indueed particle mixing. Different frietional viseosity models have been proposed and studied in the literature (a.o. [26,44-46]), however, none of these models improved the results for the system with relatively large partieles investigated in this work. Further developments in the closures for the frietional stresses are required (see also [22,24,47]). 3.4. Particle segregation rates in a freely bubbling bi-disperse fluidized bed
Finally, particle segregation rates in a freely bubbling bi-disperse fluidized bed, eonsisting of a 25% of 1 .5 mm diameter (smali) and 75% of 2.5 mm diameter (Iarge) glass beads, eomputed by the MFM, using a 45 1 20 grid, were eompared with Digital Image Analysis (DIA) experiments performed by Gold sehmidt et al. [48]. In Fig. 12 the evolution in time of the relative segregation is shown. The relative segregation s is defined for a binary mixture as x
with
-Xflotsam and Smax - 21 -Xfl otsam -
M. van Sint Annaland et al.
1 1 02
1 .0 ,------, MFM: Manger ( 1 996) 0.9 0.8
-; 0.7 'i 0.6 o
� 0. 5
�
� 0.4 '"
-..:
�
0.3
�
0.2 0. 1 0.0 +-------r---.--�
o
5
10
15
Time
rsl
20
25
30
Fig. 12. Relative segregation as a function of time in a freely bubbling bi-disperse fluidized bed consisting of 25% of 1 . 5 mm diameter and 75% 2.5 mm diameter glass beads (f1uidization velocity: 1 .20 m/s).
where < h > and x represent the average vertical position and the mass fraction of the flotsam (the smallerjlighter particles) and jetsam (the biggerjheavier particles). The figure clearly shows that the MFM presented in this work no longer overestimates the particle segregation rates as was observed with the MFM proposed by Manger [32]. Using the MFM with the closures derived by Manger almost complete segregation is predicted within 1 5 s, in strong contrast to the experimental observations (only 60% segregation after 60 s). Also Gold schmidt [22] and Huilin et al. [49] showed that MFM's using the closure equations by Manger considerably overpredicted the particle segregation rates of binary particle mixtures in freely bubbling fluidized beds. The MFM developed in this work describes the experimentally observed particle segregation rates much better and seem to even underpredict the segregation rates, which can again be attributed to the neglect of frictional stresses in the current implementation of the MFM. Due to the strong overestimation of the emulsion phase mobility, flotsam is continuously dragged downwards along the wall and jetsam is continuously dragged upwards in the centre of the bed due to the macro-scale circulation patterns in the fluidized bed induced by the bubbles (see Fig. 1 3). 3.5. Conclusions
A MFM based on the KTGF for multi-component systems was developed using the Enskog solution method of successive approximations for the description of particle mixing and segregation in multi-disperse gas-solid fluidized beds. In this theory, particle segregation and unequal granular temperatures in multi-disperse
Multi-Level Computational Fluid Dynamics Models
1 1 03
Fig. 1 3. Plots of the gas phase porosity and the fraction of flotsam (the smaller particles) after 24.2 s computed with the MFM for a freely bubbling bi-disperse fluidized bed consisting of 25% of 1 . 5 mm diameter and 75% 2.5 mm diameter glass beads (fluidization velocity: 1 .20 m/s).
systems result from the first order perturbation function. Numerical simulations with the MFM have been compared with well-defined experiments performed by Goldschmidt et al. [48]. The particle-segregation rates computed with the new MFM compare much better with experimental observations and are no longer overestimated, as was the case with M FMs presented before in the literature. However, due to neglect of frictional stresses associated with long-term multiple particle-particle contacts the emulsion phase mobility is strongly overestimated. This was also concluded by the strong overestimation of the extent of particle drift induced by a single bubble passing through a mono-disperse fluidized bed at incipient fluidization conditions. Further development in the description of frictional stresses is required to progress in the continuum modelling of multi disperse fluidized beds. Moreover better closure equations for the gas-particle drag for multi-disperse systems are required. 4. 0UTLOOK
In this chapter, the concept of multi-scale modelling was explained for dispersed gas-liquid-solid systems in general and granulation systems in particular. It was
M . van Sint Annaland et al.
1 1 04
demonstrated how the discrete particle model can be used to obtain c10sure information on the particle-particle and particle-droplet interactions which is needed by the higher level models. Subsequently, the capabilities of the MFM were demonstrated. The laUer model can eventually be used to derive c10sure information for the discrete bubble model. It is c1ear that the success of each of the models depends to a large extent on the quality of the c10sure models that are developed at the underlying level. As far as the c10sure of the gas-particle interaction is concerned, Van der Hoef et al. [4] recently derived a drag relation for mono-disperse and bi-disperse particle systems based on laUice Boltzmann simulations, which is an improvement of the model of Koch and Hili [3] used in this work. In the future, we plan to derive improved c10sure models for the particle particle and particle-droplet interactions with the help of the DEM. These c10sure models can subsequently be used at the level of the multi-fluid model.
ACKNOWLEDGMENTS
We would like to acknowledge Jeroen Link, Albert Bokkers and Willem Godlieb for their valuable contributions to this work. Nomenclature
c
C
C
d e F f f (2 ) 9
9.
k h
1
I
J
m n n
actual velocity peculiar velocity dimensionless peculiar velocity diffusion force normal restitution coefficient external forces per unit volume particle velocity distribution pair distribution function radial distribution function gravity unit vector vertical position moment of inertia identity matrix diffusion mass flux, impulse vector particle mass number density normal vector
Multi-Level Computational Fluid Dynamics Models
Np p q r R s S t u Vn V x
1 1 05
number of particle species pressure granular energy flux position particle radius relative segregation actual segregation, Sonine polynomial time tangent vector ensemble averaged velocity diffusion velocity of species n volume mass fraction
Greek symbols
ß ßo y
(5 I:
f1 Ic
p e
cp
(J
T
X ÖJ
gas-particle drag coefficient of tangential restitution rate of granular energy dissipation due to particle-particle interactions Kronecker delta volume fraction chemical potential, shear viscosity, coefficient of dynamic friction bulk viscosity granular temperature, collisional flux term particle quantity density particle diameter stress tensor collisional source term rotational velocity perturbation function
Subscripts
o
1 ,2 12 a,b c 9
max n, p s
before collision particle 1 , 2 difference between particle 1 and 2 particle a, b at the contact point gas phase maximum particle phase n, p solids phase, particle mixture
1 1 06
M . van Sint Annaland et al.
Superseripts
ex
excess
pw pp
particle-wall particle-particle
( 0), ( 1 ) first and second order Enskog approximation
Operators <>
after collision ensemble averaging
REFERENCES [ 1 ] P.N. Rowe, AW. Nienow, Powder Teehnol 1 5 ( 1 976) 1 4 1 . [2] MA van der Hoef, M . van Sint Annaland, J.A. M . Kuipers, Chem. Eng. Sei. 59 (2004) 5 1 57. [3] D.L. Koch, RJ. Hili , Annu. Rev. Fluid Meeh. 33 (20 0 1 ) 6 1 9 . [4] M .A. van der Hoef, R Beetstra, J A M . Kuipers, J . Fluid Meeh. 528 (2005) 233. [5] Y. Tsuji, T. Kawaguehi, T. Tanaka, Powder Techno!. 77 (1 993) 79. [6] B.P.B. Hoomans, J.A. M . Kuipers, W.J. Briels, W.P.M. van Swaaij, Chem. Eng. Sei. 5 1 ( 1 996) 99. [7] D. Gidaspow, Multiphase Flow and Fluidization: Continuum and Kinetie Theory Deseriptions, Aeademie Press, Boston, 1 994. [8] M.J.v. Goldsehmidt, JAM. Kuipers, W.P.M. van Swaaij, Chem. Eng. Sei. 56 (2001 ) 571 . [9] E . Delnoij, F A Lammers, J A M . Kuipers, W.P.M. van Swaaij , Chem. Eng. Sei. 52 ( 1 997) 1 429. [ 1 0] E. Delnoij, J .A. M. Kuipers, W. P.M. van Swaaij, Chem. Eng. Sei. 54 ( 1 999) 22 1 7. [1 1 ] GA Bokkers, Multi-level modelling of the hydrodynamies in gas-phase polymerisation reactors, Ph.D. Thesis, University of Twente, Ensehede, The Netherlands, 2005 [ 1 2] D. Darmana, N.G. Deen, J A M . Kuipers, Chem. Eng. Sei. 60 (2005) 3383. [ 1 3] D. Kunii, O. Levenspiel, Fluidization Engineering, Butterworth-Heinemann, Boston, 1 991 . [ 1 4] O. Simonin,. Modelling turbulent reaetive dispersed two-phase flows in industrial equipments. Proeeedings of the Third World Conferenee in Applied Computational Fluid Dynamies, Freiburg, Germany, 1 996. [ 1 5] J A M . Kuipers, W. P.M. van Swaaij, Adv. Chem. Eng. 24 ( 1 998) 227. [ 1 6] M .J .v. Goldsehmidt, R Beetstra, J.A. M. Kuipers, Chem. Eng. Sei. 57 (2002) 2059. [ 1 7] S. Ergun, Chem. Eng. Proe. 48 (1 952) 89. [ 1 8] C.Y. Wen, Y.H. Yu, AIChE Symp. Series 62 ( 1 966) 1 00. [ 1 9] B.P.B. Hoomans, JAM. Kuipers, W.J. Briels, W.P.M. van Swaaij, Diserete particle simulation of segregation phenomena in dense gas-fluidized beds, Fluidization IX, L.-S. Fan, T.M. Knowlton (Eds) Engineering Foundation, New York, 1 998, pp. 485-492. [20] B.P.B. Hoomans, JAM. Kuipers, W.P.M. van Swaaij, Powder Techno!. 1 09 (2000) 4 1 . [21 ] J . M . Link, L.A. Cuypers, N.G. Deen, J A M . Kuipers, Chem. Eng. Sei. 6 0 ( 1 3) (2005) 3425-3442. [22] M.J.v. Goldsehmidt, Hydrodynamie modelling of fluidised bed spray granulation, Ph.D. Thesis, Ensehede, The Netherlands, 200 1 . [23] G A Bokkers, M . van Sint Annaland, J.A. M . Kuipers, Fluidization XI, U . Arena, R Chirone, M. M ieeio, P. Salatino (Eds), Naples, Italy, 2004, pp. 1 87-1 94. [24] D.J. Patil, M. van Sint Annaland, J A M . Kuipers, Chem. Eng. Sei. 60 (2005) 57.
Multi-Level Computational Fluid Dynamics Models
1 1 07
[25) D.J. Patil, M . van Sint Annaland, J A M . Kuipers, Chem. Eng. Sei. 60 (2005) 73. [26) S. Chapman, T.G. Cowling, The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, Cambridge, UK, 1 970. [27) M. L6pez de Haro, E.G.D. Cohen , J . M . Kincaid, J . Chem. Phys. 78 ( 1 983) 2746. [28) J.T. Jenkins, F. Mancini, J. App!. Mech. 54 ( 1 987) 27. [29) J .T. Jenkins, F. Mancini, Phys. Fluids A 1 12 (1 989) 2050. [30) H. van Beijeren, M . H . Ernst, Physica 68 (1 973) 437. [3 1 ) J.H. Ferziger, H.G. Kaper, Mathematical Theory of Transport Processes in Gases, North-Holland Pub. Co., Amsterdam, The Netherlands, 1 972. [32) E. Manger. Modelling and simulation of gasisolids flow in curvilinear coordinates, PhD. Thesis, Telemark Institute of Technology, Porsgrunn, Norway, 1 996. [33) V. Mathiesen, An experimental and computational study of multi phase flow behaviour in circulating fluidised beds, PhD. Thesis, Telemark Institute of Technology, Porsgrunn, Norway, 1 997. [34) L. H uilin , D. Gidaspow, E. Manger, Phys. Rev. E 64 (200 1 ) 061 30 1 . [35) M.F. Ramahan , J . Naser, P.J. Witt, Powder Techno!. 1 38 (2003) 82. [36) A. Santos, S.B. Yuste, M. L6pez de Haro, Mo!. Phys. 96 (1 999) 1 . [37) Y. Song, R.M. Stratt, E.A. Mason, J . Chem. Phys. 88 (1 988) 1 1 26. [38) JAM. Kuipers, K.J. van Duin, F.P.H. van Beckum, W. P.M. van Swaaij, Chem. Eng. Sci. 47 (1 992) 1 9 1 3. [39) J.L. Sinclair, R. Jackson, AIChE J 35 ( 1 989) 1 473. [40) Y. Zhang, Y. Yang, H. Arastapoor, AIChE J 42 ( 1 996) 1 59 1 . [4 1 ) S.v. Patankar, D.B. Spalding, Int. J . Heat Mass Transfer 1 5 (1 972) 1 787. [42) J.A. M . Kuipers, K.J. van Duin, F.P.H. van Beckum, W. P.M. van Swaaij, Compu. Chem. Eng. 8 (1 993) 839. [43) GA Bokkers, M. van Sint Annaland, J A M . Kuipers, Powder Techno!. 1 40 (2004) 1 76. [44) H . Laux, Modeling of dilute and dense dispersed fluid-particle flow, Ph.D. Thesis, NTNU Trondheim, Norway, 1 998. [45) A. Boemer, H. Qi, U. Renz, I nt. J. Multiphase Flow 23 ( 1 997) 927. [46) A. Srivastava, S. Sundaresan , Powder Technol 1 29 (2003) 72. [47) L. Huilin, H. Yurong, L. Wentie, J. Ding, D. Gidaspow, J. Bouillard, Chem. Eng. Sci. 59 (2004) 865. [48) M .J .v. Goldschmidt, J . M . Link, S. Mellema, JAM. Kuipers, Powder Techno!. 1 38 (2003) 1 35. [49) L. H uili n , H . Yurong, D . Gidaspow, Chem. Eng. Sci. 58 (2003) 1 1 97.
CHAPTER 24 P o p u lation B a l an ce M od e l l i n g of G ra n u l at i o n Thomas Abberger*
Depanment of Physiology and Medical Physics, Innsbruck Medical University, Fritz-Pregl-Straße 3, 6020 Innsbruck, Austria Contents
Basic I nformation 1 . 1 . The aim of this chapter 1 . 2. The aim of modelling and simulation 1 . 3 . The key issues in modelling and simulation 1 .4. The different types of models applied i n granulation research and practice 1 . 5. The population balance as a modelling tool for particulate processes 2. The key issues 2 . 1 . Population balance equations 2.2. The kernel 2 . 3 . The solution of the population balance equation 2.4. The inverse problem in population balance modelling 2.5. The model applications 3. Background and l iterature review 3 . 1 . The population balance equation 3 . 1 . 1 . The pure aggregation form (the Smoluchowski equation) 3 . 1 .2. The general population balance equation 3 . 1 . 3 . The population balance equation in moment form 3.2. The coalescence kernel 3.2. 1 . I ntroduction 3 .2.2. The physical implication of a coalescence kernel 3.2.3. Homogeneity of kerneis 3 .2.4. Kerneis applied in the modelling of granulation 3 . 3 . Solution of the population balance equation 3 . 3 . 1 . I ntroduction 3 . 3 . 2 . Analytical solution 3 . 3 . 3 . The methods of moments and weighted residuals 3 . 3.4. The method of lines 3 . 3 . 5 . Discretized population balances 3.3.6. Monte Carlo simulation 3 .4 . The inverse problem 3.4. 1 . I ntroduction 3 .4.2. Determination of the size dependence of the aggregation frequency 1.
*Corresponding author. E-mails: [email protected]; [email protected]
Granulation Edited by A.D. Salman, M.J. Houns/ow and J. P. K. Seville c 2007 Elsevier B.V. All rights reserved
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1 110 3.4.3. Determination of the aggregation rate term 3 .4.4. Assessment of the fit 3.5. Application of population balance models i n process control 4. Forward look 4 . 1 . Multi-dimensional population balance equations 4.2. KerneIs 4.2. 1 . Collision frequency 4.2.2. Coalescence probability 4.2.3. Distribution of forces 4.2.4. Experimental validation 4.3. A look on granulation as a multi-scale process 4.3. 1 . I ntroduction 4 .3.2. A look on the granule bed 4.3.3. Application in scale-up References
T. Abberger 1 1 77 1 1 78 1 1 78 1 1 79 1 1 79 1 1 80 1 1 80 1 1 80 1 1 80 1 1 80 1 181 1 181 1 181 1 1 82 1 1 82
1 . BASIC I NFORMATION 1 . 1 . The aim of this chapter
This chapter deals with a powerful and versatile tool for the mathematical modelling of particulate processes including granulation, the population balance models (PBMs). First of all, this chapter is intended to give a systematic derivation of the population balance equation (PBE). The chapter deals with one- and multi dimensional PB Es. The one-dimensional PBE is widely used to model and to simulate the evolution of particle size distributions (PSOs). One-dimensional PBEs are weIl understood now. An expansion that finds increasing interest, the multi-dimensional PBE, is able to model more distributed properties of a granule other than size alone, such as porosity or content of an active ingredient. This chapter provides a comprehensive review of the application of the method in granulation research and practice. The focus is on granulation of fine powders using high-shear mixers and fluid-bed granulators. This chapter also deals with the solution of the PBE. It is intended to be an introduction into the methods, rather than being comprehensive. Furthermore, it deals with the inverse problem. 1 .2. The aim of modelling and simulation
The goal in granulation is the development of robust processes for the production of high-quality products with designed properties, based on insight. Modelling can help us to reach this goal. The goal of models is to simulate real processes from first principles. This aims at • •
verification of a hypothesis, making predictions,
Population Balance Modelling of Granulation • • • • •
1111
optimization of processes, control of processes, design of products, design of devices, or teaching.
If one needs to estimate a priori granule characteristics, such as size or shape, from knowledge of operating conditions and the physical and chemical properties of the powder and binder, modelling is important [1]. 1 .3. The key issues in modelling and simulation
For any model, the validity (can the outputs of the model be verified by experiments?) and the complexity of the model are crucial. The results obtained by modelling and simulation are valid only in a distinct experimental setting; therefore, an optimal solution of a problem can not be guaranteed . Thus, in practice the mathematical model needs to be adapted to the experimental findings. Another approach is not to improve the mathematical model but to adapt the experimental set-up to fit better an existing mathematical model; a typical example in granulation is the use of glass ballotini. This point can lead to controversial discussions among people from industry and academia [2]. Simulation using PBEs is a continuous simulation. Generally, in continuous simulation a dynamical behaviour of a system is described by a set of coupled equations. In each time interval, a large number of changes of the state take place. The present state is known, and the rate of change and the input at present are also known. The state at the next collocation point is approximated. A continuous behaviour has to be discretized, and integration is performed from one collocation point to the next. Simulation here is performed by numerical integration of the PBE and is so far a deductive approach. The demands for a simulation are efficiency (expense of simulation) and accuracy. Besides accuracy of the underlying model, the conversion of the model in dynamic behaviour has to be correct. A crucial point is the numerical integration algorithm. 1 .4. The d ifferent types o f models applied i n g ranulation research and practice
Different types of models are applied in granulation research and practice. They can be grouped as folIows: 1 . Modelling the process using experimental design: A number of input variables, Xi, among the process conditions and the material properties are selected, as weil as a number of output variables, Vi, among the granule properties. The
1 1 12
T. Abberger
principle is to determine for each output variable a relationship (often linear) involving each relevant input variable and the relevant interactions between variables. Thus, it is possible to optimize the different variables Xi to obtain a compromise between the results of the Vi. The PSD is included in form of a mean diameter or in form of an upper and a lower limit of the diameter. No physical assumptions on the granulation process are required with this strategy, but no deep insight is gained. Such models are applied in process control. Experimental design techniques were developed to obtain the greatest amount of information using the least possible number of experiments. Factorial design is used to elucidate the effect of variables on the response and to reveal interactions among them. For two decades, experimental design and analysis of variance and response surface methodology have been widely applied, especially in optimization of pharmaceutical granulations. An experimental approach was widely used in the past to create empirical models for the evolution of the mean particle size. The c1assic approach was to change a single parameter, e.g. the binder content, in small steps. This method could reveal an influence of derived parameters, such as the pore saturation, and provided some phenomenological insight into mechanisms acting in a granulator. More powerful are models with the potential to be based on the physics of the underlying processes: 2. Discrete element modelling (DEM): The method is widely applied to predict solid-particulate two-phase flows including granular flow. The DEM computes movements of discrete bodies that interact with their nearest neighbour. The fundamentals of DEM have been recently described in a review [3]. Just a few applications of DEM of granulation have been published until now [1 ,4-6]. 3. Population balance models: A c1assification of models as applied in granulation can be found in Refs. [7-1 0].
1 .5. The population balance as a modelling tool for particulate processes
The first PBM, describing the coagulation in a colloidal solution owing to Brownian motion, was published more than 80 years aga [1 1 ]. Owing to the high computational load and lack of the required computing power, the method could not find a widespread application for a long time period. The application and development of PBMs in granulation research has started in the late 1 960s [1 2] , a s in other areas of engineering and science. Owing to the fact that fast computations can be performed today with personal computers, this type of modelling is evolving considerably.
Population Balance Modelling of Granulation
1 1 13
Currently, the population balance is the most frequently used modelling tool to quantify the dynamics of particulate processes in differing disciplines, e.g. aerosol processes, biotechnological processes, comminution, crystallization , granulation, and polymerization. These different processes are all characterized by the presence of a continuous phase and a dispersed phase comprised of entities with a distribution of properties, such as size or composition. In a process, the entities interact with each other as weil as with the continuous phase. The phenomenological content of PBMs lies in these interactions. Such interactions may vary from entity to entity, depending upon their properties. The polydispersity of particulate processes significantly affects the behaviour of such systems. Moreover, the polydispersity makes particulate processes unsuitable for modelling within the framework using only conventional conservation equations [ 1 3]. PBEs allow analysis of how the PSO, and ideally other distributions of properties in a system, are related to the underlying microscopic interactions and kinetics of single particles. The population balance is relevant because of the dependence of the system's behaviour on the number and nature of the foregoing entities [14]. Reviews of the population balance approach have been reported by Hidy and Brock [ 1 5] and Orake [1 6] , who focused on aerosols; Randolph and Larson [ 1 7] and Rawlings et al. [ 1 8] , who focused on crystallization; and Hogg [1 9], Wang and Cameron [8], who described the model development for drum granulation. Cameron et al. [9] reviewed process systems modelling in granulation including the application of PBMs, whereas Ramkrishna dealt with generic issues of population balances in a review [20] and in a comprehensive textbook [14]. Basic information on the subject of this approach, with examples from crystallization, can be found on the Internet, provided by Hounslow [21 ] . An introduction into the method and discussions of case studies was given by Hounslow [22]. Ramkrishna and Mahoney [23] reviewed recent developments.
2. THE KEY ISSUES 2.1 . Population balance equations
PBEs describe the evolution of the distribution of one or more properties in course of time. Simulation by applying a one-dimensional PBE means calculation of PS Os at various times from a starting PSO (Fig. 1 ). The PSO is very important because it is a key controlling factor for both the agglomeration and downstream processes as weil as for the quality of the products, e.g. uniformity of mass and dissolution time of tablets.
1 1 14
T. Abberger
,
E �
.
-'
1.
.
.....
.
�
: ... .,..� .�
�
�
0 er
! .. .
O.
·· ··
,
l
.
0.8 0. 6
4
0. 4 0. 2 o
1
An evolution of a PSD in a granulation process as simulated using a one dimensional PBE. The term qo denotes the number density. Reprinted from Heinrich et 81. [24], with permission from Elsevier. Fig. 1 .
Other controlling factors such as liquid saturation of the voids exist as weil. To deal with the evolution of such distributions in addition is the subject of multi dimensional PBEs. 2.2. The kernel
The evolution of the PSD owing to coalescence is mode lied by incorporating a coalescence kernel into a PBE. The coalescence kernel (see Section 3.2) is the chief phenomenological instrument in a PBE, as it gives the functional dependence of the aggregation rate on the sizes and other properties of the particles and on the material properties and process conditions. A kernel is ideally based on a physical model and knowledge of all the variables, or in a semi empirical approach is based on so me mechanistic insight into an agglomeration process, or may be purely empirical and fitted from experimental data. 2.3. The solution of the population balance equation
The main problem is that the solution of the PBE may be mathematically challenging. When the birth and death terms are included, the PBE yields an integro-partial differential equation. Problems are encountered in the solution of
Population Balance Modelling of Granulation
1 1 15
this equation, resulting from the combined hyperbolic form, that arises if the growth term is inciuded, and the nonlinearity associated with aggregation [25,26]. Fortunately, extensive research on the solution of PBEs is going on in many different fields of science and engineering. It is an advantage of the population balance approach that progress in one field of application is available for others. Until about 1 5 years ago, the absence of the required specialized solution techniques prevented the widespread application of PBMs [27]. 2.4. The inverse problem in population balance modelling
The inverse problem in aggregation is to extract the underlying rate laws from experimental data. Experimental observation is usually limited to dynamic measurements of PSDs. The identification problem is then one of extracting the aggregation frequency from experimental size distributions measured at various times. Generally speaking, the inverse problem is to extract the behaviour of single particies from experimental data, where the direct observation of single particies is not possible due to many neighbouring particies and where the behaviour of single particies is not isolated, but within a population. The underlying rate laws, however, are based on the behaviour of single particies [28]. The inverse problem is a challenging problem and mathematically very difficult and sensitive to the quality of experimental data. Complete specification of a model requires parameter estimation. A practical use of the inverse problem beyond parameter estimation in working models is not yet sure. 2.5. The model applications
At present, PBMs are used as a learning tool to understand processes and mechanisms taking place in high-shear mixers, plough-shape granulators, drum granulators, etc. in various industries using wet granulation [29]. The assump tions made on the granulation regi me or the probability of coalescence with time give model results that are compared with experimental data, thereby confirming the validity of the models or highlighting which assumptions are not valid. PBMs developed for an application in practice can be developed to run in the prediction mode or in the design mode. In the prediction mode, the input to the program is the feed and operating conditions; the objective is to determine the characteristics of the output. In the design mode, the feed conditions and desired product characteristics are known; the objective is to determine the operating conditions that will produce the desired product. When the PBMs are coupled with material and energy balances, complete particulate process models can be developed [30]. This goal is an ambitious one.
1 116
T.
Abberger
A recent trend is to use PBMs for control purposes. Process control is favourably carried out with models of the complete granulation circuit, because the performance of the circuit is influenced by all of the unit operations carried out. 3. BACKGRO U N D AND LITERATURE REVIEW 3. 1 . The population balance equation 3. 1. 1. The pure aggregation form (the Smoluchowski equation) 3 . 1 . 1 . 1 . I ntroduction
Size x is a distributed property in a distinct population of particles. The distribution can be discrete or continuous, when the number of particles is large. There exist at time t densities n(x, t) defined by n(x,t) = average number of particles of size x per unit volume in the discrete case, and n(x,t)dx = average number of particles of size between x and x + dx per unit volume in the continuous case.
Therefore, the total number of particles, Ntot(t), at any given time is Ntot(f)
= 100 n(x, f) dx
(1 )
When this collection of particles is in move in a fixed volume, some particles will collide in a given time period and subsequently either coalesce or rebound. When the collection is diluted, the collisions are binary. Coalescence changes the number of particles, thus n(x, f) is time dependent. The possibilities for collisions of size x and y are proportional to the product n(x,t)n(y,t). Since a collision of x and y is the same as y and x, n(x,t)n(y,t) is divided by 2. Beside the number densities of particles involved in collision, their velocities as weil decide the number of collisions per time unit. Additional factors decide, whether they will coalesce or rebound. To account for all of this, a factor of proportionality, ß(x, y), called kernel is considered. Thus the expected number of change of Ntot(t) in the entire volume per unit time is
JJ ; n(x, t)n(y, f)ß(x,y)dxdy
(2)
In an application of the PBE, the population is described by the density of a suitable variable, usually the number of particles but sometimes by other
Population Balance Modelling of Granulation
1 1 17
extensive variables, such as the mass or volume of particles. The common practice is to express the distribution as a number distribution of size x at time t, n(x, t). 1 Usually, either a particle length, I, e.g. the diameter, d, or the particle volume, v, are taken as particle size. The decision whether 1 or v is taken as the particle size depends on the dominant growth mechanism. Verkoeijen et al. [31 ] recommended the use of volume a s the particle size because this size i s additive during aggregation and, if evolution of porosity can be disregarded, volume will be automatically conserved. Furthermore, the volume is independent of the particle shape. For the development of the theory, it is better to use volume. Because in most applications of PBE modelling a comparison with experimental data is made, the question of whether length or volume is taken as the particle size may be decided by the applied analysis method. 3 . 1 . 1 .2. The continuous form
In the continuous setting, equation (3 ) is known to represent the formation of particles of volume fraction between v and v+ d v by the collision and binding together of two particles whose two volumes total this volume, which is the coalescence birth, where Bcoal is the coalescence birth rate. If one of the particles has the volume u, because volume is conserved, the other must have a volume of v-u. Therefore, the number of formed particles, Nbirth, with volume v is given by 1 Nbirth = Bcoal dt = 2
Jo
(
ß(v - u, u)n(v - u, t)n(u, t) du x d v d t
( 3)
The leading factor of 1 /2 is added to avoid double counting. 2 The coalescence kernei, ß(v, u), is a function that models the physics of the aggregation process through dependence of this function on its arguments3 (see Section 3.2.2) . Equation (4) is known to describe the loss of particles of volume fraction between v and v+ d v by their collision and binding with another particle of any size (i.e. the coalescence death, where Dcoa l is the coalescence death rate). Therefore, the number of lost particles, Ndeath, in volume v is given by Ndeath = Dcoal d t =
100 ß(v, u)n(v, t)n(u, t) du x dvdt
(4)
The accumulation of particles in the size fraction between v and v+ d v is given by a at [n(v, t) d v] d t = Nbirth - Ndeath
(5)
1 Any other distribution ean be caleulated fram the number distribution by multiplying the number distribution by the desired praperty g(x), e.g. volume, [g(x)n(x,t)] . 2 A frequently applied alternative is to use v/2 as the upper bound of the integration. 3 The kernel is symmetrie: ß(v,u) ß(u,v), beeause the particles u and v obey the same physical laws. =
1 1 18
T. Abberger
Now it is possible to write down differential equations for the densities n(v, t), equations (6) and (7). The net time rate of formation of particles of volume fraction between v and v+ dv is ß(n(v, f) dv) - Dcoal + Bcoal at ==
- 1co ß(v, u)n(v, f)n(u, f) du d v
+ 2"1
r ß(v - u, u)n(v - u, f)n(u, f) du dv
Jo
(6)
This leads to {CO ßn(v f) = - J ß(v, u)n(v, f)n(u, f)du + 2"1 Jr ß(v - u, u)n(v - u, f)n(u, f)du (7) Tt o o 4 Equation (7) is a PBE, describing the aggregation, or coalescence, of free-in space systems (see Section 3.2.2) such as diluted colloidal solutions, because it expresses a simple balance of a quantity; the rate of accumulation of particles of a given size equals their rate of formation minus their rate of disappearance. The left-hand side represents the time rate of change of the number of particles with volume v. The particle size distribution function n(v, t) is assumed to be a sufficiently smooth function of its arguments, which means n(v, t) and its partial derivatives with respect to t and v are smooth functions. This assumption is reasonable for large-size distributions, although particles are discrete entities and their number is an integer. The partial differential equation (PDE), equation (7), has to be supplied with an initial condition in the time domain and boundary conditions in the size domain. The initial condition is the starting size distribution n(v, 0) = no(v) and the boundary conditions are n(O, f) = n(oo , f) = O which means that there exist no particles of size zero and all particles have finite size. Depending on the given problem, more complicated boundary conditions can exist. 5 Equation (7) is a one-dimensional mean-field model that ignores fluctuations about the mean of the number of particles of any size, detailed mechanical or thermodynamic nature of particle-particle interaction and their spatial correlation, and the shape of the aggregating particle. It does not track positions and velocities of particles in d-dimensional space. (Because it is not possible to keep track of the 4 Müller [32] was probably the first to derive a PBE in continuous form as given by equation (7).
A possible boundary condition in granulation is n(v> vmax , t) volume of a granule that can exist. 5
=
0, where vmax is the maximum
Population Balance Modelling of Granulation
1 1 19
structure of each granule in the course of a granulation process, PBEs can werk only there, when the error that is made by this assumption is not significant [33].) I nstead , the equation only describes some average behaviour of the underlying mechanisms through the coalescence kernel. The idea is that the details of the local motion and local coalescence rule, which arise from the physics of what is being modelled, are subsumed into the coalescence kernel. The model assumes that the system is diluted so that merging of two particles into one is not influenced by the presence of other particles and they merge without failure as soon as they meet [34]. The multiplication of n(v, t) by n(u, t) approximates the number density of two collided, adhering particles of sizes v and u, instead of introducing an unknown pair density into the PBE. This approximation is known as the mean-field closure hypothesis. Basically, the above closure approximation is tantamount to neglecting any correlations in the pair density, which may arise either due to the slowness of spatial mixing that results in segregation or correlation effects or due to the smallness of populations [35]. A basic assumption of the Smoluchowski equation is that each particle with the same properties and in the same environment behaves in the same manner. When equation (7) is applied, several more assumptions have to be made: • it is a batch process, • the particles in the device are randomly mixed, coalescence occurs by the combination of two particles, • coalescence is the only mechanism acting in size enlargement, • growth or shrinkage along a size axis can be disregarded, • breakage and attrition can be disregarded, and • no nuclei are formed. •
3. 1 . 1 . 3 . The discrete form
The equivalent discrete form of equation (7) is
(8) Although only one single equation is given, the population balance approach makes use of a series of coupled discrete PBEs, one for each size interval, into which the PSD is divided. Fundamentally, the whole PSD is divided into small intervals, and the PBE follows the evolution of the particle growth due to aggregation, allowing the computing at each time of the number of particles existing in each size interval. The size intervals, i, j, 6 are specified as a linear 6 It is common to use the subscripts i and j in discrete notation.
1 1 20
T. Abberger
volume-based progression, such that Vi = iV1 , where V1 is the volume of a single particle of the starting distribution (size class 1 )7 and where Vi+j = Vi + Vj. Equations (7) and (8) are referred to jointly as the Smoluchowski equation [1 1 ] in the literature. 3 . 1 . 1 .4. The stochastic model related to the Smoluchowski equation
The assumption that the modelIed process is a Markovian process is implicit in the PBM [36]. The number density n(v,t) is Iimited in time, its time derivative describes an irreversible process. Equations, which describe linear, irreversible Markovian processes, such as the Smoluchowski equation, have been very successful in the codification of large quantities of experimental data in different systems [37]. 8 The standard stochastic model related to the Smoluchowski equation is a Markov jump process where the two different clusters of size x and y coalesce to a single cluster of size x + y with rate ß(x, y). This model is ca lied Marcus-Lushnikov process [39]. In the Marcus-Lushnikov process, ML(N) (x, f) denotes the (random) number, N, of mass-x particles at time t. A weak law of large numbers, saying that as N 00 (9) N- 1 ML(N) (x, f)-+P n(x, f), x � 1 , t � 0 �
where n(x, t) is the solution of the Smoluchowski equation with n(x, 0) = 1 (x = 1 ) is expected [40]. Aldous [40] described the solution of the Smoluchowski equation as the deterministic limit of the Marcus-Lushnikov process. A deterministic model and solution require that particles are sufficiently numerous to approximate a continuum and that time evolution is continuous. The assumption of sufficiently large particle numbers is necessary in a deterministic model because the fluctuations relative to the mean become unimportant and the mean number of particles of any given size is a suitable state variable. Inherently, a deterministic model disregards the fluctuations of the number of particles of any given size. Issues of stochastic aggregation models are important in systems with low numbers of particles, when not only an average behaviour but the fluctuation about the average behaviour is also of interest and are treated in detail [14,41] or briefly in the literature [23]. The relationship between stochastic particle systems and the Smoluchowski equation was discussed in detail in a review by Aldous [42].
3 . 1 . 1 . 5 . Adaptation of the Smoluchowski equation for the modelling of
granulation
Following the argument of Kapur and Fuerstenau [1 2], regarding the collision frequency in a granulator (see Section 3.2.2), the right-hand side of equation (7) 7 This progression is particularly suited for the modelling of polymerization, where polymers are made up of monomers. 8 Consequently, an attempt to predict the size distribution of an agglomeration process using the Fokker-Planck equation directly has been made [38].
Population Balance Modelling of Granulation
1 1 21
has to be divided by the total number of particles, Ntot , to describe the population balance in a granulating device [43-45]. Sastry and Gaschignard [46] presented a more versatile form, which is in agreement to Ouchiyama and Tanaka's argument [47], regarding the collision frequency in a granulator an(v, t) 1 ß(v, u)n(v, t)n(u, t) du -- at Nrtot 0 1 ß(v - u, u)n(v - u, t)n(u, t) du ( 1 0) 2Wtot 0 where r is the degree of restriction, as defined by Ouchiyama and Tanaka [47]. For r = 1 , this reduces to the PBE as applied by Sastry and Fuerstenau [43], which has been extensively applied in the modelling of granulation. Sastry and Fuerstenau [43] discussed the effect of restriction on granules motion on the agglomeration process. They showed that the degree of restriction has an influence on the rate of the agglomeration process, but does not affect the shape of the PSD.
+
100
lv
3. 1 . 2. The general population balance equation
3 . 1 .2 . 1 . I ntroduction
The Smoluchowski equation was expanded to a general PBE in order to account for more mechanisms, or processes, than coalescence causing an accumulation of particles in a size interval, account for the distribution of more properties other than size alone, be able to deal with particulate processes that do not support the implicit restriction on spatial homogeneity over the entire process volume, and overcome the restriction on a batch process. •
•
•
•
The first general formulation of PBEs in the chemical engineering literature [48] was based on a statistical mechanics equation describing the Markov processes. Ramkrishna [1 4,20] used Reynolds' transport theorem as a starting point, and other authors applied continuum mechanics [1 7]. 3. 1 . 2. 1 . 1 . Development of the microdistributed form. The deterministic PBE of Randolph and Larson [1 7] was derived as a conservation equation for the number of particles in a population. An expanded particle distribution function n( S, t) was defined in an (m + 3)-dimensional space S consisting of the three external or spatial coordinates and m independent so-ca lied internal coordinates, such as size, binder content, composition, porosity, etc. , which are required to completely specify the state of the particle. The total number of particles in a finite subregion, R, of particle state space, S, is N(R) =
j� n(R, t) dR
(1 1 )
T. Abberger
1 1 22
R1,
The population balance in an arbitrarily chosen fixed subregion, of particle state space S is Accumulation Input - Output Net Generation (1 2) The input (output) term accounts for the physical inflow (outflow) of particles to (from) the system as weil as to growth into (out of) that subregion. The net generation is the difference between the birth and death of particles. The birth term represents an increase in the number of particles due to aggregation, nucleation, or breakage of larger particles. Similarly, the death term represents a reduction in the number of particles owing to aggregation to a higher size or breakdown to a lower size. Although birth and death of particles are physically discrete events, they become rate processes when averaged over sufficient volume, which includes the birth or death of many particles. The discrete events, which occur at the particle scale, provide the mechanistic interpretation for the rate events [49]. When no fluxes or growth across the boundaries of this subregion take place, then the time derivative of equation ( 1 2) may be stated as [ 1 7]
=
+
( 1 3) :t JR1r n(R, t) dR = JR1r (B - D) d R where B(R, t) is the birth rate and D(R, t) is the death rate. To account for fluxes
(external coordinates) and growth (interna I coordinates), the former term is expanded
:t�1 n(R, t) d R = �1 �� dR + (n �D I R1 = �1 �� d R + �Jv . (n �D ] d R r [8otn + v . (n ddXt) ] dR (14) JR1 =
x
is the set of external and internal coordinates comprising the phase space Equation ( 1 5) describes the velocity of movement of particles in the phase space
R.
R,
( 1 5) By substituting the extreme right-hand side of equation (14) into equation ( 1 3), the differential micro-distributed population balance was obtained as equation ( 1 6), because the region is arbitrary
R1 �� + v . (nvi) + v . (nVe) - B + D = O
(1 6)
or, in terms of the m + 3 coordinates,
m 0 on 0 0( ) 0 ) ( ) � + ot + ox nvx + oy nvy + o/nvz (OXi)j [n(vi)j] - B + 0 = 0
(1 7)
Population Balance Modelling of Granulation
1 1 23
The partial derivative with respect to time represents the accumulation rate of particles. The population is changed by four separate mechanisms. The divergence term is divided into two because it recognizes that the particle has external and internal coordinates. The partial derivatives with respect to the spatial coordinate axes represent the convective transport term, the physical flow of material. The partial derivatives with respect to the property coordinate axes represent the continuous generation term, this term always includes particle size (e.g. growth of particles along a size axis), but the summation sign recognizes that there may be more than one property of interest. B and 0 constitute the net generation term by birth and death [17]. The microdistributed form is suited for systems that are not weil mixed; the number density of particles is then considered to be a function of time and of the spatial position of the particles; for a mathematical perspective on this issue, see Ref. [50]. 3. 1 . 2. 1 . 2. Development of the macrodistributed form. There are many examples in population balance modelling where the spatial variation may be neglected, and where interest is in studying the global behaviour of the system. With the assumption that neither n, B nor 0 are dependent on the spatial coordinate. A macroscopic version of the PBE, equation (1 8), has been developed by integrating the microdistributed form over the three spatial coordinates [1 7] d(log V) an n = B _ 0 " Qk k nv.I n ( 1 8) at dt � V
+v + .
_
where V is the volume of the device, and k are the input and output streams to the volume V. The macroscopic PBE is the most useful form for practical applications. This equation can be applied to weil-mixed systems, where no spatial dependency of n, B or 0 exist, or averaged values are applied. The general form of the PBE must, in any case, be adapted to suit the particular problem. The PBE for a given problem is composed of those terms that describe the mechanisms of interest, such as coalescence, breakage, growth, attrition, and nucleation or processes, namely fluxes into or out of the device, which are active in this particular problem. The number density of particles is a function of all those particle properties that are considered to be relevant to the problem, and of time. 3 . 1 .2.2. One-dimensional population balance equations
One-dimensional PBEs are a simplified version of the general PBE, because they regard a single internal property, the size, as the independent, distributed property.
1 1 24
T. Abberger
3. 1 . 2. 2. 1 . The general PBE for granulation. The general PBE for modelling granulation processes is [51 ]
on(v, f) Qin . ( o(G(v, f) - A(v, f»)n(v, f) n1n ( v) Qou! nou! v) V ot V ov + Bnuc (v, f) + BcoaI(v, f) - DcoaI (v, f) _
_
_
( 1 9)
The first two terms on the right-hand side represent the flow into and out of a continuous process. Qi n and Qou! are the inlet and outlet flow rates from the granulator. V is the granulator volume. G(v, t) and A(v, t) are the growth or layering and attrition rates, respectively. Bnuc (v, t) is the nucleation rate of new granules of size v owing to the liquid binder addition of the bed. Where necessary, additional terms can also be added to include the appearance and disappearance of granules due to breakage. The general PBE allows the modelling of all rate processes including nucleation or breakage, however, population balance modelling of granulation is usually limited to the granule growth phase. Growth, nucleation and breakage term are not included in many working models of granulation, such as equation ( 1 0). Often the pure aggregation form of the PBE is applied in the modelling of granulation processes. This simplification can be acceptable. The wetting and nucleation phase, including the liquid distribution stage, is both difficult to characterize [52] and to model. In fluid-bed granulation, it is common practice to spray the binder liquid continuously onto the bed. This practice makes it difficult to differentiate adequately between the liquid distribution and granule growth stages of granulation. In comparison to the growth phase, Iittle progress has been made in modelling the nucleation phase and introducing it into a PBE. 3. 1 . 2. 2. 2. The pure growth form. Although a distinction between coalescence and layering is arbitrary, depending on an arbitrarily selected cut-off size, a pure layering form of the PBE is mathematically convenient. For a batch process, the PBE for growth along a size axis (Iayering) only becomes on(l, f) oG(I, f)n(l, f) _ 0 (20) ot + 01 where G(I, t) is the growth rate dljd t. The use of length as particle size is suitable when growth is the dominant mechanism. A PBM for the layering mechanism occurring in the granulation of iron ore fines was proposed by Kapur and Runkana [53]. Abberger and Henck [54] investigated fluid-bed melt granulation of fine lactose and PEG 4000 as meltable binder in an instrumented laboratory scale fluid-bed granulator STREA- 1 . The PEG was added as coarse flakes (d1 ,3 579 J.lM) and molten by the heated inlet air. Motivated by an interest in the quality (hardness
Population Balance Modelling of Granulation
1 1 25
and dissolution behaviour) of tablets compressed from melt granules, we performed experimental series with increasing concentrations of PEG from 9% to 29%. A PBM was applied for simulation of the PSD with an increasing concentration of binder. The model was based on the following assumptions: the mechanism of nucleation is immersion [55], each PEG flake greater than a partition size is a seed for a granule, granule growth occurs by layering of the lactose, PEG flakes which are smaller than the partition size melt and act as binder in the porous layer, the seed melts, molten PEG is sucked by capillary forces into the porous layer, where it acts as binder, the rate of pick up of fine particles is proportional to the surface of the granules, where a constant fraction of the surface is sticky enough to enable layering, thus a layer is formed whose thickness, h, is the same irrespective of the seed size, and coalescence does not occur. •
•
• •
•
•
•
A kinetic constant was obtained by parameter fitting to the sieve analysis data. It allowed to calculate the layer thickness and to estimate the fraction of lactose remaining as fines after the ending of the granulation process. Using the relationship (see Section 3.3.2) n(d, t) = n(d- h(t)), n( d, t) of the granules could be calculated from the seed size distribution. After a transformation of the number distribution into a mass distribution, and taking the calculated fraction of fines and their size distribution into account, the mean size d1 , 3 was calculated and compared to sieve analysis data (Fig. 2). Electron microscopy of sections of granules confirmed the nucleation mechanism to be immersion [56]. In conclusion, the results were found to be in qualitative agreement with the assumptions in the model. 3. 1 . 2. 2. 3. The pure breakage form. The kinetics of breakage is described by two functions, the selection function, S(u), which describes the rate at which particles u are selected to break, and the breakage function, b(u,v), [21 ] . The selection function (or breakage kernei) is the rate constant i n the foliowing expression: D(u)
( rate of breakage Of ) particles of size u
=
S(u) x ne u)
( concentration of ) particles of size u
(21 )
Therefore, S(u) i s a rate constant of a first-order process with the dimension of reciprocal time. To account for non-first-order breakage kinetics, a time dependent breakage kernel S(u,t) was introduced [57,58].
T. Abberger
1 1 26 1 200 1 000 E
2� �
"0
800 600 400
•
•
:+/;/�r=-r=
/ V o
200
.
•
o
•
I
/
15 20 10 mass fraction PEG %
5
25
30
Fig. 2. Simulated (line) and experimental (symbols) mean granule sizes in fluid-bed melt granulation of fine lactose and coarse PEG 4000 flakes [54].
The breakage function is the probability density function for the formation of particles of size v from particles of size u. It describes the number of particles of size v formed once a particle of size u has been broken. By inspecting the values of the breakage function, the breakage mechanism (attrition, fracture into two or more large pieces, and shatter, where an agglomerate is broken down into the primary particles) can be elucidated. To include breakage in the population balance, expressions for the birth and death rates owing to breakage are required. From the definition of the selection function, the death rate is as follows Dbrea(v) = S(v)n(v)
(22)
The birth rate at size v must be the weighted sum of death rates of larger particles that give fragments of size v. The fraction of deaths at u that gives birth at v is b(u,v) Bbrea(v) =
100 b(u, v)S(u)n(u) du
(23)
100 b(v, u)S(u)n(u, f) du - S(v)n(v, f)
(24)
The combination of equations (22) and (23) leads to Bbrea(v, f) - Dbrea(V, f) =
The theory concerning breakage is not as developed as that for aggregation and the expressions for breakage kerneis and breakage distribution functions are usually semi-empirical [59]. A list of breakage distribution functions can be found in [30] and three frequently applied breakage kerneis are described by Vanni [59].
Population Balance Modelling of Granulation
1 1 27
The PBE for breakage in discrete notation is [59] dN.
�I
dt
= '""' 6 M
1.=1+1
S(x1.) b (x1x1 ) N.1 - S(x1·) N.1
(25)
If the shear force in a granulator is low (drum or fluid-bed) and the particles are wet enough, breakage can be assumed as insignificant. Using high-shear mixers, however, experimental evidence for occurrence of significant breakage has been reported, and breakage should, therefore, be included in a PBM [60-62]. Sanders et al. [7] investigated the dependence of the agglomeration rate constant on the impeller speed in a high-shear granulator. Their results indicate as weil that breakage should be considered in a PBM of high-shear granulation. Hounslow and co-workers [22,63] included breakage into PBMs and could extract mechanisms and kinetic parameters of breakage in high-shear granulation. The addition of coloured tracer granules was shown to be a useful technique in the investigation of breakage. Tan et al. [64] investigated breakage in fluid-bed melt granulation. Glass ballotini were granulated by spraying PEG 1 500 onto them, in the presence of 1 % (m/m) coloured granules previously produced in three different sizes. In a second type of experiments, these mixture was fluidized without spraying binder in order to investigate breakage in the absence of agglomeration. Three different fitting experiments were performed to the data of the growth experiments, where the same coalescence kernel in all the fitting experiments was applied. In the first series, breakage was disregarded. Despite this, the mass-based PSD could be described fairly weil, however, the agglomeration only model failed to describe the number-based PSD. This was to be expected since bigger granules are more likely to break. In the second series, the agglomeration frequency extracted from the first series was used but breakage was additionally taken into account to improve the fit to the obtained PSDs. Three different breakage mechanisms (see above) were considered. The breakage model that induced the best improvement of the fit was random binary breakage with a size independent selection rate constant. The mean size was slightly overestimated, because the same aggregation frequency as in the first series was used. The apparent agglomeration rate extracted from the first series is in fact a net process made up of agglomeration and breakage. In the third series, agglomeration and breakage rates were extracted simultaneously. The extracted breakage mechanism was a combination of random binary breakage and attrition. Such a combination of mechanisms was supported by micrographs. Each of the three approaches was suited to model the evolution of the mass-based PSD. When comparing the evolution of the mean size, it was revealed that the third approach produced the best estimation, as expected. This work again showed, however, the difficulties in modelling the nucleation phase of granulation.
T. Abberger
1 1 28
3 . 1 .2.3. Multi-di mensional population balance equations
As discussed by Iveson [33], one-dimensional PBEs regarding particle size alone as independent granule property that significantly controls granule growth and thus being the only property that is modelled, are a simplification that leads to limited applicability. Although size is a key property of granules, it is weil known, however, that other internal properties of granules, such as porosity and granule binder content strongly influence the growth of granules and their quality. All such properties can vary significantly between granules [33]. Multi-dimensional PBEs allow the modelling of the time evolution of the distributions of such properties. There seems little doubt that models allowing particles to be described by multiple properties will become the norm [27]. When the advantages of multi-dimensional PBEs shall be exploited, this requires knowledge of the initial distribution and the boundaries of all the properties included in the equation, as weil as rate expressions for their development in the course of time. A coalescence kernel that is applied in a multi-dimensional PBE has to take into account the effects of all the independent properties included in that PBE on granule agglomeration (see Section 3.2.4). Porosity is a controlling factor of coalescence owing to its effect on deformability and liquid saturation. Liquid saturation is a key controlling factor for granule growth [65,66]. Annapragada and Neilly [60] showed that both the particle size and the porosity evolve during the process. They were the first to suggest that both, size and porosity, should be included in a population balance model. 9 A two-dimensional PBE for pure agglomeration accounting for size and porosity as independent parameters can be easily developed (equation (26), compare [33]). A granule with volume v - u and porosity ev- u coalesces with a suitable granule of size u and porosity eu to produce a new granule of volume v and porosity ev. The PBE requires a term for the evolution of porosity and a double integration over both the independent properties in the birth and death terms. an(v, ev, f) at
100 l"u,max ß(v, u, ev, eu, f)n(v, ev, f)n(u, eu, f) deu d u "u,minmax rl"u, + 2Ntotr Jo0 "u,min ß(v - u, u, ev-u, eu, t) 1
-Ntrot 0 1
X
n(v - u, ev-u, t)n(u, eu, t) deu d u
(26)
9 A two-dimensional PBE for coagulation of a binary mixture has already been described by Lushnikov [67].
Population Balance Modelling of Granulation
1 1 29
The porosity is not additive: GV -# GV- U + GU, but the pore volume is, as a first approximation, assumed to be additive. Therefore, for a given granule of properties v U, Gv- u, the porosity of the second granule with size U to produce a granule with properties v, Gv can be calculated by -
GU =
VGV - (v u)Gv- u -
U
(27)
Binder content has been the subject of many experimental investigations on the factors influencing granule growth. Almost all investigations showed that granule growth increases with increasing binder content for a wide range of materials in many different types of granulators. Increasing granule binder content increases the amount of liquid available to form bonds between granules and also improves granule surface plasticity [51 ]. It is now recognized that in many systems the binder is not uniformly distributed [33,68]. The homogeneity of the binder content, reflecting the liquid distribution in a device, has been shown to influence the resulting PSD [69]. Iveson [33] proposed a four-dimensional PBE for pure agglomeration considering four independent granule properties: the granule solid-phase mass, m; the binder content, expressed as mass ratio, w; the porosity, G; and the composition, expressed as mass fraction, x, of a second component. an(m, G, w, x, t) = Bcoal (m, G, W, X, t) - 0coal (m, G, W, X, t) at + C(m, G, W, X, t) + Wem, G, W, x, t)
(28)
Terms for the evolution of the distribution owing to consolidation, C, and wetting, W, are included. These terms describe the evolution of the porosity and of the binder content, respectively. Other terms could be added easily. Ramkrishna and Mahoney [23] have assessed common methods of solving one-dimensional PBEs for their ability to solve multi-dimensional PBEs. Because the solution of multi-dimensional PBEs is exceedingly difficult [20], attempts at simplification have been made. Verkoeijen et al. [31 ] facilitated the approach regarding size, porosity, and binder content as properties of interest. To obtain the facilitation, they regarded three different volumes as independent, distributed properties: the volume of solids, the volume of liquids, and the volume of air of a single granule; these volumes have additive properties. In their approach, the time evolution of these volumes instead of particle numbers is being modelled. The measured properties of interest that are the particle porosity, the moisture content, and the pore saturation, which are not additive, can all be derived from these three volumes. An extension of the approach of Verkoeijen et al. [31 ] was made by Darelius et al. [70] to account for initial non-uniformly distributed moisture and air content.
T. Abberger
1 1 30
Biggs et al. [71 ] regarded size and liquid fraction as independent, growth controlling properties, whereby each granule comprises three phases, solid, liquid, and air. The simplifying approach of Biggs et al. [71 ] was to model the granulation with a set of n number density functions of one variable each, either the volume of solid or liquid, instead of regarding one single number density function in n variables. 3. 1 . 3. The population balance equation in moment form
Sometimes knowledge of the complete PSD is unnecessary and some average quantities may be sufficient to represent it. These average quantities can be expressed as moments of the distribution function. The moment form of PBEs is widely applied in the crystallization literature, owing to its potential to create reduced order models. The procedure to form moment forms of the PBE, however, very often leads to terms that may not reduce to moments, to terms that include fractional moments, or to an unclosed set of moment equations [72]. Kerneis applied in granulation are often complex, which enforces this difficulty. There exist moment forms of the general PBE, for pure growth and for pure aggregation. Because the general PBE and the pure growth form in moment transformation do not seem to be applied in the modelling and simulation of granulation, nor to be relevant for the development of the approach, they will not be presented in this chapter; the reader is referred to Ref. [ 1 7]. 3 . 1 . 3. 1 . Moment representation of a particle size distribution
1000
We define the nth moment of n(x, t) as Mn =
� n(x, t) dx,
n? 0
(29)
Usually, only the first few moments are tracked because they contain the information about • the total particle number, Mo, • the number-based mean particle size, M1/Mo (d1 •0, when x is a length), and the coefficient of variance, (J, to express the width of the PSD as (J = 1, 1 which is sufficient in many practical applications. •
3 . 1 . 3 . 2 . The pure aggregation form
JM��2
-
The pure aggregation form of the PBE in moment form is obtained by multiplying both si des of equation (7) by � and integrating over the entire range of v; this
Population Balance Modelling of Granulation
1 1 31
yields an ordinary differential equation, ODE, dMn - O -- =
(30) Bn - n where Bn and On are given as Bn = Jooo v n B(v) d v and On = J: v n O(v) d v,
dt
respectively. Equation (31 ), which was given by Drake [73], follows from equation (30) dMn (t) __ _ 1 00 00 [(u + vt - u n - v n] ß(U, v)n(u, t)n(v, t) dv du (31 ) 2 0 0 dt This immediately shows that the total number of particles i n the system decreases in the course of time and that the total mass or volume is conserved , Jooo vn(v, t) d v i s constant in t, which i s expected from the descriptive model, however the sum of square of masses, M2 , increases. =
_
11
3.2. The coalescence kernel 3. 2. 1. Introduction
The establishment of the coalescence kernel for granulation processes is still ongoing research. A single kernel unifying all theories and considering all governing factors and their relationship does not yet exist. The determination of the appropriate kernel remains a difficult problem in the simulation of granulation or when solving an inverse problem (see Section 3.4). The experimental results described in the literature vary widely, are sometimes contradictory and many growth regimes exist. Experimental observations are offen unique to a given class of material and processes. A complex relationship exists between feed size distribution, granule properties, apparatus geometry, operating conditions, and the mechanisms of granulation, leading to the proposal of a variety of coalescence models and growth regimes [74]. This had two consequences: the development of a variety of different kerneis, and that the current approaches to kernel development tend to recommend different kerneis for different granulating systems and/or materials [75]. Kernel development started with empirical kerneis considering granule size as distributed property governing granule growth. Owing to their long history, many such kerneis exist. Such kerneis contain adjustable parameters, and their numerical value is extracted by data fitting. The insight gained into the process by such kerneis is not sufficient and the numerical value extracted might not be transferable to another experimental setup. The choice of the empirical kernel providing the best fit is a trial and error approach. Despite all their disadvantages, as discussed by Wang and Cameron [8], these authors stated that the empirical coalescence kerneis have played an important historical role in the study of the population balance and for many practical
1 1 32
T. Abberger
granulation processes, a properly selected empirical kernel may provide an acceptable level of model prediction. More generalized, physically based models are highly demanded by the granulation industry for further research and development [8]. If the coalescence kernel is based on a physical coalescence model, the PBE ideally should allow predictions of PSDs without any need for parameter fitting from experimental granulation data. Although several recently proposed kerneis have a theoretical basis, a need to include empirieal, adjustable constants even in such kerneis can remain. This may be attributed to the still limited knowledge of the influences of process parameters and material properties. Coalescence kerneis based on theoretical models should be more fundamen tally sound than the empirical kerneis, because the granule physical properties, the binder properties, as weil as the collision velocities of the granules are included in theoretical models [76]. The key for successful application of these models is to correlate the model parameters to measurable process and material parameters. Therefore, difficulties exist in application of the theoretical coalescence models. Limited application of theoretical coalescence models can be attributed by two factors [76]. Firstly, most models are based on the collision mechanisms of two isolated granules. In coalescence models, the particle pair must act indepen dently of the remainder of the dispersed phase. This is a limitation of such models [28]. In a granulator in which many granules interact with each other, the theoretical models based on binary co-linear collisions may not be applied [76]. Furthermore, few models consider angular collisions [33]. Secondly, there is still very limited knowledge on the granule-collision velocity distribution and collision frequencies in different types of granulators (see Section 3.2.2). In consequence, using a kernel or a combination of kerneis that provide the best fit to the experimental data is still the most common method [76,77]. 3. 2. 2. The physical implication of a coalescence kernel
As mentioned, the coalescence kernel describes the local motion and coalescence rules. This statement is described in greater detail below. 3 . 2 . 2 . 1 . The aggregation frequency
As can be seen from equations (3) and (4), the number of particles formed or lost in a size range between v and v+ dv owing to coalescence of two granules with diameters u and v is determined by a coalescence rate, or aggregation frequency. The aggregation frequency is usually derived by analysing the relative motion between particles culminating in their aggregation in isolation from the population balance. This approach is based on the assumption that the local motion does not compromise the spatial homogeneity of the population and on the assumption that motion of particles is faster than the rate of particle aggregation [50].
Population Balance Modelling of Granulation
1 1 33
The aggregation frequency is composed of two terms [78] Aggregation frequency = Collision frequency x Aggregation efficiency (32) Because collision of granules is necessary but not sufficient for coalescence, it is necessary to associate an efficiency of aggregation for a complete characterization of the aggregation frequency. The aggregation efficiency can be interpreted as the probability that two collided particles will aggregate to form a single particle, that is the coalescence probability [14]. Equation (32) is valid under the assumption, that collision is the step, which determines the velocity of the whole aggregation process. 3.2.2.2. The col lision frequency 3. 2. 2. 2. 1. General collision theory. A particle A moves in the course of time M through a "collision cylinder", which contains a collection of particles B (Fig. 3). The volume, V, of the collision cylinder is given as (33) where (J is the "collision cross-section" and collision frequency, fc, can be calculated as
< v)
the velocity of particle A. The (34)
where [B] is the number concentration of particles B. The velocity < v) has been replaced by the relative velocity, < Vrel ) because the particles B are not stationary. The frequency of collisions between particles A and B per unit volume, fc, is given as fc fdA] = (J ( vrel ) [A][B] (35) 3. 2. 2. 2. 2. The collision or loading frequency in a granulator. Sastry and Fuerstenau [43] divided the aggregation processes into two basic classes, "free-in space" and "restricted-in-space" aggregation. The distinguishing property between ,
=
dA+dB 2
1
-
miss
----
__ _
d B/2
hit
Fig. 3. Collision cylinder. Reprinted with permission from Prof. Thomas Bally, Department of Chemistry, University of Fribourg, Switzerland.
T. Abberger
1 1 34
the two types of aggregation is the number concentration (Iow or high) of particles in a unit volume. When the number concentration is low, each particle can collide with any other particle in the unit volume. When the number density is high, the movement of a particle is restricted and it can encounter only the particles that immediately surround it. No clear demarcation between the two classes exists. For aggregation in a diluted system, in a free-in-space system, the rate of collisions is proportional to the product of the number concentrations of the two species (compare equation (35)) (36) [Collisionslj ni(t)nit) Kapur and Fuerstenau [12] postulated that the concentration of agglomerates in a loosely packed granulating bed is more er less fixed by the packing constraints. In this situation, the movement of an agglomerate is restricted. It is likely to encounter and coalesce with its nearest neighbours, which form a cage around it. The agglo meration occurs under a restricted-in-space environment. For a restricted-in-space system, the number of random collisions between particles belonging to any two size groups, i and j, under the constraint of perfect mixing is proportional to the product of the number of species of one type with the number fraction of the second type oe
[Collisions]ij
oe
niet)
::a;it)
(37)
In deriving equation (37), Kapur and Fuerstenau [12] argued that in a randomly mixed bed in which the range of sizes is not large, the collision frequency will be approximately the same for all granules present. The normalization by Ntot(t) means that the population is averaged over a region containing that number of particles; this can be the whole granulator but may aiso be applied to separate regions [77]. Recently, Kapur and Runkana [53] modified the random collision model and, therefore, equation (37), in order to incorporate the size dependence of the coordination number of granules. In a simulation performed to compare both the collision models, random and coordination, however, similar results were produced despite the differences in the collision model. Size segregation will alter the frequency and velocity of collisions between granules of different sizes. Granules in the stationary regime of a drum, pan, or mixer will also have lower collision velocities than granules in other regions [33]. Ouchiyama and Tanaka [47] divided the granulating spaces into two types and introduced two different frequencies, the collision frequency for the free-in-space system and the loading 1 0 frequency for the restricted-in-space system. In one type of granulating spaces, most of the granules are separated from each other and in the other type the granules are in contact with their neighbours. Denoting the volume ratio of the former by �, then the collision and the loading 10 Loading means an application of force through the neighbours to the contact point between two granules which are in contact with each other.
Population Balance Modelling of Granulation
1 1 35
frequency in each space are represented by equation (38) for the collision and by equation (39) for the loading (38) [Collisions]jj , njnj n (39) [Loadinglj cx ( 1 - Onj N j tot By introducing a new parameter, the degree of restriction, r, which is equal to zero for the granulator in which most of the granules are separated from each other, e.g. a fluid-bed granulator, and equal to unity for that in which they are in contact with the neighbours, e.g. pan or drum, they could express the collision or loading frequency in a unified expression cx
:!
(40)
�t�(6 n(d, t) dO dd
(42)
[Collisions or Loading]jj cx nj
tot
In order for two granules to coalesce, it is necessary that a collision occurs when granules are separated from each other, Iike in a fluid bed. No c1ear single collision event exists in applications, where the granules are constrained in contact with one another for significant time intervals, as in the rising section of a tumbling drum, or in the quiescent zones of a fluid-bed. Here, all the granules are constantly in contact with their neighbours [79]. The collision frequency may be replaced in these cases by the loading frequency per unit volume, fL, that is the product of the total number of contacts between the two granules of sizes 0 and d per unit volume, n(O,d) dO dd, and the frequency of experience of a force leading to adherence of a pair, the loading frequency, ", according to h = n(O, d) dO dd x " (41 ) According to Ouchiyama and Tanaka [80,81], n(O,d) i s the contact number function of sizes 0 and d in a completely mixed packing. The total number of contacts between particles of the size fractions O,O + dO and d,d + dd at time t can be expressed in a restricted-in-space environment as neO, d) dO dd =
C C(O, d)
C and C(O,d) have been defined from a packing model [82] as the packing parameter and the contact number between one granule of diameter 0 and the surrounding granules of diameter d. Huang and Kono [83] assumed that the total number of collisions per unit time can be expressed as the product of the total number of contacts and the packing renewal frequency in a granulating device. Because little is known about the collision or loading frequency, several authors [81 ,83-86] resorted to a dimensionless time, defined as fC,L t, where fC,L is the collision or loading frequency and t the real time to solve the PBE. A shortcoming of this approach is that at present the function = f(t) can be obtained by data fitting only. T,
T
"-'
T
1 1 36
T.
