Modern Drying Technology, Experimental Techniques (Volume 2)

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Modern Drying Technology Volume 2: Experimental Techniques

Edited by Evangelos Tsotsas and Arun S. Mujumdar

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Modern Drying Technology

Edited by Evangelos Tsotsas and Arun S. Mujumdar

Modern Drying Technology, Edited by E. Tsotsas and A. Mujumdar Other Volumes Volume 1: Computational Tools at Different Scales ISBN 978-3-527-31556-7

Forthcoming Volumes Volume 3: Product Quality and Formulation ISBN 978-3-527-31558-1

Volume 4: Energy Savings ISBN 978-3-527-31559-8

Volume 5: Process Intensification ISBN 978-3-527-31560-4

Complete Set Modern Drying Technology Set - (Volume 1-5) ISBN 978-3-527-31554-3

Modern Drying Technology Volume 2: Experimental Techniques

Edited by Evangelos Tsotsas and Arun S. Mujumdar

The Editors Prof. Evangelos Tsotsas Otto-von-Guericke-University Thermal Process Engineering Universitätsplatz 2 39106 Magdeburg Germany

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for

Prof. Arun S. Mujumdar National University of Singapore Mechanical Engineering/Block EA,07-0 9 Engineering Drive 1 Singapore 117576 Singapore

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek Die Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliograﬁe; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de. # 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microﬁlm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not speciﬁcally marked as such, are not to be considered unprotected by law. Composition Thomson Digital, Noida, India Printing betz-druck GmbH, Darmstadt Binding Litges & Dopf GmbH, Heppenheim Cover Design Adam-Design, Weinheim Printed in the Federal Republic of Germany Printed on acid-free paper ISBN: 978-3-527-31557-4

V

Contents Series Preface XIII Preface of Volume 2 XVII List of Contributors XXIII Recommended Notation XXVII EFCE Working Party on Drying: Address List

1

1.1 1.2 1.2.1 1.2.2 1.2.3 1.3 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5 1.3.6 1.4 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.4.6

XXXIII

Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers 1 Mirko Peglow, Thomas Metzger, Geoffrey Lee, Heiko Schiffter, Robert Hampel, Stefan Heinrich, and Evangelos Tsotsas Introduction and Overview 1 Magnetic Suspension Balance 2 Determination of Single Particle Drying Kinetics – General Remarks Conﬁguration and Periphery of Magnetic Suspension Balance 4 Discussion of Selected Experimental Results 6 Infrared Spectroscopy and Dew Point Measurement 10 Measurement for Particle Systems – General Remarks 10 Experimental Set-Up 12 Principle of Measurement with the Infrared Spectrometer 13 Dew Point Mirror for Calibration of IR Spectrometer 14 Testing the Calibration 17 A Case Study: Determination of Single Particle Drying Kinetics of Powdery Material 20 Coulometry and Nuclear Magnetic Resonance 24 Particle Moisture as a Distributed Property 24 Modeling the Distribution of Solids Moisture at the Outlet of a Continuous Fluidized Bed Dryer 25 Challenges in Validating the Model 27 Coulometry 28 Nuclear Magnetic Resonance 33 Combination of Both Methods 37

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

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Contents

1.4.7 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.5.4.1 1.5.4.2 1.5.4.3 1.5.5 1.5.5.1 1.5.5.2 1.5.5.3 1.5.6 1.5.6.1 1.5.6.2 1.5.6.3 1.6

2

2.1 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 2.3.6 2.4 2.4.1 2.4.1.1 2.4.1.2 2.4.1.3

Experimental Moisture Distributions and Assessment of Model 37 Acoustic Levitation 41 Introductory Remarks 41 Some Useful Deﬁnitions 42 Forces in a Standing Acoustic Wave 43 Interactions of a Droplet with the Sound Pressure Field 47 Deformation of Droplet Shape 48 Primary and Secondary Acoustic Streaming 48 Effects of Changing Droplet Size 53 Single Droplet Drying in an Acoustic Levitator 55 Drying Rate of a Spherical Solvent Droplet 55 Drying Rate of an Acoustically Levitated Solvent Droplet 58 Drying Rate of Droplets of Solutions or Suspensions 58 A Case Study: Single Droplet Drying of Water and an Aqueous Carbohydrate Solution 59 A Typical Acoustic Levitator 60 Evaporation Rates of Acoustically-Levitated Pure Water Droplets 61 Evaporation Rates and Particle Formation with Aqueous Mannitol Solution Droplets 63 Concluding Remarks 66 References 69 Near-Infrared Spectral Imaging for Visualization of Moisture Distribution in Foods 73 Mizuki Tsuta Introduction 73 Principles of Near-Infrared Spectral Imaging 74 Near-Infrared Spectroscopy 74 Lambert–Beer Law 74 Hyperspectrum 76 Classiﬁcation by Spectral Information Acquisition Technique 77 Classiﬁcation by Spatial Information Acquisition Technique 78 Image Processing 79 Extraction of Spectral Images from a Hyperspectrum 79 Noise and Shading Correction 79 Conversion into Absorbance Image 80 Acquisition and Pretreatment of Spectral Data 81 Analysis of Absorbance Spectra 82 Visualization of Constituent Distribution 82 Applications of Near-Infrared Spectral Imaging for Visualization of Moisture Distribution 83 Speciﬁcation of the Absorption Bands of Water and Ice 83 Imaging Apparatus 83 Acquisition of Hyperspectra of Water and Ice 84 Spectral Analysis 84

Contents

2.4.2 2.4.2.1 2.4.2.2 2.4.2.3 2.4.2.4 2.5

Visualization of Moisture Distribution inside Soybean Seeds Sample 85 Acquisition of Hyperspectra 86 Spectral Analysis 86 Visualization of Moisture Distribution 87 Future Outlook 88 References 89

3

Magnetic Resonance Imaging for Determination of Moisture Profiles and Drying Curves 91 Stig Stenström, Catherine Bonazzi, and Loïc Foucat Introduction 91 Principles of MRI for Determination of Moisture Proﬁles 93 General Considerations 93 Basic NMR 94 Nuclear Magnetic Moment and Larmor Relation 94 Net Magnetization and Radio Frequency Excitation 94 Relaxation and NMR Signal 95 Factors Inﬂuencing Relaxation Times 97 Imaging Principles 97 Projection of an Object (1D Imaging) 98 Two-Dimensional Imaging 98 Slice Selection 99 Three-Dimensional Imaging 100 Imaging Sequences 101 The Spin–Echo (SE) Sequence 101 The Gradient–Echo (GE) Sequence 102 MRI Applications to Drying of Paper, Pulp and Wood Samples 102 Some General Data about the Materials 102 Overview of Previous Results 104 Pulp, Paper and Cellulose Samples 104 Wood 106 Determination of Moisture Gradients in Cardboard Samples 108 Experimental Conditions 108 Drying Experiments and MRI Parameters 109 Calibration Procedure 111 Results for Drying Proﬁles 114 Diffusion Measurements 119 MRI Applications to Drying of Agricultural and Food Samples 125 MRI and Transport Phenomena in Agricultural and Food Products 125 NMR for Characterization of Biological and Food Products 126 MRI for Measurement of Transient Moisture Proﬁles in Food and Biological Samples 128 General Data 128 Measurement of Moisture Proﬁles in a Gel during Drying 130

3.1 3.2 3.2.1 3.2.2 3.2.2.1 3.2.2.2 3.2.2.3 3.2.2.4 3.2.3 3.2.3.1 3.2.3.2 3.2.3.3 3.2.3.4 3.2.4 3.2.4.1 3.2.4.2 3.3 3.3.1 3.3.2 3.3.2.1 3.3.2.2 3.3.3 3.3.3.1 3.3.3.2 3.3.3.3 3.3.3.4 3.3.3.5 3.4 3.4.1 3.4.2 3.4.3 3.4.3.1 3.4.3.2

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3.4.4 3.4.4.1 3.4.4.2 3.4.4.3 3.4.4.4 3.4.4.5 3.5

4 4.1 4.1.1 4.1.2 4.1.3 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.3 4.3.1 4.3.2 4.3.2.1 4.3.2.2 4.3.2.3 4.3.2.4 4.3.2.5 4.4 4.4.1 4.4.1.1 4.4.1.2 4.4.2 4.4.3 4.4.3.1 4.4.3.2 4.5

5

5.1 5.2

Non-Intrusive Measurement by MRI of Moisture Proﬁles in Paddy Rice Kernels during Drying 132 Experimental Set-Up 132 NMR Preliminary Experiments 132 NMR Imaging Experiments 134 Conversion of the MRI Signal to Water Content 135 Imaging Results and Moisture Proﬁles 135 Conclusion 137 References 139 Use of X-Ray Tomography for Drying-Related Applications 143 Angélique Léonard, Michel Crine, and Frantisek Stepanek Fundamentals and Principles 143 Introduction 143 Physical Principles 144 Reconstruction 148 Instrumentation 153 Geometry of CT Systems 153 X-Ray Macrotomography (or Industrial Tomography) 155 X-Ray Microtomography 156 Synchrotron X-Ray Microtomography 157 Image Processing 157 Algorithms for 3D Image Filtering and Segmentation 157 Calculation of Morphological Characteristics 163 Phase Volume Fraction 164 Cluster Volume Distribution 164 Percolation 165 Interfacial Area 166 Interface Curvature 166 Applications 167 Convective Drying of Sludge 167 Sludge Individual Extrudates 167 Sludge Packed Bed 170 Drying Optimization of Resorcinol-Formaldehyde Xerogels 173 Contact Drying of a Packed Bed 176 Experimental Set-Up 176 Spatio-Temporal Evolution of the Drying Front 177 Future Outlook 180 References 182 Measuring Techniques for Particle Formulation Processes 187 Stefan Heinrich, Niels G. Deen, Mirko Peglow, Mike Adams, Johannes A.M. Kuipers, Evangelos Tsotsas, and Jonathan P.K. Seville Introduction 187 Measurement of Particle Size 188

Contents

5.2.1 5.2.1.1 5.2.1.2 5.2.1.3 5.2.2 5.2.2.1 5.2.2.2 5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.3.5.1 5.3.6 5.3.6.1 5.3.6.2 5.4 5.4.1 5.4.2 5.4.2.1 5.4.2.2 5.4.3 5.4.3.1 5.4.3.2 5.4.3.3 5.4.3.4 5.5 5.5.1 5.5.2 5.5.2.1 5.5.2.2 5.5.2.3 5.5.2.4 5.5.3 5.5.3.1 5.5.3.2 5.6

In-Line Particle Size Measurement 188 Measuring Principle 188 Instrumentation 189 Applications 190 Off-Line Particle Size Measurement 194 Measuring Principle 194 Measurement Results: Size and Shape 196 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability 201 Introduction 201 Particle Detection 202 Particle Image Velocimetry 208 Spectral Analysis of Pressure Drop Fluctuations 218 Positron Emission Particle Tracking 223 Particle Circulation Time 224 Fiber Optical Probe Measurement Technique 228 Calibration 231 Experimental Results 232 Measurement of Mechanical Stability of Particles during Fluidized Bed Processing 236 Introduction 236 Measurement of Attrition Dust with an Isokinetic Sensor 237 Theory 237 Experimental Results 240 Measurement of Attrition Dust and Overspray with an On-Line Particle Counter 243 Lorentz–Mie Theory as Measuring Principle 243 Measurement in High Concentrations with Small Optical Measuring Volume 244 Calibration and Evaluation 246 Experimental Results 249 Characterization of the Mechanical Properties of Partially and Fully Saturated Wet Granular Media 251 Introduction 251 Interparticle Forces 252 Mechanical Interactions 252 Adhesive Interactions 254 Cohesive Interactions 256 Frictional and Lubrication Interactions 259 Mechanical Properties of Wet Granular Media 261 Elastoplastic Measurements 262 Failure Properties 266 Conclusions 269 References 272

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6

6.1 6.2 6.2.1 6.2.1.1 6.2.1.2 6.2.1.3 6.2.2 6.2.3 6.2.3.1 6.2.3.2 6.3 6.3.1 6.3.1.1 6.3.1.2 6.3.2 6.3.2.1 6.3.2.2 6.3.3 6.3.3.1 6.3.3.2 6.3.3.3 6.3.3.4 6.3.3.5 6.3.4 6.3.4.1 6.3.4.2 6.3.4.3 6.3.4.4 6.3.5 6.3.6 6.3.6.1 6.3.6.2 6.3.6.3 6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.4.5

Determination of Physical Properties of Fine Particles, Nanoparticles and Particle Beds 279 Werner Hintz, Sergiy Antonyuk, Wolfgang Schubert, Bernd Ebenau, Aimo Haack, and Jürgen Tomas Introduction to Common Particle Properties 279 Analysis of Particle Size Distribution 280 Image Analysis by Optical and Scanning Electron Microscopy 280 Optical Microscopy 281 Electron Microscopy 281 Image Analysis 282 Laser Light Scattering and Diffraction for Dilute Particle Dispersions 283 Ultrasonic Methods for Dense Particle Dispersions 291 Acoustic Attenuation Spectroscopy 291 Electrokinetic Sonic Amplitude Spectroscopy 292 Measurement of the Physical Properties of Particles 293 Solid Density Analysis by He-Pycnometry 293 Introduction 293 Volume Determination Using Gas Pycnometry 294 Speciﬁc Surface Area by Gas Adsorption Method 296 Physical Principles 296 Surface Area Determination using the BET-Model 298 Pore Size Distribution by Gas Adsorption Method 300 Introduction 300 Assessment of Microporosity 301 Assessment of Mesoporosity 302 Simpliﬁed Assessment of Pore Volume 304 Measurement Set-Up and Test Method 305 Measurement of Particle Adhesion 307 Particle Adhesion Effects 307 Comparison between Different Adhesion Forces 308 Survey of Adhesion Force Test Methods 309 Particle Interaction Apparatus According to Butt 310 Measurement of Particle Restitution Coefﬁcient 312 Particle Abrasion and Breakage Tests 318 Survey of Test Methods and Principles 318 Compression Test 321 Impact Test 325 Testing of Particle Bed Properties 328 Bulk Density and Tapping Density 328 Angle of Repose of a Moving Particle Bed 329 Flow Behavior of Cohesive and Compressible Bulk Solids 329 Flow Criteria of Preconsolidated Cohesive Powders on a Physical Basis 332 Translational Shear Cell according to Jenike 335

Contents

6.4.5.1 6.4.6 6.4.7 6.4.8 6.4.8.1 6.4.8.2 6.4.8.3 6.4.8.4 6.4.8.5 6.5 6.6

The Shear Testing Technique SSTT according to ICE 337 Ring Shear Tester according to Schulze for Dry Powder 339 Press Shear Cell according to Reichmann for Wet Filter Cake 340 Survey of Selected Direct and Indirect Shear Testers 344 The Biaxial Shear Tester according to Schwedes 344 The Uniaxial Tester according to Enstad 344 Couette Device by Tardos 346 Powder Flow Analyzer ShearScan TS12 by AnaTec 346 Survey of Different Shear Testers 348 Measurement of Particle Bed Movement in Rotary Drums by High-Speed Camera 348 Conclusions 353 References 356 Index

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XIII

Series Preface The present series is dedicated to drying, i.e. to the process of removing moisture from solids. Drying has been conducted empirically since the dawn of the human race. In traditional scientiﬁc terms it is a unit operation in chemical engineering. The reason for the continuing interest in drying and, hence, the motivation for the series concerns the challenges and opportunities. A permanent challenge is connected to the sheer amount and value of products that must be dried – either to attain their functionalities, or because moisture would damage the material during subsequent processing and storage, or simply because customers are not willing to pay for water. This comprises almost every material used in solid form, from foods to pharmaceuticals, from minerals to detergents, from polymers to paper. Raw materials and commodities with a low price per kilogram, but with extremely high production rates, and also highly formulated, rather rare but very expensive specialties have to be dried. This permanent demand is accompanied by the challenge of sustainable development providing welfare, or at least a decent living standard, to a stillgrowing humanity. On the other hand, opportunities emerge for drying, as well as for any other aspect of science or living, from either the incremental or disruptive development of available tools. This duality is reﬂected in the structure of the book series, which is planned for ﬁve volumes in total, namely: Volume 1: Computational tools at different scales Volume 2: Experimental techniques Volume 3: Product quality and formulation Volume 4: Energy savings Volume 5: Process intensiﬁcation As the titles indicate, we start with the opportunities in terms of modern computational and experimental tools in Volumes 1 and 2, respectively. How these opportunities can be used in fulﬁlling the challenges, in creating better and new products, in reducing the consumption of energy, in signiﬁcantly improving existing or introducing new processes will be discussed in Volumes 3, 4 and 5. In this sense, the ﬁrst two volumes of the series will be driven by science; the last three will try to show how engineering science and technology can be translated into progress.

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

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Series Preface

In total, the series is designed to have both common aspects with and essential differences from an extended textbook or a handbook. Textbooks and handbooks usually refer to well-established knowledge, prepared and organized either for learning or for application in practice, respectively. On the contrary, the ambition of the present series is to move at the frontier of modern drying technology, describing things that have recently emerged, mapping things that are about to emerge, and also anticipating some things that may or should emerge in the near future. Consequently, the series is much closer to research than textbooks or handbooks can be. On the other hand, it was never intended as an anthology of research papers or keynotes – this segment being well covered by periodicals and conference proceedings. Therefore, our continuing effort will be to stay as close as possible to a textbook in terms of understandable presentation and as close as possible to a handbook in terms of applicability. Another feature in common with an extended textbook or a handbook is the rather complete coverage of the topic by the entire series. Certainly, not every volume or chapter will be equally interesting for every reader, but we do hope that several chapters and volumes will be of value for graduate students, for researchers who are young in age or thinking, and for practitioners from industries that are manufacturing or using drying equipment. We also hope that the readers and owners of the entire series will have a comprehensive access not to all, but to many signiﬁcant recent advances in drying science and technology. Such readers will quickly realize that modern drying technology is quite interdisciplinary, proﬁting greatly from other branches of engineering and science. In the opposite direction, not only chemical engineers, but also people from food, mechanical, environmental or medical engineering, material science, applied chemistry or physics, computing and mathematics may ﬁnd one or the other interesting and useful results or ideas in the series. The mentioned interdisciplinary approach implies that drying experts are keen to abandon the traditional chemical engineering concept of unit operations for the sake of a less rigid and more creative canon. However, they have difﬁculties of identiﬁcation with just one of the two new major trends in chemical engineering, namely process-systems engineering or product engineering. Efﬁcient drying can be completely valueless in a process system that is not efﬁciently tuned as a whole, while efﬁcient processing is certainly valueless if it does not fulﬁl the demands of the market (the customer) regarding the properties of the product. There are few topics more appropriate in order to demonstrate the necessity of simultaneous treatment of product and process quality than drying. The series will try to work out chances that emerge from this crossroads position. One further objective is to motivate readers in putting together modules (chapters from different volumes) relevant to their interests, creating in this manner individual, task-oriented threads trough the series. An example of one such thematic thread set by the editors refers to simultaneous particle formation and drying, with a focus on spray ﬂuidized beds. From the point of view of process-systems engineering, this is process integration – several unit operations take place in the same equipment.

Series Preface

On the other hand, it is product engineering, creating structures – in many cases nanostructures – that correlate with the desired application properties. Such properties are distributed over the ensemble (population) of particles, so that it is necessary to discuss mathematical methods (population balances) and numerical tools able to resolve the respective distributions in one chapter of Volume 1. Measuring techniques providing access to properties and states of the particle system will be treated in one chapter of Volume 2. In Volume 3, we will attempt to combine the previously introduced theoretical and experimental tools with the goal of product design. Finally, important issues of energy consumption and process intensiﬁcation will appear in chapters of Volumes 4 and 5. Our hope is that some thematic combinations we have not even thought about in our choice of contents will arise in a similar way. As the present series is a series of edited books, it can not be as uniform in either writing style or notation as good textbooks are. In the case of notation, a list of symbols has been developed and will be printed in the beginning of every volume. This list is not rigid but foresees options, at least partially accounting for the habits in different parts of the world. It has been recently adopted as a recommendation by the Working Party on Drying of the European Federation of Chemical Engineering (EFCE). However, the opportunity of placing short lists of additional or deviant symbols at the end of every chapter has been given to all authors. The symbols used are also explained in the text of every chapter, so that we do not expect any serious difﬁculties in reading and understanding. The above indicates that the clear priority in the edited series was not in uniformity of style, but in the quality of contents that are very close to current international research from academia and, where possible, also from industry. Not every potentially interesting topic is included in the series, and not every excellent researcher working on drying contributes to it. However, we are very conﬁdent about the excellence of all research groups that we were able to gather together, and we are very grateful for the good cooperation with all chapter authors. The quality of the series as a whole is set mainly by them; the success of the series will primarily be theirs. We would also like to express our acknowledgements to the team of Wiley-VCH who have done a great job in supporting the series from the ﬁrst idea to realization. Furthermore, our thanks go to Mrs Nicolle Degen for her additional work, and to our families for their tolerance and continuing support. Last but not least, we are grateful to the members of the Working Party on Drying of the EFCE for various reasons. First, the idea about the series came up during the annual technical and business meeting of the working party 2005 in Paris. Secondly, many chapter authors could be recruited among its members. Finally, the Working Party continues to serve as a panel for discussion, checking and readjustment of our conceptions about the series. The list of the members of the working party with their afﬁliations is included in every volume of the series in the sense of acknowledgement, but also in order to promote networking and to provide access to national working parties, groups and individuals. The present edited books are

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complementary to the regular activities of the EFCE Working Party on Drying, as they are also complementary to various other regular activities of the international drying community, including well-known periodicals, handbooks, and the International Drying Symposia. June 2007

Evangelos Tsotsas Arun S. Mujumdar

XVII

Preface of Volume 2 As indicated in the Preface of this series, Computational tools at different scales were presented in Volume 1 of Modern Drying Technology. However, models need parameters, they must be validated, and they do not always provoke immediate enthusiasm among manufacturing professionals, quality managers and customers. Therefore, even the most sophisticated computational tools are of limited value if not accompanied by equally powerful measurement methods. Volume 2 of the series is, therefore, dedicated to the treatment of the most relevant Experimental techniques discussed in depth in six chapters: Chapter 1: Measurement of average moisture content and drying kinetics for single particles, droplets and dryers Chapter 2: Near infrared spectral imaging for visualization of moisture distribution in foods Chapter 3: Magnetic resonance imaging for determination of moisture proﬁles and drying curves Chapter 4: Use of X-ray tomography for drying related applications Chapter 5: Measuring techniques for particle formulation processes Chapter 6: Determination of physical properties of ﬁne particles, nanoparticles and particle beds Chapter 1 presents experimental techniques such as . . . . . .

gravimetry by magnetic suspension balance, dew point mirror hygrometry, infrared spectroscopy, coulometry, nuclear magnetic resonance, acoustic levitation.