Abberger
In order to describe the collision rate in a fluid-bed, Goldschmidt (cf. [87]) was able to develop a proportionality factor, a collision rate constant, Gij, for introduction into equation (36) as
mj
Gjj = ncJtgjj
2 1 / [4 (0smi+mj ) 2mjmj _ ] djj
n
2( - "3 \7 u)
(43)
where djj is the inter-particle distance between two particles on collision, gjj a radial distribution function for mixture, Os the mixture granular temperature, mj and the mass of particles, and ü the ensemble average particulate velocity. 3 . 2 . 2 . 3 . The aggregation efficiency
To predict the aggregation efficiency, or coalescence probability, from the properties of the granules and the binder, and the operating conditions, a large number of coalescence models have been developed, making a wide range of different assumptions about the formulation and the process characteristics. Key properties in which the models differ are the deformation behaviour of the granules, binder viscosity or other binder properties influencing bond strength, and the acting separation forces. The methods used in developing the models are either energy or force balances, and most of the models [88-92] are able to predict whether the granules will stick together (successful collision) or rebound upon collision. 3. 2.2.4. The relationship between the coalescence kernel and the aggregation frequency
From equations (3) and (4), it can be easily checked that the aggregation frequency of particles of sizes u and v is proportional to the product of the total numbers of such particles, and that the coalescence kernel is a proportionality factor in the aggregation frequency. The coalescence kernel ß(u,v) expresses • •
•
the aggregation efficiency of two particles of sizes u and v, and either the "collision cross-section" and the velocity of the particles in the free-in-space environment or the contact number between one granule and the surrounding granules and the loading frequency in the restricted-in-space environment. In conclusion, the kernel has to describe the influence of
•
• •
granule size on the aggregation efficiency and either the collision or loading frequency, other granule properties except size on the aggregation efficiency, operating conditions on collision or loading frequency and the aggregation efficiency.
Population Balance Modelling of Granulation
1 1 37
The kernel is in principle measurable and because its physical properties include a probability, it is positive everywhere. The dimension of the kernel is reciprocal time. In a granulation process, the kernel cannot describe the motion and coalescence rule owing to a dependence on u and v alone. Furthermore, the assumption, that there is no influence of other particles, can be challenged in a granulation process. In order to express that the kernel has to account for a variety of influencing properties and conditions, time has been introduced as a third variable, ß(u, v,t). The time dependence of the kernel is a manifestation of the dependence of the kernei on other particles in the system or on the state of the distribution [28]. The time dependence allows to account for a shift in the granulation regime during the course of a granulation process. 3.2.2.5. The design of kerneis
3.2. 2. 5. 1 . The traditional design. The coalescence kernel is traditionally split into two parts [44] ß(u, v, f) = ßo (f)ß*(u, v) (44) where ßo ( t) is the aggregation rate term and ß*(u, v) describes the dependence of the coalescence kernei on the sizes of the agglomerating granules. The aggregation rate term ßo (t) is size-independent and includes various system parameters such as the granulator geometry, the operating conditions (e.g. drum or impeller speed), and formulation properties (e.g. binder viscosity, wettability or moisture content [45]). The variable t is, therefore, in part a dummy variable for other properties such as binder or moisture content, or operating parameters, which can, but need not change in the course of time. The relationship between the time dependence of a kernel and the granule properties has been discussed by Pearson et al. (cf. [68], see also Ref. [63]). Provided that the binder content and operation conditions remain the same, ßo (t) is generally assumed to remain constant throughout the experiment [33]. If, however, the aggregation rate term is, contrary to this assumption, not constant in the course of an experiment this could be due to invalidity of the underlying assumptions in the kernel (see Ref. [22]). Moreover, as stated by Iveson [33], it is insufficient to model the effect of parameters that show a significant distribution, such as binder content of granules, by just varying the aggregation rate term ßo (t) as an average value, as has been done in the traditional approach using the empirical kerneis. This may explain, in part, why this approach had limited success. The aggregation rate term controls the rate of change of the mean of the granule size distribution [93]. In many kerneis, the second term, ß*(u, v), expresses the influence of granule size on the collision frequency, where the assumption that each collision leads to coalescence is implicit. In some kerneis, ß*(u, v) expresses as weil the size
1 1 38
T.
Abberger
dependence of the likelihood of coalescence. The term ß*(u, v) determines the shape of the resulting PSD [75]. 3. 2. 2. 5. 2. The design suited for physical models. With this design, a kernel consists of a rate term describing the collision or loading frequency and a term describing the aggregation efficiency, P(u, V, Z1 , Z2), where Z1 and Z2 stand for all the other relevant properties besides size of the two colliding granules. This design differs considerably from the traditional design of a kerne!. A coalescence model that predicts whether two granules will coalesce or not, can be transformed into an aggregation efficiency by applying a test function 1 if test is true aggregation efficiency = P(u, V, z1 , Z2) = (45) . . o If test IS false This can lead to a high computational load. Instead of performing this test for each pair of colliding granules, where each granule has many different properties, the calculation can be facilitated by using average values for properties such as binder content, kinetic energy, or porosity. Furthermore, mostly the distribution of such properties is not known. Such a distribution of influencing properties leads to a corresponding probability distribution of P(U,V,Z1 ,Z2) according to P(u, V, Z1 , z2 ) = Pr{test is true} (46) Within a granulation regime, an increase of parameters such as moisture or binder content can lead to an increase of Pr{test is true} and, therefore, to a higher aggregation frequency. In the traditional approach, an increase of the mean value of Pr{test is true} manifests itself in an increase of the aggregation rate term. Different granulation regimes can produce different mean values of Pr{test is true} as weil. The shift from one granulation regime to another during the course of a granulation manifests itself again as a different value of the aggregation rate term. Although the collision or loading frequency is size-dependent, in many working models a separate term such as (U1 /3 + V1 /3) 2 to express this dependence has not been incorporated, because the whole collision frequency has been obtained as an average value by parameter estimation. In some PBMs of a granulation in a restricted-in-space environment [80,81 ,84,85], such a term, however, has been included.
{
3. 2. 3. Homogeneity of kerneIs
3.2.3. 1 . Definition
A separable kernel satisfying the condition
ß( cu, CV) = dß(u, v),
i s called homogeneous with exponent A.
'v'c> O
(47)
Population Balance Modelling of Granulation
1 1 39
Many kerneis of practical relevance 1 1 satisfy equation (47) [42]. The exponent A, the homogeneity degree, expresses the strength of the dependence of ß(U, v) on its arguments. It reflects the tendency of large particles to aggregate preferentially with other large particles [94]. The behaviour of the solution of the PBE depends critically on the homogeneity degree Je [95]. It is the mainstream of the literature that the homogeneity degree divides the pure aggregation process into two regimes: • •
A < 1 non-gelling and leading to a self-preserving size distribution, and A > 1 gelling.
It seems that most authors consider A = 1 as non-gelling and leading to a self preserving size distribution. 3.2.3.2. Self-preserving size distributions
Definition. Homogeneity of the kernel is the formal statement that the aggregation process does not have a characteristic scale, i.e., aggregation of particles at different scales is assumed to happen similarly except for a possible change in the rate of the process [96]. A self-preserving or self-similar size distribution is characterized by a distribution function with a maximum and a similar shape that increases in peak position with time but retains the shape of the distribution curve. By normalization a general time-invariant distribution function can be determined for the self-preserving distribution associated with a kernel. By normalization all graphs of the self-preserving distribution collapse into one single graph. The size can be normalized by the mean volume of a particle, V, where v = M;+ 1 /M;, i = 0,1 ,2, . . . , and the distribution function, 'P(I]) = 'P (vIv(t)) , is dimension less. The new independent variable I] is the dimensionless normalized particle volume. The concept of self-similarity was described comprehensively by Wright and Ramkrishna [28]. In the broadest sense, the term similarity implies a reduction in the number of independent variables in the problem as a result of some invariance relationships. Physically, the process harbours some behavioural symmetry that manifests in some quantitative manner [97]. Many pure aggregation processes lead to self-preserving size distributions [14]. This simplifies the analysis of experimental data (see Section 3.4). Numerous evidence of self-preserving size distributions in granulation was reported. 3. 2. 3. 2. 2. Similarity transformation of the population balance equation. A similarity transformation transforms the PBE into an ODE for 'P of 1], thus reducing the number of independent variables from two to one. The well-known 3. 2.3. 2. 1.
11
For a list of relevant kerneis applied in the physical chemistry literature, see Ref. [94].
1 1 40
T. Abberger
similarity transformation introduced by Swift and Friedlander [98] is as folIows: n(v, t)
where N(t) =
and
100 n(v, t) dv
100 vn(v, t)dv
(49)
(50)
(51 )
Pulvermacher and Ruckenstein [99] and Ruckenstein and Chi [1 00] investi gated under which conditions a similarity transformation is possible, and when a similarity solution exists. Pulvermacher and Ruckenstein [99] investigated for a range of kerneis known at that time if a similarity transformation is possible and if a similarity solution is possible and wh at this (exact or approximated) solution iso 3. 2.3. 2. 3. Similarity solution of the population balance equation. A self preserving size distribution often enables a similarity solution of the PBE. A similarity solution allows to solve the PBE for the full PSD even when no analytical solution of the PBE exists. To determine whether a similarity solution is possible, first the kernel must be shown to be homogeneous with A � 1 . The similarity transformation of the PBE must be possible. This transformed equation must meet the boundary conditions, equations (50) and (51 ). A similarity solution is a solution of the PBE of the type 1 2 N2 (t) (52) n(v, t) =
Population Balance Modelling of Granulation
1 141
�(I]) remains to be determined for a solution of the PBE. It is often assumed that �(I]) has a log-normal form [1 01]. Such similarity solutions can represent exact solutions over a long time period [99]. By considering the average volume at a given time and the total number of particles in the system, the entire distribution can be calculated from the similarity solution. If a unique self-similar solution exists, it is natural to expect convergence to self-similarity from rather general initial distributions [42]. This means that the similarity solution is an asymptotic solution �(I]) towards all distributions converge, regardless of the initial distribution. This shows that the self-preserving distribution is a property of the kerne!. The time to reach the self-preserving distribution is important, because it governs the applicability of the self-similar solution, if it exists. 3.2.3.3. Gelation
From equation (31 ) and the descriptive model, one expects conservation of volume and mass for any kerne!. For kerneis with A > 1 , a phenomenon occurs, however, which may be regarded as the mathematical equivalent of a phase transition called mathematical gelation. After a critical time, tc, mass, m, is lost from particles of finite size and appears in particles of infinite size, which are called in analogy to polymer science gels. For t> tc, the loss of mass of particulate material of finite size is [1 02] m
= "L, mn(m, t) < O
(54)
The usual interpretation of the result in equation (54) is that a part of the system is no longer described by the Smoluchowski equation. This part consists of a large merger that gains mass from the rest of the system with m [1 02]. Different interpretations of mathematical gelation are that the PBE has no solution for f> tc, or has no solution at all when using gelling kerneis 1 4 [34], or that a gelling kernel is physical meaningless, at least in situations where no physical gelation occurs. Conservation of mass implies that the square of the mass has to remain finite at every time: M2(t) < for all t< Therefore, gelation occurs if for a monodisperse initial size distribution no solution exists with M2(t) < 0 � t< Then tc is defined as the largest time such that M2(t) < for all t < tc [42]. To provide an order parameter for aggregation, an index of aggregation , la99' has been defined as [94] 00
00 .
00,
la99 =
{
00 .
00
��
1
- Ma (t) Ma(ta)
1
-
batch systems continuous systems
(55)
la99 varies between zero (no aggregation) and unity (complete aggregation). The
point at which mathematical gelation occurs is referred to as I�� [94]. 1 4 A kernel leading to mathematical gelation is called a gelling kerne!.
1 1 42
T.
Abberger
Sufficiently fast increasing coalescence kerneis lead to solutions exhibiting gelation. A prototype of a gelling kernel is the product kernel (see Section 3.3.2), where A = 2. The constant kernel (see Section 3.2.4) is a non-gelling kernel (A = 0). Non-gelling kemeis have diverging second moments only as lagg 1 [94]. 1 5 Smit et al. [94, 1 03] investigated a range of well-known kemeis applied in the physical chemical literature if they are gelling kerneis and in case they are, for their values of la�� ' Upon investigation if a kemel is gelling, it is possible to exclude a gelling kernel from modelling processes, where physical gelation does not occur. Using the restricted-in-space PBE, equation ( 1 0), had no effect on I�;� for any kernel investigated. An onset of mathematical gelation was determined from predictions of the sixth moment of length, which is equal to the second moment of volume. In their concluding remarks Smit et al. [1 03] stated, it is possible that: -+
•
•
•
Gelling kerneis correctly describe the collision frequency, but neglect to account for the aggregation efficiency. Kerneis need to take into account the existence of a maximum permissible size beyond which particles do not aggregate. This means banning aggregation events leading to particles larger than some critical size. It is necessary to include a strong breakage function when modelling aggregation. This approach is open to some criticism because the value of the breakage rate does not necessarily reflect the rate at which physical breakage occurs but instead imposes a value that may be artificially large in order to stop the occurrence of mathematical gelation.
3. 2. 4. Kemels applied in the modelling o f granulation
3.2.4. 1 . Purely empirical kerneis
The constant kernel ß(u, v, f) = ßo (f) . 1
(56)
is size-independent, that means the aggregation frequency is not affected by the particle sizes. This kernel has been introduced into granulation research by Kapur and Fuerstenau [12] to model random, which means size-independent coales cence. This model, despite its lack of a physical rationale, is in agreement with many experimental data [ 1 04]. It can be shown that for long times size-independent aggregation always leads to a self-similar distribution, independent of the starting size distribution [105]. The similarity solution for size-independent growth is [106] (57) 1 5 For example: For mono-sized feed and ß(u,v) constant, the relationship between and M2 for a batch process is given as [21 ] M2«tQ) ���agg gg a M2 0 =
=
•
la99
Population Balance Modeliing of Granulation
1 1 43
Kapur [1 07] obtained, in different notation, equation (57) as similarity solution, when applying the constant kernel. The experimental PS Os of limestone granulated in a drum were conform to this solution. The sum kernel ß(u, v, t) = ßo(t) . (u + v)
(58)
expresses that the aggregation frequency is proportional to the volumes of the colliding particles. This kernel expresses that the smallest particles do not coalesce easily and persist almost forever [78]. The corresponding similarity solution is known [1 4]. Kapur's kernel [1 07] ß(u, v, t) = ßo(t) .
(u + V)8 (uv)b
(59)
contains two adjustable parameters, a and b. For a = b = 0, the kernel reduces to the size-independent kernei, for a and b # O, however, the kernel describes non-random or preferential that means size-dependent growth. The effect of variation of the constants a and b on the PSO, expressed as normalized variance (Jjd4,3 , was investigated using a narrow and a wide starting PSO each time by Adetayo and Ennis [74,75]. Because this kernel is homogeneous with A a-2b, all combinations of a-2b < 1 led to self-similar size distributions regardless of the starting PSO. Values of a-2b = 1 favour growth of the largest granules, thereby a widening of the PSO over a long time period, whether the initial size distribution was narrow or wide, was visible. Here, the curves did not reach an asymptote within the investigated time period, but at least it came in sight, as one would expect from the value of }e = 1 . Adetayo and Ennis [75] concluded that a kernei, which is mathematically very versatile due to its adjustable parameters, can describe different evolutions of PSOs. Kapur [1 07] showed that a PBE including his empirical kernel admits a similarity solution, but could not obtain it. It was noticed [1 07,1 08] that this kernel despite its empirical origin can provide some information about agglomeration mechanisms. Ouchiyama and Tanaka [47] roughly described the loading frequency of two granules with diameters D and d as proportional to (D + d)2 and the coalescence efficiency was described being reciprocal proportional to (Dd). Knight [1 09] investigated the kinetics of melt granulation of fine sodium phosphate with a fairly wide size distribution using a high-shear mixer. Growth was observed with moisture/solid ratios in the narrow range of 0.20-0.26. Within experimental errors, the weight median size was dependent linearly on time with each of these mOisture/solid ratios. He stated that under the constraint that ßo(t) changes only little during the process, the linear growth kinetics is consistent with the probability of coalescence being proportional to the reciprocal geometrie
=
1 1 44
T.
mean diameter of the colliding granules,
/
ß(u, v, t) = ßo (t) JU1 /3 V1 /3
Abberger
(60)
However, Knight did not claim this relationship to be a unique solution. As pointed out by Ennis [1 1 0], a wide range of kerneis can approximate linear growth of the mean diameter provided a critical cut-off size is introduced. Sastry [44] introduced a kernel of the type ß* (u, v) = (ua + vB) (u-b + v- b) (61 ) where a = 2/3 and b = 1 . 1 6 This kernel shall reflect the following assumptions about the agglomeration process: •
•
the efficiency of coalescence of two equal-size species decreases with increasing size, whenever an agglomerate encounters two larger-size species, it tends to coalesce with the larger one.
The kernel reflects that the potential for collision increases proportional to the surface, and that the separating forces, e.g. gravity, increase proportional to the mass of the granules. The kernel is homogeneous with A = 1 /3 and, therefore, leading to a self preserving size distribution. This kernel could be applied successfully to simulate granulation of different inorganic materials. 3.2.4.2. Semi-empirical kerneis
Adetayo et al. [1 1 2] identified two stages of granulation in drum granulation of fertilizers with broad initial size distributions. Therefore, a sequential kernel was suggested [93] to model fertilizer granulation of broad size distribution feeds as for t:( t1 (62) for t> t1 and Ssat :( Serit for t > t1 and Ssat > Serit where ß 1 and ß2 are the aggregation rate terms, obtained by parameter estimation, t1 the transition time between the two stages of granulation, Ssat the saturation of the voids, and Serit the critical saturation, a characteristic void saturation necessary for the onset of the second granulation stage, as the second stage relies on plastic deformation of colliding granules. The first stage was within a non-inertial regime where growth occurred by random coalescence. The probability of successful collisions depended only on 16 In the physical chemistry literature, a kernel of this type with a Brownian motion [1 1], see also Ref. [1 1 1].
=
b
=
1/3 has been based on
Population Balance Modelling of Granulation
1 1 45
binder distribution, with all collisions involving binder being successful. The PSD narrowed during this first stage and an equilibrium size distribution was reached at t1 . The extent of granulation within the first stage, given by ß1 t, was found to be linearly proportional to Ssat and to increase with binder viscosity. Changes to the initial size distribution affected ß 1 t by changing granule porosity and, therefore, liquid saturation. When Ssat remained below Scrit, which means the second stage of granulation did not occur, the PBE solved for f> t1 gave the equilibrium granule size distribution for coalescence in the non-inertial regime only. When Ssat exceeded Scrit, the granules were sufficiently deformable for further growth. The second stage of granulation broadened the PSD. Scrit decreased with increasing binder viscosity. Hoornaert et al. (cf. [1 1 0]) investigated the granulation of an enzyme powder and inorganic fillers with an aqueous binder solution using a high-shear mixer. Several stages of growth were observed. Following the approach of Adetayo et al. [93], they proposed a sequential kernel to model the stages of nucleation, densification, and growth of the form ß( u, v, f) =
{
ßn (u + v) for f < t1 0 for t1 < f < t2 ßc ( u + v) for f> t2
(6 3)
where the subscripts n (c) denotes nucleation (coalescence), and the time of densification is from t1 to t2· Wauters et al. [77] made an aUempt to develop a PBM for a high-shear granulation, which can be applied to simulate three stages of granulation: nucleation, induction, and growth by coalescence. Owing to the complex mechanisms of nuclei formation, they could not find a kernel for the nucleation stage. They could find a joint kernel for both the induction and the growth stage, however: ß( u, v, t) =
{0
A e -Bt
for Ssat < 1 --- 1 for Ssat ?
(64)
This kernel predicts that the induction period with no growth proceeds as long as the void saturation is below unity. When the surfaces get wet, a discontinuity with onset of coalescence occurs, where the growth is independent of granule size. The term in the kernel describing the growth stage for Ssat � 1 was found empirically. The ratio of the empirical constants A and B, AlB, was found to be directly proportional to the solution phase ratio derived by Sherington. Experimental validation was performed with previously published data from a high-shear mixer. The PSD at the end of the nucleation stage was used as starting size distribution for the simulation of the induction and growth stages. In a comparison of the sum kernei, the kernel of Adetayo and Ennis [75] (see this
1 1 46
T. Abberger
section) and their own kernei, the latter produced the best fit to the experimental data. The reason for this better performance could not be c1arified. 3.2.4.3. Model-based kerneis 3.2. 4. 3. 1 . Coalescence models accounting for plastic deformation 3.2. 4. 3. 1 . 1 . A model of plastic deformation for surface-dry granules.
Plastic deformation leads to energy dissipation and creates an enlarged area of contact that helps to hold the granules together [1 1 3]. Ouchiyama and Tanaka [1 081 considered surface-dry, deformable granules in a drum granulator (Fig. 4). They assumed that in the constant-angular-velocity region of the drum, an axial compressive force acts on each pair of granules with diameters 0 and d. This deforms the granules and creates a contact zone between them with a cohesive strength proportional to the area of the contact, S. In the tumbling region of the drum, each granule pair is then exposed subsequently to pairs of forces, F1 and F2 , perpendicular to a tangent common to the contacting granules that tend to separate the granules. The compressive forces were assumed to be independent of granule size, whereas the tangential separating forces were assumed to be proportional to the volumes of the granules in contact. At the contact point, the bending moment exerts a tensile stress. Successful coalescence occurs when this tensile stress is smaller than the tensile strength of the bond. In other words, the compressive force has to be greater than the force creating the tensile stress. The coalescence probability, P(D,d), was described by Ouchiyama and
s
TUMBLING DRUM
Fig. 4. Ouchiyama and Tanaka's model of coalescence. Reprinted from Iveson et al. [1 1 3]. with permission from Elsevier.
Population Balance Modelling of Granulation
Tanaka [1 08] as P(D, cf)
,n - )0
_
[ -{ 1
}]
2 ' (Dcfy-3ry/2 / «D + cf) / 2)2Y_4_ 3ry/ 2 /3 64-3ry/2
1 1 47
n
(65)
where 6 is a characteristic limiting size that makes the coalescence probability equal to zero between granules of the same size, because the separating forces owing to the kinetic energy exceed the binding forces. For simplification, it is assumed that no coalescence occurs between granules having sizes larger than 6. That is [80] P(D, cf) = 0 for D ?:. 6; cf ?:. 6 Equation (65) requires five constants, namely y, lJ , ,1" �, and n. Two of these constants, lJ and �, are related to the elastic and plastic behaviour of the colliding particles. The surface area of contact, S, between two colliding particles is given by [1 08] (66) where Q is the compressive force between two colliding granules. According to the theory of Hertz, values of lJ = 0 and � = 1 describe plastic behaviour (cf. [1 08]), and values of lJ = � = 2/3 describe elastic behaviour [1 14]. The parameter ,1, is given as ,1, = Qmax /( Qmax - Qmin ) . The limiting size, 6, is related to the tensile strength, (Jst , and the deformability, K, of a granule as [1 1 5] 6 = A1 K2/3 (Jst (67)
(
f
where A1 and are constants independent of the granule size and K = S/Q . K is related to both the yield strength of the material and the ability of the surface to be strained without rupture of the granules or degradation [1 1 6]. From equation (67), Kristensen et al. [1 1 6] obtained equation (68) by geometric considerations (1':,.1/ D) 3 62/a = A1 (68) (Je where (Je is the compressive strength. The nominator expresses the normalized strain produced by the impact. The strain depends primarily on the packing of the particles and the liquid saturation. Significant strain arises when the liquid saturation is increased to the limit where the cohesive strength of the agglomerate is governed by the strength of mobile liquid bondings. From equation (68), Kristensen et al. [1 1 6] concluded that the rate of growth by coalescence between agglomerates is controlled primarily by the saturation degree of the agglomerate, because it is the liquid saturation that controls the strain behaviour. Kristensen et al. [1 1 6] concluded furthermore that a high rt
1 1 48
T.
Abberger
value of 6 is associated with a high coalescence probability, and therefore a high growth rate. Ouchiyama and Tanaka [81 ] carried out simulations of a batch granulation using their model of aggregation efficiency, where the evolution of the mean diameter in the course of the simulation showed an S-shape, corresponding to the three granulation regimes of nucleation, transition, and ball growth, as previously described by Kapur and Fuerstenau [1 1 7]. Experimental validation, however, was not provided. The uncertainty of the bond strength (Tst is a main drawback for a quantitative application of this model [1 1 3]. Contrary to many other models, this model does not consider collision velocities, because it assumes that in a restricted-in-space environment granules are permanent in contact to each other. 3.2. 4. 3. 1 . 2. Modification of the model for surface-wet granules. The modifi cation of Ouchiyama and Tanaka's model by Huang and Kono [83] has been based on the existence of a liquid bridge between two granules, which causes the adhesive force between the colliding granules. The probability of coalescence is treated as the probability that the liquid bridge can withstand the separation forces imposed on the colliding granules in the granulator. The force creating the tensile strength, here the force of the liquid bridge, h, has to be greater than the force creating the tensile stress, which is the net force acting on the granule resulting from granule-granule collision in the granulator. The probability for coalescence of two granules, PrcoaJ, is (69) where (Tt is the tensile stress, crst the adhesive stress, Mo the critical bending moment with respect to the contact point 0 of the colliding granules, and R the radius of the liquid bridge. Because only very low-viscosity binding liquid was considered in the development of the model, only the static phenomena surface tension and pressure difference forces were supposed to contribute to the bridge strength. The tensile strength is then a function of the surface tension of the liquid, its contact angle to the powder material, the particle diameters, and the volume of the liquid bridge. This volume is the result of the granule collision intensity, the local deformability (defined as the ability for local porosity reduction), and the moisture content of the feed, because these factors determine the amount of liquid, which is squeezed to the surface during a collision. For an ideally liquid bridge, the probability for coalescence for two granules of diameter 0 and d, P(O,d), was derived as
[
P(O, d) = 1
-
( 0d)r- 1 62 « 0 + d) /2)2r-4
ln
(70)
Population Balance Modelling of Granulation
1 149
where (j is the maximum limiting size for pair formation and n a parameter to enable mathematical adjustability. The probability of coalescence in a real system, P(D, d, Ci, Pi), was given as (71 ) The non-ideality of the coalescence probability is represented by a function of the operating conditions, Ci, and material properties, Pi, as h(Ci, pJ The model was validated in the granulation of pre-wetted aluminium hydroxide and rehydratable alumina powders in a spouted fluid-bed granulator. 3.2. 4. 3. 1 . 3. Applications of the model in the calculation of the aggregation efficiency. Although formulated for surface-dry granules, Ouchiyama and Tanaka's coalescence model was applicable to simulate the aggregation efficiency in fluid-bed spray granulation. Watano et al. [84,85] investigated the granulation of a mixture of lactose, corn starch, and hydroxypropycellulose by spraying purified water onto the powder bed using an agitation fluid-bed granulator. In this device, the granules were fluidized by air and tumbled by agitator rotation. Because the movement and flow pattern of granules were claimed to have many similar features to those in the tumbling granulator, Ouchiyama and Tanaka's coalescence model was applied. The idea of Watano et al. [84,85] was to correlate the deformation behaviour of the granules with their moisture content. With the formulation used, granulation was feasible with moisture contents ranging from 0% to 20% before blocking or defluidization occurred. The two parameters 17 and � were taken to be functions of the moisture content in the range of 0% to 20%, therefore. The parameters n and y were empirically determined as exponential functions of the moisture content by data fitting. Abberger investigated fluid-bed spray granulation of lactose and corn starch with an aqueous solution of polyvinylpyrrolidone in an instrumented laboratory scale fluid-bed granulator STREA-1 [86]. Two series of experiments were performed using lactose in order to investigate the effect of free moisture. The first series was with a target content of 5% free moisture. According to calculations of the free moisture from the operating conditions based on a thermodynamic model [1 1 8, 1 1 9], 44 ml of the granulating liquid was added at a rate of 30 ml/min to obtain a 5% free moisture level. The spray rate was reduced to the equilibrium value [1 1 8] of 1 1 .9 ml/min, and then increasing volumes were sprayed continuously onto the powder bed. The second series was with target content of 1 0% free moisture. In this case, 78 ml of liquid was added at a rate of 30 ml/min. Then again, increasing volumes were sprayed onto the powder bed at a rate of 1 1 .9 ml/min. For each granulation, sampies weighing about 5 9 were taken after the addition of the first 44 or 78 ml, respectively, and after the addition of the total volume of granulating liquid. These sampies were dried, and the free moisture was calculated from the loss on drying.
T. Abberger
1 1 50
Using corn starch, two experimental series were also performed. With the first series, increasing volumes of granulating liquid were sprayed onto the powder bed at a rate of 20 mljmin. With the second series, 200 ml of pure water was sprayed at a rate of 20 mljmin on each batch. Subsequently, increasing volumes of binder liquid were sprayed at a rate of 20 mljmin onto the batch. Ouchiyama and Tanaka's coalescence model [1 08] was applied to simulate the evolution of the PSDs. In each of the lactose series, the first granulation with an R2 value to the log-normal distribution of at least 0.99 was used as the starting PSD for the simulation. The applied values for the constants as weil as the value for the required limiting size (5 were obtained by data fitting. Figure 5 shows the evolution of the cumulative number distribution with time for the 1 0% series and Fig. 6 for the 5% series with lactose as powder. Figure 7 shows the evolution of the cumulative number distribution for the starch granulations without any previously added water, and Fig. 8 shows the evolution of the cumulative number distribution for the starch granulations with a previous addition of 200 ml of pure water. With the assumption that the granules underwent plastic deformation, the evolution of the size distribution could be modelled weil for both materials. With lactose, the evolution could be mode l ied weil independent of the statistical distribution that existed between 5% and 1 0% of the free moisture content within
0.9 0.8
:g 0.7 � 0.6 c 0
Q; E
..c
:::l c Q) >
�
s E :::l Ü
0.5 0.4 0.3 0.2 0.1 o
:
�� � .7 : V /� J 1/ ; 1 : , ; 1/ /J / !/ f iI .�V I
�t
..----_.-
. .,
'
..
o
200
�IT 1 -+
400
600
800
&
=
--+
_
TI I --
1 000 1 200 1 400 1 600 1 800 2000 2200 Diameter [�ml
- - - . . - starting PSD • experiment, t 4 min 1 2 sec experiment, t 12 min 36 sec =
-�
model experiment, t = 8 min 24 sec experiment, t 1 6 min 48 sec
-
+ •
=
Fig. 5. Simulated and experimental cumulative number distribution of the lactose 1 0% series. Reprinted from Abberger [86], with permission from Elsevier.
Population Balance Modelling of Granulation
. = i I --- � .� -1 --+ t -L -t- I -f-- J:- �- \� I -t. � I T l- I --- ---tI�I _I , -i' ----rI - ----rI I ' t-f 1 --1 -1 ---+ ----L -
0.9
+
0.8
c 0
Ci; 0 . 6
1
.0 :::J c Q)
-
I
-�
�
- 'I
�-
�
,
I
I
1 600
1 800
2000
r t- �- 1 --- , -1 T I - 1, ; --j -: - -- l i�i ---I - - I -- -r �- +--- !I� �- -+ - +- ----- --- I --� �I I -r-- --+ I !
0.5
I
0-
I
.e:: 0.4
1il "S E 0.3
:::J ü
-
+
ß 0.7 .;g E
1 1 51
I
,
-
I
- -� ,
0.2 0.1 0
200
0
I
I
I
400
600
800
1 000
1 200
1 400
2200
Diameter [11m] , .. starting PSD experiment, t
•
-=
4 min 1 2 sec
+
model experiment, t
=
21 min 00 sec
Simulated and experimental cumulative n umber distribution of the lactose 5 % series. Reprinted from Abberger [86], with permission from Elsevier.
F i g . 6.
.<���� �. ; {f V( 0.8 · ,i �' / Ij 13 0.7 .;g ' � t/ Ci; 0.6 li 0.5 li 0.4 � "S t7 0.3 .' 1.7 0.2 .y 0. 1 o �� 0.9
;
•
c 0
.0
E
:::J c Q) >
'I
E
:::J ü
o
200
400
800
600
1 000
1 200
Diameter [11m] -- model
. . . starting PSD •
experiment, t
=
•
experiment, t
=
2 min 30 sec
7 min 30 sec
+ •
experiment, t experiment, t
= =
5 min 00 sec 1 1 min 1 5 sec
Fig. 7. Simulated and experimental cumulative number distribution of the starch series. Reprinted from Abberger [86], with permission from Elsevier.
1 1 52
T. Abberger
0.9
§ 0.8
� ....--b.. �. �---+---+----!----+-----j +--./-;""'�j ::
J 0.7 E� 0 . 6 :/ rr! §
0 . 5 +--:'---;1;,/F� --t-------\ -----+-- ---t----I
.� 0.4 : 10 !g iü 0 . 3 �:; �f�-�---�---+----�---'�--� 0.2 +'J �---+------+-----+----+-- ---j 0 . 1 IJ O� o
t-200
-
----j-----+ ---+ 600 400 800
-
-
---t------j 1 000 1 200
-
Diameter [Ilm] •
.. starting PSD experiment, t = 2 min 30 sec
-
+
model experiment, t = 5 min 00 sec
Fig. 8. Simulated and experimental cumulative n umber distribution of the starch series with previous addition of 200 ml pure water. Reprinted from Abberger [86], with permission from Elsevier.
each series. The best fit of the model to the data was obtained using values of ( = 1 , A = 1 , Y = 9, and n = 5 as the model parameters for all the granulations. These four values are within the limits of the coalescence probability model. When using a value of '1 = 2, the best fit was obtained for the lactose series and the starch series with previously added water. For the starch series without added water, the best fit was obtained using '1 = O. In the best fit, (; was constantly equivalent to 2900 11m for both lactose series, and constantly equivalent to 1 1 00 11m for both starch series. The best fit was always obtained when ( = 1 , which was regarded to be indicative of plastic deformation behaviour. Agglomerates have to contain sufficient liquid to render them plastically deformable [66]. In experiments with lactose, the apparent saturation degree required to see significant growth was in the range of about 30-60% [120]. Holm et al. [121] showed that lactose becomes plastically deformable at liquid saturations between 30% and 80%, dependent on the porosity of the sampie. The hypothesis obtained from the results of the lactose series was the existence of a local plasticity within a granule in fluid-bed spray granulation caused by the deposition of spray droplets onto the granules, with their subsequent absorption into the voids leading to regions of saturated voids. Under the assumption that the area, which is deformed during collision, is not
Population Balance Modelling of Granulation
1 1 53
greater than the area of saturated voids, the deformation is plastic, although the saturation of the whole granule is low, e.g. in the pendular state. In the pendular state, one would expect brittle fracture of granules. Although a good fit was obtained in most of the experimental series in this work, the general applicability of this type of modelling has not yet been documented. Huang and Kono [1 22] were the first to focus on local effects owing to the structural heterogeneity of granules on growth. They stated that the local deformability controls granule growth in granules with low moisture contents. They noticed in addition that the distribution of the voidage saturation in the colliding granules can be heterogeneous with a locally high voidage saturation at the contact area. The overall voidage saturation of the granulation charge can be very low, e.g. in the pendular state. 3. 2. 4. 3. 2. Kerneis accounting for viscous energy dissipation 3.2. 4.3. 2. 1 . The viscous Stokes number. In systems where the impact forces are low, like in a fluid bed, andjor the granules are extremely rigid, relative little permanent deformation occurs during collisions. Then coalescence can only occur, if there is a liquid layer present at the surface of the primary particles or granules to bind them together. Ennis et al. [88] modelled this situation by considering the impact of two solid, non-deformable spheres, each of which is surrounded by a thin viscous layer. Coalescence occurs when the kinetic energy of the colliding granules will be dissipated completely in the viscous binder layer and due to elastic losses in the solid phase, otherwise the liquid bridge will be elongated excessively and rupture during rebound. The ratio of the kinetic energy to the viscous dissipation is described by the viscous Stokes number, Stv, 8pRUc Stv (72) 9f1 where p is the granule density, R the harmonie mean granule radius, Uc half the relative velocity of impact, and f1 the viscosity of the binder liquid. Coalescence occurs when the Stokes number is smaller than the critical Stokes number, St�, which was given as
=
St�
= (1 + �) In (:J
(73)
where e is the coefficient of restitution, which is unity in the case of rigid particles or agglomerates, and which is lower, the more deformable the spheres are, and h is the thickness of the surface layer and ha is the characteristic height of the surface asperities (Fig. 9). Agglomerate growth will be promoted by a low value of Stv and a high value of St�. As granules grow in the course of a granulation, Stv increases. This leads to three regimes of granulation. The non-inertial regime occurs when Stv < < St�. All
T. Abberger
1 1 54 u
u
2x 9. Schematic of model developed by Ennis et al. [88]. Reprinted from Iveson et al. [1 1 3], with permission from Elsevier.
Fig.
collisions are successful regardless of the size of the colliding granules. The inertial regime occurs when 8tv � 8t�. In this regime, the Iikelihood of coalescence is size-dependent. Collisions between two small or one small and one large granule are more Iikely to be successful than collisions between two large granules. In the coating regime when 8tv > > 8t�, no collision is successful. From equations (72) and (73), a critical combination of granule sizes capable of coalescence, D*, can be calculated. D* is proportional to 8t*. 8t* , on the other hand, increases with liquid content. Thus, D* increases with the amount of free liquid available for coalescence, which is a controlling factor for the rate and the extent of granulation. The model is only valid for non-deformable, surface-wet granules in which the viscous forces are much larger than the capillary forces. Adetayo and Ennis [74] critically discussed this model. None of the coalescence models is completely satisfactory. Therefore, a generalized coalescence model is required [1 23]. Liu et al. [90] extended the model of Ennis et al. [88] by additionally accounting for plastic deformation in the granule matrix. They considered two c1asses: surface-wet granules and surface-dry granules where liquid is squeezed out to the surface by the impact. Coalescence occurs when the kinetic energy of impact is all dissipated through viscous dissipation in the liquid layer and plastic deformation of the granule. The model gives conditions in dimensionless groups for two types of coalescence, types l and 11 (Fig. 1 0). Type I coalescence occurs when the kinetic energy is lost by viscous dissipation in the surface layer before their surfaces touch. Type 1 1 coalescence occurs when granules are slowed to a halt during rebound, after their surfaces have made contact. With type 11 coalescence, the kinetic energy is dissipated by both the binder layer and the plastic deformation of the granule. In addition to relative velocity and liquid film thickness and viscosity, mechanical properties of the granules characterized by the elastic modulus and the yield stress are considered. With type 11 coalescence, two sub-types may be
Population Balance Modelling of Granulation
00
1 1 55
Rebound
Dumb beils formed from type I or ty pe coalescence
with 1)"=0
11
Dumbbells fonned from ty pe coalescence with 1)">0
11
Fig. 1 0 . The model of coalescence by Liu et al. [90]. Reprinted from Liu and Litster [76], with permission from Elsevier.
distinguished, depending on whether permanent deformation does occur or not. The permanent deformation can be calculated as a function of the Stokes deformation number. The Stokes deformation number is the ratio of the kinetic energy to the energy required for deformation [1 24]. So me parameters in the viscous Stokes number model are not identifiable online at present. The most important unidentifiable parameter is the liquid film thickness. An approach to overcome this is to replace unidentifiable parameters by easy to measure parameters which can be correlated to the unidentifiable model parameters. Moisture content substitutes for film thickness and apparatus rotation rates for collisional velocity [8]. 3.2.4.3.2.2. The kerneIs based on the viscous Stokes number. The kernel of Adetayo and Ennis [74,75] is applying a test according to equation (45). Collisions with an effective size equal or less than a critical value are successful. 1 for W ,,::;: W* (74) P(u, V, z1 , z2 ) = o for W> W* where W is an effective volume and W* the critical value or cut-off size. It is expected to vary with both the binder and material properties. From equation (65), Adetayo and Ennis [74,75] could show by algebraic manipulations that in the case of plastic deformation for coalescence to occur an
{
1 1 56
T.
Abberger
effective average diameter, Dav, has to be smaller than a Iimiting diameter D * , Dav < D * , where Dav was given as (Dd)y/4 Dav (75) ((D + d)/2y/2 - 1 The effective volume, W, was introduced analogous to equation (75) as
=
---'--_ '. ��
W
= (u +
(UV)b
(76)
v)a
where a and b are constants, which are still empirieal, but should be in princi pie measurable quantities. To obtain the dimension of a volume, 2b-a has to equal unity. The limiting size, D* , was calculated from the work of Ennis et al. [88] as D*
= 1 6,u St*
(77)
pv
Assuming spherical granules, the critical volume, W*, was obtained as 3 1 6,u W* St* (78) 6 pv
= ?: (
)
Equation (78) shows that W* increases with St* ; St* on the other hand increases with the liquid content. Thus, this kernel is in agreement with numerous experimental observations that increasing the granule void saturation increases the rate and extent of granulation. Depending on both the value of W* and the starting size distribution, a range of behaviour of the evolution of a size distribution including published experimental data could be simulated. The kernel could be applied for simulating the evolution of the average diameter with an S-shape. The simulations showed that W* has a strong influence on the resulting size distribution for a given initial distribution. At present, however, there is only a qualitative understanding as to how W* varies with process and material variables, so that the kernel is not yet predictive. Cryer [1 25] modelled the fluid-bed granulation process with an aggregation efficiency that was obtained as the probability that an average Stokes number is smalier than the critical Stokes number1 7 (79) The Stokes number is dependent on the sizes of the colliding granules and the collisional velocity. 80th parameters are necessary for the calculation of the
1 7 Cryer's original notation has been ß density function for the Stokes number.
=
ßo t� f(
Population Balance Modelling of Granulation
1 1 57
Stokes number. These input variables are measurable or are related to measurable operating parameters of the fluid-bed process. The calculation of the Stokes number was simplified. The median diameter of the batch instead of the harmonie mean diameter for each colliding pair was used for the calculation of the Stokes number. Owing to this simplification, the same aggregation efficiency was ascribed to each pair of colliding granules regardless of size at a certain time step. To account for the uncertainty in independent parameters of the Stokes number, the deterministic equivalent modelling method was applied. Here, uncertain inputs and outputs of a model are represented as polynomials of random variables. The calculation of the Stokes number using the deterministic equivalent modelling method produced a probability distribution of the Stokes number for each set of input data. It was assumed that particie size, d, and collisional velocity, Uc, were normal distributed. The mean value and the standard deviation of the initial PSD could be obtained from particle size analysis, and the mean value of the collisional value and the standard deviation of the collisional velocity could be calculated from operating conditions. A new Stokes number distribution was calculated at each time integration step because both the PSD and the collision velocity are dependent on time. Figure 1 1 shows qualitatively that the cumulative Stokes number distribution shifts towards greater values in the course of a granulation experiment. This changing distribution of the Stokes number was correlated to growth regimes: Region 1 is characteristic to the non-inertial regimes, all Stokes numbers within the fluid-bed are less than St* . Regions 2-4 represent the inertial regime, where the amount of successful coalescence is proportional to the probability of the Stokes number being smaller than St *. Region 5 represents the coating regime because all Stokes numbers are greater than St* and no collision is successful. 1 . 0 . . . . . . . .
G> .
. . . . . . . .
.....
. . . . @) . .
. .. . . . . ..
G>
Increasing
SI'
1 1 . Qualitative representation of Stokes number kernel developed by Cryer. Reprinted from Cryer [1 25], with permission from American Institute of Chemical Engineers.
Fig.
1 1 58
T.
Abberger
To increase the adjustability of the model, the critical Stokes number was given as the purely empirical relationship (80) where 1X1 and 1X2 are constants obtained by data fitting. Uu and Utster [76] stated that for type I or II coalescence [90] with no permanent deformation, the two granules are held together after collision with no flat contact in between, whereas for type 1 1 coalescence with permanent plastic deformation, granule pairs are held together with flat contact area. The probability of the two types of granule pairs to survive further impact is different. As the bond strength of pairs formed from type I coalescence and type II with no permanent deformation are similar, it was assumed that the chance of these two types of granule pairs to survive further impact is the same. It was assumed, however, that granule pairs formed from type 1 1 with permanent deformation will have a higher chance to survive subsequent impact, or in other words, they show a high coalescence rate. On the basis of these assumptions, Uu and Utster [76] proposed a coalescence kernel as
{
ß 1 for type I or II coalescence with no permanent deformation ß2 for type 1 1 coalescence with permanent deformation o rebound (81 ) where ß1 and ß2 are the rate constants. For each colliding pair of granules, it was checked for which regime the test was true and the corresponding rate constant was ascribed. These constants were obtained by parameter estimation. A graphical representation in the form of a regime was provided. Experimental validation was performed using glass ballotini and previously published data of a fertilizer granulation. 3. 2.4.3. 3. Kernel based on kinetic theory of granular flow. Tan et al. [87] investigated the fluid-bed melt granulation. Using DEM, they could show in the first step that the distribution of particle velocities in a fluid-bed is in accordance to a kinetic theory of granular flow. This theory describes the mean and randomly fluctuating motion of particles within a continuous granular medium. In the next step, they derived a coalescence kernel based on this theory of granular flow. This kernel accounts for the collision frequency by a collision constant according to equation (43). They extracted from the collision frequency a size-dependent term as ß(u, v, t) =
(82)
Population Balance Modelling of Granulation
1 1 59
The same term is included in a previously proposed kernel [22] called the equi kinetic energy kernei: ß(/i Ij, t) = ßo(t) . (li + ,
�)2
(83)
In the development of the equi-kinetic energy kernei, the rate of collisions was taken to be proportional to the collision cross-section and the relative average velocity of granules (compare Section 3.2.2.2. 1 ). Following the study of turbulence, the velocity of a granule, V(t) , in a device was considered to be the sum of the average velocity, 11, and a random component, V'(t), according to V(t) = 11 + V (t) (84) From the assumption that the random component of velocity determines the relative average velocity follows [Collisions]ij
cx
(li
+ �)2 · 1 V; v;1
(85)
-
With the assumption, V'(t) is inversely proportional to a granules volume, the kernel was obtained. The kernel assumes equal distribution of the particles kinetic energy and favours collisions between large and small particles. The aggregation efficiency is assumed to be size independent in this kernei, however, a size dependence of the aggregation efficiency should not be neglected [63]. The kernel could be applied successfully in simulation of fluid-bed melt granulation [87] and granulation using a high-shear mixer [7,22,63]. 3.2.4.4. Kerneis for multi-dimensional population balance equations
Biggs et al. [71 ] developed a kernel for a two-dimensional PBE describing the time evolution of size and binder distributions. They suggested that when two granules collide, at least one of the granules must have a binder content above some critical value. They derived a kernel according to 1 for b1 or b2 > bcr P(u, V, b1 , b2 ) = (86) o for b1 and b2 ::S; bcr
{
where b 1 and b2 are the binder volume fractions of the two colliding granules and bcr the critical volume fraction. Size was not assumed to have directly an effect on the aggregation efficiency. Experimental validation was performed using two different formulations and high-shear mixers, together with two different methods of binder addition. Darelius et al. [70] developed a kernel where liquid saturation and granule size are determining the probability of successful collision. This was set to be
1 1 60
T.
Abberger
proportional to the product of the heights of the liquid layers of the two colliding granules. The height of the liquid layer was expressed for each spherical granule as the volume of liquid on the surface divided by the surface area. The liquid volume on a granule was obtained by dividing the total liquid volume in a size dass by the number of granules in this size dass. This kernel is (87) where q'i is the volume of liquid in class i, q{*i the volume of liquid in the voids in class i, and the subscript s refers to volume of solid. Experimental validation could be successfully performed in a granulation of microcrystalline cellulose with an aqueous solution of polyvinylpyrrolidone K90 in a high-shear mixer. 3.3. Solution of the population balance equation 3. 3. 1. Introduction
Because an analytical solution is in by far most ca ses not known, almost all of the solutions to the PBE reported in the literature are obtained by numerical methods. Common techniques used for numerical solutions of PDEs mostly fall into three classes: finite difference and finite volume methods, finite element methods, and spectral methods. The laUer two methods are considered as subsets of the method of weighted residuals. Some approaches try to solve the continuous PBE by approximating the size distribution function over the whole domain through orthogonal collocation. Most approaches divide the size distribution into sections. The distribution function n(v,t) is approximated within these sections either by splines [1 26] or by finite elements [1 27-1 3 1 ] . In simulations of granulation, discretized PBEs (see Section 3.3.5) are widely applied. Short but recent reviews of the numerical methods to solve the PBE can be found in Refs. [ 1 3 1 , 1 32]. The choice of the solution technique depends mostly on the particle formation mechanisms. If aggregation occurs, a range of solution techniques are possible, depending on other mechanisms occurring beside aggregation. Requirements on the solution vary with the nature of the application. Product and process design impose the highest accuracy requirements, as the goal is prediction, as weil as the robustness of the system with respect to system parameters. The accuracy of the solution method can be tested with kerneis and initial conditions for which analytical solutions are available. It is obvious that an inaccurate solution could lead to misleading conclusions about the nature of the modelled process. Speed of evaluation is more important in online process control applications as control moves need to be computed in a real-time environment. The availability of distributed online measurements for feedback aliows tolerance of reduced accuracy through correction of system state estimates [23].
Population Balance Modelling of Granulation
1 1 61
3. 3. 2. Analytical solution
3.3.2. 1 . Analytical solution of the pure aggregation form
Analytical solutions are known only for a few, simple kerneis and initial conditions. They were often obtained by Laplace transforms. 3. 3. 2. 1. 1 . The kerneis for which analytical solutions are available. It has long be recognized that three kerneis are mathematically tractable, the constant, ß(u, v) = 1 , the sum, ß( u, v) = ( u + v), and the product kernei, ß(u, v) = (uv), for a review see Ref. [1 5]. For certain linear combinations of these three kerneis, analytical solutions exist as weil [1 33]. Because the sum and the product kernel are of minor (sum) or no (product) importance in the modelling of granulation, only the analytical solution for the constant kernel will be given. 3. 3. 2. 1 . 2. Analytical solution using the constant kernei. For a free-in-space system and applying the constant kernei, the discrete PBE is (88) where
(89) i=1 Summing over all values of k results in dNtot ßo(t) � '" nßo (t) 2 ß0 (t)Nto2 t = = N (90) .� n j dt 2 � 2 tot k=1 '+j=k When ßo(t) is time invariant, the integration yields 1 ßo t No 1 or Ntot = + (91 ) = No 2 N 1 + (ßoNot/2) tot The resemblance of equation (91 ) to the rate equation describing a chemical reaction of the second order is obvious. The solution of the PBE for time invariant ßo(t) and a monodisperse starting size distribution is [1 1], see also Refs. [1 5,1 1 1] No (2ßo tNo) k- 1 nk(t) = (92) (2 + 2ßo tNo) k+ 1 In a restricted-in-space system, the right-hand side of equation (90) has to be divided by Ntot . If ßo(t) is again time-invariant, an exponential decrease of the total number of granules and a corresponding exponential increase in the granule's mean diameter, d, result d(t) = do exp ( (ßo /3) t) (93) In the restricted-in-space system, the process is pseudo-first-order [43]. 00
L: ni = Ntot
_
_
I
�
-
-
1 1 62
T.
Abberger
The solution for a monosized initial PSD for the cumulative number oversize,
Ri, is [1 2]
(94) Clearly, the size distribution is self-preserving. The fraction of the particles in a given size range is a function only of particle volume normalized by the average particle volume. Hogg [1 9] noticed the resemblance of the resulting cumulative number distribution to the RRSB-distribution. Clearly, a random process leads to a random distribution. 3.3.2.2. Analytical solution of the pure g rowth form
{
For size-independent growth, equation (2 0 ) has the solution [21 ] n(1 - !J.I, 0) for I;;:;!J.I (95) n(1, t) - 0 for k M where !J.I = J� G(t) dt . This solution can be applied to simulate layering of fine particles onto seeds, when the rate of pick up of fines is proportional to the surface of the rolling granule. Then a layer is formed whose thickness is the same irrespective of the seed size. That, however, is an idealized postulate [53]. From equation (95) it follows that in the course of a granule growth by size-independent layering, the distribution function will shift parallel on the size axis toward larger sizes without changing the shape. The number of granules does not change. 3. 3. 3. The methods of moments and weighted residuals
3.3.3. 1 . I ntroduction
The method of weighted residuals (MWR) solves the PBE by assuming a trial solution for the population density, n * (v,t). The trial function is a combination of a known base function of size v, cDj(v), and an unknown function of time, 8i(t) , N
n *(v, t) = n(v, 0) + L 8i(t)
(96)
A standard choice of base functions are the Lagrange interpolation polynomials. Problem specific trial functions may be better. The goal in the MWR is the determination of the N scalars {8i(t)} � 1 ' This is done by minimizing the residual, R(n*(v,t)). The residual is defined to be
= *�;, t) - ;](n *(v, t))
R(n*(v, t)) an
(97)
where the operator ;] is accounting for all terms in the PBE except the time derivative. The trial solution is substituted into the PBE. The sm aller the residual
Population Balance Modelling of Granulation
1 1 63
is, the better is the trial solution. The residual is minimized by forcing it to zero in a weighted average over a domain of v
lVi+1 R(n*(v, t))wj{v) dv VI.
=
0
(98)
where {Wj{V)}; 1 is the weighting function or test function. The principal difference between the collocation or the Galerkin method is the selection of the weighting function. When the weighting function has been defined, equation (98) becomes a set of N ODEs with the 8i(t) as their solutions. These solutions are substituted into equation (96). By increasing N and solving equation (98) again, the magnitude of the residual decreases with increasing N and the solution of equation (96) converges to the true solution of the PBE. 3.3.3.2. The method of moments
The MWR reduces to the method of moments, MOM, when the base functions are chosen to be Laguerre polynomials and the weighting functions are chosen as [72]
wj{v) = vj, j is an integer number
(99)
Because only a few moments are tracked, the number of equations to solve with this method is the smallest for all numerical methods to solve the PBE. This is advantageous when the PBE has to be coupled with other equations, e.g. for material flow. The MOM tracks moments of the PSD instead of the entire PSD. Unless the moments themselves bear sufficient information, the method poses the inversion problem of obtaining the complete information about the distribution from the moments. The basic idea of the MOM as developed by Hulburt and Katz [48] is to express the right-hand side of equation (31 ) in terms of moments, Mk, only. The derivation of a closed set of equations for the moment evolution does not require a priori assumptions of the distribution function. The standard MOM requires, however, an exact closure, which means that the equations describing the moment evolution involve only functions of the moments themselves. Therefore, the method is limited in its applicability, especially when aggregation or breakage occurs in a process. The traditional way to achieve closure is to assume some functional form of n(v,t). Two forms that are often been used are the log-normal and the gamma distribution. By choosing three moment equations (usually for the first three moments) and expressing all the unknown moments as functions of the total particle number, the size, and the width parameter of one of the two previously
1 1 64
T.
Abberger
mentioned distribution functions using their known properties, it is possible to obtain a c10sed set of three ODEs with the Mo (t), M1(t), and M2 (t) as their solution [1 34]. Lee [1 35] has given an example of this approach. The properties of the log normal distribution are
Mk = Mov: exp
G �) �
(1 00)
Lee [1 35] used for the width parameter wg = 3 1n (Jg, and
.
MoM-2 2 vg = :3 /M� (101) 2 M1 /2 ' In (Jg = In -M21 MO 2 All the missing moments Mk can now be expressed a s known functions of k , Mo, M1 , and M2 .
Recent refinements to overcome the c10sure problem without assuming a given size distribution are some methods of interpolation [1 34,1 36] and the quadrature method of moments (QMOM) [1 37]. A detailed explanation of the QMOM was given by Marchisio et 81. [1 38,1 39]. The c10sure problem and the problem of the distri bution reconstruction were comprehensively discussed by Diemer and Olson [140]. 3.3.3.3. Finite elements
Finite elements are a widely used method to solve PDEs. Consequently, this method has been applied to solve the PBE. In the finite element method, the solution is approximated by polynomials, the base functions, which are piecewise defined on certain subdomains of the size domain, the elements. Each of them contains several collocation points. The first step in this approach is to truncate the infinite size domain of the PBE to a finite one. This truncated domain is partitioned into N discrete subdomains. Nicmanis and Hounslow [ 1 29, 1 30] used standard Lagrange interpolation polynomials of order p-1 ,
n( v, t) � n� ( v, t) = L n( t)
(1 02)
i=1
where p is the number of nodes or collocation points in element e, and ni are the nodal values of the density distribution. The goal is the determination of the nt(t). In the PBE, the base function is substituted for the unknown true number density function. The integrals in the PBE have to be evaluated with the base functions via numerical integration. A weighted residual is formed by multiplying by a weight function and integrating over the domain of the element. This leads to a system of p ODEs with the nie(t) as their solution. For their time integration, a
Population Balance Modelling of Granulation
1 1 65
Runge-Kutta fourth-order technique has been shown to be stable and accurate in a comparison of several techniques [1 28]. The finite element algorithm leads to convergence of the approximation nh(v, t) to the true solution of the PBE. The choice of the element location is important for an efficient solution [1 8]. Mantzaris et al. [1 28] and Nicmanis and Hounslow [1 29, 1 30] discussed the method in detail with examples from biotechnology and crystallization, respectively. Rigopoulos and Jones [1 3 1 ] developed a finite element scheme for any combination of the mechanisms nucleation, growth, aggregation, and breakage. The obtained solutions were tested against existing analytical solutions. The method was found to produce accurate results, while being relatively easy to implement. This paper provides furthermore a detailed introduction into the solution of the PBE using the finite element method. In a model, where movement of steep fronts along the spatial coordinate occurs, present either in the initial distribution or arising in the course of the process, a dense space grid in the classical finite element method is required to eliminate oscillations. The moving finite elements avoids this problem by allowing the movement of the spatial grid [141]. This method is applied as weil in the solution of multi-dimensional PBEs (see [1 28]). 3. 3.4. The method of fines
The method of lines (MOL) is a different method to solve PDEs. For the discretization of integro-partial differential equation models into differential algebraic equations, the MOL approach [142] discretizes the spatial domain to replace the continuously distributed spatial coordinate z with discrete grid points Zk, as depicted in Fig. 1 2. The grid points replace the continuous coordinate of the spatial or property distributed domain. First step of the MOL is the discretization of the spatial domain. One dimensional domains are described by the spatial coordinate z. The continuous independent variable Z must be discretized into a finite number k of discrete grid points Zk or Zk(t) to allow the transformation of a PDE for the time- and space dependent state variable x(z,t) into k differential algebraic equations for time dependent states Xk(t). There are several techniques for the MOL. They differ by the partition of the domain and the approximation of the partial derivatives. Two of them are the finite difference method and the finite volume method. The finite difference method is the oldest representative of the MOL. The finite difference method consists in defining the different unknowns by their values on a discrete (finite) grid, and in replacing differential operators by difference operators using neighbouring points.
1 1 66
T.
Abberger
t
-;;-
u =
MOL
�q
PDE x(z, I) u(z, I)
I I I -;;-
OBE
;
=
�Or---�IC�---+� Z
Fig. 1 2. Discretization of integro-partial differential equations into differential algebraic equations with the MOL approach. Reprinted from Köhler et al. in [ 1 43], with permission from CRC Press. Copyright obtained by Copyright Clearance Center.
These discretization schemes can be applied on fixed spatial grids as weil as on moving grids. The MOL was evaluated in a crystallization application [144] and was applied in a simulation of granulation [145,1 46]. 3. 3. 5. Discretized population balances
3.3.5. 1 . I ntroduction
These discretization techniques, frequently referred to as method of classes, are widely used and might lead to a system of ODEs that can be solved by integrating over time using a standard technique; where mostly a Runge-Kutta fourth-order technique is applied. The discretized population balances (DPBs) are usually easy to implement. When a coarse discretization is applied only a moderate number of ODEs has to be solved, thus the result is obtained quickly. DPBs replace partial differentials of the PBE with finite differences (except in the time domain), integrals with sums, and number density with numbers of particles in some size range Ni J:i+1 n(v) dv [21 ]. The integrand contains the unknown number density. The size range contained between two sizes Vi and Vi+ 1 is called the ith section. Various formulations either for pure aggregation or accounting for additional rate processes exist. In the pure aggregation form, a coupled set of ODEs is sought. dN· (i+1 (1 03) -it (B(v, t) - D(v, t)) dv =
I
=
Jv
I
A closed set of equations can be obtained by expressing the right-hand side of equation ( 1 03) in terms of numbers of particles in a size range. According to Kumar and Ramkrishna [147], there exist two major ways to achieve this, either
Population Balance Modelling of Granulation
1 1 67
application of the mean value theorem of integrals on the coalescence or breakage frequency (calied the M-I approach) or on the number density (calIed the M-II approach). It has been stressed that DPBs are not simply numerical techniques to solve a PDE, but approximations to the physical problem. The discretization is coarser and not the full information about the size distribution, that is the number density n(v,t) is conserved. Discretization, particular in its coarse version, is a conscious approximation , which in stressing accuracy on some properties of interest, must necessarily relax on others [147]. The method focuses on accurate calculation of some moments, whereas the PSD is approximated. A problem in the development of a DPB is that aggregation causes a discontinuous change of particle size, so the problem is how to discretize the coalescence birth and death terms in a PBE. This difficulty lead to the development of methods that make correct predictions for one or two moments only. The number of classes applied depends on the process and the resulting PSD, but should not be less than 30. The upper limit depends on the reasonable numerical effort and might be 1 00 at present, when the DPB is coupled with equations for material flow. In order to describe spatially homogeneous systems, up to 1 000 classes are applied. This effort is reasonable, when the goal is distribution reconstruction instead of keeping track of moments only [148]. Reviews of DPBs can be found in the work of Attarakih et al. [ 1 32,1 49], Kostoglou and Karabelas [1 50], Kumar and Ramkrishna [147], Nopens and Vanrolleghem [151], Vanni [59], and in the textbook by Ramkrishna [14]. 3.3.5.2. Discretization
The discretization is deciding for the numerical stability and accuracy on the one hand and the computational load on the other hand. The choice of the discretization is dependent on the dominant mechanism, layering or agglomeration. A uniform discretization in which each interval spans the same constant range in particle sizes, appears to be natural, but would require such a large number of intervals when agglomeration occurs, that the advantage of the method would be deteriorated. 18 The use of a geometrie series in which the width of the ith interval is proportional to the width of the i- 1 th interval reduces the number of equations strongly. Batterham et al. [1 52] used a geometrie discretization in which each class is twice the volume of the proceeding class Vi+1 = 2 1 /q ' Vi
or
(1 04)
18 The limit as the grid becomes finer is the direct numerical aUack on the discrete PBE, equation (8), by solving it for each particle size.
T. Abberger
1 1 68
where Vj is the volume and Ij the length of a particle in the ith interval and q is an integer (unity in the approach of Batterham et 81.). The rationale of this discretization may be that discrete outputs of some measurement methods have the same dis cretization scheme; sieve sets with this size step are common. For the application of a DPB, experimental data of the initial size distribution are required in each size class. When the applied experimental method has the same discretization like the DPB, no assumption about a distribution function, e.g. log-normal, is required. Hounslow [21 ] mentioned the particular utility of this series when dealing with aggre gation events; partieIes can aggregate into a given size elass only if one of the parti eles, prior to forming an aggregate, was in the size elass immediately smaller than the elass of interest, and should an aggregate be formed by partieIes both from the same elass it will always be of such a size as to be counted in the next elass. However, this results in a fixed and coarse grid. Numerical solutions need to be checked for accuracy and convergence. This is accomplished by comparing the numerical results for two grids that differ only slightly. A numerical technique that uses a fixed grid cannot be used for this purpose [59,1 53]. 3.3.5.3. The zero-order methods
With the so-called zero-order methods [1 50], the particles are assumed to be uniformly distributed in a size range, ni = NJ(Vi+1 - Vi). The PSD is approximated by a histogram. The approximation of a distribution by a histogram with the zero order methods is of course a cruder approximation than achieved with the higher order methods, where n( v, t) is approximated by polynomials, but it is possible to obtain results with a degree of accuracy that is sufficient for many purposes and to assure the conservation of at least two moments (e.g. total number and mass), which can be sufficient for practical and control purposes. The approximation of the PSD by a histogram is considered to be satisfactory for pure aggregation [1 54]. The problems with the extension of DPBs for nucleation and growth have been discussed by Kumar and Ramkrishna [1 55]. With the DPB for pure aggregation proposed by Gelbard et 81. [1 56], one prechosen moment is conserved k� 1 "" r Tl = 2" � � ßij,kQf,i Qfj - Qf,k � ßi,kQf,j i= 1 j=1 i=1
d Qf,k
k�1 k� 1 1 "" "" 1 -
1 3- 2 �C - 2" ßk,kQf,k - Qf,k � ßi,kQf,i i=k+1
(1 05)
where Q is a distribution function, defined by f, the frequency index, and i, j, and k n are size sections. The terms ßx,y are double integrals of the type nßq _
lxX l Xx-1
X Y
Xy_ 1
0 (u, v)g(u, v)ß(u, v) dY d X IXUY vY(Xx - XX�1 ) (Xy - XY�1 )
(1 06)
Population Balance Modelling of Granulation
{
1 1 69
where g(u, v) is a function of its arguments, rx is a shape factor, y is given as 0 to express the number of particles of volume v (1 07) y = 2/3 to express the surface of particles of volume v 1 to express the volume of particles and 0(u,v) is a test function
{ 01
if test is true (1 08) if test is false Gelbard et al. [1 56] compared their zero-order approximation to a spline approximation for the coagulation of an aerosol. As expected, the accuracy of the zero-order method increased with the number of sections, but did not reach the accuracy of the spline approximation. A drawback of this DPB is the high computational load owing to the many double integrals that have to be calculated. Therefore, the method has been applied rarely in published results. It is, however, mentioned because it represents the M-I I approach to achieve closure of the DPB. Hounslow et al. [1 57] used the same discretization like Batterham et al. [1 52] and considered all possible events leading to birth and death of particles in each interval. They derived two separate expressions for birth processes in the ith class as weil as two separate expressions for death processes (Table 1 ). Therefore, the DPB for pure aggregation consists of four terms. The equation is formulated in a way that with each of the four interaction types, only those interactions are considered, which change the number of particles in the ith section. This is achieved by considering aggregation of particles in those fractions of the size ranges, which change the number of particles in the ith section. The equation is capable of correct predictions of the total number and the total mass. It is given as i-2 1 ' l dNi i 1 . " ß(J - , j' - 1 )Ni2 i N dT - 1-1 � 2J- + ß(J' - 1 ,};� N ' J=1 i- i (1 09) - Ni L i-iß(i,j) Nj - Ni L ß(i, j) Nj j= 1 j=i 0(u, v) =
J + 2'
_
00
Table 1 .