By magnetic suspension of the specimen, weight measurements can approach the accuracy theoretically provided by a microbalance. Therefore, the mass of wet single particles, the change in this mass with time in the course of drying and single-particle drying kinetics can be determined accurately, provided that the particle is not too

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

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Preface of Volume 2

small. Additionally, dry mass, adsorption isotherms and kinetics of adsorption or desorption can be determined. What the magnetic suspension balance achieves with one particle is achieved by infrared spectroscopy for an entire particle system such as a ﬂuidized bed. By measuring the water concentration in the gas phase at the outlet and the inlet of a dryer, the hold-up of water can be derived precisely. From its change with time the drying kinetics of the particle system are obtained and can be scaled-down to the single particle with some appropriate model. In this way, single-particle drying curves become accessible, even for ﬁne powders. On the other hand, the moisture content of the particle system can be monitored very precisely, which is important for understanding and controlling particle formation in spray ﬂuidized beds. Dew point mirror hygrometry is discussed together with infrared spectroscopy, because the former has been used to calibrate the latter. Coulometry is very accurate in measuring small amounts of water, but takes some time and care, which is a problem if the mass of water has to be determined for every individual particle in a sample consisting of many particles. Such a task corresponds to the measurement of moisture distribution at the outlet of a continuous dryer or in a certain particulate product. It can be solved by using coulometry to calibrate nuclear magnetic resonance, and then performing serial measurements by NMR, which is faster and more comfortable. Finally, if single droplets are to be investigated rather than porous particles, then acoustic levitation – which is capable of suspending a small object in a ﬂuctuating pressure ﬁeld of the gas phase – is the method of choice. Drying kinetics can be derived from the optically recorded decrease in droplet diameter with time, from the slight change in the distance between the center of the droplet and the pressure ﬁeld node with droplet weight, or from measured outlet gas moisture contents in the case of a slight gas sweep. The technique can be validated with drops of pure water and then applied to obtain data on the drying behavior of multicomponent liquid mixtures. Despite their capabilities, the methods from Chapter 1 cannot provide insight into the interior of particles or other porous bodies. Other experimental approaches are necessary for this purpose, and are discussed in the subsequent Chapters 2, 3 and 4. The approach of Chapter 2 makes the sacriﬁce of cutting the sample into very thin slices. This sacriﬁce is rewarded by the fact that such thin slices can be illuminated, and absorbance spectra (the so-called hyperspectrum) can be recorded in the nearinfrared region. Calibration, spectroscopic data processing and image analysis provide images of the distribution of the constituents in space. The target constituent can be water (or rather ice, because the sample is usually frozen before treatment in the micro-slicer) as demonstrated with measured distributions of moisture in soybean seeds. However, the method can also visualize the distribution of other constituents, such as sugar, pigments or foreign substances in food materials. Chapter 3 is dedicated to magnetic resonance imaging – a non-invasive method that does not require destruction of the sample. First, the principles of the method and the way from the simple determination of total water in Chapter 1 to spatial distributions of water content in one, two or three dimensions are explained.

Preface of Volume 2

Then, several applications of MRI to paper, pulp and wood materials are discussed – some of them by reference, some others in considerable detail. The measurement of moisture proﬁles across multilayer cardboard samples during drying is very thoroughly presented. This example shows that all the information attainable by rather conventional methods (especially the drying curve) can also be obtained by means of MRI. However, MRI offers more, namely insight into the mechanisms of mass transfer in the product and to differences between such mechanisms. The latter can arise from differences in structure caused by design (e.g. in lamellar composites), by manufacturing (e.g. by the paper machine) or by nature (e.g. in wood). Apart from moisture distributions, the mobility of water in the drying material can also be obtained by magnetic resonance. The experimental results can unveil the – otherwise invisible – allocation of water within microstructured products. They can also provide diffusion coefﬁcients that can be correlated with moisture content and used in improved models for the process. Finally, applications of MRI to studies of the drying of agricultural and food materials are presented. Structural heterogeneity and anisotropy are rather the rule than the exception for this class of products, they correlate with moisture distribution, especially in the case of efﬁcient drying processes at relatively high temperatures, and can give rise to non-uniform shrinkage, stresses and damage. Poor properties of dried gels or broken paddy rice kernels are possible consequences that must be avoided, wherein MRI can be an important help. Since this requires a careful application of the method, limitations and possible pitfalls are critically addressed throughout Chapter 3. Chapter 4 discusses X-ray tomography, which is an alternative to MRI. Whereas MRI is based on emission by speciﬁc nuclei after appropriate excitation, attenuation by various species is the basis of X-ray tomography. Attenuation is made to tomography by rotation and reconstruction. Rotation provides views from different directions through the object, creating a spatial grid from the intersection points of the respective beams. Reconstruction computes (therefore: computed tomography) from integral attenuation data (from the single views) the attenuation taking place locally, in every volume element of the grid. Since the attenuation depends on the kind and amount of atoms present, spatial distributions of constituents can be obtained in the next step. Such constituents can be the solid and the liquid phase during drying. Observation of the distribution of the liquid phase provides – as previously discussed – insight about drying mechanisms and kinetics. Observation of the solid phase can help to quantify shrinkage, identify cracks, and correlate structural changes with product and process properties. Convective drying of sludge, convective drying of carbon gel monoliths and vacuum contact drying of pharmaceuticals are the examples used in Chapter 4 to explain the application of X-ray CT. Furthermore, methodic aspects such as image ﬁltering and segmentation, and the derivation of morphological characteristics are treated. Equipped with the methods of Chapters 1 to 4, we can (hopefully) understand drying much better, but we still do not have satisfactory access to, for example, how products emerge from processes that combine particle formation with drying, how

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particles move in dryers, or how powders ﬂow during processing, handling or ﬁnal use. To answer such questions we must widen our horizon from drying as a unit operation to drying as a part of solids processing and particle technology. This includes the use of various additional experimental techniques, as described in Chapters 5 and 6. A large part of Chapter 5 focuses on experimental techniques which originate from the investigation of particle formulation processes coupled with drying (wet granulation, agglomeration or coating) in ﬂuidized, spout-ﬂuid or spouted beds. These are: . . . . . . . .

modiﬁed spatial ﬁltering, dynamic image analysis, image analysis for particle detection, particle image velocimetry, spectral analysis of pressure drop ﬂuctuations, positron emission tracking, ﬁber optical probe, isokinetic sensor and particle counter for attrition dust and overspray.

Modiﬁed spatial ﬁltering is a laser-optical technique to measure in-line particle size and velocity. It is explained with applications to continuous spray ﬂuidized bed granulation of detergents and batch granulation of pharmaceuticals. Dynamic image analysis is an off-line optical method that provides particle size and shape. Particle detection by image analysis is used to see particles and bubbles, to calculate porosities and to map the spatial distribution of the phases in the particle system. However, it works only near some transparent wall, so that it is applicable only to essentially two-dimensional geometries, like spouted beds. Particle image velocimetry is subjected to the same restriction, but provides more information, namely particle velocities. Unlike convectional PIV, it does not require the addition of a tracer, because the product particles themselves fulﬁll this function. Global information about phase distribution, dynamic behavior, stability and bubbling state of the entire particle system (e.g. ﬂuid-spout bed) can be extracted from pressure drop ﬂuctuations by Fourier transform of the frequency spectra. More speciﬁc insight into the particle system is provided by positron emission particle tracking. The particle to be tracked becomes detectable by the emission of g-rays, which results from the decay of a radioactive marker. In this way position trajectories can be obtained, collision events can be identiﬁed and particle velocities can be calculated. Particle velocity ﬁelds are also accessible – after calibration – by means of the ﬁber optical probe. This probe is equipped with both emitting and detecting optical ﬁbers, and can be inserted in the bed like an endoscope. The jet zones created by spray nozzles in ﬂuidized beds can be identiﬁed and investigated in this way. Finally, attrition dust and overspray created in spray ﬂuidized beds can be detected at the gas outlet, either by appropriate selection and conventional analysis (isokinetic sensor) or by aerosol spectroscopy (on-line particle counter). The remaining part of Chapter 5 gives a more general overview of the mechanics of wet or dry granular media (interparticle forces, mechanical interactions, elastoplastic

Preface of Volume 2

behavior, failure properties), including references to a large number of methods for measurement and testing. After the transition provided in the last part of Chapter 5 and with a certain intended overlap, Chapter 6 treats the characterization of ﬁne particles, powders and particle systems from the point of view of general particle technology. Many experimental techniques are discussed, such as . . . . . . . .

optical and electron microscopy, laser scattering and diffraction, ultrasonic spectroscopy, pycnometry and gas adsorption, atomic force microscopy, free fall, impact and compression testing, shear testing, high-speed cameras.

Laser scattering and diffraction provide size distributions of dilute particle ensembles, whereas in dense particle systems the same objective can be attained by ultrasonic spectroscopy methods. Solid density, surface area and pore size distribution of either powders or consolidated porous bodies can be obtained by a combination of pycnometry with gas adsorption techniques. Particle interaction devices based on the principle of atomic force microscopy can give direct insight into the forces acting between particles in contact. The same forces are manifested in the results of free fall, impact or compression measurements, which can be translated to restitution coefﬁcients, to probabilities for breakage, abrasion or attrition, and to size distributions (selection functions) for the resulting fragments. Furthermore, the forces between particles in contact deﬁne the ﬂow of powders and granules, which – in turn – become visible by shear testing. Therefore, several shear testing facilities and their use are presented in detail in Chapter 6, along with a thorough treatment of the mechanics of cohesive powders and preconsolidated materials. High-speed cameras are indispensable for free fall or other impact measurements, but they can also be used to track the movement of particles in some types of equipment, such as rotary drums. Chapter 6 ﬁnishes with the presentation of such results, which are of interest for contact dryer operation. Several topics considered from the computational point of view in Volume 1 are further treated in Volume 2 with respect to experimentation. To these belong: .

.

.

Simultaneous drying and particle formation in spray ﬂuidized beds (Chapter 6 in Vol. 1, Chapter 5 and parts of Chapter 1 in Vol. 2); Discrete modeling (simulation methods in Chapters 2 and 5 of Vol. 1, experimental techniques for the determination of necessary particle–particle interaction parameters in Chapters 5 and 6 of Vol. 2); Thermomechanical aspects (deformations, shrinkage, stresses, damage in Chapters 1, 3 and 4 of Vol. 1, and Chapters 3 to 6 of Vol. 2);

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Preface of Volume 2 . . . .

Drying of gels (Chapter 3 of Vol. 1, Chapter 4 of Vol. 2); Drying of wood (Chapter 1 of Vol. 1, Chapter 3 of Vol. 2); Drying of droplets (Chapter 5 of Vol. 1, Chapter 1 of Vol. 2); Balance, scoping, scaling and detailed models for drying of particle systems in Chapter 7 of Vol. 1, measuring methods providing data on equilibrium and kinetics for such models in Chapters 1 to 4 of Vol. 2.

As pointed out in the general preface, thematic threads, multiscale considerations and interdisciplinary approaches are essential common features of the Modern Drying Technology series. Concerning the scales, Chapter 1 of Vol. 2 concentrates on particles and particle systems. The focus of Chapters 2 to 6 remains on particles and particles systems, however, the resolution of several experimental methods presented in these chapters reaches down to the pore scale. Measuring principles for some methods arise from the atomic or sub-atomic level and the results of some others reﬂect molecular scale phenomena. Links to food engineering, electrical engineering, medical engineering, physics, mechanics, and material science are especially pronounced in Volume 2. A key feature of this volume is that – dealing with experimental techniques – it does not only refer to scientiﬁc principles but, often, also to commercial equipment. This cannot be avoided, because all authors report primarily about their own experiences with measurements, which have been gained with speciﬁc instruments. Therefore, mention of the types and company names are useful pieces of information for documentation. It is neither indication of a preference, nor recommendation, and certainly not advertisement or endorsement of the product. In the same context it should be stressed that discussion of some rather expensive experimental techniques does not imply that good research is a privilege of the well-endowed institutions. On the contrary, it is the ﬁrm opinion of the editors that good science is done by good scientists, who understand the currently available tool-boxes and wisely select those instruments that a certain problem requires and deserves. As to the acknowledgements, they are for Volume 2 identical to those in the series preface. We would like to stress them by reference, but not repeat them here. July 2008

Evangelos Tsotsas Arun S. Mujumdar

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List of Contributors Editors Prof. Evangelos Tsotsas Otto-von-Guericke-University Department of Process and Systems Engineering P.O. Box 4120 39016 Magdeburg Germany E-mail: Evangelos.Tsotsas@vst. uni-magdeburg.de Prof. Arun S. Mujumdar University of Singapore Department of Mechanical Engineering 9 Engineering Drive 1 Singapore 117576 Singapore E-mail: [email protected] Authors Prof. Mike Adams The University of Birmingham School of Engineering Edgbaston Birmingham B15 2TT United Kingdom E-mail: [email protected]

Dr. Sergiy Antonyuk Technical University HamburgHarburg Solids Process Engineering & Particle Technology 21071 Hamburg Germany E-mail: [email protected] Dr. Catherine Bonazzi INRA-AgroParisTech JRU for Food Process Engineering 1 Avenue des Olympiades 91744 Massey cedex France E-mail: Catherine.Bonazzi@ agroparistech.fr Prof. Michel Crine Université de Liège Départment de Chimie Appliquée Bâtiment B6c, Sart-Tilman 4000 Liège Belgium E-mail: [email protected] Dr. Niels G. Deen University of Twente Faculty of Science and Technology P.O. Box 217 7500 AE Enschede The Netherlands E-mail: [email protected]

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

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List of Contributors

Dipl.-Ing. Bernd Ebenau Otto-von-Guericke-University Department of Process and Systems Engineering P.O. Box 4120 39016 Magdeburg Germany E-mail: [email protected]

Dr. Werner Hintz Otto-von-Guericke-University Department of Process and Systems Engineering P.O. Box 4120 39016 Magdeburg Germany E-mail: [email protected]

Prof. Loic Foucat QuaPA (Research Unit for Quality of Animal Products) INRA 63122 Saint Genes Champanelle France E-mail: [email protected]

Prof. Johannes A.M. Kuipers University of Twente Faculty of Science and Technology P.O. Box 217 7500 AE Enschede The Netherlands E-mail: [email protected]

Dipl.-Ing. Aimo Haack Otto-von-Guericke-University Department of Process and Systems Engineering P.O. Box 4120 39016 Magdeburg Germany E-mail: [email protected]

Prof. Geoffrey Lee Friedrich-Alexander University Division of Pharmaceutics Cauerstrasse 4 91058 Erlangen Germany E-mail: [email protected]

Dipl.-Ing. Robert Hampel Otto-von-Guericke-University Department of Process and Systems Engineering P.O. Box 4120 39016 Magdeburg Germany E-mail: [email protected]

Dr. Angélique Léonard Université de Liège Départment de Chimie Appliquée Bâtiment B6c, Sart-Tilman 4000 Liège Belgium E-mail: [email protected]

Prof. Stefan Heinrich Technical University HamburgHarburg Solids Process Engineering & Particle Technology 21071 Hamburg Germany E-mail: [email protected]

Jun.-Prof. Thomas Metzger Otto-von-Guericke-University Department of Process and Systems Engineering P.O. Box 4120 39016 Magdeburg Germany E-mail: [email protected]

List of Contributors

Jun.-Prof. Mirko Peglow Otto-von-Guericke-University Department of Process and Systems Engineering P.O. Box 4120 39016 Magdeburg Germany E-mail: [email protected] Dr. Heiko Schiffter University of Oxford Department of Engineering Science Parks Road Oxford OX1 3PJ United Kingdom E-mail: [email protected] Dr. Wolfgang Schubert Titania A/S 4380 Hauge i Dalane Norway E-mail: wolfgang.schubert@ kronosww.com Prof. Jonathan P.K. Seville The University of Birmingham School of Engineering Edgbaston Birmingham B15 2TT United Kingdom E-mail: [email protected] Prof. Stig Stenström Lund University Department of Chemical Engineering P.O. Box 124 22100 Lund Sweden E-mail: [email protected]

Prof. Frantisek Stepanek Institute of Chemical Technology Faculty of Chemical Engineering Technická 1903 166 28 Praha 6 – Dejvice Czech Republic E-mail: [email protected] Prof. Jürgen Tomas Otto-von-Guericke-University Department of Process and Systems Engineering P.O. Box 4120 39016 Magdeburg Germany E-mail: [email protected] Prof. Evangelos Tsotsas Otto-von-Guericke-University Department of Process and Systems Engineering P.O. Box 4120 39016 Magdeburg Germany E-mail: Evangelos.Tsotsas@vst. uni-magdeburg.de Dr. Mizuki Tsuta National Agriculture and Food Research Organization (NARO) Food Engineering Division Instrumentation & Information Engineering Lab. 2-1-12 Kannondai Tsukuba Ibaraki 305-8642 Japan E-mail: [email protected]

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XXVII

Recommended Notation . .

.

.

Alternative symbols are given in brackets Vectors are denoted by bold symbols, a single bar, an arrow or an index (e.g., index: i) Tensors are denoted by bold symbols, a double bar or a double index (e.g., index: i, j) Multiple subscripts should be separated by colon (e.g., rp;dry : density of dry particle)

A aw B b C (K) c D D (d) d E F _ FðVÞ f f G G g H H H h hðaÞ ~hðhN Þ Dhv I

surface area water activity nucleation rate breakage function constant or coefﬁcient speciﬁc heat capacity equipment diameter diffusion coefﬁcient diameter or size of solids energy mass ﬂux function volumetric ﬂow rate relative (normalized) drying rate multidimensional number density shear function or modulus growth rate acceleration due to gravity height enthalpy Heaviside step function speciﬁc enthalpy (dry basis) heat-transfer coefﬁcient molar enthalpy speciﬁc enthalpy of evaporation total number of intervals

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

m2 — kg1 m1 s1 m3 various J kg1 K1 m m2 s1 m J — m3 s1 — — Pa kg s1 m s2 m J — J kg1 W m2 K1 J mol1 J kg1 —

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Recommended Notation

J J _ JÞ jðm; K kðbÞ L MðmÞ ~ MðM; MN Þ _ MðWÞ _ mðJ; jÞ m_ N N _ NÞ NðW n n n _ NÞ nðJ P P p

_ QðQÞ _ qðqÞ R R ~ NÞ RðR r r S S s T t u u V _ VðFÞ v v W _ WðMÞ w X

numerical ﬂux function Jacobian matrix mass ﬂux, drying rate dilatation function or bulk modulus mass transfer coefﬁcient length mass molecular mass mass ﬂow rate mass ﬂux, drying rate volumetric rate of evaporation number molar amount molar ﬂow rate molar density, molar concentration number density outward normal unit vector molar ﬂux power total pressure partial pressure/vapor pressure of component heat ﬂow rate heat ﬂux equipment radius individual gas constant universal gas constant radial coordinate pore (throat) radius saturation selection function boundary-layer thickness temperature time velocity, usually in z-direction displacement volume, averaging volume volumetric ﬂow rate speciﬁc volume general velocity, velocity in x-direction weight force mass ﬂow rate velocity, usually in y-direction solids moisture content (dry basis)

— various kg m2 s1 Pa m s1 m kg kg kmol1 kg s1 kg m2 s1 kg m3 s1 — mol mol s1 mol m3 m3 mol m2 s1 W kg m s2 kg m s2 W W m2 m J kg1 K1 J kmol1 K1 m m — s1 m K, 8C s m s1 m m3 m3 s1 m3 kg1 m s1 N kg s1 m s1 —

Recommended Notation

x x x x0 ~x(x N) Y y y (v) ~y(y N) z

mass fraction in liquid phase particle volume in population balances general Eulerian coordinate, coordinate (usually lateral) general Lagrangian coordinate molar fraction in liquid phase gas moisture content (dry basis) spatial coordinate (usually lateral) mass fraction in gas phase molar fraction in gas phase spatial coordinate (usually axial)

Operators r r. D

gradient operator divergence operator difference operator

Greek letters aðhÞ bðkÞ b d dðDÞ e e e e h u k l m m n p r P s s s s t

heat-transfer coefﬁcient mass-transfer coefﬁcient aggregation kernel Dirac-delta distribution diffusion coefﬁcient voidage emissivity small-scale parameter for periodic media strain efﬁciency angle, angular coordinate thermal diffusivity thermal conductivity dynamic viscosity moment of the particle-size distribution kinematic viscosity circular constant density, mass concentration summation operator surface tension Stefan–Boltzmann constant for radiative heat transfer standard deviation (of pore-size distribution) stress dimensionless time

— m3 m m — — m — — m

W m2 K1 m s1 s1 m2 s1 — — — — — rad m2 s1 W m1 K1 kg m1 s1 various m2 s1 — kg m3 N m1 W m2 K4 m Pa —

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Recommended Notation

F w w v v (y) Subscripts a as b bed c c cr D dry dp eff eq f g H i i,1,2,. . . i,j,k in l m max mf min N o out P p pbe ph r rel s S surf V

characteristic moisture content relative humidity phase potential angular velocity mass fraction in gas phase

at ambient conditions at adiabatic saturation conditions bound water bed cross section capillary at critical moisture content drag dry at dewpoint effective equilibrium (moisture content) friction gas (dry) wet (humid) gas inner component index, particle index coordinate index, i; j; k ¼ 1 to 3 inlet value liquid (alternative: as a superscript) mean value maximum at minimum ﬂuidization minimum molar quantity outer outlet value at constant pressure particle population balance equation at the interface radiation relative velocity solid (compact solid phase), alternative: as a superscript at saturation conditions surface based on volume

— — Pa rad s1 —

Recommended Notation

v w w wb wet 1

vapor, evaporation water wall at wet-bulb conditions wet at large distance from interface

Superscripts, special symbols v volumetric strain * rheological strain * at saturation conditions or hi average, phase average a or hia intrinsic phase average ~ spatial deviation variable

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XXXIII

EFCE Working Party on Drying: Address List Dr. Odilio Alves-Filho Norwegian University of Science and Technology Department of Energy and Process Engineering Kolbjørn Hejes vei 1B 7491 Trondheim Norway odilio.ﬁ[email protected] Prof. Julien Andrieu (delegate) UCB Lyon I/ESCPE LAGEP UMR CNRS 5007 batiment 308 G 43 boulevard du 11 novembre 1918 69622 Villeurbanne cedex France [email protected] Dr. Ir. Paul Avontuur Glaxo Smith Kline New Frontiers Science Park H89 Harlow CM19 5AW UK [email protected] Prof. Christopher G. J. Baker Drying Associates Harwell International Business Centre 404/13 Harwell Didcot Oxfordshire OX11 ORA UK [email protected]