Binary interaction types for aggregation
Term in equation ( 1 09) 1 2 3 4
Birth or death in interval i Birth Birth Death Death
Collisions between particles in interval i- 1 1 -4 i-2 i- 1 i- 1 1 -4 i-1 i-4 oo
1 1 70
T. Abberger
Discretized terms to extend equation (1 09) for nucleation and growth have been described too [1 57], and the equation has been adapted for the application in continuous systems at steady state [1 58]. Several authors [86,93, 1 59] applied a modified form of equation ( 1 09) to simulate granulation. The coalescence kernel ß (iJ) is calculated as ß(Xj,Xj), where Xi and Xj are representative particle sizes in the sections i and j, namely the mean volumes. This DPB represents the M-I closure approach. In an application, equation (1 09) has to be solved as many times as the number of intervals there are in the division of the PSD. It spans the smallest particle range for the starting powder, up to the largest volume expected for a granule, this typically results in 30 to 40 equations. To allow a finer discretization than allowed by the term Vi+ 1/V; = 2, Utster et al. [1 60] expanded equation ( 1 09). As the value of q in the discretization increases, the discretization step is smaller. Thus, larger values of q lead to a more accurate approximation of the PSD, but are computationally more demanding. The computational load is proportional to q3 . Nicmanis and Hounslow [1 30] compared the performance of the DPB of Utster et al. [1 60] and a finite element method. Clearly, the finite element method showed superior performance. 3.3.5.4. The pivotal methods
With these methods, all particles in a section are supposed to be of the same size. The methods focus on accurate calculation of moments instead of calculation of the whole PSD. The particle population in the ith size range is represented by a size Xi (the grid point or pivotal point) such that Vi< Xi< Vi+ 1 . Again ß(iJ) i s calculated a s ß(Xi,X). A pivot concentrates the particles in the interval at a single representative point. Thus, the number density function is represented by [14] (1 1 0) where (j is the Dirac delta function. The difficulty that arises in a non-uniform grid is, where to allocate born particles that do not have exactly the size of the grid point Xi' 3. 3. 5.4. 1 . The fixed pivot approach. The approach of Kumar and Ramkrishna [147] was a significant advantage. They developed a DPB for aggregation and breakage (Fig. 1 3) or aggregation or breakage alone, which allows conserving any two pre-chosen moments of the distribution. A second major improvement of this numerical technique is that the underlying grid can be chosen arbitrarily. Two property balances were developed to assigning fractions of particles that do not exactly match Xi to both the adjoining pivots, Xi and Xi+ 1 , by linear
1 1 71
Population Balance Modelling of Granulation dN· __ I =
dt
aggregatian-breakage
•
�I Death of floc of sire. ;
Binh of floc ofsire. i by collision with smaller
floes
Death
Birth
Death
Birth
Breakage
Breakage
Aggregation
Aggregation
floc of siz.e, i
Death of floc of size. i
Binh offloc ofsize. ;
by collision with any
by breakage
other flocs
flocs
by breakage
of (arger
offloc of
size� i
Fig. 1 3. Aggregation and breakage dynamics. Reprinted from Biggs and Lant [ 1 6 1 ] , with permission from Elsevier. class bo.mdary (v,)
•
Pivot
Fixed pivot
,�, . , I
X,
class
Moving pivot
newly fonned panieie through aggregation or breakage
•
1
•
(X)
I
•
dass boundary
Pivot
newly
breakage
fonned panieie through aggregation or
, ,
i
t
.
I
i
V,.,
class i+1
clas i-I
.
.
VI- Xi ' V ! .
I I
Xi,
class i
V,.,
Xi+1
Vi+'J.
class i+1
1 4. Schematical representation how the two different pivotal techniques deal with newly formed particles that do not coincide with an existing pivot. Reprinted from Nopens et al. [1 62], with permission from Elsevier. Fig.
interpolation (Fig. 14, left-hand side). With this strategy, any two pre-chosen moments are conserved. Internal consistency with respect to any two moments is enforced. By internal consistency it is meant that for any pre-chosen moment of the distribution, there exist two ways to obtain them. The first one is by discretizing the continuous PBE, and the second one is by deriving these moments from the discrete PBEs. In other words, this means that the result for this moment should be the same for the DPB and the continuous PBE [14]. The set of equations for simultaneous aggregation and breakage for conservation of both mass and numbers are given as
M
+ L n;,kS(xk)Nk - S(x;)N; k=;
(1 1 1 )
1 1 72
T.
Abberger
where (5j,k is the Dirac delta function and the factor '1 is responsible for the reallocation of the born particles to the adjoining pivots. For the case of conservation of number and mass, it is given as (1 1 2) The term ni,k is interpreted as the contribution to the population at ith representative size owing to the breakage of a particle of size Xk (breakage birth) and is given for the conservation of numbers and mass as (1 1 3) Equation (1 1 1 ) consists of four terms. The first is the aggregation birth term and it contains the factor '1 for the reallocation of the born particles to the adjoining pivots if they do not coincide with a pivot. If they do coincide, '1 becomes unity. The second term describes the loss of particles owing to aggregation (aggregation death) and does not require any reallocation, because particles only disappear from the ith class. The third term describes breakage birth and requires again a factor for reallocation, ni,k' The fourth term describes breakage death. The version for the conservation of numbers and mass, as given in equations (1 1 1 )-( 1 1 3) yields identical results as obtained by the DPB of Hounslow et al. [1 57], when the same geometrie grid is applied [147]. Kumar and Ramkrishna [1 47] tested the performance of their DPB for pure aggregation, pure breakage, and combined aggregation and breakage. For the pure breakage case, the predictions were accurate even when a coarse grid was used. With the predictions involving aggregation , the accuracy was high for small and medium sizes, even for coarse grids, but suffered from over-predictions in the large particle size range. The reasons for these over-predictions were steep gradients in log-scaled plots at larger sizes in the number density functions. A steep variation in number density is called a front. The over-predictions were as severer as the degree of homogeneity of the applied kerneis (constant, sum and product) increased and as time progressed. Such over-prediction is a feature of other DPBs proposed in the past as weil [1 53]. The over-predictions were due to the inadequacy of a uniform number density approximation to represent a steeply decreasing number density within an interval. If within an interval [Vi, Vi+1 ) there are more particles of size Vi than of the pivotal size Xi, where Xi > Vi, but all particles are ascribed to have the pivotal size Xi of this interval, then the main source of error is that the coalescence kernel includes this too large pivotal size
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instead of a more relevant but lower size Vi, and consequently is leading to a too high value of the kernel and a false accelerated aggregation rate. The front moves to larger sizes at a faster calculated rate than the real rate. By refining the grid such that the number density does not vary significantly over a section width, the over-predictions could be reduced, but a method was searched to avoid an increase of computational load owing to a grid refinement. A solution for this problem was a grid, where the size range containing steep variations is represented by a fine grid and the rest is covered by a coarse grid without enlargement of the number of sections. Kostoglou and Karabelas [1 50] evaluated four DPBs for aggregation, namely the methods of Batterham et al. [1 52], Marchal et al. [1 63], Gelbard et al. [1 56], and Hounslow et al. [1 57] by comparison with analytical solutions for the constant and the sum kernel with monodisperse and gamma initial distri butions. The method of Hounslow et al. showed the best performance. Vanni [59] reviewed seven DPBs for aggregation. He extended the DPBs of Gelbard et al. [1 56], Utster et al. [1 60], and Marchal et al. [1 63] for breakage, and tested these and the DPB of Kumar and Ramkrishna [147] for aggregation-fragmenta tion of particulate suspensions using the constant, the sum, and the hydrodynamic kernel for aggregation and the constant, the power law, and the exponential kernel for breakage by comparison with rigorous solutions. The conclusion was that the approaches by Gelbard et al. [1 56] coupled with the extension for breakup, and by Kumar and Ramkrishna [1 47] were accurate and the most robust and versatile methods. The implementation of Kumar and Ramkrishna's method was simple, contrary to the method of Gelbard et al. [1 56]. The method of Utster et al. [1 60] combined with the breakage extension by Vanni [59] performed weil under certain conditions. Balliu et al. [ 1 64] carried out simulations on a granulation model to compare the accuracy and efficiency of the methods of Kumar and Ramkrishna [1 47] and Hounslow et al. [1 57]. The pivotal technique by using a more flexible pattern was shown to be capable of predicting more accurate results in the large size ranges (such as 1 .00-1 .26 mm) of the domain where errors are usually present owing to steep moving fronts. Kumar and Ramkrishna [1 47] provided as a guideline that zero-order methods containing no double integrals and focusing on conservation of both numbers and mass are computationally efficient and accurate. 3. 3. 5. 4. 2. The moving pivot approach. In order to overcome the problem of steep gradients, Kumar and Ramkrishna [1 53] proposed the so-called moving pivot technique that accounts for the variation of the number density in a size range by allowing a varying pivot location (Fig. 14, right-hand side). The favourable features of the fixed pivot approach, like arbitrary choice of the grid and conservation of any two pre-chosen moments, were maintained. The equation in the form for conservation of total number and mass, following the
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(1 - 1 (jj,k) ß(Xj, xk)NjNk
development by Nopens and Vanrolleghem [151] is
d Nj dt
-
j>k L (XjHk)Eli M
2"
M
- Nj L ß(Xj, xk)Nk + L Nß(Xj)B� - S(xj)Nj j=j k= 1
(1 1 4)
(1 1 5) where (1 1 6) Nopens and Vanrolleghem [1 5 1 ] discussed the moving pivot approach: equation (1 1 4) describes the time variation of Ni and looks similar to equation ( 1 1 1 ). However, the first and the third term are different. The difference in the first term is the fact that the summation now involves aggregated particles that are formed between the cl ass boundaries Vj and Vi+ 1 (and not between pivots as was the case in the fixed pivot approach). A similar difference occurs in the third term where the integral, equation (1 1 6), has different integration limits as the integrals for ni, k' equation ( 1 1 3). A closer look at equation ( 1 1 5) reveals that only two terms are responsible for changing the pivots Xi, one term for aggregation birth and one for aggregation death. The equation is a determination of the average diameter (volume in this case) of every size class when new particles are born into them. In this way, the pivots are allowed to move inside the class boundaries depending on the amount and the sizes of particles that are born into the class either by aggregation or by breakage. The pivots are dynamic quantities, functions of both time and the coalescence and breakage functions, and follow the changes in the number density according to the following relation, when the volume is preserved [1 65]: J:i+ 1
vn(v, f) dv (1 1 7) Vj<Xj< Vj+1 Vi n(v, f) d v This definition of the pivot as M1/Mo in each class, as the mean size, is Xj(f) = J,'Vi+1
'
consistent with the mean value theorem of integrals such that it moves in the interval as the number density changes.
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Comparisons of both pivotal techniques carried out by Kumar and Ramkrishna [1 53] and by Nopens and Vanrolleghem [1 5 1 ] showed the superiority of the moving pivot approach. 3.3.5.5. The error of discretization
In discretizing an equation defined over an infinite domain, an inherent error is incurred due to not taking into account the portion of the function Iying outside the domain of discretization. This type of error is termed finite domain error, FDE, [1 56]. It causes a non-zero lower and upper residual below and above the discrete limits of integration. The lower and the upper residuals are given as [1 66]
rVmin
FDE6(Vmin , f) = J o FDE�(vmax, f) =
n(v, t) dv, and
1Vmax00 n(v, t) d v
(1 1 8)
where the subscript 0 denotes a residual of the zeroth moment of the distribution. The discrepancy between the continuous number of particles, rvc(t), and its discrete counterpart, tr(Vmin,Vmax,t), can be interpreted by defining the error of discretization. The error of discretization, Eo, is defined as the difference of sums between the continuous and discrete number of particles for the intervals (0, (j) ) and [Vmin, vma x], respectively [1 65] (1 1 9) Excluding an integration error, the discretization error is only due to the FDE Eo (f) = FDE6(Vmin , t) + FDE�(vmax, t)
(1 20)
In a DPB with a fixed discretization, the size domain spanned is defined by two parameters, the minimum size, Vmin, and the number of discrete equations considered, neq. For any value of neq, there is an optimal value for Vmin that minimizes the FDE [1 58]. As larger the number of neq is, the smaller, of course, is the optimal value of vmin, and of the resulting FDEL. When applying a DPB, there always should be an empty interval at each end of the PSD to avoid a significant finite domain error. A finite domain error can be moni tored by checking that J:max m,n vn(v, t) dv is conserved during the computations [1 56]. In order to minimize the FDE in a batch process, Attarakih et al. [1 65] developed a moving grid and extended the moving pivot technique of Kumar and Ramkrishna [1 53] for unsteady-state continuous systems. 3. 3. 6. Monte Garlo simulation
Monte Carlo methods are an attractive way of tackling the PBE owing to the existence of a stochastic model related to the Smoluchowski equation. Two Monte
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Carlo algorithms to simulate coalescence and breakage were explained in detail by Goodson and Kraft [1 67]. Monte Ca rio methods were reviewed by Ramkrishna [14] and Cameron et al. [9]. The method seems to get more important for the multi dimensional PBE than for the one-dimensional, where the weil-known solution methods seem to have the potential to fulfiil the demands on a solution. 3.4. The inverse problem 3. 4. 1. Introduction
The traditional approach to solve the inverse problem in granulation proceeds in two steps. In the first step, a given kernel form is assumed and then experimental batch granulation data are fitted to find the adjustable parameters in ß*(u, v) that are included in many kerneis. In the second step, the value of the aggregation rate term, ßo(t) , is calculated. In doing so the PBE is solved using various values of the parameters until the best fit is achieved. Serious implications can foilow from the applied numerical method on the identification of model parameters [144]. The inverse problem is difficult due to two reasons: •
•
The inversion of the data is generaily iil-posed, which means that smail errors in the input data, n(v,t), produce large errors in the extracted information, ß(u,v, t) [28] . This i s critical because experimental data i s subject to stochastic fIuctuations and one seldom knows the exact data [97]. Pre-smoothing of the data is required, thereby substantiaily raising the required amount of data [14]. Rawlings e t al. [ 1 8] discussed the assessment of the uncertainty of the extracted information . Even a good fit of a chosen kernel cannot guarantee that it is the best. The fit is only valid within the range of conditions, where it was obtained. In addition, kerneis with physical characteristics that are inconsistent with the nature of the process might provide the best fit.
The task of identification is considerably simplified by restricting to systems where the population evolves owing to aggregation alone [97] . The comparison of forward simulations with data can assess the quality of the inversion. This is a redeeming feature of inverse problems in general [23]. 3. 4. 2. Determination ofthe site dependence of the aggregation frequency
This problem is typicaily approached in two different ways: either by the indirect method by finding the kernel or combination of kerneis that provide the best fit to the experimental data via trial and error, or •
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in cases where the PSDs show self-preserving behaviour to extract the aggregation frequency by a direct method taking advantage of the constraints that the observed self-preserving distribution places on the aggregation frequency.
With the indirect method, preliminary elimination of candidate kerneis is usualiy accomplished by comparing the characteristics of the kernel and the trend of the experimental size distribution [75]. Criterions for acceptance or rejection of a kernel are the influence on the variance (broadening or narrowing), the non-geliing beha viour of a kernel and the self-preserving characteristics of the kernei. For a system where no physical gelation occurs, geliing kerneis may be rejected as a priori being unsuitable. Although when a geliing kernel provides the best fit to experimental data, an extrapolation to higher values of /a99 is unsafe [94]. In granulation, no experimental evidence for gelation is known. The theoretical models for coalescence [88,1 08] predict a limiting size above which no coalescence occurs. The selection of the coalescence kernel proceeds in two steps. In the first step, one of the kerneis is selected and the PBE is solved using the kernel to be tested with the size distribution at the earliest time as the initial condition. The model parameters are fitted by trial and error so as to obtain a fit of the peak of the PSD. In the second step, the simulated and experimental PSDs may be compared to determine which kernel best describes the data. Each kernel gives rise to a different shape of the PSD. The direct method has been developed by Ramkrishna and co-workers [28,78,97]. It involves inverting the PBE for the kernei. Self-preserving size distributions are restricted to purely coalescing (or purely breaking) systems. The method cannot be applied, therefore, when in an aggregation process significant simultaneous breakage occurs. Because with self-preserving PSDs many curves coliapse into a single curve, this leads to pre-smoothing of the data. To circumvent the problem of fluctuations of experimental data, a regularization procedure has been inciuded [28,97], where a weli-posed approximation instead of the ili-posed problem is solved. 3. 4. 3. Determination of the aggregation rate term
The values of the extracted aggregation rate term are dependent on ß*(u, v) Once the dependence of the aggregation rate on size is known, it is possible to extract the aggregation rate term. Bramley et a/. [1 68] developed a differential method to extract it from the data, once ß* (u,v) is fixed by using ODEs, either moment equations or a DPB. Hounslow et a/. [63] provided a discussion of this differential method, see also Peglow et a/. [1 69].
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3. 4. 4. Assessment of the fit
To assess the goodness of fit between a model and experimental data, both the coefficient of correlation, R2 , and the sum of square errors method can be applied. The difference between the simulated and the experimental data can be estimated with the x2 test. The best constants are estimated by minimizing the sum-of-squares error (SSE) between experimental and the simulated PSDs. SSE = 2.: 2.: (Ni,j, sim - Ni,j, exp ) j
i
2
(121)
where j i s the number of data sets and Ni the number of granules in size interval i. In other words, one seeks the constants that minimize an objective function. Various methods are known to minimize this objective function. Adetayo (cf. [77]) used the cumulative undersize instead of a density distribution as optimization criterion, because this is what is directly determined in a sieve analysis. Tan et al. [87] used a l -minimization to extract agglomeration and breakage rate constants from the measurements of PSDs. In order to extract agglomeration and breakage rates simultaneously, they applied a recently developed technique that accounts for the error of the data. 3.5. Application of population balance models in process control
Several approaches including PBMs are available for controlling the granulation process at one scale, and for scaling-up to another [29]. When using PBMs for process control, the applied terms, the coalescence kernei, and the rate constants have to be derived from experiments. Compared with the models generated by experimental design, the one-dimensional PBE models focus only on the PSD, motivated by the majority of industrial particulate process control problems, where the goal is to design the PSD. The PBMs of most particulate processes are uncertain. Typical sources of model uncertainty include unknown or partially known time-varying process parameters, exogenous disturbances, and unmodelled dynamics. It is weil known that the presence of uncertain variables and unmodelled dynamics, if not taken into account in the controller design, may lead to severe deterioration of the nominal closed-Ioop performance or even to closed-Ioop instability [72]. The first notable attempt of the application of PBE models in the control of particulate processes was the controllability analysis by Semino and Ray [1 70]. In crystallization, an output feedback control has been described by Chiu and Christofides [72,1 71 ] , but without experimental validation. The PBE models were converted into lower dimensional control relevant models using moments.
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Adetayo et al. [1 59] included a PBE model with a sequential coalescence kernel into a steady state simulation of a fertilizer granulation circuit. This study was motivated by the high recycling ratios where continuous production of fertilizers in rotating drums suffers from. Zhang et al. [1 72] examined the recycle size distribution control strategy for the continuous granulation of a fertilizer in a granulating circuit consisting of a rotating drum, drier, c1assifier, and crusher. The submodel of the granulation drum consisted of population and mass balances. There are several possible choices for the controlled variable including PSD ex-granulator, granule moisture content, slurry flow rate, product flow rate, and recycle flow rate. The recycle size distribution was chosen as the control variable, because it can be measured by flow rate sensors. It was found by carrying out three case studies of disturbances that the chosen control strategy was able to return the plant to the set point. A validation of the model of Zhang et al. [1 72] using data obtained in an industrial plant was attempted [1 73]. Model predictive control, which is a control framework that has spread in the process industry during the last decades, has also received a great deal of attention in the field of particulate processes in the last decade. Model predictive control including PBEs was implemented on a granulation drum [1 74]. Heinrich et al. [24,145,146] simulated continuous fluid-bed granulation using a model of the whole granulation circuit including granulator, zigzag sifter, mill, and cyclone. Binder liquid was sprayed onto seeds. The mechanism of granule growth was assumed to be layering. Undersized granules and milled oversized granules were returned into the granulator as seed material. This process was modelled using a PBE consisting of growth and flux terms. They demonstrated that an unsteady start-up phase occurs, which can lead to instability (oscillating behaviour). The nuclei size and flow rate have a decisive influence on the stability and the duration of the unsteady start-up phase, thus constituting a central control parameter. When the decomposition of the oversize by the mill is large, the entire surface of the particles is enlarged thus reducing the growth of the mean diameter in the granulator after recycling this seeds into the granulator. After the start-up phase, the process reaches a stable point producing a constant granulate spectrum. Experimental validation of the model was carried out successfully. Techniques based on PBE models are under development for control of both fluid-bed and high-shear granulation [29]. Wang and Cameron [8] and Cameron et al. [9] reviewed model-based control of granulation processes.
4. FORWARD LOOK 4. 1 . M u lti-dimensional population balance equations
There is a need for multi-dimensional PBEs, consequently this is an evolving area of research, as weil as development of solution techniques.
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4.2. KerneIs
Kernel development remains a challenge, although substantial progress was made. 4.2. 1. Collision frequency
In granulation research, much of the work done in model development focused on modelling the coalescence probability. There is a need for work in order to establish sound models for the collision frequency in all relevant types of granulators based on knowledge of granular motion. There can be different patterns of movement in different types of granulators. First results of accounting for collision frequency based on random, independent movement of granules have been recently published (see Section 3.2.2). 4. 2. 2. Coalescence probability
Those aspects in which the recent models describing the coalescence probability still need to be improved, were discussed by Knight [1 75] in a review of current challenges in granulation technology. 4. 2. 3. Distribution of forces
The theoretical models for predicting the likelihood of granule coalescence always require knowledge of the impact velocity or shear field in the granulator. Most workers assume some average velocity as representative of the entire granulator. In reality, however, there will be a distribution of impact velocities [33]. In a mixer granulator, the granules are subjected to a range of forces and stresses, depending on their positions and distances from the impeller and chopper blades [1 09]. Furthermore, there will be an upper velocity limit beyond which collisions result in granule breakage [1 24]. Owing to such a distribution, coalescence rates within the device will show a range. Most kerneis yet represent this range by an average value for the whole batch. In this field, there is still a need for active research. 4.2. 4. Experimental validation
As was briefly discussed on an I FPRI workshop in 2004: Because the kernel includes a coalescence frequency and a coalescence probability, the experi mental validation of a kernel should be split as weil . For validation of physical models predicting a coalescence probability of single granules, we need to design and perform smart experiments, which in fact enable the validation of such models on the level of single granules.
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4.3. A look on g ranulation as a m ulti-scale process 4. 3. 1. Introduction
Granulation is a multi-scale process that embraces a range of objects of a scale starting at the particle scale and ending at the equipment or system scale: Particle < Granule < Granule bed < Vessel < Granulation circuit The challenge in the near future is not only to study processes at any of these scales separately, but to integrate all of them into a complete process model (see Ref. [8]). The challenge is linking the micro(particle)- and macro(unit operation) scale by taking into account the scales between them successfully [1 76]. This is challenging, because different physical laws are relevant at each scale. Correlations between phenomena at different scales occur and spatial and temporal changes have to be coupled. Owing to their potential to link the evolution of the PSD to the microscale, PBEs will be part of this holistic look on granulation. 4. 3. 2. A look on the granule bed
There is a need for research, how to link the PBE to the granular flow and the force distribution in a granular bed. Fortunately, in the last decade there was substantial progress made in elucidating the processes on the granular bed level. A method applied for this purpose is the measurement of fluxes inside a granulator using positron emission particle tracking. The granular bed can be spatially inhomogeneous with respect to • • •
flow patterns, PSD, and distribution of acting forces.
Segregation has the potential to occur in many commercial granulators. If size segregation does occur in a granulator, the assumption of a random mixture of particles within the whole device becomes invalid [33]. One possibility to overcome this problem is to design granulators with improved mixing properties. Such an improvement of equipment is one of the challenges discussed by Knight [1 75]. Another possibility to account for inhomogeneity effects in a granulator is to model the granulator as several separated regions although there is no physical division of the granulator. For each region, a PBM with the required boundary conditions is created, together with a model for the flow of granules between the different regions. If there exist regions with different flow patterns or acting forces, it might be
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speculated that each region needs to be modelIed by a different kernel because the agglomeration rate might be different then. Wang and Cameron [8] discussed the idea of zone models for a drum granulator. In fluid-bed spray granulation, the existence of a spray zone supports the development of zone models. 4. 3. 3. Application in scale-up
An application of PBMs, which still has to be developed, is their application for scale-up purposes. The development of a working model for a small-scale device, however, is difficult, because experimental fluctuations over the mean are enforced. Unavoidable little fluctuations in operating parameters have a greater effect than in a large-scale device. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [ 1 0] [1 1 ] [1 2] [1 3] [ 1 4] [ 1 5] [ 1 6] [ 1 7] [ 1 8] [ 1 9] [20] [21 ] [22] [23] [24] [25]
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[71 ] CA Biggs, C. Sanders, AC. Scott, A.w. Willemse, AC. Hoffman, T. Instone, AD. Salman, M.J. Hounslow, Powder Technol. 1 30 (2003) 1 62. [72] T. Chiu, P D . Christofides, AIChE J . 46 (2000) 266. [73] R.L. Drake, J. Atmos. Sci. 29 ( 1 972) 537. [74] AA Adetayo, B.J. Ennis, Powder Technol. 1 08 (2000) 202. [75] AA Adetayo, B.J. Ennis, AIChE J. 43 ( 1 997) 927. [76] L.X. Liu, J D . Litster, Chem. Eng. Sci . 57 (2002) 2 1 83. [77] PAL. Wauters, B. Scarlett, L.X. Liu, J.D. Utster, G.M.H. Meesters, Chem. Eng. Comm. 1 90 (2003) 1 309. [78] T. Tobin, R. Muralidhar, H. Wright, D . Ramkrishna, Chem. Eng. Sci. 45 ( 1 990) 349 1 . [79] S . M . Iveson, Chem. Eng. Sci. 56 (2001 ) 221 5. [80] N . Ouchiyama, T. Tanaka, Ind. Eng. Chem. Process Des. Dev. 20 ( 1 98 1 ) 340. [81 ] N. Ouchiyama, T. Tanaka, Ind. Eng. Chem. Process Des. Dev. 21 ( 1 982) 29. [82] N . Ouchiyama, T. Tanaka, Ind. Eng. Chem. Fundam. 1 9 (1 980) 338. [83] C. -Co H uang, H.O. Kono, Powder Technol. 55 ( 1 988) 35. [84] S. Watano, T. Morikawa, K. Miyanami, Chem. Pharm. Bull. 43 ( 1 995) 1 764. [85] S. Watano, T. Mori kawa , K. Miyanami, Chem. Pharm. Bull. 44 ( 1 996) 409. [86] Th. Abberger, Eur. J. Pharm. Biopharm. 52 (2001 ) 327. [87] H .S. Tan, M .J .v. Goldschmidt, R. Boerefijn, M.J. Hounslow, AD. Salman, J A M . Kuipers, Powder Technol. 1 42 (2004) 1 03. [88] B.J. Ennis, G . I . Tardos, R. Pfeffer, Powder Technol. 65 ( 1 99 1 ) 257. [89] S . M . Iveson, J.D. Litster, AIChE J. 44 ( 1 998) 1 51 0. [90] L .X. Liu , J . D . Utster, S.M. Iveson, B.J. Ennis, AIChE J . 46 (2000) 529. [91 ] S.J.R. Simons, J . P. K. Seville, M . J . Adams, Chem. Eng. Sci. 49 ( 1 994) 233 1 . [92] G . I . Tardos, I . Talu, http://www- che.engr.ccny.cuny.edu/tardos/download/ChinaPaper-2000.pdf, 2000. [93] AA Adetayo, J . D . Litster, S . E . Pratsinis, B.J. Ennis, Powder Technol. 82 ( 1 995) 37. [94] D.J. Smit, M . J . Hounslow, W.R. Paterson, Chem. Eng. Sci. 49 ( 1 994) 1 025. [95] P.G.J. van Dongen, M . H . Ernst, Phys. Rev. Lett. 54 ( 1 985) 1 396. [96] 0.0. Pushkin, H. Aref, Phys. Fluids 14 (2002) 694. [97] R. Muralidar, D. Ramkrishna, J. Colloid Interf. Sci. 1 1 2 ( 1 986) 348. [98] D.L. Swift, S.K. Friedlander, J. Colloid Sci. 1 9 ( 1 964) 621 . [99] B . Pulvermacher, E . Ruckenstein, J . Colloid Interf. Sci. 46 ( 1 974) 428. [1 00] E. Ruckenstein, J.C. Chi, J. Colloid Interf. Sci. 50 ( 1 975) 508. [ 1 0 1 ] M. Kostoglou, AJ. Karabelas, J. Aerosol Sci. 30 ( 1 999) 1 57. [1 02] N. Menci, S. Colafrancesco, L. Biferale, J . Phys. I France 3 ( 1 993) 1 1 05. [1 03] D.J. Smit, M . J . Hounslow, w.R. Paterson, Chem. Eng. Sci. 50 ( 1 995) 849. [1 04] T.B.Drew (Ed.), Advances in Chemical Engineering Vol . 1 0, Academic Press, New York, 1 978. [1 05] B. Pulvermacher, E. Ruckenstein, Chem. Eng. J. 9 ( 1 975) 2 1 . [ 1 06] S.K. Friedlander, C.S. Wang, J. Colloid Interf. Sci. 22 ( 1 966) 1 26. [ 1 07] P.C. Kapur, Chem. Eng. Sci . 27 ( 1 972) 1 863. [1 08] N. Ouchiyama, T. Tanaka, Ind. Eng. Chem. Process Des. Dev. 14 ( 1 975) 286. [1 09] P.C. Knight, Powder Technol. 77 ( 1 993) 1 59. [1 1 0] B.J. Ennis, Powder Technol. 88 ( 1 996) 203. [1 1 1 ] S. Chandrasekhar, Rev. Mod. Phys. 1 5 ( 1 943) 44. [1 1 2] AA Adetayo, JD. Utster, M. Desai, Chem. Eng. Sci. 48 ( 1 993) 395 1 . [ 1 1 3] S . M . Iveson, J . D . Utster, K . Hapgood, B.J. Ennis, Powder Technol. 1 1 7 (2001 ) 3. [1 1 4] S. Timoshenko, J . N . Goodier, Theory of Elasticity, McGraw-HiII, New York, 1 95 1 , pp. 372-377. [1 1 5] N . Ouchiyama, T. Tanaka, Ind. Eng. Chem. Process Des. Dev. 2 1 ( 1 982) 35. [1 1 6] H . G . Kristensen, P. Holm, T. Schcefer, Powder Technol. 44 ( 1 985) 239. [ 1 1 7] P . C. Kapur, D.W. Fuerstenau, Trans. AlME. 229 ( 1 964) 348. [1 1 8] Z. Ormos, K. Pataki, B. Csukas, Hung. J . Ind. Chem. 1 ( 1 973) 463.
Population Balance Modelling of Granulation [1 1 9] [1 20] [121] [1 22] [1 23] [1 24] [1 25] [1 26] [1 27] [1 28] [1 29] [1 30] [131] [1 32] [1 33] [1 34] [1 35] [1 36] [1 37] [1 38] [1 39] [1 40] [141] [1 42] [1 43] [ 1 44] [1 45] [1 46] [1 47] [1 48] [1 49] [1 50] [151]
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Th. Abberger, Pharmazie 54 ( 1 999) 6 1 1 . H . G . Kristensen, P. Holm, A. Jaegerskou, T. Schrefer, Pharm. Ind. 46 ( 1 984) 763. P. Holm, T. Schrefer, H . G . Kristensen, Powder Technol. 43 ( 1 985) 2 1 3 . C.-C. Huang, H .O. Kono, Powder Technol. 5 5 ( 1 988) 1 9. L.x. Liu, J . D . Litster, Modelling coalescence in granulation. Proceedings of the 26th Australian Chemical Engineering Conference (Chemeca 98), Port Douglas, Australia, 1 998. G . I . Tardos, M . I . Khan, PR Mort, Powder Technol. 94 ( 1 997) 245. S. Cryer, AIChE J. 45 ( 1 999) 2069. P.Y. H uang, J . D. Heliums, Biophys. J. 65 ( 1 993) 334. F. Gelbard, J.H. Seinfeld, J. Comp. Phys. 28 ( 1 978) 357. N.v. Mantzaris, P. Daoutidis, F. Srienc, Comput. Chem. Eng. 25 (200 1 ) 1 463. M . Nicmanis, M.J. Hounslow, Comput. Chem. Eng. 20 ( 1 996) S26 1 . M . Nicmanis, M.J. Hounslow, AIChE J. 44 ( 1 998) 2258. S. Rigopoulos, A.G. Jones, AIChE J. 49 (2003) 1 1 27. M . M . Attaraki h , H .-J. Bart, N . M . Faqir, Chem. Eng. Sci. 59 (2004) 2567. RL. Drake, T.J. Wright, J. Atmos. Sci. 29 ( 1 972) 548. J.C. Barrett, J.S. Jheeta, J. Aerosol Sci. 27 ( 1 996) 1 1 35. K.W. Lee, J . Colloid Interf. Sci . 92 ( 1 983) 3 1 5. M. Frenklach, Chem. Eng. Sci. 57 (2002) 2229. R McGraw, Aerosol Sci . Tech. 27 (1 997) 255. D.L. Marchisio, RD. Vigil, RO. Fox, Chem. Eng. Sci. 58 (2003) 3337. D.L. Marchisio, J.T. Pikturna, RO. Fox, R D . Vigil, A.A. Barresi, AIChE J. 49 (2003) 1 266. RB. Diemer, J . H . Olson, Chem. Eng. Sci. 57 (2002) 221 1 . M . do Carmo Coimbra, C . Sereno, A. Rodrigues, Chem. Eng. J . 84 (200 1 ) 23. W. E. Schiesser, The Numerical Method of Lines-Integration of Partial Differential Equations, Academic Press, New York, 1 99 1 . AVande Wouwer, P.Saucez, W.Schiesser (Eds.), Adaptive Method of Lines, Chapman & Hall/CRC, Boca Raton, 2001 . S. Motz, A. M itrovic, E.-D. Gilles, Chem. Eng. Sci . 57 (2002) 4329. S. Heinrich, M. Peglow, M. Ihlow, M. Henneberg, L. Mörl, Chem. Eng. Sci. 57 (2002) 4369. S. Heinrich, M. Peglow, M. I hlow, L. Mörl, Powder Technol . 1 30 (2003) 1 54. S. Kumar, D. Ramkrishna, Chem. Eng. Sci. 5 1 ( 1 996) 1 3 1 1 . A. Paschedag, Chem. Ing. Tech. 75 (2003) 1 835. M . M . Attarakih , H .-J. Bart, N . M . Faqir, Chem. Eng. Sci . 59 (2004) 2547. M. Kostoglou, A.J. Karabelas, J. Colloid Interf. Sci . 1 63 ( 1 994) 420. I. Nopens, P. A. Vanrolleghem, Comparison of discretisation methods to solve a population balance model of activated sludge flocculation including aggregation and breakage, Proceedings of the I MACS 4th MATHMOD Conference, Vienna, Austria, 2003. R J. Batterham, J. S. Hall, G. Barton, Simulation of full-scale balling circuits. Proceedings of the 3rd International Symposium on Agglomeration, Nürnberg, Germany, 1 98 1 . S . Kumar, D . Ramkrishna, Chem. Eng. Sci. 5 1 ( 1 996) 1 333. Y.P. Kim, J . H . Seinfeld, J. Colloid Interf. Sci. 1 35 ( 1 990) 1 85. S. Kumar, D . Ramkrishna, Chem. Eng. Sei . 52 ( 1 997) 4659. F. Gelbard, Y. Tambour, J . H . Seinfeld, J. Colloid Interf. Sei. 76 ( 1 980) 541 . M.J. Hounslow, RL. Ryall, V.R MarshalI, AIChE J. 34 ( 1 988) 1 821 . M . J . Hounslow, AIChE J. 36 ( 1 990) 1 06. AA Adetayo, J . D. Litster, I .T. Cameron, Comput. Chem. Eng. 1 9 ( 1 995) 383. J.D. Litster, D.J. Smit, M.J. Hounslow, AIChE J . 4 1 ( 1 995) 591 . CA Biggs, PA Lant, Powder Teehnol . 1 24 (2002) 201 .
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CHAPTER 25 G ra n u le Structu re Daniel Ba rrera-Medrano, * Ag ba D . Sal man , Gavin K . Reynolds and M ichael J. Hou nslow
Parlicle Products Group, Deparlment of Chemical and Process Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK Contents
I ntroduction Importance of granule structure 3. First attempts to look into granule structure 4. Solvent extraction 5. Imaging techniques 5 . 1 . Quantification of granule structure 5.2. XRT (X-ray tomography) 5.2. 1 . XRT sampies of different materials and granulation conditions 5.2.2. Application of X-ray tomography to the description of single granules: method development References 1.
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2.
1 1 90 1 1 92 1 1 93 1 1 98 1 1 98 1 1 99 1 20 3 1 206 121 1
1 . I NTRODUCTION
The term structure describes the way a system is internally built-up from its basic components. For agglomerates, structure can then be defined as the spatial arrangement of the basic components of a granule, which are: primary solids, binder and intra-particle porosity. Scale information should also be given alongside structural information. In this case, macro-structure would refer to the powder bed or the tablet structure, meso-structure to internal agglomerate structure and micro-structure would de scribe the structure of the basic components. To quantify structure the following must be known [1]: • •
•
Amount of each component: quantified by its phase volume. Size of the defined phases, which can be calculated using chord length distributions. Distribution of the phases throughout the system, describing the granule homogeneity. * Corresponding author. E-mail: [email protected]
Granulation Edited by A.D. Salman, M.J. Hounslow and J. P. K. Seville , 2007 Elsevier Sv. All rights reserved
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These characteristics can quantify the structure of an isotropic, spatially un limited structure. They do not account for the granule's shape, outer morphology or radial concentration gradients. 2. I M PORTANCE OF G RANULE STRUCTU RE
The structure of an agglomerate is a key factor in determining the final properties of the product, whether as independent agglomerates or tablets. It is therefore very important to understand how the structural characteristics of an agglomerate are going to affect its properties as weil as how the manufacturing method is going to affect the structure achieved by the agglomerate. This way it would be possible to build links between manufacturing and final product properties that would allow for the structuring of agglomerates from the beginning of their processing in order to obtain a desired product performance. Early work shows how the granulation methods have a direct effect on the properties exhibited by the final product, but does not relate this effect to the granule structure [2]. Knowing how to measure and describe the internal structure of agglomerates would also allow its incorporation into fundamental modelling of granulation [3], allowing the use of structural characteristics in simulation tools, physical models or to predict structure-dependant granule behaviour [1]. Properties of granulated material are determined by its composition, size dis tribution, shape and internal structure [1]: • • •
Composition is fixed usually by chemical requirements to achieve certain properties. Size distribution is usually chosen to meet criteria such as appearance, de-dusting and bulk density targets. Therefore, it is the agglomerate morphology, shape and structure that ulti mately determine the properties of the granule.
The granule structure will determine important properties such as the inter granular bonding during compression (important for tabletting), breakage or dis solution rates. The intergranular bonding behaviour during compression is described in Ref. [4] as are the resulting tablets properties and structure [4,5]. Previous work by Seager et al. [6,7] described three types of structure depending on the manufacturing process of the granules (Fig. 1 ), summarized in Table 1 . These models show different types of intergranular bonding during compression of the granules (Fig. 2): •
For pre-compressed granules (roller compacted granule), the binder particles are present as discrete particles within the granules and little intergranular
1 191
Granule Structure Hi gh
Wet Massing
bul k dens i ty granul es Preco.press fon
( fi l e .... trh of bi nder
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( s urface sne l l
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and sudace
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bi nder)
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Structure of granules prepared by different process methods (from Seager [7]). (Reprinted with permission from Wilmington Media.) Fig. 1 .
Table 1 . Characteristics of granules prepared by different processes (adapted trom
Seager [7])
Granulation process
Granule property State of binder in granules
Concentration of binder at surface
Bulk density
Discrete particles or particle fragments Film matrix
Very low
High
Low
Low
Spray granulation Film matrix
Moderate
Moderate
Spray coating
High
Very high
Pre-compression Wet massing
Surface shell
Main bonding mechanisms Particle fusiona Particle interlockingb Plastic deformation Binder cohesion Interparticulate bondingC Binder cohesion Interparticulate bondingC Binder cohesion Interparticulate bondingC
a Cold melting during compression. b Particle fracture during compression. c Precipitation of dissolved drug during compression.
•
•
bonding occurs (bonds are only formed between drug crystals), leading to the formation of low-strength tablets. The opposite occurs in the case of spray-dried granules. The high concentra tion of the plastic binder at the surface creates large areas of intergranular binder-to-binder contact, even at low-compaction pressure. For wet-massed granules, the granules make contact between binder and binder, binder and crystals and the crystals themselves. The area of intergranular binder bonding is smaller, resulting in tablets weaker than those produced from spray-dried granules.
1 1 92
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Fig. 2. Internal structure of a typical spray-coated powder (from Seager [7]). (Reprinted with permission from Wilmington Media.)
Granule Precompressed
Wel Massed
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.�.• A
•
Bonds Form Between � � Ug
_ _ _
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Fig. 3. Schematic representation of granule structure and intergranular bonding during compression (adapted from Rue et al. [4]).
Spray-coated granules are characterized by the presence of a surface layer of binder (Figs. 1 and 3). More recent work shows the importance of structural characteristics on the properties shown by agglomerates, such as breakage [8,9] or the behaviour of granules under stress [ 1 0]. The void fraction, as weil as the size and spatial distribution of pores within the granule, is also a key characteristic since the presence of pores has a direct influence on properties such as wet and dry strength, dissolution and disintegration in a liquid medium [1 1]. •
3. FIRST ATTEMPTS T O LOOK I NTO G RANU LE STRUCTU RE
The first attempts to look inside single agglomerates used an abrasion technique combined with chemical analysis to study the position and concentration of binder
Granule Structure
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throughout the granules [12]. Granules of magnesium carbonate were created using polyvinylpyrrolidone (PVP) as binding agent using wet massing. They studied the distribution of binder within the granule and its effect on local strength as drying occurred by calculating the radial distribution of binding agent at dif ferent stages during the drying process. In order to do this, they used an attrition method previously described in Refs. [ 1 3] and [14] by which the outer layers of the specimens were removed and analysed for PVP content using infrared spectroscopy. The core weight was recorded and the diameter measured. Elastic modulus and hardness measure ments were then made, and the process repeated until the core weight was reduced to about 1 0% of the original weight. As a result of their work it is found that the granules have two concentric regions with different properties. The hardness was found to increase towards the outer layers of the granule. The Young's modulus of elasticity followed a similar pattern to the hardness, decreasing towards the centre of the granule up to a point where it stayed roughly constant. The amount of PVP was found to be higher in the outer layers of the granules. The extent of these depends on the drying profile that the sam pies are subjected to. Non-uniform distribution of binder within agglomerates can be coupled to mal distribution of the active component (when talking about a pharmaceutical com position). Therefore, any attrition during storage or further processing can cause fines with a composition different from the bulk, resulting in lower product quality. Optical techniques were also developed [1 5] to determine the distribution of PVP binder in fluidized-bed-dried granules, by labelling the binder with a fluo rescent material and assessing its position within the granules by light micro scopy. They used fluorescein isothiocyanate (FIC) to label the binder and make it fluoresce under light excitement. After that a mixture of the labelled PVP and normal PVP was created to achieve suitable fluorescence, and this mixture was then used to granulate pow der mixtures in a fluidized-bed. Sampie granules were taken and observed using a fluorescence microscope. Sampie granules were also embedded in wax and cut into 20 �m thick sections with a microtome. The sections were also inspected with a fluorescence microscope and they report that the distribution of PVP within the granules could be seen perfectly. Unfortunately, no quantitative results are given in their work about how the binder distributes within the agglomerates, only the method is explained. 4. SOLVENT EXTRACTIO N
Seager et 81. [6] were the first who tried to study the structure of agglomerated material as related to the manufacturing process and final product conditions.
D. Barrera-Medrano et al.
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Previous work from the same authors [7] had suggested that properties of gran ules are governed by the distribution of the binding agent within them, which is in turn determined by the method of manufacture. A solvent extraction method was then developed [6] to study the position of the binder within granules prepared by three different methods (roller compaction, wet massing and spray drying) and relate the product structure with the production process mechanism (Fig. 4). In order to study the structure by a solvent extraction technique an appropriate combination drug and binder was chosen with different properties of solubility. The system chosen was paracetamol with a hydrolysed gelatine binder. The solvent used consisted of a solution of 60/40 (v/v) chloroform and ethanol. The paraceta mol readily dissolves in this mixture and the gelatine binder is not affected. There fore the paracetamol is dissolved and washed away and the binder is kept intact. After the extraction process was finished the binder residue was observed using SEM. As expected, different structures are seen for the different manu facturing techniques. •
Roller compaction In the roller-compaction process, the binder was finely divided prior to addition to help the bonding process between it and the paracetamol crystals. Different proportions of binder were tested and in every case the binder was present as discrete particles forming the bonds between -
Structure after wet massing and screening
1 �
concentra ed solution binder
Structure during drying
;;� �. ��� Structure of dried product
Structure of residue after solvent extraction
Fig. 4. Schematic diagram of the mechanism of the solvent extraction method for binder matrix formation (adapted from Seager et al. [6]).
Granule Structure
•
•
1 1 95
the paracetamol crystals. The binder particles showed different morphologies depending on the operation pressure of the compactor. Wet massing In the case of wet-massed granules, the binder was found to be in the form of a solid sponge-like structure holding together the paracetamol crystals. The structure had the same characteristics at different binder levels, except for visible differences in thickness. Spray-drying - The structure was remarkably different in the case of spray dried granules. For this manufacturing method the granules consisted of spherical particles composed of an outer shell of binder with an inner core of paracetamol powder. The structure was the same at all binder levels except for the thickness of the outer shell. -
Although quite vague, this is the first reference of work trying to relate granule structure with process manufacture, introducing the solvent extraction method [6]. Three different kinds of structure for the different ways of manufacturing the granules were described: wet-massed granules showed the binder distributed throughout the agglomerates in a sponge-like matrix, spray-dried granules showed the binder concentrated as a shell at the surface of a sphere, and pre-compressed granules where the binder was present as discrete particles embedded in the agglomerates which were formed largely from interparticulate bonds between the paracetamol crystals (Fig. 5). This method leads onto investigations focused on the effect of the structural characteristics of granules on their bonding and tabletting properties [4,5]. The solvent extraction method was also applied to fluidized-bed granules [ 1 6]. Two different size ranges from the fluidized-bed granules (250-500 and 500-1 000 )lm) were analysed to discover that the fluidized-bed granules had a more porous structure than wet-massed ones, resulting from the random nature of the agglomerationjfluidization process and the absence of shear during the fluidization. Individual solid particles or aggregates formed by electrostatic at traction become coated or partially covered with the granulation solution, leaving a layer of sticky binder. Other particles collided with these sticky crystalsjag glomerates forming aggregates, that then themselves became coated with further deposits of binder solution and this process continued as the aggregates grew into granules, giving a characteristic open structure. The solvent extraction technique was also used to dissolve the agglomerates and then describe the structure of the granules in terms of the size distribution of the primary particles left behind [1 7, 1 8]. Granules were made with calcium car bonate (CaC03) and silicon carbide (SiC) powder, and distilied water was used as a binder. The structure of the composite granules formed was discussed on the basis of the size distributions of the SiC particles contained in the granule, dividing them into six kinds of structure models, which were affected by the granulation conditions (Figs. 6 and 7).
1 1 96
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n"m Fig. 5. SEM photographs of the binder extraction methods (adapted from Seager et al. [6]): (a) view of wet-massed granules; (b) view of the state of the binder after solvent extraction process; (c) wet-massed granule; (d) wet-massed granule after solvent extraction process; (e) surface appearance of wet-massed granule; (f) surface appearance of wet-massed granule after solvent extraction method .
•
The granules were dried for 1 h at 1 20°C. Different sieve sizes were selected for further studies. To prevent the SiC particles in the granule from being affected by further physical/chemical treatment they were solidified by heating the granules for 1 h at 1 000°C. These are named a-granules.
1 1 97
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Fig. 6. Representative projections of five composite granules (a) composed of the binary
mixture of CaC03 and SiC powders and of the SiC agglomerates contained within it (b and c) using image analyser. (Adapted from Sugimoto et al. [ 1 8].) (Reprinted with permission from Elsevier.)
Models of composite structure
Coagulum of SiC-agg lomerates
o
Fig. 7. Estimated composite structure models of a granule. In the models. the white part denotes the CaC03 component and the black denotes and agglomerate of SiC particles. (Adapted from Sugimoto et al. [ 1 8].) (Reprinted with permission from Elsevier.)
•
•
To separate the SiC particles from the granule, the CaC0 3 was dissolved with a HCI solution. The SiC agglomerates are named b-agglomerates. Further treatment applied attempted to break up clusters of SiC that had been formed during the treatments by using EDTA · · · 2Na in order to break bonds due to the presence of calcium silicate (Ca 2 Si04) which might be produced by heating the granule composed of SiC and CaC03 . The solution added did not have any effect on agglomerates of pure SiC that had been formed in the granulation process. These SiC agglomerates contained in the b-granules are named c-agglomerates.
The structure of the binary composite granules made of CaC0 3 and SiC powders is discussed in terms of the size distributions of SiC agglomerates
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(c-agglomerates) contained in the granules. They grouped the structure into three classes (A, B and C) according to the characteristics of the dispersion of Sie agglomerates in a single granule. Each of these groups was further divided into two-subgroups according to the mean diameters of the a, b and c-granules (sizes Dp , dpb and dpc, respectively). 5. I MAGING TECHNIQUES
Following the definition of structure as the spatial arrangement of the basic components of a granule [1], a technique capable of measuring it should give the spatial arrangement inside the granule either in two or three dimensions. Some of the techniques that can provide this kind of information are (from Kohlus [1]): •
•
•
•
SEM (scanning electron microscopy): standard tool to image microstructures. It has a high spatial resolution and good material contrast, therefore allowing the identification of different phases present in a granule. It is only a two-dimen sional technique though, and in order to image internal structures they have to be exposed, requiring slicing of the specimen to be analysed. An example of the application of SEM in characterizing agglomerate morphology can be seen in Ref. [ 1 9]. I R (infrared) microscopy: in this case infrared signal can be used for material identification. It presents the same disadvantages as SEM, and its spatial reso lution is much lower. MRI (magnetic resonance imaging): non-destructive three-dimensional tech nique. Uses nuclear magnetic resonance properties of the material. High spatial resolution but its success depends on the nature of the specimen to be analysed. XRT (X-ray tomography): non-destructive three-dimensional technique. Utilizes the X-ray absorption properties of the material. It has the highest spatial reso lution and if the X-ray source is of sufficient quality, the contrast between different materials is sufficient to be able to identify them and analyse the agglomerate structure (Fig. 8).
5.1 . Quantification of g ranule structure
A segmentation step is necessary in order to quantify granular structure from images, meaning that each point in the image has to be classified as part of one of the defined phases [1]. In the segmentation process, the main area of uncertainty arises when partial voxeling happens. This effect happens when two or more phases occur in a single voxel. When only one phase is present in a voxel the signal intensity will be characteristic of that phase, but when more than one phase is present the signal
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(a)
(h)
Fig. 8. Comparison of MRI and XRT images of single granules. (a) Cross section through a single granule using MRI, nominal resolution 35 x 35 x 50 11m (from Sochon [20]); (b) cross section through a single granule using XRT, nominal resolution 4.25 x 4.25 x 4.25 11m.
will be a combination of the contributions of the different phases. The quantitative limitations imposed by the partial voxeling effect have been subject to study in fields like medical imaging, and different approaches have been used in order to quantify and correct for this problem (e.g., [21 ]). Most research into this topic has been done in the field of medical imaging using MRI as the technique. A set of five key descriptors in order to quantify granule structure are proposed in [1 ] using imaging techniques as the basis for this analysis and include the amounts of the phase volumes, their sizes and a homogeneity measurement. 5.2. XRT (X-ray tomography)
X-ray tomography was initially developed by Hounsfield and Cormack [22-24]. For developing computer-assisted tomography both Hounsfield and Cormack shared a Nobel Prize for medicine in 1 979, a field in which this method was most likely to prove useful. XRT has been primarily used in medical applications, and further developed and applied in other areas of research, such as geosciences [25,26] or materials sciences [27]. This has been possible due to the fast technical development of its basic components (X-ray source, detector, specimen holder). The main advantages of XRT over other imaging techniques is that it allows for a non-destructive, three-dimensional evaluation of the internal structure of objects, with a continuously increasing special resolution as its physical components develop (it is claimed that features in the nanometre scale can be resolved).
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XRT measures variations in material density generating images of different cutting planes of the material, and three-dimensional maps of density and ele mental distributions can be obtained with high resolution and short scanning time. A more detailed description of how the technique works can be obtained in Refs. [28,29,30]. Owing to its origin weil outside the powder technology area, its applications are only starting to be explored in this area, but the potential of the technique is immense after the selection of the most appropriate scanning configuration, the use of the most suitable X-ray sources and detectors, selection of an appropriate X-ray energy, possible calibration and minimization of the artefacts created by the technique. A very interesting application of XRT to particle technology can be seen in Ref. [31]. XRT is used to characterize the internal structure of agglomerates. Two "test" granules were created with two different binders and two different primary powders, by dropping a single droplet of binder onto a bed of powder. XRT showed different structures: loosely packed for non-cohesive powders that let the binder disperse through the powder surrounding the nuclei and densely packed with cohesive powders with which the nuclei contract towards themselves. Further work was done on the potential of XRT to characterize granular struc ture that would then be used as an input for DEM modelling to verify and validate existing models [32]. A model granule was created and XRT used to characterize the three-dimensional location of the primary particles and their respective dia meters (Figs. 9 and 1 0). Simulations of a spherical-shaped granule produced within the DEM code were compared to those of the XRT characterized granule, showing different behaviour between the two different agglomerates, due only to structural and shape differences. XRT has also been used to calculate the total porosity, pore size distribution and geometric structure of pores in pharmaceutical granules and compare the results to data obtained with more conventional methods (mercury porosimetry and gas adsorption) [1 1]. Results showed that XRT is less precise in the deter mination of total porosity than the more conventional methods, but on the other hand the main advantage of XRT is that it provides detailed information about the true pore geometry and distribution within the granules in a non-destructive man ner. It also accounts for internal occluded pores, although its resolution may not yet resolve narrow pore channels. In this work, the granule is considered as a two component system: air and solid matter, with no differentiation between binder and primary particles. This way, the images resulting form XRT analysis had to be transformed to binary ones, hence the need to find a threshold value (Fig. 1 1 ). The effect of the amount of binder in the structure and behaviour of granules under stress has also been studied using XRT [ 1 0]. For this analysis the cross sections provided by the XRT analysis of the sampies had to be transformed into binary images by choosing a threshold value. As before, this transforms the
1 20 1
Granule Structure 1.0 Onwn Z-2.87Omm
(a )
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1.0 •
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2.0
3.0
3.0
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Fig. 9. X-ray microtomographs o f model granule. (a) Side view, (b) t o ( d ) cross sections at different heights (from Golchert et 81. [32]). (Reprinted with permission from Elsevier.)
(b) Fig. 1 0 . Model granule. (a) DEM reconstruction based on XRT characterization and (b) original X-ray image of granule (from Golchert et 81. [32]). (Reprinted with permission from Elsevier.)
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Fig. 1 1 . Reconstructed cross-section images fram XRT analysis of two different granules done under different granulation conditions, showing the difference in structure. (Adapted fram Farber et al. [1 1 ].) (Reprinted with permission fram Elsevier.)
(b) Fig. 12. Reconstructed cross-section images fram XRT analysis of granules at two dif ferent granulation times: (a) 1 80 s and (b) 900 s (fram Bouwman et al. [ 1 0]). (Reprinted with permission fram Elsevier.)
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1 mm
/ (a)
Fig. 1 3. Shadow image (a) of a single granule with three reconstructed slices through it at different cutting planes. The light areas correspond to materials that attenuate X-rays less (white corresponding to the background air), the darker areas correspond to more atten uating materials.
sam pie in a two-component system: air and solid, without differentiating between solid and binder (Fig. 1 2). On a scale bigger than single-granule analysis, XRT has been used in the powder technology area to measure density variations in tablets [33] and on an even bigger scale to characterize powder mixing [34]. As it can be seen, not much work has been done using XRT to resolve the structure of single granules. However, the application of this technique to the powder technology area offers great potential to develop physical insight on the single-granule scale, which would offer a great deal of information about how the agglomeration process works. Current work using XRT is focused on how different processing conditions affect the structure of agglomerates [35], and different methodologies to extract as much information as possible from XRT analysis on agglomerates are being developed [35] (Figs. 1 3-1 5). With the increasing availability of high-quality X-ray sources (synchrotron ra diation) and the development of the physical instruments that compose an XRT scanner (detectors, specimen holders, X-ray sources and computing power) this non-destructive technique has the potential to become an extremely useful tool in power technology, aliowing the resolution of each individual phase within a single agglomerate.
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mm
1
mm
2
3
(a)
(b)
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(d)
Fig. 14. Central cross sections of sampies at different impelier speeds, taken after 1 0 min of granulation time: (a) 200 rpm, (b) 400 rpm, (c) 600 rpm and (d) 800 rpm.
(b)
Fig. 1 5. Central cross sections of sampies at different granulation times (constant impelier speed of 200 rpm): (a) 2 min, (b) 4 min, (c) 6 min, (d) 1 0 min and (e) 1 5 min.
5. 2. 1 . XRT sampIes of different materials and granulation conditions
The following figures show different structures obtained by using X-ray tomo graphy to visualize the internal structure of agglomerates made up of different materials and obtained under different granulation conditions.
Granule Structure
1 205
1 mm Fig. 1 6. Example o f three cross sections through a typical high-shear granule made of CaC03 and polyethylene glycol (PEG). An X-ray shadow image of the corresponding granule is shown in (a).
(a )
1
•
mm
Fig. 1 7. Example of three cross sections through a typical fluidized-bed granule made of glass ballotini and PEG. The corresponding X-ray shadow image is shown in (a).
Figures 1 6 and 1 7 show the typical structures of granules made under high shear conditions and in fluidized beds. High-shear granulation agglomerates are typically compact and rounded whereas fluidized-bed granules tend to show a much more opened structure, giving the products very different properties. Figure 1 6 shows three cross-sectional images of a typical high-shear granule made using calcium carbonate primary powder and polyethylene glycol as binder. Figure 1 7 shows cross sections of a typical fluidized-bed granule made using glass ballotini primary particles bound together using a malten polyethylene gly col spray in a fluidized bed. The structure is much more porous compared with that shown by the high-shear granule. Figures 1 8-22 correspond to cross section of granules manufactured from different materials and under different granulation conditions, showing some of the different internal structures that XRT has discovered within single granules. The linear attenuation coefficient of the materials plays a key role in being able to identify different phases within an agglomerate. The bigger the difference in the linear attenuation coefficient, the better the contrast that can be obtained. The
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Fig. 1 8 . Central cross sections of granules made with: (a) Na 2 C0 3 and zeolite as primary particles, bound together using LAS acid (proportions 63:23 : 1 4) in a food mixer; (b) pol ystyrene particles and a water binder which is subsequently evaporated off (binderless g ranule).
(a)
(b)
Fig. 1 9. Central cross sections corresponding to two granules extracted from the same batch. The g ranules were manufactured in a high shear mixer using calcium carbonate as primary particles and a mixture of polyethylene glycol and H PC as binder (liquid to solid ratio of approximately 0. 1 3). As it can be seen, the same conditions create two completely different structures.
linear attenuation coefficient for the different materials depends on the voltage applied to the X-ray source, hence the XRT scan can be tuned in order to obtain the best results. Figure 23 iIIustrates the different linear attenuation coefficients as a function of voltage for some materials commonly used in granulation.
1 207
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(a )
(b)
1 mm Fig. 2 1 . Central cross sections of high-shear granules after 30 s of granulation time. The granules are made of CaC03 and PEG added as solid flakes. In both cases, the gran ulations conditions are identical except the temperature, wh ich is of 60°C for the cross sections in (a) and of 80°C in (b).
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CaC03 CaS04 Na2S04 NaOH Na2C03 K2C03 polyethylene ZnO
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5. 2. 2. Application of X-ray tomography to the description of single granules: method development
XRT analysis on single granules provides a great deal of data in the form of a stack of adjacent cross-sectional images showing the internal microstructure of the sampie. A method developed to analyse these images to extract information about the structure of the granules can be found in Ref. [35] and is summarized here. The XRT images can be understood as a group of spatial coordinates (position vectors Xij, k = (ij,k)) with an associated greyscale intensity value, gij, k, which provides information on the material attenuation coefficient which is a function of the material density. Therefore, every pixel belonging to the granule can be ex pressed as a pair of position vectors with an intensity value, as seen in Fig. 24. The centre of mass of the particle, g, can be calculated by averaging the greyscale and the coordinates for every pixel within the granule for each of the cross sections obtained after XRT (equation (1 )) Once the centre of mass is known a scalar defining the position of all the granule pixels referred to it can be calculated (equation (2)). L: gij.kK x ij,k = --== (1) - L: gij.k ij,k .
_ _
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y
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24. Schematic diagram showing a stack of XRT slices of a granule as a three-di mensional array of spatial coordinates and greyscale i ntensity values.
Fig.
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i+1
Bin i+1
Fig. 25. Schematic representation of the binning procedure. The binning of the d ata con sists on dividing the radial axis in bins. The average greyscale value of all the pixels included in each bin is calculated and assigned to a radial distance corresponding to the middle point of the bin. This process is carried out in the three dimensions, by constructing spherical shells around the calculated centre of mass.
Once the scalar is known for each of the pixels in each image that belong to the granule all the images are transformed into pairs of greyscale intensity and radial distance to the centre of mass. The data is then binned by radius (see Fig. 25) and results can then be analysed in the form of radial distributions of greyscale intensity values. After the binning is done the data is in the form of pairs that can now be plotted. Many details have to be taken into account when carrying out this process, such as beam hardening, or the normalization of the radial distances. Details can be found in Ref. [35]. This method interprets the data from XRT in the form of radial dis tributions of greyscale intensities in within the granule as an indication of structure. As an example of the results obtained, Fig. 26 shows the radial profiles cor responding to the scans shown in Fig. 1 5. The granules used for this experiment were manufactured in a Zanchetta Roto Junior laboratory scale mixer, with a capacity of 1 0 L and a diameter of 30 cm. The unit contains a vertically mounted three-blade impeller which was set at a speed of 200 rpm and a lid-mounted chopper set at a speed of 1 400 rpm. Temperature is controlled through a water filled jacket and set to 60 oG. Granules were produced from Durcal 40 (an industrial form of comminuted calcium carbonate) as primary particles and po lyethylene glycol f1akes (PEG) as a binder. The PEG had an average molecular weight of 1 500 Da and a melting point of approximately 45 °G. This grade of Durcal (D40) has an Xso size of approximately 24 Jlm (volume basis). The binder was added using the melt-in technique, whereby the powder is preheated to the
121 1
Granule Structure
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desired temperature at a low impeller speed, and the binder is then added at once as a solid at room temperature at the start of the experiment. Each of the Iines in Fig. 26 corresponds to the average of five granules per sampling time and the x-axis has been normalized by dividing the radial distance by the radius of gyration. High-greyscale intensities correspond to higher ab sorption of the X-rays. As it can be seen, there is a consolidation towards the edge of the granules (higher density areas towards the edge), as weil as in creased density with increasing granulation time. This can be understood by looking at the cross sections, as they show a core of binder that decreases as granulation time goes, although it is still present even after 1 5 min of granulation time (due to the low shear at which the experiment was carried out).
REFERENCES [ 1 ] R. Kohlus, U nilever R & D, Vlaardingen, The Netherlands, presented at the 4th World Congress in Particie Technology, Sydney, 2002. [2] D.E. Fonner, G.S. Banker, J. Swarbrick, J. Pharm. Sei . 55 ( 1 966) 1 81-1 86. [3] G.K. Reynolds, CA Biggs, AD. Salman, M.J. Hounslow, Powder Technol 1 40 (2004) 203-208. [4] P.J. Rue, H. Seager, J. Ryder, I. Burt, I nt. J. Pharm. Tech. Prod. Manuf. 1 ( 1 980) 2-6. [5] H . Seager, P.J. Rue, I. Burt, J. Ryder, J . K. Warrack, I nt. J. Pharm . Tech. Prod. Manuf. 2 ( 1 981 ) 4 1 -50. [6] H. Seager, I. Burt, J . Ryder, P. Rue, S. Murray, N . Beal, J . K. Warrack, I nt. J . Pharm. Tech. Prod. Manuf. 1 ( 1 979) 36-44. [7] H . Seager, Manuf. Chemist Aerosol News ( 1 977) 25-35.