Prof. Antonello Barresi (delegate) Politecnico di Torino Dip. Scienza dei Materiali e Ingegneria Chimica Corso Duca degli Abruzzi 24 10129 Torino Italy [email protected] Dr. Rainer Bellinghausen (delegate) Bayer Technology Services GmbH BTS-PT-PT-PDSP Building E 41 51368 Leverkusen Germany rainer.bellinghausen@bayertechnology. com Dr. Carl-Gustav Berg Abo Akademi Process Design Laboratory Biskopsgatan 8 20500 Abo Finland cberg@abo.ﬁ Dr. Catherine Bonazzi (delegate) AgroParisTech – INRA JRU for Food Process Engineering 1, Avenue des Olympiades 91744 Massy cedex France [email protected]

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

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EFCE Working Party on Drying: Address List

Paul Deckers M.Sc. (delegate) Bodec, Process Optimization and Development Industrial Area t Zand Bedrijfsweg 1 5683 CM Best The Netherlands [email protected]

Prof. Dr. Istvan Farkas (delegate) Szent Istvan University Department of Physics and Process Control Pater K. u. 1. 2103 Godollo Hungary [email protected]

Prof. Stephan Ditchev University of Food Technology 26 Maritza Blvd 4002 Plovdiv Bulgaria [email protected]

Dr.-Ing. Dietrich Gehrmann Wilhelm-Hastrich-Str. 12 51381 Leverkusen Germany [email protected]

Dr. German I. Efremov Pavla Korchagina 22 129278 Moscow Russia [email protected] Prof. Trygve Eikevik Norwegian University of Science and Technology Department of Energy and Process Engineering Kolbjørn Hejes vei 1B 7491 Trondheim Norway [email protected] Dr.-Ing. Ioannis Evripidis Dow Deutschland GmbH & Co. OHG P.O. Box 1120 21677 Stade Germany [email protected]

Prof. Dr.-Ing. Adrian-Gabriel Ghiaus (delegate) Technical University of Civil Engineering Thermal Engineering Department Bd. P. Protopopescu 66 021414 Bucharest Romania [email protected] Prof. Dr.-Ing. Gheorghita Jinescu University Politehnica din Bucuresti Faculty of Industrial Chemistry, Department of Chemical Engineering 1, Polizu street Building F Room F210 78126 Bucharest Romania [email protected] Prof. Dr. Gligor Kanevce St. Kliment Ohridski University Faculty of Technical Sciences ul. Ivo Ribar Lola b.b. Bitola FYR of Macedonia [email protected]

EFCE Working Party on Drying: Address List

Prof. Dr. Markku Karlsson (delegate) UPM-Kymmene Corporation P.O. Box 380 00101 Helsinki Finland [email protected] Ir. Ian C. Kemp (delegate) GMS, GSK Priory Street Ware, SG12 0XA UK [email protected] Prof. Dr. Ir. P.J.A.M. Kerkhof Eindhoven University of Technology Department of Chemical Engineering P.O. Box 513 5600 MB Eindhoven The Netherlands [email protected] Prof. Matthias Kind Universität Karlsruhe (TH) Institut für Thermische Verfahrenstechnik Kaiserstr. 12 76128 Karlsruhe Germany [email protected] Prof. Eli Korin Ben-Gurion University of the Negev Chemical Engineering Department Beer-Sheva 84105 Israel [email protected] Emer. Prof. Ram Lavie Technion – Israel Institute of Technolgy Department of Chemical Engineering Technion City Haifa 32000 Israel [email protected]

Dr. Ir. Angélique Léonard (delegate) Université de Liège, Département de Chimie Appliquée Laboratoire de Génie Chimique Bâtiment B6c - Sart-Tilman 4000 Liège Belgium [email protected] Jean-Claude Masson RHODIA, Recherches et Technologies 85 avenue des Frères Perret BP 62 69192 Saint-Fons Cedex France [email protected] Prof. Natalia Menshutina Mendeleev University of Chemical Technology of Russia (MUCTR) High Technology Department 125047 Muisskaya sq.9 Moscow Russia [email protected] Jun.-Prof. Dr. Thomas Metzger Otto-von-Guericke-University Thermal Process Engineering P.O. Box 4120 39016 Magdeburg Germany [email protected]. de Prof. Antonio Mulet Pons (delegate) Universitat Politecnica de Valencia Departament de Tecnologia dAliments Cami de Vera s/n 46071 Valencia Spain [email protected]

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EFCE Working Party on Drying: Address List

Prof. Zdzislaw Pakowski (delegate) Technical University of Lodz Faculty of Process and Environmental Engineering ul. Wolczanska 213 93-005 Lodz Poland [email protected] Prof. Patrick Perré (delegate, next chairman of WP) AgroParisTech 14 Rue Girardet 54042 Nancy France [email protected] Dr. Roger Renström Karlstad University Department of Environmental and Energy Systems Universitetsgatan 2 65188 Karlstad Sweden [email protected] Prof. Michel Roques Université de Pau et des Pays de lAdour ENSGTI, 5 rue Jules- Ferry 64000 Pau France [email protected] Dr. Carmen Rosselló (delegate) University of Iles Baleares Dep. Quimica Ctra Valldemossa km 7.5 07122 Palme Mallorca Spain [email protected]

Emer. Prof. G. D. Saravacos (delegate) Nea Tiryntha 21100 Nauplion Greece [email protected] Dr.-Ing. Michael Schönherr BASF, GCT/T - L 540 Research Manager Drying Process Engineering 67056 Ludwigshafen Germany [email protected] Prof. Dr.-Ing. Ernst-Ulrich Schlünder Lindenweg 10 76275 Ettlingen Germany [email protected] Dr. Alberto M. Sereno (delegate) University of Porto Department of Chemical Engineering Rua Dr Roberto Frias 4200-465 Porto Portugal [email protected] Dr. Milan Stakic Vinca Institute for Nuclear Sciences Center NTI P.O. box 522 11001 Belgrade Serbia [email protected] Prof. Stig Stenstrom (delegate) Lund University Institute of Technology Department of Chemical Engineering P.O. Box 124 22100 Lund Sweden [email protected]

EFCE Working Party on Drying: Address List

Prof. Ingvald Strommen (delegate) Norwegian University of Science and Technology Department of Energy and Process Engineering Kolbjørn Hejes vei 1b 7491 Trondheim Norway [email protected] Prof. Czeslaw Strumillo (delegate) Technical University of Lodz Faculty of Process and Environmental Engineering Lodz Technical University ul. Wolczanska 213 93-005 Lodz Poland [email protected] Prof. Radivoje Topic (delegate) University of Belgrade Faculty of Mechanical Engineering 27, marta 80 11000 Beograd Serbia [email protected] Prof. Dr.-Ing. Evangelos Tsotsas (delegate, chairman of WP) Otto-von-Guericke-University Thermal Process Engineering P.O. Box 4120 39016 Magdeburg Germany [email protected]. de

Dr. Henk C. van Deventer (delegate) TNO Quality of Life P.O. Box 342 7300 AH Apeldoorn The Netherlands [email protected] Michael Wahlberg M.Sc. Niro Gladsaxevej 305 2860 Soeborg Denmark [email protected] Prof. Roland Wimmerstedt Lund University Institute of Technology Department of Chemical Engineering P.O. Box 124 22100 Lund Sweden [email protected] Dr. Bertrand Woinet (delegate) SANOFI-CHIMIE, CDP bât. 8600 31-33 quai armand Barbès 69583 Neuville sur Sa^ one cedex France bertrand.woinet@sanoﬁ-aventis.com Prof. Ireneusz Zbicinski Lodz Technical University Faculty of Process and Environmental Engineering ul. Wolczanska 213 93-005 Lodz Poland [email protected]

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j1

1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers Mirko Peglow, Thomas Metzger, Geoffrey Lee, Heiko Schiffter, Robert Hampel, Stefan Heinrich, and Evangelos Tsotsas

1.1 Introduction and Overview

Knowledge of the amount of moisture contained in particles before, during and after drying is an elementary requirement in drying technology. This moisture amount, for example for quality control, can easily be determined on more or less large samples of particles by weighing. However, other tasks, such as the design of industrial convective dryers impose much more serious challenges. To reliably design a convective industrial dryer, kinetic data referring to the speciﬁc product are necessary. Since information on drying kinetics is usually not available, it has to be gained experimentally. In this case, it is not sufﬁcient to measure the mass of moisture contained in the product at a certain point of time, but the change of this mass with time has to be resolved as accurately as possible. Additionally, the change of mass with time must refer to the single particle. The reason for this second requirement is that gas conditions change in particle systems. This results – even if every particle has exactly the same properties and the particles are perfectly mixed – in more or less signiﬁcant differences between the drying kinetics of the entire particle system and the drying kinetics of the single particle. Experimental techniques for the determination of single particle drying kinetics will be discussed in Section 1.2, with emphasis on the magnetic suspension balance. On the other hand, it is evident that measurements on single particles will give only very low signals and, hence, be confronted with severe limitations of resolution and accuracy, even when using very sensitive instruments. This is especially true for small particles (powdery products). Therefore, we may be forced to investigate drying kinetics of an entire particle system such as a packed or ﬂuidized bed. This is typically done by measuring gas humidity at the outlet of the dryer, instead of solids moisture content. It should be borne in mind that the results of such indirect measurements must be scaled down to the single particle by an appropriate model in order to obtain unbiased access to product-speciﬁc drying kinetics. Important instruments for

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

2

measuring gas humidity (infrared spectrometer, dew point mirror) will be presented in Section 1.3 along with some examples of scaling down. Even if we are not interested in drying kinetics, but merely in quality control, measurement of the amount of moisture contained in a sample may not be sufﬁcient. The reason is that the particles have a more or less broad residence time distribution in continuous dryers, which results in a moisture distribution in the outlet solids. This kind of distribution can only be resolved by measuring the moisture content of many individual particles. Methods for accomplishing this non-trivial task, namely coulometry and nuclear magnetic resonance, are the topic of Section 1.4. In the same section, an example of modeling the distribution of moisture in dried solids (in a population of particles) will be given. Until Section 1.4 it is assumed that the product to be dried consists of solid particles containing moisture in their porous interior. While this is true for many drying processes, the feed of some others – namely spray drying – is a liquid. Determination of drying kinetics for the droplets cannot be conducted with the same methods as for solid particles, but requires the application of speciﬁc measuring techniques. This topic will be covered in Section 1.5 by detailed discussion of acoustic levitation. Common to all the experimental techniques of the present chapter is that they do not provide immediate access to the moisture proﬁles developing in the interior of particles, droplets or other bodies during drying. Direct measurement of such proﬁles requires other experimental approaches, which will be presented in Chapters 2–4.

1.2 Magnetic Suspension Balance 1.2.1 Determination of Single Particle Drying Kinetics – General Remarks

Before presenting the magnetic suspension balance as a modern instrument for measuring single particle drying kinetics a short review of other methods, which can be used for the same purpose, will be given. These involve the use of . . .

a conventional microbalance a balance in combination with a drying tunnel an acoustic levitator.

A straightforward method to measure a drying curve is to put one wet particle on a conventional microbalance and record its change in weight (Hirschmann and Tsotsas, 1998). To avoid heat transfer from the plate of the balance, a miniature wooden stand can be used. The particle is ﬁxed in the crossbeam of this stand between the sharp tips of very thin wood bars. In this way, it is surrounded by air, providing uniform heat and mass transfer from all sides. However, such measurements are limited to ambient conditions and difﬁcult to reproduce exactly.

1.2 Magnetic Suspension Balance

When hanging the specimen in a drying tunnel, connection to the balance must be provided by means of a cord or thin wire. Since forces and force ﬂuctuations are transferred in this way from the specimen to the balance, a certain noise in the data is unavoidable, so that it does not make sense to use the most accurate microbalance. Therefore, a common balance with a sensitivity of merely 0.1 mg was used by Groenewold et al. (2000). The specimen consisted of 50 particles glued at sufﬁcient distance from each other on a net of watertight material, as proposed by Blumberg (1995). Due to the distance between the individual particles, the measurement can be assumed to closely approximate single particle kinetics. Experiences with the mentioned gravimetric methods are summarized in Tab. 1.1. As this table shows, both methods are limited with respect to operating conditions such as gas temperature and gas velocity. Measurement up to the relatively high gas velocity of 2 m s1 indicated in Tab. 1.1 for the drying tunnel is possible only by post treatment of the primary experimental results. This smoothing has been performed by averaging and a cubic spline, as proposed by Kemp et al. (2001). A serious further limitation concerns the minimum size of particles that can be investigated – due to both balance accuracy and difﬁculties in handling and ﬁxing objects smaller than about 1 mm. Co-axial ﬂow with respect to the hanging sample (DaSilva and Rodrigues, 1997; Looi et al., 2002) may have some advantages in comparison to crossﬂow against the specimen in the drying tunnel, but it is not fundamentally different. The difﬁculty common to all gravimetric methods arises from the requirement of suspending the particle in gas while simultaneously measuring its weight by connection to a balance. One solution is to refrain from gravimetric measurement and concentrate all efforts in reasonably suspending the particle in a ﬂow ﬁeld. This leads to acoustic levitation. The principles of acoustic levitation and its application to droplets will be discussed in detail in Section 1.5. Here, it should just be mentioned that the method has also been applied for particles by Groenewold et al. (2002) using a closed 45 kHz instrument. For better stability, a liquid droplet was suspended ﬁrst and the wet particle was then placed in this droplet. To determine the evaporation rate a small air purge was applied, and the change of outlet air humidity was measured by means of a high accuracy dew point mirror. This is very similar to the procedures that will be discussed in Section 1.3. Experiences from these measurements are also summarized in Tab. 1.1. They reﬂect problems of stability of suspension at high

Tab. 1.1 Applicability of different methods for the determination of single particle drying kinetics according to Kwapinski and Tsotsas (2006).

Method

dp, mm

T, C

Flow velocity, m s1

Microbalance Drying tunnel Levitator Magnetic suspension balance

min. 1 min. 1 1–2 min. 1

20–30 30–60 max. 30 max. 350

0 max. 2 0.02–0.065 max. 1

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temperatures and strong purges, which would evidently destroy the oscillating pressure ﬁeld and, thus, also the suspension force acting on the particle. An alternative strategy is to still use a balance, but refrain from any material connection between specimen and weight measuring cell. The realization of this idea in a magnetic suspension balance will be discussed in the following. 1.2.2 Configuration and Periphery of Magnetic Suspension Balance

A schematic representation of the principle of a magnetic suspension balance (MSB) is shown in Fig. 1.1. As already mentioned, the force to be measured is transmitted in a contactless way from the specimen to the microbalance. This is achieved by means of a magnetic force coupling, consisting of an electromagnet and a permanent magnet. The fact that the measuring device is disconnected from the sample chamber enables the microbalance to be kept always under ambient conditions, while high temperatures (up to 350 C) and high pressures (up to 500 kPa) may be realized in the sample chamber. The MSB used by the authors was produced by Rubotherm (Bochum, Germany). It is equipped with a feature called measuring load decoupling, which is conducted by ﬁrst lowering the suspension magnet in a controlled way to a second stationary position a few millimeters below the measuring position. Then, a small carrier to which the sample is connected is set down on a support. Now the sample is decoupled from the balance. The suspension magnet is in a freely suspended state, and only its own weight is transmitted to the balance. This so-called zero point position, which corresponds to an empty balance pan in a normal weighing procedure, allows for taring and calibration of the balance at all times, even when recording measurements

Fig. 1.1 Schematic representation of the MSB.

1.2 Magnetic Suspension Balance

under process conditions in the measuring cell. The resulting correction of zero point and sensitivity drifts increases the measuring accuracy signiﬁcantly, especially in the case of long term measurements (Rubotherm, 2004). Apart from drying kinetics, chemical reactions (polymerization, decomposition, combustion, corrosion), formulation processes (e.g. coating), phase equilibrium (e.g. sorption) and material properties (surface tension, density) can also be investigated in the MSB. The conﬁguration installed in the laboratory of the authors (Fig. 1.2) is used mainly for determination of drying kinetics or sorption equilibrium. Therefore, it includes a periphery capable of establishing different atmospheres of conditioned air. The design of this humidiﬁer is identical to the set-up for calibration of IR spectrometers that will be described in Section 1.3.4. Additionally to the measurement of weight, gas humidity can be measured at the inlet of the MSB (after the air conditioner) and at the outlet of the MSB by means of a dew point hygrometer and an IR spectrometer, respectively. The gas feed can be pressurized air with a moisture content of 0.5 g kg1 or completely dry ﬂask gas. Mass ﬂow rates are adjusted by a mass ﬂow controller, calibrated by means of a ﬁlm ﬂow meter. A correction for buoyancy should be applied to MSB data according to the relationship (Rubotherm, 2004): ML ¼ MBL þ V L rg

ð1:1Þ

Here, ML and VL are the mass and volume of the load (including load cage and basket), respectively; MBL is the value of the balance display and rg is the gas density.

Fig. 1.2 Experimental set-up of magnetic suspension balance (MSB).

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Furthermore, for drying samples in the range of milligrams the buoyancy of the sample should be taken into account. Thus, the expression MS ¼ M BLS ðP; T; wÞM BL ðP; T; wÞ þ V S rg ðP; T; wÞ

ð1:2Þ

can be used to calculate the mass of the sample, MS. Here, MBLS is the value that the balance displays with sample, MBL is the value that the balance displays without sample and VS is the volume of the dry sample. The inﬂuence of changing state variables in the sample chamber (pressure P, temperature T, relative humidity w) is considered in Eq. 1.2. However, the buoyancy effect contributed by water (moisture), which is usually less than 1 mg, is neglected. 1.2.3 Discussion of Selected Experimental Results

In the following, applications of the magnetic suspension balance are illustrated on the basis of results by Kwapinski (Kwapinski and Tsotsas, 2004a, b, 2006). The materials used in these experiments (molecular sieve 4A, g-Al2O3 and SiC) have very different pore diameters, see Tab. 1.2. Zeolite and alumina oxide are highly hygroscopic, while silicium carbide has very low hygroscopicity. Figure 1.3, as an example, shows results on the kinetics of desorption of water from one single particle of zeolite 4A. This particle with a diameter of 2 mm was ﬁxed with glue onto the tip of a thin needle suspended in the sample chamber of the MSB. First, water was adsorbed on the particle by exposing it to air with a relative humidity of w0 ¼ 0.60. Then, the experiment was started by suddenly reducing the relative humidity of the air from this initial value to a value of win ¼ 0.05 at the inlet of the sample chamber. The progress of particle moisture content until reaching the new, lower equilibrium value is plotted in Fig. 1.3 for different gas velocities. To obtain results representing the kinetics of mass transfer in the interior of the particle, it is desirable to reduce the relatively small inﬂuence of gas-side mass transfer as far as possible by measuring at high gas velocities. This, however, has an adverse effect on the accuracy of weighing, so that a compromise must be found. In this context, it should be mentioned that the ﬂow of conditioned air during the presented experiments was from the bottom to the top of the sample chamber. This creates a ﬂow force on the particle – similar to the buoyancy force. Consequently, smaller indications of mass are obtained by the balance with increasing ﬂow velocity. The resulting minor error can be corrected by calibration, so that weighing results independent of ﬂow Tab. 1.2 Selected properties of experimental materials.

dp, mm dpore, mm rp, kg m3 ep, %

zeolite 4A

c-Al2O3

SiC

2.0 and 5.0 0.0004 720 33.5

1.4 0.01 1040 70–75

1.0–1.8 0.12–5.1 1610–2330 25–49

1.2 Magnetic Suspension Balance

Fig. 1.3 Experimental desorption curves of water from 4 A zeolite at 25 C; Comparison of process kinetics for different velocities of the air.

velocity are obtained. Even without correction, the results are sufﬁcient for many practical applications. The results of similar experiments with a single particle of g-Al2O3 are depicted in Figs. 1.4 and 1.5. Here, the ordinate shows directly the mass, which decreases during desorption of water. The relative random error of measurement by the MSB is indicated. This error increases with increasing gas ﬂow velocity, but is still reasonably small at u ¼ 0.2 m s1. On the other hand, such a velocity is sufﬁcient for the process to take place in the particle-side controlled regime. Experiments with bigger particles

Fig. 1.4 Desorption of water from g-Al2O3 in the MSB at u ¼ 0.1 m s1; (T ¼ 25 C, w0 ¼ 20%, win ¼ 5%).

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Fig. 1.5 Desorption of water from g-Al2O3 in the MSB at u ¼ 0.2 m s1; (T ¼ 25 C, w0 ¼ 20%, win ¼ 5%).

revealed that the relative error increases with particle size for the same gas velocity. The reason is the larger vibrations of large particles. Though still occurring, such vibrations are better damped in the MSB than in other gravimetric devices, due to the indirect contact by the suspension magnet. The mentioned relative error also depends on the moisture load, which is changing during the desorption process, and differs for different particle sizes and materials. Figure 1.6 presents results for the materials of Tab. 1.2 under otherwise the same conditions. All materials were conditioned at T ¼ 25 C and w0 ¼ 0.30. At t ¼ 0 there was a sudden change of relative humidity of the ﬂowing air to win ¼ 0.05. The amount of water that can evaporate from zeolite is deﬁned as unity in Fig. 1.6 and is larger than for the two other materials. The relative error for SiC, with a total water loss of

Fig. 1.6 Desorption data for zeolite 4A, g-Al2O3 and SiC.

1.2 Magnetic Suspension Balance

about 10 times less than zeolite, will be proportionally larger. This ratio is not constant, but depends on the operating conditions. It should, however, be pointed out that SiC is usually considered to be completely non-hygroscopic. In fact, the weak hygroscopicity indicated by Fig. 1.6 could not be detected by conventional gravimetric methods, but can be detected in the MSB. Using the MSB it is also possible to gain equilibrium data. Examples of isotherms for the adsorption of water on molecular sieves are shown in Fig. 1.7. In such experiments, more than one particle may be placed into a basket, suspended from the balance. Even with many particles in the basket, the time to reach a constant mass is much shorter than required by conventional methods, due to the favorable ﬂow of conditioned air. The temperature range of Fig. 1.7 can be widened to 350 C. Such high temperatures and vacuum may be necessary to determine the mass of dry particles, that is, the reference in the deﬁnition of solids moisture content. To ﬁnd this mass, experiments as depicted in Fig. 1.8 were made. Initially, the temperature should be raised slowly to 100 C in an environment of N2. After 100 C the temperature can be increased more quickly. In the presented experiment this was done stepwise. The temperature trajectory should, ideally, be piecewise linear, but, in reality, some inertial effects and overshooting are present. The ﬁnal measurement was taken at 350 C and in vacuum, after the mass had reached a constant value. The change of condition at the end of the experiment from dry gas at ambient pressure and small ﬂow to vacuum is the reason for the small jump in the mass indication. This is due to the removal of the ﬂow and represents the small inaccuracy that has been previously discussed and can be corrected by calibration. Recent work (Suherman, 2007; Suherman et al., 2008) shows that the drying kinetics of single polymer granules with diameters from 2.5 to 2.9 mm can be measured with good reproducibility by using the MSB. The accuracy of the instrument under speciﬁc operating conditions can be evaluated by time series analysis and other statistical methods. Furthermore, it is shown in this work how the time series analysis can contribute to a reliable identiﬁcation of the end of the drying process.