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[8] A. Samini, M . Ghadiri, R Boerefjin, A Groot, R Kohlus, Powder Techno! . 1 30 (2003) 428-435. [9] P.C. Knight, Powder Technol. 1 1 9 (2001 ) 1 4-25. [1 0] A M . Bouwman , M.J. Henstra, D. Westerman, J .T. Chung, Z. Zhang , A Ingram, J.P.K. Seville, HW. Frijilink, I nt. J. Pharm. 290 (2005) 1 29-1 36. [1 1 ] L. Farber, G . Tardos, J . N . Michaels, Powder Technol 1 32 (2003) 57-63. [ 1 2] M . H . Rubinstein , K. Ridgway, J. Pharm. Pharm. 26 ( 1 974) 24-29. [ 1 3] K. Ridgway, M . H . Rubinstein, J. Pharm. Pharm. 23 (Supp!.) ( 1 97 1 ) 1 1 S-1 7S. [ 1 4] K. Ridgway, M.H. Rubinstein, J . Pharm. Pharm. 23 ( 1 97 1 ) 587-589. [ 1 5] M . E. Aulton, M. Banks, I. Davies, Drug Dev. Ind. Pharm. 4 ( 1 978) 537-539. [ 1 6] M . J . Gamlen, H. Seager, J . K. Warrack, I nt. J. Pharm. Tech. Prod. Manuf. 3 ( 1 982) 1 08-1 1 4 . [ 1 7] M . Sugimoto, D. Tojima, K . Yamamoto, S. Rengakuji, J . Soc. Powder Techno!. Japan 36 ( 1 999) 685-691 . [ 1 8] M . Sugimoto, I. Takehiko, Y. Ken-Ichi, M. Tosihiaki, Powder Techno!. 1 30 (2003) 442-449. [ 1 9] L. Rodriguez, C. Cavailari , N. Passerini, B. Albertini, M.L. Gonzalez-Rodriguez, A Fini, I nt. J. Pharm. 242 (2002) 285-289. [20] R Sochon, MEnG Research Project, The University of Sheffield, 2005. [21 ] MA Gonzalez-Bailester, AP. Zisserman, M. Brady, Med. Image Anal. 6 (2002) 389-405. [22] G . N . Hounsfield, A method and apparatus for examination of a body by radiation such as X-ray or gamma radiation, Patent Specification 1 2839 1 5, 1 972. [23] A.M. Cormack, J. Appl. Phys. 34 ( 1 963) 2722-2727. [24] A M . Cormack, J. Appl. Phys. 35 ( 1 964) 2908-291 3. [25] RA. Ketcham, WD. Carlson, Comput. Geosci. 27 (2001 ) 381-400. [26] A Macedo, S. Crestana, Soil Tiilage Res. 49 ( 1 998) 249-253. [27] L. Salvo, P. Cloetens, E. Maire, S. Zabler, J.J. Blandin, J .Y. Buffiere, W. Ludwig, E. Boiler, D . Bellet, C. Josserong , Nucl. Instru m . Meth. Phys. Res. B 200 (2003) 273-286. [28] B . P. Flannery, H W. Deckman, w.G. Roberge, K.L. D'Amico, Science 237 ( 1 987) 1 439-1 444. [29] ASTM, ASTM designation E 1 44 1 -92a, Annual Book of ASTM Standards, Section 3, ASTM, Philadelphia, 1 992, pp. 690-7 1 3 . [30] J . Barruchei, J .Y. Buffiere, E . Maire, P. Merie, F. Peix, X-ray tomography in material science, Hermes Science Publications, Paris, 2000. [31 ] D.J . Golchert, L. Farber, L.X. Uu, J D. Uster, N.W. Page, Proc. World Congress of Particle Technology 4, Sydney, Australia, 2002. [32] D.J. GOlchert, R Moreno, M. Ghadiri , J. Utster, Powder Techonol . 1 43-144 (2004) 84-96. [33] I.C. Sinka, S.F. Burch, J.H. Tweed, J . C. Cunningham, Int. J. Pharm. 271 (2004) 2 1 5-224. [34] C.Y. Yang, X.Y. Fu, Powder Technol. 1 46 (2004) 1 0-1 9. [35] D . Barrera-Medrano, PhD Thesis, The University of Sheffield, 2007.
CHAPTER 26 M o r p h o l ogy a n d Stre n gth Deve l o pm e n t i n Sol i d a n d Sol i d ify i n g I nterparticle B ri d ges i n G ra n u les of P ha rm a ce utical P owders G . I . Tardos, 1 , * L. Farber, 2 D . B i ka 2 and J . N . M ichaels2
1 The City College of the City University of New York, New York, NY 10031, USA 2Merck and Co. Inc., West Point, PA 19456, USA Contents
1. 2. 3. 4. 5.
Introduction The key issues Background and literature review Extended summa ries of the contribution Experimental 5. 1 . Materials 5.2. Solutions 5.3. Bridges 5.4. Bridges between tablets 5.5. Granule formation 5.6. Granule strength measurement 5.7. Polymer films 5.8. Optical microscopy 5.9. X-ray powder diffraction 6 . Theoretical 6. 1 . Crush strength model 6.2. Re-crystallized bridge model 6.3. The auto-adhesion model (JKR theory) 7. Strength of solid bridges and dry granules: results and discussion 7. 1 . Slightly soluble systems: ethanol-based granulating solutions 7.2. Soluble systems: aqueous granulating solutions 8. Evolution of drying material bridges: results and discussion 8. 1 . Lactose bridges 8.2. Mannitol bridges 8.3. Granules 9. Conclusions 1 0. Forward look Acknowledgements Appendix: Prediction of dry bridge strength References
*Corresponding author. E-mail: [email protected]
Granulation Edited by A D. Salman, MJ. Houns/ow and J. P. K. Seville ( 2007 SV '
Elsevier
All rights reserved
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1 . I NTRODUCTION
Granulation is used extensively in industry to produce larger granules from fine powdery particles to improve flowability and appearance, reduce dustiness and to ensure thorough mixing of different ingredients. This last application is a very important unit operation in the pharmaceutical industry to produce non-segre gating mixtures of dry powders that would otherwise strongly segregate due to differences in size, shape, density and surface properties. The so-ca lied "wet" granulation process uses liquids that are dripped, sprayed or poured into a shearing mass of powder. The granulating fluid is typically composed of water and/or alcohol and may contain surfactants and polymeric binders such as hydroxypropyl cellulose (HPC) or polyvinylpyrrolidone (PVP). The process by which large dry granules are formed from fine powders by using liquid binders is quite complex. An accepted view holds that the liquid solution wets and spreads in the interstices between primary particles, forming liquid bridges that hold them together by capillary and viscous forces. These wet or "green" granules are subsequently dried and liquid eva po rates from the bridges to leave behind solid bridges or "necks" that impart mechanical strength to the dry granule. The process of solid bridge formation from pendular liquid bridges between particles is not unique to granulation and in fact plays a significant, albeit un wanted role in powder caking. In this case, liquid (water) is extracted from the surrounding atmosphere and condenses in the interstices between particles to form liquid bridges that subsequently dry. The result is the formation of large, strong lumps in the otherwise free-flowing powder that have to be broken to ensure powder flow. There is very little in the open literature that describes the morphology and properties of solid bridges that are formed between primary particles during granule formation and/or powder caking. While the strength of solid bridges has been recognized by Pietch [1] to have a strong influence on the tensile strength of agglomerates (granules and lumps), the intrinsic strength of the bridge itself was not studied in detail. To simplify the problem, the solid bridge is assumed, in most cases, to be non-porous and of similar chemical composition and physical prop erties as either the primary powder particles or the polymeric binder material used. This, however, is an overly simplistic view of a very complex problem especially if the original fine powder is itself soluble in the binder solution. In this case, the liquid partially dissolves some solid powder and forms liquid bridges of a very complex composition. Upon drying, these bridges exhibit intricate patterns of crystallization that are both time and composition dependent. This behaviour imparts complex morphology to the drying bridge as weil as time-dependent strength to the forming dry granule.
Interparticle Bridges in Granules of Pharmaceutical Powders
1 21 5
2 . THE KEY ISSUES
Figure 1 shows a schematic of a dry granule produced with granulating fluid containing a polymeric binder. Assuming some solubility of primary particles in the fluid, the liquid bridges are multi-component solutions that may form solid bridges of complex microstructure when dried. A few scenarios are shown in the figure. The bridge on the left consists of filaments of polymer, while the bridge on top contains both the polymer and a solidified crystalline bridge formed by re crystallization of the base powder. The bridge on the right is pure re-crystallized base powder. The bridge at the boUom is a combination of a small primary particle embedded in re-crystallized base powder. Clearly, these are only some of a large variety of combinations that could exist in reality. The questions that need to be answered are (i) what kind of solid bridge will actually form inside the granule as liquid eva po rates and further, (ii) what will characterize its strength, and (iii) where will it break when subjected to a mechanical load? Will it break by fracture of the body of the bridge or by adhesive failure at the interface with the primary particle? Answers to the above questions are central to the strength of formed dry granules since it impacts all further down-stream operations such as pneumatic transport, fluidization, comminution, tabletting, dissolution, etc. Knowledge of dry granule strength is also very important because it is a measure of the quality of bonding of various components inside the granule. Intimate bonding and good mixing of ingredients are both reflected in high dry strength. Since granule strength measurements are relatively simple, one gains a straightforward meas ure of important intrinsic granule properties that would otherwise require very sophisticated instrumentation and procedures to obtain. We describe in this chapter extensive work to study, on one hand, the strength and morphology of solid bridges inside dry granules of complex composition, and Solid Particles
� Polymer (binder) � bridge
C----.J
� �
Solidified bridge from saturated solution Dry particle (crystalline) bridge
Fig. 1 . Schematic of dry inter-particle bridges formed by co-precipitation of base powder and polymer.
1216
G . 1 . Tardos e t al.
on the other, the evolution in time of drying bridges made of complex solutions of binder and base powder. In the first part, we measure the strength of dried mannitol and lactose granules and characterize them with X-ray tomography and microscopy to shed light on the morphology, composition and attachment of the solid bridges to particles inside the granules. We also pro pose a theoretical framework based on crack-propagation theory to explain the findings. The sec ond part is a mostly experimental, micro-Ievel study of bridge solidification. It is weil known from previous work (see, for example, Ref. [2]) that it is very difficult to identically reproduce bridges formed between two small grains of powder due to variability in local shape and surface properties. For this reason, we describe model bridges with well-defined geometries to investigate the solidification kinetics and phase composition of drying bridges. The model geometries used in the present work are drying of a droplet on an inert substrate and evaporation from a solution stretched in the form of a pendular bridge between two flat plates. Further, evidence is given to show that real bridges between small particles actually exhibit similar behaviour as the model geometries mentioned above. 3. BACKGROUN D AND LITERATURE REVIEW
Wet granulation is an intermediate step in processing that leads to the manu facture of tablets. The process is used intensively in pharmaceutical applications because it assures homogeneous mixing of different powdery ingredients that otherwise would tend to segregate. It is also used in many other applications including the sOlid-detergent industry, to produce chemically active powders of several different ingredients that are free flowing and have pleasant appearance. The process of wet granulation entails the introduction of a liquid binder into a continuously moving and deforming powder bed of small particles contained in a processing vessel. Coalescence and growth of the initial powder feed results in the formation of "wet" or so-ca lied "green" granules [3-5]. Strong solid bridges that hold the granule together develop from liquid bridges during a subsequent drying step. In traditional granulation theory it is assumed that a binder such as a polymer is required to hold particles together once granules form in the granulator and are dried. It has been also suggested that even though some base powders may be somewhat soluble in the granulating liquid, the polymeric binder is still required to assure appropriate granule strength. Ongoing work performed in our laboratory shows however that base powders that are strongly soluble in the liquid binder play a major role in the formation and strength of solid bridges inside a granule [6]. Formation and strength of liquid bridges between fine particles has been stud ied extensively (see, for example, Ref. [2]. More recently, Pepin and co-workers [7] applied the knowledge gained from the study of these bridges to the strength
Interparticle Bridges in Granules of Pharmaceutical Powders
1217
of moist agglomerates such a s "green" granules. Solid bridges, o n the other hand have been studied to a much lesser extent. Shinohara's chapter in the Handbook of Powder Technology, Chapter 4 [8] dedicates to the subject a short subsection where the basic assumption is that the material in the solidified bridge has iden tical properties as the material of the particles that it holds together. Pietch [1] in his monograph on agglomeration processes takes a very similar approach. How ever, it has been shown by Tardos and Gupta [9] that solid bridge properties strongly depend on the composition and drying rate of the bridge itself. In the work described here (see also Ref. [1 0]) we measure the strength of granules containing bridges made of several ingredients such as binders and dissolved base powders and observe the microstructure of individual solid bridges and their time evolution directly in an effort to understand the factors that determine inter particle bridge strength. The choice of base powders used during the work described herein was dictated by funding and was justified by their extensive use in many pharma ceutical formulations employing wet granulation. Use of lactose and mannitol base powders for this investigation does not take away from the generality of the results since these materials exhibit overly complex structures and behaviour that may be generalized to other complex systems. Mannitol is a compound that can exist in several crystalline polymorphie forms and is soluble in water. Lactose is also water-soluble and exists in two anomeric forms (IX and ß); it can crystallize from aqueous solution into stable andjor unstable monohy drate or anhydrous forms or remain amorphous. Moreover, conversion from one anomer andjor crystal form of lactose to another may occur spontaneously even at room temperature depending on relative humidity (RH). It is also known that the source of lactose, even of the same grade but produced by different suppliers, can strongly affect the granulation process, suggesting that variability in phase purity between suppliers and form stability during processing may be significant. Hence, we also present results for these different materials to show that slight variations in composition can have a major impact on specific results. 4. EXTENDED SUMMARIES OF THE CONTRIBUTION
Work described in the first part of this chapter is an experimental study of solid bridges formed between particles inside granules of several pharmaceutical base powders such as lactose and mannito!. Particles are held together in the granule by re-crystallized bridges of the base powder and by several polymerie binders such as HPC and PVP. We studied an ethanol-based system where base pow ders were only slightly soluble in the binder and where the main binding agent was the polymer. We found that in this system bonds are very strong when the
1218
G . I . Tardos e t al.
polymer is present and compare to the strength of individual polymerie films. In the absence of polymer, dry bridges between particles attain the strength of the theoretical base powder crystal (Griffith strength). In a second, more complex aqueous system, both base powders and polymers were highly soluble. Bonding between particles in this case was due to a com bination of base powder-polymer bridges. We found that the bridge strength is a direct funetion of the total amount of liquid present in the original liquid bridge, i.e., large liquid bridges form stronger dry bridges. This is mainly due to the total amount of (solid) material present in the bridge upon drying. Compatibility be tween the polymerie binder and the base powder also strongly influences the strength of the bridge. When the polymer is ineompatible with the solid powder such as for example PVP and mannitol, the bond strength is decreased some times by as much as 50%. This is due to the fact that upon drying and re crystallization, the polymer and powder separate into different phases and the final bridge is weakened. This is especially true for the PVP film which in itself is brittle and therefore makes a weak bridge. When polymer and powder are com patible such as in the case of H PC and both base powders are used (lactose and mannitol), the bridge strength is increased when the polymer exceeds a certain eoncentration but does not reach either the strength of the pure polymerie film or the strength of the theoretical crystal. In part two of the work, an experimental procedure was developed to study directly the process by which liquid bridges between small particles in a granule form and solidify. The evolution of saturated solutions of lactose and mannitol in a liquid bridge was studied on a system situated on a microscope slide. Solidifi cation and crystallization kinetics and phase composition during and immediately following bridge formation were observed directly. It was shown that bridges on the mieroscope slide and in the granule behave very mueh the same regardless of the different length and diffusion-scales of the two systems. We found that solid bridge formation takes plaee in several eonsecutive but distinet steps. In the case of lactose, considerable shrinkage of the initial liquid bridge takes plaee prior to the onset of crystallization. Further bridge solidification at ambient conditions oceurs via simultaneous crystallization and vitrification within minutes. As a result, a "solid" or "green" bridge usually contains both a crystalline and a non-crystalline phase, the erystalline phase being predominately a-Iactose monohydrate. Most of the non-crystalline phase eventually converts to crystalline ß-Iactose but the process may take many hours or even days. Results for this process are compared for sam pies obtained from different manufacturers of eommercially available lactose. In the case of mannitol, different polymorphie forms erystallize as the dryingjcrystallization process progresses. A formed "solid" bridge usually eontains several polymorphs of mannitol. The relevance of the behaviour of the two model systems to a real granulation and tabletting process is discussed.
1219
Interparticle Bridges in Granules of Pharmaceutical Powders
5 . EXPERI MENTAL 5.1 . Materials
All materials used during this experimental program are described in Table 1 . Lactose monohydrate from three different manufactures, spray-dried lactose and the anhydrous lactose were used in different phases of this study in addition to one grade of mannito!. So me of their physical characteristics are given in Tables 1 and 2 where base powder (sugar) characteristics and polymer and surfactant properties are given, respectively. Granules for strength measurements were prepared from lactose (Meggle) or mannitol powders with ethanol (HPLC grade, Aldrich #27,074-1 ) or water (USP) as granulating fluids. In several experiments, Table 1 . Properties of mannitol and lactose
Powder Mannitol Lactose (monohydrate)
Lactose (spray dried) Lactose (anhydrous)
Origin SPI Polyols Roquette DMV Pharma Meggle Foremost Farms Foremost Farms Quest
Trade name/ grade SD-200 Roquette 35 Pharmatose 200M Granulac 200 NF Lactose 312 Spray dried Sheffuke Brad Lactose NF
Solubility in water es (g/ml) 0.18 0. 1 8 0.21
Solubility in ethanol Cs (g/ml) 0.01 0.01 0.0001
0.21 0.21
0.0001 0.0001
0.21
0.0001
0.21
0.0001
Table 2. Properties of H PC and PVP
Polymer
Grade
Molecular weight
Saturation concentration in water (%)
Polyvinylpyrrolidone (PVP) Hydroxypropyl cellulose (HPC)
K29/30
50 K
43
Klucel EXF
80-1 00 K
5-7
1 220
G.I.
Tardos et al.
hydroxypropyl cellulose (HPC) and polyvinylpyrrolidone (PVP) were used as polymerie binders (see properties given in Table 2). In a few experiments surfactants such as sodium lauryl sulfate, Polysorbate 80 and Triton X were also dissolved in the granulating fluid. 5.2. Solutions
Solutions were prepared using corresponding amounts of powder (lactose and mannitol, respectively) and H PLC grade water. Powder to water ratios were 1 :5.6 and 1 :4.6 for mannitol and lactose, respectively, i.e., the saturation limits for the excipients at 22°C [1 1 ]. Typically, the solution cleared after 1 5 min of stirring with magnetic stirrers, suggesting that the solutions were not completely saturated. These solutions are however referenced in the text as "saturated". In most cases, freshly prepared solutions were used within 30 min after mixing of the powder in water. In some cases, the same solutions were used after several days. No visual changes in the solution were observed during that period. 5.3. Bridges
Two different bridge geometries were investigated: (i) a single droplet on a flat glass slide and (ii) a liquid droplet stretched between two glass slides situated a small distance apart. The two geometries are depicted schematically in Fig. 2. For the first geometry, a droplet of saturated solution was dropped from a syringe from approximately 1 cm distance on a conventional microscope glass slide that had been cleaned by dipping it into a soap solution followed by rinsing in de ionized water and drying with compressed air (Fig. 2(a)). In some cases, several solid particles of either the same excipient or microcrystalline cellulose (Avicel PH1 01 ) were placed on the slide; these were added to study the effect of seeding the crystallization of the bridge. This situation is represented in Fig. 2(b). In the case of the bridge between two slides, a droplet was placed on a clean micro-
a
,
J
.
�
:2dZ ;{0J 4r c
glass silde
Fig. 2. Schematic representation of model inter-particle bridges: (a) droplet on a slide; (b) droplet on a slide with several grains of the original powder used as nucleating agents; and (c) bridge between two microscope glass slides.
1 22 1
Interparticle Bridges in Granules of Pharmaceutical Powders
scope slide with a syringe, and a second glass slide was brought into contact with the droplet. This resulted in immediate redistribution of the liquid and formation of a liquid bridge between the two glass slides. I mmediately after the contact and formation of the bridge, slides were pu lied slightly apart and fixed, so that the distance between the slides was constant through each drying experiment. Bridge geometry is shown schematically in Fig. 2(c). Overall, the distance bet ween slides va ried in a range 0.6-1 mm. The bridge microstructure was moni tored as it dried in each of these geometries using optical microscopy. Typical ambient conditions of these experiments were 23°C and 65% RH. 5.4. Bridges between tab lets
To investigate the microstructure and strength of inter-particle bridges directly, we produced macroscopic bridges between tablets of lactose or mannito!. The tablets, approximately 1 0 mm in diameter and about 6 mm thick, were com pressed in a manual tablet press at approximately 9.2 MPa to produce smooth surfaces with minimal change in porosity. A schematic representation of the formation process of liquid bridges between tablets is shown in Fig. 3. The tablets were fixed in a vertical position on two holders, and the bridge was formed by filling the gap with granulating fluid and several particles of base powder to ensure saturation. After drying at room tem perature and 25% RH for 48 h (at similar conditions as the granules themselves) the pair was broken in three-point bending mode using the Texture Analyzer as described below. The doublet made of two tablets with the solidified bridge between them was laid flat on its side and broken with the force applied on the middle of the bridge. Both X-ray tomography and microscope images were taken of the tablet pair before and after breaking and an example is shown in Fig. 4. One can easily see the measured, delimited area of the broken bridge in the figure; this value was used in the calculation of the bridge strength (Tables 3 and 4). Binder solution Liquid bridge
/
Double stick tape Holder
Tablets Fig. 3.
Holder
Grains of powder
Procedure to form macroscopic bridges between two base powder tablets.
1 222
G.I.
Tardos et al.
Photograph of broken bridge between two tablets showing the method of meas uring the area of the broken bridge used to determine its strength.
Fig. 4.
5.5. Granule formation
"Granules" produced with ethanol as the granulating fluid were prepared by compressing a bed of partieIes in a rectangular die as shown schematically in Fig. 5. Binder solution was added in an amount to ensure complete liquid saturation after consolidation. The consolidation pressure used ( 1 .5 MPa) was sufficient for liquid distribution and particle consolidation, but not enough for par ti e1e deformation. The advantage of this method is the formation of a single "granule" in the shape of a beam whose strength can be measured reproducibly [1 2 , 1 3] . The sam pie was dried at room temperature and 25% RH. Granules produced with aqueous granulating fluids were prepared by drop granulation in a unit specially constructed to produce very low shear during granule formation. The low-shear environment was required for these granules, since shear forces during agglomeration can overwhelmingly control granule properties. Granules produced under low shear more e1early exhibit the material factors that control their properties such as wetting and spreading of binder and the solubility of the primary partieIes in the granulating fluid. The "very low-shear granulator" (VLSG) used during this work was a horizon tally rotating bowl filled with powder to a specified level. The binder was fed to the bowl through a loss-of-weight system, a peristaltic pump and a straight copper tube of inner diameter of 1 /8 inch. During granulation, the granulating fluid drop lets gently fell onto the surface of the powder and were partially buried into the
Table 3 . Strength of dry granules formed in slightly soluble systems (ethanol-based granulating solutions)
Powder O"ta blet (Mpa)
Polymer
Mannitol (Roquette 35)
None PVP
H PC Lactose
None PVP HPC
Polymer concentration (wt.%)
0.7 1 .6 2.8 4.4 0.7 1 .4 0.75 1 .5 3.0 0.73 1 .5
a Back-calculated using equation (6) with b
(equation 6 ) a O"cr
Cs (g/g)
(h q
0.010 0.01 7 0.026 0.038 0.054 0.01 7 0.024 0.000 0.0075 0.01 5 0.030 0.0073 0.01 5
0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.37 0.37 0.37 0.37 0.37 0.37
=
0.288 and c
=
0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.40 0.40 0.40 0.40 0.40 0.40
O"G (MPa) (equation 7)
O"sb
(MPa)
(MPa)
0.47 3.10 3.40 3.40 4.50 2.00 2.80 0. 1 6 1 .00 1 .64 1 .81 2. 1 1 2.87
5.87 34.0 31.2 26.6 30.4 1 9.7 26.6 1 6.7 20.4 1 6.8 35.6 35.7
4.43
O"film
(MPa)
20--40
1 0-20 20--40 1 0-20
1 1 .5
0.42.
->.
N N VJ
Table 4. Strength of dry g ranules formed in very soluble systems (water-based g ranulating solutions)
Powder Mannitol ( SD200 )
Polymerl surfactant None Triton X SLS Polysorbate 80 PVP
HPC
Lactose
Polymer concentration (wt.%)
None PVP HPC
1 .0 1 .0 1 .0 3.0 3.0 3.0 5.0 7.0 1 0.0 30.0 3.0 3.0b 5.0 5.0b 30.0 5.0
Cs (gIg)
rl i q
(Jsb (MPa) (equation (MPa) (measured) (measured) 6) a
0. 1 8 0.18 0.18 0.1 9 0.1 9 0.19 0.21 0.21 0.21 0.23 0.25 0.28 0.48 0.21 0.21 0.23 0.23 0.21 0.51 0.26
0.19 0.23 0.28 0.212 0.207 0.2 1 8 0.19 0.24 0.31 0.31 0.32 0.31 0.37 0.33 0.22 0.42 0.34 0.12 0.38 0.45
0.69 0.69 0.69 0.69 0.69 0.69 0.65 0.65 0.65 0.65 0.65 0.65 0.60 0.70 0.70 0.64 0.70 0.60 0.60 0.64
8
a Back-calculated using equation (6) with b = 0.717 and b Granulating solution pre-saturated with mannito!.
c = 0.5.
(Jer
0. 1 2 0.14 0.17 0.057 0.083 0.075 0.095 0.12 0. 1 3 0.1 5 0.20 0.24 0.43 0.21 0. 1 5 0.54 0.24 0.13 2 . 03 1 .12
1 .14 1.10 1.10 0.46 0.69 0.59 0.65 0.61 0.54 0.57 0.68 0.75 0.54 1 .03 1 .09 1 .45 1 .06 1.11 2.32 2.49
(JG (MPa) (equation
7)
(MPa) (measured)
(Jfilm
(MPa) (measured) (Jta blet 0.80
4.98
20-40
0.73 1 0-20
0.93 2.25
4.70
1 .03 20-40 1 0-20
1 .47 G) :-
-l tIl a. 0 (f) C1l ..... Q) :-
I nterparticle Bridges in Granules of Pharmaceutical Powders
1 225
I F = 50 kg .. 0.01 mmls v =
Fig.
5. Procedure to form beam-shaped granules (test specimens).
Fig. 6.
Typical granules produced in the very low-shear granulator (VLSG).
powder with a metallic plough. The liquid tended to wet a region of the powder and spread radially to form a spheroid-shaped granule approximately 5-8 mm in diameter. Upon the formation of up to 1 00 granules, the remaining ungranulated powder was separated by sieving from the granules, and the granulated material was then dried in an oven at 50°C. Pietures of granules produeed in this manner are shown in Fig. 6, while an X-ray miero-tomographie seetion of a granule is shown in Fig. 7. The granules are quite homogeneous but not very dense, with porosities of the order of about 70%. Granule moisture eontent was measured direetly by weighing the wet and dry granules, and also by using an automatie gravimetrie moisture analyzer (Sartorius LabServe MA-40).
1 226
G . I . Tardos et al.
Fig. 7. X-ray tomographie eross-seetion of a granule produeed in the VLSG.
5.6. Granule strength measurement
To measure the dry strength of the beam-shaped granule bars, three-point bending measurements were performed using the TA-XT2i HR Texture Analyzer (Texture Technologies Corp., Scarsdale, NY). The pracedure is described in more detail in Bika e t 81. [6]. The crush strength was determined fram Ref. [14]: (Jcr =
3LFmax 2fw
(1)
where L i s the distance between the fulcrums, Fmax the load at breakage, t the thickness of the beam and w its width (see Ref. [1 5] for more in-depth analysis). The crush strength of spheroidal granules formed fram the VLSG were meas ured by compression between parallel platens. Prior to measurement, granules were maintained in a humidity-contralled box at room temperature and 25% RH for 48 h. Dry granules were crushed at 25% RH and ambient temperature using the Texture Analyzer. During each measurement, the total force, F at breakage and the diameter of the granule, dg, were determined. Assuming the granule
Interparticle Bridges in Granules of Pharmaceutical Powders
1 227
cross-sectional area to be circular in the plane of the punch, the crush strength is calculated by 4F (2) (Jer = ndg2 -
The crush strength can also be a function of the contact area between the particle and the platen of the instrument. In the present application, however, it was assumed that the granules are very brittle and relatively weak and failed by crack initiation caused by tension in a diametrical plane parallel to the applied force. This assumption was supported by the fact that most granules were seen to split into two halves and no plastic impressions were observed on the fractured granules. 5.7. Polymer films
Mechanical testing of the polymers used in this study was conducted on free standing films. To produce an H PC film, about 1 0 mg of 5% by weight polymer solutions in water was poured into the dish and allowed to dry at ambient tem perature and 1 5% RH. After drying, films were conditioned at ambient temper ature and 1 5% RH prior to testing. This procedure resulted in semi-transparent, macroscopic crack-free, freestanding films with thickness ranging from 0.05 to 0.5 mm. The final moisture content was measured by loss on drying at 50°C for 48 h to be about 1 .2% by total weight. The films were removed from the casting surface, cut into strips or dumb-bell specimens of standard sizes and subjected to tensile testing. All sampies were tested using the Texture Analyzer according to ASTM and ISO standards [1 6, 1 7]. All tests were performed at room temperature and 1 5% RH. The elongation force was recorded as a function of the displacement. The film stress was calculated from the relationship: F (3) (Jf = A
where F is the measured peak force preceding breakage, and A the initial cross sectional area of the specimen. The reported film strength values are averages of 1 0 tensile measurements. PVP films were cast on plastic weighing boats laid with Teflon paper as a substrate. 50% wjv PVP solutions were poured into the dish and allowed to dry and equilibrate at room temperature and 1 5% RH. The resulting freestanding films were from 0.3 to 0.6 mm in thickness, yellow, transparent and fragile. During drying numerous cracks developed throughout the film. The moisture content was found to be 6-7% by loss on drying at 50°C for 48 h. To perform tensile testing of these sampies, smalI, non-cracked pieces were isolated and tested under three-point
G . 1 . Tardos et al.
1 228
bending using the Texture Analyzer. Average values of 1 0 tests are reported for the tensile (bend) strength calculated using equation (1 ). 5.8. Optical m icroscopy
An Olympus SZX 1 2 stereomicroscope and an Olympus BH1 2 microscope equipped with standard image acquisition cameras and software were used for "Iow-magnification" and "high-magnification" observations, respectively. 5.9. X-ray powder d iffraction
Powder X-ray diffraction (PXRD) measurements were made with a Bruker Siemens D5000 using Cu Ka radiation (tube operated at 40 kV/40 mA). The hardware included a parallel beam mirror, 1 and 0.6 mm diverging beam splitters and a graphite monochromator. The powder sam pie was lightly packed into the standard sam pie holder and the top surface was smoothed using a glass micro scope slide. Data were collected in a 20 range from 5 to 45° under lock-coupled scan mode with a step size of 0.02° and a step time of 1 s. To study the granule's crystalline structure and to identify the crystalline phases present in the dry body, some granules were kept either in a humidity-controlled dry box (1 5% RH/23°C) or on a bench top (�65% RH/23°C). After several days they were hand ground with a mortar and pestle and analysed by XRD.
6. THEORETICAL 6. 1 . Crush strength model
We reproduce here the equation to predict crush strength of a granule (Jcr from the knowledge of the solid bridge "neck" strength between particles (Jsb, which is derived in the appendix (equation (A.7)): (Jcr = nb2
1
-
I:
--
I:
[ ] Cs Vb
�
ppop/8
2c
(Jsb
(4)
here is the porosity, es the total dissolved solids concentration in the liquid bridge and Vb the liquid bridge volume. The quantities Pp and dp are the primary particle density and diameter, and b and c are numerical coefficients given in Table A 1 . The basic assumptions in the above equation are that particles forming the agglomerate are spherical and the solid bridge is formed by evaporation of a liquid bridge that conserves its shape as it shrinks and precipitates its dissolved I:
1 229
I nterparticle Bridges In Granules of Pharmaceutical Powders
solids. We rewrite the above equation by using the "liquid ratio" defined as P Vb V liiq = Pb Vp = Pnb b/6 p pp �
(5)
where P b is the binder density. With this, equation (4) becomes 2c 1 2 c C = nb 8- :3 Lliiq O"sb O" r _
where CL
=
[4n ]
I::
(6)
Cs /Pb is the solid concentration in the binder solution expressed in gIg.
6.2. Re-crystal lized bridge model
If the base powder has appreciable solubility in the granulating fluid, the solid bridges will be formed by re-crystallization (or precipitation) of the base powder as the bridge dries. An upper limit to the strength of this bridge can be calculated assuming that the final bridge is a non-porous brittle solid with the same mecha nical properties as the base powder. In this case, the bridge tensile strength is described by the Griffith model [1 5]: O"G
=
2EOY J ne
e
-
( 7)
here Eo is the Young's modulus, y the surface energy and a characteristic defect size. In calculating the ideal lactose and mannitol solid bridge strength, we used Young's moduli of compacts tabulated by Rowe and Roberts [1 8]. These values were extrapolated to zero porosity using the expression developed by Boccaccini [ 1 9], = Eo(1 - cf, where is the compaci's porosity and k = We also assumed that the characteristic flaw size equals the primary particle size. The values of Eo and y used to calculate the mannitol and lactose bridge strengths are listed in Table 5 .
E
Table 5.
2.
Surface energy and Young's modulus for mannitol and lactose
Material Mannitol Lactose monohydrate (Meggle)
a Values
[;
y
(mN/m)
2
67 7
1 7.5 1 9.0
from Rowe a n d Roberts [ 1 8] a t zero porosity and corrected for particle size according to the expression E 1 /E2 = (dp2/dp1) 1 /3 as proposed by Kendall et al. [20] . Par ticle size used, dp = 30 Jlm for both powders.
1 230
G . I . Tardos et 81.
6.3. The auto-adhesion model (JKR theory)
In the absence of dissolved solids in the liquid bridge (no polymeric binder or evaporative re-crystallization), dry granules are held together by auto-adhesive forces and the compact's strength can be calculated by [21 ] : (Je
y
= 24.7z(8) (j p
(8)
assuming that the interfacial fracture energy is equal to the surface energy, y, and the characteristic defect size equals the primary particle size, C = dp . The porosity function in equation (8) can be taken as either z(s) = 1 3.3(1 - 8)4 (according to Kendall et al. [20]) or Z(8) = (1 - 8)/8 (according to Rumpf [22]). We used in this study the second expression but it can easily be shown that for accepted values of the porosity the two expressions give values that are almost identical. 7. STRENGTH OF SOLID BRI DGES AND D RY GRANU LES: RESULTS AND DISCUSSION 7. 1 . Slightly soluble systems : ethanol-based g ranulating solutions
We consider first the granules made with ethanol-based granulating fluids. Since lactose is essentially insoluble and mannitol is only sparingly soluble in ethanol, we expect primary particle solubility to have little or no effect on dry bridge strength. The bend strengths of these granules are plotted in Fig. 8. For all systems, the strength increases with polymer concentration in the granulating fluid. The dry bridge strength corresponding to each point in Fig. 8 was calculated using equa tion (6) and tabulated in Table 4. In these calculations, we assumed that the primary particles were in contact (a = 0), which is consistent with the way that the beam-shaped granules were made under compression in a die; according to Table A 1 , this gives b = 0.288 and C = 0.42. The liquid ratio (liq was estimated from the measured porosity of the compact and the respective densities of the liquid and powder, according to equation (5). We assumed complete saturation of the liquid bridges with mannitol or lactose at the start of drying and took the solid concentration es to include all dissolved solids present in the liquid bridges. Also given in the table is the theoretical Griffith strength of solid bridges in the mannitol beam made with pure ethanol calculated from equation (7), the tensile strength of pure H PC and PVP films, and the strength of a macroscopic bridge containing PVP and lactose between two lactose tablets. The Griffith model is inappropriate for lactose granulated with pure ethanol, because lactose is essentially insoluble and therefore does not re-crystallize to
Interparticle Bridges in Granules of Pharmaceutical Powders
1 231
6 �======�----1 Binder: PVP
�
:iE
5
'& c: � 3
s::.-
4
U;
E 2 ca GI
m
1
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produce solid bridges. For this reason, we calculated the theoretical compact strength using the JKR model employing equation (8). This yielded a value of 0 . 1 MPa, in good agreement with the measured strength of 0 . 1 6 MPa and sup ports the assumption used in the calculation of bridge strength that the primary particles were in contact. The bend strength of mannitol granulated with pure ethanol was 0.47 M Pa, approximately three times larger than the JKR strength. This indicates that this granule is held together by dry mannitol bridges. The strength of the bridge is calculated with equation (6) to be 5.87 MPa, in reasonable agreement with the theoretical ("Griffith") strength of 4.43 MPa. In the lactose granules made with ethanol-based polymer solutions, the dry bridges consist of pure polymer, and the bridge strength should be independent of polymer concentration. The increase in granule strength with polymer con centration shown in Fig. 8 should be simply due to an increase in the volume of the dry bridge as more polymer is avaifable. As seen in Table 4, the bridge
1 232
G . I . Tardos et al.
strengths of the lactose granules made with HPC and PVP show no consistent variation with polymer concentration. This supports the validity of the crush strength model, i .e., the result in equation (6). The bridge strengths of the man nitol granules made with polymerie binders also do not vary consistently with polymer concentration, suggesting that these bridges also behave Iike pure poly mer bridges. This is consistent with the low mannitol solubility in ethanol. The bridge strength of the PVP bridges in the mannitol and lactose granules lies within the range of values measured for free films and macroscopic bridges between tablets. This indicates that the microstructure of the granule bridges does not differ significantly from either that of the model bridge between tablets or that of the freestanding films. The strengths of the HPC bridges are consist ently larger than that of the free films. The reason for this difference is not understood. Interpreting the above results in view of the schematic of bridges in Fig. 1 , it is Iikely that in the granules made with ethanol-based polymer solutions, the bridges that form between particles are of the polymerie filament kind. The filaments may not be as thin or disconnected as in the figure, but their strength is essentially that of the polymer film. In this case, the mechanical properties of the polymers control the strength of the dry granules. 7.2. Soluble systems: aqueous granulating solutions
We now consider lactose and mannitol granules made with water and aqueous polymer or surfactant solutions. Mannitol and lactose both exhibit significant sol ubility in water; therefore, re-crystallization of each sugar may be expected to contribute to the strength of bridges in the dry granules. Dry crush-strength data obtained for granules made with mannitol are plotted in Fig. 9 as a function of the liquid ratio, 'iiq . Aside from the very strong granules obtained with 5% H PC and 30% PVP, bridge-strength values cluster around a straight line through the origin. As shown, addition of PVP to the granulating fluid reduces the dry bridge strength especially at the lower concentrations of polymer of 3-7%. Similarly, granules made with aqueous surfactant solutions fall con sistently below this line, indicating that the dried granules are weaker than those made without surfactant, regardless of the type of surfactant used. As shown by the black dia monds in Fig. 9, the crush strength of mannitol granules made with water in the VLSG increases Iinearly with 'iiq . This is con sistent with assuming a value of 2c = 1 in the crush-strength model, equation (5). Referring to Table A1 , this corresponds to values of a = 2% and b = 0.7 1 7. The non-zero value of the dimensionless separation distance between primary par ticles, a, is consistent with the granules being formed at low shear, e.g. , not fully consolidated. Bridge strengths, ()sb, corresponding to all points in Fig. 9 for all
1 233
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granules made in the VLSG were computed using these model parameters and are tabulated in Table 5. Also included in the table are values of the tensile strength of pure polymer films and bend strengths of macroscopic bridges bet ween mannitol tablets. As seen in Table 5, there is generally good agreement between the bridge strength calculated from equation (6) and the bend strength of macroscopic bridges between mannitol tablets. This indicates that the macroscopic bridge is a good model of the microseopie bridges between primary particles in the granules. All dry bridge strengths are, however, much smaller than the measured strength of pure polymer films or the theoretical Griffith strength. The discrepancy between the theoretical (Griffith) and measured strength of pure mannitol bridges can be understood by considering the micrograph of a macroscopic bridge shown in Fig. 1 0. The Griffith strength was calculated assuming that a bridge is a single crystal of mannito!. As shown by the micrograph, the microstructure is much more complex, and it seems likely that the polycrystalline nature of the bridge signifi cantly reduces its tensile strength. The dry bridge strength of mannitol granules made with a 3-wt. % HPC granulating solution was equal to that of granules made with pure water, 1 . 1 M Pa. These bridges are an order of magnitude weaker than the pure H PC films. This indicates that co-precipitation of HPC and mannitol forms a dry bridge with the mechanical strength of a pure mannitol bridge. This would be consistent with a solid bridge in which the H PC and mannitol are fully separated, with the
1 234
G . I . Tardos et al. Ungranulated mannitol particles
Fig.
Recrystallized mannitol bridge between particles
1 0. Scanning electron micrographs of mannito!.
mannitol part dominating the bridge strength. Increasing the H PC concentration to 5% by weight increases the bridge strength by 0.4 MPa, suggesting that the HPC part of the bridge begins to confer additional strength at this concentration. Consistent with this, the bend strength of the macroscopic bridge between man nitol tablets also increases with increasing HPC concentration. This suggests that HPC filaments form between primary particles that are sufficiently strong to reinforce the underlying mannitol bridge. Pre-saturating the 3-wt. % HPC granu lating solution with mannitol had no impact on dry bridge strength suggesting that the liquid bridges become saturated with mannitol in situ during granule formation. Granulating with aqueous PVP solutions produced dry bridges that were con sistently weaker than the pure mannitol bridges. The bridge strength exhibited no consistent variation with PVP concentration between 3 and about 30 wt.% . The tensile strength of the bridge was similar to that of a macroscopic bridge between mannitol tablets but 40 to 80 times smaller than that of a pure PVP film. These results indicate that co-precipitation of PVP and mannitol produces dry bridges that are significantly weaker than pure mannitol bridges. This could reflect poor adhesion between mannitol and PVP in the heterogeneous bridge. Surprisingly, addition of surfactants to the granulating solution also produced dry bridges that were substantiaily weaker than the pure mannitol bridges. Triton X 1 00, SLS and Polysorbate 80 each reduced bridge strength (relative to pure water) by 40-50%. This indicates that improving the wetting of primary particles by reducing the interfacial tension of water, which is expected to allow the granulating fluid to distribute more effectively between the primary particles [23], does not translate into higher strength solid bridges.
Interparticle Bridges in Granules of Pharmaceutical Powders
1 235
Table 5 also contains a much more limited set of data for lactose granules. This shows that the bridge strength of the pure lactose bridges is also about 1 . 1 M Pa. This value is approximately five times smaller than the theoretical (Griffith) strength but equal to the bend strength of a macroscopic bridge between lactose tablets. In contrast to mannitol, bridges formed from 5% H PC and 30% PVP granulating solutions are both approximately twice as strong as the pure lactose bridge. While these are significantiy weaker than the corresponding pure polymer films, they do show that the polymers augment the strength of the solid bridges holding the lactose granules together. Referring back to the schematic picture of the granule in Fig. 1 , we observe that bridges in the aqueous system, where both polymer and base powder are highly soluble in the liquid, are of the kind depicted on the right. These are re-crystallized bridges that contain both base powder and polymer, intermixed to some degree both physically and spatially. Morphology, strength and attachment to the original base powder particle result from a complex combination of wetting and crystal lization characteristics of the new material formed between the particles. Micro graphs of fracture surfaces of polymer films, depicted in Fig. 1 1 , show clearly that each of the aqueous systems studied in this work produces bridges with sub stantially different microstructure. The aqueous surfactant-mannitol and PVP-mannitol systems differed quantita tively from the other aqueous systems in that the presence of surfactant and polymer reduced the tensile strength of the dry inter-particle bridges. This sug gests that it might be useful to categorize polymers and surfactants in terms of their "compatibility" with the base powder(s) when the base powder solubility in the granulating solution is appreciable. H PC can be considered to be compatible with both lactose and mannitol as adding it to the granulating solution yields dry bridges of equal or greater strength than that of the pure sugar (lactose or mannitol) bridge. In contrast, PVP is incompatible with mannitol since all dry mannitol bridges con taining PVP were substantially weaker that pure mannitol bridges. Similarly, Triton X 1 00, SLS and Polysorbate 80 are each incompatible with mannitol.
8. EVOLUTION OF DRYIN G MATERIAL BRIDGES : RESULTS AND DISCUSSION 8.1 . Lactose bridges
Figure 12 illustrates a typical evolution of a saturated lactose monohydrate (Meggle - Granulac 200, see Table 1 ) bridge between two glass slides upon drying at room temperature and medium conditions of RH ('"'- 50%). The glass slides are situated perpendicular to the li ne of view and the black rings apparent in the figure represent the outer edges of the liquid bridge. The rings occur due to
1 236
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5% HPC/water films
Tardos et al.
30% PVP/watcr films
Mannitol
Lactose
Fig. 1 1 . Scanning electron micrographs of fracture surfaces produced from saturated so lutions of mannitol or lactose with H PC or PVP.
the curvature of the air/liquid interface at the centre of the bridge and as it touches the glass slide. The liquid material inside the bridge is totally transparent. The liquid bridge initially shrinks considerably during the first 60 min. The ratio of the bridge diameters measured at the beginning and at the end of this step varies from about 33% for the central (transparent) cross-section to about 48% for the top or boUom of the bridge (shown as black rings in the figures). Crystallization starts at the liquid/substrate interface close to the outer diameter of the bridge as indicated by arrow "1 " in the image taken after 1 60 min. This crystalline region grows relatively rapidly (see images taken at 2 1 0 and 260 min). Crystallization also starts at other locations at the liquid/substrate interface close to the outer diameter of the bridge (see points "2", "3" and "4"). Typically, several such clusters grow at the interface. Their growth occurs relatively fast (of the order of tens of minutes). However, the central part of the bridge remains crystal free. To illustrate this, the glass slides were pulled apart from each other after 260 min; this resulted in some necking in the middle of the bridge followed by separation in
Interparticle Bridges in Granules of Pharmaceutical Powders
• •
Fig. 1 2.
1 237
•
Solidification of a lactose liquid bridge (starting material: spray-dried lactose).
the middle of the bridge, see side view on the image taken at 1 0,OOO min, ro tated). An image of the boUom part taken at 265 min (immediately after sepa ration) demonstrates that the central part of the bridge is non-crystalline. Finally, this central part also crystallizes, although the timescale for this process is sev eral days. To study the process in more detail, the "droplet on a slide" configuration was employed with the same grade of lactose and under similar ambient conditions as used before and this can be seen in Fig. 1 3. The droplet undergoes the same major changes as the bridge described above. First, the liquid droplet shrinks due to loss of water through evaporation. Typically in this case however, the droplet height and not its outer diameter decreases (this is due to the absence of ad hesion to the top slide that in the previous case keeps the bridge height constant).
1 238
Fig. 1 3.
G . 1 . Tardos et al.
Solidification of a droplet on a slide (starting material: spray-dried lactose).
This can be seen from the change in shadows in the pictures of the droplet taken at 0 and 1 0 min. At so me point, crystals nucleate at the interface close to the outer perimeter of the droplet as shown by the arrows. These crystals grow and serve as nucleation centres for other crystals, which grow as a cluster and form a
1 239
I nterparticle Bridges in Granules of Pharmaceutical Powders
crystalline region: Fig. 1 3 shows a few of these regions after 30 min. Several such clusters can be observed to grow at the interface. The growth of such crystalline regions occurs relatively fast (of the order of minutes). Further crystallization proceeds much slower, as shown in the droplet images taken at 30 min and 1 5 h. Moreover, the central part of the droplet remains crystal free for a much longer time. In the end, it also crystallizes as seen in Fig. 1 3, which shows an image of a dried drop after 20 days. Typical XRD patterns for droplets at different stages of solidification are shown in Fig. 14. The upper pattern corresponds to the initial powder that consists of crystalline a-Iactose monohydrate and amorphous lactose. After the rapid crys tallization at the drop perimeter (1 h), the majority of crystals are a-Iactose mono hydrate. Also notable is the high background in the range of 1 8-22° 28 that indicates the presence of amorphous lactose. After 6 h, the peaks at 1 0.5 and 21 ° corresponding to anhydrous ß-Iactose are weil detected in the spectra. After six days, the ß-Iactose peaks increase considerably while the peaks of a-Iactose remain practically constant. Additionally, the background decreases, confirming some conversion of amorphous phase to ß-Iactose. The typical evolution of a nucleated crystal at the drop periphery is shown in Fig. 1 5. A single plate-like crystal nucleates in the region of the outer diameter and starts to grow. Eventually, its shape evolves, and other crystals nucleate in a space adjacent to this crystal and grow further. The cluster grows very fast as can be inferred from the time depicted, in minutes, on the micrographs in Fig. 1 5. We used XRD to compare the crystalline content of solidified droplets formed from solutions of several different powders. These powders contained either well defined initial crystalline forms (either a-monohydrate or ß-anhydrous) or mixtures
initial powder
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1 240
Fig. 1 5 .
G . I . Tardos et al.
Solidification of a lactose droplet on a slide (starting material: spray-dried lactose).
of crystalline and amorphous forms (such as spray-dried lactose). We found, as c1early depicted in Fig. 1 6, that the initial crystalline forms present in the powder do not affect the final composition of the dry droplets since all crystallized droplets contained the same mixture of ß-anhydrous and a-monohydrate phases. We were initially concerned that different phases would nucleate differently in liquid bridges between real particles than in droplets on a glass surface. To test this, we studied the effect of seeding the droplet with lactose or microcrystalline cellulose particles (another common pharmaceutical excipient used in binder granulation). Insertion of particles of a-Iactose or microcrystalline cellulose (Avicel PH 1 0 1 ) into the centre of the droplet did not have any effect on the nucleation
I nterparticle Bridges in Granules of Pharmaceutical Powders
5
15 20, deg
10
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1 241
25
Fig. 1 6. XRD pattems of a-monohydrate (am) and ß-anhydrous (ß) lactose powders and of re-crystal lized bridges made from the solutions of these powders (am-r and ß-r, respectively).
process. Nueleation always started at the edge of the droplet, and the crystalline clusters grew there first. If a partiele of either of the solids was placed elose to the edge, nueleation usually started at this point simultaneously with one or several other places at the outer boundary. This suggests that neither lactose mono hydrate nor microcrystalline cellulose partieIes promote crystallization of the sat urated liquid bridge. Since the glass substrate also serves as a nueleation site for heterogeneous nueleation, the major factors determining nueleation appear to be the solution concentration and the curvature of the liquid/air interface. Comparison of the solidification of three droplets prepared from a-Iactose monohydrate obtained from different manufacturers is shown in Fig. 1 7. Figures 1 7(a)-(c) are micrographs obtained under polarized light at different time points. Crystalline matter appears white. It can be seen, that after 1 0 min all the periphery in the Foremost lactose droplet and most of the periphery in DMV lactose droplet are crystallized, whereas only several crystals are present in the Meggle droplet. The central part of the droplets remains crystal free in all droplets. After 35 min, the DMV droplet has the most crystalline material, while the Meggle has the least. Additionally, some crystals are seen in the central portion in the DMV droplet. As was shown before, the majority of the crystalline material at this point is a-Iactose monohydrate. The morphology of crystalline regions is similar in the DMV and Foremost droplets. In contrast, only isolated crystalline regions are present in the Meggle droplet, similar to what was observed for spray-dried lactose. Moreover, the amount of crystalline material in Meggle is much smaller than in the other two droplets at this point in time, indicating that the crystallization rate is persistently slower in the Meggle droplet. After days, XRD analysis reveals that the amor phous regions in all droplets crystallize such that they contain approximately the same amount of anhydrous ß-Iactose. However, the crystallization rate of
4
1 242
G.1.
Tardos et al.
(a)
(b)
(c) Fig. 1 7. Solidification of lactose liquid bridges produced with lactose from different man ufacturers (F, Foremost; M, Meggle; D, DMV).
ß-Iactose in the Meggle drop was also slower. It can be concluded from these experiments that the crystallization kinetics of both (X-monohydrate and an hydrous ß forms as weil as the morphology of developing crystalline regions are clearly different for lactose from Meggle and from two other manufacturers. These results demonstrate that formation of inter-particle bridges from lactose solutions is a multi-step process that continues for extended periods of time and results in formation of a bridge of complex phase composition and microstructure. This is shown schematically in Fig. 1 8. During the first step, Le., shrinkage, the saturated liquid solution of lactose in water becomes supersaturated. Volume changes during the first step were measured using changes in the bridge dia meter since the bridge height was kept constant. If a bi-conical shape of the
Interparticle Bridges in Granules of Pharmaceutical Powders
1 243
Lactose: schematic of the solidifying bridge
o Non-crystalline (liquid)
(X-lactose monohydrate
• ß-Iactose, althydrous Fig. 1 8 .
Schematic representation of lactose bridge evolution.
bridge is assumed as a first approximation, the bridge contains only about 1 7% of the initial volume at the end of the shrinkage step. Assuming that the loss is caused by water evaporation, 88% of the initial water is lost during this step. Thus, at the end of the first step, the bridge loses most of its water and becomes a highly supersaturated lactose solution. This supersaturated solution appears to be a very viscous, plastic body. The properties of this plastic bridge strongly affect and may even control the mechanical properties of granules at this stage. The next step in the solidification process is crystallization of thermodynami cally stable a-Iactose monohydrate from the supersaturated solution. Only part of the bridge volume crystallizes during this step. Typical crystallization times range from minutes to a few hours. The rest of the material remains amorphous. Finally, during the next step, the amorphous part of the bridge crystallizes as anhydrous ß-Iactose, producing a bridge that contains both crystalline anomers. However, the timescale of this last conversion is days and sometimes even weeks. It is known that a-Iactose monohydrate is the thermodynamically stable cry stalline form of lactose at room temperature in air. ß-Iactose anhydrous is meta-stable below 96°C in air, although it is quite stable kinetically at room tem-
1 244
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perature. 80th a- and ß-Iactose are thermodynamically stable in water at room temperature, and the equilibrium a-to-ß ratio is 65/35. Hence, when a-Iactose is dissolved in water, part of it converts to ß-Iactose and both anomeric forms are present in the solution. Similarly, when ß-Iactose is dissolved in water, part of it converts to a-Iactose. Typical a-to-ß conversion and equilibration times vary from seconds to a few hours depending on the presence of impurities in water. If water is allowed to eva porate very slowly so that the equilibrium is maintained in the solution, only a-Iactose crystallizes. In this case, crystallization is controlled by thermodynamics. Unlike the process described above, bridge solidification does not occur at equilibrium since both a- and ß-Iactose phases are detected in the solidified bridge. Evaporation of water results in a solution in which lactose exists at very h igh degree of supersaturation before it starts to crystallize. The fact that nu c1eation agents do not play any significant role in growth of a-crystals suggests that its crystallization kinetics are fast only at a high degree of supersaturation. The presence of ß-Iactose crystals suggests that the high supersaturation affects either the a-to-ß equilibrium ratio in the solution or the kinetics of ß-to-a muta rotation, so that ß does not transform into a during/after a crystallization but rather crystallizes itself. Additionally, the high supersaturation level of the solution means a lack of available water that may make crystallization of anhydrous ß-Iactose favourable over crystallization of the hydrate. Crystallization kinetics of ß-Iactose are however much slower than those of a. As a result, the amorphous part of the bridge transforms slowly into crystalline ß-Iactose. Thus, initial solidification of lactose bridges occurs on a timescale comparable to that of granulation and drying, and then continues for relatively long periods of time, causing changes in bridge microstructure and, potentially, to its physical and chemical properties. It is known that a- and ß-Iactose have different physical properties and different affinity to water vapour (see, for example, Ref. [1 1 ]). Thus, the phase composition in a lactose bridge may affect not only the mecha nical properties of granules, but also dissolution, stability and mechanical prop erties of tablets made of these granules. Since compression of tablets is often completed within hours after the granulation process is completed, crystallization of ß-Iactose may occur in the tablets weil after their fabrication. Thus, the cry stallization processes in the bridge may affect the granulation process and, po tentially, milling, compression, and the mechanical and dissolution performance and stability of tablets. That the kinetics of crystallization and the morphology of developing crystalline regions are c1early different for lactose from different manufacturers may be ex plained by the fact that the crystallization process is often sensitive to the pres ence of even minor quantities of impurities. It can be expected therefore, that lactose from d ifferent manufacturers contain different impurities and/or different levels of those impurities.
I nterparticle Bridges in Granules of Pharmaceutical Powders
1245
8.2. Mannitol bridges
The "droplet on a slide" configuration was studied first. After several minutes from the time the droplet of a saturated solution was deposited on a slide, the first man nitol crystal nucleated and started to grow (see Fig. 1 9(a)). Apparently, a relatively low supersaturation level is required at room temperature to provide nucleation and growth of mannitol crystals. Similar to lactose droplets, nucleation of mannitol takes place at the periphery of the droplet (see images taken at 1 5 and 20 min). Initially, relatively narrow plate-like crystals nucleate and grow from a nucleation site in different directions along the droplet surface. Typically, the fastest growing crystallites were the ones that grew along the perimeter of the droplet, with a rate of up to several millimetres per minute. Eventually, the habit of the newly nucle ated crystals changes from plates to needles. These grow as a bunch, along the liquid droplet surface towards the centre of the droplet. Finally, after practically no free liquid is left on a slide, white agglomerates start to grow vertically on top of the bunches, closer to the periphery of the droplet. They grow "out of plane" of the droplet, normal to the surface. It is interesting to note that they start growing after most of the liquid has evaporated and only some residual liquid is observed be tween the needles. The solidification process is typically complete after 30--40 min. A typical image of the solidified droplet at higher magnification is shown in Fig. 1 9(b), in which different crystalline morphologies are clearly revealed. It is known that at least three crystalline polymorphs of D-mannitol (IX, ß and b) exist [1 11. It was reported by Kim et al. [241 that each form has a distinct mor phology when produced by evaporation of an aqueous solution: needle-like crys tals (b), parallelepiped-like (ß) and large (up to several millimetres) lichen-like crystals growing normal to the solution surface (IX). The presence of these crystal forms in the solidified droplet was confirmed by XRD. Crystals with similar morph ologies were extracted from several solidified droplets, grouped, gently hand milled and analyzed by X-ray powder diffraction. Corresponding XRD patterns are shown in Fig. 20. Three morphologies exhibit distinct diffraction patterns. The phase that forms at the beginning of the process is ß-mannitol, the same crystal form as the mannitol powder itself. However, both the needles and agglomerates that form subsequently have different diffraction patterns, corresponding to predominantly b and IX-mannitol, respectively. Thus, all the three forms of mannitol are formed sequentially in the water droplet during solidification. As a result, a bridge formed from mannitol solution consists of all three polymorphs and has a very complex microstructure. We estimated that the b- and IX-polymorphs constitute, at the end of the process, a larger volume of the crystallized droplet than the initial ß-polymorph. The formation of a solid bridge from a mannitol solution between two glass slides is shown in the Fig. 21 . Initially, the liquid bridge shrinks. Then, similar to the case of the "droplet on the slide", ß-crystals nucleate and grow at the periphery of the bridge (Fig. 21 (c), arrow #1 ). Their growth, however, is limited to the outer perimeter
1 246
G.I. Tardos et al.
a.
I -plates; 2-needles; 3-agglomerates
b. Fig. 1 9. Solidification of a mannitol droplet on a slide.
of the bridge/glass interface. At some point, bunches of needle-like o-crystals (see Fig. 21 (e), arrows #2) also nucleate at the glass/bridge interface and start to grow. However, they grow mainly along the liquid surface from one glass slide to another,
1 247
Interparticle Bridges in Granules of Pharmaceutical Powders
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contacting the upper slide as they grow. Finally, a hollow solid bridge forms. It consists of several bunches of needles which are b-mannitol (Fig. 21 (g), arrow #2). Also at some later point, white agglomerates form and start to grow at the periphery of the foothold of the bridge (see Fig. 21 (e) and (g), arrow #3). It Can easily be seen from the above that, similarly to lactose, formation of inter particle bridges from mannitol solutions is a process that results in bridges of complex composition and microstructure. Apparently, the supersaturation level of the solution controls what polymorph will nucleate and which will grow faster. It is likely that the phase composition of the bridge as weil as the size of the crystallites and their interconnection depends on drying kinetics, although this needs to be investigated further. It can be expected that the phase composition and micro structure of the bridge will control its mechanical properties. Lastly, different polymorphs may have different behaviour when exposed to various environmental conditions. It was reported during some earlier work in our laboratory, for example, that water suspensions of Pearlitol (an rx/ß mixture) result in rapid conversion of rx into ß. Thus, if a bridge is composed of several polymorphs, transformations may occur if the bridge is exposed to different environmental conditions. This may affect not only the mechanical properties of the bridge, but also the physical and perhaps chemical properties of tablets made of the granules containing these bridges. 8.3. Granules
To verify that the "glass slide approach" used during this study is relevant to solid bridges formed in real agglomerates, granules were fabricated from ß-mannitol and DMV (X-lactose monohydrate using saturated solutions of the initial materials
1 248
G . I . Tardos et al.
Fig. 21 . Solidification of a mannitol liquid bridge: (a)-(f) top view of the bridge during solidification, (g)-(h) top and bottom glass slides separated after solidification, respectively.
as granulating fluids. XRD patterns of initial and granulated material are shown in Fig. 22. XRD confirms that anhydrous ß-Iactose appears after granulation in the (X-lactose monohydrate granules. Similarly, 6-mannitol is present in the dried ß-mannitol granules. Thus, although the typical bridge dimensions/diffusion
Interparticle Bridges in Granules of Pharmaceutical Powders
1 249
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distances in granules are in the range of microns and not hundreds of microns as in the model experiments on the glass slide, the composition of the dried bridges is similar. The fact that the newly re-crystallized material in granules differs in crystalline form (mannitol) or in both the crystalline form and the anomeric form (lactose) from the initial material confirms earlier conciusion from the experiments
1 250
G.I.
Tardos et 8/.
with bridges on a glass slides that nueleation on the surfaees of the primary partieles does not dominate erystallization in the drying liquid bridge. 9. CONC LUSIONS
From the study of the ethanol-based system, where base powders were only very slightly soluble in the binder, we found that the main binding agent was the polymer. I n this system, bonds between partieles are very strong when the poly mer (HPC or PVP) is present and eompare to the strength of individual polymerie films sinee there is no interferenee to the film formation from the base powder. In the absence of polymer, dry bridges between particles attain the strength of the theoretieal erystal (or Griffith strength) sinee in this ease there is no interferenee from the polymer to the erystal formation of the base powder. In the more eomplex system where both the base powders and polymers were highly soluble in the binding solution, bonding between particles was due to a eombination of base powder-polymer bridges. The strength of these bridges is eharaeteristie for eaeh system and depends mainly on the total amount of liquid present in the original liquid bridge, i.e., large liquid bridges form stronger dry bridges. Compatibility of the polymerie binder with the base powder strongly influenees the strength of the bridge. When there is ineompatibility as in the ease of mannitol with PVP, the bond strength is deereased sometimes by as mueh as 50%. When the polymer is eompatible with the base powder, the bridge strength is inereased but does not reaeh either the strength of the pure polymerie film or the strength of the theoretieal erystal . A simple theoretieal model based o n the assumption that solid bridges formed by evaporation of liquid bridges between particles maintain their shape, proved to be quite accurate in predieting solid bridge neck strength in both ethanol and water-based systems. It was also shown that a good measure of the strength of the bridge eould be obtained experimentally from solid bridges made between two tablets of similar base powders. This is important sinee such measurements in this case are relatively simple and the strength measurement is straightforward and unambiguous. From the second part of the study it was found that solidification of liquid bridges and formation of dry bridges from saturated solutions of lactose and mannitol is a complex, multi-step proeess. Dry solid bridges contain polymorphs andjor anomeric forms that differ from those of the starting material. Lactose bridges that form from an aqueous solution of IX-lactose monohydrate consist of IX-lactose monohydrate and anhydrous ß-Iactose. A very viscous su persaturated solution is formed as an intermediate step, but eonverts slowly into the crystalline anhydrous ß-Iaetose. The crystallization processes in the liquid bridge start to oeeur within several minutes but then continue for several weeks,
I nterparticle Bridges in Granules of Pharmaceutical Powders
1 25 1
causing slow changes in bridge composition and microstructure. Significant differences in crystallization kinetics were observed in bridges made from lactose produced by different manufacturers. Similar conclusions can be drawn for man nitol bridges formed from an aqueous solution of crystalline ß-mannitol. These consist of three polymorphs and have complex microstructure. 1 0. FORWARD LOOK
The approach proposed in this work allows the study of the micro-kinetics of bridge development as weil as its phase composition and morphology at different stages of solidification. It can be used in further studies with more complex bridges. The effect of polymeric binders such as PVP and H PC on the micro structure and evolution can be undertaken using similar tools. The study of the presence of surfactants or alcohol in the solution on phase composition and crystallization kinetics should also be undertaken. The effect of drying conditions on crystallization kinetics and bridge phase composition should also be studied, since we have observed that drying conditions can have a strong effect on both crystallization kinetics and bridge phase composition. To complete the picture of drying bridges between particles, mechanical prop erties of individual bridges must also be measured. This is an ongoing compli mentary study where, in addition of observing bridges between two microscope slides, we also measure their strength in situ as the bridges evolve in time. The correlation of strength development and morphology as the bridge dries and crystallizes is also being studied. ACKNOWLEDGEMENTS
The authors wish to thank Dr Jim Zega and Dr Larry Rosen for fruitfuI discussions. APPENDIX: PREDICTION OF DRY BRI DGE STRENGTH
Dry, solid bridges may form between particles as a result of a multitude of proc esses such as sintering, melting, dissolution, evaporation and re-crystallization of the material. During bridge formation, particles' surfaces deform, melt, dissolve and/or re-crystallize and therefore the initial shape of the particles at the contact point changes while a new solid with distinct properties is formed. The force required to separate two particles after a bridge has formed between them can be calculated from (A.1 )
1 252
G.I. Tardos et al.
where rsb is the radius of the narrowest portion of the bridge or "neck" and (Jsb its strength. The assumption in equation (A. 1 ) is that the bridge has a cylindrical shape and breaks at its narrowest point (and not at the interface with either partieIe). The force and the corresponding stress can be either tensile (com pression or tension) or shear. To calculate the strength of an agglomerate (J, from the knowledge of the inter partieIe force F, one usually uses the well-known correlation proposed by Rumpf [25]: (A.2) Here Z is a porosity dependent function given as Z(8) = (1 -8)/8 by Rumpf and Z(8) = 1 3.3(1 -8)4 by Kendall [26]. The difficulty in this computation is the prediction of the "neck" size rSb, and assigning a value to its strength (Jsb. For the case of a solid bridge formed between two spherical particles from the evaporation of a liquid bridge, simple considerations of conservation of mass yield a correlation between the initial volume of the liquid bridge Vb, the volume of the dry bridge, GSVb and the size of the dry "neck". Here Gs is the solid concentration in the liquid. Pietsch and Rumpf [22], gave a semi-analytical solution to this problem (see also Ref. [27]). Their result can be rewritten in the following form: (A.3)
where b and c are coefficients given in Table A 1 as a function of the partiele-par tiele separation distance a/dp• These values were obtained by assuming that the bridge volume is small (as would be the case for solid bridges formed by evap oration) and the meniscus of the bridge surface is circular. A simple analytical solution can also be developed [28] by considering the bridge between partieIes to remain cylindrical during evaporation, i.e., the meniscus remains straight. This yields a somewhat over-predicted solid Table A 1 .
Coefficients b and c i n equation (A.3)
a* = a/dp
b
c
0 1% 2% 3%
0.288 0.381 0.717 1 .1 7
0.21 0.326 0.494 0.68
1 253
I nterparticle Bridges in Granules of Pharmaceutical Powders
bridge neck size: (A.4) Equation (A.4) gives for a/dp = 0 an exponent of c = 0.25 and a coefficient b = 0.44 or only slightly higher then the more precise equation in Table A 1 . This is demonstrated in Fig. A 1 , where equations (A.3) and (A.4) are plotted for a/dp = O.
The difference is due to the shape of the bridge that neglects the concave part of the outer meniscus and assumes this to be linear. A further correlation between the size of the neck rSb/dp is obtained from an experimental result by Pepin et al. [7]. Rewriting their result (from their Fig. 9) gives: (A. 5) Comparison of the results from equations (A.3) and (A.5) is given in Fig. A2. It can be seen that for bridge volumes larger than 0. 1 , equations (A.3) and (A.5) give values that are quite close, but at sm aller bridge volumes the dimensionless distance a* = a/dp, starts to have an influence. In a different approach by Kudoh et al. [29], the ratio of the solid bridge neck diameter and the particle diameter, dp, is given by
0: 0 2. � u (]) Z (/) (/) (]) c 0 ·00 c (])
E (5
Analytical Solution _ _+--_ 1
y=0.446 x /4
0.1
I
y 0.288 X 021 R2 0.987 =
=
0.01 -j---t----+---+--,---i 1 E-06 0.00001 0.0001 0.001 0.01 0.1 10 Dimensionless Bridge Volume, VS/[( Dp3)/8)] Fig. A1 .
Neck radius vs. bridge volume for touching particles.
1 254
G.I.
Tardos et 81.
1 0 ,----,--�--_.--�
-<>- a*=O
..J::
�
ü)
� () Q) z
-- a*=0.01 -- a*=0.02 � a*=0.03
-
- Simons et al. [2002]
0.1 +----+�����--�--�
h*=0.421 Vb*1/3 ---+---t---+---j--j 0.01 +0.1 0.0001 0.001 0.01 10 1 00 Bri d ge Volume. b* Fig. A2.
Analytical solution for bridge neck radius.
(sb
dp
=
[ ] X12x X
1 .64 eS vb
pp�/8
(A.6)
here es is the solid concentration in the liquid, Vb the initial volume of the liquid bridge as above, Pp the density of the particle and the dimensionless ratio of the rate of drying over the dissolution rate constant. One has to note that none of the equations above give a linear dependence of the bridge neck radius on the total bridge volume as in equation (A.6), casting some uncertainty on the accuracy of this correlation. Using equations (A. 1 ) and (A.3) in (A.2) (Rumpfs equation ) yields a direct dependence of the granule strength on the volume of the liquid bridge and the solids concentration as folIows: O"cr
1 - [; = nb2 [;
[
es Vb
] 2C
�
pp u p/8
O"sb
(A.7)
We can use equation (A. 7) as written to evaluate O"cr or we can use it to calculate the bridge strength O"sb from the measured granule strength O"cr since the crush strength is usually easier to measure. Plotting the granule strength as a function of the dimensionless bridge volume yields the best fit for b and c, as suming the total porosity of the granules remains constant. The model can, then, be validated by comparison of the calculated bridge strength with independent measurements of the strength of the materials involved in bridge formation.
Interparticle Bridges in Granules of Pharmaceutical Powders
1 255
Nomenclature
c
CL Cs
dp
dg E
Eo
F k L
rliq
t
Vb w
Crack or defect size (m) Dimensionless solid concentration in binder solution (gIg) Solid concentration in binder solution (g/cm 3) Particle diameter (m) Granule diameter (m) Young's modulus (MPa) Zero porosity Young's modulus Load to failure (N (or g)) Numerical exponent Distance between fulcrums in three-point bending (m) Liquid ratio defined in equation (4) Thickness of bending object (m) Liquid bridge volume (cm 3) Sam pie width (m)
Greek y < v
Pp Pb (Jfilm (Jc (Jcr (Jsb (Jta blet (JG
Surface tension (N/m) Porosity (dimensionless) Poisson's ratio Particle denisty (g/cm3 ) Binder density (g/cm 3 ) Thin-film tensile strength (MPa) Auto-adhesive compact strength (MPa) Granule crush strength (MPa) Solid bridge strength (MPa) Strength of bridge between two tablets (MPa) Griffith strength (MPa)
REFERENCES [1] [2] [3] [4] [5] [6]
W. Pietch, Wiley, New York, 1 99 1 , pp. 3 1 -32. B. Ennis, J. Li, G . I . Tardos, R. Pfeffer, Chem. Eng. Sci. 45 ( 1 990) 3071 -3088. G . I . Tardos, I . M . Khan, P.R. Mort, Powder Techno! . 94 ( 1 997) 245-258. B.J. Ennis, G . I . Tardos, R. Pfeffer, Powder Techno! . 65 ( 1 99 1 ) 257-272. S.M. Iveson, J . D. Litster, K. Hapgood, B.J. Ennis, Powder Techno!. 1 1 7 (200 1 ) 3-39. D. Bika, G . I . Tardos, S. Panmai, L. Farber, J . N . Michaels, Powder Techno! . 1 50 (2005) 1 04-1 1 6. [7] X. Pepin , S.J.R. Simons, S. Blanchon, D. Rossetti , G. Couarraze, Powder Techno! . 1 1 7 (200 1 ) 1 23-1 38. [8] K. Shinohara, Chapter 4 in: "Handbook of Powder Science and Technology", M . E . Fayed, L. Otten (Eds.), Chapman & Hall, New York, 1 997, p p . 1 1 9-1 20.
1 256
G . 1 . Tardos et 81.
[9] G . 1 . Tardos, R Gupta, Powder Techno!. 86 ( 1 ) ( 1 996) 29-35. [ 1 0] L. Farber, G . 1 . Tardos, J . M . Michaels, Chem. Eng. Sci. 58 (2003) 451 5-4525. [ 1 1 ] Pharmaceutical Excipients 2000, American Pharmaceutical Association and Pharmaceutical Press, 2000. [1 2] M . J . Adams, D. Williams, J.G. Williams, J. Mater. Sci. 24 ( 1 989) 1 772. [1 3] B.J. Ennis, G. Sunshine, Tribo!. I nt. 26 ( 1 993) 3 1 9. [14] T. H . Courtney, Mechanical Behaviour of Materials, McGraw Hili , New York, 1 990. [1 5] D.G. Bika , M. Gentzier, J . N . Michaels, Powder Techno!. 1 1 7 (2001 ) 98-1 1 2. [ 1 6] ASTM Standard 0638-01 : Standard Test Method for Tensile Properties of Plastics, January 1 , 200 1 . [ 1 7] ISO 527-1 , Plastics - Determination of Tensile Properties-Part 3 - Test Conditions for Films and Sheets, August 1 , 1 995. [ 1 8] RC. Rowe, RJ. Roberts, Advances in Pharmaceutical Sciences, Academic Press, New York, 1 995. [ 1 9] A.R Boccaccini, J. Mater. Sci. LeU. 13 ( 1 994) 1 035. [20] K. Kendall, M. Adams, B. Briscoe, In: Tribology in Particulate Technology, 10P PubIishing, Bristol, 1 987, p. 1 1 0. [21 ] K.L. Johnson, K. Kendall, A.D. Roberts, Proc. Royal Soc. A324 ( 1 97 1 ) 301 , [1 26]. [22] W.B. Pietsch, H. Rumpf, Chem. Ing. Tech. 39 ( 1 967) 885-893. [23] B.C. Hancock, P. York, RC. Rowe, Int. J. Pharm. 1 02 ( 1 994) 1 67-1 76. [24] A.1. Kim, M.J. Akers, S.L. Nail, J . Pharm. Sci. 87 ( 1 998) 931 and references therein. [25] H. Rumpf, Particle Technology, Chapman and Hall, London, 1 975 [26] K. Kendall, in: M. Adams, B. Briscoe (eds), Tribology in Particulate Technology, 10P Publishing , Bristol, 1 987, p . 1 1 0. [27] P. Pierrat, H .S. Caram, Powder Techno!. 9 1 ( 1 997) 83-93. [28] D. Maugis, J. Adhesion Sci. Techno! . ( 1 987) 1 05-134. [29] N. Kudoh, M. Kuramae, T. Tanaka, Kagaku Kogaku Ronbunshu, Vo!. 2, p. 625, 1 976, referenced in: K. Shinohara (ed .), Fundamantal and rhelological properties of powders, Chapter 4, in: M . E . Fayed, L. OUen (eds), Handbook of Powder Science and Technology, Chapman and Hall, 1 997, p. 1 44.
CHAPTER 27 Liq u id B ri dges i n G ra n u les Stefaan J . R. S i mons *
Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom Contents
1 . Introduction 2. Adhesive forces arising from liquid bridges 2. 1 . The Young-Laplace equation 2.2. Numerical solution of the Young-Laplace equation 2.3. The rupture distance of a liquid bridge 2.4. The static liquid bridge force: capillary and surface tension effects 2.5. The viscous contribution to the general force expression 2.6. Rupture energy of a liquid bridge 3. Direct observation and measurement of liquid bridge behaviour 3. 1 . The micro-force balance 3.2. Particle wettability in relation to the geometry of a liquid bridge: approximated liquid bridge profiles 3.2. 1 . The toroidal and parabolic models 3.2.2. Comparison of the toroidal and parabolic approximations 4. Relating particle-binder i nteractions to granule behaviour 4. 1 . Compression of plastic agglomerates 4.2. Experimental validation of the hardness equation 4.3. An industrial case study: predicting pharmaceutical granulation performance from micro-scale measurements 4.3. 1 . Granulation of paracetamol 4.3.2. Binder selection criteria 4.3.3. Experimental procedure 4.3.4. Results and discussion 5. Conclusions References
1 . Introduction
1 257 1 259 1 260 1 262 1 265 1 266 1 270 1 271 1 273 1 274 1 276 1 278 1 283 1 292 1 294 1 298 1 302 1 303 1 303 1 305 1 308 1312 1315
Many granulation processes rely on the addition of a binder (which is either sprayed, poured or melted onto a bed of dry particles) that will spread over the *Corresponding author. E-mail: [email protected]
Granulation Edited by A.D. Salman. M.J. Hounslow and J. P.K. Sevil/e ( 2007 Elsevier B.v. All rights reserved
1 258
S.J.R. Si mons
particles on mixing to form liquid bridges between them. These bridges then create sufficient adhesion between the particles to enable them to stay together as nuclei agglomerates, which then go on to pick up more "wet" particles and grow and compact to form distinct granules. The growth mechanisms may aiso include breakage and deformation. In most cases, the liquid bridges go on to form solid bonds, either by drying, reacting or simply changing phase with temper ature. Such processes can be referred to as wet or binder-induced granulation. Liquid bridges can be defined as lens-shaped liquid menisci (with the curved surface in contact with another fluid) supported by at least one solid surface [1]. The configuration assumed by a liquid bridge between two particles is termed "pendular". Tumbling drums, fluidised beds and high-shear mixers are devices commonly used to provide the appropriate conditions of agitation to the bed of powder, yet introducing a mechanical shear stress that may rupture bonds al ready formed within an agglomerate. The growth rate of granules, which depends on the equilibrium between bond formation and bond disruption, is therefore influenced by the type of apparatus used for granulation. It is clear that the modelling of pendular liquid bridges and their behaviour is of great importance to wet granulation processes. The prediction of growth kinetics, for instance, frequently includes parameters such as the strength of agglomer ates [2,3], which in turn depends on the strength of individual liquid bridges [4]. In the published literature, work has concentrated on both the experimental inves tigation of the force developed by a liquid bridge [5,6] and on its modelling [7]. To describe the configuration assumed by a liquid bridge, some models assume that the liquid-to-solid contact angle remains either constant or zero throughout sep aration and that the liquid bridge shape can be described by either a toroidal approximation or a catenoid function [8]. In other approaches, the liquid bridge shape is not presupposed and results from the minimisation of the system free energy for a constant volume condition using the Young-Laplace relationship [7,9]. Very few models in the literature take into account the wetting hysteresis of the liquid on the solid surfaces [ 1 0, 1 1 ] . In addition to bridge strength, several workers have also measured and the oretically predicted the pendular bridge rupture distance [7]. The rupture distance is a parameter which is required for discrete element modelling (DEM) of granules in the pendular or funicular state where bridges will break and reform as granules deform during collisions. The post-rupture liquid distribution on the particles is also important. Dabros and van de Yen [ 1 2] discussed the dispersion of droplets at the surface of similar sized spheres in agitation. When the size, shape and surface energy of the particles vary, the liquid distribution is expected to change. This is demonstrated experimentally through the occurrence of wetting segre gation when powder mixtures of varying surface energy are co-granulated [1 3] .
Liquid Bridges in Granules
1 259
In many industries, granulation processes are often applied to mixtures of powders in which the component solids do not exhibit the same surface prop erties. Large discrepancies in surface energy create problems during granulation, as powders can be selectively wet at the expense of others [14]. In the phar maceutical industry, most drugs have a low surface energy and therefore are poorly wet by common granulation liquids [1 5]. However, the behaviour of pen dular liquid bridges when the liquid-to-solid contact angle is large has not been extensively covered in the literature. The majority of models dealing with pendular liquid bridges either assume zero [1 6], small [8] or fixed contact angles [9, 1 7]. When the wetting hysteresis is important, the solid-liquid interfaces at the boundaries of the liquid bridge can remain constant with particle separation until a critical separation is reached, at which point the bridge liquid recedes from one particle surface and the corresponding solid-liquid interface reduces. The re duction of the solid-liquid interfacial area with particle separation is accentuated by low wetting hysteresis that drastically alters the shape of pendular liquid bridges, their rupture distance and post-rupture liquid volume distribution on the solid particles. In this chapter, the current theory on liquid bridges between pairs of particles will be presented, followed by a detailed review of the work carried out by the author and co-workers at University College London on the modelling of liquid bridges and the relationship between the micro- and macro-scale granule be haviour, developed from direct measurements and observations of liquid bridges between smooth spheres and between real pharmaceutical powders and binders. 2. ADHESIVE FORC ES ARISING FROM LIQUI D BRI DGES
The formation of wet agglomerates is governed by the balance between the rupture energy of liquid bridges and the particle kinetic energy, and hence a knowledge of the liquid bridge adhesive force (also referred to as the strength of the liquid bridge), in relation to the type of liquid binder and the surface properties of the particulate, is required for a fundamental understanding of granule growth. Liquid bridge forces arise from both capillary and surface tension effects, which are static forces, and from a viscous component, which becomes more important during dynamic separation. The force that holds the particles together is ulti mately related to the ability of a liquid binder to wet the particles to form effective bonds. Therefore, the study of the geometry assumed by a liquid bridge is es sential in determining the adhesive force. Liquid bridges formed between two particles assume a lens-shaped profile, which can be described theoretically by the Young-Laplace equation. Being able to solve this equation for various con ditions is important in the development of agglomeration models.
1 260
S.J.R. Si mons
2.1 . The Young- Laplace equation
The configuration assumed by a liquid bridge, at rest, is implicitly defined by the Young-Laplace equation: (1) Equation ( 1 ) relates the difference in hydrostatic pressure I1 P = P-Pext across the vapour-Iiquid or liquid-liquid interface (if the surrounding medium is a liquid) to the local radii of curvature (1 and (2 (Fig. 1 ) and to the interfacial tension '}'L between the liquid bridge and the external medium [ 1 8]. P and Pext are the pressures inside the bridge and in the external medium, respectively. The configuration of the liquid bridge can be readily obtained from equation ( 1 ) once the local radii of curvature are rewritten in analytical terms, which, by using a cylindrical coordinates system, results in [9]: y" I1P 1 (2) 1 'YL ' / 2 ( 1 + y' 2)3/2 Y( 1 + y 2) where y' an y" are the first and second derivatives of the liquid bridge profile, which is described by the function y(x). For relatively "Iarge" liquid bridges, the geometry of the liquid bridge is influ enced by the gravitational distortion. In this situation, the profile mean curvature is not uniform throughout the liquid bridge and equation ( 1 ) must therefore change accordingly. As detailed by Mazzone etal. [8], gravity has negligible effects on the bridge geometry when equation (3) is satisfied: gL2 11p (3) I1PR where 9 is the gravitational acceleration, L is some characteristic length of the bridge and I1p the difference between the densities of the liquid binder and the external medium. "SmalI" liquid bridge volumes are defined as those meeting (3), as opposed to "Iarge" volumes where gravity does have an effect on the geometry of the bridge.
Fig. 1.
Geometrie parameters deseribing a liquid bridge between unequal spheres.
1 26 1
Liquid Bridges in Granules
The solution of the Young-Laplace equation has been studied by Orr et al. [ 1 8] for liquid bridges formed between a sphere and a flat surface, in terms of elliptical integrals. He also classified possible liquid bridge geometries according to the meridional curvature, defined as -d/dx(sin Q! IR), where Q! is the angle made by the normal to the meniscus with the axis of symmetry, as indicated in Fig. 1 . In Fig. 2 the meridional curvature is negative in (a)-(c); it is negative in the top part and positive in the bottom branch of (d) and vice versa in (f); it is zero in (e) and positive for (g)-(i). Thick lines represent the inflection points. Considering the mean curvature, it is negative in (a) (which leads to a pressure inside the
(a) Nodoid segment
Fig. 2.
(b) Catenoid segment
( d ) Unduloid segment
(e) Cylindcr segment
(g) Unduloid segment
(e) Zone of sphere
(e) Unduloid segment
(f) Unduloid segment
(i) Nodoid segment
P rofiles of axisymmetric menisci of uniform mean curvature (after Orr et al. [ 1 8]).
1 262
S.J . R. Simons
meniscus lower than that of the surrounding medium), it is zero in (b) and positive in all the other situations. Equation (2) can be rearranged into a Bernoulli-type differential equation and, following classical integration, equation (4) is obtained, where B is an integral constant [9]: Y = l1P Y2 + B (4) 1 2 2 1 ' ) 2YL ( +y / By substituting either of the two y' i with cotg(Oi+ ßi) into (4) (i refers to either point A or B in Fig. 1 ), the constant B can be evaluated, which, for point A, becomes P B = YA sin(OA + ßA) 11 Yi (5) 2YL If the coordinates of both points A and B are substituted into (4), the constant B can be eliminated: l1P YA sin(OA + ßA) - Ys sin(Os + ßs) (6) 2YL Yi y� -
Equation (6) allows l1P across the interface to be calculated once the interfacial tension YL and the boundary values of the bridge profile, YA, Ys, (GA + ßA), (Os + ßs), are known. However, equation (2) can only be solved analytically in a few cases, for instance, when the angle 0 + ß = 90° on both the equi-sized par ticles. Hence, in general, a numerical solution is required. 2.2. N umerical solution of the Young- Laplace equation
A numerical method to solve the Young-Laplace equation is given in Ref. [1 7], where a symmetrical liquid bridge, between equi-sized particles of radius R, is considered, as indicated in Fig. 3. e
+
x
Fig. 3. The Lian et al. physical model for a liquid bridge between equi-sized spheres (afte r Lian et al. [ 1 7]).
1 263
Liquid Bridges in Granules
The solution of the bridge profile can be approximated through a truncated Taylor series to obtain the recurrence equation:
Yi+1
�
;
Yi + Y; (Xi+1 - Xa + Y;' (Xi+ 1 - Xa2 + . . . i =
0,1,2, .. ,
(7)
where Y and X are dimensionless coordinates with respect to the particle radius R. Rearranging equation (4) and equation (2), the expressions for Y; and Y;' can be determined by considering that at Xc, Yc = sinß and Y� = cotg (ß + B):
Y' = I
(
sin ß sin(ß + B) + H* ( Y� - sin2 ß)
1 �
) -1 2
Yi
'2 Y;' = +y i + 2H*(1 + y?)3/2
(8)
(9)
1
where H* is the dimensionless mean curvature, H* = I1PR/2YL ' Owing to the configuration symmetry, Lian et al. [ 7] studied only the half profile, from the neck position Yo, to the contact point with the particle, Yc' Liquid bridge configurations were evaluated from contact through to rupture by consid ering a fixed contact angle B and a constant liquid bridge volume. The config urations assumed by the liquid bridge for different separation distances a, can be determined by specifying values for both H* and the half-filling angle ß. When the solutions of the Young-Laplace equation were analysed, two possible configu rations resulted in agreement with equation (2) for the selected set of volume and contact angle (Fig. 4). The two possible solutions were also noted by Erle etal. [1 9] and De Bisschop etal. [9], who identified the stable configuration as the one that minimizes the free Helmotz energy E of the liquid bridge. In the analysis presented in Ref. [9], the rupture configuration was recognised as occurring when the two solutions be came coincident. If we regard u(x) as the profile of the particle wetted by the liquid binder and Xc the abscissa of the binder to particle contact point (Fig. 3), the free Helmotz energy E can be written as [9]: E=
2n
l::xC [2YLY(1 + y'2) 1 /2 - 2YL cos Bu(1 + J2) 1 /2] dx + (Pext - P)Vbr (10)
where the first term under the integral represents the energy stored within the liquid bridge surface, the second term is the energy contribution due to the sur face of the particle wetted by the binder, - PVbr is the energetic contribution due to the "PV-work" and Pext Vbr is a constant ( Vbr is the volume of the liquid bridge), whose physical meaning is the energy involved in displacing the suspending medium and replacing it with the liquid bridge.
S.J.R. Simons
1 264 so
(b) ..
Vb: = 0.03 Vb: = 0.005 0.10
O.lt!
o
0.00
0.30
Vb,*
Dimensionless separation, 2a* . I
,.
�
12
�
Cö 2:
10
m E
•
� Cf) c
Cf) Cf)
C o ·üi a5
(cl
_____ � Vb: = 0.03
•
E .'+-�--,.--�--r-----,-� 0.00 0.10 C.2D 0.30 0
u. ci �
••
'
....._-;:�..::.:::: "'.._......._.___
_.�"""
(5
Dimensionless separation , 2a*
, 0.20
0.10
0.30
ij5 E
� \
(d)
Vb,* 0.005 =
C o ·üi
,
0.00 1
Dimensionless separation, 2a*
o u.. Cf) Cf)
•
=
.•
(5
.o. +0.00
__--,._ � __._ ---,�
0.10
0.20
0.30
Dimensionless separation, 2a*
Stable (--) and unstable ( - - - - ) numerical solutions of the Young-Laplace equation at different dimensionless separation distances a*( = aiR) for a range of dimen sionless liquid bridge volumes Vbr and zero contact angle in terms of (a) the dimensionless neck radius, (b) the half-filling angle ß, (c) the dimensionless mean curvature H*, and (d) the dimensionless total liquid bridge force F* (after Lian et al. [ 1 7]). Fig. 4.
The solution method proposed by Lian et al. [1 7] introduces a significant sim plification by assuming a constant contact angle e throughout separation. In real cases, this situation does not apply because the contact angle varies according to the interaction exhibited with the particle. Effects of contact angle hysteresis will be detailed in Section 3.2. Another question arises as to whether the volume of the liquid bridge can be assumed constant during separation. Simons and Fairbrother [20] and more re cently Pepin et al. [21 ] have shown that this volume, during separation, is either constant or varying according to the wettability of the powder. Between two per fectly wettable particles, the liquid binder tends to saturate the particles first, by forming a liquid reservoir around them, before being available to form liquid
Liquid Bridges in Granules
1 265
bridges. Under such conditions, during separation, the volume of the binder can vary at the expense of the volume held in the reservoirs. To avoid the complexity of the solution of equation (2), simplified models exist for the description of the geometry assumed by a liquid bridge. These can then be used to derive parameters such as the rupture distance, post-rupture liquid dis tribution and apparent contact angles. Among these, the toroidal approximation, which approximates the liquid profile with an are of circumference, has gained some popularity amongst researchers. We have developed a novel parabolic approximation. 80th these methods will be discussed in Section 3.2. 1 and their solutions compared with experimental data. 2.3. The rupture distance of a liquid bridge
When the separation distance of a liquid bridge held between two particles is increased, the meniscus displaces until a certain critical bridge separation is attained, at which point the bridge becomes unstable and ruptures. The rupture of a liquid bridge is a very rapid process that involves some complex phenom ena, which can only be studied using a relatively fast camera (i.e. 500 framesjs) [22]. Recorded sequences of pendant drops deformed under the effect of grav ity show that near rupture the meniscus is similar to an umbilical cord, of finite length and very small radius, joining the two liquid masses which are about to separate. The phenomena involved in the disruption of a cylindrical meniscus were studied by Plateau [23] in terms of the increasing instability of the shape due to the formation of capillary waves generated by external disturbances. The capillary waves narrow the thin umbilical cord and eventually the bridge breaks. Ouring rupture some satellite drops may form as a consequence of this process so that the volume of the bridge is not exactly conserved [22], while viscous dissipation also occurs due to the rapid process of liquid redistribution of the separated droplets. Oe 8isschop and Rigole [9] stated that as separation distance is increased the half-filling angle (ß in Fig. 1 ) decreases continuously and rupture occurs when it reaches a minimum. It was subsequently observed by Mazzone et al. [8] that a minimum half-filling angle is indeed reached, but that stable bridges can exist on increasing the separation distance beyond this point with ß actually increasing before rupture. As shown by Lian et al. [17] (see Fig. 4(b)), theory predicts this observed rise in the half-filling angle before the critical separation distance is reached. Following on from the solutions shown in Fig. 4, Lian etal. [ 1 7] derived a simple relationship between the rupture distance and the bridge volume. 8y plotting dimensionless volume V�r against the dimensionless rupture distance
S.J.R. Si mons
1 266
a�ax = amax/ R, they proposed the following relationship: a;;'ax
�
(1 + 0.58)
yrv:;;
(1 1 )
where 8 is the solid-liquid contact angle expressed in radians. It will be shown in Section 2.6 how this very useful equation can be used in the calculation of liquid bridge rupture energies. 2.4. The static liquid bridge force : capillary and surface tension effects
The static force exerted by a liquid bridge is made up of two parts; that due to the surface (interfacial) tension and that due to the hydrostatic pressure within the bridge, determined from the Young-Laplace equation ( 1 ). To calculate the liquid bridge force formed between two particles, two different approaches are commonly used, which lead to slightly different values. In the first case, the force is determined by considerations at the neck of the bridge [24], as in equation ( 1 2), while the second method considers the interfaces between the particles and the liquid bridge [ 1 8], as in equation ( 1 3): ( 1 2) ( 1 3) with the symbols defined as before. In equation ( 1 2) the surface tension and the capillary pressure terms multiply the circumference and the area of the neck, respectively, while in equation ( 1 3) the circumference and the area of the contact between the particle and the liquid are used instead (see Fig. 1 ). In both equation ( 1 2) and equation ( 1 3), which are developed for spheres of identical size (f? r dissimilar particles R is replaced by the geometrie average radius R; k = 2RARB/ RA + RB), the effect of gravity is neglected. When "smalI" volumes of binder are administered between highly wettable particles in contact (contact angle, 8"'0°), liquid bridges assume a nodoid con figuration [1 8] with a negative mean curvature ((1 > 0, (2 < ° and 1 (1 1 > 1 (2 1 ), as indicated in Fig. 5. The pressure deficiency (i.e. �P< O) across the liquid bridge leads to a higher adhesion force than the case where �p> 0, according to either equation ( 1 2) or equation (1 3). The magnitude of the liquid bridge force is difficult to compute exactly, even for simple geometries (sphere-to-plane or sphere-to-sphere), because the three-di mensional bridge forms an interface of constant curvature to satisfy equation ( 1 ). Fisher [24] developed the toroidal (circular) approximation, assuming that an are of a circumference can approximate the exact nodoid configuration of a liquid
1 267
Liquid Bridges in Granules
R ß
Particle Fig. 5.
Nodoid configuration of a liquid bridge.
bridge formed between perfeetly wettable particles in eontaet (i.e. At particle eontaet (i.e. a = 0): r1 = R(sec ß - 1 )
f) =
0) (Fig. 5). (14)
r2 = R(1 + tan ß - sec ß)
( 1 5) Substituting equation (14) and equation (1 5) into ( 1 2) then yields equation (1 6), whieh has been shown to eompare favourably with the values obtained via the exaet solution of the Young-Laplace equation ( 1 ) for the eonditions mentioned above [8, 1 7] : F = 2nRYL (1 6) 1 + tan ß/2 Following substitution of equation (14) and equation ( 1 5) into equation (1 3), the torroidal approximation of the boundary method is F = 2nRYL
[
2 (2 - ( + 1 2 (1 + (2 )
]
(1 7)
where ( = tan(ß/2). This yields values of F within a few percent of those given by equation ( 1 6) for half-filling angles between 1 0 and 40° (coalescence limits for liquid bridges between spheres are 30 and 45° for c1osed-packed and cubic arrangements, respectively [25] and below 1 0° the contribution of the surface tension is negligible [26]). A parabolie approximation has been developed that results in a much simpler and more robust mathematical expression that can be used to evaluate the prin cipal physieal and geometrie liquid bridge parameters (i.e. contaet angle, eurva ture and strength of the liquid meniseus) [21 ,27,28]. The development of this approximation, its experimental validation and the comparison with the traditional toroidal method, will be detailed in Section 3.2. The configuration assumed by the liquid bridge in Fig. 5 is not a general case. In many granulation processes, particles exhibiting different surface energies are
S.J.R. Simons
1 268
processed together and, as a result, some particles can be selectively wet at the expense of others [14]. In this scenario, during particle separation, the liquid binder can recede from those particles exhibiting lower surface energies which, as separation distance is increased, turns the profile of the liquid bridge from a nodoid geometry to one that is unduloid [28]. The geometry assumed by a liquid bridge in such conditions will be discussed in Section 3.2.2. Different workers [1 7,29,30] have investigated, theoretically, the effects that separation has on the strength of liquid bridges formed between perfectly wet table particles. The trend reported in Fig. 6 shows a decrease in the adhesion force (calculated using equation (1 6)) throughout separation as a consequence of the thinning of the bridge neck and the increase of the capillary pressure. It should be noted that, as the relative bridge volume cp becomes smaller, the magnitude of the force becomes more sensitive to the variation in the interparticle distance. The trend shown in Fig. 6 is valid only for the case of quasi-static separation, constant volume and () = O. It will be shown later how this trend differs under non perfect wetting conditions, non-constant volumes and dynamic situations where viscous forces become dominant. Experimental data reported in [6,8,20] agree with the trend of Fig. 6, although the force appeared to reach a maximum at small but non-zero separation distances (Fig. 7), which is not predicted by theory. Mason and Clark [6] attributed this rise to an initial finite contact angle greater than zero that then reduces to zero as separation increases. The decrease in contact angle leads to a change in the profile curvature. In this situation, the 3.0 2,5 2,0
Ii.
\5 . ioD 0,5 0
0
0,05
0.10 a*
0,\5
0.20
Fig. 6. Theoretical dimensionless adhesion force F* (= F/IR) of a liquid bridge between two equal spheres against the dimensionless separation a* (= aiR). The parameter,
1 269
Liquid Bridges in Granules
o
100
200
400
300
Separation, x 1 0·3 cm
Fig. 7. Force/separation curves for oil bridges between two polythene sphere (radii 1 5 mm) suspended in water (after Mason and Clark [6]).
2.50
Ci)
2.00
c:
�
1 .50
�
1 .00
Q) z
�. .�
� k._.
u
Measured force
•
Theoretical Force
�''''''
�. �
E!
•
Q)
�...
I
---, .... � --
f:!
0 LL
I
...�
0.50 0.00 o
2
4
6
8
10
12
14
16
18
Separation (microns)
Force versus separation for a silicon oil liquid bridge holding two glass silanised ballotini of 23 11m radii suspended in air (after Simons and Fairbrother [20]).
Fig. 8.
capillary pressure reaches a minimum, which leads to the initial increase in the liquid bridge force. Si mons and Fairbrother [20] measured liquid bridge forces between particles in the micron size range (Fig. 8), using the micro-force balance described later in
1 270
S.J . R. Si mons
Section 3.1 . Although the judgment of where the particle contact occurred was an arbitrary decision made by microseopie observation, the same trend as shown in Fig. 8 is clearly visible. 2.5. The viscous contribution to the general force expression
During dynamic liquid bridge separations, the shear stress inside the liquid, caused by a velocity gradient in the direction orthogonal to that of separation, gives rise to an additional force, which depends on the viscosity of the liquid binder. The expression of the viscous force between two equi-sized spheres held by an infinite liquid bridge (the particles are submerged in the liquid) is given by equation ( 1 8), which is valid when the particle radius is large in comparison to the distance of closest approach (R»a) [31 ,32]. In equation ( 1 8), IJ is the viscosity of the liquid whilst the radius R is replaced by the geometrie average radius, R, for particles of dissimilar size. In this situation, at low Reynolds numbers (Re = vpR/1J , with v being the particle separation speed), the flow of liquid in the region between the surfaces may be described by the lubrication approximation [33], which assumes the flow to be similar to that between parallel plates where the velocity field is large in the direction orthogonal to that of separation and derivatives in the direction of separation are dominant. 3 1 da Fvis = "2 nIJR2 adt ( 1 8) Although for liquid bridges of finite volume such an analysis of the viscous con tribution ignores the existence and influence of the bridge meniscus on the region of closest approach of the particles, the use of equation ( 1 8) is justified in the limit of small « 1 0 -3) capillary numbers (Ca = I/rf/YL, the ratio between viscous and surface tension effects), small gap distances (a* '"'-' 0.0 1 ) and sufficient bridge vol umes (Vbr '"'-' 0.05) [34]. In fact, small capillary numbers imply that the viscosity does not affect the liquid bridge interface, while the restraints on the distance of closest approach and on the volume of the bridge justify a lubrication analysis for the viscous contribution. Under these circumstances, equation ( 1 8) can be added to either equation ( 1 2) or equation ( 1 3) for dynamic separations. By choosing equation ( 1 2), the more general expression of the liquid bridge force becomes 3 1 da F = 2nr1 YL - nr21 I1P + "2 nIJR2 adt ( 1 9) The force curves generated by equation ( 1 9), calculated using parabolic approx imations to the bridge profile (Section 3.2. 1 ), have been compared with exper imental data obtained by the author and co-workers [35] and found to be accurate for spherical particles. A model for the hardness of wet granules developed from the basis of this expression is derived in Section 4. 1 and compared with experimental results.
1 271
Liquid Bridges in Granules
2.6. Rupture energy of a liquid bridge
The rupture energy of a liquid bridge is usually calculated by integration of the force exerted by a meniscus throughout separation, from contact to rupture. Simplifications of the force expression are usually introduced, due to the diffi culty in dealing with the general problem of the liquid bridge deformation. Two models, proposed by Si mons et al. [26] and Pitois et al. [36], are discussed below. In both the models only the energy arising from capillary forces is eval uated. The model proposed by Simons et al. [26] is derived from the integration of the total liquid bridge force calculated using the toroidal approximation equation ( 1 6) and is written as: X tan ß (20) F = nYLR(1 + X tan ß - X sec ß) x sec ß - 1 where X = ( 1 + (aj2R)) and ß is the half-filling angle, defined as in Fig. 1 . In the integration of equation (20) through separation distance a, ß was considered to be a constant. This approximation, due to the difficulty in being able to predict ß for each value of a, seems reasonable for particies that exhibit a strong inter action towards the binder, where the solid-liquid interface stays almost constant (Section 3.2.2) [27]. Furthermore, it has been shown theoretically by Lian et al. [1 7] (see Fig. 4(b)) that the overall change in ß is small for perfectly wetted spheres. The expression of the dimensionless rupture energy, W = WjyL Ff , calculated between any two configurations Xmin and Xmax is thus:
[�
]�
W* = 2n 2 (tan 2ß cos ß - tan ß) + X sin 2ß + tan 2ß cos 3ß ln(X sec ß - 1 )
,
Xmax
(21 ) i n which Xmin = 1 and Xmax = 1 + amaxf2 where amax is the rupture distance cal culated using equation ( 1 1 ). A plot of W* against the dimensionless liquid bridge volume Vbr then leads to: W* = 3.6
F;r
(22)
) -1 /2]
Pitois et al. [36] used a cylindrical approximation to the bridge profile, leading to the following expression for the total force:
[
(
F = 2nYLR cos e 1 - 1 +
2V � n a2
(23)
By using the approximation that e stays constant throughout separation, equation (23) can be integrated with respect to the separation distance a, to obtain the
1 272
S.J.R. Simons
rupture energy, which in non-dimensional form reads as:
[
W* = 2na* cos
If a'1 = and a2 = (1
0
W* =
J
8
(
( + a:;2)
1- 1
2 V* n(
1/2
)1
� 2
(24)
a1
*
l
0.58) yt\7fr (see equation (1 1 », equation (25) is obtained: 2 b 2n cos 8 ( 1 + 0. 5 6) (1 - C) � + J � r (25)
+
[
where C = (1 + 2 Vbr/n(1 + is the contact angle expressed in radians, while W* and Vbr are defined as above. It can be seen that equation (22) and equation (25) depend only on global parameters, such as volume and contact angle. Rossetti et al. [37] have compared these two models with experimental data on liquid bridges obtained from the study of pairs of particles with similar and dissimilar surface energies, using the micromanipulation technique described in Section 3. 1 . They found that the model predictions were i n reasonably close agreement in all cases, although equation (25) was slightly better than equation (22) when the assumption of perfect wetting was not valid, due to the inclusion of the contact angle. In dynamic situations, as experienced in a granulator, the rupture energy of liquid bridges plays a less significant role. Lian et al. [38] have studied, using computer simulations, the deformation behaviour of moist agglomerates formed in a gaseous system. The model is focused on the dissipation mechanisms of the kinetic energy upon reciprocal collision of two agglomerates, which is iIIustrated in Fig. 9. Dis sipation of kinetic energy for the moist deformed agglomerates was not solely due
0. 56)2, 8
•
( a)
( b)
(e)
Fig. 9. Visualizations of computer simulated wet agglomerates for an interstitial fluid viscosity of 1 0 mPa s after i mpact at relative velocities of (a) 0.5 m/s, (b) 2.0 m/s and (c) 5.0 m/s (after Lian et a/. [38]).
Liquid Bridges in Granules
1 273
to the viscous resistance and breakage of the interstitial liquid bridges, but also due to rearrangement (plastic deformation) of the particle structure, which involves friction dissipation according to the theories of Johnson [39]. By setting the vis cosity of the binder at 1 0 mPa s and the collision velocities in a range between 0.5 and 5 mjs, the viscous force was found to account for the dissipation of about 60% of the initial kinetic energy. Energy dissipated by friction was also very significant (�30%), whilst the energy dissipated as a result of rupturing the internal liquid bridges was only a small proportion, at around 5%. It appears that there are limiting conditions to when either surface tension or viscosity dominate the energy dissipation, while there is sufficient evidence that friction plays an important role [21 ] . These limits depend not only on the values of these parameters, but also on the volume of liquid, since this governs, to a certain extent (Section 3.2. 1 ) the bridge curvature and, hence, the capillary forces. 3. DI RECT OBSERVATION AND MEASUREMENT O F LIQUID BRI DGE BEHAVIOU R
Micro-mechanistic approaches to determine granule properties and granulation performance have gained favour over the recent years, since many believe that it is the interfacial properties that are the governing parameters. The challenge is to relate what is observed at the solid-solid, solid-liquid and solid-vessel interfaces to multi-particle granules that often have unknown structures and compositions, particularly in relation to binder distribution, and that are experiencing complex shear conditions. Nevertheless, progress is being made in the fundamental un derstanding of such effects as granule strength [21 ,40], deformation [38,41] and attrition [42]. At UCL, micromanipulation techniques have been developed by the author and co-workers over the past decade that have had significant success in elucidating liquid bridge behaviour under a range of conditions, in both gaseous [20] and liquid media [37], with simulant (spherical) and real (irregular) particles [21 ,35], with good and poor wetting [27,28] and at room and high temperatures [43]. Among the major investigations that have taken place, the most important have been those involving particles of different surface energies, which have resulted in a new, parabolic approximation for bridge profiles [27,28] and a predictive model for granule strength [35]. Recently, a case study has been conducted on behalf of an international pharmaceutical company, to establish whether the mi cromanipulation approach can be used to select the optimal drugjexcipientjbinder system for successful granulation. These latter three studies will be detailed in the following sections, demonstrating the usefulness of micro-scale data to the prediction of macro-scale granule behaviour. First, however, the micromanipu lation device, known as a micro-force balance (MFB), will be described.
1 274
S.J.R. Si mons
3. 1 . The micro-force balance
The MFB takes the form of a specially adapted microscope stage, coupled, via a digital camera, to an image analysis and video recording system. A schematic of the complete experimental apparatus is shown in Fig. 1 0. The MFB itself is shown in more detail schematically in Fig. 1 1 . The procedure for forming, observing and taking measurements of liquid bridge behaviour is as folIows. Initially, a rigid micropipette, with a particle attached to one end, is clamped onto micromanipulator B, with the particle being placed under the objective lens
Video recorder
BX60 Microscope
Olympus
Computer
» 6 Stage Fig.
1 0. Schematic of the M F B equipment layout. Camera
M icroscope BX60
Follower movement Driven movement
Microman. A flexible micropipette
e�. -
�
reflectiv
M icroman. C feeding micropipette
�
@ @
� incorporating RO
PEC + LVDT
M;,ro� B rigid micropipette
Driven remotely by PEC + LVDT Fig.
1 1 . Schematic of the experimental set-up of the MFB in a gaseous medium.
Liquid Bridges in Granules
1 275
of the microscope. This pipette is held static throughout each experiment. Fine adjustment in all three dimensions is achieved using the individual plane mi crometers of the micromanipulator. The second partieIe, attached to a pre-calibrated (for its spring constant) flex ible micropipette, is then placed under the objective in contact with the first par tiele. Again, fine adjustment can be made using the micrometers of the micromanipulator. This micromanipulator A also incorporates a 30 11m expansion piezo-electric crystal (PEC), which allows the pipette to be driven remotely. Since piezo-electric crystals exhibit non-linear expansion and hysteresis with respect to applied voltage, a linear variable differential transducer (LVDT) is fitted to monitor the PEC's expansion. To form the bridge, binder liquid is fed through a third micropipette onto the partieIes. The feeding micropipette is pre-Ioaded with the binder before being mounted on micromanipulator C. Once a drop of liquid binder is formed on the particle attached to the rigid pipette, the two partieIes are first brought together to form the bridge and then separated until the rupture of the bridge occurs. This is achieved by either ap plying a signal causing the PEC to expand or by acting manually on the micro manipulator. At this point, the flexible pipette is driven away and the force of the liquid bridge causes the flexible pipette to bend, with the bend being proportional to the force. Under electronic control, separation can take place at different speeds in the range 0.5-1 0 I1m/s. On the 90° bend nearest to the pipette tip a small piece of aluminium foil is fixed (see Fig. 1 1 ). Owing to the separation movement imposed, the bend in the flexible pipette deflects proportionally to the strength exerted by the bridge. The deflection of the pipette is calculated as the difference in displacement between the base of the pipette and the centre of the bend, whose displacement is acquired by an optical folIower with a resolution in the order of 75 nm. To control the optica! folIower, a reflecto-optic (RO) sensor is used to linearly detect the position of the edge of the reflective foil in its field. The RO sensor works by transmitting a beam of light and measuring how much is reflected back. The output from the sensor, when focused on the edge of the reflective foil, reads a constant voltage. Movement onto the reflective foil causes an increase in the output voltage and movement away, a decrease. To keep the sensor focused on the edge of the foil, control electronics are used to drive a second 1 5 11m expansion PEC. This expansion is measured by a LVDT. The flexible pipette is pre-calibrated to determine its spring constant (usually between 0.05 and 0.5 I1Nfl.,lm) and the total force exerted is thus calculated as illustrated in Fig. 1 2, which shows the steps to formation and separation of a liquid bridge. In Fig. 1 2(a), the flexible pipette (whose spring constant is ks), is ap proached by the rigid pipette onto which a liquid droplet has been previously administered. At a certain elose distance between the two partieIes, the flexible pipette "jumps" towards the other pipette to form the liquid bridge, with "e" being
1 276
S.J.R. Si mons ( a)
(b) Frcr
folIower movement Xr
=
ks
e
(e)
driven movement Xd
Schematic showing the method used to calculate the strength of a liquid bridge during separation: (a) particles separated, (b) liquid bridge formation, and (c) liquid bridge separation. Fig. 1 2.
the deflection with respect to the undisturbed configuration (Fig. 1 2(b)). Figure 1 2(c) shows the separation sequence. When the thick base of the flexible pipette is driven away (distance Xd), the centre of the bend follows but is "retarded" by the strength of the bridge and, in general, the distance Xf is different from Xd. The force of the bridge can eventually be calculated as: (26) The separation of particles and monitoring of the LVDTs is computer controlled via an analogue-to-digital interface. A complete description of the device and the computer code can be found in Ref. [44].
3.2. Particle wettability in relation to the geometry of a liquid bridge : approximated liquid bridge profiles
Theoretical and experimental studies of liquid bridge forces and geometries have traditionally been carried out between pairs of similar and highly wettable par ticles, while the situation where the particles have different surface energies has generally been neglected. When different particles are formulated together, which is not unusual during the production of pharmaceutical and agricultural products, surface energy differences can cause preferential agglomeration of some species to occur, due to the fact that some particles are selectively wetted at the expense of others [14]. Particle wettability directly affects the geometry of a liquid bridge and the consequences are also reflected in other properties, such as the force of adhesion, the rupture energy and the post-rupture liquid distribution. The MFB described in the previous section has been used to observe and measure these
Liquid Bridges in Granules
1 277
phenomena in a series of experiments involving glass spheres treated to exhibit different surface effects [27,28]. The experiments were carried out using clean glass ballotini in the size range 40-1 30 j.lm radius. Glycerol liquid bridges were formed between pairs of glass ballotini, either silanised (using a 2% solution of dimethyldichlorosilane in oct amethylcyclotetrasiloxane) or kept in their natural state and the resulting geome tries investigated during liquid bridge separation and rupture. The viscosity and surface tension of the glycerol were measured as 1 630 mPa s and 63 mN/m, respectively, at 20 °C. The micromanipulation technique was used to observe the liquid bridge formation and rupture behaviour and to measure the liquid bridge geometry directly. A glycerol droplet was fed onto the surface of one of the particles using the feeding micropipette, which was then withdrawn. The two particles were brought into contact to form a liquid bridge and then axially sep arated with a constant speed of �1 j.lm/s. The separation process was recorded with the camera and stills from the video were used for further image analysis. Glycerol exhibits good wettability towards untreated glass and moderate wett ability with respect to silanised glass. During separation, the liquid binder can easily recede from particles exhibiting lower surface energies (poor wettability), which, as separation distance is increased, turns the profile of the liquid bridge from a nodoid geometry to one that is unduloid. This is the case for a liquid bridge formed between untreated and silanised glass ballotini (see Fig. 1 3). On the contrary, between two untreated glass particles a nodoid geometry is observed
Evolution of the shape of a glycerol bridge between two glass spheres with increasing separation distance. The particle A is untreated whereas the particle B is si lanised. Glass spheres of 1 1 9 (Iett) and 1 23 (right) firn radii. Fig. 1 3.
1 278
S.J.R. Si mons
Fig. 1 4. Evolution and rupture of a pendular glycerol bridge displaying fixed solid-liquid i nterfaces. Glass spheres of 1 25 (left) and 1 1 1 (right) �m radii . 80th particles are untreated glass ballotini.
throughout separation, which results from a pinning of the three-phase contact line, leading to a reduction in the contact angle (Iarge hysteresis) whilst the solid-liquid interface is almost constant, as illustrated in Fig. 1 4. A parabolic model was developed using physical data obtained from the micromanipulation experiments to approximate the various geometries [27,28]. This model will be detailed below and compared with the torroidal model introduced in Section 2.4. 3.2.1. The toroidal and parabolic models
The toroidal approximation can be split into two categories, namely, whether the meniscus of the liquid bridge assurnes a convex or a concave profile. This is not the case for the parabolic approximation, where a single equation can be used to describe both curvatures. Usually in the literature, the meniscus is considered to be concave [9, 1 7,24] while in certain real cases, depending on the volume admin istered and the binder-to-particle wettability, a convex profile can result. 3.2. 1 . 1 . The concave toroidal model
A schematic of the toroidal approximation for a concave geometry is shown in Fig. 1 5. The reference axes were chosen to simplify the expression of the liquid bridge profile. Two unequally sized spheres of radius RA and RB are separated by a distance 8. The liquid bridge has a constant radius of curvature r2 in the plane of the page and r1 (evaluated at the narrowest point of the meniscus) in a plane perpendicular to the page. The x-axis is the axis of symmetry and the origin is taken as the point where the bridge is at its narrowest. The liquid bridge contacts each sphere at the ordinates YA and YB, with a half filling angle of ßA and ßB, respectively, and forms the contact angles 8A and 8B on each sphere. Equating the vertical (y) components of the bridge geometry gives: (27) RA sin ßA + r2 sin(8A + ßA) = r1 + r2 RB sin ßB + r2 sin(8s + ßB ) = r 1 + r2
(28)
1 279
Liquid Bridges in Granules
x
...
Fig. 1 5.
...
a
Schematic of the toroidal approximation for a concave profile.
(x) components gives: a a1 + a2 RA(cos ßA - 1 ) 8Br2 COS(8A + ßA) + RB(cos ßB - 1 ) + r2 cos( + ßB)
Similarly, equating the horizontal =
=
+
(29)
The equation for the upper toroidal bridge profile is given by equation (30) for a concave bridge, which occurs when (ßA + ßB + 8A + 8B) < 2n:
x2 + -r1 -r2)2 (y
=
r�
( 30)
which can be rearranged to give:
x
( 31 )
x -r2
The volume of revolution of the meniscus, Vm,A, from the point = COS(ßA + 8A) (contact with particle A) to the point at which = 0, is given by:
(32)
Substituting equation (31 ) into equation (32), gives: Vm,A = n
jO
-r2 cos(fiA +OA)
(2r� + 2r1r2 + rf -x2 -2(r1 + r2)Jr� -x2)dx
(33)
Integration of equation (33) leads to: Vm,A =
n [(2r� + 2r1r2 + rf)x - � -(r1 + r2)xJr� -x2 -r�(r1 + r2) arcsin r2] 0 �
-r2 cos(ßA +()A)
( 34)
1 280
S.J.R. Simons
(
)
and when the integration limits are substituted, equation (35) folIows:
Vm,A _- cos(UA + ßA) 2 + 2 -r1 + (r1 ) 2 COS3«(JA-=--+ ()A) -3 r2 r2 nr� (35) - ( 1 - �:) (COS«(JA + ßA) sin«(JA + ßA) + � + (JA + ßA ) A similar expression exists for the volume of revolution Vm , s , obtained from in tegration of equation (34) from x = 0 to x = r2 cos(ßs + (J s), where the profile l)
(
contacts particle B:
-
)
- --
--
Vm,S _ UB + ßB) 2 + 2 -r1 + (r1 ) 2 COS3«(JB + (JB) 3 - ( 1 - �: ) (COS«(JB + ßB ) si n «(JB + ßB) + � + (JB + ßB )
-- - cos( n�
l)
�
�
-
- --�--
(36)
To find the exact value of the volume of liquid in the bridge, the volumes of the spherical caps enclosed at each end of the profile need to be subtracted. For the two spheres A and B, characterised by index i, this expression is given by: nR( (2 Vcap,i = 3
-
3 cos
ßi + COS3 ß;)
(37)
The volume of the bridge is eventually calculated as: Vbr = L
i=A,S Vm,i - Vcap,i
(38)
Equations (37) and (38) are also valid for the convex model. The area Abr of the meniscus interface can be calculated by:
(
j
Abr = 2n
1
+ r2 cos(ßs+8s)
+r2 COS(ßA+IJA)
y(x)V1 + y'2(x)dx
which, after the i tegration limits are imposed, becomes: Abr = 1 + 0.. (n r2
(JA - ßA - (JB - ßB - COS«(JA + ßA) - COS«(JB + ßB))
(39) (40)
3.2. 1 .2. The convex toroidal model
A convex shape forms when the two spheres are close together and/or when the liquid forms a relatively large contact angle with the two particles, as indicated in Fig. 1 6. The upper and lower liquid bridge profiles are, in general, approxi mated by two different ares of circumference for which r2 and r1 represent the radii of curvature in the plane of the page and in a plane perpendicular to it, respectively. The geometrical condition for the concave shape to occur is + + + > 2n. Since, in general, the upper and lower profiles are not
(ßA ßB (JA (Js)
1 28 1
Liquid Bridges in Granules
y
x
a/ • .-
Fig. 1 6.
a
I
a2 '
·
.
Schematic of the toroidal approximation for a convex profile.
described by the same circumference, the centres of the two circumferences are not necessarily Iying on the x-axis, as indicated in Fig. 1 6 for the upper profile. The expressions of the volumes and area of revolution can be determined in the same way as for the concave case by using the following expression for the convex profile: (41 )
m,A, V )
As i n the concave case, the volume of revolution, i s evaluated by integrating (contact with particle A), to the + equation (32) from the point = point at which x = 0, When (41 ) is substituted into equation (32), equation results: 0
Vm,A = n
1
- r2
COS(ßA +OA l
x -r2 COS(ßA (JA (42) (2r� + 2r1 r2 + r� - x2 + 2(r1 + r2)Jr� - x2)dx (42)
[
The integration of equation (42) gives:
Vm,A = n (2r� + 2r1 r2 + d)x -�3 + (r1 + r2)x Jr� - x2 +r�(r1 + r2) arcsin �r2 0 (43) and when the integration limits are substituted, equation (44) folIows: Vm,A _- COS(0A + ßA) 2 + 2 r--1 + (r1- 2 - COS3 ({JA + ßA) -3 r2 r2 nr� - G: - 1 (COS(OA + ßA) sin(OA + ßA) + � + ßA - OA) (44) A similar expression exists for the volume of revolution Vm , s , obtained from integration of equation (33) from x = to x = r2 cos (ßs es), where the profile
)
]
(
°
-r2
cos(f3A+8A l
))
---,,---'--'-
+
1 282
S.J.R. Si mons
contacts particle B:
(
)
Vm.B -COS(IluB + ßB) + - + ( ) COS3«()B3 + ßB) � - G: 1 ) (COS«()B + ßA) sin«()B + ßB) + � + ßB - ()B) _
nr
-
2
2 r1
r2
r1
-
r2
2
- -----'--=----'-...::.:..
(45)
The area Abr of the meniscus interface can be calculated from equation (39) by using equation (41 ) and after the integration limits are imposed, equation (46) results:
3.2. 1 .3. The parabolic model
Figure 1 7 is the schematic of the parabolic bridge profile approximation. The solid-liquid interface is a spherical cap, which has a maximum height of h;, L is the length of the liquid bridge and Ymin the minimum liquid neck radius of the pendular bridge. The x-axis is the symmetry axis of the system and the origin is set at the intersection between the x-axis and the half-cord YA. The liquid-to-solid contact points are P and Q on the two spheres, with co-ordinates of (0, YA) and (L, YB ), respectively. The heights of the spherical caps on the particles, h;, are related to Y; (i = A,B) by: �=
J� - � - �
�n
y(x), the function of the upper half of the liquid bridge profile, is approximated by a second-order polynomial equation in the form of: (48) in which the values of the three unknown parameters !X2, !X1 and !Xo, come from the solution of the system given by equation (49), the symbols being defined as y
Fig. 1 7. Schematic of the parabolic approximation.
1 283
Liquid Bridges in Granules
{ Y(O)=YA YB
above:
cap,A cap,B
V = n J� y2 (x)dx = Vbr + V y ( L) = m
+V
(49)
The area of the liquid bridge, Abr, is calculated using equation (50), which leads to equation (51 ) once equation (48) is replaced and integrated between the integration limits:
lL y(x) V1 + y 2 (x)dx (50) n (0( 1 (1 + 1 61X2 IXO - 21X1 R + (-1 + 1 61X2 IXO - 41(1 ) arcsin h(1(1 ) ) Abr = 2n
Abr =
(
'
321X2
n
321X� (( - 1 + 1 60(2 1X0 - 41(1 ) arcsin h(2L1X2 + 1( 1 ) ) + 321X�
+
)
n 2LIX2 + 0( 1 )(1 + 8L2 1X2 + 1 61X2 1X0 + 8LIX2 1X 1 - 21(1 ) 1 + (2Loc2 + 0( 1 )2
)
(51 )
3.2.2. Comparison of the toroidal and parabolic approximations
To approximate the liquid bridge profile using either the toroidal or the parabolic model, some geometric quantities must be given or calculated through image analysis from a sequence of liquid bridge separations (see, for example, Figs. 1 3 and 1 4). These quantities are the particle radii the half-filling angles the separation distance a and the volume of the bridge Vb r, The application of the toroidal method for both the convex and the concave profile requires the determination of the contact angles and and the profile radii of curvature r1 and r2 . These parameters can be calculated iteratively through the solution of equations (27)-(29) and (38), Depending on the volume of the liquid bridge, a transition from a convex profile to one that is concave can occur during liquid bridge separation (see Fig. 1 4), The toroidal approximation, therefore, involves two sets of equations to be solved for the same sequence of separation. When the liquid bridge profile changes its configuration from a convex to a concave curvature, it will assume a cylindrical configuration, which cannot be solved by the toroidal model since r 1 -+ The parabolic approximation is defined by the three parameters 0(2 , 0( 1 and 1X0, which can be calculated by solving the system equation (49). lt is useful to note that by varying 0(2 , 0( 1 and 1X0, the single equation (48) can be used to approximate both convex and concave menisci. Hence, the parabolic approximation results in a mathematically simpler and much more robust expression than that of the toroid.
RA,B,
00 .
eA eB
ßA,B,
1 284
S.J.R. Si mons
Since the toroidal and the parabolic approaches are not the solution of the Young-Laplace equation ( 1 ) they do not comply with the constraint on the total mean curvature being constant along the profile of the liquid bridge. However, calculated values of the principal geometrie parameters (contact angle, rupture distance) have been shown to be in fairly close agreement with experimental data, as will be described in the next section. The curvature of the profile has a role in the evaluation of the liquid capillary pressure and ultimately on the force exerted by the liquid bridge. Mazzone et al. [8] parameterised the dimensionless force versus the normalised bridge volume on the separation distance and compared the toroidal approximation with the numerical solution of the Young-Laplace equation (1). They showed that when the particles are nearly in contact only a slight discrepancy is noted between the two methods throughout the volume range. However, as the separation distance reaches just 1 0% of the particle radius, the toroidal method significantly underestimates the force as obtained from the numerical solution. Models intended to describe the process of liquid bridge separation always as sume the contact angle between the particle and the binder to be fixed and equal to zero throughout separation [9]. However, this assumption is reasonable only for perfectly wet particles and therefore is not a general case. Predicting the behaviour of real cases is complex due to the difficulty of modelling the phenomena at the three-phase contact line. As has been shown in Figs. 1 3 and 14, the interface can either be "pinned" or recede, depending on whether the wettability between the particle and the liquid binder is good or poor, respectively. This situation can be explained in terms of the contact angle hysteresis. The pinning of a solid-liquid interface can continue until the contact angle between the binder and the particle reaches the receding values. At this point, since no further reduction of the contact angle appears feasible, the solid-liquid interface reduces. When the difference between the advancing and receding contact angle is large, the three-phase con tact line is pinned and a reduction of the solid-liquid interface is not likely to occur, unless the receding contact angle is reached. The two cases of liquid bridges formed between particles with either good or poor wettability will be discussed separately to better highlight their peculiarities. 3.2.2. 1 . Liquid bridges formed between particles with good wettability
Some useful simplifications can be made to use the parabolic and the toroidal methods to model the configurations assumed by liquid bridges during separation of pairs of particles both exhibiting good wettability towards the binder. An example is shown in Fig. 1 8, where a glycerol liquid bridge is formed between untreated glass particles and the last recorded frames before bridge rupture and the post rupture liquid distribution are shown. Despite the fact that small reductions in the solid-liquid interface might occur even for particles of good wettability, it can be assumed that these interfaces stay fixed during separation. This condition translates to the fact that the spherical cap
Liquid Bridges in Granules
1 285
Fig. 1 8 . Last recorded liquid bridge configuration and post-rupture liquid distribution for the separation of a glycerol liquid bridge (Vbr = 1 383 x 1 03 1lm3) formed between two un treated glass particles of radii RA = 92 11m (Iett) and RB = 91 11m (right).
heights on the particles, hj, or equivalently the half-filling angles, ßj where i = A,B (Fig. 1 5) remain constant during separation while the three-phase contact line is pinned. When the geometry of the particles, the volume and the initial configuration of the bridge are given (or calculated by image analysis), it is possible to calculate the liquid bridge profiles at different separation distances by solving the system equation (49) for the parabolic approximation or that formed by equations (27)-(29) and (38) for the toroidal method in which the appropriate equations for the convex and the concave profile must be chosen. The solution of these two systems leads to the determination of the unknown values in equation (48) for the parabolic model and in equations (31 ) and (41 ) for toroidal concave and convex shapes, respec tively. To assess the validity of the approximations made (e.g. type of profile and fixed interface) the theoretical profile can be compared with that obtained from experimental observations in terms of the apparent contact angles measured at the liquid contact with particles A and B. The apparent contact angle can be calculated from the approximated liquid bridge profiles by means of equation (52) for spheres A and B, respectively, in which Y 'A and y ' B represent the abscissa of the point of contact:
� + tan -\y�) - sin -1 (�:) es = � - tan- 1 (y's ) - sin - 1 (�:) 8A =
(52)
Figure 1 9 represents a typical situation of the contact angle values for a pair of untreated glass particles (good wettability) held by a glycerol liquid bridge, as shown in Fig. 18. Data are plotted against a* , the separation distance normalised with respect to the geometrie average radius (R = 2RARs/RA + Rs). These graphs c1early show that the approximation of keeping the solid-liquid interfaces
1 286
S.J.R. Si mons 8o .-------����1
j� 60 �--1r----�--� :;;. Q)
� 40 �----��-'" Ö
� 20 �------�����- o
60 .------f+P��� $ 50 ���------�L-� � � � 40 �-����---� 30 �--�L-----��-g 20 +-------a-- __
(I)
c:
8 1 0 +-------��--
O �������
0.00
(a)
0.50
1 .00 a'
1 .50
2.00
(b)
0 ��������4J�� 0.00 0.50 1 .00 1 .50 2.00 a'
Fig. 1 9. Experimental and calculated apparent contact angles for the experiment pre
sented in Fig. 1 8. P refers to the parabolic and T to the toroidal model, both calculated with the approximation of fixed solid-liquid interfaces: (a) refers to particle A and (b) to particle B.
fixed is not adequate for the untreated glass-glycerol system. The differences found with respect to the parabolic and toroidal models are to be attributed to small reductions in the solid-liquid interface with consequent rearrangement of the three phase contact line. From Fig. 1 9 it can be seen that initially the contact angles drop quickly, which is weil predicted by both profile approximations. However, after a normalised separation of approximately 0.5 for both spheres A (Fig. 1 9(a)) and 8 (Fig. 1 9(b)) the agreement between theory and experiment is lost. The predicted contact angles drop towards zero whereas the measured contact angles level off at a value of approximately 25°, which can be assumed to be the receding contact angle for glycerol on these spheres. This decrease and then levelling effect of the contact angles indicates that the three-phase contact line is initially pinned on the particles, but that, after a certain particle separation, the contact line begins to slip on the particle surfaces since the reduction of the solid-liquid area is more en ergetically favourable than further pinning of the contact angle. Despite the fact that the assumption of fixed interfaces seems to be invalid for the prediction of the contact angles of the liquid bridge, it is more applicable when used to predict the distance at which rupture occurs, as will be shown later. The model can also be applied to binders that show a nearly 0° receding contact angle towards the particle. A second approach to modelling the profile of glycerol liquid bridges by using the toroidal and the parabolic approximations is to measure the geometrie pa rameters of the interface at any stage during separation. In Fig. 20 this approach has been used to predict the contact angles on both particles. 80th the parabolic and the toroidal approximations are able to give good agreement with the ex perimental results. However, since the model requires some a priori knowledge of the sOlid-liquid interface, it cannot be considered to be predictive, but rather a model used to approximate a known liquid bridge configuration. The advantages of this laUer approach lie in the possibility of calculating the liquid bridge force
1 287
Liquid Bridges in Granules
80 ,-------1
Q) �
i
60 t-_�
and measured hA measured hA e� me= �� ntw ri2 x �= == � � -+- P
-G- T and
_ _
� 40 +---=-��---- '"
� 20 r------��� o (,J
50 +-----� -' -____l�-�------� 40 +� --�����--� 30 t------���� � N 20 +_----" 8 10 +-----�
Q)
O +-�����
(a)
0.00
0.50
1.00 a'
1.50
2.00
O +-�����
(b)
0.00
0.50
1.00
1.50
2.00
a'
Fig. 20. Experimental and calculated apparent contact angles for the experiment pre sented in Fig. 1 8. P refers to the parabolic and T to the toroidal model, both calculated with parameters of solid-liquid interfaces measured during separation: (a) refers to particle A and (b) to particle B.
from an approximated profile (either toroidal or parabolic) without the need to solve the Young-Laplace equation ( 1 ), although the error induced on the capillary pressure by the approximated profile increases with separation distanee. One useful parameter that can be predicted using the toroidal and parabolie approximations is the separation distance at which the bridge ruptures. The simple criterion proposed by Lian et al. [1 7] (see Section 2.3) to evaluate the liquid bridge rupture distance can lead to ambiguous results when a large contact angle hys teresis exists during liquid bridge separation and a diseretional judgment is required on deciding whether the advancing or the receding contact angle should be used in equation (1 1 ). A geometrie rupture criterion has therefore been developed together with the parabolie approximation, which is based on the eonservation of the liquid bridge area just before and after rupture [27,28]. This approximate rupture model has also been tested with the toroidal approximation, wh ich gave the same order of aecuraey in the prediction of the bridge rupture distanee. The rupture criterion is iteratively applied by assuming a virtual rupture of the liquid bridge at each separation distance during the bridge elongation. The solid-liquid interfacial area is assumed to be held constant. If we consider the rupture of a liquid bridge of low volume ( < 1 04 �m 3) between two spherieal par ticies, the liquid binder tends to redistribute on the two particies by forming drop lets that can be regarded as perfeet eaps of spheres (see Fig. 21 and the last frames in the sequences shown in of Figs. 14 and 1 8). To quantify the amount of binder lett on eaeh particle, it is assumed that, at each rupture, be it either virtual or real, the volume of the binder distributes between the two droplets in proportion to the amount on either side of the bridge at its thinnest point. For instanee, if we eonsider a virtual rupture for the configuration shown in Fig. 1 5, the volume of liquid lett on sphere A, VA, would be calculated according to equations (35)-(38). Figure 21 illustrates the post-rupture droplet shape: Uj is the liquid droplet ra dius, 7j the liquid droplet cap maximum height and Ci the half-cord length, which
1 288
S.J.R. Si mons
�J Fig. 2 1 .