Fig. 1.7 Isotherms for adsorption of water on zeolite 4 A.

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Fig. 1.8 Measurement for the determination of the mass of dry zeolite by use of the MSB.

This helps to accurately determine dry mass. Statistical methods can also support data smoothing. Instead of the previously mentioned cubic splines, Suherman (2007) used the moving average technique to this purpose. By smoothing the primary data the signiﬁcance of measurements can be extended towards smaller moisture contents at the end of the drying process. A coarse estimation of the applicability range of the MSB is given in Tab. 1.1. Concerning this table, it should be noticed that the maximum operating velocity of u ¼ 2 m s1 assigned to the drying tunnel could be attained only in combination with numerical smoothing of the primary data. In contrast, gas velocities of up to u ¼ 1 m s1 can be realized in the MSB without smoothing. Without smoothing, the MSB has an advantage with regard to the maximum possible gas velocity. Nevertheless, such information is only indicative, because the applicability range shrinks unavoidably with decreasing particle diameter, due to the decrease in weight. Additionally, it becomes more and more difﬁcult to ﬁx one particle without signiﬁcant contact with some solid support. Consequently, the applicability of all gravimetric methods – including the MSB – ends at a particle diameter of about 1 mm. For powdery materials with much smaller particle size alternative methods are needed. Such alternatives will be discussed in the following section.

1.3 Infrared Spectroscopy and Dew Point Measurement 1.3.1 Measurement for Particle Systems – General Remarks

As discussed in the previous section, the determination of the drying kinetics of materials with a particle size below 1 mm can hardly be conducted by single particle experiments; the accuracy and resolution of the methods available for this purpose

1.3 Infrared Spectroscopy and Dew Point Measurement

are not high enough. Consequently, it is necessary to measure the temporal change in moisture content of an entire particle system and then extract from this information single particle drying kinetics. The particle systems considered are packed beds and ﬂuidized beds. The use of a packed bed corresponds to the well known thin layer method (TLM, see, e.g. Hirschmann et al., 1998). In TLM a shallow packed bed is placed on a sieve with air ﬂow in the direction of gravity. The moisture content of the packed bed is measured by interrupting the experiment and weighing. Alternatively, outlet gas humidity can be measured and used to calculate the corresponding change in the moisture content of the solids. Even for very thin layers the results of this method cannot be set equal to single particle drying kinetics, but have to be scaled-down to the single particle by an appropriate model. Such modeling is not trivial, due to axial dispersion in the gas ﬂowing through the packed bed. Additionally, it is difﬁcult to prepare a particle layer of small but uniform thickness. Differences in thickness lead, however, to ﬂow maldistribution, because the gas prefers pathways of minimal bed thickness and, thus, minimal ﬂow resistance. Such ﬂow bypasses can hardly be modeled. Moreover, they depend on the skills of the person who has prepared and conducted the experiment. Gas bypass is also present in a ﬂuidized bed, due to bubbling. However, this bypass is a property of the particle system – rather independent from the operator. Furthermore, reliable models are available for scaling ﬂuidized bed drying results to the single particle. Because of these advantages, the route from ﬂuidized bed measurements to single particle drying kinetics will be discussed in detail in this section. The ﬁrst step is the determination of the change in solids moisture content in the ﬂuidized bed with time. Conventionally, one takes samples out of the bed during the drying process and measures the moisture content by weighing. This is intermittent, changes the hold-up and provides just a few points along the drying curve of the ﬂuidized bed. Therefore, it is better to determine the decrease in solids moisture content in the ﬂuidized bed dryer indirectly, by measuring the gas moisture content at the outlet. For the simple case of a batch dryer one needs to quantify the moisture content of the gas at the inlet and at the outlet of the dryer and the mass ﬂow rate of the dry ﬂuidization gas. The evaporation ﬂow rate is then given by _ g ðY out Y in Þ _v¼M M

ð1:3Þ

Taking into account the initial moisture content of the solids X0, the temporal change of moisture can be determined from ð 1 _ g ðY out Y in Þdt X ðtÞ ¼ X 0 ð1:4Þ M M dry Obviously, the measurement of the gas moisture contents Yout and Yin determines the quality of the method. Before discussing this measurement, by infrared spectroscopy and dew point determination, a short outline of the experimental set-up will be given.

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1.3.2 Experimental Set-Up

A schematic diagram of the laboratory scale ﬂuidized bed dryer used in our work is presented in Fig. 1.9. The cylindrical ﬂuidization chamber has an inner diameter of 152 mm. A sintered metal plate with a pore size of 100 mm serves as the air distributor in order to ensure a uniform ﬂow of ﬂuidization gas. To control the gas inlet temperature the apparatus is equipped with an electrical heater. For granulation or agglomeration processes a two-component nozzle with an adjustable gas ﬂap (Type 970/0 S4, Schlick Co.) is installed. The liquid is delivered to the nozzle by a piston pump (Sewald Co.). Pressurized air is used as the ﬂuidization gas in order to attain as constant as possible ﬂow rates. In this way, the variation of mass ﬂow rate could be kept below 0.1 kg h1. Using a blower would lead to signiﬁcantly higher ﬂuctuations. The gas ﬂow rate is measured by means of a mass ﬂow meter (ELFLOW, Bronkhorst M€attig Co.). Additionally, several probes are installed to record temperatures at the gas inlet and outlet, and pressure drops of the distributor plate and the hold-up. As mentioned above, the accuracy of the described approach depends directly on the precision of the measurement of gas moisture content. This requires . .

high accuracy short measurement period.

Both requirements can be fulﬁlled by employing infrared (IR) spectroscopy. In our case, two IR spectrometers of type NGA 2000 MLT (EMERSON Process Management Co.) were installed at the inlet and at the outlet of the ﬂuidization chamber.

Fig. 1.9 Scheme of fluidized bed dryer.

1.3 Infrared Spectroscopy and Dew Point Measurement

1.3.3 Principle of Measurement with the Infrared Spectrometer

The basis of IR spectroscopy is absorption of infrared radiation caused by the gas being measured. While the wavelengths of the absorption bands are speciﬁc to the type of gas, the strength of absorption is a measure of concentration. By means of a rotating chopper wheel, the radiation intensities coming from the measuring and the reference sides of the cell of the instrument produce periodically changing signals within a detector. The detector signal amplitude thus alternates between concentration dependent and concentration independent values. The difference between the two is a reliable measure of the concentration of the absorbing gas component. Figure 1.10 depicts a scheme of the IR spectrometer. A heating coil in the light source (1) generates the necessary infrared radiation. This radiation passes through the light chopper wheel (2) and a ﬁlter cell (4) that screens interfering wavelengths out of the radiation spectrum. Due to the shape of the chopper wheel, irradiation of equal intensity alternates between the measuring side (6) and the reference side (7) of the analysis cell (5). Only the measuring side is swept by the gas to be analyzed. Subsequently, the radiation passes individual optical ﬁlters around a second ﬁlter cell (8) and reaches the pyro-electrical detector (10). This detector compares the measuring side radiation, which is reduced because of absorption by the gas, and the

Fig. 1.10 Scheme of IR spectrometer.

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reference side radiation. Cooling and heating of the pyro-electrical material of the sensor lead to an alternating voltage signal. The ﬁnal measuring signal of the IR spectrometer is equivalent to the volume concentration of the absorbing gas component. In our case, this component is water vapor. Volume concentration is equal to molar fraction ~y, which can be converted into the mass moisture content by the relationship Y¼

~ w ~y M ~ g 1~y M

ð1:5Þ

1.3.4 Dew Point Mirror for Calibration of IR Spectrometer

To achieve the highest precision for the determination of the moisture content in the gas phase the IR spectrometers need to be calibrated frequently since the pressure in the measuring chamber and, therefore, also the measured volume concentration of water, depend on the ambient pressure. For the calibration, a gas ﬂow with deﬁned moisture content must be supplied to the IR spectrometers. The accuracy of calibration of the spectrometers will depend directly on the accuracy of the measurement of moisture of the provided calibration gas. Dew point mirrors are amongst the most established and recognized devices for the precise determination of moisture content in gases, because of their simplicity and the fundamental principle employed. From the measured dew point temperature Tdp, the saturation pressure p of the water and hence the moisture content can be acquired: Y¼

~ w p ðT dp Þ M ~ g Pp ðT dp Þ M

ð1:6Þ

In a dew point instrument a gas sample is conducted into the sensor cell that contains a miniature temperature-controlled polished metal mirror (Fig. 1.11). This

Fig. 1.11 Operating principle of a dew point mirror.

1.3 Infrared Spectroscopy and Dew Point Measurement

mirror is made of a highly conductive material, typically copper, and plated with an inert material such as gold. It sits on a solid-state thermoelectric heat pump cooling by means of the Peltier effect. As the temperature of the mirror drops and reaches the dew (or frost) point temperature, water is pulled out of the vapor phase of the sample gas and water droplets (or ice crystals) nucleate on the mirrors surface to form eventually a uniform condensation layer. The exact temperature, measured by a platinum resistance thermometer (PRT) directly embedded underneath the mirrors surface, depends only upon the moisture content of the gas and the operating pressure. An optical system, consisting of a visible light emitting diode (LED) and photodetectors, is used to detect the point at which this occurs. The LED provides a light beam of a constant intensity, which is focused by a collimated lens to become the incident beam on the mirror surface, ﬂooding it with a pool of light. Some instruments only detect the reﬂected light using a single photodiode; more sophisticated instrumentation uses a second detector to monitor the scattered light. As dew droplets form on the mirror, the reﬂected light decreases whilst the amount of scattered light increases. The output from each photodiode is digitized with an analog to digital converter to derive numerical representations of the photodetectors. The resulting signals are, in turn, tied into an electronic loop that controls the current applied to the heat pump device. This, in essence, modulates the cooling power to maintain the mirror temperature at the dew (or frost) point of the gas sample. At an equilibrium point, where evaporation rate and condensation rate at the surface of the mirror are equal, the mirror temperature, read by the PRTembedded in the mirror, represents the saturation point for the water vapor in the sample gas, in other words the dew (or frost) point. Whilst the combined condensation of water-soluble gas constituents may be acceptable in small amounts, accumulation of such contaminants over an extended period of time can affect the accuracy of the measurement. Cooled mirror hygrometers usually have the facility to execute a contamination compensation routine to prevent this effect. When the system initiates the dynamic contamination control (DCC) routine, the heat command signal drives the thermoelectric heat pump in reverse, which in turn heats the mirror to a temperature above the dew point to drive off the excess condensate. When the mirror is free from condensation, the optical control loop is typically zeroed to eliminate the effect of contaminants, which may have built up on the mirror surface. Following this re-zeroing of the optical control loop, normal operation of the device is resumed. For mirror temperatures above 0 C, water vapor condenses on the mirror as liquid water (dew point). When measuring temperatures are below the freezing point of water, the condensate can either exist as ice (frost point) or as super-cooled liquid (dew). Whether the condensate is ice or water depends on several factors, such as the purity of the water, the surface morphology of the mirror and the period of time over which the measurement has been made. Alternatively, because of delayed nucleation the condensate may initially appear as a liquid (water) but change into a solid (ice) after a certain period of time.

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For water to freeze, the molecules must become properly aligned to each other, so that it is more difﬁcult to liberate a molecule from ice than from super-cooled liquid water. Therefore, different saturation temperatures are measured for super-cooled water and ice, the former being lower than the latter. This phenomenon affects all cooled mirror instruments and may result in inaccurate interpretation. If the condensate present over a mirror is ice, the mirror temperature at equilibrium will be higher than if the condensate were super-cooled liquid. The errors involved are typically about 10% of water vapor pressure. In order to distinguish between water and ice, some hygrometers are equipped with a microscope which allows the user to visually inspect the surface of the mirror during measurement and look for frost or dew formation. However, the addition of a microscope is usually an expensive option, and it can be difﬁcult to discern water from ice formation, particularly at low dew point temperatures. In the present work an Optidew Vision (Michell Instruments Co.) dew point mirror was used. The measuring range of this dew point hygrometer is from 30 to 50 C with an accuracy of 0.2 K. It is integrated in a device for calibration of IR spectrometers, as depicted in Fig. 1.12. The NGA 2000 IR spectrometer can be calibrated with a simple two-point calibration, since the signal from the pyro-electric sensor is assumed to be linear within the measuring range. Synthetic air from the ﬂask with a dew point of 30 C was used as the so-called zero-gas. The second calibration point was obtained by moistening the synthetic air in a fritted wash bottle to adjust to a dew point of approximately 21 C. The measuring conditions in the analysis cell of the IR spectrometer were controlled in such a way that a gauge pressure of 5 mbar and a ﬂow rate of the sample gas of 400 ml min1 were attained. The ﬂow rate was determined by means of a ﬁlm ﬂow meter (Type SF-2CE, Horiba Stec Co.). The actual values of gas moisture were quantiﬁed by means of the dew point mirror for both calibration points. According to the manufacturer, the accuracy of the IR spectrometer is 1% of the ﬁnal value of the upper limit of the measuring range. By default, the measuring range is set from 0 to 10% volume concentration of water vapor. To increase the accuracy, the upper limit of the measuring range was reduced to 2.8%, which corresponds to a moisture content of 17.92 g kg1. Consequently, the accuracy of measurement of volume concentration is increased to 0.028% so that the moisture content can be

Fig. 1.12 Scheme of the calibration device.

1.3 Infrared Spectroscopy and Dew Point Measurement Tab. 1.3 Measured moisture contents for justification of the linearization.

Dew point [ C]

Y (dew point) [g kg1]

Y (IR) [g kg1]

15.85 11.35 6.65

11.25 8.35 6.06

11.26 8.39 6.16

determined with an accuracy of approximately 0.18 g kg1. To prove the linearization of the IR spectrometer three additional dew points were adjusted directly after the calibration. The results, summarized in Tab. 1.3 and depicted in Fig. 1.13, demonstrate that the linear calibration is very satisfactory for the measurement of moisture content. The deviation of the values obtained from the IR spectrometer and the dew point mirror is less than the accuracy of 0.18 g kg1. 1.3.5 Testing the Calibration

As mentioned above, the closure of water balance is essential for the determination of solids moisture content. The closure does not only depend on the measurement of gas humidity but also on the precise determination of gas ﬂow rate and liquid ﬂow rate, whereby the latter is important only in the case of agglomeration and granulation processes. In principle, there are two simple methods to assess the overall accuracy of the instrumentation. The ﬁrst method is a differential approach, where a certain liquid ﬂow rate is injected onto the particles and the instantaneous evaporation rate is quantiﬁed. Under steady state conditions the evaporation rate must be equal to the spraying rate _v¼M _ g ðY out Y in Þ _l¼M M

ð1:7Þ

For the tests the mass ﬂow rate of the ﬂuidization gas and atomizing air of the nozzle was adjusted to 50.61 and 0.89 kg h1, respectively. To minimize the transition time to steady state, non-hygroscopic a-Al2O3 with a Sauter mean diameter d32 ¼ 0.31 mm was used as the bed material. Fig. 1.14a shows the temporal change of gas moisture

Fig. 1.13 Results for testing the linearization of the IR spectrometer.

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Fig. 1.14 Experimental results for testing the differential water balance at spraying rates of 0.082, 0.110 and 0.134 g s1; (a) temporal change of gas moisture content; (b) comparison of evaporation rate from the IR spectrometer with gravimetrically determined spraying rate.

obtained for the three different spraying rates which are summarized in Tab. 1.4. The occasional sharp decrease in outlet moisture content is caused by the switching of the pistons of the pump that feeds water to the nozzle. When this happens, the liquid ﬂow is interrupted for 1 to 2 s, which is readily detected by the spectrometer. Figure 1.14b presents the comparison of the actual spraying rate with the evaporation rate determined by applying Eq. 1.7. As one can see, the deviation is very low. Only for the highest spraying rate was a slight systematic difference observed. To quantify the error of the differential balance, the deviation of spraying rate from evaporation rate _ l M _ g ðY out Y in Þ _v¼M DM

ð1:8Þ

is presented in Fig. 1.15 for undisturbed steady state conditions. As one can see, the error of the differential balance is approximately 2 mg s1 for the ﬁrst two spraying rates, but increases slightly and becomes systematic for the highest spraying rate. The resulting deviations are summarized in Tab. 1.4. In total, it can be concluded that the differential balance is successfully closed, so that the instantaneous evaporation rate can be determined with an accuracy of approximately 3%. The second approach for proving the quality of closure of the moisture balance is an integral method. Here, a certain amount of liquid is sprayed onto pre-dried particles so that the particle moisture content increases. After a certain time the Tab. 1.4 Maximal deviation of differential balance.

_ l [mg s1] M

_ v [mg s1] DM

Error [%]

82.08 110.64 134.23

2 2 þ4

2.43 1.80 þ2.97

1.3 Infrared Spectroscopy and Dew Point Measurement

Fig. 1.15 Calculated deviation of differential moisture balance.

spraying is shut down and the moisture is removed again from the particles. Gas outlet humidity is detected during the entire process. By integral evaluation of these signals the total amount of evaporated water can easily be quantiﬁed: ð _ g ðY out Y in Þdt ð1:9Þ Mv ðtÞ ¼ M For these trials the same test material was utilized as in the previous experiments. The spraying rate was adjusted to 0.13 g s1. Results for two gas ﬂow rates of 50.66 and 30.15 kg h1 are presented in Fig. 1.16 and Fig. 1.17, respectively. Diagram (a) depicts in each case the temporal change of gas moisture content while diagram (b) illustrates the deviation of integral moisture balance obtained from DMv ¼ M l ðtÞMv ðtÞ

ð1:10Þ

The evolution of gas moisture content reﬂects clearly the pre-drying, the spraying and the drying periods. Since the gas mass ﬂow rate was reduced for the second trial,

Fig. 1.16 Experimental results for proving the integral water balance at a gas mass flow rate of 50.66 kg h1; (a) temporal change of gas moisture content; (b) deviation of cumulative mass of water.

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20

Fig. 1.17 Experimental results for proving the integral water balance at a gas mass flow rate of 30.15 kg h1; (a) temporal change of gas moisture content; (b) deviation of cumulative mass of water. Tab. 1.5 Final deviation of integral balance.

Exp.

M_ g [kg h1]

Ml [g]

Mv [mg s1]

Error [%]

1 2

50.66 30.15

82.026 81.627

82.156 81.219

0.16 þ0.50

the gas outlet humidity reaches signiﬁcantly higher values of about 16 g kg1. The initial increase in the deviation of moisture balances indicates the accumulation of water in the bed material. Actually, this value can be directly converted into a moisture content of particles if the dry solids mass is known. The second experiment shows a similar behavior of gas humidity, but a different evolution of DMv. The temporal change in this value indicates that the accumulation of water in the particles increases continuously, even at constant gas outlet moisture. At the end of the experiments – after the drying period – the value of DMv should return to zero. This would mean that we have found in the gas outlet all the water that we have sprayed into the bed and would, thus, correspond to perfect closure of the integral moisture balance. The measured ﬁnal values of DMv are summarized in Tab. 1.5. They show that the error of the integral moisture balance is less than 1% for both cases, which is a very nice validation for the accuracy of the experimental set-up and the instrumentation. 1.3.6 A Case Study: Determination of Single Particle Drying Kinetics of Powdery Material

After successful validation of the instrumentation and the experimental set-up, derivation of ﬂuidized bed drying curves from outlet gas humidity measured by IR spectroscopy will be illustrated. As already discussed, such ﬂuidized bed drying curves can be used – in a second step – to derive single particle drying kinetics of

1.3 Infrared Spectroscopy and Dew Point Measurement Tab. 1.6 Parameters of fluidized bed drying experiments.

Exp

Tg [a]

M0,wet [g]

X0 [kg kg1]

M_ g [kg h1]

Yin [g kg1]

1 2 3 4

50 50 40 60

200.23 200.52 200.25 200.45

0.1788 0.1786 0.1874 0.1854

21.37 20.56 21.31 20.79

0.66 0.66 0.65 0.65

powdery materials, which is not accessible directly because of their too small particle diameter. To this purpose, drying experiments were conducted with powdery polymer (particle diameter: d ¼ 168 mm, dry particle density: rp ¼ 1123 kg m3). All experiments were carried out under approximately the same process conditions with respect to the mass ﬂow rate of ﬂuidization gas, initial bed mass and gas inlet moisture content. Operating parameters are summarized in Tab. 1.6. Figure 1.18 shows a typical result for the temporal change of moisture content during the drying process. After feeding the wet batch into the apparatus the gas outlet moisture changes rapidly while the inlet moisture (both measured by IR spectroscopy) remains constant throughout the entire experiment. Initially, the outlet moisture exceeds somewhat the theoretical maximum of adiabatic saturation moisture. This phenomenon is caused by the thermal capacity of the apparatus, mainly the air distributor, and the bed material. After a relatively short period the outlet moisture starts to decrease towards the value of the inlet. From this data the temporal change of particle moisture content can directly be withdrawn, taking into account the initial moisture of particles X0. The value of X0 was determined by drying a sample of approximately 40 g in a vacuum oven at 80 C for 24 h. Additional measurement of the ﬁnal moisture content of the solids enables one to check the closure of water mass balance.

Fig. 1.18 Typical measurement results of drying in a batch fluidized bed (Exp. 1 from Tab. 1.6); (a) outlet gas humidity; (b) solids moisture content.