Liquid droplet after rupture on a spherical particle i.
are all related by:
T2 + c? (53) 2 T; In the proximity of the effective rupture, the area of the liquid bridge Ab r and the area of the droplets AdroP should be almost equal because the liquid bridge can not adsorb any more energy from the surroundings to be turned into new liquid bridge surface. The area rupture criterion states that rupture occurs when equa tion (54) is satisfied, where Adrop is calculated by equation (55): (54) Adrop - A br = 0 u; =
I
I
Adrop =
(55) L 2nu; T; ;=A,B In Fig. 22, the evolution of Ad rop and Ab r calculated using both approximations is plotted versus normalised particle separation for the case of two untreated glass spheres, 1 0 1 )lm RA and 1 00 )lm RB [27,28]. The liquid-vapour interfacial area the droplets would have if rupture occurred at a separation weil before the ob served rupture, is much superior to that of the liquid bridge, which indicates that the liquid bridge is perfectly stable. With elongation, the bridge liquid-vapour interfacial area increases, while the droplets' interfacial area levels off to a con stant value. Variations in Adrop with a* occur when the solid-liquid interfaces vary and/or the position of the minimum liquid neck on the bridge profile changes. Even though the toroidal and the parabolic approximations have different math ematical expressions, their agreement is excellent in terms of the predicted in terfacial area. 3.2.2.2. Liquid bridges fermed between particles with geed and peer wettabilities
The study of liquid bridges formed between particles of different wettabilities is summarised in Ref. [28]. From the batch of ballotini used in the work described in the previous subsection, a sampie was soaked for 30 min in a silanising agent
1 289
Liquid Bridges in Granules O P Adrop o P Abr O T Adrop /!' T Abr
1 .8E+05
�
1 .6E+05
"'E
�
B
10
a
�
�
Ö
1 AE+05 a
(1j
.,.
1 .2 E+05
@
B
I
observed rupture
@
1 .0E+05
8.0E+04 0.0
004
0.8
1 .2
1 .6
2 .0
2 .4
a* Fig. 22. Evolution of Adrop and Abr versus a* for the ca se of two untreated glass spheres, 1 0 1 Ilm RA and 1 00 Ilm RB' The arrow i ndicates the observed rupture distance. P refers to the parabolic and T 10 the toroidal model, both calculated with the approximation of fixed solid-liquid i nterfaces.
(2% solution of dimethyldichlorasilane in octamethylcyclotetrasiloxane) to modify the surface properties of the particles. The method of liquid bridge formation as weil as the speed of separation ("'1 Ilm/s) remained the same. The silanisation of the glass particles was intended to reduce the high wetting hysteresis shown by the glycerol on untreated glass. For pendular liquid bridges, a large or small wetting hysteresis drastically changes the shape adopted by the liquid bridge, as can be seen in Fig. 1 3. In this figure, a glycerol bridge has been created between a non-silanised glass sphere (A) and a silanised glass sphere (B). With increasing interparticle distance, the three-phase line is pinned on the non-silanised particle A, but reduces on particle B as the liquid recedes fram the solid surface. To verify the applicability of the parabolic approximation to the case where one particle is silanised, the apparent contact angle of both particles, as calculated by equation (52), can be compared with the values measured experimentally. Be cause of the large interface reduction observed on the silanised particle, the parabolic model can only be applied using experimental va lues of the spherical cap heights, hj, which can be measured at any stage of the separation. The prediction of the contact angles for the experiment shown in Fig. 1 3 is very good, except for the last recorded configuration before rupture, where the par abolic model fails to account for the change in curvature of the liquid bridge in the proximity of particle B. Figure 23 shows that the contact angle remains more or less constant on the dewetting particle B, whereas the angle made by glycerol on particle A reduces with increasing particle separation.
1 290
S.J.R. Simons 1 00 Cl 80
c
Ql
� Ql
0> c '"
ö
�
c 0 c..>
60
0
40
6
�
A theor. -D A exp. A B theor o B exp. <>
20 0 0.500
e
�
1 .000
A
A
0
&
0
A
0
8
0
8
<>
1 .500
0
0
<>
<>
2.500
2.000
a * [-] Fig. 23. Evolution of measured and calculated contact angles versus normalised sepa ration distance for the case of the experiment shown in Fig. 1 3. A and B refer to the two particles, of which B is silanised.
1 60 ,----1 40 +-----����---__ L 234.6E __ L 272.7E __ L 301.4E
�----��----�60 t-��----��-
-+-- L 375.3E
80
L-----r-----' O+-�+_�������_r�_r�_+�� �----� 40 ��----
:<
L 234.6P
:<
L 272.7P
:<
L 301 .4P
:<
L 375.3P
20 +----o
50
1 00
1 50
200
x film)
250
300
350
400
Fig. 24. Evolution of the bridge profile between particle A, silanised, RA = 47 11m, and particle B, unsilanised, RB = 1 1 4 11m. The legend indicates the liquid bridge length and the last shape for L = 375.3 11m corresponds to the last bridge i mage before rupture.
Figure 24 shows the initial and the pre-rupture configurations of the liquid bridge between two particles during separation, measured experimentally and calculated using the parabolic approximation. Just before rupture for L � 375.3 J.lm, the shape is unduloid. For this case, the third-order polynomial equation is unable to account for the more complex bridge shape. The liquid bridge shape shows a clear reduction of the sOlid-liquid interface on the silanised particle (A, RA = 47 j.lm), on which the origin of the liquid bridge length is taken. On the contrary, the three-phase contact line on particle B
Liquid Bridges in Granules
1 29 1
(untreated, RB = 1 14 /lm) is pinned and the solid-liquid interface remains con stant (the reverse of the experiment from which Fig. 1 3 was obtained). In Ref. [28] a fourth-order polynomial was used to fit the last configuration before rupture. However, this cannot be used as a predictive tool, not even for a fixed interface approximation, because it requires too many parameters that are not known a priori, as, for example, the values of the tangent of the liquid bridge at the point of contact with the particles. Nevertheless, the fourth-order polynomial model does allow the verification of a peculiar property of the dewetting phe nomena, that is, that the increase of the liquid bridge area during separation is balanced by the reduction of the dewetting interface. 3.2.2.3. Post-rupture liquid distribution
In the previous sections, it has been shown that the particle wettability signifi cantly influences the geometry of the liquid bridge. As a consequence, the post rupture liquid distribution is also affected. The amount of liquid remaining on the particles after rupture will determine whether or not the formation of new liquid bridges is favoured or inhibited. Small amounts of liquid left on a particle will have less probability of forming new liquid bridges, which may result in segregation of particles exhibiting different wettabilities in a mixed formulation. On a theoretical basis, it seems reasonable to assume that after rupture the liquid binder distributes proportionally to the volumes of the two spherical par ticles. The validity of this assumption, however, is restricted to cases of similar and well-wetted particles and to liquid bridges perfectly symmetrical along the axis of separation. It can be seen in Fig. 1 3 that for particles of different wett abilities, the liquid distribution after rupture favours the particle exhibiting the strongest adhesion to the liquid, represented by the pinning of the three-phase contact line. Figure 25 illustrates the experimental binder volume distribution versus the solid fraction, as measured on particle A. The particle solid fraction is calculated as the ratio between the volume of particle (A) and the total volume of the two particles, Vs ( = VsA + VsB). VA represents the volume of liquid left on particle A after rupture. The experimental conditions are shown in Table 1 . Figure 25 seems to show a relation between the solid fraction and the post rupture liquid distribution for liquid bridges formed between well-wetted particles (exps. A1-A7). Deviation from the theoretical trend (indicated by the line y = x) can be attributed to the dewetting of the solid-liquid interface, which, even when smalI, can influence the geometry of the liquid bridge and therefore the post rupture liquid distribution (e.g. see Fig. 1 8). A different situation is observed for liquid bridges formed between particles exhibiting good and poor wettability. In experiments A8 and A9 the liquid is almost completely redistributed on the un treated particle (particle A in exp. A8 and particle B in exp. A9) that exhibits higher wettability.
1 292
S.J . R. Simons 1 .0 0.8 �
.0 >
0 0 ;K
0.6
� 0.4 >
f!, +
y=x
0.2 0.0 0.0
o exp. A1 x exp. A2 f!, exp. A3 o exp. A4 ;K exp. A5 o exp. A6 + exp. A7 f!, exp. AB
0.2
VsANs [-]
0.4
0.6
0.8
1 .0
o exp. Ag
Fig. 25. Binder volume fraction versus particle solid fraction measured on particle A. In experiment A8 particle A is untreated whilst in experiment A9 particle A is silanised (see Table 1 ). Table 1 . Experimental conditions between particles of untreated and silanised (marked with an asterisk) glass particles, attached by glycerol liquid bridges Experi- Vbr X 1 03 VA!Vbr VA! Vbr (T) ment Jlm3 RA (Jlm) RB (Jlm) VsA!Vs VA! Vbr (E) (P)
A1 A2 A3
A4
A5 A6 A7 A8 A9
2 1 75 622 10 3720 1 383 1 322 1 42 6850 1 0500
1 25 47 49 101 92 92 56 1 19 1 34*
111 1 14 44 1 00 91 91 1 03 1 23* 1 03
0.588 0.065 0.582 0.51 1 0.5 1 2 0.506 0. 1 32 0.454 0.648
0.709 0.044 0.499 0.7 1 0 0.659 0.593 0.365 0.980 0.0 1 0
0.532 0 . 1 60 0.532 0.506 0.479 0.509 0.364 Not applicable Not applicable
No solution 0. 1 02 0.705 0.500 0.495 0.501 0.477 Not applicable Not applicable
E, experimental; P, parabolic; T, torroidal .
For the experiments between untreated particles, the post-rupture liquid dis tribution has also been estimated using both the parabolic and toroidal models using the fixed interface approximation. The predictions of both models are pre sented in Fig. 26. 80th models adequately predict the extent of liquid volume redistribution on the particles at rupture. 4. RELATIN G PARTICLE-BI N DER I NTERACTIONS TO G RANULE BEHAVIOUR
Models that are used to describe wet granulation growth kinetics usually rely on the agglomerate mechanical properties to determine, for instance, the success of coalescence after inter-agglomerate collisions. These models either assume elastic collisions between agglomerates with a layer of free liquid dissipating the
1 293
Liquid Bridges in Granules o P fixed interface
1 .0 ..!...
0.8
--
0.6
.0 > <
>
'0 Q)
lii 'S u (ij u
-
o T fixed interface -
y=x
o o 0.4 0.2 0.0 0.0
0 0 0.2
0.4
0.6
experimental VA l Vbr [-]
0.8
1 .0
Fig. 26. Prediction of liquid volume distribution between the two particles using the toroidal T, and parabolic P model with the fixed interface approximation.
kinetic energy of the impact [2], or pre-suppose the deformability of the agglom erate to build the growth kernel [3]. In the case of elastic collisions of moistened particles, viscous forces control coalescence [45]. Experimental work on wet agglomeration processes frequently shows that, initially, loose agglomerates are formed [45-47], which consolidate with agitation and increase in their moisture content. Models that are based on elastic collisions with a layer of free liquid would hold for the later stages of the granulation process [2]. The agglomerate hardness is clearly linked to its inner porosity but there is unfortunately no constancy of this factor [48]. Throughout wet granulation, agglomerates harden as they become less porous. The addition of liquid binder facilitates this porosity reduction as the binder can lubricate the interparticle contact points. However, when the mass is over-wet, further lubri cation can also reduce the hardness of the agglomerates. Parallel to this, a number of simulations have proven the role of liquid viscosity, liquid surface tension and interparticle friction forces in the resistance to defor mation of moist agglomerates [49] (see Section 2.6). Wet agglomerates mostly behave plastically until the yield strength is attained, where they rupture through crack propagation. The relative importance of the material properties and the agglomerate texture in the overall deformability is still controversial. Most models generally assimilate particles to spheres. There is a realistic probability that fric tion forces will increase the further the particle shape deviates from a sphere. Inside agglomerates, the shape of pendular liquid bridges is an important factor which determines the size and porosity of the agglomerate as weil as its resistance to deformation. We have already seen how the volume of liquid of a pendular bridge is either constant or varying during separation according to the wettability of the powder (Section 3.2.2) [20,27,28]. When the bridging liquid poorly wets the powder, it is possible to obtain liquid bridges of fixed volume, as there is a clear three-phase contact line on both particles. In addition, when the wetting hysteresis
1 294
S.J.R. Si mons
of the particle surface is high, the apparent liquid-to-solid contact angle changes with interparticle distance as long as the three-phase line is pinned on the solid surface [27]. Conversely, when there is a reduced wetting hysteresis, the three phase line recedes and the bridge liquid dewets the particle with a constant ap parent contact angle [28]. If the volume is fixed with a clear three-phase contact line, a certain range of bridge liquid volume can be observed for the same particles. The bridge volume can then not be determined from the properties of the materials, but va ries according to the operating conditions of the wet granulation. On the other hand, if the bridge liquid perfectly wets the particles, a continuous liquid film forms on the particles and surrounding objects or particles, precluding the existence of a three-phase contact line. In this situation, there is a funicular saturation state of the agglomerate, regardless of the absolute saturation of the mass. The bridge liquid volume is not constant during particle separation, but there is a greater chance of relating this volume to the particle properties. On the particulate level, liquid bridges are responsible for the strength of a wet agglomerate, since they hold the particles together. On the wet agglomerate level, the hardness is related to three factors: the liquid binder surface tension and viscosity and the interparticle friction. A simple model has been developed [35], based on the powder and liquid binder properties, which shows that the forces due to interparticle friction are generally predominant in wet agglomerates made from non-spherical particles. This will be discussed in the following sections. Although mechanical interlocking is not predicted, this model yields accurate prediction of wet agglomerate hardness independently measured on wet masses of varying composition. This theoretical hardness could prove an interesting tool for wet granulation research and technology and represents where future research in this area should be focused, namely, on the use of micro-scale data to inform models across the length scales, from single liquid bridges to granule behaviour. 4.1 . Compression of p lastic agglomerates
A perfectly plastic wet agglomerate is compressed between flat punches at a speed of Vi. During compression, a certain number of structural modifications will occur. We assume for simplification that the agglomerate is formed of n touching particles at the interparticle contact of which liquid bridges can be found. The agglomerate liquid saturation is known and the liquid perfectly wets the solid particles. The shape of the agglomerate is assumed to be cylindrical with a radius of Rag and a length of M. We will assume in the following that neither the solid particles nor the liquid binder exhibit elastic deformation during the agglomerate compression. Exper imental studies reported in the literature [46] have observed plastic deformation of moist agglomerates. From a global point of view, plastic agglomerates deform
1 295
Liquid Bridges in Granules
against hard surfaces with a hardness of n, which is the ratio between the applied load, L', and the contact area, Ac, of the agglomerate with the hard surfaces between which it is compressed: L' n= (56) Ac Experimentally, wet agglomerates can be submitted to deformation at variable speed with recording of the force necessary for deformation. The contact area Ac resulting from deformation increases with the absolute displacement. If neither the porosity of the assembly nor the co-ordination number of the particles is assumed to evolve initially during plastic deformation, the contact area of the agglomerate with the flat punches can be obtained from simple geometrical con siderations. Consider a cylindrical agglomerate as described in Fig. 27. After an absolute compression of d, the agglomerate has flattened on both sides when in contact with the compression punches and resembles the sche matic given in Fig. 28. From the agglomerate volume conservation, equation (57) can be derived: Vag = MnR�g = Ac(2Rag
[2
+ 2M Rag tan - 1
d)
(RagRag � ) (Rag -
-
_
h(d)
-
-
h(d)
)
(Rag ) ] 2"
d
-
(57)
where Vag is the volume of the agglomerate, M the test cylinder length, Rag the cylinder radius, Ac the contact area of the agglomerate with one flat punch and h(d) is the cylinder height which is not stressed after an absolute agglomerate compression of d. The number of particles n inside the agglomerate is given by equation (58), with v the average particle volume: Va n = �
1+---- M
Fig. 27.
Cylindrical agglomerate.
1 296
S.J.R. Si mons
h(d)
Fig. 28.
c �
Compression of a cylindrical wet agglomerates.
The co-ordination number is given by equation (59) [51 ] :
Vbr Vag
with k ;:::::; 3 for a packing of spheres. 1 The volume of one liquid bridge is estimated by: c=
c
(59)
=� (60) n where and are the liquid and solid volume fractions, respectively. The average interparticle distance H is given by equation (61 ), with Ci, the average particle diameter:
=
�
(61 ) The average solid-solid contact area AAB between two solid particles i n the wet agglomerate is estimated by:
2 (Vag
2
ncl 2 = ---- AAB = - nd (6 ) n c where is the true surface area of the powder and the powder true density. The solid volume fraction at the right-hand side of equation (62) estimates the effect of porosity and liquid content on the disruption of solid-solid interfacial area. The term nc? in equation (62) implies that if particles were perfect spheres, the average solid-solid interparticle area would be taken as zero. Because the deformation of the mass is assumed plastic, the applied load L' corresponds to the yield strength of the mass at each moment. With increasing contact area, this force increases as the mass shows more resistance to defor mation . If we consider that the mass hardness defined by equation (56) can be constant at the beginning of deformation, then the mass yield strength can be
S
-'--
'--
1 297
Liquid Bridges in Granules
calculated on an elemental surface which, in the case of a wet mass, can be the area occupied by a solid particle. One particle in the agglomerate assembly has c neighbours and NE, the number of interparticle contacts per unit area that are broken when one particle is moved, is given by: NE =
2 (�) /3
(63)
In an agglomerate in which the liquid perfectly wets the solid particles, it can be considered that liquid covers the surfaces of the surrounding particles. In this case, �p in equation (1 9) will equal zero. In addition, the viscous force term needs to consider each particle as a whole and not just the interparticle contact. Hence, equation ( 1 8) can be re-expressed as: Fvisc = 3nd1J vi (h -
S
(64)
where the term si CPL corrects the viscous force with the structural information of the wet agglomerate. The separation distance where rupture occurs can be predicted using the par abolic approximation, assuming that this occurs through the liquid's thinnest neck, Ymin (Fig. 1 7). For perfectly wetting Iiquids, liquid bridge volumes can be related to Ymi n by an empirical relationship [21]: Vbr :::::; 1 .673Y�in (65) The capillary force Fcap, developed by one liquid bridge is then given by: (66) Fcap = 2nYmin YLV where YLV is the surface tension of the vapour-Iiquid interface. The friction force of one interparticle contact is estimated by equation (67), developed from the expression for the work of adhesion of the liquid on the solid [21 ] : Aa (67) Ffric = Y Lv (cos e + 1 ) b H where Aab is the interparticle contact area and H is the interparticle distance. Combining equations (56, 63-67), the elemental hardness Qca lc can be derived as:
1 [(
Qcalc = 2
3nd1J Vi
s
CP L
) (1) 2/3 V
(
+ 2ny min YLv + YLV(cos e
+
1)
2 3 / ] ) H (v) Aab c
(68) The term 1 /2 at the left-hand side of equation (68) arises from the fact that particles are randomly oriented inside the agglomerate. The elemental forces are equally distributed and only the cose fraction is measured, with e the angle
1 298
S.J.R. Si mons
made by each individual force vector the normal to the punch surface. If all possible e values are averaged, the calculated mass hardness can be given by equation (68). 4.2. Experimental validation of the hardness equation
Equation (68) has been tested against data obtained from the crushing of cy lindrical pellets made from a range of pharmaceutical powders and binders and from glass ballotini and silicon oils. The powders were sodocalcic glass beads of an average radius of 35 �m (GB) [50]; a lactose DCL 1 1 (L 1 ), separated in three fractions (L 1 A), (L 1 B) and (L 1 C), with 90 and 1 80-�m-mesh sieves; a lactose EFK sieved into coarse (L2) and fine (L3) fractions with a 1 00-�m-mesh sieve; and a lactose 1 50 mesh (L4) [21 ] . Sugar beads, Suglets 30-35 (SB 1 ) and Suglets 250-355 (SB2) were also used as a comparison to the glass ballotini. Finally, a crystalline drug powder (DP) magnesium stearate NF-VG-1 -726 (MGST), which exhibits low interparticle friction. The liquid binders were silicon oils of increasing viscosity 96, 996 and 97920 mPa s, water, a 0.2% wjw sodium dodecyl sulphate aqueous solution and aqueous solutions of hydroxypropyl methylcellulose (HPMC) and polyvinylpyrroli done (PVP) of increasing viscosity and varying surface tension. The hardness of pellets made from glass beads (GB) are reported in Ref. [50]. The hardness of pellets made from (L 1 ), (L2), (L3), (DP) and (MGST) are re ported in Ref. [21 ] , where pellets of 1 6 mm diameter and 1 7 mm height were compressed at 1 0 mmjs. In this work, pellets of 1 8 mm diameter on 1 7 mm length were made from (L4), (SB 1 ) and (SB2) moistened with silicon oils of increasing viscosity. The pellets were carefully retrieved from the die on a pre-tared micro scope slide, weighed and then deformed radial to the cylinder axis between the two flat punches of an TAXt2 ® texture analyser (stable micro systems). The upper punch was lowered onto the pellets at speeds of between 0. 1 and 1 0 mmjs. From the weight of the pellet and a knowledge of its composition, the pellet density and porosity could be calculated. Three pellets at least were character ised for each powder. The slope of the force versus contact area curve was taken as the mass hardness. Table 2 summarises the physical properties of the powders used in the com pression study. The mass hardness is calculated from the slope of the graph of force versus contact area (Fig. 29) calculated from equations (56) and (57): The agglomerate standardised stress can be plotted versus capillary number to compare the results with that of Iveson etal. [50] (Fig. 30). The curve shown is the best-fit line to their data. In Fig. 30, the behaviour of agglomerates made from sugar beads is similar to that of agglomerates made from glass beads. Iveson et al. [50] stated that, at
1 299
Liquid Bridges in Granules Table 2.
Physicochemical properties of the powders used in the experiments
L1A
L1 B
L1C
L2
L3
DP
MGST GB
210 230 1 35 (�m) 45 27.8 2.6 32 s (m g- 1 ) 0.193 0.145 0.069 0 . 1 96 0.043 0.342 5.3 ps(g ml- 1 ) 1 . 54 1 .54 1 .54 1 .54 1 .54 1 .27 1 .06 d50
A
Shape
A
A
A
A
B
P
35 0.0697 2.457 S
L4
SB1
SB2
57.51 0.189 1 .54 A
545 0.0073 1 .51 1 S
302.5 0.01 3 1 .51 2 S
The shape descriptors are A, angular; B, beam; P, platelet; and S, spherical.
8.E-Ol 7.E-Ol
g
Qm
6.E-Ol
u.. Q.)
5.E-Ol
�;::s
4.E-Ol
�
2.E-Ol
e oE
3.E-Ol
V) '" Q.)
l .E-Ol O.E+OO O.E+OO
3.E-04
2.E-04
2.E-04
1 .E-04
5.E-05
Contact area Ac (m2) Fig. 29. Measurement of mass hardness from experimental forces and calculated contact
area.
I . B+03
o Ll
I .E+02
D
I . E+OI •
o
{]J 8 o o
I .E- 1 O
•
•
I . E+OO
0
I .E-08
I .E-06
I
.E -04
I . E-02
I . E+OO
Fig. 30. Stress of wet agglomerates versus capillary n umber.
I
I . E-O I
. E+ 02
1 "1;1
I Ei>
x
c: 11 .!:I r:/l
L
2
0
L 3 DP
0
MGST
•
SB
•
GB
x L4
S.J.R. Si mons
1 300
low capillary numbers Ca < 1 0 -4 , the standardised stress is independent from the deformation speed, and friction is the predominant parameter in controlling the wet mass hardness. Above Ca = 1 0 -4 , the contribution of viscous forces to the deformation of the wet mass becomes predominant. Powders with non-spherical shapes show a different behaviour. Agglomerates made from lactose and drug powder exhibit higher stresses for equivalent cap illary number, whereas agglomerates made from magnesium stearate exhibit lower stresses than that of agglomerates made from glass beads. In Fig. 3 1 , the measured mass hardness is plotted versus theoretical mass hardness calculated using equation (68). From this figure, we can see that ag glomerates made from L 1 , L2, L3, L4, SB1 , SB2 and DP exhibit measured hard ness that can be predicted from equation (68). The hardness of agglomerates made from glass beads are also weil predicted below 1 05 N m -2 . Above this limit, which corresponds to capillary numbers that exceed 7 1 0 -2 , the mass hardness is over estimated. The hardness of agglomerates made with magnesium stearate is over esti mated by equation (68). The wet masses made from magnesium stearate have a low porosity and the liquid saturation of the pores created by the solid particles approaches 80%. It can be shown, therefore, that such agglomerates are actually in the funicular saturation state and that the particles cannot be considered as being in contact, but rather as being suspended in liquid with some air present. Hence, the model is not applicable. Further investigations on the measured mass hardness can be made by ne glecting the capillary, friction and viscous elements of equation (68) in turn. For x
I . E+06 ,-------,--,--,
S•
I . E+05
"!
� E
i'l
I .E+04
o Ll
•
o L2
o't/
ö L3
o DP o MOST
Q
� c:
0
I . E+03 •
I .E+02
-1"'------+---+---1
I .E+02
I .E+03
I . E+04
nc•1c (N.m·2 ) Fig. 3 1 .
Measured versus calculated mass hardness.
I . E+05
I .E+06
•
SB
x
L4
•
OB
1 30 1
Liquid Bridges in Granules I .E+06 ,------,---r---,--,
r-.. '7
•
I .E+05 *
•
E
� 1 .E+04 �
1l
E
c:
o
"
" ""
�
� LI o L2 " L3 o DP o
B
0
I .E+03
MGST
SB x L4 • GB •
I .E+02 -\L------+---l---+---� I .E+06 I .E+05 I .E+04 I . E+03 I .E+02 ilcalc
(N .m-2 ) neglecting friction
Fig. 32. Measured versus theoretical hardness calculated with (68) but neglecting the elemental friction forces of the i nterparticle contacts.
instance, by neglecting friction (Fig. 32) the measured hardness is underesti mated for the lactose and drug powders. For the glass and sugar beads, capillary forces are dominant at the low deformation speeds used. The hardness for magnesium stearate is still overestimated, probably due to the reason given above and the difficulty in measuring particle surface area for such a powder (changing the powder SUrface area of magnesium stearate from 5.3 to 2.78 m 2jg ensures a prediction of the measured mass hardness with an error of 1 7%). The simple model for the hardness of wet agglomerates given in equation (68) is valid only for particles which can be considered independent from one another during deformation and when the liquid bridge volume ensures that pendular liquid bridges can exist between touching particles. If particles have a shape that deviates significantly from the sphere or if they tend to aggregate, the model fails. Equation (68) shows that capillary, viscous and friction forces can be added to describe the yield strength of an agglomerate assembly. The contribution of vis cous forces is weil accounted for up to Ca = 1 . The contribution of friction forces depends on the accuracy of physicochemical parameters of both the powder and liquid binder, such as the particle surface area, the powder density and the liquid surface tension and contact angle with the particle. For the wet masses made from magnesium stearate powder, the measured powder sUrface area and the high saturation level could be the origin of the overestimation of the mass hard ness. In addition, the model has been developed based on crude assumptions about the particle shape and texture properties of the agglomerate.
1 302
S.J . R. Simons
4.3. An i nd ustrial case study: predicting pharmaceutical granulation performance from m icro-scale measurements
The selection of an appropriate polymerie binder to be used to agglomerate drug with excipients is a critical issue for the development of high-shear wet granu lation processes for pharmaceutical tablet systems. The aim of the study reported here, conducted on behalf of Merck Sharp & Dohme Ud., was to determine the potential for successful granulation through measurement of the interactions of the polymer solutions with individual drug particles. Pharmaceutical powders frequently exhibit poor flow and compaction behav iour, making granulation necessary prior to tabletting. A granulation technique is selected to produce porous, free-flowing material that compacts at low pressures to form non-friable tablets. Although it is possible to produce binderless granules, it is usually desirable to incorporate a binding agent in the formulation to enhance granule and tablet strength. The ability for a binder to distribute between particles can be seen as the result of the competitive effect between the adhesion of the binder with the particle and the cohesion for itself. The more the binder is able to adhere to the drug (favoured by a high work of adhesion) compared to its tendency to self-associate (favoured by a low work of cohesion), the better the spreading and subsequent binding, which ultimately favours the mechanical properties of the agglomerate resulting from the formation of more uniformly distributed solid bridges during the drying phase. Pharmaceutical granules ofter a further complexity in fully understanding the formation and breakage - that iS, they are usually made up of mixtures of solid species (e.g. drug and excipient) that can exhibit very different interfacial be haviour when in contact with the liquid binder (which then is dried to a solid, often polymerie, bond). During pharmaceutical granulation, the objective is to produce granules that have, on average, a uniform (and repeatable) distribution of drug particles within the bulk carrier (excipient) solid. This can be difficult to achieve and both drug depletion and enrichment in granules can occur (Fig. 33). Excipients
o
CJ
�
�
C) Y
c:J
Dry power
Drug
p ------+� Granulation
�
Binder Solution
/
-------+�
�/t
Dry binder
Drying
Wet Granule
Dry Granule
Fig. 33. Schematic representation of the action of binder during the processes of gran ulation and drying.
Liquid Bridges in Granules
1 303
Most of the studies reported in the literature tend to focus on the effects on drug/ excipient distribution as a function of differences in primary particle size (see, for instance, Refs. [52,53]). Drug particles are usually very much smaller than excipi ent particles, which may be as large as 1 00 )lm and be comparable to the median final target granule size of approximately 200 )lm. Hapgood etal. [54] conclude that coarse granules tend to always be drug-enriched since the drug particles are the finest component and preferentially granulate provided that the particles are ca pable of sustaining liquid bridges. This laUer point is very important and is, in part, due to the wetting behaviour exhibited by the liquid binder on the particles (it can also be dependent on the amount of liquid required to saturate the excipient and, possibly, hydrate the binder before liquid is present on the particle surfaces). Hence, it would appear that a crucial step in optimising granulation performance would be to select the most appropriate drug/excipient/binder system to enhance the formation of liquid bridges between both solid species. 4.3.1. Granulation of paracetamol
Paracetamol tablets can be produced via high-shear wet granulation of paracetamol crystals (the drug) with pharmaceuticaily inactive materials (excipients) inciuding a polymerie binder. Typical binders are PVP, HPMC and hydroxypropyl cellulose (HPC), used in aqueous solutions of concentrations ranging between 0.25-7.0% wtbinder /mIH20. The binder solution is sprayed onto the powder bed as it is being mixed. Usually a chopper blade, rotating at very high speeds (ca. 1 000 rpm) is used to aid in the mixing process and to break-up any large agglomerates. The objective is to encourage a uniform mixture of the components. The resulting granulated material is then dried and fed to a tableUing machine that compresses the material in a die to produce uniformly sized and shaped tablets with the desired average content of drug. 4.3.2. Binder selection criteria
During pharmaceutical granulation, the objective is to produce granules that have, on average, a uniform (and repeatable) distribution of drug particles within the bulk carrier (excipient) solid. This can be difficult to achieve and both drug depletion and enrichment in granules can occur [54]. One reason for this is the different surface properties of the solid species that can lead to different degrees of wetting with the binder liquid. A crucial step, therefore, is the choice of the most appropriate drug/ excipient/binder formulation to enhance the formation of liquid bridges between both solid species and, hence, that of granules. To mini mise formulation development time, it is desirable to make an early decision on the type of binder for a drug, based on the binder's intrinsic ability to spread across the surface of the drug and adhere the drug into granules. In
1 304
S.J . R. Si mons
principle, the more the polymer spreads across the surface of the particles, the larger the surface area of contact within the granules and the greater the strength of adhesion. The ability for the binder to spread across the drug is determined by the spreading coefficient, SB O : SBO = WaBO - WeB (69) The more the binder is able to adhere to the drug (favoured by a high work of adhesion, Wa BO ) compared to its tendency to self-associate (favoured by a low work of cohesion, WeB), the beUer the spreading and subsequent binding. Two approaches to binder selection can be taken. In the first approach, the thermo dynamics of the final, dry product are considered; in the second, spreading of the solution is considered. The result of drying is that the binder forms bonds between particles. If one assumes that the amount of bonding after drying is entirely determined by the thermodynamics of the dry materials, the binder can be selected on the basis of the dry polymer having a high spreading coefficient equation (69). The dry spreading coefficient can be predicted from the surface polarities of the dry binder and drug, usually derived from contact angle measurements of probe liquids such as water and diiodomethane. Examples of such predictions can be found in Ret. [55], where the spreading coefficient on paracetamol was predicted to increase in the order: Starch < PVP < Acacia < HPMC Measurements of the granule friability, tablet strength and capping index of pa racetamol wet granulated with these binders were found to be in !ine with this ranking. Rowe [55] showed that selection between binder systems for a drug can be gauged simply from the surface polarity of the drug concerned. A disadvantage of this approach is that it does not consider the effect of the solvent. During gran ulation, the binder solutions form wet bridges between the particles, allowing wet granules to be formed. If it is assumed that the amount of bonding after drying is entirely determined by the contacts set up during wet granulation, the binder can be selected on the basis of it giving a high spreading coefficient of the liquid across the surface. The effect of the binder on the spreading coefficient is usually measured through the consequential decrease in the contact angle of the liquid on the material. Hence, the approach is usually to select the binder giving the smallest contact angle. This can be measured in many ways. The most common tech niques - contact angle tensiometry and goniometry - involve powders or com pacts, and suffer from many artefacts associated with the structure of the sampie, e.g. solvent penetration between the particles. The most direct approach to measuring the relevant interactions between the liquid and solid is to measure the forces experienced between two drug particles separated by a liquid bridge usi ng an MFB. This approach for studying drug materials is described below.
Liquid Bridges in Granules
Fig. 34.
1 305
An SEM image of a crystal of paracetamol.
To imprave the wet spreading coefficient, wetting agents are often added to binder solutions. It could be that a combination of the wet and dry spreading coefficients needs to be considered to optimise the binder distribution and sub sequent granule formation. This was the focus of the work reported here. 4.3.3. Experimental procedure
4.3.3. 1 . Materials
Needle-shaped crystals of paracetamol (Fig. 34), supplied by Sigma Aldrich, were adhered to the glass micropipettes using Loctite™ Super Glue G EL. PVP (Plas done K-29J32) was obtained fram ISP. H PMC (methocei, 6 cps grade) was ob tained from Oow. Liquid binder was prepared with Analar water (BOH). Sodium lauryl sulphate (SLS) and sodium docusate (SO) wetting agents, in their solid state, were supplied by Merk Sharp and Oohme Ud. The concentrations for the pure binders were 4% wtbjmlH20 and for the mix of binder and wetting agent, 4% wtb jmlH2 0 + 0.5% wtwajmlH20 ' The solutions were all prepared in distilied water. Table 3 gives the values of the liquid vapour surface tensions (Y Lv) measured using a Kruss 1 2 tensiometer. Table 3 shows that both wetting agents are surface active and are able to lower the surface tension of the pure binders, sodium docusate being the more active wetting agent. 4.3.3.2. Micromanipulation
The MFB apparatus was used to manually elongate, along their axis, liquid bridges (of either H PMC or PVP solution) formed between paracetamol crystals
S.J.R. Si mons
1 306 Table 3.
Surface tension
YLv
of polymerie binders used
Solution PVP 4% PVP 4% + SD 0.5% PVP 4% + SLS 0.5% HPMC 4% HPMC 4% + SD 0.5% HPMC 4% + SLS 0.5%
Surface tension (mN/m) 62. 1 29.3 38.9 46. 1 27.6 36.8
SLS, sodium lauryl sulphate; SD, sodium docusate.
�
Flexible DOSlng Pipette :
==:111."
I
,
,
I
�\Ij !A -
,
.manipulator
Binder Solution
,
,
I
:
:
'
,
,
.� -
Fig. 35. Schematic of Method 1 used to measure the liquid bridge force between a res ervoir of liquid binder and a single paracetamol crystal. The measurement of the deflection of the feeding pipette leads to the calculation of the liquid bridge force.
previously attached to the tips of the micropipettes, in a similar fashion as that described in Section 3. 1 . The movement of the flexible pre-calibrated micropi pette was recorded and analysed to determine the maximum adhesion force exerted by the liquid bridges. Two methods were used to manipulate the particles and to obtain images of the separation sequence. Method 1 (Fig. 35) involved measurements on liquid bridges between a drug particle and a reservoir of solution binder held on the flexible micropipette; Method 2 (Fig. 36) involved measurements between two drug particles held by a liquid bridge. Adhesion forces were measured simulta neously. In each experiment, images were taken of two micropipettes, one of which was highly flexible in the direction of bridge separation with its tip in contact
1 307
Liquid Bridges in Granules
D
= 1+----,
�
camera
,
video recorder
-
,
,
! , , , , , , , ,
...
�
-
-
J ! '
..
lJ
Fig. 36. Schematic of Method 2 used to measure the liquid bridge force of a binder liquid bridge and two paracetamol crystals. The measurement of the deflection of the bent pipette leads to the calculation of the liquid bridge force.
with the other side of the liquid bridge, either directly or through wetting a drug particle bonded to it. The second pipette was rigid with respect to the bridge forces, had a crystal always bonded to its tip and was moved through its mi cromanipulator to form and break the liquid bridge. The maximum force exerted by a liquid bridge, separated using either Method 1 or 2, was calculated from the maximum displacement of the flexible micropipette with respect to its initial, un disturbed position (see Fig. 1 2). This micropipette was previously calibrated by attaching known weights to determine its spring constant, as described in Section 3. 1 . Receding contact angles were measured through detailed analysis of the im ages of liquid bridge stretching. The baseline of the particle surface was taken before liquid contact and the tangents to the liquid profile were taken at the points of liquid contact. The contact angle was then measured from the angle between the baseline and tangent. Since this method does not account for the asperities and irregularities of the crystal surface, the values obtained are only indicative of the crystal-to-binder wetting behaviour. Other parameters, such as the reservoir volume, the volume of binder depos ited onto a crystal and the geometry of the crystal were calculated directly from the images. The volume of the binder reservoir was calculated as the solid of revolution generated by a parabola (i.e. the approximation of the binder menis cus) around the axis of the feeding pipette, whilst the volume of binder left on the
1 308
S.J.R. Simons
Fig. 37. Reservoir volume left on the feeding pipette before (left) and after contact with the paracetamol crystal.
crystal was calculated as the difference of the reservoir volumes before and after the particle-binder contact, as illustrated in Fig. 37. Measurements of the maximum adhesive force and of the volume left on the crystal were carried out using feeding pipettes of different thickness. For the force measurements, very flexible pipettes (diameter of the thin end "-'70 j.tm) were usedto increase the pipette deflection, while for the volume measurements thicker pipettes (diameter of the thin end "-' 1 30 j.tm) were employed. In the latter set of experiments, the amount of volume left on the crystal is the result of the balance of the binder adhesiveness between the pipette and the paracetamol. Since paracetamol exhibits high interaction with all the solutions tested, a thin pipette would favour the migration of all the binder towards the crystal, hindering any comparison between the different binders. To reduce any geometrie influ ence, pipettes with similar tip diameters of "-' 1 30 j.tm were employed. 4.3.4. Results and discussion
4.3.4. 1 . Residual fil m deposition
In a previous study [56], a set of experiments was carried out to investigate the binder deposition on the crystal after contact with the binder solution. In that set of experiments, paracetamol crystals were engulfed in either HPMC 1 % or PVP 1 % solution, washed using a saturated paracetamol solution and then dried. Obser vations of the crystal engulfed in the HPMC 1 % solution showed more dark patches than those observed when the crystal was contacted with the PVP 1 % solution. This behaviour seemed to confirm higher adhesion with the crystal in favour of the HPMC solution. Experiments to investigate the residual film deposition were repeated in the present study using HPMC 4% and PVP 4% as binder solutions. In this set of experiments, the crystal was engulfed and dried to remove any side effects in troduced by the crystal washing. Figures 38 and 39 show a comparison for the
1 309
Liquid Bridges in Granules Before contact
A fter drying
Fig. 38. Observations of crystal engulfed in PVP 4% solution . Before contact (Ieft) and after drying.
two solutions and illustrate the crystal faces before and after the engulfment drying process. The images do not show large differences in the crystal faces which indicates that the results obtained in the previous experimental study were affected by paracetamol deposition (from the saturated solution) and were not then due to binder transfer, as previously interpreted. This implies that the distribution of such binders during (high-shear) granulation would be poor without the addition of wetting agents. 4.3.4.2. Liquid bridge adhesiveness and volume deposition
An extensive experimental programme was undertaken to measure the maximum liquid bridge force and the volume captured by a paracetamol crystal when put into contact and separated from a reservoir of binder. The binder solutions tested are those listed in Table 3.
1 31 0
S.J . R. S imons Before contact
Fig. 39. Observations of crystal engulfed in HPMC 4% solution. Before contact (Ieft) and after drying.
Figure 40 shows the maximum force versus the volume of binder reservoir recorded during the liquid bridge deformation. The force was expected to de crease with the surface tension of the binder, although it is not solely dependent on that parameter. In fact, the PVP 4% + SLS 0.5% solution presents higher value of the adhesive force in comparison to the H PMC 4% solution, despite a lower liquid-vapour surface tension. The total force of the liquid bridge is the result of two effects: that due to the liquid-vapour surface tension and that due to the capillary pressure within the bridge, which depends on the geometry assumed by the liquid bridge during separation. The differences of the total force recorded using the method illus trated in Fig. 35 can be accounted for by differences in the capillary pressure within liquid bridges of different binders. Unfortunately, it is difficult to evaluate the variations of the capillary pressure for the experiments recorded. It is also observed that for the lower surface tension solutions, PVP 4% + SD 0.5%
1 31 1
Liquid Bridges i n Granules
40.00 35.00 30.00
Z 25.00 � Q)
20.00
u..
1 5.00
� 0
•
t�9.ii-'����iti��'==---1 -1
1 0.00 ;:�:"����rj!.ll�_
0 pvp 4% • hpmc 4% 6 pvp 4% + sls 0.5% • hpmc 4% + sls 0.5%
5.00 +------j • hpmc 4% + sd 0.5% -
•
0.00 O.OE+OO
1 .5E-04
1 .0E-04 Vfeed [mi]
5.0E-05
o pvp 4%
+
sd 0.5%
2.0E-04
Fig. 40. Maximum liquid bridge force, measured using method iIIustrated in Fig. 35, versus volume of binder formed on the feeding pipette [57]. O pvp 4% • hpmc 4%
1 .0E-03
I .:t=
Q) :;
Ll. pvp 4% + sls 0.5% • hpmc 4% + sls 0 . 5%
1 .0E-04 1 .0E-05
0 •
Ll. O
1 .0E-06 1 .0E-07 0 .00
0.50
Ll. •
1 .00 Vfeed113/p [-]
o pvp 4% + sd 0.5% • hpmc 4%
+ sd 0.5%
Ll.
1 .50
2.00
Fig. 41. Volume of binder left on the paracetamol crystal (Vleft) versus volume of liquid on the feeding pipette (Vfeed), parameterised towards the wet perimeter of the crystal (P) [57].
(29.3 N/m) and H PMC 4% + SD 0.5% (27.6 mN/m), the values of the liquid bridge force are of comparable magnitude. Figure 41 shows the results of the experiments carried out to measure the amount of volume captured by the crystal after contact with the reservoir of binder and indicates that the solutions with lower Iiquid-vapour surface tension captured more volume of binder. The amount of liquid left on the surface of the crystal is a balance between the adhesion energy at the crystal-binder interface and the cohesion of the binder for itself. Whichever of the two is larger will determine whether the binder remains at the solid-liquid interface or recedes from it. The lower liquid-vapour surface tension promoted by the addition of the wetting agents favours the deposition of liquid on the crystal because it reduces the cohesiveness of the liquid for itself
1312
S.J.R. Simons
(note: the sOlid-liquid surface tension would also be reduced). Hence, the spreading and distribution of the binder on the solid improves with decreasing surface tension. It should also be noted that H PMC 4% + SO 0.5% has a higher viscosity than PVP 4% + SO 0.5%, which would infer slower rates of wetting for the former compared with the laUer. The kinetic effects on the weUing/deweUing process due to viscosity were not studied here. The volume left on the crystal is an important parameter in the understanding of the manner in which the liquid distributes among particles during the parti ele-binder mixing. The higher the volume left on a crystal the beUer the binder distribution among crystals, which ultimately favours a homogeneous growth of the granules. In this scenario the binder is more evenly distributed within the bulk mass, forming a more homogeneous mixture. Since the mechanical strength of agglomerates is the result of the adhesive force of solid bridges formed during the drying phase, the distribution of binder just before drying is a fundamental pa rameter to achieve uniform and improved mechanical properties. In this analysis, it is assumed that all the binders are able to form solid bridges of adhesive strength higher than that measured for liquid bridges. The wet granulation phase should promote a homogeneous binder distribution, which is a prerequisite to the final mechanical properties of the agglomerate, obtained after granule drying. Therefore, a binder should be chosen for its spreading ability rather than for the adhesive force of single liquid bridges. From this experimental work, PVP 4% + 0.5% SO seems to be the optimal binder for agglomeration of paracetamol. Another binder solution to take into consideration is the HPMC 4% + 0.5% SO, which has even beUer spreading ability but higher viscosity. The high viscosity though could retard the redistribution of liquid avail able on the surface of the crystal during particle mixing [45]. While having good binder distribution in a granulator promotes bridge formation and, hence, granule growth, the strength of the resultant granules depends on the dry binder bonds. Hence binder selection should be based on both the dry and wet binder surface energies.
5. CONCLUSIONS
This chapter has detailed the current theoretical and experimental treatment of liquid binder bridges developed between particles in granules. The i mportance of these bridges in developing sufficient adhesion forces to keep particles together and in governing granule growth, deformation and fracture behaviour has been demonstrated. Novel, micro-scale approach es to the study of these interactions have also been described, in particular, the micromanipulation work carried out by the authors at UCL. The influence of both liquid and solid properties
1313
Liquid Bridges in Granules
in determining the nature of the interactions has been elucidated using such techniques and is now being applied to the prediction of both granule properties and granulation performance - relating micro-scale observations to meso- and macro-scale behaviour. Nomenclature
a*, aj a, ai C Ci d d e
9
h( d) hi k ks
ri
u
Ui Vi V X
Y, Yi
y ' , Y 'i y"
Ymin
Abr, AbU
Ac AAS Adrop B C Ca F Fb
Dimensionless separation distance with respect particle radius, ge neric or calculated between two configurations (i = 1 ,2) Liquid bridge separation distance, generic or between particle and liquid bridge neck (i = 1 ,2) (m) Co-ordination number of particle assembly Droplet cord length on the ith (i = A,B) particle (m) Absolute agglomerate deformation (m) Average particle diameter (m) Deflection of flexible micropipette (m) Gravity acceleration (9.81 m/s2 ) Non-deformed agglomerate cap height (m) Height of cap of sphere for the ith (i = A,B) particle (m) Packing constant Flexible micropipette spring constant (N/m) Liquid bridge radii of curvature (i = 1 ,2) (m) Analytical description of the profile assumed by a particle contacting a liquid bridge, U = u(x) (m) Liquid droplet radius on the ith (i A, B) particle (m) Relative particle separation velocity (m/s) Average particle volume (m 3) Horizontal axis (m) Liquid bridge ordinate, generic or calculated at point A, B (i = A,B) (m) First derivative of Y, generic or calculated at point A, B (i A,B) Second derivative of Y (m- i ) Minimum bridge neck ordinate (m) Area of the liquid bridge profile, generic or of configuration i (i = 1 ,2) (m2 ) Contact area of an agglomerate with a flat punch (m2 ) Solid-solid contact area (m 2 ) Liquid droplet area (m2 ) Integration coefficient, B = YA sin(8A + ßA)(I1P j2YdYÄ (m) Dimensionless parameter, c V(1 + 2Vbr)1j3 /rr(1 + 8/2)2 Capillary number Force between particles (N) Liquid bridge force calculated at the particle-meniscus boundary (N) =
=
=
1 31 4
S.J.R. Simons
Fca p Ffric
Capillary force (N) Friction force (N) Liquid bridge force calculated at the neck of the meniscus (N) Total viscous force in a liqui,9 bridge (N) Geometrie average radius, R = 2RARB / RA + RB(m) Dimensionless mean curvature, H* = I1PR/2y Average particle separation distance in an agglomerate (m) Applied load (N) Characteristic length of liquid bridge (m) Length of test cylinder (m) Number of interparticle contacts per unit area (11m 2) Pressure, generic or for configuration i (i = 1 , 2) (Pa) External medium pressure (Pa) Particle radius, generic or for particle ith (i = A,B) (m) Agglomerate radius (m) True surface area of a powder (m2) Spreading coefficient of binder on a drug particle (J) Stokes number, St = 2mvo/3n1/R2 Liquid droplet cap height on the ith (i = A,B) particle (m) Volume of an agglomerate (m 3) Volume of liquid bridge (m 3) Dimensionless liquid bridge volume with respect cubed particle ra dius Volume of cap of sphere for the ith (i = A,B) particle (m 3) Volumes of revolution of the liquid bridge meniscus (m 3) Volumes of revolution of the liquid bridge meniscus, from particle A to liquid bridge neck and from neck to particle B, respectively (m3) Rupture energy of liquid bridge (J) Dimensionless rupture energy of liquid bridge, W* = WIYL R2 Work of adhesion (J) Work of cohesion (J) Dimensionless factor, X = (1 + (a/2R)) Dimensionless liquid bridge abscissa with respect particle radius, evaluated at the contact with the particle Driven movement (m) FolIower movement (m) Dimensionless liquid bridge abscissa with respect particle radius, evaluated at point i Dimensionless X calculated at minimum and maximum liquid bridge separation distance Dimensionless liquid bridge ordinate with respect to particle radius First derivative of dimensionless liquid bridge ordinate evaluated at point i Second derivative of dimensionless liquid bridge ordinate evaluated at point i
Fn
C.viS
R
H* H L L M NE
P, Pi
Pext R, Ri Rag
S SB O St 7i
Vag Vb r
V br Vca p ,i Vm
Vm ,A, Vm ,B
Xm in, max
Y"i
Liquid Bridges in Granules
1 31 5
GREEK
ß, ßi
t;
Y
YL YLV IJ
(), Bi ()i P Ps
4YL 4Ys
Q Q'
Half-filling angle, generic or calculated at point A, B (i = A,B) (rad) Voidage fraction in an agglomerate Surface tension (N/m) Surface tension of liquid binder towards external medium (either gas or liquid) (N/m) Vapour-liquid surface tension (N/m) Dynamic viscosity (Pa s) Contact angle generic or calculated at point i (i = A,B) (rad) Intrinsic contact angle (rad) Mass density (kg/m 3) True powder mass density (kg/m 3) Liquid volume fraction in an agglomerate Solid volume fraction in an agglomerate Hardness of a material Angle between normal to liquid bridge profile and x-axis (rad)
REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [ 1 0] [1 1 ] [1 2] [ 1 3] [ 1 4] [ 1 5] [1 6] [ 1 7] [ 1 8] [ 1 9] [20] [21 ] [22] [231 [241 [251 [26] [27]
J.F. Padday, Pure Appl . Chem. 48 ( 1 976) 485. Adetayo, B.J. Ennis, AIChE J. 43 ( 1 997) 927. N. Ouchiyama, T. Tanaka, Ind. Eng. Chem. Process Des. Dev. 21 (1 982) 35. Z. Ning, R Boerefijn , M. Ghadiri, C. Thornton, Adv. Powder Technol . 8 ( 1 997) 1 5. J. Crassoux, E. Charlaix, H . Gayvallet, J .-L. Loubet, Langmuir 9 ( 1 993) 1 995. G . Mason, C.G. Clark, Chem. Eng. Sci. 20 ( 1 965) 859. G . Lian, C. Thornton, M.J. Adams, Powders and Grains 93, C. Thornton (Ed.), AA Balkema, Rotterdam, 1 993. D.N. Mazzone, G . I . Tardos, R Pfeffer, Powder Technol . 5 1 (1 987) 71 . F . R E . Bisschop, W.J.L. Rigole, J. Coll. I nt. Sei. 88 ( 1 982) 1 1 7. T.Y. Chen, JA Tsamopoulos, RJ. Good, J . Coll. I nt. Sci. 1 51 ( 1 992) 49. E. Wolfram, J . Pinter, Acta Chim. Hung. 1 00 ( 1 979) 433. T. Dabros, T.G.M. van de Ven, J. Coll. I nt. Sei. 1 63 ( 1 994) 28. M . J . Crooks, H .W. Schade, Powder Teehnol 19 (1 978) 1 03. SA Sehildeerout, J . Pharm . Sei. 36 ( 1 984) 502. P.E. Luner, S . R Babu , S.C. Mehta, Int. J. Pharm. 1 28 (1 996) 29. Y. Pomeau, J. Coll. Int. Sei. 1 1 3 ( 1 986) 5. G. Lian, C. Thornton, M . J . Adams, J. Coll. I nt. Sei. 1 61 ( 1 993) 1 38. F . M . Orr, L.E. Scriven , P. Rivas, J. Fluid Meeh. 67 ( 1 975) 723. M .A. Erle, D.C. Dyson , N.R Morrow, AIChE J. 17 ( 1 97 1 ) 1 1 5. S.J.R Simons, RJ. Fairbrother, Powder Teehnol. 1 1 0 (2000) 44. X. Pepin , S.J.R Simons, S. Blanchon, D. Rossetti, G. Couarraze, Powder Technol. 1 1 7 (2001 ) 1 23. J.F. Padday, J . Fluid Meeh. 352 (1 997) 1 77. J . Plateau, The Figures of Equilibrium of a Liquid Mass, Annual Report of the Smithsonian I nstitution, Washington, DC, 1 864, p. 338. RA Fisher, J. Agrie. Sei. 16 (1 926) 492. RW. Coughlin, B. Elbirli, L. Vergara-Edwards, J. Coll. Int. Sei . 87 ( 1 982) 1 8. S.J.R Simons, J.P.K. Seville, M.J. Adams, Chem. Eng. Sei. 49 ( 1 994) 2331 . X. Pepin , D. Rossetti , S . M . Iveson, S.J.R Simons, J. Coll. Int. Sei . 232 (2000) 289. AA
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[28] X. Pepin, D. Rossetti, S.J . R. Simons, J. Coll. Int. Sci. 232 (2000) 298. [29] H. Schubert, Int. Chem. Eng. 21 ( 1 98 1 ) 363. [30] H. Schubert, Kapillaritat in porosen feststoffsystemen, Springer, Berlin, Heidelberg, 1 982. [31 ] O. Pitois, P. Moucheront, X. Chateau, J . Coll. Int. Sci. 231 (2000) 26. [32] A Cameron, Basic Lubrication Theory, 2nd ed, Wiley, Chichester, 1 976. [33] D.Y.C. Chan, R.G. Horn, J. Chem. Phys. 83 ( 1 985) 531 1 . [34] X. Pepin, S. Blanchon, G . Couarraze, J . Pharm. Sci. 90 (2001 ) 332. [35] S.J.R. Simons, X. Pepin, D. Rossetti, Int. J. Min. Proc. 72 (2003) 463. [36] O. Pitois, P. Moucheront, X. Chateau, Eur. Phys. J. B 23 (200 1 ) 79. [37] D. Rossetti , X. Pepin, S.J.R. Si mons, J. Coll. Int. Sci . 261 (2003) 1 6 1 . [38] G. Lian, C. Thornton, M.J. Adams, Chem. Eng. Sci. 53 ( 1 998) 338 1 . [39] K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1 985. [40] S.M. Iveson, JA Beathe, N.w. Page, Powder Technol. 1 27 (2002) 1 49. [41 ] J . Fu, A D. Salman, M.J. Hounslow, Proc. World Congress of Particle Tech. 4, paper 1 1 3, July 2 1 -25, Sydney, Australia, 2002. [42] A Samimi, M. Ghadiri, R. Boerefin, R. Kohlus, Proc. 7th Int. Sym. Agglom., May 29-3 1 , Albi, France, 2 (2001 ) 769. [43] P. Pagliai, S.J.R. Si mons, D. Rhodes, Powder Technol. 1 48 (2004) 1 06. [44] R.J. Fairbrother, A microscopic investigation of particie-particle interactions in the presence of liquid binders in relation to the mechanisms of "wet" agglomeration processes, PhD Thesis, University of London, 1 999. [45] B.J. Ennis, G. Tardos, R. Pfeffer, Powder Technol. 65 ( 1 99 1 ) 257. [46] H . G . Kristensen, P. Holm, T. Schaefer, Powder Technol. 44 ( 1 985) 227. [47] S.M. Iveson, J . D . Litster, B.J. Ennis, Powder Technol. 88 ( 1 996) 1 5. [48] S.M. Iveson, J.D. Litster, Powder Technol. 99 ( 1 998) 243. [49] C. Thronton, Kona 1 5 ( 1 997) 8 1 . [50] S.M. Iveson, N.w. Page, J.D. Litster, Proc. 7th Int. Symp. Agglom., May 29-3 1 , Albi, France, 2 (2001 ) 541 . [51 ] S.Y. Chan, N . Pilpel, D.C.H. Cheng, Powder Technol. 34 ( 1 983) 1 73. [52] Y. Zhang, K.C. Johnson, Int. J . Pharma. 1 54 ( 1 997) 1 79. [53] H . Vromans, H.G.M. Poels-Jansseen, H . Egermann, Pharm. Dev. Tech. 4 ( 1 999) 297. [54] K. Hapgood, H.E. Hartman, C. Kaur, R. Plank, P. Harmon, JA Zega, Proc. World Congress of Particle Tech. 4, paper 706, July 2 1 -25, Sydney, Australia, 2002. [55] R.C. Rowe, Int. J. Pharm. 58 ( 1 990) 209. [56] S.J . R. Simons, D. Rossetti , P. Pagliai, R. Ward, S. Fitzpatrick, Powder Technol 1 40 (2004) 280. [57] S.J.R. Simons, D. Rossetti, P. Pagliai, R. Ward, S. Fitzpatrick, Chem. Eng. Sci. 60 (2005) 4055.
CHAPTER 28
Pend u la r Cap i l l a ry B ri dges Christopher D . Wi llett,a, b S i mo n A. Johnso n , a M ichael J . Adams b , * a n d Jonathan P . K . Sevi lie b
a Unilever Research and Development Port Sunlight, Quarry Road East, Bebington, Wirral CH63 3JW, UK bCentre for Formulation Engineering, Department of Chemical Engineering, University of Birmingham, Birmingham B15 2TT, UK Contents
1 . Introduction 2. Fundamental properties 2. 1 . Free liquid surfaces 2.2. Bridges between solid bodies 2.3. The capillary forces 3. The toroidal approximation 3. 1 . Toroidal geometry 3.2. The force of attraction 3.3. Constant volume bridges 4. Israelachvili's approximation 5. Evaluation of the Laplace-Young equation 5. 1 . The dichotomy of liquid bridges 5.2. Bridge rupture 5.3. Comparison with experimental data 5.4. Closed-form approximations for equal spheres 5.5. Bridges between unequal spheres 6. Influence of wetting hysteresis 7. Influence of gravity 8. Future look References
1317 1319 1319 1319 1 32 1 1 323 1 323 1 324 1 327 1 328 1 330 1 330 1 332 1 332 1 334 1 336 1 340 1 344 1 349 1 350
1 . I NTRODUCTION
It is weil established that liquid junctions play a major role in granulation proc esses. Essentially they are responsible for the forces of attraction that bind to gether the primary particles in an agglomerate. Under static conditions, only capillary forces act between the particles and their strength depends on such factors as the geometry, surface free energy and surface topography of the * Corresponding author. E-mail: [email protected]
Granulation Edited by A.D. Salman, M.J. Hounslow and J. P. K. Seville
, 2007 Elsevier B .v. All rights reserved
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C . D . Willett e t 81.
particles, the separation distance between the particles and also the size of the liquid bridge together with the surface tension of the liquid. In this chapter, the special case of pendular liquid bridges between nominally smooth and rigid spherical particles will be considered. Such bridges have been studied in great detail because of their generic importance in a wide range of fields involving wet granular matter [1], as weil as for applications to granulation e.g. Ref. [2]. Pen dular bridges are isolated liquid junctions between particles. When a granule is completely saturated, this is termed the 'capillary state'. The intermediate case, in which the interstitial voidage is partially saturated, is known as the 'fenicular state'. The capillary and fenicular states are more difficult to evaluate theoretically because of the 3D geometry; analytical solutions are limited to 2D [3]. The pri mary particles are often angular so that the spherical geometry is a reasonable approximation. Calculations have been made for solids of revolution and, in ex treme cases such as cones, the behaviour is quite different to spheres [4]. In the static state, the capillary forces may be sufficient to distort particles that are deformable. This is a coupled problem because the resulting effect on the particle geometry will influence the capillary forces [5]. Such coupling may be ignored for most practical granulation systems when the capillary forces between the primary particles are being considered. This is because such particles behave effectively as rigid bodies in this context. However, for a capillary junction between two agglomerates during impact, the deformation of the agglomerates due to the kinetic energy also introduces this type of coupling. There is an additional com plexity that the local compaction of the agglomerates causes the liquid binder to migrate to the contact zone. Moreover, it is possible that viscous forces will be come important during impact, depending on the capillary number [6]. Provided that the length scale of the liquid bridge is large compared with the asperity heights, the influence of roughness may be regarded as simply providing a lower bound to the effective gap between the particles. When the length scale is comparable to that of the asperities, it is necessary to undertake a microscopic analysis, which could assume single asperity contact because of the acute radius of curvature of particles. To first order, asperities could be treated as spherically capped features and the analyses described in this chapter could then be applied. A particular focus of the current chapter is to describe c1osed-form approxi mations for calculating the forces and stability associated with capillary bridges. This avoids the difficulties of exact calculations that require numerical integration. A similar approach will be described in order to assess the influence of wetting hysteresis and gravity. For bridges that are greater than some critical size, gravity causes a distortion of the bridge geometry and hence will influence both the capillary forces and the bridge stability. For liquids that do not perfectly wet the particles, wetting hysteresis commonly occurs and some of the fundamental as pects of this problem will be described. Discrete simulation schemes, e.g. gran ular dynamics studies of wet agglomerate impact [7,8], are an important
Pendular Capillary Bridges
1319
application of the closed-form approximations. They are used as computationally efficient algorithms for the interaction laws. 2. FUNDAMENTAL PROPERTIES 2.1 . Free liquid surfaces
Liquid surfaces obey strict thermodynamic laws, which exactly determine their equilibrium geometry. A pressure difference, f.,.P, must exist across a non-planar liquid-vapour surface in order to balance the liquid-vapour interfacial tension at the surface, Ylv' The relationship between the two parameters is given by the Laplace-Young equation [9]: (1 ) where ( is the curvature of the meniscus. This can be expressed in terms of the two orthogonal principal radii of normal curvature, r1 and r2 as shown in Fig. 1 and given by (2) where any radius is taken to be positive if it is subtended from the liquid. r is the radius of curvature of the surface. Plateau [1 0] first observed that the curvature at a gravity-free liquid-vapour surface must be the same at each point on that interface, in order to satisfy equation ( 1 ). 2.2. Bridges between solid bodies
Consider a liquid bridge between two infinitely long parallel cylinders in close proximity as shown in Fig. 2. By defining orthogonal axes, e1 parallel to the axes of the cylinders and e2 between their centres, we see from equation (2) that r1 ,
Fig. 1 . General representation of a meniscus surface in three-dimensions, the curvature of which can be represented by two orthogonal radii , r1 and r2 (as shown, r2 is positive while r1 is negative).
1 320
C . D. Willett et al.
Fig. 2. A hypothetical liquid bridge between two infinitely long cylinders, defining or thogonal axes, e1 and e2 , and corresponding meniscus radii , (1 and (2 . In this case, (1 -+ 00 and (2 = constant.
Fig. 3. One half of a generic liquid bridge between two equal spheres, defining orthogonal axes e1 and e2 and corresponding meniscus radii, (1 and (2 ' In this case, both (1 and (2 are functions of position in order to maintain constant mean curvature.
the radius of curvature of the meniscus in the plane of the axis e1 , tends to infinity. Then from equation (2) (2, the radius of curvature of the meniscus in the plane of the axis e2, is constant and hence the meniscus geometry is circular. As drawn in Fig. 2, the contact angle is sufficiently small for (2 , and hence r, to be negative. This leads to a negative Laplace pressure and an attractive contribution to the force between the cylinders. Now consider a liquid bridge between two spheres, one half on which is shown in Fig. 3. By using the same axis definitions as for the pair of cylinders, it is immediately clear from equation (2) that values of both (1 and (2 must vary with position on the surface in order to maintain a constant value of r given by the Laplace-Young equation (equation (1 )). To solve for the values of (1 and (2 along the length of the bridge requires an iterative mathematical solution of this rela tionship [1 1 ] . This approach has been adopted by the many workers (e.g. see Refs. [ 1 2- 1 5]), most notably by Orr et al. [ 1 6] who solved the Laplace-Young equation by employing elliptical integrals for the general case of arbitrary contact
Pendular Capiliary Bridges
1 32 1
angle. In principle, the work of Orr et al. [ 1 6] is a complete analysis of the geo metry of gravity-free bridges between spheres of arbitrary radius and contact angle. However, the application of their method requires a priori knowledge of the surface geometry and the solution of elliptical integrals. Although the solution of the Laplace-Young equation is sufficient to describe the profiles of liquid bridges, some workers have adopted the alternative ap proach of minimising the free energy of the system, using the calculus of varia tions. Erle et al. [1 1 ] used this method to find the minimum surface area of the vapour-liquid interface, but not the solid-liquid or solid-vapour interfaces and their solutions therefore only apply to a zero contact angle; they are of the same form as those obtained from the Laplace-Young equation. Oe Bisschop and Rigole [ 1 7] formulated the problem differently so as to obtain solutions for non zero contact angles. 2.3. The capillary forces
If a solid body in air is partiaffy introduced into a mass of liquid, there may be a resultant force on the solid body as the new liquid-vapour-solid system attains thermodynamic equilibrium. In the absence of gravitational effects, this resultant force is caused by two properties of the liquid mass. The first, F;" is due to the surface tension that acts over the three-phase contact line and is equal to the line integral of the liquid-vapour surface tension along that line. The second, Ft1p, is due to the difference in hydrostatic pressure between the interior and exterior of the liquid mass and is equal to the product of the surface integral of the pressure field and the projected surface area of the solid-liquid surface. Consider a differentially thin slice through the cross-section of a gravity-free liquid bridge between two equal spheres; the forces on that slice must be in equilibrium under static conditions. Orr et al. [1 6] developed analytical solutions for the profiles of liquid bridges between solid bodies with an arbitrary contact angle. They demonstrated that a range of different types of liquid bridge geome tries existed with each possessing a minimum radius or 'neck'; some of the profiles had virtual necks, where the neck is external to the bridge. Because the bridge must be everywhere in equilibrium, the attractive force for an axi-sym metric liquid bridge is the same at every axial location along its length; here the neck (or virtual neck) is chosen as a standard location for calculating the force. In the general case, the surface tension contribution is given by (3) where rN is the radius of the circular neck cross-section. This contribution is positive and attractive. The second contribution due to the reduced hydrostatic pressure is given by (4)
1 322
c. D. Willett et al.
which, by introducing equation ( 1 ) becomes FI1P = - n Y�v � (
(5)
This contribution is attractive if ,. is negative or repulsive if ,. is positive. Thus, the total attractive force, F, is given by
( ;�)
F = 2nYlv(N 1 -
Hence, if we define a dimensionless force as F f= 1 - (N 2 2,. - nYlv(N and a dimensionless bridge curvature, �: _
� = ('! (
(6)
(7)
(8)
we obtain: , � F= 1 -(9) 2 which relates the dimensionless force to the dimensionless curvature alone. Equation (9) applies to all axi-symmetric pendular liquid bridges, regardless of the curvatures of the solid bodies and of the contact angle. The evaluation of any attractive force due to a pendular liquid bridge is given by equation (9) and reduces to a determination of the values of ,. and (N. Furthermore, if � « - 1 , the surface tension contribution is negligible and FI1P » Fy• A range of gravity-free axi-symmetric liquid bridge profiles for different values of � are exemplified in Fig. 4. The curves are generated by a technique described in detail in Ref. [1 8]. Values of � = 0, 1 , and 2 correspond to simple geometries; namely, the catenoid, cylinder and spherical profiles. For � = 2, the spherical curvature, equation (9) gives f= = 0, indicating that the interparticle force is zero and that the free liquid droplet is in mechanical equilibrium because FI1P = - Fr For � < 2, the interparticle force is attractive with the repulsive contribution from the Laplace pressure being zero for a bridge with a catenoid profile, � = O. For � < 0 both contributions to the interparticle force are attractive and for � = - 1 they become equal. The surface tension contribution becomes negligible for � « - 2. If the curvature is greater than that for a sphere (� > 2), the overall inter particle force becomes repulsive, in agreement with Orr et al. [1 6]. For equal spheres, it is often convenient to define an alternative dimensionless force in terms of the radius of the sphere, R, rather than that of the neck of the liquid bridge, thus: F_ p= (1 0) 2nYlv R
_
1 323
Pendular Capillary Bridges y
5 ,-------,--, o (catenoid) 0.25 4 3
0.5
2
0.75 1
O +-
(cylinder)
1 .5 2 (spherical free droplet)
���-.
--
o
--��
--
,_--�
--
4
5
Fig. 4. A range of possible liquid bridges, between, arbitrary solid bodies, differing only in the value of the dimensionless mean curvature, � . Hence the dimensionless attractive force, f: is unique to each curve.
This is the conventional definition used by most workers because particle size is generally more accessible than the size of the liquid bridge. 3. THE TOROIDAL APPROXIMATION
As discussed previously, an iterative mathematical procedure is required to ac curately describe the profiles of liquid bridges between spheres; therefore simpler approximations are often used. Of these, the 'toroidal approximation' is perhaps the most widely used due to its closed form [6, 1 9-24]. 3.1 . Toroidal geometry
As discussed previously, a liquid bridge between two parallel infinite cylinders will possess a circular cross-section because the curvature in the plane of the cylinder axis is zero. For liquid bridges between a pair of spheres this is not the case and the bridge profiles are therefore necessarily complex [1 1 ]. Consequentiy, much of the early work on liquid bridges between particles made use of the simple as sumption that the bridge may be described by intersecting circular arcs. Figure 5 shows the resulting geometry of this toroidal approximation. Since, at equilibrium, the pressure within the bridge must be uniform in order to prevent internal fluid flow, the curvature of the meniscus must be constant over its surface, which must be the case in order to satisfy the Laplace-Young equation. It may readily be seen
1 324
c. D. Willett et al.
F i g . 5. The geometry of the toroidal approximation with particles of radius R, separated by a distance 2S, connected by a liquid bridge of half-filling angle ß and contact angle q>.
from Fig. 5 that the toroidal approximation does not satisfy this requirement, since the total curvature varies from (1 frA + 1 /rN) - 1 at the neck to (1 frA + 1 /rc) - 1 at the contact line, and this leads to the errors associated with this approximation. For a pair of equal spheres of radius R, separated by a distance 2S, connected by a liquid bridge with a contact angle ep, and a half-filling angle ß, it can be shown by simple geometrie arguments [1 8] that the radii obtained from the toroidal approximation are given by (rN - rA) =
�
tan (n/2 ß
_ ep) + R sin ß
(1 1 ) (1 2)
n
rc = R sin ß
[ 0,1 ,
]
(1 3)
(ß + ep» n/2 (14) (ß + ep) < n/2 where A = S + R(1 - cos ß), following the standard convention that the radii are positive if the centre of curvature lies on the liquid side of the meniscus. =
3.2. The force of attraction
Fisher [20] was the first to correctly develop the force equations using the toroidal approximation. He calculated the force at the neck of the bridge (ofien ca lied the 'gorge' method) and showed that for spheres in contact: 2nRYlv F= ( 1 5) 1 + tan(ß/2) Adams and Perchard [6] argued that the force should be estimated at the con tact line because that is where the force is transmitted to the particles (known as the 'boundary method'). In fact, both methods are in error due to the approximation
1 325
Pendular Capillary Bridges
associated with the assumed bridge geometry, although as we shall show below, the errors are normally small unless the relative size of the bridge is large. As mentioned previously, if the effects of gravity on a capillary bridge are ignored, the force arises from two effects. The first, F,., is due to the surface tension directly and the second, Ff..p, arises from the reduced hydrostatic pres sure associated with the curvature of the liquid bridge. From Fig. 5, for the gorge and boundary methods we obtain: Fy,gorge = 2nrNYlv ( 1 6) F",boundary = 2nrcYlv sin (ß + (p )
(1 7) (1 8)
(1 9) It has already been pointed out that since the force of attraction must remain constant along the axis of symmetry of a stable liquid bridge then, in principle, it may be determined at any point. However, in the case of the toroidal approx i mation, the bridge does not possess a constant curvature and the calculated force will be a weak function of the position along the axis. Nevertheless, by using equations ( 1 1 )-(1 9) it is possible to demonstrate in a general way how bridge geometric parameters will influence the force. Assuming a zero contact angle, the dimensionless force can be calculated as a function of the half-filling angle and the dimensionless half separation distance, S*( = SIR) as parameters; Fig. 6 shows the results. Several general conclusions can be drawn. Firstly, the force decreases strongly with separation, and the differences between the forces calculated on the basis of the two methods are relatively small. Secondly, the dependence of the force on the half-filling angle, ß, is more complex; the force decreases monotonically with increasing ß at zero separation, but shows a maximum for non-zero separations. The value of ß corresponding to the maximum force is larger for larger separations. The reason for the counter-intuitive decrease in force with increasing ß at zero separation is that the pressure deficit force, Ff..p, dominates under these conditions and the decreasing bridge curvature as ß tends to zero causes a large pressure deficit. Although this trend would not be expected to persist when the length scale of the bridge is comparable to molecular di mensions [25], the Laplace-Young equation is found to apply for liquid bridges between smooth surfaces with values of r as small as a few nanometres [26]. In reality, real surfaces are not perfectly smooth and surface roughness introduces an effective minimum separation, as pointed out by Pietsch [27]. In general, the boundary method gives a greater estimate of the force than the gorge method , the difference between the two methods increases with filling angle. The accuracy of these two approximations is discussed in the next section.
1 326
c. D . Willett et al. (a)
1 .0 ...".----,,.---,
0.8 " " \ \ \
\ 40° \\
0.6
\
0.4
\ \ \ \ \ \
0.2
10-5
10-4
10.3
10"
10.1
10°
S* (h)
101
�r� �u�
1.0 ...,..,,----, S* = 0
0.8
0.6
0.4
0.2
0.0
-1-'---""--;---;----1 o 10 20 30 40 50 60 ßn
Fig. 6. The variation in the dimensionless attractive force between equal spheres as a function of (a) the dimensionless half-separation distance with constant half-filling angle and (b) the half-filling angle with constant dimensionless half-separation distance, eval uated using the toroidal approximation for zero contact angle by both 'gorge' and 'bound ary' methods.
The maximum attractive force is predicted to be given when the two spheres are in contact and the liquid content tends to zero. (2 0 )
Fmax = 2nRYlv Hence, it is useful to define a dimensionless force,
F* ,
as
F_ =_ F* = � 2nR Fmax Ylv which is consistent with the arguments leading to equation ( 1 0).
(2 1 )
1 327
Pendular Capillary Bridges
3.3. Constant volume bridges
It has been demonstrated how the attractive force owing to surface tension is influenced by bridge parameters such as ß, R and S* . However, it is often of practical interest to evaluate ß as a function of separation distance. In this re spect, there are two main approximate conditions that commonly occur in nature. The first assumes that the liquid bridge is volatile and the surface of the liquid is in equilibrium with the surrounding vapour [28]. The second assumes that the liquid is involatile so the bridge volume is constant. Here, the condition that the liquid bridge volume, V, remains constant during particle separation is assumed and therefore the bridge volume as a function of the geometrical parameters must be calculated. For particles in contact, with a zero contact angle, Keen [1 9] provided an expression for the bridge volume as (22)
Jacques et al. [29] derived an expression for separated spheres. Their solution was corrected by Si mons et al. [21 ] and is most simply represented as A3 BA2 n A3 (A - S)3 V = 2n AB2 - A2 B tan ß - --2- 2. - ß + --2- - "3 - R(A - S)2 + �3 cos ß cos ß (2 3)
[
(
)
--'---]
where A = S + R( 1 - cosß)
(24)
B = R sin ß + A tan ß
(25)
and This provides an accurate expression for a zero contact angle. However, a new expression for an arbitrary contact angle may be derived. Consider a general liquid junction having a profile that is given by the function f(x) and the enclosed particle profile as g(x), as shown in Fig. 7. The volume of the liquid bridge is given by V = 2n
where
lA f(X)2 dx - 2n isA g(x)2 dx
(26)
and g(X)2 = 2R(x - S) - (S - X)2
(28)
1 328
C. D. Willett et al. g(x) f(x)
R
y
ß
x
Fig. 7. Showing a section of a general liquid bridge with liquid surface described by f(x) and solid surface described by g(x).
+
Evaluation of equation ( 26) yields: V
�
2
fA - fN)' + r,l
(� :�) -
+ ';'(fr
fA)sin-1 (�) � ]
+ (- 1 tA(rN - rA)(� - A2 ) 1 /2 - R(A - S)2
_
(A
S)3
(29)
This is a general equation for the bridge volume as a function of the radii of curvature and is in an alternate form to that given by Lian et al. [ 1 5]. In order to establish a force-separation relationship for bridges of constant volume it is necessary to use an iterative process. Orr et al. [1 6] argued that in general the toroidal approximation provided a reasonably accurate estimate of the force. For example, for ß < 1 0° and
IsraelachviIi [30] considered a sphere separated by a distance 0 from a semi infinite flat plate (Fig. 8). In the case that there is no autoadhesive force (such as that due to van der Waals interactions) acting between the two solid surfaces, he argued that the energy change resulting from the creation of a liquid bridge is
1 329
Pendular Capillary Bridges
ß
R
Schematic representation of a sphere connected to a flat surface via a small liquid bridge of toroidal geometry.
Fig. 8.
given by the energy of formation of a solid-liquid interface, less the energy of the solid-vapour interface which is lost: ,1 W = 2nR2 sin 2 ß(Ysl - Ysv) (30) where Ysv and Ysl are the solid-vapour and solid-liquid interfacial tensions. The interfacial tensions are related by Young's equation, given by Ylv COS
(31 ) (32)
Since the force is given by F = d,1W/dD, this results in F = -4nR2 ßY lv cos
(��)
(33)
The volume of the bridge may be represented in a cylindrical geometry by V = nR2 sin2 ß(D + ci) - (nRJ /3)(1 - cos ß)2 (2 + cos ß) (34) where d is the immersion depth of the sphere in the liquid. If ß is smalI, sin ß � ß, cos ß � (1 - ß2/2), the immersed profile of the sphere is approximately parabolic and d � Rß2/2. Hence in the limit as ß -+ O: (35)
For a constant volume liquid bridge, d V/dD = 0, and differentiation of equation (35) gives dß 1 (36) dD (Rß + 2D/ß)
1 330
C. D . Willett et al.
Substitution of this into equation (33) gives 4nRYIY cos cp F= (1 + Djd)
(37)
Willett [1 8] examined the accuracy of this approximation for liquid bridges be tween a sphere and a flat using exact numerical methods and showed that it overestimates the force both at large separation distances and at contact for relatively large liquid bridges. It may be noted that in the contact limit (S = 0), equation (37) reduces to a value of the force that is exactly twice the maximum sphere-sphere force from equation (20). 5. EVALUATION OF THE LAPLACE-YOUNG EQUATION 5. 1 . The d ichotomy of liquid bridges
Liquid bridges will attempt to adopt geometrie configurations that mini mise the total Gibbs free energy of the system, and this gives a possible method for calculating their shape. However, the mathematical formulation of the surfaces generated following this condition is not trivial [1 6, 1 7]. Erle et al. [1 1 ] showed that for a pendular bridge between two spheres of specified bridge volume and particle separation distance there are in fact two solutions to the Laplace-Young equation, a phenomenon they termed the 'di chotomy of liquid bridges'. Lian et al. [ 1 5] showed that if both branches of the solutions of the Laplace-Young equation are obtained then one would possess a greater Gibbs free energy. They also showed that the lower Gibbs free energy solution is equivalent to the minimum free energy solution obtained from the first variational principle. The solution of the Laplace-Young equation is much simpler than the calculus of variations. Therefore, any computational method is best based on this approach for simplicity and efficiency. For liquid bridges that have rotational symmetry, the generation of a three dimensional body reduces to a two-dimensional problem, and the Laplace-Young equation may be used to generate successive points on a meridional surface until specified boundary conditions are met. The first application of this method was by Hotta et al. [1 2] who generated liquid bridges between a sphere and a flat under the influence of a gravitational field. Figure 9 shows the computational basis for the numerical solution of the Laplace-Young equation. For axi-symmetric bridges, the values of the bridge curvature are obtained by appropriate differ entiation of the meridional profile y(x). 2 - 3/2 2 - 1 /2 2 (38) 1+ �(x) = 1 + -
[�
(��) ]
[ ��
(��) ]
1 /7 2 // /
1 331
Pendular Capillary Bridges
Laplace surface
\
y(x)
'i
--L-________
_ _
Axis of symmetry
Fig. 9. The calculation scheme for an axi-symmetric liquid bridge of profile y(x) with characteristic radi i r1(x) and r2(x).
700 600 R
� §
�
E
�
500 400 300
=
16000 units
1
Bridge �k
200 100 O +--�--,--.--�--,-� 16000 16100 16200 16300 16400 16500 16600 16700
Numerical Units Fig. 1 0 . Two constant curvature profiles for the same values of bridge volume, particle separation distance and contact angle.
Hence, a profile y(x) with values of dyjdx and d2Y/dx2 at each point on the profile that satisfies equation (38) to give a constant value for � will provide a 'gravity-free' solution to the Laplace-Young equation. Figure 10 shows two liquid bridge profiles generated in the above way for the same values of the contact angle, bridge volume and particle separation distance. Natural systems will attempt to minimise the Gibbs free energy and bridge geometries with the lower surface energy will prevail. However, in theory it is possible for liquid bridges to possess the higher surface energy configuration and remain meta-stable. For a liquid bridge to achieve the lower energy state, the contact line must be allowed to move freely over the surface of the particles. If this is not the case, e.g. for unclean or rough particles, the high-energy configuration
1 332
c. D. Willett et al.
may be meta-stable particularly if the total energy change in the transformation to the equilibrium state is smalI. Fairbrother and Si mons [31 ] present photographic evidence of a liquid bridge profile that appears to exist in such a non-equilibrium state ( � � 0.5). In their experiments, rough glass ballotini of relatively small particle sizes were used, hence these surfaces may provide a sufficient energy barrier for the high-energy profile to be stable. In using the computational method, care must be taken to ensure that this dichotomy does not cause confusion. It was shown by Lian et al. [ 1 5] that the attractive force for the high-energy solution is always smaller than for the lower energy solution. Practically, both solutions must be calculated in order to ensure that the lower energy solution is obtained.
5.2. Bridge rupture
Clearly, if two particles connected by a liquid bridge of constant volume are separated, eventually the bridge will rupture. Erle et al. [1 1 ] first pointed out that capillary bridges rupture with a finite, rather than a zero, neck radius. Oe Biss chop and Rigole [ 1 7] used the calculus of variations to analyse the stability of such bridges and assumed that the reduction in the filling-angle (assuming a constant three-phase contact angle) eventually led to the rupture of the bridge at the point where the filling angle is a minimum. Mazzone et al. [1 3] showed that this resulted in an underestimate of the rupture distance of up to 35% and con cluded that the mechanism described by Oe Bisschop and Rigole [1 7] was in correct. Mazzone et al. [ 1 3] showed that the two distinct solutions to the Laplace-Young equation converged at a critical separation distance, beyond which a solution did not exist. They identified this point as corresponding to rupture, which was analysed in greater detail by Lian et al. [ 1 5], who proposed the following simple empirical relationship for the rupture distance between two spheres of equal size. 2Sc = (1 + 0.5cp)V1 /3 (39) where cp is in radians and is valid for cp < 40°. The parameter Sc is the critical value of the half-separation distance at which rupture occurs. Equation (39) was obtained by curve fitting to a set of nominally exact theoretical solutions for the convergence criteria mentioned earlier. 5.3. Comparison with experimental data
There is a paucity of accurately measured liquid bridge forces and rupture dis tances. McFarlane and Tabor [32] measured the force between spheres in contact
Pendular Capillary Bridges
1 333
with a flat plate. Their experiments involved six different fluids and the results were found to be consistent with equation (37) for S = 0 and rp = O. Mason and Clark [33] measured the forces between a pair of 30 mm diameter spheres at a range of different separations for liquid bridges consisting of a mixture of di-n-butyl phthalate and liquid paraffin immersed in water, which had the same density. This enabled data to be obtained for relatively large liquid bridges under neutral buoyancy conditions. The force-separation behaviour was measured for six liquid bridge volumes and although their results were found to agree with theory at large separation distances, this was not the case for small separation distances. Hotta et al. [1 2] measured forces between spheres of radius 7.66, 5.00 and 3.06 mm and the surface of water and also for liquid junctions formed with water between the spheres and a flat plate for a range of separation distances. The results for spheres interacting with a free liquid surface showed agreement with their theoretical predictions to within 1 0%. However, for the sphere-on-flat arrange ment, the measured values showed a considerable reduction in the attractive force at e10se contact as had been observed previously by Mason and Clark [33]. The theoretical calculations of Erle et al. [1 1 ] were in agreement with the data of Cross and Picknett [34] who measured the capillary forces for spheres in contact with spheres and flat surfaces. The experimental data for spheres of radii 240 and 550 flm were consistent with values obtained from the toroidal approxi mate theory. It should be noted, however, that their results for systems with a finite contact angle are less satisfactory, showing significant scatter. Mazzone et al. [ 1 3] measured forces between two steel spheres of radii 1 .985 mm for a range of separation distances and four liquid bridge volumes. The liquid used was di-n-butyl phthalate which had a contact angle of 1 0°. Interest ingly, they also showed the same deviation from theory at small separation dis tances as Mason and Clark [33] and Hotta et al. [1 2] had observed. Mason and Clark [33] also measured the point of rupture of liquid bridges be tween two equal spheres and between a sphere and a flat surface. The values obtained for equal spheres are in good agreement with equation (39) for a contact angle of 7°. More recently, Fairbrother and Si mons [31] measured liquid bridge forces and rupture distances between small (�50 flm) spheres of glass ballotini of roughly equal size. The rupture distances for liquid bridges between equal-sized spheres for contact angles of 0°, 34° and 50° were within 1 0% of the distances calculated using the expression of Lian et al. [15] (equation (39)). Bayramli and van de Ven [14] measured forces between unequal spheres for zero and non-zero contact angles. Although their experiments were carefully carried out, they observed hysteresis as the spheres were brought together and then moved apart. Their results for zero contact angle were in good agreement with numerical solutions. Willett et al. [35] compared experimental force-separation data with those ob tained from numerical solutions of the Laplace-Young equation for liquid bridges
1 334
C. D. Willett et al. (a)
(b) 250
300 250
Vol ume ( n I )
200
V"lume (ni) 9.6 1 3.2 • 24.7 • 59.3
0 1 3.6
Z
200
•
o
3 1 .3
Z
• 74.2
C 1 50 "-
•
150
C
"-
100
1 00 50
50 0
0
1 00
200
300
400
0
500
0
2S (�)
(d) Volume
400
300
500
700 600
(ni)
0 25.3 • 6 1 .8 • 1 27.8
� IOO
200
2S ijun)
(e) 200
1 50
100
Z
C
"-
"-
(ni)
Volume
500
• •
1 62.4 280.2
400 300 200
50
100 0
0
1 00
200
300
2S (�)
400
500
0
0
1 00
200
300
400
500
600
2S ÜJ.m)
Fig. 1 1 . The measured total capillary force for a range of liquid bridge volumes as a function of the separation distance between two spheres, where the ratios of the radii are (a) 1 , (b) 2/3, (c) 1 /2 and (d) O. The curves represent the values calculated by numerical solution of the Laplace-Young equation (for
of silicone fluid between smooth sapphire spheres of both equal and unequal size. Figure 1 1 demonstrates the excellent agreement that can be obtained, both for the capillary force and the rupture distances. These data were obtained under conditions where the effects of gravity were negligible and the contact angle was zero. It may be seen that the smaller-than-expected forces at elose contact ob served by a number of workers such as Mason and Clark [33] were absent. 5.4. C losed-form approximations for equal spheres
While the Laplace-Young equation provides an exact solution for the hydrostatic component of the total capillary force and also the rupture distance, it is cumber some for the routine interpretation of experimental data and the algorithms involved
Pendular Capillary Bridges
1 335
are computationally expensive for implementing in many-body simulations. Con sequently, approximate solution procedures or approximate descriptions of the exact solutions, which may be expressed in closed-form, have been develop ed. One approach to developing a closed-form approximation for the capillary forces as a function of the separation distance, at a constant bridge volume, is to apply the principle of reduced variables. This requires a parameter for scaling the separation distance that will reduce the force-separation curves at different vol umes to a single function. In order to identify an appropriate scaling parameter, Willett et al. [35] developed an approximate toroidal model which had an analytical solution for the case of a small bridge with a zero contact angle between two large equal spheres at a small separation distance: (40) where S+(= S* jV* 1 /2 = SjL) is a scaled dimensionless half-separation distance and L( = ( V/R) 1 /2 ) is a characteristic length. The dimensionless force is, to a first approximation, only a function of S + . Figure 1 2a shows a dimensionless plot of the attractive force between equal spheres as a function of the separation distance calculated using equation (6) for a range of bridge volumes and a solid-liquid contact angle of zero. A similar plot is shown in Fig. 1 2b except that the force is plotted as a function of S+ which provides a reasonable superposition of the curves in Fig. 1 2a as predicted by equation (40). The quality of this superposition deteriorates with increasing con tact angle as is shown in Fig. 1 2d for a contact angle of 40°. The curves in Fig. 1 2b for a contact angle of zero are indistinguishable for dimensionless volumes of < 1 0 - 5 ; this is also found to be the case for any contact angle. The following polynomial in S+was the best fit for V* = 1 0 - 7 : cos q; p= (41 ) 1 + 2.1 (S+) + 1 0.0(S+)2 which provides a closed-form approximation for the total capillary forces between equal spheres as a function of the separation distance and for a fixed bridge volume. The accuracy of this expression is exemplified in Fig. 1 3a where the exact results are compared to the approximate values. The errors increase with increasing volume. However, the maximum error for any contact angle is 4% for V* = 0.001 , which corresponds to a filling angle, 2ß, of about 20°. A considerably more complex expression is required for greater volumes and contact angles and this is given in Willett et al. [35]. The expression is valid for q; < 50° and V* < 0. 1 and gives an error in the force estimate of less than 3%. This is exemplified in Fig. 1 3b which shows a comparison of the approximate and exact results for a pair of contact angles and bridge volumes.
1 336
C. D. Willett et al. (a) 1 .0
(b) 1 .0
0.8
0.8
k.
k.
0.6 0.4
0.05
k.
0.4 0.2
0.2
( c)
0.6
0.10
0.15
0.20
0.25
S' 1 .0
(d) 1 .0
0.8
0.8
k.
0.6 0.4 0.2
0.6 0.4 0.2
0.0 0.00
0.10
0.20
0.30
0.40
S' Fig. 1 2. Dimensionless plots of the capillary force as a function of the separation distance between equal spheres; as calculated by numerical solution of the Laplace-Young equa tion and using equation (6). The contact angles are zero for (a) and (b), and 40° for (c) and (d) [35].
In summary, it has been established that there is close agreement between experiment and theory for the capillary forces between two identical spherical bodies in the case of perfectly wetting liquids and gravity-free conditions. How ever, unequal spheres, imperfectly wetting liquids and also gravity introduce ad ditional complexities that will be discussed in later sections. 5.5. Bridges between unequal spheres
Most of the theoretical work on the capillary forces between spheres has focuss ed on those with equal radii. However, if such bodies are employed to represent particles in an assembly it is likely that the interactions in a real powder will involve particles of different radius and perhaps also with an imperfectly wetting liquid. Figure 1 4 shows a schematic diagram of a pair of unequal spheres con nected by a liquid bridge with a finite contact angle. For the case of a sphere of radius R in contact with a flat surface (i.e. a sphere with a radius tending to infinity), the maximum force is given at the point of
Pendular Capillary Bridges
( a)
1 .0
r----r======;-] - Equation
o V· = 10-3
0.8
• •
t...
(41 )
y' = 10"
(b) 1 .0 �-------;=====:;-) •
0.8
V· = 10-1
0.6
0.6
0.4
0.4
0.2
0.2
0.+-.---.0 0.4 0.8 S+ 1.2 1.6 2.----.---,--,--==10
0.0
1 337
y'= 0. 1 0. 91 = O· y·= O.OI . q> = O· Y·= O. 1 0. q>= 40· Y·= O.O I . 91= 40·
- NUl11crical solution
0.0 -+----f'=-�'--r-�:::...,-.-----1
0.00 0.10 s' 0.20 0.30
Fig. 1 3. Dimensionless plots of the capillary force as a function of the separation distance between equal spheres for a range of dimensionless liquid bridge volumes. The points in (a) were calculated by numerical solution of the Laplace-Young equation and using equation (6), the curve using the closed-form approximation given by equation (4 1 ); a contact angle of zero was used in both the cases. The points in (b) were calculated using the most accurate closed-form approximation given in Willett et al. [35], the curves by numerical solution of the Laplace-Young equation and using equation (6); contact angles of either zero or 40° were used in both the cases [35].
Fig. 1 4. A schematic representation of a liquid bridge of volume V and surface tension y between two spheres of radii R1 and R2 separated by a distance 2S with a neck radius (N, a liquid-solid contact angle qJ, and half-filling angles ß 1 and ß2.
contact as the liquid content and contact angle approach zero [32]: Fmax,S-f = 4nRYIY
(42)
1 338
C. D . Willett et al.
which is in agreement with Israelachvili's approximation given in equation (37). For two equal spheres of radius R, the corresponding solution was found earlier as 2nRYlv (see equation (20)) . It would be logical to suppose that there is a smooth monotonie dependence, between these two limits, of F on the ratio of the radii of the two spheres, as this ratio changes from unity to zero. Derjaguin [36] established that, for van der Waals forces, there is a simple ex pression that relates the force of attraction between two bodies of unequal radi i and their dimensions. He showed that for a small separation distance, the force between two spherical bodies of radii R1 and R2 is approximately the same as that between two equal spheres having a radius R1 ,2 equal to the harmonie mean of the unequal pair. 1 1 1 1 (43) R1 ,2 R1 + R2 It is generally assumed without proof (e.g. IsraelachviIi [30], Cross and Picknett [34]) that, by analogy, this relationship may be applied to capillary bridges. In spite of the above simplification, the effect of unequal spheres has generally been examined by considering the geometry of the bridge profile itself. Rose [37] em ployed the toroidal approximation in order to obtain expressions for the bridge volume and surface area. Mehrotra and Sastry [22] also used the toroidal ap proximation to estimate the effects of unequal radii on the force of attraction. The inaccuracy in the toroidal approximation resulted in a prediction of unequal forces of attraction on each of the two particles, a condition that was later improved by an averaging procedure to give equal forces of attraction [23]. Figure 1 5 shows plots of dimensionless total capillary force as a function of the scaled dimensionless separation distance calculated by the numerical solution of the Laplace-Young equation and using equation (6) for spheres having equal and unequal radii and for different bridge volumes and contact angles. All dimen sionless quantities containing the sphere radius, R, (i.e. P , S* , V* and S + ) were replaced by the Derjaguin radius, in order to identify the errors involved with this approach. The coincidence of the curves for spheres having different radius ra tios demonstrates that the total capillary force for a liquid bridge between a pair of unequal spheres (with radii R1 and R2) is indeed close to that calculated for a pair of equal spheres having the Derjaguin radius, R1 ,2, of the pair (equation (43)). This also means that the closed-form approximations for equal spheres described above can be used to calculate the total capillary force for unequal spheres by appropriate substitution of the Derjaguin radius. Deviations from the solutions for equal spheres occur only when the bridge volume is large compared to those of the spheres and at small and large separation distances. Willett et 81. [35] found that the use of the Derjaguin radius in equation (41 ) was more accurate than Israelachvili's approximation (equation (37)). In addition, for the accurate closed-form expression given by Willett et 81. [35], if the dimen sionless volume, V*, is less than 0.0 1 , the errors are < 2% for a zero separation
=2(
)
1 339
Pendular Capillary Bridges (a) 1 .0 0.8
i.t.
(�) 0.7
V·= O. I rp = O·
0.6
RfR,
V·= O.l rp= 40·
0.5
0.6
0.4
i.t. 0.3
0.4
0.2 0.2 0.0
0. 1 0.0
0.2
0.6
0.4
0.8
1 .0
S+ (c)
(d) 0.7
1 .0 V·= O.O I rp = O·
0.8
i.t.
0.0 0.0 0.2 0.4 0.6 0.8 1 .0 1 .2 1 .4 S+ 0.6
V·= O.O I rp = 40·
0.5
0.6
0.4
i.t. 0.3
0.4
0.2 0.2 0.0
0. 1 0.0 0.2 0.4 0.6 0.8 1 .0 1 .2 1 .4 S+
0.0 0.0 0.2 0.4 0.6 0.8 1 .0 1 .2 1 .4 1 .6 S+
Fig. 1 5. Dimensionless plots of the capillary force as a function of the scaled half-separation distance, calculated by numerical solution of the Laplace-Young equation and using equation (6), for spheres with the following radius ratios: 1 , 1 /2, 1 /4, 1 /8 and 1 / 1 6 . The dimensionless liquid bridge volumes and contact angles used in the calculations are shown in the figures [35].
(becoming less for sm aller volumes), decreasing to near zero at intermediate separations, with a steady over-prediction of the force at separations approaching the rupture distance. The error at large separations results in an over-prediction of bridge rupture distances. In addition to considering the effect of unequal radii on the geometry and subsequent attractive force between spherical particles, the maximum range of influence of the force, given by the rupture point, is also of interest. The work of Lian et al. [1 5] applies strictly to a pair of equal spheres and Willett et al. [35] found that the use of the Derjaguin radius in equation (39) overestimated the rupture distances for unequal spheres. The results of detailed calculations for contact angles of and were used to obtain an improved expression for the rupture distance:
0° 40° ( 1 � (:� 1) ) [\1*1 (3 + (2�1 - �) \1*2(3]
2S� =
+
+
(44)
1 340
C. D. Willett et al.
(V*1/3 ��3)
For equal spheres, this approximation reduces to 2S�
= ( 1 +�)
+
(45)
which predicts a slightly greater rupture distance than equation (39).
6. INFLU ENCE OF WETTING HYSTERESIS
For a perfectly clean system, with perfectly smooth solid particles, a simple bal ance of forces at the contact line restricts the contact angle to a constant value, given by the Young equation (see equation (31 )). For this reason most workers have assumed a constant contact angle during relative motion of the solid bodies (e.g. Lian et al. [ 1 5] , Orr et al. [16]). However, it is usually the case that the velocity of a moving contact line will influence the contact angle. It is now ac cepted that since the contact angle varies with slip velocity there is a step change at zero where the transition from advancing to receding occurs [38]. There is also a finite difference between a slowly advancing and a slowly receding contact line. This behaviour is called contact angle, or wetting, hysteresis [39,40], and a given contact line speed results in a maximum or advancing contact angle, ({Ja, and a minimum or receding contact angle, ({Jr' The immediate consequence of this for liquid bridges is the assumption that the contact line is freely mobile does not always apply. This is a common phenomenon for most imperfectly wetting systems even when the contact angle is relatively small. It arises when the wetted solid is not perfectly smooth or is chemically heterogeneous [41]. In such cases, the con tact angle is greater than the equilibrium value when the liquid advances and it is smaller when the liquid is retracted. These non-equilibrium values are termed the advancing and receding contact angles, respectively. A characteristic of such sys tems is that, when a force acts on the fluid, the three-phase contact line will remain stationary at intermediate values of these contact angle limits; this is termed pin ning. When either of these limits is reached, the three-phase contact line will slip. Consider an isolated equilibrium liquid bridge between two solid particles, in which the liquid does not perfectly wet the solid material and thus exhibits a finite contact angle at the three-phase boundary. If the two particles move relative to one another, the bridge must deform accordingly. In this respect, two extreme modes of deformation are possible and are shown schematically in Fig. 1 6. It is possible that the bridge may deform by the contact line being fixed and the contact angle allowed to vary (pinning) or by maintaining a constant contact angle and allowing the contact line to move along the surface (slipping). In reality, the type of deformation is dictated by the energy barriers and the free energy of the system.
1 34 1
Pendular Capillary Bridges
1 6. Showing the two possible bridge deformation mechanisms in response t o particie approach. (a) Variable contact angle for a stationary, or pinned, contact line. (b) A constant contact angle for a freely mobile, or slipping, contact line. Fig.
(a)
(b)
Fig. 1 7 . Photographs of a liquid bridge formed from glycerol (YIV 64 mN/rn) during (a) separation and (b) approach between two smooth sapphire spheres with radii of 2.381 mm. =
Bayramli and van de Ven [14] observed that capillary bridges sometimes showed contact angle hysteresis, which they measured but for which they pro vided no theoretical analysis. More recently, Willett et al. [42] examined this phenomenon both experimentally and theoretically. Figure 1 7 shows the wetting hysteresis they typically observed for liquid bridges of glycerol between equal sized sapphire spheres. Figure 1 8 shows cyclic force-separation curves between different separation limits for four liquids. Except for the PDMS, which exhibits a zero contact angle, hysteresis in the force is clearly evident as a result of the corresponding wetting hysteresis. The relationship between the force and wetting hysteresis is shown schemat ically in Fig. 1 9. If the contact angle is greater than the receding value, an in crease in the separation distance will result in an increase in the force due to pinning (a -+ b). This will be accompanied by a reduction in the contact angle until the receding value is achieved when the force will decrease (b -+ c). If the separation distance is then decreased, the contact angle will increase until the
Measured force-separation cycles (full lines) for liquid bridges formed from (a) PDMS (viscosity = 1 1 0 mPa s, Ylv = 21 mN/m), (b) triolein (Ylv = 36 mN/m), (c) poly (ethyl ene glycol) 400 (Ylv = 47 mN/m) and (d) glycerol (Ylv = 64 mN/m) between sapphire spheres with radii of 2.381 mm. Loci of constant filling and contact angles are also shown (dashed lines). These are calculated for the measured dimensionless volumes which are given in the figures [42]. Fig. 1 8.
ßr
S' Fig. 1 9. A schematic representation of the relationship between the wetting and the force hysteresis.
1 343
Pendular Capillary Bridges
advancing value is achieved (c ---. d). That is, pinning will again occur which will correspond to a reduction in the force. A further reduction in the separation distance to the initial value position will occur by slipping at the three-phase contact line with the contact angle fixed at the advancing value (d ---. a). Thus, the experimental data for a given cycle are approximately parallel to the calculated loei of constant filling and contact angles as shown in the Fig. 1 8; it is possible to estimate the advancing and receding contact angles on this basis. The small deviations from the trends in the calculated loei represent non-equilibrium phe nomena such as micro-slip in the pinning phases. The slipping mode corresponds to an equilibrium contact angle and a minimum free energy solution for a pendular bridge. As explained earlier, wetting hysteresis arises from physical or chemical inhomogeneities that represent local energy barriers. In this section, a thermodynamic analysis will be undertaken in order to explore the underlying factors. The total free energy for a liquid bridge, � W, is given by the following expres sion [1 7]: (46) where Alv and AI are the Iiquid-vapour and solid-liquid interfaeial areas; it should be noted that equation (46) ignores a constant term given in Ref. [1 7] so that the calculated values of �W refer to an arbitrary reference state. According to Young's equation, the equilibrium contact angle,
= cos-1 (
{SV - (SI (Iv
)
(47)
which allows equation (46) to be written in the following dimensionless form:
=
(48)
=
where �W(; ( �WlrlvR2 ) and A*( AjR2 ) are the dimensionless free energy and interfaeial areas. Thus, equation (48) shows that the dimensionless free energy can be expressed simply in terms of the solid-liquid and Iiquid-vapour interfaeial areas and the equilibrium contact angle. Values of these areas as a function of the separation distance between two spheres of radius R were calculated in Ref. [42] for a dimensionless bridge volume of 0 . 1 and a range of contact angles. Substitution of these areas in equation (48) together with a selected value of the equilibrium contact angle, allowed the free energy for different non-equilibrium contact angles to be calculated as a function of the separation distance. The minimum free energy (�W; � W;e) corresponded to the equilibrium contact angle. The increase in the free energy, averaged over all separation distances from zero to the rupture value, as a function of the deviation of the
=
1 344
c. D. Willett et al. 0.30 0.25
.$ �
0.20
•
��
0.15 0. 10
A "
0.05
0 0
0
0 0
0.00 -60
-40
-20
0
20
40
60
lP - lPeq Fig. 20. The i ncrease i n the free energy, averaged over all separation distances from zero to the rupture value, as a function of the deviation of the contact angle from the equilibrium values, epeq, of 0° (0), 20°( 0 ), 40° (ß) and 60° (\7) [42].
contact angle from the equilibrium value is shown in Fig. 20. For deviations of < 20°, the increases are very small which supports the view that pinning arises simply because the bridge is in a metastable state; i.e. the energy gain for equi libration is small compared to the energy barriers associated with surface in homogeneities. 7. I N F LU ENCE OF G RAVITY
In most theoretical and experimental work on liquid bridges between spheres it is assumed that gravity has a negligible eftect on the bridge shape and the resultant capillary forces. Often, this has been justified on the grounds that the variation in bridge pressure due to the hydrostatic head caused by the gravitational field is small compared with the reduced Laplace hydrostatic pressure arising from the curvature of the bridge surface [1 6,43]. However, in many cases of technological interest, this is not necessarily the case; examples include some granulation processes with coarse particles and drainage in filters. In a wider context, the study of the eftects of gravity is relevant to the general case of imposed accel eration, which might occur in high shear granulation, for example. The first rigorous calculation of the eftect of gravity on liquid bridges was by Hotta et al. [ 1 2] who included the eftect of an axial gravitational field in their numerical solution procedure for bridge profiles between a sphere and a flat surface. The solutions were compared to their experimental results and showed acceptable agreement; however, no general procedure for assessing the eftects of gravity was provided.
1 345
Pendular Capillary Bridges
The effect of gravity on free droplets of liquid is characterised by the Eötvös number, also known as the Bond number, Bo [44]: Bo =
d�Apg
(49)
)!Iv
where db is the droplet diameter and Ap the density difference across the air-liq uid interface. Hence, Bo corresponds to the ratio of the gravitational and surface tension forces. Mazzone et al. [ 1 3] attempted to quantify the effect of gravity on liquid bridges by solving the Laplace-Young equation for a pair of equal spheres in close contact. It was shown that for a small gravitational field acting in the axial direction, the attractive force between equal-sized spheres in close contact is increased for the upper sphere and decreased for the lower one with the differ ence being equal to the weight of the bridge. It was proposed that the effect of gravity was negligible if a characteristic Bond number was less than about the order of unity, with the characteristic radius being that of the particles to which the bridge is attached [16,43]. R2 Apg Bo = (50) )!Iv
The Laplace-Young equation (equation ( 1 )) may be written in the following form to include the effect of gravity for spheres in vertical alignment: AP(z) = AP(O) + zApg = )!Iv
[(
1
1
)
1 /2 + ((Z)2 r(z)
-
( 1 + ((Z)2 1(Z)
])
(51 )
3/2
where the dot notation refers to differentiation with respect to the axial co-ordinate z, and r(z) is the meridional profile of the bridge (Fig. 21). The parameter AP(z) is the local pressure difference ac ross the air-liquid interface, and AP(O) is the local pressure difference at the three-phase contact line on the upper sphere. The term in the square brackets is the local curvature of the bridge, �(z), which has a constant value when the influence of gravity may be neglected. The bridge geometry for equal or unequal spheres was calculated by Adams et al. [45] by numerical integration of equation (51 ) using the method described previously; the liquid-solid contact angle was set to zero for these calculations. The total attractive force acting on each sphere, Fj, was obtained from
2 nR· Fi
')!Iv
= sm2 ßi .
- -21 �8ism. 2ßi
1=
[
]
ApgRf 2 1 --- - - cos ßi + - cos3 ßi 2 )!Iv 3 3
(52)
where i = U or I such that u and I refer to the upper and lower spheres and the upper sign refers to the upper sphere, ßi is the half-filling angle (see Fig. 2 1 ) and �i is the curvature at the three-phase contact li ne for each sphere; i.e. �u � ( O ) and �I = �(h). The three contributions to the force arise respectively from the
=
1 346
C . D . Willett et al.
Fig. 21 . A schematic representation of a capillary liquid bridge defining the co-ordinate system.
surface tension, capillary pressure, and buoyancy. The term in square brackets is equal to Vb/nR?, where Vb is the partial volume of the sphere that is submerged. An overall force balance shows that the difference in the forces between the upper and lower solid bodies arises from the weight of the bridge (= VApg) [1 3]. This provided an independent verification of the accuracy of the calculations. If one of the solid bodies is actually a flat surface, the associated buoyancy term is zero and it is also more appropriate to express the total attractive force in terms of the bridge radius at the three-phase contact line, 'j (= Rj sin ßJ For the case of a zero contact angle, the surface tension term associated with the flat is also zero and the solution simplifies to Fj = - nifY'v �j for 1/Rj = 0, where 'u = r(0) or " = r(h) depending on whether the flat surface is above or below the sphere. Figure 22 shows measurements of the attractive capillary force as a function of the separation distance for a sapphire sphere-plane system, compared with the theoretical values, with and without gravity. The calculated curves shown in Fig. 22 correspond to the lower energy branches. There is an increasing deviation of the measured data from the values calculated without gravity as the bridge volume increases. The gravity-free experimental data clearly demonstrate that rupture occurs at the maximum separation distance for which a solution to equa tion (51 ) exists. Intuitively, it would be expected that one consequence of the effect of gravity on the bridge shape would be to decrease the rupture distance by comparison with the gravity-free solution. Figure 23 shows the dimensionless bridge force F;(= Fj/2nRjY lv) calculated for upper and lower equal spheres as a function of the half-separation distance S* (= S/Rj) for a dimensionless bridge volume of 0.1 . The corresponding Bond number (equation (50)) for this bridge is 5. There is a
1 347
Pendular Capillary Bridges 600 ,------, 500
Z
400
2: 300 u..
200 1 00
o
400
800 1 200 2$ (�m)
1 600
Fig. 22. The capillary forces as functions of the separation distance between an upper sphere of radius 2.381 mm and a lower planar surface for a separation velocity of 1 Ilm/s. The experimental data for the sphere have been measured for silicone fluid (viscos ity = 1 1 0 m Pa s, p = 960 kg/m3 , Ylv = 20.6 mN/m, 4> = 0°) liquid bridge volumes of 0.620 (0), 2.261 ( 0 ) and 5.736 111 (L'1). The corresponding calculated forces are shown which include (fuil lines) and neglect (dashed lines) the influence of g ravity [45].
1 .0 .,------, 0.8 0.6 0.4 0.2 0.0 +----,-----.---,---,' 0.0 0.05 0 . 1 0.1 5 0.2 0.25 $. Fig. 23. Calculated dimensionless force between equal spheres as a function of the di mensionless half-separation distance for the case when gravity is included (fuil lines) and neglected (dashed line). Bo = 5, V* = 0. 1 . For the case when gravity is included, the two solutions refer to the force associated with the upper and lower spheres [45].
clear divergence of the forces fram the gravity-free theoretical data. In addition, the data confirm the hypothesis that gravitational effects reduce the rupture distance. Adams et al. [45] showed that the Bond number defined by equation (50) is actually not appropriate since both the sphere radius and the bridge volume
1 348
C. D. Willett et a/. 1 0 4 �--�----�
CD 102
S
101 0.05
1 0° 1 0 .1
0.1
GF
1 0 .2 1 0 -5
/ '" .
s�= 0.2 1 0 -4
1 0-3
1 0-2
1 0 -1
10°
V'
Fig. 24. A map of the influence of g ravity on the stabilities of pendular bridges between equal spheres showing the following regions: Gravity Free (GF), Transit iana/ (TR), Gravity Cantrolled (GC) and Camp/ete Draining (CD). Contours of constant half-rupture distance are also shown [45].
Table 1 . Summary of gravity effects
V*
Bo < 0.01 0.01 - 0.1 5
Regime Gravity-free Transitional
0. 1 5 - 2
Gravity-controlled
>2
Complete draining
Comment No influence of gravity Rupture distances affected by gravity but no draining Bridge angle decreases continuously with separation; controlled draining No stable bridge
are important in determining the effects of gravity. This is shown graphically in Fig. 24, which is a map of the effects of gravity on the Bo - \1* plane. Essentially, this diagram delineates the various regimes of behaviour that are summarised in Table 1 in terms of a modified Bond number, \l* Bo. Draining is an important manifestation of the influence of gravity. This has been defined as the continuous reduction in the upper filling angle, with increasing separation distance. In the absence of gravity, this angle first decreases and then increases with increasing separation [1 7]. At sufficiently large values of \l* Bo, a stable bridge cannot be formed even when the spheres are in contact; this is termed complete draining. The modified Bond number is also useful in correlating the effects of gravity on the critical separation for rupture, as shown by Adams et al. [45]: 2� � (1 - 0.48\1* Bo) \1* 1 /3 (53)
ßu,
Pendular Capillary Bridges
1 349
This modified Bond number prescribes the influence of gravity on the stability and capillary forces for pendular liquid bridges, and indicates that gravitational effects can even be important for relatively small particles. For example, those with a radius of 1 mm and the largest possible liquid bridge volume correspond to the gravity-controlled regime. Previous criteria have been found to be conserv ative [1 6,43) so that it was necessary to calculate any possible effects for each particular case. 8. FUTURE LOOK
It is apparent from the work described in this chapter that effects such as wetting hysteresis and gravity introduce considerable complexity when predicting the strength of capillary junctions between particles. The focus has been on the development of analytical expressions or c1osed-form approximations that are simple to compare with experimental data and computationally inexpensive to evaluate in discrete simulation schemes. However, it may be necessary to em ploy computer simulation to account for some of the factors that may be involved with practical systems, such as allowing for viscous effects when the particles are in relative motion. For example, finite element analysis has been used to examine the viscous contribution to the total liquid bridge force [46) and the break-up of viscous junctions by filamentation [47]. Inviscid axi-symmetric capillary junctions fail at a finite neck radius but viscous bridges eventually may form a thinning neck that greatly increases the rupture distance. Numerical simulation would also be required to predict the behaviour of non-axial inertial effects on liquid bridges greater than the critical volume. The current chapter has also been primarily concerned with involatile liquids so that the bridge volume may be taken as a constant. For volatile Iiquids such as water in thermodynamic equilibrium, bridges of constant curvature will be formed as determined by the Kelvin equation. However, the time-scales for evaporation and condensation may be sufficiently long compared with the collisional events that occur in granulation processes that it may be an acceptable approximation to treat such bridges as being of constant volume. Much of the recent work is driven by the need to understand the behaviour of micro or nanoparticles. It is remark able that continuum mechanics may be applied to capillary bridges at extremely small length-scale. For example, it has been found that the Kelvin equation is applicable to liquid junctions with radii of curvature as small as about 5 nm [26,48]. It is also the case that the relationship between the rupture distance and the bridge volume (equation (44)) has been verified for volumes as small as 1 0 - 1 6 m 3 [49]. Atomic force microscopy is becoming increasingly used to study capillary bridges at small dimensions both for smooth contacts [50] and those with nanoscale roughness [51].
1 350
C. D. Willett et al.
Perhaps the greatest challenge in the context of granulation is to develop an analytical microseopie description of the mechanical and fracture properties of assemblies of wet particles of the type that are formed by agglomerates. One of the main effects of capillary bridges is likely to be the enhancement of the inter-particle friction that arises from the increase in the normal load at contact points [52].
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1 351
[35] C.D. Willett, M.J. Adams, SA Johnson, J.P.K. Seville, Langmuir 16 (2000) 9396-9405. [36] B.V. Derjaguin, Kolloid Zeits 69 ( 1 934) 1 55-164. [37] W. Rose, J. Appl. Phys. 29 ( 1 958) 687-691 . [38] C.G. Ngan, E.BV Dussan, J. Fluid Meeh. 1 1 8 ( 1 982) 27-40. [39] D. Li, AW. Neumann , Colloid Polym. Sei. 270 ( 1 992) 498-504. [40] L.w. Schwartz, S. Garoff, J. Colloid I nterf. Sei. 1 06 ( 1 985) 422-437. [41 ] J.F. Joanny, P.G. de Gennes, J. Chem. Phys. 81 ( 1 984) 552-562. [42] C.D. Willett, M.J. Adams, SA Johnson, J.P.K. Seville, Powder Teeh. 1 30 (2003) 63-69. [43] H . M . Prineen, J. Colloid I nterf. Sei. 26 ( 1 968) 249-253. [44] R Clift, J . R Graee, M . E . Weber, Bubbles, Drops and Particies, Aeademie Press, New York, 1 978. [45] M.J. Adams, S.A. Johnson, J . P.K. Seville, CD. Willett, Langmuir 1 8 (2002) 6 1 80-61 84. [46] H. Zhou, J.J. Derby, I nt. J . Numer. Meth. Fluids 36 (2001 ) 841-867. [47] O.E. Yildirim, OA Basaran, Chem. Eng. Sei. 56 (2001 ) 2 1 1 -233. [48] M . M . Kohonen, H .K. Christenson, Langmuir 1 6 (2000) 7285-7288. [49] N. Maeda, J . N . IsraelachviIi, M . M . Kohonen, Proe. Natl. Aead. Sei. USA 1 00 (2003) 803-808. [50] D.L. Malotky, M .K. Chaudhury, Langmuir 1 7 (2001 ) 7823-7829. [51 ] Y.I. Rabinovieh, J.J. Adler, M.S. Esayanur, A. Ata, RK. Singh, B.M. Moudgil, Adv. Colloid I nterf. Sei. 96 (2002) 21 3-230. [52] M.J. Adams, B.J. Briseoe, J.Y.C. Law, P.F. Luekham, D.R Williams, Langmuir 1 7 (2001 ) 6953-6960.
CHAPTER 29 S u b- G ra n u le Sca le M o de l l i n g Fra nti sek Stepanek *
Department of Chemical Engineering, Imperial College London, South Kensington campus, London SWl 2AZ, UK Contents
1 . Introduction 2. Computational methods 2. 1 . Encoding of granule microstructure 2.2. Computer simulation of g ranule microstructure formation 2.2. 1 . Reconstruction of primary particle populations 2.2.2. Primary particle packing 2.2.3. Binder spreading a n d solidification on particle assemblies 2.3. Characterization of granule microstructure 2.4. Calculation of macroscopic properties from microstructure 2.4. 1 . Effective transport properties 2.4.2. Effective dissolution rate 3. Application examples 3 . 1 . Dependence of granule porosity on binder solidification rate 3.2. Dependence of granule porosity on composition 3.3. Dependence of g ranule dissolution rate on composition and porosity 3.4. Effective transport properties of wet particle assemblies 4. Forward look 4. 1 . Computer-aided granule design 4.2. Virtual prototyping References
1 353 1 355 1 355 1 357 1 359 1 36 1 1 362 1 364 1 365 1 365 1 367 1 368 1 369 1 370 1 372 1 372 1 375 1 375 1 376 1 377
1 . I NTRODUCTION
A granule can be regarded as a composite material consisting of primary solid particles, a continuous (matrix-forming) or localized (solid bridges) binder, and percolating or closed gas cavities (Fig. 1 ). The macroscopic properties of such a composite material depend on the properties of the constituent phases, their volume fractions, and their spatial distribution, i.e., on the microstructure. In order to be able to design granules with required macroscopic properties rationally [1 ,2], it is important to know the functional relationship between the granule composition and microstructure and the effective macroscopic properties * Corresponding author. E-mail: [email protected]
Granulation Edited by A.D. Salman, MJ. Hounslow and J. P.K. Seville ( 2007 Elsevier B. V. All rights reserved
1 354
F. Stepanek es = 0.6 eL
=
0.2
eG = 0.2
Fig. 1 . Schematic representation of the microstructure of a granule as a multi-component porous medium (Ieft). The composition of a granule can be plotted using a triangular diagram (right) (adapted from ref. [ 1 5]).
as weil as the relationship between the granulation process conditions and the resulting granule microstructure. Which macroscopic properties are of interest, depends on the downstream processing steps that the granule will undergo and on the end-use application. One or more of the following situations can serve as typical examples: •
•
•
•
The granule is a delivery form for active ingredients that need to be transferred into solution during end use, such as in pharmaceuticals, food products, or laundry detergents [3]. The effective dissolution rate of the granule is the main macroscopic property of interest. The granule is a porous carrier containing active sites that need to be contacted with a fluid phase during end application, such as in catalysts or adsorbents [4]. The effective transport properties (diffusivity, permeability, and thermal con ductivity) of the porous granule are of interest. The granule will undergo a drying or impregnation downstream processing step, or the granule contains volatile or hygroscopic ingredients. The effective transport properties (permeability and diffusivity) of the granule are of interest. The granule will be further processed by mechanical compaction or will be exposed to significant static or dynamic load, impacts, or shear. The effective mechanical properties of the granule are of interest in that case.
The objectives of sub-granule scale modelling are (i) to predict one or more of the above-mentioned macroscopic properties from the knowledge of granule microstructure and (ii) to predict the effect of raw material properties and gran ulation process conditions on the microstructure. This chapter describes com putational methods suitable for the simulation of granule microstructure formation, granule microstructure and morphology characterization, and calcu lation of the effective transport properties and the effective dissolution rate of a granule as function of its composition and microstructure.
1 355
Sub-Granule Scale Modelling
Several driving forces have lead to the development of these computational methods. The first is the need to speed up the product development cycle. His torically, the rate-Iimiting step in product innovation has been the discovery of new active ingredients. However, the introduction of high-throughput experimen tation and chemical informatics tools means that granule formulation and process development methodologies also have to be rationalized in order to keep up with the increased rate at which new candidate actives need to be tested. The second driver is the emergence of instrumental analytical techniques for accurate and relatively affordable structural characterization of porous and multiphase mate rials, such as desktop X-ray micro-tomography [5]. The third driver is the con tinuing validity of the Moore's law, which makes it possible to perform even computationally rather intensive tasks on an affordable desktop workstation. 2. COMPUTATIONAL METHODS
The text in this section is divided into four parts: first, we introduce the phase volume function as a means of digital encoding of granule microstructure; this is followed by the description of computational algorithms for the simulation of granule microstructure formation; algorithms for the calculation of granule micro structure and morphology characteristics are discussed next; finally, methods for the calculation of effective macroscopic properties from the granule microstruc ture are described. 2.1 . Encoding of g ranule m icrostructure
R3
The microstructure and morphology of a granule are fully specified by the spatial distribution of the constituent phases. This can be formally represented by the so called phase function f; -+ {O; 1 } N , which assigns each point from the real space a value of 1 if the i-th phase is present in that point, and a value of 0 if it is not, i .e., , 1 if x E phase i f;(x) = (1) o otherwise By definition, only one phase can be present in any point of the real space, i.e., :
{
� �W = 1
�E�
m
In practice, the coarse-grained phase functions, termed phase vo/urne func tions, are specified on a discrete grid of cubic volume elements of real space, termed voxe/s (in analogy with two-dimensional picture elements, or pixels). The phase volume function � represents the volume fraction of each voxel occupied
F. Stepanek
1 356
by phase i and can therefore have values from the interval < 0; 1 > . More than one phase can now be present in each voxel; however, the sum of the phase volume functions in each voxel must still give unity. Granule microstructure encoded using phase volume functions for three phases - gas, liquid, and solid - is shown in Fig. 2. The visualization was obtained by plotting iso-surfaces at value � = 0.5 for the solid and liquid phase and applying a grey-scale level to the surface according to the enciosed phase. Figure 3 illustrates (in two dimensions) the principle of encoding the structure of a multi-phase medium by phase volume functions.
Fig. 2. 3D (Iett) and cross-section (right) view of a computer-generated granule encoded
by the phase volume fractions. (Primary solid particle is light grey, liquid binder is dark grey, inter-phase boundaries are denoted by a solid line.)
gas
�'" liqui
/
�
\,
Y
solid
I'----r"
1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
�7O}-
F 0.0
0.0
o/'Vo:ä--
0.9
1 .0
1 .0
1 .0
�J 0.0
0.0
0.0
0.0
��
'\\
1 .0
0.9
1 .0
1.0
1 .0
1.0
1.0
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0.0
0.0
0.0
0.0
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0.0
0.0
0.0
0.0
0.0
t3O� 0.1
1 .0
)
�I--
0.1
1.0
fs E (0; 1 )
0
Fig. 3 . I llustration of structure encoding of a three-phase medium using the solid- and
liquid-phase volume functions (gas phase can be calculated as complement to 1 ).
Sub-Granule Scale Modelling
1 357
Phase volume functions representing a granule microstructure can generally be obtained by one of the following methods: 1 . by three-dimensional imaging of a real granule, using a tomographic tech nique; 2. by stochastic reconstruction from a two-dimensional micrograph of granule cross-section; and 3. by computer simulation of granule formation (diagenesis). In the first approach, a three-dimensional voxel array capturing the granule microstructure is obtained directly by micro-tomography of a real granule. X-ray micro-tomography is based on the relative difference in X-ray attenuation of the phases forming the object being investigated, which usually means that solid phase and porosity can be distinguished relatively accurately, while the binder may have to be doped (e.g., by iodine or barium) in order to make it distinguish able from the primary solid particles. The spatial resolution limit of current desk top X-ray micro-tomography instruments is �1 J.lm and improving. The second approach also starts from a digital image of a physical granule, but the image is two-dimensional: typically, SEM of polished or microtomed granule embedded in an epoxy resin. The final three-dimensional granule structure is generated by a stochastic reconstruction algorithm, based on matching of sta tistical properties (typically, porosity and the pore-space auto-correlation function) evaluated from the 20 image. There is a rich literature on the subject of stochastic reconstruction of porous and multi-phase media, see, e.g . , a recent review by Kosek et al. [6] or original papers by Adler [7,8]. The third approach, called "virtual granulation", is entirely computational. The granule microstructure is generated by computer simulation of the granule for mation process, i.e. , the elementary steps of primary particle packing, binder spreading, and binder solidification. This methodology, after Stepanek and Ansari [9], is described in the following text. 2.2. Computer simulation of granule m icrostructure formation
The microstructure formation process is simulated as a sequence of the ele mentary steps of primary particle packing and binder droplet deposition, liquid binder spreading on the primary particles, and binder solidification (as a result of drying for solution binders, cooling for melt binders, or chemical reaction for reactive binders), according to an overall algorithm shown in Fig. 4. A single primary solid particle is first placed into the centre of a simulation unit cell in which the granule will be constructed. The unit cell can be thought of as a moving coordinate frame following the trajectory of this seed particle through the
F. Stepanek
1 358
size and shape distributions
physical and process parameters -'
collision sequence
Fig. 4. Algorithm for the construction of a virtual granule by random sequential deposition of primary particles and binder droplets with binder spreading and solidification (from ref. [9]) .
granulation process equipment (e.g., a fluid bed, drum, or pan granulator). All collisions between the growing granule and other objects (particles, binder drop lets) appear as if these objects were entering the simulation unit cell, as illustrated in Fig. 5. The particle and droplet deposition processes are modelIed as discrete events in the overall granule formation simulation, while the binder spreading and solidification processes are modelIed as continuous processes. As shown in Fig. 4, the times at which the discrete deposition events occur as weil as the nature of the collision (particle vs. droplet, direction and velocity of movement) are read from an input file, which is generated externally to the granule-scale sim ulation - it may be the result of a discrete element method (DEM) simulation of g ranular flow, positron emission particle tracking (PEPT) observation of granular flow, or generated as a pseudorandom sequence from the kinetic theory of
1 359
Sub-Granule Scale Modelling ,-----+ air out
binder droplet binder in
/ l
powder in granules out
/
primary particle
+
�
\ \
air in Fig. 5. Computational unit cell for the construction of a virtual granule, representing a moving coordinate frame centred in a seed primary particle.
granular flow. This allows the de-coupling of granule-scale simulations from process-scale simulation. Snapshots taken during the formation of a single virtual granule according to the algorithm from Fig. 4 is shown in Fig. 6. The individual steps of the simulation will now be described. 2.2.1. Reconstruction of primary partic/e populations
The primary particles from which the virtual granule is constructed are randomly chosen from a population with specified size and shape distribution. Each primary particle is encoded by the phase volume function of the solid phase as described above and can therefore assume any shape. The shape of a general non-spher ical particle can conveniently be described as the so-ca lied Gaussian "blob", i .e., an ellipsoid modulated by a Gaussian-correlated random surface [ 1 0]. A Gauss ian-correlated random field Y(r) with correlation length L is obtained from a fjeld of Gaussian-distributed independent random variables X(r) by the application of a linear filter Y(ro) = L eXP ll r - ro l1 2 L2 X(r) (3) Ilr-roll ::: L
(
/ )
and renormalization. The geodesic rather than Cartesian metric is used for the calculation of the distance l r-ro l since the points are not in a plane but on a closed surface topologically equivalent to the surface of a sphere. A single primary particle class is characterized by a set of five numbers: the mean radius of gy ration (g , two aspect ratios sy and sz, the surface roughness amplitude a, and the surface roughness correlation length L. Each primary particle within that class,
1 360
F. Stepanek
-
-
-
Fig. 6. Simulation sequence showing the formation of one virtual granule according to the algorithm from Fig. 4.
+
=
Fig. 7. Construction of a single primary particle by mapping a Gaussian-correlated random surface onto an ellipsoid.
however, is an original entity as it is generated from a different initialization of the independent random field X(r). The construction of a single primary particle by modulating an ellipsoid by a Gaussian-correlated random surface is illustrated in Fig. 7. The parameters characterizing each particle class can be evaluated by shape analysis from digital images of real particles, typically obtained either by visible light microscopy of particles spread in a mono-Iayer on a microscope slide or by a particle-sizing instrument based on image capture of particles in free fall. The procedure of evaluating particle shape parameters (mean radius of gyration, its amplitude, and correlation length) is illustrated in Fig. 8. A binary image of the particle projection is obtained from a grey-scale image by segmentation (Fig. 8a,b). The radius of gyration as function of the rotation angle (Fig. 8c) is then extracted from the particle contour by calculating the Euclidean distance of each surface point from the centre of mass. The mean radius of gyration rg, and the surface amplitude, a, can be calculated from the radius of gyration function
Sub-Granule Seale Modelling
1 36 1
(b)
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.� g
:I:
:§.
[0>
Ö
60
.2 e:
40
.9 15 ä> t:: 0 u
i 20 '"
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o L-���--�--� o 4 rotation angle [radian)
08 0.0 0.4 0.2
. '
. .
. . . . .
<1.2 . . . . . .
<1.4 0.5
(d )
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rolation angle [radian I
2.5
Fig. 8. Morphologieal eharaeterization of primary particles: (a) optieal images of primary
particles; (b) extraeted single particle eontour; (e) radius of gyration as funetion of rotation angle for thai partiele; and (d) auto-eorrelation funetion of Ihe gyration radius.
r(w) direetly, rg
1
= -2n
12n r(w)dw and a üJ=Ü
=
max(r) - min(r)
(4)
respeetively. The surfaee raughness eorrelation length, L, is the zero-th moment of the auto-eorrelation tunction R(S) , whieh is defined by 1t - rg ) dw J� ( r(w + 9 ) - r9 ) (r(w) R( 9) (5) '211 ( r(w) - rg 2 dw JÜ ) =
The auto-eorrelation tunetion of the radius of gyration funetion fram Fig, 8e is plotted in Fig. 8d for illustration. The above-deseribed method of primary particie shape reeonstruetion is not the only possibility - a method based on Fourier analysis has also been used [1 1]. 2.2.2. Primary partic/e packing
Aigorithms for the eonstruetion of elose random paeking of partieles ean be eat egorized as either based on the dynamie simulation of particie motion (i.e., the Newton's law is solved for the particies) or as based on loeal or global
F. Stepanek
1 362
minimization of potential energy of the particles. In principle, both methods can be used for the construction of 3D computer models of agglomerates. Model ag glomerates of spherical primary particles have been generated by the DEM [1 2] and a version of the ballistic deposition algorithm [1 3] has been used for the construction of virtual agglomerates consisting of primary particles of arbitrary shape [9, 1 0] as weil as for randomly packed layers [14, 1 5]. Particle packing according to the ballistic deposition algorithm proceeds in the following way. Starting from an initial position on the boundary of the simulation box (cf. Fig. 5), the incoming object (droplet or primary particle) moves in discrete spatial steps in the direction of a vector Vtet. which is the sum of an "attractive", VatI> and a "repulsive", vrep, component. The attractive vector is oriented from the centre of mass of the incoming object to the centre of the simulation box and its magnitude is set to[vatt[ = 1 . The repulsive vector is the sum of vectors oriented from the collision points (i.e., voxels in which the incoming object is in contact with the existing structure in the simulation box) and its magnitude is ° ;( [vrep [ ;( 1 , calculated as the ratio of the overlap volume to the maximum allowed fraction of the volume of the incoming object. The algorithm stops when [vtet [ = 0, i .e., when the incoming object has found a stable position, which represents a local min imum of potential energy with respect to the centre of the simulation box. Note that the ballistic deposition algorithm represents a limiting case of a DEM sim ulation with perfectly inelastic collisions and zero friction. 2.2.3. Binder spreading and solidification on partic/e assemblies
The spreading and solidification steps are both modelled using the volume-of fluid (VoF) method for interface tracking - solid-liquid interface in the case of solidification and gas-liquid interface in the case of spreading. During binder spreading, the three-phase contact Iines are propagated at a velocity, ULG, de pendent on the local value of the instantaneous contact angle, (J, according to the constitutive equation = I1( (cos (Ja - cos (J) (J
ULG
(6)
where (J is surface tension of the liquid binder, 11 the viscosity, ( the "friction coefficient" [1 6] (a binary liquid-substrate interaction parameter), and (Ja equi librium advancing contact angle. Other constitutive relationships for the contact-line velocity as function of the instantaneous contact angle can of course be used if they are found to describe the spreading dynamics of a particular binder-substrate combination more ac curately than equation (6). The local contact angle is calculated from the solid, "s, and liquid, "L, interface normal vectors (7)
1 363
Sub-Granule Scale Modelling
which are obtained from the gradient of the corresponding "mollified" [1 7] phase volume function:
(8) At each time step, the three-phase contact lines are propagated according to equation (6) and the two-phase (gas-liquid) interfaces are then allowed to relax to a shape constant mean curvature. The local relaxation velocity at each l iquid in terface point is proportional to the difference between the local curvature and the average curvature of the liquid cluster to which that point belongs, ( ) until I( = The interface curvature is calculated from the normal vector according to (9) A VoF simulation of the spreading of a liquid-binder droplet on an assembly of a few primary solid particles in the absence of solidification is iIIustrated in Figs. 9a * K -K ,
1(
*
.