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22

A better way of presenting the results is to use, instead of the plot of Fig. 1.18b, the drying curve, where the drying rate _v¼ m

_ g ðY out Y in Þ M Abed

ð1:11Þ

that refers to the total surface area of the particles is plotted vs. the particle moisture content. Such a diagram is shown in Fig. 1.19a. Direct comparison between drying processes conducted under different process conditions is easier in terms of drying curves because time has been eliminated. To check the reproducibility of results, drying at 50 C was repeated twice. Direct comparison of the data in Fig. 1.19a shows a very good agreement between the two trials throughout the entire experiment. This is additional proof of the reliability of the method. As mentioned above, measurements in a ﬂuid bed dryer do not represent single particle behavior but can be used to scale down to the single particle level by applying an adequate model. In this study, the ﬂuidized bed drying model introduced by Groenewold and Tsotsas (1997) – see also Burgschweiger and Tsotsas (2002), Groenewold and Tsotsas (2007) – has been employed. The model distinguishes between bubble phase and suspension phase. All parameters such as bypass ratio, Sherwood number from particle to suspension phase, and number of transfer units from suspension to bubble phase are set. The only degree of freedom concerns single-particle drying kinetics in the form of a normalized drying curve. This curve is ﬁtted to ﬂuidized bed drying data in the course of scale down. In calculations of ﬂuidized bed drying at conditions other than those used for ﬁtting, single particle drying behavior is an input, so the model works in a fully predictive mode. The inhibition of the drying rate of particles at low moisture contents in terms of single particle drying kinetics can be considered in different ways. One possible approach is normalization in order to describe measured drying curves by reduction to just one normalized (or characteristic) drying curve for the considered product.

Fig. 1.19 (a) Reproducibility of drying curves measured in a batch fluidized bed; (b) normalized single particle drying curve and critical moisture content derived from Exp. 1 (Tab. 1.6) by application of a fluid bed drying model.

1.3 Infrared Spectroscopy and Dew Point Measurement

This method was introduced for normalization of drying curves measured in batch drying by van Meel (1958), and since then it has been applied in the original or in modiﬁed forms by many authors (van Brakel, 1980; Shibata, 2005; Groenewold, 2004). _ v, The normalized drying rate f is deﬁned as the quotient of the actual drying rate m _ v;I and the drying rate of the ﬁrst drying period m f ¼

_v m _ v;I m

ð1:12Þ

and the normalized solids moisture content, F, is represented by F¼

XX eq X cr X eq

ð1:13Þ

where Xeq is the equilibrium moisture content. Both f and F take values between 0 and 1. Remember that drying is assumed to be gas-side controlled in the ﬁrst and particleside controlled in the second drying period (at X < Xcr). By normalization the two _ v;I ) periods are separated from each other. Gas-side phenomena (i.e. the drying rate m are supposed to be predictable from ﬁrst principles. Particle-side phenomena are described empirically by the function f(F). Successful normalization leads to a function f(F) which is invariant with drying conditions (Tsotsas, 1994; Suherman et al., 2008). Applying this concept, the normalized drying curve of a single particle as well as the critical moisture content are derived by scaling down from measurement results by iterative adjustment in a computer program that implements the ﬂuidized bed drying model. For this derivation the data from experiment 1 (Tab. 1.6) has been used. The normalized drying curve is presented graphically in Fig. 1.19b, with a critical moisture content of Xcr ¼ 0.07 for this product. Figure 1.20 illustrates the opposite exercise, by comparing calculations conducted with the normalized drying curve that has been derived from one experiment with the

Fig. 1.20 Comparison between measured and calculated fluidized bed drying curves at different temperatures.

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24

results of three ﬂuidized bed experiments carried out at different gas inlet temperatures. The results show that at high moisture content the measured drying rate is higher than the calculated one. As mentioned above, this is a thermal effect mainly caused by the supply of heat to the ﬂuidized bed from the equipment, in particular from the distributor plate. Before every drying experiment, the entire apparatus is warmed to the inlet gas temperature. After the start of the experiment, heat transfer takes place between the equipment and the drying gas and/or the equipment and the particles, since both the average gas temperature and the particle temperature are clearly lower than the gas inlet temperature in the ﬁrst drying period. As a result of this additional energy, drying rates increase. Towards the end of the drying process, the drying rate reaches very small values, which are still determined from the difference between the outlet and inlet gas humidities. Since the respective measured quantities become almost identical and exhibit a certain noise, scatter of the drying rates is unavoidable at low moisture contents. Nevertheless, the derivation of drying rates appears to be accurate enough till solids moisture contents of about 0.002 in the present experiments. In spite of such restrictions, Fig. 1.20 shows quite good agreement between measurement and simulation in the signiﬁcant range of moisture content. This is true, in particular, for the inﬂuence of temperature. Consequently, the concept of normalization works well for the present example. This is not always the case (Suherman et al., 2008), so that it may be better to use, for example, some diffusion model instead of the normalization method for other products. Then, diffusion coefﬁcients will be the quantities to determine by ﬁtting of the ﬂuidized bed drying model to the experimental results. Apart from this, the described procedure remains essentially the same.

1.4 Coulometry and Nuclear Magnetic Resonance 1.4.1 Particle Moisture as a Distributed Property

In this section, we address the problem of measuring the relatively low moisture content of a large number of particles on an individual basis with the necessary precision. This problem arises when particulate material is dried and particle moisture at the outlet of the dryer is not uniform. In such a case, the characteristics of the distribution of particle moisture decide the quality of the drying process. In general, the outlet moisture content of any product must be below some speciﬁed value for quality reasons, but over-drying is undesirable because of energy costs, capacity restrictions or product damage. In the following, we choose the example of a continuous ﬂuidized bed dryer (as sketched in Fig. 1.21) to illustrate, ﬁrst, how the moisture content distribution may be approximated by a simpliﬁed population balance model and, then, how it can be measured. Subsequently, measured moisture distributions will be compared with the model.

1.4 Coulometry and Nuclear Magnetic Resonance

Fig. 1.21 Scheme of continuous fluidized bed dryer.

1.4.2 Modeling the Distribution of Solids Moisture at the Outlet of a Continuous Fluidized Bed Dryer

The objective of the present approach is to provide an analytical solution for distributed moisture content of particles at the dryer outlet. To this purpose, we take a certain functional form of the normalized drying curve, Eq. 1.14, and, in contrast to previous studies (Burgschweiger and Tsotsas, 2002; Kettner et al., 2006), do not include energy balances for the solid phase or any balances for the gas phase. Particles (of uniform diameter dp and density rp) are conveyed into the dryer at a constant particle ﬂow rate N_ 0 , all having the same initial moisture content X0. Discharge of particles is by an internal weir pipe, the height of which controls the total hold up of solids (Nbed particles). Furthermore, the dryer is assumed to be sufﬁciently small so that the spatial distribution of solids has no inﬂuence. In this case, particles with the same residence time t also have the same moisture content X(t) and the residence time distribution of the particles in the dryer (corresponding to that of a continuous stirred tank reactor) is the only reason for a distribution of moisture content. For the drying kinetics of a single particle, we assume the functional form of the normalized drying rate 8 > for F 1 < 1 _v m ð1:14Þ ¼ f ¼ pF _ v;I > m for F < 1 : 1 þ Fðp1Þ _ v is the particle drying rate and where p is an adjustable parameter, m _ v;I ¼ rg bðY as YÞ m

ð1:15Þ

is the rate of the ﬁrst drying period (rg: dry gas density, b: gas-side mass transfer coefﬁcient, Yas: adiabatic saturation moisture, Y: moisture content in the bulk of the

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26

Fig. 1.22 Influence of parameter p on normalized drying curve of single particle.

gas). The dimensionless moisture content F is deﬁned according to Eq. 1.13. Figure 1.22 illustrates how this function, which is the same as the function for ideal liquid–vapor equilibrium in distillation, can describe a wide range of drying curves by variation of parameter p. For such conditions, the following analytical expression can be derived for the cumulative number distribution of particle moisture at the outlet of the dryer: 8 X 0 X > > for X X cr exp N bed > < K t NðX Þ¼ X eq X crKpt t > X X eq p1 > > :N bed exp cr exp ðX X cr Þ for X < X cr t X cr X eq Kpt ð1:16Þ Equation 1.16 contains three characteristic dimensionless quantities, the rate constant K¼

6 rg b ðY as YÞ rp dp

ð1:17Þ

the mean residence time t ¼

N bed N_ 0

ð1:18Þ

and the critical time tcr ¼

X 0 X cr K

ð1:19Þ

Typical results are plotted as normalized distributions Q0 ¼ N/Nbed in Fig. 1.23 for the operating parameters given in Tab. 1.7 and different single particle drying curves (by variation of p). For particle moistures X > Xcr, the curves are identical, since the drying rate of the ﬁrst drying period is independent of p. In the second drying period, however, the distributions differ signiﬁcantly. A decrease in the value of p, which corresponds to a decrease in drying rate, shifts the distribution to

1.4 Coulometry and Nuclear Magnetic Resonance

Fig. 1.23 Normalized cumulative number distributions of particle moisture for different values of parameter p (remaining parameters according to Tab. 1.7).

higher moisture contents. Moreover, the width and shape of the distribution are also strongly affected. 1.4.3 Challenges in Validating the Model

In the experiments for testing the above model, g-Al2O3 beads with Sauter diameter dp ¼ 1.8 mm and particle density rp ¼ 1040 kg m3 are used. Since the initial moisture content of these particles is around 0.65, the water contained in a single particle is at most around 2 mg. After drying, most of this moisture will have been removed so that we need a method to detect amounts of water in the range of a few hundred mg with good precision. Gravimetric methods have here reached their limit: the relatively high dry particle mass of 3.2 mg and strong hygroscopic behavior of the Tab. 1.7 Parameter settings for the curves of Fig. 1.23.

Parameter

Symbol

Value

Unit

Mass of bed material (dry) Particle ﬂow rate (dry) Particle diameter Particle density (dry) Gas density (dry) Mass transfer coefﬁcient Saturation moisture Moisture in gas bulk Initial particle moisture Critical moisture Equilibrium moisture

Mbed _p M dp rp rg b Yas Y X0 Xcr Xeq

1 2 1 1000 1 0.05 21 1 1 0.8 0.001

kg g s1 mm kg m3 kg m3 m s1 g kg1 g kg1 kg kg1 kg kg1 kg kg1

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Fig. 1.24 Measurement principle of coulometer for detecting water in solid samples.

material (leading to signiﬁcant moisture uptake during weighing) prevent an accurate measurement of moisture content. When searching for an appropriate measurement method, we also have to bear in mind that a sufﬁcient number of particles (at least 100) have to be characterized for a reliable comparison of experimental and theoretical distribution functions. In the following, we present the methods of coulometry and nuclear magnetic resonance; we will see, by analysis of their advantages and disadvantages, that a combination of both techniques is suitable for fast and accurate moisture measurements. 1.4.4 Coulometry

The principle of coulometry is to determine the quantity of a species by measuring the electric charge Q (in Coulomb) required to completely decompose this species by a well-known electrolytic reaction. Since small electric currents can easily be controlled, measured and integrated over time, the method is suitable for detecting very small species quantities. For example, an electrolysis current of 1 mA reduces water into hydrogen and oxygen at a rate of merely 0.0933 mg s1. The ﬁrst electrolytic cell to continuously measure small amounts of water in gas ﬂows was proposed by Keidel (1959) who already anticipated a wide range of applications to liquids and solids if water is transferred into a gas stream by controlled evaporation at low rates. The water detection system which is discussed in the following, namely WDS 400 by Sartorius, is very similar to this ﬁrst device; its major components are sketched in Fig. 1.24. The wet solid sample is put into an oven (see also Fig. 1.25b) which may be heated to a temperature of 400 C according to a pre-set temperature protocol. The oven is continuously swept by a dry inert or noble gas at a constant ﬂow rate of 100 ml min1 taking up the evaporated water (and possibly other volatile substances). The gas mixture ﬂows through a ceramic membrane that serves as a carrier for phosphorus pentoxide P2O5. Due to the extreme hygroscopicity of this substance, all water vapor is absorbed and phosphorus pentoxide is converted (in several hydration steps) to orthophosphoric acid P2 O5 þ 3H2 O ! 2H3 PO4

ð1:20Þ

1.4 Coulometry and Nuclear Magnetic Resonance

Fig. 1.25 Desktop coulometer (a) with oven (b) into which a powder sample is loaded (by courtesy of Sartorius Co.).

Gas components other than water will pass through the membrane without reaction. Voltage is applied to the membrane by two electrodes (printed on its surface) to dissociate the phosphoric acids, the ﬁnal step of the respective anodic and cathodic reactions being 4PO 3 ! 2P2 O5 þ O2 þ 4e

4H þ þ 4e ! 2H2

ð1:21Þ

Figure 1.26 shows the electrodes on the membrane which have a strongly interlaced geometry to get a large active area and short paths for the electrolytic reaction. The electric current through the electrolytic cell is measured as a function of time; integration yields the total electric charge consumed by electrolysis, which may be directly converted into a mass of water. Since hydrolysis and electrolytic recovery of phosphorus pentoxide are simultaneous reactions, care must be taken that the cell does not get saturated with water. To this purpose, a maximum electrolytic current (for the given device 100 mA) must not be exceeded, that is

Fig. 1.26 Electrolytic cell with magnification of the two interlaced electrodes (light gray) that are printed on the membrane (dark gray) (by courtesy of Sartorius Co.).

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water vapor must not be produced in the oven at too high rates (at a maximum 9.3 mg s1). On the other hand, too low electrolytic currents – associated with too low evaporation rates – will be measured with a higher relative error so that water content is obtained at lower precision (integration over time has no effect on the error). In conclusion, best results are obtained for elevated but not too high evaporation rates (here several mg s1). It should be noted that the value of the electrolytic voltage is not critical as long as it is well above 2 V, which is the decomposition voltage of water (Keidel, 1959). The efﬁciency of the cell depends on impurities and is regularly assessed by calibration measurements with a well-deﬁned amount of water. Since free water would evaporate too rapidly and lead to an overload of the detector, a standard substance, sodium wolframate containing crystalline water (Na2WO42H2O), is used; typically, 20–25 mg of standard substance (with 1.07% water) are used. If the efﬁciency is too low, the electrolytic cell has to be refreshed by cleaning with water and coating with an acetone solution of 85% orthophosphoric acid (H3PO4). Before performing the next analysis measurement, the cell must be dried and the acid converted into phosphorus pentoxide by electrolysis. The dehydration will, however, not be complete (HPO3 is considered the prevailing component) since the cell becomes an insulator with increasing concentrations of P2O5 (Keidel, 1959). For quantitative analysis of water in solid samples, the following procedure is applied: 1. 2. 3. 4.

Open the oven door and insert the sample scoop Close the oven door (a short time interval later) Heat the oven according to a pre-set temperature protocol Measure and integrate the electrolysis current over a given time interval.

It is obvious that such a measurement will not only detect the water from the sample, but also residual moisture in the ﬂow of carrier gas and moisture that enters the system when opening the oven door; (recall that saturated air at 20 C contains 17.3 mg ml1 water vapor and the total oven volume is 26 ml). From this, it is obvious that tare measurements without a solid sample are of paramount importance if small solids moisture contents are to be quantiﬁed. Such a tare measurement has to be done directly before quantitative analysis to account for changes of relative humidity in ambient air; furthermore, exactly the same procedure has to be respected as in the subsequent analytic measurements, that is same open time of oven, same temperature protocol and measurement duration. We will now return to our task of characterizing particles from a ﬂuidized bed dryer with respect to their moisture content, which corresponds to measuring water amounts in the range 100–2500 mg. Recalling that the temperature protocol ideally has to be chosen so as to evaporate water from the sample at a rate of several mg s1, we will apply two different protocols. The ﬁrst, which is applied to particles with rather low moisture, accomplishes a temperature increase to 130 C in one step and in total takes 10 min (see Fig. 1.27a). The second is intended for larger amounts of water; in order to prevent too high release rates, an intermediate temperature of 60 C is ﬁrst assumed before heating to 130 C in a second step; overall measurement duration is

1.4 Coulometry and Nuclear Magnetic Resonance

Fig. 1.27 (a) Temperature protocol and (b) electrolysis current for a particle with low moisture content (Mw ¼ 161 mg, sample A).

14 min (see Fig. 1.28a). To obtain reproducible results, argon (99.998 vol.%) at a ﬂow rate of approximately 100 ml min1 is used as a dry carrier gas in all measurements. Tare measurements of electrolysis current for the two chosen temperature protocols are given in Fig. 1.29. One may assume a constant background level that originates from residual moisture in argon (a gas ﬂow of 100 ml min1 with 0.002 vol.% water vapor corresponds to a vapor ﬂow of 1.48 mg min1 or an electric current of 0.26 mA). The different durations of the two protocols result in different contributions from argon to the total detected moisture (14.8 and 20.7 mg for protocols 1 and 2, respectively). The signal above this background results from the moisture entering the oven during (sample) loading. Its shape depends slightly on the chosen temperature protocol but not its integral value (39.8 and 39.5 mg for protocols 1 and 2, respectively). In this light, we may understand the detection limit of the device that is given as 1 mg. In the following, ﬁve samples (A–E) with increasing moisture content are characterized. The complete measurement results are given for the driest and for the wettest sample in Figs. 1.27 and 1.28, respectively. In Figs. 1.27a and 1.28a the oven temperature is plotted along with the value set by the protocol. Figures 1.27b and 1.28b show the electrolysis current which is corrected by the tare measurement.

Fig. 1.28 (a) Temperature protocol and (b) electrolysis current for a particle with high moisture content (Mw ¼ 2171 mg, sample E).

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Fig. 1.29 Tare measurements for the two temperature protocols shown in Figs. 1.27 and 1.28; the converted electric charge is equivalent to 54.6 mg (protocol 1) and 60.2 mg (protocol 2) of water.

Figure 1.30 summarizes the corrected electrolysis currents and computed water amounts for all ﬁve samples. Having seen that the coulometric method can produce quantitative results of the desired high quality, we conclude our description by recalling its major advantages and disadvantages. The major advantages may be listed as: .

In the coulometric method, water is clearly distinguished by a chemical reaction, whereas in gravimetric methods, for example the magnetic suspension balance, weight loss during heating is recorded and the assumption must be made that water loss is the only reason for the weight change. In reality, however, elevated temperatures may also lead to weight loss by chemical reactions in the solid or evaporation of volatile substances.

.

The mass of water Mw is measured directly so that only the wet sample Ms,wet (original state) needs to be weighed to obtain the moisture content from X ¼ Mw/ (Ms,wet Mw). In gravimetric methods, the dry solid mass Ms,dry must also be

Fig. 1.30 Electrolysis current for five particles spanning a wide range of moisture content.

1.4 Coulometry and Nuclear Magnetic Resonance

measured to compute the moisture content as X ¼ (Ms,wet Ms,dry)/Ms,dry. This brings the problem of removing all water without any other changes to the sample. Furthermore, in the case of low moisture contents, the weight difference Ms,wet Ms,dry cannot be measured accurately due to limited balance precision, and this may reﬂect in a large error in X. .

The coulometric method may also be used for a rough quantitative distinction of surface water, capillary water and the more tightly bound water of crystallization if the temperature rise is performed in appropriate steps. The major disadvantages of the coulometric method are:

.

The sample as deﬁned by a porous structure containing a certain amount of water is destroyed so that the measurement cannot be repeated.

.

Sample water content and release behavior of the water must be known approximately so as to choose the optimal temperature protocol: on the one hand, the electrolytic cell must not get saturated; on the other hand, the release rate should not be too low so as to keep the measurement period short (see above). When looking at the stochastic behavior of particles in a continuous ﬂuidized bed dryer, such information is not available!

.

The measurement of one sample takes a relatively long time (about 20 min). If many samples need to be measured to describe stochastic behavior, this is a severe drawback.

.

The humidity of a relatively big gas volume (oven) needs to be corrected in a tare measurement.

1.4.5 Nuclear Magnetic Resonance

An alternative method to measure the amount of water contained in a wet sample uses the magnetic spin of its hydrogen nuclei 1H (protons, compare with Chapter 4). If protons are put in a magnetic ﬁeld, their magnetic moments will behave according to quantum mechanical rules and take one of two stationary states: parallel or antiparallel to the external magnetic ﬁeld B0. The parallel state is thermodynamically favorable so that a macroscopic magnetization M is observed, which is proportional to the number of protons; it increases with magnetic ﬁeld strength and decreases with temperature according to Boltzmanns law. In the unperturbed state, magnetization M stays aligned with the magnetic ﬁeld B0. However, if the two are not parallel, magnetization will rotate around the magnetic ﬁeld vector with nuclear magnetic resonance frequency v0, as shown in Fig. 1.31, and produce an electromagnetic signal that can be measured. The NMR frequency depends on the nucleus and on the magnetic ﬁeld B0; for protons, a magnetic ﬁeld of 7Tproduces a frequency of about 300 MHz. In order to get the magnetization vector M tilted with respect to B0, a small additional magnetic ﬁeld B1 is applied which rotates in the x–y-plane with NMR

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34

Fig. 1.31 Precession of magnetization M in an external magnetic field B0.

frequency v0. By adjusting the magnitude of B1 and the pulse duration, the ﬂipping angle can be tuned to 90 , which will produce the highest resonance signal. In practice, the same electromagnetic coil ﬁrst produces the rotating B1-ﬁeld and then (after a short dead time) measures the signal of the rotating M-vector. This NMR signal decays with the so-called transverse relaxation time T2 because the rotating protons get out of phase due to small variations of NMR frequency in time and space; in consequence, the component of M orthogonal to the z-axis becomes zero. On a longer time scale (characterized by longitudinal relaxation time T1), the magnetization will relax back to its equilibrium state, that is parallel to B0. This type of NMR measurement is referred to as free induction decay (FID) because the protons may relax after the initial pulse without further perturbation. The initial magnitude of the FID signal is proportional to the number of protons. However, the signal of adsorbed water decays faster than that of free water because of its strong interaction with the solid (Metzger et al., 2005). This is one reason why the overall signal does not decay exponentially. Experiments on the wet g-Al2O3 samples were performed in a Bruker Avance 300 MHz NMR spectrometer (see Fig. 1.32) with micro-imaging option. The sample was put in an NMR glass tube and set into the 5 mm resonance coil in a central position (see Fig. 1.33a). To insert the glass tube into the narrow opening, a conical Teﬂon guide was put on top of the resonance coil (see Fig. 1.33b). Free induction signals are plotted in arbitrary units in Fig. 1.34 for the ﬁve samples that have also been characterized by coulometry (see above). Additionally, the NMR signal for an empty tube (i.e. without sample) is shown as a dashed line. For good signal-to-noise ratio, 100 scans were added together with a time delay of 1 s to assure longitudinal relaxation. The magniﬁcation of the very ﬁrst data points (Fig. 1.34a) shows an initial contribution to the signal that is independent of the sample (dashed line) and decays in about 40 ms; it probably results from the resonance coil itself. The semi-logarithmic plot of the NMR signal (Fig. 1.34b) conﬁrms shorter decay times for relatively dry samples where adsorbed water is dominant; it also reveals that decay is not strictly exponential. On the basis of these ﬁndings it has been decided that the ﬁrst data points have to be discarded and that the initial signal amplitude is not estimated by an exponential

1.4 Coulometry and Nuclear Magnetic Resonance

Fig. 1.32 Bruker Avance 300 MHz NMR spectrometer (courtesy of Bruker Biospin Co.).