(� - -
Fig. 9. Volume-of-fluid simulation of the elementary steps of granule microstructure for mation: (a) liquid droplet spreading; (b) spreading with deposition of additional primary particles (indicated by arrows); and (c) spreading with binder solidification (adapted from ref. (9]).
1 364
F. Stepanek
and 9b. Binder solidification can be approached in two principally different ways, depending on the solidification mechanism. If binder solidification occurs as a well defined phase transition (e.g., re-crystallization of a solution binder, solidification of a melt binder, or the formation of a solid phase fram a reactive binder), the un derlying problem is also that of a moving interface, the solid-liquid interface velocity being calculated from the drying rate, heat-transfer rate, or reaction rate depending on the solidification mechanism [9]. This case is illustrated in Fig. 9c. On the other hand, binder solidification often occurs as a gradual increase of viscosity (e.g., for polymer-based solution or some melt binders), rather than in the form of a sharp phase transition. In that case, the effect of solidification is mode lied by gradually increasing the viscosity in equation (6) as function of concentration (drying) or temperature (cooling) and stopping the spreading simulation when a threshold value is reached at which the binder is effectively solid. 2.3. Characterization of granule m icrostructure
Once the 3D model of granule structure is constructed, it is often desirable to reduce the information about the spatial distribution of the constituent phases into volume-averaged morphological measures, such as porasity, etc., which can then be correlated with effective macrascopic properties. Several classes of morphological descriptors for disordered media are available [6, 1 8] ; only the most commonly used ones will be briefly reviewed here. The phase volume fraction of a phase j in the granule is defined by
rPj = � !fjd V
( 1 0)
where 0 is the VoF function of that phase and the sampling volume of the granule (typically, a sphere located in the centre of mass of the granule and covering 90% of its volume - so that the external shape of the granule does not affect the volume-averaged quantities). Porasity is the phase volume fraction of the gas phase. The characteristic length-scale of a phase is typically defined in one of four ways: (i) as the correlation length calculated fram the auto-correlation function of that phase; (ii) as the mean chord length calculated fram the chord-Iength dis tribution; (iii) as the ratio of phase volume to phase surface area of that phase; (iv) as the mean covering sphere diameter calculated fram the distribution of covering spheres. Let us now define some of these terms mathematically. The auto-cor relation function of phase j is defined (similarly to equation 5)
V
(1 1 )
1 365
Sub-Granule Scale Modelling
The correlation length Lc,j is defined as the zero-th order moment of the auto correlation function, i.e., Lc,j =
100 Rj(z)dz
(12)
The second above-mentioned measure of the characteristic length-scale, the mean chord length, is simply the mean of the chord-Iength distribution function i.e., the length distribution of line segments passing through the phase of interest. The third measure of the characteristic length-scale is defined by j� fjd V ( 1 3) LA, J. = --"--"--'-- --,;-;O ü . 5� r dA 2 [f(1 f)] J .J v J --
-
In the specific case of the phase j being the gas phase, LA,) is directly related to the equivalent hydraulic diameter up to a multiplication constant. The fourth above-mentioned measure of the characteristic length-scale of phase j within the granule structure is the mean covering diameter. The covering radii distribution function is generated by first constructing the distance function [1 9,20] that de termines the maximum possible radius of a sphere that fits entirely into the phase j as function of the position of its centre, and then finding the distribution of sphere radii that entirely cover the phase of interest. In the specific case of the gas phase, the distance function can be used for the calculation of simulated mercury intrusion curve [6]. Higher-order moments of each of the above-mentioned distribution function can of course also be used for the characterization of the microstructure, though the zero- (phase volumes) and first-order (character istic lengths) measures tend to be most useful for correlation with macroscopic properties. 2.4. Calculation of macroscopic properties from microstructure 2.4.1. Effective transport properties
As al ready mentioned in the introduction, the effective transport properties diffusivity, permeability, and thermal conductivity - of granules are important parameters in a number of applications. The aim of the calculation procedure is to obtain the values of these transport properties from the knowledge of the granule microstructure [6,7,21 ,22]. Let us iIIustrate the principle of the calculation on the case of effective thermal conductivity [ 1 5] (Fig. 1 0). A macroscopic temperature gradient ( T2- T1 )/f:.Z is imposed on a computa tional unit cell containing a statistically representative sampie of the multi-phase medium of interest. The steady-state heat conduction problem (Fourier's law) V (lc/vT) = 0
(14)
1 366
F. Stepanek
I 1
öL
Fig. 1 0. Calculation of effective thermal conductivity by imposing a temperature gradient across a unit cell containing a statistically representative sampie of the microstructure of interest, and solving the Fourier's law (from ref. [1 5]).
is then solved on the multi-phase medium using the local values of thermal conductivity of each phase, Aj, subject to the temperature gradient in the z direction and periodic boundary conditions in the x- and y-directions. The overall heat flux across the simulation box, 0', is then used for the calculation of the effective thermal conductivity from the macroscopic Fourier's law, Le., Aeff
=
Ci
I1Z
- A T2 - T1
( 1 5)
where A is the cross-section area of the simulation box perpendicular to the macroscopic temperature gradient. The effective thermal conductivity as function of the composition (phase volume fractions, rfJ), thermal conductivities of the phases, Aj, and microstructure can then be systematically calculated and corre lations derived, as has been done recently for the case of partially liquid-saturated particle assemblies of various shape by Kohout et al. [1 5]. The calculation of effective diffusivity proceeds in a similar manner as that of thermal conductivity, except that a macroscopic gradient of concentration (cr c1)/I1Z is imposed and the steady-state diffusion problem (Fick's law) is solved V (Dj VC)
=
0
( 1 6)
where Dj is the diffusivity in phase j. The effective diffusivity Deff is obtained from the macroscopic diffusion flux analogous to equation (15). Finally, the calculation of
1 367
Sub-Granule Scale Modelling
permeability [7] is based on imposing a macroscopic gradient of pressure (P2 -P1 )/ cell and solving the Stokes equation in the pore space ( 1 7) where I] is the dynamic viscosity, v the velocity, and P the pressure. Permeability is then evaluated from the converged velocity field according to the macroscopic Darcy's law V' I1Z = - 1] ( 1 8) A (P2 - P 1 ) where V' is the total volumetric flow-rate across the simulation box in the z-direction and A the cross-section area of the simulation box in the direction perpendicular to the pressure gradient. An example of calculated effective diffusivity and permeability of wet particle assemblies as function of relative saturation and particle size and shape can be found, e.g., in ref. [23]. The special case of multi-scale porous media is described in ref. [6]. I1Z across the computational
K
K
2.4.2. Effective dissolution rate
The effective dissolution rate of a granule can be determined from the knowl edge of granule microstructure and morphology by modelling the convec tion-diffusion transport of dissolved components from the granule surface and locally eroding the surface at a rate corresponding to the local mass fluxes. The single-granule dissolution methodology has been described by Stepanek [1 0], based on similar methodology for the dissolution of porous media, developed originally by Bekri [24]. An input to the simulation is a 3D granule structure encoded in a computational unit cell by the phase volume functions as de scribed in Section 2. 1 . The simulation proceeds iteratively in three steps: First, the velocity field in the surrounding liquid phase is calculated by solving the Stokes and continuity equations, i.e., r,.'v2 v
(1 9) 0 where I] is the viscosity, v the velocity, and P the pressure. Typically, periodic boundary conditions are applied in all the three directions for the velocity, and a macroscopic pressure gradient is imposed in one direction. Once the velocity field is calculated, the convection-diffusion equation aCi at
-
=
=
Vp;
Vv
=
-vVcI + DI V2 c·I
(20)
(where Ci is the concentration of component i, t the time, and Di the diffusion coefficient of component I) can be integrated for a short period of time. The granule structure is eroded (i .e., the values of the phase volume functions updated) simultaneously with the solution of equation (20) according to mass
F . Stepanek
1 368
Fig. 1 1 . Simulation sequence showing the erosion of a granule during diffusion-limited dissolution. (The granule skeleton is grey, the concentration profile of one the components in the fluid phase is shown by the contour map.)
fIuxes at the solid-liquid interface. The surface erosion rate is related to the local mass flux by dfi Mi dt = p; (-D;VCi + VCi)nS (21 ) -
where � is the phase volume function of component i, Mi the molar mass of component i, Pi the density of component i, and ns the solid interface normal vector (oriented from solid to the surrounding liquid phase). The evolution of a granule during dissolution simulation is shown in Fig. 1 1 . As the phase volume functions are updated, the geometry of the domain on which equation ( 1 9) is solved, is changing. However, it is usually sufficient to update the velocity field only after the volume of the granule changes by a significant amount (e.g., 5% of the original volume) rather then after every time step, and in the meantime obtain the velocity vector in newly formed liquid-phase points by interpolation. During the simulation of granule dissolution, the connectivity of the granule skeleton is also periodically checked. If a disconnected solid-phase cluster is detected (typically a partially dissolved primary solid particle whose binder bridge has already dissolved completely), it is removed from the simulation unit cell . The "shrinking core" and the "break-up" dissolution mechanisms can thus be distin guished (under shrinking core, the granule remains as a single entity during the dissolution, under break up, fragments detach from the granule during dissolu tion). In either case, the dissolution curve (i.e., the amount dissolved vs. time) is obtained from the dissolution simulation by integrating equation (21 ) .
3 . APPLICATION EXAMPLES
In this section, several works in which the above-described methodology of sub granule-scale modelling has been applied for the calculation of granule micro structure and macroscopic properties, are reviewed. The first two examples are concerned with the computation of granule porosity as function of formulation and
1 369
Sub-Granule Scale Modelling
process variables and its experimental validation. The latter two examples deal with the calculation and experimental validation of effective transport properties and dissolution rate.
3. 1 . Dependence of granule porosity on binder solidification rate
The granule formation algorithm described in Section 2.2 has been used for the calculation of granule porosity as function of the binder solidification and spread ing rate, and the frequency of droplet and particie deposition on the surface of a growing granule in the limiting case of low-shear granulation (negligible contri bution of external deforming forces) and granule growth by the layering mech anism [9]. The characteristic times of binder spreading, binder solidification, and surface deposition have been introduced in order to reduce the dimension of the parameter space to be investigated. The characteristic time of spreading, has been defined as the time required for the three-phase contact line to cover a distance equal to the droplet diameter. The characteristic time of solidification, has been defined as the time required for the solidification front to cover the has been chosen as same distance, and the characteristic time of deposition, the mean time between particie collisions in the granulation equipment. Granule porosity as function of the ratio / for several values of the ratio / and a fixed ratio of primary particies and droplets depositing on the growing granule surface is plotted in Fig. 1 2. The cross-sections of representative microstructures corresponding to three different t/ ratios are also shown. Let us discuss the observed trends by first examining the limiting cases of t/ -> 0 and t/ -> x . In the former case, the solidification time is much longer than the spreading time, i.e., there is sufficient time for the binder to completely spread within the granule structure before it solidifies (cf. also the cross section). The porosity in that case is determined by the available pore volume fraction within a ciose-packed structure of the primary particies saturated by the binder to a degree dependent on the binder/solids ratio. In this particular case, the binder/solids ratio is high so that the asymptotic porosity for t/ -> 0 is zero. The other asymptotic limit ( / -> oc ) corresponds to a situation where the binder droplet solidification is very rapid. The porosity of the granule then corresponds to that of a random ciose packing of primary solid particies and "frozen" binder droplets. The intermediate cases around t/ 0.1 lead to granule structures where the binder is partially distributed within the structure and a layer of solidified binder of varying thickness separates the primary particies. In this intermediate range, the porosity is also most sensitive to the collision frequency (the ratio t/ ) At a fixed solidification rate, increasing the particie deposition rate gene rally leads to a higher porosity - a liquid binder droplet that would Twet.
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1 370
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otherwise penetrate into the granule structure by capillary flow will be retained in place if a new solid particle is deposited on the surface. 3.2. Dependence of g ranule porosity on composition
In the previous case, it has been mentioned that granule porosity in the limiting case of slow solidification should only depend on the packing density of the primary solid particles and the binder content. This hypothesis has been tested in [25) both computationally and experimentally. Granules were prepared by fluid bed granulation of sugar spheres (Suglets, NP Pharm, France) with in situ melt binder (PEG-8000, mp 61 °C). Sugar spheres of two different size ranges have been used: Sl with dp = 250-355 j..lm and S2 with dp = 1 80-250 j..l m . The gran ulation was carried out in three steps: (i) mixing and heating-up of a mixture of primary solid and binder particles; (ii) granulation period, during which the tem perature was raised above the melting point of the binder and granulation oc curred; and (iii) cooling-down period during which the temperature was reduced to ambient and binder solidified. The binder/solids ratio and S2ISl mixing ratio were systematically va ried and the porosity of the resulting granules has been determined by measuring their envelope density (the composition and the density of the primary solids and the binder were known). At the same time, virtual granules of the same composition (S2/S1 ratio and binder/solids ratio) have been generated computationally for the limiting case of asymptotic spreading 0). (rwetlrsol --*
Sub-Granule Scale Modelling
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1 371
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F i g . 1 3. Granule porosity as function of binderjsolids ratio (by mass) for granules made of
S1-type primary particles (from ref. [25]).
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0 . 1 5 +-----,----,.---1 0.6 0.0 0.9 0.3 1 .2 52/51 ratio [w/w] Fig. 1 4. Granule porosity as function of small to large primary particle mixing ratio (by mass) for constant binder ratio (from ref. [25]).
Computed and experimentally measured porosity of granules as function of the binder ratio for Sronly granules is plotted in Fig. 1 3. Porosity is a decreasing function of the binder ratio - the packing density of the partie/es is fixed and the pore space becomes increasingly saturated by the binder as the binderjsolids ratio is increased. A small difference between sim ulated and measured porosity is apparent; in the simulations, the primary par tie/es were regarded as mono-sized spheres, while in fact the Suglets are slightly aspherical and the size is dispersed over a small interval. Figure 14 shows granule porosity as function of the mixing ratio between large (Si ) and small (S2) primary solid partie/es for a fixed binder ratio. The packing density of a binary
1 372
F. Stepanek
mixture of unequal partieIes is known to go through a maximum [26], and there fore the porosity of granules can be controlled by the partieIe size distribution of the primary partieIes. This phenomenon has been reproduced both computa tionally and experimentally - both sets of data show a e1ear minimum of porosity as function of the mixing ratio. 3.3. Dependence of g ranule d issolution rate on composition and porosity
The dissolution rate of granules as function of granule porosity, binderjsolids ratio, solubility and diffusivity of primary partieIes, and binder has been system atically investigated in [1 0] by using the methodology described in Section 2.4.2. A population of virtual granules with varying binderjsolids ratio and porosity has first been generated by means of the algorithm described in Section 2.2. The region in the granule composition space occupied by these granules and the correlation between porosity and binderjsolids ratio are plotted in Fig. 1 5. Each granule has then been subjected to a virtual dissolution test under eight different conditions: two hydrodynamic regimes (diffusion-Iimited dissolution in a stagnant liquid and dissolution under relative liquid-partiele velocity equal to the terminal settling velocity) and four combinations of material properties (high- and low solubility binder, and fast- and slow-diffusing binder). Examples of the dissolution curves for three different granules (porosity of 7%, 1 2%, and 21 % and binderj solids ratio of 0.41 , 0.35, and 0.1 7, respectively) under terminal settling velocity and a situation where the primary solid partieIes have both higher solubility and diffusivity than the binder (case "E" from ref. [1 0]) are shown in Fig. 16. The dissolution rate is e1early increasing with increasing porosity. The jumps on the radius VS. time plot correspond to fragments breaking off from the mother gran ule, and are an indication of the disintegration mechanism. Notice that the granule with lowest porosity (7%) dissolves practically only by the shrinking core mech anism, while for the high-porosity granule (21 %) the break off is most significant. 3.4. Effective transport properties of wet particle assemblies
The effective thermal conductivity [1 5] and the permeability [23] of primary par tiele assemblies partially saturated by a liquid have been determined computa tionally and compared with experimental measurements. The system used for the experiments consisted of glass spheres with narrow size distribution as model solid partieIes with water and n-hexane as high- and low-thermal conductivity liquid, respectively. A range of volume fractions of the solid phase has been realized by mixing large- and small-diameter glass spheres at varying ratios (the
Sub-Granule Scale Modelling
1 373 Primary Sol i ds
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F . Stepanek
1 374
same principle as the S2/S1 mixing described above). The sizes used were 68 11m (code name AH), 200 11m (AC), and 628 11m (BL). The effective thermal conduc tivity has been measured by the transient hot-wire method; permeability was determined by measuring the flow-rate and pressure drop of gas flowing through a column containing the partially saturated particle layer. The simulations were performed according to the procedure described in Section 2.4. 1 . Selected results are illustrated i n Figs. 1 7 and 1 8 for effective thermal con ductivity and permeability, respectively. The effective thermal conductivity is for AC-type particles with a varying degree of pore-space saturation ranging from 0 (dry system) to 1 (complete saturation). Owing to the relatively high thermal conductivity of water, the effective thermal conductivity of the saturated system is more than seven times higher than that of the dry system. The knowledge of thermal conductivity as function of liquid content is crucial for quantitative de scription of processes such as drying. An equally important parameter for drying and other applications (e.g., adsorption or catalysis) is permeability. Permeability as function of liquid saturation has been calculated [23] for a range of granular microstructures, such as mono-sized and poly-dispersed spherical, cubic, and rectangular particles, both hydrophilie and hydrophobie. A power-Iaw function for permeability, valid over a wide range of compositions and particle shapes, has been found [23]. A direct comparison of measured and computed permeability as function of porosity for a mixture of spherical particles is shown in Fig. 1 8. There is small offset between the experimental and computed values, due to slight over prediction of packing density in the simulations. 0.9
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1 375
Sub-Granule Scale Modelling 0.006
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4. FORWARD LOOK 4.1 . Computer-aided g ranule design
Let us now consider the integration of the sub-granule scale modelling methods described in this chapter into an overall design process for granular products. As already mentioned in the introduction, rational design of structured chemical products requires that two functional relationships be established: the so-called process function, relating a set of raw material properties and processing pa rameters to the granule microstructure; and the so-called property function, re lating the microstructure to the effective macroscopic properties of the product. Schematically these relationships are shown in Fig. 1 9, which has been derived from the general "product design" diagram proposed in [27]. The functional relationships can be established through experiments, theory or simulation, or their combination. Product design can be defined as a systematic activity whose aim is to find the inverse of these functions, i.e., to determine product composition (formulation) and processing conditions that result into a product with specified end-use properties. The term "computer-aided product design" then refers to a situation where mathematical modelling or computer simulations are used at least in some parts of this process. The computational methods described in this chapter cover all aspects of the design cycle - sim ulation of granule microstructure formation for the process function, granule dis solution and transport properties calculation for the property function, and granule
1 376
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I} -------n [ r-I GranuIe m-ic-ro-st-ru-c-tu-re--'I } Processing
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Fig. 1 9. Formal representation of the computer-aided granule design process.
microstructure characterization for both - and can be used either individually or in combination with experiments. 4.2. Virtual prototyping
The term "virtual prototyping" refers to a situation where new products are not only designed but also tested using computer models - by simulating the product end use, or other process in which the product performance is of interest. A physical prototype is then only manufactured in order to confirm predictions of the virtual prototyping activity, but not as part of the design loop. Virtual prototyping is already applied, e.g., in the automotive or aerospace industries, where the achieved savings are most significant in particular when the physical tests are destruetive in nature (crash tests). In the context of granular products, the sim ulation of granule dissolution that was described in Section 3.3 is an example of virtual prototyping. Two conditions have to be met for virtual prototyping to be a viable alternative to physical prototyping: one technical and other economic. The technical con dition is that the computer models have to be sufficiently aceurate so that their outputs can be treated with the same confidence as the results of physical tests. Referring again to the automotive industry, computational fluid dynamics (CFD) models for aerodynamics tests, and finite element analysis (FEA) models for crash tests are already reaching that level of accuracy. In principle, there is no reason why this should not also be the case for virtual prototyping of granules studies have shown that both the calculation of transport properties [1 5,23] and of granule porosity [25] can be rather accurate. The second condition is related to the availability of material properties required as input parameters into the models. If reliable property estimation methods exist for all required material properties (e.g., solubility, diffusion coefficients, ete.), these properties can be calculated from the knowledge of the molecular structure and fed into virtual prototyping models. If material properties have to be
Sub-Granule Scale Modelling
1 377
measured due to the absence of good property estimation methods and a group of materials is repeatedly employed in the products being virtually tested, then their properties can be measured once, maintained in a material property da tabase, and readily recalled each time they are required in a virtual prototyping model. However, if each new product also contains a new material (e.g., a new active in a granule) which is very different from any previously characterized substance and the experimental effort required to fully characterize, the new material is comparable to the effort required for the preparation and physical testing of the complete product, then of course the application of virtual proto typing would not bring any overall time saving. With this caveat in mind, computer-aided design and virtual prototyping of chemical products are rapidly developing areas with applications not only in granulation but also polymers [20], catalysis [6], and materials engineering. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [ 1 0] [1 1 ] [ 1 2] [ 1 3] [ 1 4] [ 1 5] [1 6] [1 7] [1 8] [1 9] [20] [21 ] [22] [23] [24] [25] [26] [27]
M. Hili, AIChE J . 50 (2004) 1 656-1 661 . J . N . Michaels, Powder Technol. 1 38 (2003) 1-6. M.F. Edwards, T. Instone, Powder Technol. 1 1 9 (200 1 ) 9-1 3. E.M. Holt, Powder Technol. 1 40 (2005) 1 94-202. L. Farber, G . I . Tardos, J.N. Michaels, Powder Technol. 1 32 (2003) 57-63. J. Kosek, F. Stepanek, M. Marek, Adv. Chem. Eng. 33 (2005) 1 37-203. P . M . Adler, Curr. Topics Phys. Fluids 1 ( 1 994) 277-306. N. Losic, J .-F. Thovert, P.M. Adler, J. Coll. Interf. Sci. 1 86 ( 1 997) 420-433. F. Stepanek, M A Ansari, Chem. Eng. Sci . 60 (2005) 401 9-4029. F. Stepanek, Chem. Eng. Res. Des. 82 (2004) 1 458-1 466. E.J. Garboczi , Cem. Conc. Res. 32 (2002) 1 62 1 -1 638. C. Thornton, M .T. Ciomocos, M.J. Adams, Powder Technol. 1 05 ( 1 999) 74-82. D. Coelho, J.-F. Thovert, P.M. Adler, Phys. Rev. E 55 ( 1 997) 1 959-1 977. X. Jia, R.A Williams, Powder Technol. 1 20 (2001 ) 1 75-1 86. M. Kohout, AP. Collier, F. Stepanek, Int. J . Heat Mass Trans. 47 (2004) 5565-5574. A Clarke, TD. Blake, K. Carruthers, A. Woodward, Langmuir 1 8 (2002) 2980-2984. w.J. Rider, D.B. Kothe, J. Comput. Phys. 1 4 1 (1 998) 1 1 2-1 52. C.H. Arns, M A Knackstedt, K.R. Mecke, Coll. Surf. A 241 (2004) 351-372. S.M. Sweeney, C.L. Martin , Acta Mater. 51 (2003) 3635-3649. Z. Grof, J. Kosek, M. Marek, P.M. Adler, AIChE J. 49 (2003) 1 002-1 0 1 3. E.J. Garboczi, D.P. Bentz, N.S. Martys, P.Z.Wong (Eds. ), Experimental Methods for Porous Media, Academic Press, New York, 1 999. M . E . Kainourgiakis, E.S. Kikkinides, A Galani, I . N . Tsimpanogiannis, Y.C. Yortsos, Transp. Por. Media 58 (2005) 43-62. M . Kohout, A.P. Collier, F. Stepanek, Powder Technol. 1 56 (2005) 1 20-1 28. S. Bekri, J .-F. Thovert, P.M. Adler, Chem. Eng. Sci . 50 ( 1 995) 2765-2791 . MA Ansari, F. Stepanek, Optimisation of binder and porosity distribution in granules. Proc. 8th Int. Symp. Agglomeration , Bangkok, Thailand, March 1 6-1 8, 2005, pp. 1 79-1 85. S. H utin, P. Accart, D . Oulahna, JA Dodds, Polym. Int. 52 (2003) 581-585. E. Favre, L. Marchal-Heusler, M. Kind, Trans. IChemE Part A 80 (2002) 65-74.
S U BJ ECT I N D EX 3-A, 575-577, 579 Abrasion technique, 1 1 92 Adhesion, 325, 330, 333, 342-343, 345, 351 , 354 Adhesion forces, 605 Adhesive failure, 832 Adhesive force, 1 259, 1 308, 1 31 0, 1312 Adjunct, 691 Admix, 675, 678, 682 ADPI, 575-576 Agglomerates, 4 1 8, 69 1 , 8 1 5 Agglomeration, 1 99, 208, 2 1 0-21 1 , 325, 332, 336, 34 1 , 344, 347-351 , 353, 356, 358, 366-371 , 4 1 8 Aggregation efficiency, 1 1 33, 1 1 36, 1 1 38, 1 1 42, 1 1 48-1 1 49, 1 1 56-1 1 57, 1 1 59 Aggregation rate constant, 1 027 Akkermans number, 685-686 Area rupture criterion, 1 288 Atomization , 336, 35 1 , 357-358, 364, 455, 465, 856, 859, 886, 890 Attenuation coefficient, 1 205, 1 208 Attrition, 453, 853, 856, 859, 870-87 1 , 887-889, 898, 980 Attrition constant, 1 028 Axial circulation , 1 2 Axial stress, 744 Bacteria, 555-559, 580, 583 Barium sulphate, 205 Base powder, 673, 675, 682-684, 686-687 Batch , 443, 853-854, 858, 872-879, 882, 884, 889-893 Batch fluidized-bed, 445 Beam testing, 764 Benbow-Bridgwater analysis, 202 Bentonite ciay, 21 1 Beverage powders , 656 Bifidobacterium, 557
Binder, 853-857, 859-887, 889-893 Binder deposition , 1 308 Binder solidification, 1 353, 1 357, 1 363-1 364, 1 369 Binder spreading, 1 353, 1 357-1 358, 1 362, 1 369 Binder surface tension, 1 0 Binder viscosity, 9 Binder viscosity, drum granulation, 232-233 Binderless, 29 1 , 294 Binders, 834 Bleach, 675, 678, 687 Bleeding, 680, 689 Bond formation, 957-961 Bond number, 1 345 modified, 1 348 Bonding forces, 995 Bonding mechanisms, 341 Bottom-driven high shear granulator, 470 Bottom-spray processing, 428 Brazilian test, 688, 763, see also Diametral compression test Bread improvers, 569 Breakage, 453, 700, 853, 857, 859, 864, 868-872, 882, 884, 886, 889, 893, 898-899, 979, 1 1 1 9, 1 1 22-1 1 27, 1 1 42, 1 1 63, 1 1 65, 1 1 67, 1 1 70-1 1 74, 1 1 76-1 1 78, 1 1 80 Breakage selection rate constant, 1 028 Breakfast cereals, 664 Bridge volume, 1 263, 1 265, 1 268, 1 27 1 , 1 284, 1 294, 1 301 , 1 3 1 4 Brittle, 995, 1 0 1 0 Brittle material, 763 Bubble size and shape, 1 098 Bubbling, 1 049-1 050, 1 052-1 053, 1 057, 1 062-1 063, 1 067 Buckingham's theorem, 7 1 2 Builder, 678, 683, 687 Bumping, 1 4
1 380 Caking, 665 Calcium carbonate, 209, 21 1 Calcium phosphate, 21 1 Capillary, 1 2 1 0, 1 26 1 , 1 265, 1 267-1 270, 1 273, 1 284, 1 287, 1 298, 1 300-1 301 Capillary bridge 1 3 1 7 Bond number 1 345 buoyancy force 1 346 contact angle 1 324 draining 1 348 effect of gravity 1 31 8, 1 344 effect of wetting hysteresis 1 31 8, 1 340-1 344 rupture 1 332-1 334, 1 339-1 340, 1 346-1348 volume 1 327-1 329 Capillary force 8 1 8, 1 321 c1osed-form approximation 1 334-1 335, 1 338 Derjaguin radius 1 338 effect of gravity 1 344-1 349 equal spheres 1 334 experimental data 1 332-1 334, 1 34 1 -1 342, 1 346-1347 hysteresis 1 340-1 344 Israelachvili's approximation 1 328 Laplace-Young equation 1 3 1 9, 1 345 surface tension 1 321 toroidal approximation 1 323 unequal spheres 1 336 Capillary number, 936-938, 974 Capillary pressure, 826 Capsules, 4 1 8 Cascading velocity, 377, 400-402, 405, 4 1 1 Catenoid, 1 258 Centre of mass, 1 209-1 2 1 0 Centripetal, 853, 879, 882-885 Cereal bars, 664 Certification, 555, 576, 579, 582 CFD, 377, 380, 397-398, 4 1 3-41 4 Chopper speed, 6 Chord length, 690, 698-699 Clamp, 579-580 Classifying discharge, 449 Classifying particle discharge, 21-22, 53-54, 59, 77, 79, 1 8 1
Subject Index Cleaning, 676-677 Coalescence, 853, 856, 859, 861 , 864, 867-870, 872, 874-878, 882, 884, 890, 893, 898-899 Coalescence kernei, 238-240, 1 1 09, 1 1 1 4, 1 1 1 7, 1 1 1 9, 1 1 27-1 1 28, 1 1 31 -1 1 32, 1 1 36-1 1 37, 1 1 42, 1 1 58, 1 1 70, 1 1 72, 1 1 77-1 1 79 Coalescence models, 947-956 Coalescence probability, 1 1 1 0, 1 1 33, 1 1 36, 1 1 46-1 1 49, 1 1 52, 1 1 80 Coater disc coater, 364-366 fluidised-bed coater, 337, 347, 355, 358-360, 364 pan coater, 364-366 rotating drum coater, 364-366 spouted bed coater, 360-362 Wurster coater, 362-364 Coating, 23, 79, 81 , 84-90, 1 58, 1 73, 1 8 1 , 685, 687 coating efficiency, 338, 348, 35 1 , 352, 355, 357, 367 coating quality, 338, 372 dry coating, 330-33 1 , 333 melt coating, 331 , 337 modelling of coating, 366-372 wet coating, 330, 335-336 Coating variability, 377, 379-380, 382, 385, 387, 389-390, 392, 394-395, 397-399, 412, 4 1 4 Co-extrusion, 2 1 4 Cohesion, 1 041 , 1 062-1 064, 1 067 Cohesive failure, 8 1 8 Cohesive forces, 1 041 , 1 053, 1 059, 1 062-1 063, 1 067 Cohesive stress, 707 Cohesivity, 8 1 7 Collision frequency, 1 1 1 0, 1 1 20-1 1 2 1 , 1 1 33-1 1 35, 1 1 37-1 1 38, 1 1 42, 1 1 58, 1 1 80 Collision model, 1 076 Collision rates, 983 Compact, 736-737 Compact strength, 277 Compaction, 425, 982 Compaction equations Cooper and Eaton, 748-749 Heckei, 750-751
Subject Index Kawakita, 749-750 Walker, 748 Compaction mechanisms, 744-755 Compaction problems, 766 binding, 770 chipping, 770 cracking, 766-769 disintegration, 772 dissolution, 772 mottling, 772 picking, 769 pitting, 770 tensile strength, 771 weight control, 771 -772 Compaction simulator, 761 -762 Compressibility factor, 265-266, 268, 275 Computer simulation, 1 030, 1 353, 1 357, 1 375 Concave toroidal model, 1 278 Cone-and-plate shearing device, 820 Confectionery, 660 Consolidation, 1 98, 200, 208, 853, 856, 859, 86 1-862, 866-867, 870, 872, 875-877, 88 1-882, 884, 886, 889-89 1 , 893, 929, 938-940 Consolidation rate constant, 944-945 Contact angle, 904, 1 01 7, 1 258, 1 263-1 268, 1 272, 1 278, 1 280, 1 284-1 287, 1 289, 1 294, 1 301 , 1 304, 1 307, 1 324, 1 362 advancing, 1 342 hysteresis, 1 342 receding, 1 340 Contact angle hysteresis, 1 264, 1 284 Contact area, 1 0 1 3 Contact line, 1 32 1 pinning, 1 340 slipping, 1 340 Continuous, 443, 853-855, 858, 861 , 869, 872, 876, 878, 885, 887-888, 890-893 Continuous fluidized-bed, 448 Continuous operation, 99, 1 04 Continuous processing, 451 Continuous product discharge, 448 Control, 466, 854, 856-857, 862-864, 869-870, 872, 874, 876, 879, 887-888, 890-892 Convenience foods, 648
1 38 1 Convex toroidal model, 1 280 Conveying, 680-682 Cracks, 1 0 1 3 Critical impact velocity, 993 Critical separation distance, 1 265 Critical stress intensity factor (Kid, 766 Cross section, 1 1 99-1 201 , 1 204-1 209, 121 1 Cross-linking, 569 Crystallisation, 594-595, 647 Cultures, 558-559, 580 Dairy powders, 644 Damage ratio, 1 0 1 3 De-aeration, 258, 262, 278 Deformation, 980 Deformation of particles, 229 Degree of wetting, 22, 1 00, 1 08, 1 1 1 , 1 1 3-1 1 4 , 1 1 6-1 1 8, 1 20-1 2 1 , 1 23-1 24, 1 26-1 29, 1 3 1-1 32, 1 34-1 35, 1 40-142, 1 79, 1 83 Delivery number, 853, 872, 885-886 DEM (Discrete Element Modeling), 377, 380, 397, 398, 4 1 4 , 1 020, 1 030, 1 200-1 201 Densification, 5, 674, 680, 683 Densities bulk, 1 98, 2 1 3 tapped, 1 98, 2 1 3 Density, 674, 678-680, 684, 687, 689-690, 692, 694, 700, 855-856, 859, 865, 867, 870, 872-874, 886, 891-892 Density distribution, 753-754 Derjaguin radius, 1 338 Detergent, 673-679, 681-683, 685-691 , 693-695, 697, 699 Detergent enzymes, 567, 572, 574 Dewetting, 1 289, 1 291 , 1 3 1 2 Diagenesis, 1 357 Diagnostic and guidance systems, 543 abnormal situation management (ASM), 504 expert system G2, 543 Failure Mode Effects Analysis (FMEA), 544 fault trees, 543 HAZOP, 543-544,547,552 hierarchical coloured Petri net (CPN) approach, 544
1 382 Kaiman filters and extended Kaiman filters, 543,548 operator guidance systems (OGS), 544 pattern recognition techniques, 45 root-cause analysis, 45 Diametral compression test, 762-764 Die, 1 89-1 90, 1 92-1 93, 1 96 , 200-201 , 205, 207, 2 1 2 , 2 1 4 Die fill, 74 1 -743 Diffusion, 1 366-1 368, 1 372, 1 376 Dimensionless analysis, 7 1 0 Dimensionless flow stress, 937 Dimensionless groups, 7 1 2 Dimensionless nucleation number, 91 0 Dimensionless spray flux, 908-909 Direct pelletization, 780, 782, 784, 789-790, 792, 794, 799-800 Discharging, 443 Discrete element, 270 Discrete element model, 1 074 Discretization, 1 1 65-1 1 70, 1 1 75 Discretized population balance, 1 1 09, 1 1 66 Disintegration, 1 0 1 1 Disintegration time, 772 Dispensing, 679-68 1 , 689 Dispersion , 686, 8 1 5, 853, 855-856, 859-865, 872, 874, 886, 888-889, 893 Dispersion map, 848 Dispersive mixing, 81 6 Dissolution, 209, 2 1 3 , 673-674, 678-680, 686, 688-690, 692, 694-695, 697-698 1 353-1 354, 1 367-1 369, 1 372-1 373, 1 375-1 376 Distribution of binder, 1 1 93 Distributive mixing, 8 1 6 Distributor design, 1 04 1 , 1 048-1 049 Dosage form design, 725-726 DPI, 3 1 3, 3 1 8, 32 1 Drop penetration time, 906, 920 Drop size distribution, 455 Drum coaters, 420 Drum critical speed, 248 Drum flight arrangement, 248 Drum granulation, 2 1 9-251 Drum granulation models, 249-250 Drum rotational speed, 225-227 Dry granulation, 289-291 , 308-309, 3 1 2 , 32 1
Subject Index Dry material handlingjrecirculationj production of seeds, 453 Dry powder inhalation, 289, 3 1 3-31 4 Dry product treatment, 464 Drying, 853, 856-857, 859-861 , 866 fluidised bed, 1 90, 1 99 freeze, 1 99 Drying liquid bridge, 1 250 Ductile, 995, 1 0 1 0 Dumb-bells, 1 96, 1 99, 205-207 Dynamic mechanical thermo analysis, 603 Dynamic strength, 1 006 Dynamic-yield strength, 1 002 EHEDG, 575-577, 579-582 Elastic, 995 Elastic deformation, 745, 752 Encapsulation, 325-326, 329, 331 Ennis coalescence model, 948 End-point, 477-480, 494 Enzoguard, 565-566 Enzymes, 555-557, 559-565, 567-575, 577, 579-581 , 583, 585, 587, 675, 687 Eötvös number, 1 345 Equipments, 4 1 8 Erosion, 8 1 8 Erosion kinetics, 83 1 , 840 Excipient, 1 99, 209, 21 1 -2 1 2 , 2 1 4 External seed production, 454 Extrudates, 1 90-1 9 1 , 1 95-1 97, 1 99-200, 203-207, 2 1 0 Extruder gear, 1 92 ram, 1 94-1 95, 2 1 3 , 2 1 4 screen, 1 93-1 94, 1 96 , 2 1 2 screw, 1 90, 1 92, 1 95, 202, 204 Extrusion, 1 89-2 1 5, 425, 627, 651 , 665 Extrusion pressure, 486-489 Extrusion spheronisation, 571 Fabric, 676-677 Fat bridges, 6 1 0 FDA, 575, 578 FDA's PAT initiative, 730 Feeding systems, 26 1 Fermentation, 557, 560, 580, 583 Fermipan, 557 Fertilizer granulation, 241 -243 Filtermat, 586-588
Subject Index Finite element, 269, 1 1 60, 1 1 64-1 1 65 Flange, 579 Flow field , 853, 872, 879, 882, 889 Flow pattern , 853, 875, 878-879 , 882-884, 888-890, 893 Flow regime, 879-880, 882, 884-885, 1 080 Fluid bed agglomeration, 6 1 9 Fluid-bed coating, 564, 576 Fluid bed granulator, 780, 785, 802 Fluidisation, 685, 1 04 1 -1 059, 1 06 1 -1 065, 1 067-1 068 Fluidized bed, 21-27, 29, 3 1 , 33--43, 45-59, 6 1 -65, 67-69, 71-75, 77, 79-85, 87, 89-9 1 , 93-95, 97, 99-1 03, 1 05, 1 07-1 09, 1 1 1-121 , 1 23-1 29, 1 31 -1 37, 1 39, 1 4 1 , 1 43-1 81 , 1 83-184, 291 , 294, 296, 298-299, 301 -302, 308-309, 3 1 3 , 3 1 8-31 9, 32 1 , 1 1 93, 1 1 95, 1 204-1 205 Fluidized-bed equipment, 424 Fluidized-bed granulation, 674, 684-686 Fluidized-bed granulators, 426 Flux number, 700 Food, 555, 558, 574-579, 581 , 583-585 Food protection, 575 Food safety, 574-575 Force feed, 26 1 Force-displacement, 753 Force-feeding, 261 Forces, 1 259, 1 269-1 270, 1 273, 1 276, 1 293-1 294, 1 297, 1 299-1 301 , 1 304, 1 307, 1 3 1 2 Fracture, 994 Fracture mechanics, 765-766, 997 Fracture pattern, 1 032 Fragmentation, 749, 752-753, 8 1 8, 983, 1 008 Frequency analysis, 479--480 Friction forces, 1 293, 1 301 Froude number, 71 1 , 7 1 3, 858, 872-874, 878, 883-886, 889 Fungi , 556 Gas distributors, 439 Gas handling, 430 Geldart's group, 1 047, 1 054 Glass transition, 578, 595 Glycerol monostearate, 2 1 0
1 383 Grains, 4 1 8 Granular flow, 874, 879-880, 882, 888, 891 Granulating liquid, 7 1 2 , 7 1 5 , 7 1 9 , 72 1-722, 727, 729 Granulating liquid requirement, 72 1 Granulation, 21-25, 27, 29, 3 1 , 33, 35, 37, 39, 4 1 , 43, 45--47, 49-51 , 53-55, 57, 59, 6 1 , 63, 65, 67, 69, 71 , 73, 75, 77, 79-81 , 83-85, 87, 89-9 1 , 93, 95, 97-1 03, 1 05, 1 07-1 09, 1 1 1-1 1 3, 1 1 5-1 1 7, 1 1 9, 1 2 1 , 1 23, 1 25, 1 27, 1 29, 1 3 1 , 1 33, 1 35, 1 37, 1 39, 1 4 1 , 1 43-1 8 1 , 1 83, 1 90-1 9 1 , 207, 209-2 1 0 , 220, 673-679, 681-687, 689-693, 695, 697, 699-700, 1 2 1 3-1214, 1 2 1 6- 1 2 1 8 , 1 222, 1 240, 1 244, 1 248 Granulation endpoint detection, 7 1 0 Granulation growth models, 235-237 Granulation index, 690 Granulation kinetics, 244-246 Granulation performance, 1 273, 1 302-1 303, 1 3 1 3 Granulation process control, 705, 7 1 3 , 7 1 7, 7 1 9 Granulation systems control of, see Process control diagnosis of, see Diagnostic and guidance systems dynamic analysis of, 5 1 0,549 future challenges, 549 mathematical modelling of, see Population balance models measurement of, see Process measurement operational aspects of, see Process optimization regime separated devices, 549 steady state analysis of, 51 1 Granule, 673, 675, 679-681 , 683, 686-692, 694-699 Granule design, 737-738 Granule flow, 739-741 Granule friability, 1 304 Granule growth, 2 1 , 53, 59-60, 1 79 Granule impact energy, 992 Granule strength, 1 2 1 3, 1 2 1 5- 1 2 1 6 , 1 226, 1 231 , 1 254 Granule T, 562-563, 567, 572
1 384 Granule TX, 567 Gravitational distortion, 1 260 Gravity feed, 26 1 , 275 Greyscale, 1 208- 1 2 1 1 Growth, 333, 335-336, 338, 341 , 347-350, 352-353, 356-358, 362, 366, 368-372, 683, 685-686, 700, 853, 856-857, 859-870, 874-875, 877, 889, 892, 929-930, 946, Growth regime map, 233-235, 933-934 Half-filiing angle, 1 263, 1 265, 1 271 Hamaker constant, 8 1 8 Handling, 673, 68 1 -682, 697 Hard metal, 289, 300, 306-308, 3 1 0, 3 1 2 Hardness, 1 1 93, 1 270, 1 293-1 295, 1 297-1 301 Heat and mass transfer, 22-24, 26, 85, 1 00, 1 08, 1 1 9-1 20, 1 23, 1 56 High shear granulation, 3, 563 High shear granulators, 42 1 , 469 High-shear granulation mixer, 674, 676, 678, 683-684, 687 High-pressure, 425 High-shear, 1 204-1 205, 1 207 Horizontal axis, 4 Horizontal axis ploughshare mixers, 1 1 Horizontal fluidized-bed, 450 Hydrodynamics in spout fluidized beds, 1 079 Hydrophobie nucleation , 922 Hygiene, 575, 577-578 Hygienic design, 555, 574, 576-578 Hygroscopicity, 598, 682 Hygrosensitivity, 599 IAFIS, 575 IAFP, 575 I D FA, 575 I mage processing, 477-478, 489-495 Imaging techniques, 1 1 89, 1 1 98-1 1 99 I mpact tests, 1 007 I mpact, wear, 982 Impelier speed, 6 In process computer program, 7 1 4 Induced particie drift, 1 098 Induction behaviour, 931
Subject Index I nfiltration, 820, 825 Infiltration Kinetics, 826 infrared (IR) moisture sensor, 481 , 483-484 I n-process control, 7 1 0 , 722, 726 I nstant yeast, 557 Instrumentation, 466 Interparticie forces, 1 04 1 , 1 047, 1 055, 1 057-1 058, 1 062-1 063 I nterparticie forces, 340-345 Inverse problem, 1 1 09-1 1 1 0, 1 1 1 5, 1 1 31 , 1 1 76 IR, 1 1 98 JOhanson, 264, 268, 276 Kawakita, 688 Kinetic energy, 1 259, 1 272, 1 293 Kinetic theory of granular flow, 1 087 Kinetics, 982 Lactic acid bacteria, 556 Lactobacilii, 557 Lactose, 1 94, 203, 206, 209, 2 1 1 Laplace-Young equation, 1 3 1 9, 1 345 Laundry, 675, 688 Layering of seeds, 782 Life cycie concept, see Systems perspective Likelihood of erosion, 845 Liquid bridge force, 707 Liquid bridges, 606, 8 1 8, 1 04 1 , 1 058-1 059, 1 063, 1 258-1 260, 1 264, 1 266- 1 267, 1 270, 1 272, 1 276, 1 284, 1 286, 1 289, 1 291-1 292, 1 294-1 295, 1 301 , 1 303, 1 305-1 307, 1 3 1 1 , 1 31 3, 1 3 1 7 see also capiliary bridge; capiliary force Liquid carrying capacity, 677, 685 Liquid feed system, 460 Liquid handling, 455, 465 Liquid phase migration , 1 92, 1 94, 204-205, 21 1 , 2 1 3 Liquid to solid ratio, 5 , 675, 677, 690, 693, 697 Load transmission, 995 Loss angle, 605 Loss modulus, 604 Low-pressure extruders, 425 Lubricant, 2 1 0 , 737-738, 744, 754, 765, 769
Subject Index Macrostructure, 689-690 Marumerizer, 560 Marumerization, 1 89-1 90, 1 95 Material charging, 443 Material properties, 262, 267 Mathematical modeling, drum granulation, 235-241 Mathematical modelling, 1 375 Matrix granule, 568 Maximum granule pore saturation, 931 Mechanically fluidized bed, 624, 650 Mechanisms, 982 Mechanisms of granule growth, 235-237 Melt pelletization, 801-809 coalescence, 804-805, 808, 809 distribution, 804-805 immersion, 804-805, 808, 809 layering, 804-805, 808 Melting, 5 Meniscus, 1 26 1 , 1 265, 1 267, 1 270, 1 278-1 280, 1 282, 1 307, 1 3 1 4 Mesostructure, 686 Method of binder addition, 5 Method of Lines, 1 1 09, 1 1 65 Method of moments, 1 1 63-1 1 64 Micelles, 2 1 3 Micro organism, 556-557 Microcrystalline cellulose (MCC), 1 94, 200 Micro-Force Balance (MFB), 1 273-1274, 1 276, 1 304-1 305 Micromanipulation, 1 272-1 273, 1 277, 1 305, 1 3 1 2 Microstructure, 689, 700, 1 353-1 357, 1 363-1 368, 1 375-1 376 Minimum fluidisation, 1 042, 1 044-1 046, 1 048, 1 050, 1 053, 1 056-1 058, 1 062, 1 064 Mixer, 420, 857-858, 860, 868-869, 872-886, 888-893 high shear, 1 91 -1 92 planetary, 1 91-1 92 Mixer load, 9 Mixing, 8 1 6 Mixing behaviour, 22, 1 2 1 , 1 81 Mixing rule, 687 Modelling, 775, 98 1 , 1 258, 1 284, 1 286 Modelling for granulation, 506-509 black-box, 520,530 hybrid models, 5 1 2
1 385
population balance models, see Population Balance Models reduced order models, 5 1 7 role of, 5 1 0 , 5 1 2-5 1 3 , 5 1 9 Moisture content, drum granulation, 223-225 Moisture measurement, 477, 481 Molten binder, 780, 784, 802, 804-808 MOM, 562, 564 Moments, 1 1 09, 1 1 30, 1 1 40, 1 1 42, 1 1 62-1 1 64, 1 1 67-1 1 68, 1 1 70-1 1 7 1 , 1 1 73, 1 1 78 Morphology of re-crystallized material, 1 234 Monte Carlo, 377, 380, 384-390, 393, 396-397, 399, 4 1 2 Monte Carlo simulation, 1 1 09, 1 1 75 MRI, 1 1 98-1 1 99 MSD, 569-570 Multi stage drying, 570, 574 Multi-dimensional population balance, 1 1 1 0, 1 1 28, 1 1 59, 1 1 79 Multi-fluid model, 1 086 Multi-level mOdeling, 1 072 Multi-scale, 853, 887-888, 894 Multiscale, multitask perspectives, 506-5 1 0 length and time scales, 506 scale map for granulation processes, 508 multiscale integration frameworks, 509
Nataphos, 570-572, 574 Nauta blender, 560 Neural networks, 271 Neutral angle, 258, 269, 276 Nip, 258, 261 , 265, 268, 277, 281 Nodoid configuration, 1 266 Nozzle arrangements, 459 NSF, 575, 577, 579 NUcieation, 2 1 , 59-60, 63, 853, 859, 86 1 -864, 869, 886, 889-890, 899 Nucleation area ratio, 9 1 0 Nucleation formation mechanism, 901 Nucleation process, 902 Nucleation ratio, 926 Nucleation regime map, 920-922 Nucleation regimes, 903
1 386 Number density, 1 1 1 4, 1 1 1 9-1 1 20, 1 1 23, 1 1 30, 1 1 34, 1 1 64, 1 1 66-1 1 67, 1 1 70, 1 1 72-1 1 74 Numerical techniques for population balance models, 5 1 3-51 4 Hounslow's discretization methods, 5 1 4-51 6 I mmanuel and Doyle I I l's finite element method, 5 1 5 Kumar and Ramkrishna's fixed and moving pivot methods, 5 1 4 Monte Carlo methods, 5 1 4 wavelet methods, 5 1 4 Nusselt number, 71 1 One-dimensional population balance, 1 1 23 Operating principles, 4 1 8 Oscillatory shear device, 820 Oversized grains, 453 Overspray, 453 Packed beds, 1 04 1 , 1 043-1 044 Packing, 1 9 1 , 1 98, 204, 208, 21 1 Packing density, 822 Pan coating, 379, 381 , 385, 403 Parabolic approximation, 1 265, 1 267, 1 273, 1 278, 1 282-1 283, 1 285, 1 287, 1 289-1 290, 1 297 Paracetamol, 1 304-1 309, 1 3 1 1-1 3 1 2 Partial voxeling, 1 1 98-1 1 99 Particle morphology, 1 355, 1 359-1 361 Particle packing, 1 353, 1 357, 1 36 1 -1 362 Particle size and shape, 1 0 1 9 Particle size distribution, 1 90, 1 94, 202, 205, 209, 21 1 , 2 1 4 Particle size distribution, drum granulation, 222-229 Paste, 1 97, 1 99-200, 202, 204-205, 2 1 0, 2 1 2-21 4 Peak pressure, 266, 268, 276-277 Pellet properties aspect ratio, 781 dissolution profile, 785 shape parameter, 781 Pelletization, 4 1 9 , 422-423 Pelletization aid, binder, 790-794 crystallite-gel model, 790, 791 microcrystalline cellulose (MCC), 783, 790-794, 799 sponge model, 790-79 1
Subject Index Pellets, 557, 570 Pendular, 1 258, 1 278, 1 282, 1 289, 1 293, 1 301 Pendular liquid bridge, 1 3 1 7 see also capillary bridge; capillary force Penetration time, 904 Percolation theory, 728 Pertume, 675-676, 678, 682, 687 Permanent plastic deformation, 954 Permeability, 826, 1 354, 1 365, 1 367, 1 372, 1 374-1 375 Pharmaceutical granules, 1 303 Phase ratio, 243 Phase volume, 675-676, 689-690, 693, 698-699 Plastic deformation, 745-746, 752-753, 766, 995, 1 1 44, 1 1 46, 1 1 50, 1 1 52, 1 1 54-1 1 55, 1 1 58 Pneumatic behaviour, 21 , 24, 47, 49, 1 00, 1 79 Pneumatically fluidized bed, 6 1 9, 650, 659 Polyethylene glycol, 801 , 803, 808-809 Population balance equation (PBE), 367-371 Population balance mOdelling, 237-238, 1 024 Population balance models (PBM), 51 3-52 1 , 537,544 birth rate, 5 1 3-51 5 coalescence kerneis, 5 1 7-51 8, 521-523,541 control relevant models, 523-525, 538 death rate, 5 1 3-51 5 growth rate, 51 1 , 51 3,523-524 linear models, 51 0,51 8-51 9 liquid mass balance, 524 multi-dimensional population balances, 518 multiple model approach, 5 1 8 population balance models, 5 1 3,51 5, 52 1 ,537 powder mass balance, 524 Pore size, effective, 906 Porosity, 673, 680, 684, 688-694, 697, 699-700, 854-856, 859, 861 , 870, 882, 1 0 1 9, 1 1 89, 1 200, 1 353, 1 357, 1 364, 1 368-1374, 1 376
1 387
Subject Index Porosity of tablets, 738, 745, 747, 772 Porous particie, 923-924 Positron emission particle tracking (PEPT) , 1 1 Post hardening, 668 Pouring , 5 Powder caking, 1 21 4 Powder coating, 289, 3 1 5 Powder flux, 908 Powder layering, 4 1 9 Powder motion , 1 1 Power consumption, 477-480, 489, 494 Power consumption method, 709, 7 1 3-71 5, 720, 722, 724-726 Power consumption profile, 709, 71 7-720, 722 Power-draw, 853, 872, 874 Pre-compressed, 1 1 90, 1 1 95 Pressure agglomeration, 627 Pressure swing granulation, 29 1 -292, 32 1 Prilling , 560-56 1 , 564, 568 Primary particle, 688-689, 692, 694-695 Primary particle size, 1 1 Principle of similarity, 7 1 0 Probiotics, 556-559 Process analytical technology (PAT), 775 Process control feedback/feed-forward control, 530-531 fuzzy logic control, 530 model predictive control (MPC) based on linear models, 532-535 multi-level, non-linear model predictive control (ML-NMPC), 522,533-537 multi-level control under uncertainty, 538-540 relative gain array (RGA), 5 1 1 Process measurement, 51 9-52 1 indirect minitoring parameters, 52 1 ,530-532 measurement of particle size distribution, 520 measurement of solid moisture, 520 soft sensors, 5 1 3 Process optimization, 52 1 algorithm of, 525-526 dynamic optimization (optimal control), 512,525-526 mini-max optimization, 540-542
objective functions for optimization, 525-526 simulation results and discussion, 526-530 steady state optimization, 521 -527 Process time, 8 Processing gas handling, 464 Processing options, 428, 442, 461 , 472 Product design, 1 375 Product examples, 22, 24, 1 56 Product forms, 4 1 8 Product properties, 4 1 8 Properties, 1 1 90, 1 1 92-1 1 95, 1 1 98, 1 204 Quality by design , 731 Quality control (tablet), 775-776 Quantification, 1 1 89, 1 1 98 Radial distributions, 1 209 Rate of liquid addition, 6 Rate processes, 899 Reaction , 853, 856, 860-86 1 , 879 Recycie, 854, 857, 887-888, 892 Reduced order models, 5 1 7-51 8 lumped regi mes i n series, 5 1 8 model reduction for multi-dimensional population balances, 5 1 8 reduced order models using the method of moments, 5 1 8 Relaxation time, 602-603 Release, 258-259, 324-328, 331 , 364 Residence time, drum granulation, 227-229 Resistance, 991 Reynolds number, 71 1 Robust formulations, 726 Roll compaction , 256 Roll pressing, 255 Roll speed, 276 Roller compaction , 629, 652, 1 1 94 Roll-gap, 280 Roping, 1 4 Rotary fluid bed processor, 780, 781 fluidizing air temperature, 807 particle movement, 781 , 795, 807 rotating friction plate, 781 , 785, 803, 806 rotor speed, 788, 795, 797, 80 1 , 807 spray nozzle, 780, 787, 795, 806 Rotating drums, 420
1 388 Rotational frame, 1 7 Rotor-processing (tangential spray), 428 Rumpf Model, 842 Rupture, 8 1 8, 1 334, 1 339-1 340, 1 346-1348 Rupture distance, 1 258, 1 265, 1 271 , 1 284, 1 287, 1 289 Rupture energy, 1 259, 1 271-1 272, 1 276 Saturation, 5, 853, 861-862, 870, 874-875, 890, 893 Scale-up, 24, 1 79, 289, 305-308, 289, 303, 306, 307, 32 1 , 705, 7 1 0, 7 1 2, 7 1 7, 853-859, 861 , 863-865, 867-869, 871-894, 9 1 9 Scale-up invariant, 7 1 0 , 71 1 , 7 1 7 , 722 Scale-up precision, 72 1 Schmidt number, 71 1 Screw feeder, 277 Sealing, 262 Seals, 578-579 Seeds (nuclei), 453 Segmentation, 1 1 98 Segregation, 1 1 0 1 Self-agglomerating, 291 Self-preserving, 1 1 39, 1 1 4 1 , 1 1 62, 1 1 77 Self-similar, 1 1 39, 1 1 4 1 -1 1 43 Self-similarity, 1 1 39, 1 1 4 1 S E M , 1 1 94, 1 1 96, 1 1 98 Semi-brittle , 995, 1 0 1 0 Semi-brittle granules, 967 Separation distance, 1 264-1 265, 1 268, 1 271 , 1 277, 1 283-1 285, 1 287, 1 290, 1 297, 1 3 1 4 Shape reconstruction, 1 36 1 Shear, 995 Shear rate, 859-860, 868-869, 879-880, 883-885 Shear strength, 1 003 Shear stress, 857, 864, 866, 868, 871 , 875, 883-884, 890 Sherwood number, 71 1 Similarity criteria, 71 1 Simulation of a granulation process, 1 084 Single particle, 4 1 8 Sintering, 608, 1 041 , 1 058, 1 061-1 062, 1 065-1068
Subject Index Size distribution particle size distribution, 520, 530-532, 537, 550 binder size distribution, 544 Size enlargement, 4 1 9 Slip, 258, 265, 280 Slugging, 1 04 1 , 1 047-1 048, 1 052 Smoluchowski equation, 1 1 09, 1 1 1 6, 1 1 1 9-1 1 21 , 1 1 4 1 , 1 1 75 Solid bridges, 607, 1 202, 1 21 4-1 2 1 7 , 1 229-1 231 , 1 234-1 235, 1 247, 1 250-1252 Solids circulation, 1 04 1 , 1 049, 1 05 1 -1 052 Solvent extraction, 1 1 89, 1 1 93-1 1 96 Specific energy, 853, 872, 875-878 Spray angle, 455 Spray area, 385-386, 388, 390, 393-395, 4 1 2 Spray coating, 4 1 9 Spray crystallization, 453 Spray dryers, 461 Spray drying, 423, 453, 559, 570, 572, 576, 6 1 3 , 646, 657 Spray flux, 853, 860, 872, 874, 886, 889-890 Spray granulation, 4 1 9 Spray nozzle, 455 Spray pattern , 455 Spray shape, 385-386, 388, 390, 393-394, 4 1 2 Spray systems, 455 Spray-coated, 1 1 92 Spray-dried, 1 1 9 1 , 1 1 95 Spray-drying, 674, 676, 68 1 , 684 Spraying , 5 Spreading, 856, 859, 863, 889 Spreading coefficient, 1 304-1 305 Spray flux, 9 1 5-9 1 6 Stareh , 555-556, 564-565, 568-569, 571 -574 Steady growth , 929, 931 Steady-state, 22, 53, 70, 78, 1 09, 1 25, 1 27, 1 31 -1 33 Steam jet agglomeration, 6 1 6 , 657 Stickiness, 569-570. 584-586, 588 Sticky region, 584-585 Stokes, 853, 858, 863-868, 876, 891 Stokes deformation number, 932, 1 022 Stokes number, 684, 1 1 53, 1 1 55-1 1 58
1 389
Subject Index Storage modulus, 604 Strain rate, 1 003 Strength, 675-678, 680, 683, 688, 689, 697 Stress, 688, 755 Stress amplification, 834 Structural characteristics, 1 1 90, 1 1 92, 1 1 95 Structure, 673, 675, 678, 680, 686, 688-700, 853, 855, 86 1 -863, 867, 870, 875, 89 1 , 893, 1 01 9, 1 1 89-1 1 95, 1 1 97-1 205, 1 207-1209 Structure-property relationships, 1 353-1354, 1 365-1 368 Superheated steam granulation, 1 35 Superposition, 603 Supra molecular structure, 593 Surface energy, 1 258, 1 276 Surface tension, 945, 1 0 1 7, 1 259, 1 266-1 267, 1 270, 1 273, 1 277, 1 293-1294, 1 298, 1 301 , 1 306, 1 3 1 0-1 3 1 2 , 1 321 Surfactant, 676-677, 679-680, 683-684, 686-687, 691 Swept volume, 853, 872, 877-879, 886, 889 Synchrotron, 1 203 Systems perspective, 500-509 accomplishments, 506 definition, 500 impact of Iife cycle perspective, 503-504 importance of systems approach, 504-505 ISOj1 EC1 5288, 502 life cycie activities, 502 life cycie concept, 502-504 life cycle phases, 503 systems framework, 501-502 Tablet, 377-380, 382, 385-390, 392, 394-397, 403, 406-4 1 4, 688, 690, 737, 745, 753, 756-758, 760-76 1 , 767-768, 770-773 Tablet ejection, 758-759 Tablet presses, 758-760 Tablet shape, 377, 406, 409-4 1 0 Tablets, 4 1 8 Tabletting, 425, 637, 654, 661
Tensile strength, 708, 996, 1 000 Tensile strength measurement, 7 1 6 , 724-725 Tensile strength , 708 Tensile strength, tablet, 771 Three-phase contact line, 1 294 Throughput, 256, 261-262, 264, 276, 278, 281 Tip speed, 869, 872-875, 879, 882-883, 885, 891 , 893 Tomography, 673, 695-697, 1 1 89, 1 1 98-1 1 99, 1 203, 1 206 Top-driven high shear granulator, 472 Top-spray processing, 428 Toroidal approximation, 1 258, 1 265, 1 271 , 1 278-1 279, 1 28 1 , 1 283-1 284, 1 287, 1 323 Toroidal vortex motion, 1 4 Torque, 477-478, 480, 489, 494, 853, 872-875 Tracer experiments, 985 Transformation, 858-860, 864, 866-867, 869-870, 875, 887, 891 , 893 Transport properties, 1 353-1 354, 1 365, 1 369, 1 372, 1 375-1 376 Triaxial testing, 774 Undesired agglomeration, 665 Uniaxial compression, 268 Unsteady operation, 22, 1 28 USDA, 575 Validation, 555, 579, 581 , 1 1 1 0, 1 1 45, 1 1 48, 1 1 58-1 1 60, 1 1 78-1 1 80 Van der Waals Forces, 6 1 1 , 996 Variables, 987 Variables affecting granule strength, 1016 Vertical axis, 4 Video-imaging, 377, 38 1 , 385-388, 390, 401-402, 404, 4 1 2 Viscoelasticity, 601 Viscosity, 1 270, 1 272, 1 277, 1 293-1294, 1 298, 1 3 1 2 Viscous contribution, 1 270 Viscous forces, 1 293 Viscous Stokes number, 940 Voidage, 906
1 390 Volume-of-fluid method, 1 362 VTF equation, 603 Wall friction, 258, 266, 276 Washburn equation, 904 Weil-mixed fluidized bed, 452 Wet granulation, 4 1 9 Wet granulation process, 7 1 2 , 7 1 7 , 723 Wet granulators, 420--421 Wet granule breakage, 962-964, 968 Wet pelletization, 786-801 moisture content, 787-788, 798, 800-801 required granulation liquid, 782, 792 spray rate, 787, 796, 798 Wet-massed, 1 1 9 1 , 1 1 95-1 1 96 Wettability, 338-340, 1 264, 1 276-1 278, 1 284-1 285, 1 29 1 , 1 293 Wetting, 338-340, 350, 853, 856-857, 859-86 1 , 863, 889, 900, 1 258, 1 268, 1 272-1 273, 1 289, 1 296-1297, 1 303, 1 305, 1 307, 1 309, 1 3 1 2
Subject Index Wetting hysteresis, 1 258, 1 289, 1 294, 1 340 WLF equation , 603 Work of compaction, 752-753 Wurster-processing, 428, 442 X-ray computed tomography, 741 X-ray tomography, 904 XRT, 1 1 89, 1 1 98-1 203, 1 205-1 206, 1 208-1 209 Yeast, 555-557, 580-581 , 583-588 Yeast extract, 555, 580-581 , 583-588 Yield , 688 Yield stress, 752 Young-Laplace, 1 258-1 260, 1 262-1 264, 1 266, 1 284, 1 287 Young's modulus, 752, 765-766, 1 021 Zeolite, 676, 678, 682 Zig-zag-sifters, 450