ﬁt but instead approximated by the ﬁrst reasonable value (measured after 34.5 ms). The reproducibility of these values was found to be around 1%. Summarizing the advantages of the described NMR method we may state that, in contrast to the method of coulometry: .

No approximate knowledge is needed about the moisture content of the sample because the same measurement protocol is applied to wet and dry samples.

.

The wet sample is not destroyed so the measurement may be repeated.

.

Experimental time can be made short, depending on the desired accuracy (100 s for the chosen protocol).

.

The measured particle moisture is affected by the gas in the test tube (about 2 cm3) only because of sampling – establishing new sorption equilibrium – and not because of the measurement method itself (cf. opening of oven door in coulometry). The resulting error may be reduced by ﬁlling the empty part of the tube with inert material.

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36

Fig. 1.33 (a) NMR resonance coil and sample (arrow) in glass tube with Teflon cylinder and glass spheres to achieve a central position; (b) Teflon cone to guide tube into coil.

Fig. 1.34 Free induction decay for five samples and empty tube (a) first ten data points and (b) decay behavior over a longer period of time (semi-logarithmic plot).

1.4 Coulometry and Nuclear Magnetic Resonance

The major disadvantages of the proposed NMR method are: .

.

The need for calibration. Ideally, the signal is proportional to the mass of water Mw so that only one point would be required. Unfortunately, we will see that strict proportionality is not observed and that a calibration curve is needed instead. The high cost of the system, also in terms of operation and maintenance (especially the need for liquid helium and nitrogen to cool the superconducting magnet).

However, NMR devices can be found in all major research institutions because of their wide range of scientiﬁc applications. And the problem of calibration may be solved by combining the method with precise coulometric experiments. 1.4.6 Combination of Both Methods

In Figure 1.35, the NMR signals of the ﬁve selected samples are plotted versus the mass of water which has been measured (afterwards) by the method of coulometry. The non-zero signal of the empty tube is also shown. From the data points it becomes clear that one-point calibration (assuming proportionality) is not reasonable; furthermore, the comparison between linear and quadratic ﬁt reveals that the correlation is not strictly linear so that a quadratic calibration curve is chosen. Several additional data sets (not shown here) could conﬁrm the accuracy of the calibration curve. With this newly developed method, we will now measure distributions of particle moisture. 1.4.7 Experimental Moisture Distributions and Assessment of Model

The experiments for testing the model from Section 1.4.2 are carried out in a continuous laboratory scale dryer as depicted in Fig. 1.21, with a diameter of 150 mm

Fig. 1.35 Calibration of NMR signal by coulometry.

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Tab. 1.8 Experimental and simulation parameters for particle flow rate variation.

Symbol

Exp. 1

Exp. 2

Exp. 3

Unit

Mbed _p M

0.982 1.7 17.39 0.09 1.12 · 103

0.820 1.3 13.78 0.08 1.96 · 103

0.976 1 11.67 0.06 2.37 · 103

kg g s1 g kg1 kg kg1 s1

Y Xeq K

and a batch size of approximately 3 l. The instrumentation provides various measurements of temperature, pressure, pressure difference, gas ﬂow rate, and inlet and outlet gas moisture. Three experiments were run with different particle ﬂow rates, but the same inlet solids moisture content (X0 ¼ 0.65 kg kg1), gas ﬂow rate (125 kg h1) and gas inlet temperature (80 C). The latter corresponds to an adiabatic saturation moisture content of Yas ¼ 22.3 g kg1. Additional process parameters are summarized in Tab. 1.8. In the model equations, the particle ﬂow rate N_ 0 and mean residence time t are affected. Furthermore, an increase in particle ﬂow rate increases the moisture load of the dryer, resulting in an increase in moisture content in the gas phase. Both effects cause a change in particle moisture content distribution and need to be considered. The presented analytical model contains the model parameter p to adjust the shape of the normalized drying curve to the respective material. As discussed in the previous sections, the drying curve needs to be derived from experimental data. In this study, such measurements were carried out in the magnetic suspension balance. Single particle drying was performed at a gas inlet temperature of 40 C, a gas inlet moisture content of 0.633 g kg1 and a pressure of 1022 mbar. For these conditions, the adiabatic saturation moisture content is 10.62 g kg1. The gas ﬂow rate was set to 100 ml min1, corresponding to a gas velocity of 3.6 mm s1. The drying curves for two different runs under the same process conditions are presented in Fig. 1.36.

Fig. 1.36 Drying curves of g-Al2O3 particles (dp ¼ 1.8 mm) measured in MSB at Tin ¼ 40 C, Yin ¼ 0.633 g kg1, Re ¼ 0.38.

1.4 Coulometry and Nuclear Magnetic Resonance

One can see that the drying rate is approximately constant at 0.379 g s1 kg1 till a moisture content of about X ¼ 0.3. Assuming that this is the ﬁrst period drying rate, we can also calculate it from Eq. 1.15. The mass transfer coefﬁcient b can be determined from the Sherwood correlation of Eq. 1.59. For the given conditions the values, Sh ¼ 2.33 and b ¼ 0.038 m s1 are obtained with a Reynolds number of _ v;I ¼ 0:433 g s1 m2 is estimated from Eq. 1.15, Re ¼ 0.38. In turn, a drying rate of m which is somewhat higher than the measured value. This slight difference can have several reasons. First, the Sherwood number can be smaller than calculated due to non-ideal ﬂow conditions. Figure 1.37 shows that – instead of using the previously discussed basket or needle – the single particle was placed in a wire hoop. This may inhibit gas ﬂow and diffusion around the particle. For a Sherwood number of Sh ¼ 2 one would obtain an evaporation rate of _ v;I ¼ 0:372 g s1 m2 , which matches perfectly the experimental data. Another m explanation is the reduction of vapor pressure due to hygroscopicity of the material. This effect can be accounted for by modifying the normalization method and deﬁning the (then not constant) ﬁrst period drying rate as _ v;I ¼ rg b ðY eq ðX ; T p ÞY in Þ m

ð1:22Þ

Here, Yeq denotes the equilibrium moisture content resulting from the sorption isotherm X(w). The modiﬁed normalization concept has been extensively discussed by Burgschweiger et al. (1999) and applied successfully by subsequent authors (e.g. Burgschweiger and Tsotsas, 2002), but it is too complex for use with the present analytical model. Therefore, conventional normalization after van Meel (1958) is used here. In

Fig. 1.37 Suspended g-Al2O3 particle (dp ¼ 1.8 mm) for determination of single particle drying curve in the MSB.

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Fig. 1.38 Normalized drying curve for g-Al2O3 particles (dp ¼ 1.8 mm, Xcr ¼ 0.3) and fitting by means of Eq. 1.14 with p ¼ 4.

this frame, a critical moisture content of Xcr ¼ 0.3 is read from the single particle data of Figure 1.36 and the evaporation rate of the ﬁrst drying period is determined from Eq. 1.15 with Sh ¼ 2. The equilibrium moisture content Xeq is derived from the sorption isotherm provided by Groenewold et al. (2000). In this way, the normalized data of Fig. 1.38 are obtained for the test material. To calculate moisture distributions for the dried solids from Eq. 1.16, one needs to ﬁt the drying curve according to Eq. 1.14 by adjusting the parameter p. The result of this ﬁtting is also depicted in Fig. 1.38. For dimensionless moisture contents F > 0.5 the ﬁtting does not represent the experimental data very well, due to the symmetric shape of the curve according to Eq. 1.14. This drawback is a natural price to be paid for applying an analytical solution that does not allow for an arbitrary functional approximation of the normalized drying curve. Anyway, it is sufﬁcient to justify the method, including its experimental background, as the ﬁnal results will show. Another crucial model parameter is K. According to Eq. 1.18, K depends on the diameter and density of the particle, the gas density and the adiabatic saturation moisture, which can all be either measured or calculated. Furthermore, it depends on the gas-side mass transfer coefﬁcient in the ﬂuidized bed. For this coefﬁcient several models have been suggested in the literature. In the present study we applied a Sherwood correlation recommended by Burgschweiger and Tsotsas (2002), where axial dispersion in the gas is considered in the kinetic coefﬁcient. Finally, K depends on the moisture content in the gas bulk, Y. To predict this moisture content, a model for the gas phase is required (ideal back-mixing, simple plug ﬂow or some more complicated model). However, and in order to keep the present approach analytical, the parameter K was determined simply by ﬁtting to the experimental results. In Tab. 1.8 the obtained values for Y and K are provided.

1.5 Acoustic Levitation

Fig. 1.39 Comparison of the experimental and calculated distributions of solids moisture at the outlet of a continuous fluidized bed dryer for different particle flow rates (parameters according to Tab. 1.8).

Distributions measured at different particle ﬂow rates and distributions calculated by Eq. 1.16 are plotted in Fig. 1.39. An increase in particle ﬂow rate leads to a decrease in residence time and, consequently, to higher solids moisture contents. For higher particle ﬂow rates (higher moisture loads) the gas moisture content Y increases (see also Tab. 1.8). Thus the relative humidity will increase, and the equilibrium state of the solids moves towards higher moisture contents. With the given set of parameters the experimental moisture distributions can be reproduced in a qualitatively satisfactory manner by the model. Deviations can be attributed to imperfect ﬁtting of the normalized drying curve by Eq. 1.14. An extended model, incorporating the mass and energy balances for the solid and gas phase, would provide better agreement between experiments and simulation. However, the respective solutions are more complicated and, thus, less instructive than the here presented simpliﬁcations.

1.5 Acoustic Levitation 1.5.1 Introductory Remarks

The free suspension of a small droplet or particle near a pressure node of a standing acoustic wave is called acoustic or ultrasonic levitation. The gravitational force acting on the sample is compensated by the sound pressure of the ultrasonic ﬁeld acting in a net upwards direction. The ﬁrst systematic description of acoustic levitation was published by King (1934). In the 1970s the American space agency became interested in this phenomenon as a tool for containerless processing under microgravity conditions. Currently acoustic levitation is applied to examine the

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drying behavior of suspended droplets and particles in the ﬁelds of chemistry, engineering and pharmacy. One central question when considering acoustic levitation is whether the sound pressure per se inﬂuences the drying behavior of a droplet or particle suspended in a standing wave? Although some work indicated that this inﬂuence may be negligible (Seaver et al., 1989; Tian and Apfel, 1996), more recent studies have demonstrated and provided a theoretical background for the perturbation of droplet drying rate by an acoustic ﬁeld (Yarin et al., 1999). The most recent advances in this technique include the application of IR-thermography to measure the droplet surface temperature proﬁle during drying (Tuckermann, 2002) and moisture detection in the exhaust gas stream using a dew point hygrometer (Groenewold et al., 2002), compare with Section 1.2.1. One new application is the determination of the drying kinetics of aqueous solutions of proteins and carbohydrates (Schiffter and Lee, 2007a, b). 1.5.2 Some Useful Definitions

An acoustic ﬁeld is characterized by its gas particle velocity and sound pressure. The gas particle velocity, B, is the velocity of a particle on a longitudinal pressure wave, given as the product of gas particle displacement, z, and angular frequency, v: B ¼ z v ¼ z 2pf

ð1:23Þ

The sound velocity level (SVL or Lv) gives the ratio of a gas particle velocity, B, to a standardized reference particle velocity, Bref: Lv ¼ 20 log

B Bref

ð1:24Þ

Bref is taken to be the lowest SVL detectable to the human ear, that is 5 108 m s1. The unit of SVL is the decibel (dB) which is therefore dimensionless. The sound pressure, Psound, is that of the root-mean-square pressure deviation caused by a sound wave passing through a ﬁxed point. It is the product of the medium density, r0, the speed of the sound wave, u0, and the gas particle velocity: Psound ¼ r0 u0 B

ð1:25Þ

Figure 1.40 illustrates how the sound pressure wave is p/2 out of phase to the gas particle displacement wave. The logarithmic ratio of Psound to a standardized reference sound pressure (Pref ¼ 2 105 N m2) is called the sound pressure level (SPL or Lp): Lp ¼ 20 log

Psound P ref

ð1:26Þ

1.5 Acoustic Levitation

Fig. 1.40 Shape of a horizontal sound pressure wave, Psound, and its associated gas particle displacement wave, z. Note that the Psound is p/2 out of phase with z.

1.5.3 Forces in a Standing Acoustic Wave

A standing acoustic wave is formed within a closed tube whose length, Lr, is an integral multiple of the half-wavelength, l/2, of the incident sound pressure wave: l Lr ¼ n ; 2

n ¼ 1; 2; 3; . . .

ð1:27Þ

The relation between the sound pressure waves frequency, f, and the tube length is given by: f ¼

u0 u0 ¼n ; l 2 Lr

n ¼ 1; 2; 3; . . .

ð1:28Þ

Interference of the incident and reﬂected sound pressure waves produces a series of nodes and anti-nodes in ﬁxed positions. The gas particle displacement, z, is zero at each node, and maximal at each anti-node, with the nodes and anti-nodes separated by a distance p/2. In an acoustic levitator (Fig. 1.41) a standing sound pressure wave is formed between an ultrasonic transducer at x ¼ 0 (e.g. a piezocrystal) which produces the incident wave, and a reﬂector placed at a distance Lr ¼ n l/2 (n ¼ 1, 2, 3, . . .). A particle or droplet can be suspended or levitated in the vicinity of one of the sound pressure nodes, where the sound pressure acting upwards on the surface of the particle or droplet is positive and balances the gravitational force acting downwards. King (1934) derived an expression for the sound pressure, Pa, exerted by a standing sound pressure wave in a gas of density r0, at the surface of a rigid particle of radius a, and density r1: Pa ¼ prC1 sinð2khÞ f ðaÞ

ð1:29Þ

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Fig. 1.41 Representation of incident standing sound pressure wave formed between transducer and reflector in an acoustic levitator. At the pressure nodes the gas particle displacement is 0, whilst that at the empty nodes is a maximum.

where C0 (in ms1) represents the constant of the solution applicable to the onedimensional wave equation, k is the wavenumber ¼ v/u0, h is the displacement of the center of the spherical particle from a node at h ¼ n p/k, a ¼ k a, and f (a) is given by: f ðaÞ ¼

1 F 0 F 1 þ G0 G1 2 2 F 1 F 2 þ G1 G2 2 a 5 a 3ð1r0 =r1 Þ 2 2 2 2 a3 a H0 H1 H1 H2

þ

1 X n¼2

ð1Þn

n þ 1 ðF n þ 1 F n þ Gn þ 1 Gn Þ 2 a nðn þ 2Þ a2n þ 3 H2n H 2n þ 1

ð1:30Þ

The coefﬁcients Fn, Gn, and Hn are functions of a and can be expressed as polynomials of 1/a2 (given by King, 1934) together with: H2n ðaÞ ¼ F 2n ðaÞ þ G2n ðaÞ

ð1:31Þ

Equation 1.29 shows that the sound pressure acting on the particle in the standing wave is periodic and varies with the relative position of the center of the sphere to the nodes and anti-nodes. This behavior differs therefore from the sound pressure acting on a particle in a translating sound pressure wave, which is always positive.

1.5 Acoustic Levitation

Additionally, the sound pressure in the standing wave is much stronger than that in a translating wave. The standing sound pressure wave can therefore levitate a given droplet or particle, with its position relative to the nodes and anti-nodes depending on the waves amplitude and also on the particles radius and the relative density, r0/r1. The acoustic levitation of a deformable droplet – relevant for droplet drying studies – was analyzed by Yarin et al. (1998). A one-dimensional sound pressure wave is approximated by assuming an inﬁnite levitator with sound pressure: Psound ¼ A0e e

ivt

v cos x u0

ð1:32Þ

where A0e is the effective amplitude. Figure 1.42a shows this standing sound pressure wave with its nodes and anti-nodes. In this representation it is x ¼ z þ L to take account of the vertical displacement, L, of the center of the spherical droplet at z ¼ 0 from the adjacent anti-node at x ¼ 0. The positions of the nodes and anti-nodes are therefore: u0 p np þ n ¼ 0; 1; 2; . . . nodesðz ¼ 0Þ : x ¼ z þ L ¼ v 2 ð1:33Þ u0 anti--nodes : x ¼ z þ L ¼ np n ¼ 0; 1; 2; . . . v

Fig. 1.42 Representation of incident standing acoustic wave taken from Yarin et al. (1998). (a) The positions of the nodes and antinodes in the sound pressure wave calculated from the numerical solution of Yarin et al. (1998). (b) The acoustic levitation force, FL, in dependence on both x and L, the distance between the center of the sphere and the adjacent anti-node. Note the region of positive acoustic levitation force.

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The effective amplitude, A0e, is selected to make Eq. 1.32 consistent with a levitator tube length of Lr, yielding: A0e ¼

A0 cosðvLr =u0 Þ

ð1:34Þ

A0 is the amplitude at the transducer surface, that is x ¼ 0. The approximated standing sound pressure wave described by Eqs. 1.32 and 1.34 gives node positions that are at most 5% removed from the exact solution for a levitator tube length of Lr (Yarin et al., 1998). This standing sound pressure wave is disturbed by the presence of a droplet levitated in the vicinity of one of the nodes, resulting in an additional scattered sound pressure wave: Pssound ¼ A0e eivt Ps ðrÞ

ð1:35Þ

where the dimensionless function Ps ðrÞ of the radius vector r is found from the Helmholtz equation: 2 v Ps ¼ 0 ð1:36Þ rPs þ u0 The total sound pressure existing at the spheres surface is now the sum of the sound pressures of the incident wave, Psound, plus the scattered wave, Pssound . Yarin et al. (1998) solved this problem by numerical evaluation of the associated boundary integral solutions to Eq. 1.36, and obtained the total sound pressure acting at the droplet surface, Pa. The resulting acoustic levitation force, FL, was then obtained by integrating Pa over the droplet from top to bottom. Their numerical result for FL in dependence on L could then be compared with the analytical result given for FL from Kings Eq. 1.29 in terms of L: A0e 2 sinð2a LÞ f ðaÞ ð1:37Þ F L ¼ pr0 a2 r 0 u0 where f(a) is as given in Eq. 1.30. The results in Tab. 1.9 illustrate the closeness of Yarins approximation to Kings analytical solution in Eq. 1.37. For a sound pressure wave of intermediate length (a ¼ 1) the acoustic levitation force is positive in the Tab. 1.9 A comparison of the one-dimensional acoustic levitation force, FL, existing along the standing sound pressure wave and acting on a sphere as calculated numerically by Yarin et al. (1998), and also from King (1934) analytical solution. FL is rendered dimensionless by dividing with r0 u20 a2 , and L by dividing with a;. A0e =r0 u20 ¼ 1:0, a ¼ 1.0, data taken from Yarin et al. (1998).

L

FL (Yarin et al.)

FL (King)

0 0.1 p/4 ¼ 0.785 1.0 p/2 ¼ 1.55

0.0096 0.2737 1.4148 1.2849 0.0466

0 0.2840 1.4294 1.2998 0.0594

1.5 Acoustic Levitation

range of L between 0 and p/2 (Fig. 1.42a), as predicted by Eq. 1.37. Furthermore, the maximum FL exists at L ¼ p/4. The numerical result differs from the analytical result by 1% (Yarin et al., 1998). For measurements with an acoustic levitator we must know at what sound pressure level acting at the spheres surface, SPLeff, the device is working. SPLeff is directly related to the effective amplitude of the standing sound pressure wave, A0e in dyne cm2 (Yarin et al., 1998): SPLeff ¼ 20 logðA0e Þ þ 74

ð1:38Þ

The sound pressure level at the sound source, SPL, is related to SPLeff by using Eq. 1.34, to yield: SPL ¼ SPLeff þ 20 log½cosðv Lr =u0 Þ

ð1:39Þ

Yarin et al. (1998) give two techniques for determining SPLeff in a levitator. First, the drop-out method that determines A0e by exploiting the balance of FL from Eq. 1.37 and gravity acting on the sphere, FG ¼ 4/3 pa3r1g, that exists when the sphere is levitated stably at some point between L ¼ 0 and p/2. A sphere is levitated within the standing acoustic wave at known driving voltage, U0, of the transducer. U0 is then reduced to the point U0m, where the sphere drops out of the wave because FL is now too small to compensate FG. At this drop-out point the effective amplitude, A0em, can be directly calculated from the properties of the levitated sphere: 1=2 4 a r1 r0 g u20 A0em ¼ ð1:40Þ f ðaÞ 3 Providing the amplitude of the transducer varies linearly with U0, then A0e can now be determined from: A0e ¼ A0em

U0 U 0m

ð1:41Þ

SPLeff is then directly available from Eq. 1.38 and is valid for the sphere size used in the experiment. The second technique calculates SPLeff from the aspect ratio (¼ horizontal radius (rh)/vertical radius (rv)) of a levitated droplet. As we shall see in Section 1.5.4.1, a droplet suspended in an acoustic ﬁeld will be deformed in shape by the asymmetric nature of the acoustic force acting on it. Yarin et al. (1998) used a numerical technique to solve the Bernoulli equation to give droplet shape as a function of Pa. By comparing measured aspect ratio with this solution the SPLeff can be calculated at any time during droplet drying. 1.5.4 Interactions of a Droplet with the Sound Pressure Field

A levitated droplet is inﬂuenced in its behavior by the standing sound pressure wave in four ways: 1. Deformation of the droplet, owing to anisotropic axial and radial levitation forces.

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2. Acoustic streaming ﬁeld near the surface of the levitated droplet which leads to acoustic convection and also solvent vapor accumulation, both of which phenomena greatly inﬂuence droplet drying rate. 3. Heating of the droplet, owing to oscillations of the ultrasonic transducer which change the temperature of the ambient drying air. 4. Increasing SPLeff during evaporation as the droplet size decreases. Any use of acoustic levitation to examine droplet or particle drying kinetics must recognize these effects. 1.5.4.1 Deformation of Droplet Shape A levitated droplet may deviate from a spherical shape because the sound pressure exerted by the standing wave is not uniform over the surface of the sphere. The extent of shape distortion depends on droplet size, the surface tension of the liquid, and the sound pressure (Trinh and Hsu, 1986; Marston et al., 1981). For example, a higher sound pressure/SPL produces greater distortion and therefore a higher aspect ratio at ﬁxed droplet size (Trinh and Hsu, 1986). The problem of predicting levitated droplet shape in dependence on sound pressure, Pa, was ﬁrst analyzed by Marston et al. (1981) for small deformations (Trinh and Hsu, 1986). Tian et al. (1993) extended this by including adjustment between the drop and its surrounding ﬁeld; the acoustic force that causes drop distortion is itself modiﬁed by the change in droplet shape. Yarin et al. (1998) adopted a numerical iteration technique to satisfy the equilibrium of FL and FG: bottom ð

2p

Pa

qr 4 rds ¼ pa3 r1 g qs 3

ð1:42Þ

top

where Pa is a function of droplet shape and L. Figure 1.43 reproduces a graphical comparison of experimental data of aspect ratio versus Psound taken from Trinh and Hsu (1986) with the predictions of Marston et al. (1981); Tian et al. (1993); Yarin et al. (1998). The deviation observed with Marstons prediction illustrates the importance of recognizing the coupling of droplet shape distortion with FL. Of particular interest is the distribution of Pa across the z-axis of the droplet surface shown in Fig. 1.44. At the top (z 0.5) and bottom (z 1.2) of the droplet it is Pa > 0 and the droplet surface is compressed. In the equatorial range (0.7 z 0.3) it is Pa < 0 and the droplet surface is stressed (Yarin et al., 1998). The result will be an oblate spheroid shape of the originally spherical droplet (Tian et al., 1993). 1.5.4.2 Primary and Secondary Acoustic Streaming The sound pressure ﬁeld around a droplet levitated in the standing wave results in streaming of the gas. The solution of the equations for an unsteady compressible boundary layer in the gas near the droplet surface gives the velocity of this acoustic streaming, huacoustici, as the time-average of multiple cycles of the standing acoustic

1.5 Acoustic Levitation

Fig. 1.43 Influence of sound pressure on the aspect ratio of droplets of silicone oil levitated in an acoustic levitator (a0 ¼ 450 mm, a ¼ 0.16). The filled squares show the original experimental data taken from Trinh and Hsu (1986). The three

curves represent the predictions given by Marston et al. (1981); Tian et al. (1993); Yarin, Paffenlehner and Tropea (1998). This figure has been redrawn from Yarin, Paffenlehner and Tropea (1998).

wave. The velocity ﬁeld is illustrated in Fig. 1.45 (Yarin et al., 1999) by the streamlines near the droplet surface. The distribution of huacoustici over the droplet surface is periodic, as seen in Fig. 1.46. In this representation x is the arc length of the droplet circumference measured from the bottom. The values of huacoustici given at x ¼ 0, x ¼ x2 and x ¼ x3 correspond to the points O1, O2 and O3 of the droplet surface shown

Fig. 1.44 The distribution of sound pressure, Pa, acting on the droplet surface along the z-axis calculated for a n-hexane droplet of a0 ¼ 1061 mm at a transducer voltage of 156 V. Note the periodicity of Pa across the axis of the droplet surface, with Pa > 0 at the top and bottom of the droplet. In the equatorial range Pa < 0. Figure reproduced from Yarin et al. (1998).

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Fig. 1.45 Sketch of the acoustic streaming field near a levitated droplet and the system of secondary toroidal vortices. The points O1, O2 and O3 refer to the calculated acoustic streaming velocities given in Fig. 1.46. This figure is taken from Yarin et al. (1999).

in Fig. 1.45. At the surface of the droplet a sound pressure boundary layer is thus formed by primary acoustic streaming. The radial thickness of this sound pressure boundary layer, d IAS, is given by Yarin et al. (1999) and Lee and Wong (1990): 1=2 2n0 dIAS ¼ ð1:43Þ v where n0 is the kinematic viscosity of the gas. For the example of a water droplet of diameter d ¼ 1.0 mm levitated in air (n0 ¼ 1.5 105 m2 s1) using a 56 kHz frequency transducer, dIAS ¼ 9.23 mm is obtained (Yarin et al., 1999). This is much smaller than the diffusional boundary layer around the levitated droplet calculated to be 92 mm; but as we shall see later, its inﬂuence on droplet evaporation rate can be substantial.

Fig. 1.46 (a) Sketches of a levitated droplet showing its coordinates, x: the arc length of the droplets circumference from the bottom point O1, y: the normal to x. (b) The distribution of uacoustic along the arc length, x, of the levitated droplet. The positions x ¼ 0, x ¼ x2 and x ¼ x3 represent the points O1, O2 and O3 in Fig. 1.45. Both graphs taken from Yarin et al. (1999).

1.5 Acoustic Levitation

Primary acoustic streaming results in an enhanced convection of solvent vapor away from the droplet surface. For a small spherical droplet where k 1, the solution for huacoustici reduces to (Yarin et al., 1999; Burdukov and Nakoryakov, 1965): huacoustic i ¼

45 B2 2x sin 32 v a a

ð1:44Þ

For a water droplet levitated at an SPLeff of 165.7 dB, Eq. 1.44 predicts a velocity of primary acoustic streaming of up to 0.93 m s1 along the arc length of the droplet circumference (cf. Fig. 1.46) (Yarin et al., 1999). This convective movement of the gas around the droplet must result in a Sherwood number, Sh > 2.0. Yarin et al. (1999) give the resulting distribution of the time-averaged Sh across the arc length x1 of the circumference of a small levitated droplet as: 1=2 45 B cos2 ðx 1 =aÞ ð1:45Þ hShi ¼ 2 4p ðvD10 Þ1=2 ½1 þ cos2 ðx1 =aÞ 1=2 The distribution of Sh is symmetrical about the vertical axis through point O3 in Fig. 1.45. The average Sh over the surface of the sphere is: hShi ¼ K acoustic

B ðv D10 Þ1=2

ð1:46Þ

where D10 is the binary diffusivity of the solvent vapor in the gas, and Kacoustic is approximated by: 1=2 2 jhu v a=u0 acoustic i j r K acoustic ¼ pﬃﬃﬃ ð1:47Þ !1=2 A0e =ðr0 u20 Þ p ð x 2 huacoustic ir d x x2

The quantity r ¼ a sin(x/a) is the r-coordinate of the droplet (cf. Fig. 1.46) that is set dimensionless with the initial droplet radius a0. The term uacoustic is set dimensionless with the gas particle velocity, B, and jhu acoustic ij r is averaged over the droplet surface. As droplet shape and hence r will change continuously during evaporation, Kacoustic has to be re-calculated continuously during the drying process. The Sh deduced from Eq. 1.46 will therefore be a time-function during droplet evaporation. For a small spherical droplet a good approximation of Sh is, however, given by: 1=2 45 B ð1:48Þ hShi ¼ 4p ðv D10 Þ1=2 This illustrates how, because of primary acoustic streaming, Sh depends directly on gas particle velocity, B, and hence on SPL via Eq. 1.25. These equations do not consider liquid ﬂow with the levitated droplet, which increases uacoustic by up to 10%. The corresponding increase in Sh is, however, negligible for mass transfer considerations (Rensink, 2004). The effects of secondary acoustic streaming on droplet evaporation rate are the opposite of that of primary acoustic streaming. Figure 1.45 illustrates that secondary

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acoustic streaming consists of a system of toroidal vortices around the levitated sphere. This system is caused by interaction of the primary acoustic streaming pattern with the walls of the levitator tube, or by droplet displacement from the pressure node. Secondary acoustic streaming has been veriﬁed experimentally (Trinh and Robey, 1994) and the mathematical problem solved (Lee and Wong, 1990; Yarin et al., 1999). In the vortices the solvent vapor from the evaporating droplet can accumulate. Kastner determined experimentally the large scale of the vortices (Kastner, 2001). For the example of ethanol the accumulation of solvent vapor in the vortices proceeded to saturation within 0.6 s for a 2 ml droplet evaporating at 25 C. This accumulation of solvent vapor in the vortices is predicted to decrease diffusional mass transfer from the droplet surface to the surrounding gas phase. To overcome the hindering effect of secondary acoustic streaming on droplet evaporation rate a forced ventilation gas stream needs to be introduced along the levitator axis. The accumulated solvent vapor is now removed from the vortices by forced convection (Seaver et al., 1989; Trinh and Robey, 1994). Yarin et al., (1997) visualized a ventilation gas stream passing around a levitated 5 ml n-hexadecane droplet inside an acoustic levitator at a SPLeff of approximately 156 dB. The images reproduced in Fig. 1.47 show how a ventilation gas stream of oriﬁce Reynolds number Re0 ¼ 70 moving up the levitator axis is trapped by the vortices of secondary streaming. Increase in Re0 up to 190 is sufﬁcient to prevent formation of the vortices, and the ventilation gas stream passes around the levitated droplet. According to Rensink (2004), the minimal ﬂow velocity of a ventilation gas stream necessary to neutralize the secondary acoustic streaming pattern by blow-out (uvent) is given by: uvent

A0 r 0 u0

Fig. 1.47 Utilization of ventilation gas stream passing through an ultrasonic levitator operating at SPLeff of 156 dB. A 5 ml n-hexadecane droplet is levitated and subjected to increasing ventilation gas velocity equivalent to orifice Reynolds numbers of Re0 ¼ 70, 190 and 290. Pictures taken from Yarin et al. (1997).

ð1:49Þ

1.5 Acoustic Levitation

Recall that A0 is the amplitude of the sound pressure wave at the transducer source surface (Eq. 1.34). For a water droplet levitated at a SPL of 165.7 dB the predicted uvent is 4.3 m s1. A ventilation gas velocity lower than uvent can, however, be sufﬁcient to prevent accumulation of solvent vapor in the toroidal vortices. This was shown to be true experimentally by Rensink (2004) for different solvent droplets. 1.5.4.3 Effects of Changing Droplet Size As elucidated in Section 1.5.4.1, a droplet levitated in a standing sound pressure wave is deformed to an oblate spheroid because the sound pressure acting on the droplet is not uniform along the sphere surface. During evaporation both the shape and the position of the droplet will, however, change. The droplet shape converges to that of a sphere (Kastner, 2001). The total pressure difference across the droplet surface comprises three parts (Tian et al., 1993):

Pi P o ¼ DPs þ DPG þ DP st

ð1:50Þ

where Pi and Po are the pressures at the surface approached from the inside or outside, respectively; DPs is the contribution from the sound pressure wave, DPG is induced by gravity, and DPst is the difference in uniform static pressure inside and outside the droplet. In the absence of a sound pressure wave DPst ¼ 2s=a

ð1:51Þ

where s is the surface tension of the liquid. Now, as the droplet shrinks during evaporation the decreasing radius of curvature will make DPst dominant over DPrad (Trinh and Hsu, 1986). The aspect ratio will therefore approach unity as the contribution from DPrad in Eq. 1.50 becomes less. Figure 1.48 shows experimental

Fig. 1.48 Influence of shrinking droplet size on aspect ratio during evaporation; k ¼ v/u0, a: droplet radius). Data taken from Trinh and Hsu (1986).

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data for evaporating water droplets. The decrease in k a at ﬁxed SPL causes the aspect ratio to decrease and approach unity. Simultaneously the displacement of the droplet center from the nearest pressure node, Dz, decreases because the evaporating droplet rises in the standing sound pressure wave within the range 0 < L < 2p (Yarin et al., 1999). This is caused by a decreasing resonance shift of the levitator as droplet size decreases. When the droplet is introduced into the standing sound pressure wave it will immediately be deformed into an oblate spheroid (see Section 1.5.4.1). This change in droplet shape alters the scattered sound pressure wave, shifts hereby the resonance of the levitator, and decreases the sound pressure acting on the droplet surface, Pa (Trinh and Hsu, 1986). During evaporation the droplet size decreases and hence the resonance shift induced by the droplet will be progressively ameliorated. The result is a continual increase in SPLeff, which returns to its unperturbed value when the droplet has disappeared. Figure 1.49 shows how the SPLeff increases with decreasing droplet size during evaporation (Yarin et al., 1998). The SPL needed to levitate the drop is directly proportional to the liquids density, r1. An increase in SPLeff means, however, a higher gas particle velocity, B, and hence increased Sh in Eq. 1.46. This occurs during droplet evaporation in a sound pressure ﬁeld and is expected to inﬂuence evaporation rate. The decrease in droplet size during drying and the resulting increase in SPLeff will raise FL and cause a rise of the levitated droplet in the standing wave. Furthermore, as the mass of the levitated droplet decreases, the balance of gravitational and levitation forces, FG and FL, dictates that the droplet rises in the standing wave: 4 A0e 2 sinð2a LÞ f ðaÞ ð1:52Þ p a3 r1 g ¼ pr0 a2 r 0 u0 3

Fig. 1.49 Increase in SPLeff as droplet volume decreases during evaporation for four solvents. The SPLeff was calculated from the change in the aspect ratio of the droplets during drying. Fig. taken from Yarin et al. (1998).

1.5 Acoustic Levitation

Fig. 1.50 Position of droplet within sound pressure wave is dependence on its mass. Dz is the distance between the center of mass of the droplet and the adjacent pressure node. The upper line shows how Dz changes with decreasing volume at constant density. The lower line shows the behavior as density decreases at constant volume. These data were taken from Kastner (2001).

As droplet mass (4/3 pa3r1) decreases because of solvent evaporation, the sine function must decrease proportionately and the droplet rises within the sound pressure wave. Figure 1.50 taken from Kastner (2001) illustrates the inﬂuence of loss of mass on Dz of a droplet according to Eq. 1.52. A decrease in droplet volume at constant droplet density has a much weaker effect on Dz than does a decrease in density at constant volume. In terms of drying of a solution droplet, the change in Dz is caused by progressive resonance amelioration and by decreasing droplet size till a solid porous particle has emerged (critical point). The subsequent change in Dz of the particle after the critical point is caused by change in density during solvent loss, since particle size now remains constant. This can be exploited to determine particle drying kinetics after the critical point (Yarin et al., 1999; Kastner et al., 2001). 1.5.5 Single Droplet Drying in an Acoustic Levitator 1.5.5.1 Drying Rate of a Spherical Solvent Droplet Mass transfer from an evaporating droplet suspended in a gas phase was also discussed in Chapter 5, Vol. 1 of this series, in the context of spray dryer simulation. In general, two approaches can be applied. The ﬁrst is to solve the conservation equations for a motionless sphere in an inﬁnite stagnant medium, and to employ an empirical correction factor to account for forced convection around the droplet (Frohn and Roth, 2000). The second is to use ﬁlm theory with analysis of the effects of forced convection on layer thicknesses for heat and mass transfer (Sirignano, 2000).

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The ﬁrst approach leads to the d2-law and is a steady-state, gas phase model at constant temperature. A single, spherical droplet of initial radius a0 and ﬁxed surface temperature, Tph, is suspended in a still gas phase of ﬁxed temperature T1. At the droplet surface the saturation vapor pressure of the liquid, p , exists, whilst in the gas phase there is a lower vapor pressure, p1. Solution of the one-dimensional diffusion _ v , yields (Frohn and Roth, 2000): equation for vapor ﬂow rate at the droplet surface, M ~ RTÞ ~ _ v ¼ 4p D10 aðtÞfp p1 g M=ð M

ð1:53Þ

~ is liquid molecular mass, where D10 is the diffusivity of the vapor in the gas phase, M ~ _ drop , is given and R is the universal gas constant. The rate of shrinkage of the sphere, M by: _ drop ¼ 4p r1 a2 ðtÞ da M dt

ð1:54Þ

Conservation of mass at the receding droplet surface speciﬁes that: _v¼M _ drop M

ð1:55Þ

to yield for the time-proﬁle of a(t), otherwise known as the d2-law: a2 ðtÞ ¼ a20 b t

b¼

~ p 2D10 M p 1 ~ T ph T 1 r1 R

ð1:56Þ

ð1:57Þ

Droplet lifetime, tl, is then given by: tl ¼

~ ph T 1 Þ r1 a0 RðT ~ ph p1 Þ 2D10 MðP

ð1:58Þ

The d2-law is valid in still gas, but can be corrected in an empirical fashion to account for forced convection of the gas phase. A good approximation is that of Ranz and Marshall (1952) determined for a suspended solvent drop: Nu ¼ 2 þ 0:6 Re1=2 Pr 1=3 Sh ¼ 2 þ 0:6 Re1=2 Pr 1=3

ð1:59Þ

To describe the evaporation rate under forced convection conditions around a pure solvent droplet Eq. 1.57 is therefore changed to (Tuckermann et al., 2002): ~ p 2D10 M p1 Sh ð1:60Þ b¼ ~ T ph T 1 2 r1 R The above equations do not account for any inﬂuences of the sound pressure ﬁeld on gas movement around a levitated droplet, that is, acoustic streaming.

1.5 Acoustic Levitation

The alternative approach to droplet drying kinetics according to Sirignano (2000) is based on ﬁlm theory to determine the radii, r, of the heat (index: t) and mass transfer (index: m) ﬁlms around an evaporating sphere in a moving gas phase (forced convection): r film;t ¼ a r film;m

Nu Nu 2

Sh ¼ a Sh 2

ð1:61Þ

Nu and Sh are the modiﬁed Nusselt and Sherwood numbers that account for the ﬁlm thinning effects of Stefan ﬂow: Nu ¼ 2 þ

Nu2 Ft

Sh2 Sh ¼ 2 þ Fm

ð1:62Þ

The correction factors Ft and Fm are functions of the ﬁlm thicknesses for heat and mass transfer, d t and d m: dt dt;0 dm Fm ¼ dm;0 Ft ¼

ð1:63Þ

d t,0 and dm,0 are the initial ﬁlm thicknesses at t ¼ 0. The result of Abramzon and Sirignano (1989) for the time-proﬁle of a(t) is analogous to Eq. 1.60: a2 ðtÞ ¼ a20 ðtÞbfilm t bfilm ¼

2 r0 D10 Sh lnð1BM Þ r1 2

ð1:64Þ

ð1:65Þ

Here BM ¼

yph y1 1yph

ð1:66Þ

is the Spalding transfer number that represents the driving force for vapor diffusion through a stagnant ﬁlm (Frohn and Roth, 2000). y is the mass fraction of solvent vapor in the gas. For a spherical droplet in an environment with no forced convection it is Sh ¼ 2.0, and Eq. 1.66 simpliﬁes to: bfilm ¼

2 r0 D10 lnð1BM Þ r1

ð1:67Þ

which is directly analogous to the d2-law. Again, these equations take no account of the inﬂuence of sound pressure ﬁeld on evaporation rate.

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1.5.5.2 Drying Rate of an Acoustically Levitated Solvent Droplet The problem of determining the effect of a sound pressure wave on the evaporation rate of a levitated droplet was tackled by Yarin et al. (1999). For a small sphere the average Sh over the sphere surface is a function of gas particle velocity, B, as given by Eq. 1.48. Since Sh is deﬁned as

hShi ¼

k 2a D10

ð1:68Þ

where k is the time-averaged mass transfer coefﬁcient at the droplet surface, it follows that k¼

1 45 1=2 B D10 2 4p ðvD10 Þ1=2 a

ð1:69Þ

_ v , is therefore: The vapor ﬂow rate at the droplet surface, M _ v ¼ 4pka2 ðc ph c 1 Þ M

ð1:70Þ

1=2 1=2 45 D10 B ðc ph c 1 Þ ¼ 2pa v 4p where c is the mass concentration of solvent vapor in the gas. Conservation of mass _ drop in Eq. 1.54, gives: on equating Eq. 1.70 with the rate of shrinkage of the sphere, M a2 ðtÞ ¼ a20 bacoustic t bacoustic ¼

45 4p

1=2 1=2 c ph c 1 D10 B v r1

~ p1 Þ=ðRTÞ ~ for an ideal gas: Since ðc ph c 1 Þ ¼ Mðp 1=2 ~ D10 1=2 p 45 BM p bacoustic ¼ 1 ~ v 4p T ph T 1 r1 R

ð1:71Þ

ð1:72Þ

ð1:73Þ

Equations 1.71 and 1.73 are analogous to the d2-law Eqs. 1.56 and 1.57 with the inﬂuence of primary acoustic streaming, uacoustic, being accounted for. The droplet lifetime, tl, is given in this case by: tl ¼

~ ph T 1 Þ r1 a20 RðT ~ p1 Þ f45D10 =ð4pvÞg1=2 BMðp

ð1:74Þ

which is shorter than that predicted by the d2-law by the factor given by Eq. 1.48 for Sh. 1.5.5.3 Drying Rate of Droplets of Solutions or Suspensions The ﬁrst drying period of a droplet of a solution or suspension resembles that of a pure solvent droplet. It can therefore be described by the same equations, but taking into account the lowering of the vapor pressure by the dissolved substance. The

1.5 Acoustic Levitation

temporal decrease in droplet volume, DV, gives directly the evaporation rate during this constant-rate drying period (Kastner, 2001): _ cr ¼ r1 DV M Dt

ð1:75Þ

Ignoring the effect of the dissolved substance, a2 ðtÞ=a20 decreases linearly with time according to either Eq. 1.56 (d2-law), Eq. 1.64 by Abramzon and Sirignano or Eq. 1.71. After the critical point has been reached, the volume of the particle now existing should remain constant (Sherwood, 1929). Continued evaporation of solvent from the particle decreases both its mass and its density. As discussed in Section 1.5.4, this will cause the particle to rise (Dz decreases) within the ultrasonic ﬁeld to maintain the balance between FL and FG given by Eq. 1.52 at constant SPLeff. This particle movement can be used to determine the quantity of solvent evaporated in the second drying period, provided the SPLeff and hence A0e does not change after the critical point, and is known. The evaporation rate in this falling-rate drying period is then given directly from Eq. 1.37 (Yarin et al., 1999; Kastner et al., 2001): 2 A0e 2 _ fr ¼ pr0 a f ðaÞfsinð2aL1 Þsinð2aL2 Þg ð1:76Þ M Dt g r0 u0 determined from the droplet position at two times, L1 and L2, separated by Dt. Once _ fr is known, the mean particle density, rp, the mean moisture mass fraction of the M droplet, x1, and the mean particle porosity, e, can be calculated as time-functions (Kastner et al., 2001): M l ðtÞ þ M s Vp M l ðtÞ x 1 ðtÞ ¼ M l ðtÞ þ M s Ms eðtÞ ¼ 1 rs V p rp ðtÞ ¼

ð1:77Þ

Ultrasonic levitation is therefore one of the few techniques suitable for examining the drying process of a solution droplet during both drying periods. The _ fr ) and residual solvent mass fraction (x1) of a droplet/ _ cr or M evaporation rate (M particle can be determined at any desired point of time during evaporation. Furthermore, a droplet or particle can be removed from the levitation tube at any time for further analysis. 1.5.6 A Case Study: Single Droplet Drying of Water and an Aqueous Carbohydrate Solution

Recent studies of the drying behavior of levitated single droplets include pure solvents (Tuckermann et al., 2002), inorganic colloidal solids (Kastner et al., 2001), enzymes (Weis and Nardozzi, 2005), and surfactants (Frost et al., 1994). A study of

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water and an aqueous solution of a carbohydrate useful in drug delivery (Schiffter and Lee, 2007a, b) illustrates the strengths and also the limitations of such experiments with an acoustic levitator. We present some selected results. 1.5.6.1 A Typical Acoustic Levitator A standard levitation system based on a published design (Yarin et al., 1999) is shown in Fig. 1.51. A 58 kHz levitator is ﬁxed within a plexiglas chamber, with the piezoelectric transducer in the roof and the reﬂector in its base. A drying gas is introduced into the levitator chamber through a hole in the center of the reﬂector, and is conditioned using a controlled evaporation mixer (CEM). A liquid ﬂow controller type L1-FAC-33-0 humidiﬁes the drying gas to 0.2–10.0 gwater h1. A gas ﬂow controller type F-201C-FAC adjusts the drying gas ﬂow rate to between 0 and 2.0 l min1. The drying gas temperature T1 is adjusted in the mixing unit W-202330-T to produce the conditioned drying gas stream. The image of a levitated droplet is recorded continually using a JAI CF-M4 2/3 monochrome CCD camera with bellows and a Nikon 60 mm macrolens 0.8 diameter frame connected to a PC via a PcDIG LVDS frame grabber (32 bit). Images are recorded and analyzed using Image Pro Plus software version 4.51 (Media Cybernetics).

Fig. 1.51 Design of an acoustic levitation system for measuring droplet drying kinetics and development of particle morphology. The plexiglas levitation chamber is covered by a plexiglas cover not shown in this illustration.

1.5 Acoustic Levitation

Fig. 1.52 Photographic sequence of droplet appearance during drying in the acoustic levitator. This droplet is of pure water of initial diameter approximately 500 mm drying at T1 ¼ 40 C in still air at an SPLeff of 162.47. The oblate spheroid shape of the droplet is evident from these photographs.

1.5.6.2 Evaporation Rates of Acoustically-Levitated Pure Water Droplets Figure 1.52 shows a typical sequence of droplet proﬁles obtained for pure water of a0 ﬃ 500 mm drying at T1 ¼ 40 C, 0% RH and a drying air ﬂow rate, uda, of 0 m s1. The SPLeff of 162.47 (at 20 C) required to levitate this droplet size results in the oblate spheroid shape evident in these photographs. From measurements of the vertical and horizontal diameters, dv and dh, a surface-equivalent radius is calculated and plotted in Fig. 1.53 as a2 ðtÞ=a20 versus evaporation time, t (labeled plot A). Figure 1.53 also contains the proﬁle predicted for water under these conditions using Eqs. 1.56 and 1.57 according to the d2-law (labeled plot B). For this calculation Tph was taken to be the adiabatic saturation temperature, Tas, p1 was taken to be zero (sink condition) and p was set to the value for the saturated water vapor pressure at Tas. The measured rate of evaporation (plot A) is clearly higher than that predicted by the d2-law (plot B). The deviation from the d2-law is quantiﬁed using Eq. 1.60 to calculate the Sherwood number at each time point of the experimental plots. The resulting temporal course of the ﬁtted Sh(t) is shown in Fig. 1.54 for three different T1, in which the maximum Sh(t) observed at T1 ¼ 40 C is 3.6, substantially larger than that of 2.0 for pure diffusion-controlled evaporation through a stagnant boundary-layer. This result clearly demonstrates the substantial inﬂuence of the sound pressure on the evaporation rate of droplets of this size over a wide temperature range. Figure 1.53 also contains the proﬁle calculated using Eq. 1.46 to account for the effects of primary acoustic streaming on Sh(t) (labeled plot C). Equation 1.46 also does not accurately predict the experimental data, since the measured evaporation rate (plot A) is now lower than that predicted (plot C). The evaporation rate determined in the levitator is higher than that predicted by the d2-law, but lower than that expected by considering the effects of huacoustici on mass transfer. This phenomenon can be attributed to the reduction in mass transfer caused by secondary

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Fig. 1.53 Evaporation of single droplets of pure water in an acoustic levitator. Plots of change in relative radius with evaporation time. A: Experimental result; B: prediction according to d2-law (Eqs. 1.56 and 1.57); C: prediction according to effects of primary acoustic streaming on Sherwood number (Eq. 1.46). The remaining plots are experimental results obtained using drying air ventilation at the flow rates uda.

acoustic streaming around the droplet. Rensink (2004) demonstrated how a forcedventilation gas stream ﬂowing axially through a levitator chamber can attenuate this phenomenon. Figure 1.53 contains the experimental plots of a2 ðtÞ=a20 versus t determined at two drying air ﬂow rates, uda, axially through the levitator chamber. Increasing uda causes a higher droplet evaporation rate than that measured in still air, that is uda ¼ 0. Clearly, the use of a forced-convection drying air stream will increase the evaporation rate under all conditions. In Fig. 1.53 it is, however, the attenuation of secondary acoustic streaming that causes the higher evaporation rate at uda ¼ 0.88 m s1. At this value of drying air ﬂow rate there is now good agreement

Fig. 1.54 The temporal variation of Sherwood number during single droplet drying at three different drying air temperatures. The Sherwood number was calculated by fitting Eq. 1.60 to the experimental data. Results taken from Schiffter and Lee (2007a, b).

1.5 Acoustic Levitation

Fig. 1.55 Measured and predicted values of Sherwood number for single droplet drying of pure water under conditions of drying air forced convection. The irregular plots are results obtained by fitting Eq. 1.60 to the experimentally determined values of droplet radius versus evaporation time. The straight lines are those predicted by Ranz and Marshalls correlation (Eq. 1.59). Data taken from Schiffter and Lee (2007a, b).

between the experimental plot and that predicted from Eq. 1.46 (plot C). According to Rensink (2004) this drying air ﬂow rate prevents the accumulation of water vapor in the levitator tube by destroying the vortices and hence neutralizes the retarding effect of secondary acoustic streaming on the droplet evaporation rate. If uda is higher than that necessary to neutralize secondary acoustic steaming, then a further increase in evaporation rate is observed (Fig. 1.53 for the example uda ¼ 2.21 m s1). This additional, convection-driven evaporation can most conveniently be analyzed using Ranz and Marshalls correlation between Sh and uda (Eq. 1.59). Figure 1.55 illustrates the example of uda ¼ 1.77 m s1 at T1 ¼ 40 C and uda ¼ 1.7 m1 s at 25 C. Reasonable agreement is obtained between the measured proﬁles of Sh(t) calculated by ﬁtting Eq. 1.60 to the a(t)-proﬁle and that predicted by Eq. 1.59. The experimental results are, however, only predicted accurately by Ranz-Marshall when uda is higher than that value found necessary to neutralize secondary acoustic streaming. With lower values of udaEq. 1.59 is inaccurate, because the drying air stream in this ﬂow range contributes to neutralizing an accumulation of solvent vapor within the vortices. 1.5.6.3 Evaporation Rates and Particle Formation with Aqueous Mannitol Solution Droplets The sequence of photographs in Fig. 1.56 shows the drying of a single droplet of a 10 wt% aqueous solution of mannitol. The position of the critical point and subsequent particle formation can be seen. Figure 1.57 shows a2 ðtÞ=a20 versus t for this system dried at T1 ¼ 60 C and 0% RH in still air. The plot is initially slightly concave to the x-axis up to a clear break at the critical point of drying tcp. The droplets aspect ratio decreases linearly up to the critical point, as DPst becomes more dominant in

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Fig. 1.56 Sequence of photographs of drying of a single droplet of a 10 wt% aqueous solution of mannitol at T1 ¼ 60 C. Note the oblate spheroid shape of the droplet and also the identifiable position of the critical point.

Eq. 1.50 with decreasing droplet size causing the droplet shape to converge to a sphere. At the critical point there is a sudden increase in aspect ratio which coincides with incipient formation of solid at the droplet surface. The critical point is thus clearly identiﬁable from the sharp changes occurring in both a2 ðtÞ=a20 and the aspect ratio.

Fig. 1.57 Results from single droplet drying of a 10 wt% aqueous solution of mannitol at T1 ¼ 60 C. The plot of relative droplet/ particle radius versus evaporation time shows a clear break point at the critical point. Also shown are the values for horizontal and vertical droplet/particle diameter, dv and dh. Data taken from Schiffter and Lee (2007b).

1.5 Acoustic Levitation

Fig. 1.58 Evaporation rate profiles for the single droplets of aqueous mannitol solution in dependence on the relative humidity of the drying air at T1 ¼ 60 C.

_ cr , is readily calculated from The droplet evaporation rate up to the critical point, M _ Eq. 1.75 and that after the critical point, M fr , from Eq. 1.76. In our experience Dz for use in Eq. 1.76 can be subject to substantial, erratic scatter. Indeed, Yarin et al. (1998) note that this parameter is highly sensitive, for example to horizontal displacements of the droplet in the standing sound pressure wave. The evaporation rate proﬁles given in Fig. 1.58 show the inﬂuence of RH at T1 ¼ 60 C in still air. A clear distinction between the initial constant-rate and subsequent falling-rate periods is evident, with the position of the critical point _ cr can be predicted from boundary-layer being clearly identiﬁable. The value of M theory. For a spherical solution droplet evaporating in still drying air at constant temperature (Charlesworth and Marshall, 1960): _ cr ¼ 2plda dDT=Dhv M

ð1:78Þ

where lda is the thermal conductivity of the drying air at the droplet surface temperature, d is the mean average droplet diameter between t ¼ 0 and tcp, DT is the difference between the temperature of drying air, T1, and the droplet surface temperature given by the adiabatic saturation temperature, Tas, and Dhv is the enthalpy of evaporation of water. The evaporation time up to the critical point, tcp, is then given by Schiffter and Lee (2007a, b): _ cr tcp ¼ DM w;cr =M

ð1:79Þ

where DMw,cr is the total mass of water lost between t ¼ 0 and tcp. This is given by 4/3 p (a30 a3cr )rpxw, with acr being the droplet/particle radius at the critical point and xw the weight fraction of water in the solution. _ cr are some three The results in Tab. 1.10 show that the measured values for M times larger than those predicted by Eq. 1.78. Consequently, the measured values for tcp are much smaller than those predicted by Eq. 1.79. These discrepancies are a

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Tab. 1.10 Single droplet drying kinetics of aqueous mannitol

10 wt% (rm,0 ¼ 100 kgm3) solution at drying air temperature T1 ¼ 60 C in still air (uda ¼ 0). Symbols: RH ¼ relative humidity _ cr ¼ drying rate before critical point; tcp ¼ time to of drying air; M critical point; ap ¼ dry particle radius; a0 ¼ initial droplet radius. Data taken from Schiffter and Lee (2007b). RH [%]

_ cr Measured M [kg h1] · 106

_ cr Predicted M [kg h1] · 106

Measured tcp [s]

Predicted tcp [s]

ap/a0

5 10 20 40

29.3 26.5 23.5 15.2

8.95 8.33 7.22 5.27

202 234 332 453

503 554 669 950

0.59 0.57 0.53 0.49

consequence of the effect of huacoustici around the levitated droplet, as we have already seen in Section 1.5.6.2 with pure water. It is likely that these discrepancies between measured and predicted evaporation rates will depend on the initial SPLeff required to levitate a particular droplet size. Tian and Apfel (1996) found, for example, no inﬂuence of a sound pressure ﬁeld of low SPL of <150 dB on droplet evaporation rate and obtained a good agreement with Eqs. 1.56 and 1.57. _ cr results in a decrease in the quotient of the dried particle to initial Lower M droplet radii, ap/a0 (Tab. 1.10), at the same solids content. Since a(t) changes only marginally after the critical point, the value of ap/a0 represents that size at which the precipitating mannitol forms a mechanically-stable crust at the droplet surface. The _ cr is reduced. If the droplet dries time to this point is shifted to longer values when M p ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 3 to a solid particle then ap =a0 ¼ rm;0 =rs , where rs is the true density of the solid. A solid, fully-crystalline particle would fully dry to ap/a0 ¼ 0.405. The measured values in Tab. 1.10 are all substantially higher than this theoretical result and give a quantitative measure of degree of particle porosity or hollowness. The drying behavior of the mannitol solution droplets is thus characterized by a sharp critical point caused by crystallization from a super-saturated surface solution, followed by a rapid decline in evaporation rate as moisture must now penetrate through the permeable crystalline crust.

1.6 Concluding Remarks

The present chapter has presented experimental techniques such as: . . . . . .

gravimetry by magnetic suspension balance dew point mirror hygrometry infrared spectroscopy nuclear magnetic resonance coulometry acoustic levitation.

Additional Notation Used in Chapter 1

With the help of examples, we have shown how these techniques can be used to: . . . . .

measure single particle drying kinetics determine kinetics of single drying droplets measure the distribution of moisture in a population of particles monitor the change of solids moisture content in convective dryers derive drying curves for the entire hold-up of dryers that can be scaled-down to single particle kinetics if an appropriate model is available.

What the discussed experimental techniques do not provide is resolution of the spatial distribution of moisture in drying solids. Methods capable of delivering this information are the subject of Chapters 2–4. Additional Notation Used in Chapter 1

A a B B BM c F F f h K L Lp Lr Lv M N_ p Q Q T U

amplitude of pressure standing wave droplet radius gas particle velocity magnetic ﬁeld strength Spalding transfer number mass concentration of vapor force correction factor, function frequency displacement drying rate constant vertical displacement sound pressure level (SPL) tube length sound velocity level (SVL) magnetization particle ﬂow rate shape parameter of drying curve normalized cumulative number density electric charge relaxation time voltage

kg m1 s2 m m s1 T — kg m3 kg m s2 — s1 m or dimensionless s1 m — m — T s1 — — C s V

wavenumber times particle radius droplet evaporation constant boundary layer thickness gas particle displacement wavenumber

— s1 m m m1

Greek letters

a b d z k

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l t o

wavelength residence time angular frequency

Subscripts and superscripts

a BL BLS cp (or: cr) cr (or: I) da e (or: eff) fr G h IAS L L m m S s st t v vent 0 0 (or: g) hi

acoustic balance display without sample balance display with sample critical point constant rate drying air effective falling rate gravity horizontal acoustic boundary layer load cage and basket levitation drop-out mass transfer sample scattered static heat transfer vertical ventilation initial, inlet, driving surrounding medium, gas time-average over cycles spatial average over droplet

Abbreviations

FID IR LDE MSB NMR PRT RH SPL SVL TLM

free induction decay infrared light emitting diode magnetic suspension balance nuclear magnetic resonance platinum resistance thermometer relative humidity sound pressure level sound velocity level thin layer method

m s s1

References

References Abramzon, B., Sirignano, W. A., 1989. Droplet vaporization model for spray combustion calculations. Int. J. Heat Mass Transfer 32: 1605–1618. Blumberg, W., 1995. Selektive Konvektions- und Kontakttrocknung im Drehrohr. Disser-tation, Universit€at Karlsruhe, Germany. van Brakel, J., 1980. Mass transfer in convective drying. Mujumdar, A. S., Advances in drying, Hemisphere, New York, USA. Burdukov, A. P., Nakoryakov, V. E., 1965. On mass transfer in an acoustic ﬁeld. J. Appl. Mech. Tech. Phys. 6: 51–55. Burgschweiger, J., Tsotsas, E., 2002. Experimental investigation and modelling of continuous ﬂuidized bed drying under steady-state and dynamic conditions. Chem. Eng. Sci. 57: 5021–5038. Burgschweiger, J., Groenewold, H., Hirschmann, C., Tsotsas, E., 1999. From hygroscopic single particle to batch ﬂuidized bed drying kinetics. Can. J. Chem. Eng. 77: 333–341. Charlesworth, D., Marshall, W. 1960. Evaporation from drops containing dissolved solids. AIChE J. 6: 9–23. DaSilva, F. A., Rodrigues, A. E., 1997. Equilibrium and kinetics of n-hexane sorption in pellets of 5A zeolites. AIChE J. 43: 2524–2534. Frohn, A., Roth, N., 2000. Dynamics of droplets. Springer, Berlin, Germany. Frost, A. E., Seaver, M., Rubel, G. O., 1994. Delayed appearance of the liquid-condensed phase in 1-octadecanol ﬁlms on levitated water drops. J. Chem. Phys. 100: 3268–3275. Groenewold, C., M€oser, C., Groenewold, H., Tsotsas, E., 2002. Determination of singleparticle drying kinetics in an acoustic levitator. Chem. Eng. J. 86: 217–222. Groenewold, H., 2004. Wirbelschichttrocknung mit indirekter Beheizung. Dissertation, Ottovon-Guericke-University Magdeburg, Germany. Groenewold, H., Tsotsas, E., 1997. A new model for ﬂuidized bed drying. Drying Technol. 15: 1687–1698.

Groenewold, H., Tsotsas, E., 2007. Drying in ﬂuidized beds with immersed heating elements. Chem. Eng. Sci. 62: 481–502. Groenewold, H., Hirschmann, C., Burgschweiger, J., Tsotsas, E., 2000. Comparison of convective drying kinetics of active and inactivated Al2O3. Bull. Pol. Acad. Sci. 48: 269–382. Hirschmann, C., Tsotsas, E., 1998. Impact of the pore structure on particle-side drying kinetics. Proceedings of 11th International Drying Symposium, Thessaloniki, 216–223. Hirschmann, C., Fyhr, C., Tsotsas, E., Kemp, I. C., 1998. Comparison of two basic methods for measuring drying curves: thin layer method and drying channel. Proceedings of 11th International Drying Symposium, Thessaloniki, 224–231. Kastner, O., 2001. Theoretical and experimental studies of mass transfer from single droplets in an acoustic levitator. Dissertation, Universit€at Erlangen, Germany. Kastner, O., Brenn, G., Rensink, D., Tropea, C., 2001. The acoustic tube levitator – a novel device for determining the drying kinetics of single droplets. Chem. Eng. Technol. 24: 335–339. Keidel, F. A., 1959. Determination of water by direct amperometric measurement. Anal. Chem. 31: 2043–2048. Kemp, I. C., Fyhr, B. C., Laurent, S., Roques, M. A., Groenewold, C., Tsotsas, E., Sereno, A. A., Bonazzi, C. B., Bimbenet, J. J., Kind, M., 2001. Methods for processing experimental drying kinetics data. Drying Technol. 19: 15–34. Kettner, C., Peglow, M., Metzger, T., Tsotsas, E., 2006. Distributed product quality in ﬂuidized bed drying. Proceedings of 15th International Drying Symposium, Budapest, Volume B, 745–750. King, L. V. 1934. On the acoustic radiation pressure on spheres. Proc. R. Soc., London, Ser. A. 147: 212–240. Kwapinski, W., Tsotsas, E., 2004a. Experimental determination of single-

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particle kinetics and equilibria for convective drying, desorption or adsorption by a magnetic suspension balance. Proceedings of 14th International Drying Symposium, Sao Paulo, Volume A, 1419–1426. Kwapinski, W., Tsotsas, E., 2004b. Determination of kinetics and equilibria for adsorption of water vapour on single particles by a magnetic suspension balance. Chem. Eng. Technol. 27: 681–686. Kwapinski, W., Tsotsas, E., 2006. Characterization of particulate materials in respect to drying. Drying Technol. 24: 1083–1092. Lee, C. P., Wong, T. G., 1990. Outer acoustic streaming. J. Acoustic. Soc. Am. 88: 2367–2375. Looi, A. Y., Golonka, K., Rhodes, M., 2002. Drying kinetics of single porous particles in superheated steam under pressure. Chem. Eng. J. 87: 329–338. Marston, P. L., Lo-Porto-Arione, S. E., Pullen, G. L., 1981. Quadrupole projection of the radiation pressure on a compressible sphere. J. Acoustic. Soc. Am. 69: 1499–1501. van Meel, D., 1958. Adiabatic convection batch drying with recirculation of air. Chem. Eng. Sci. 9: 36–44. Metzger, T., Klotchov, A., Vergeldt, F., van As, H., Tsotsas, E., 2005. Magnetic resonance imaging to monitor moisture proﬁles in a drying nano-porous sphere. Proceedings of 7th World Congress of Chemical Engineering, Glasgow, C14-004. Ranz, W., Marshall, W., 1952. Evaporation from drops. Parts I and II. Chem. Eng. Prog. 48: 141–173. Rensink, D., 2004. Evaporation of acousticallylevitated oscillating droplets of homogeneous and heterogeneous media. Dissertation, Universit€at Erlangen, Germany. Rubotherm, 2004. Magnetic Suspension Balance. Bochum, Germany. Schiffter, H., Lee, G. W. J., 2007a. Singledroplet evaporation kinetics and particle formation in an acoustic levitator. Part 1: evaporation of water microdroplets assessed

using boundary-layer and acoustic levitation theories. J. Pharm. Sci. 96: 2284–2295. Schiffter, H., Lee, G. W. J., 2007b. Singledroplet evaporation kinetics and particle formation in an acoustic levitator. Part 2: drying kinetics and particle formation from microdroplets of aqueous mannitol, trehalose or catalase. J. Pharm. Sci. 96: 2296–2309. Seaver, M., Galloway, A., Manuccia, T. J., 1989. Acoustic levitation in a free-jet wind tunnel. Rev. Sci. Instrum. 60: 3452–3458. Sherwood, T. K., 1929. The drying of solids II. Ind. Eng. Chem. 21: 976–980. Shibata, H., 2005. Comparison of drying rate curves of porous solids in superheated steam to those in air. Drying Technol. 23: 1419–1434. Sirignano, W. A., 2000. Fluid dynamics and transport of droplets and spray. Cambridge University Press, Cambridge, UK. Suherman, 2007. Drying kinetics of granular and powdery polymers. Dissertation, Ottovon-Guericke-University Magdeburg, Germany. Suherman, Peglow, M., Tsotsas, E., 2008. On the applicability of normalization for drying kinetics. Drying Technol. 26: 90–96. Tian, Y., Apfel, R. E., 1996. A novel multiple drop levitator for the study of drop arrays. J. Aerosol Sci. 27: 721–737. Tian, Y., Holt, R. G., Apfel, R. E., 1993. Deformation and location of an acoustically levitated liquid drop. J. Acoust. Soc. Am. 93: 3096–3104. Trinh, E. H., Hsu, C., 1986. Equilibrium shapes of acoustically levitated drops. J. Acoust. Soc. Am. 1335–1338. Trinh, E. H., Robey, J. L., 1994. Experimental study of streaming ﬂows associated with ultrasonic levitators. Phys. Fluids 6: 3567–3579. Tsotsas, E., 1994. From single particle to ﬂuid bed drying kinetics. Drying Technol. 12 (6): 1401–1426. Tuckermann, R., 2002. Gase, Aerosole, Tropfen und Partikel in stehenden Ultraschallfeldern. Dissertation, Universit€at Braunschweig, Germany.

References Tuckermann, R., Bauerecker, S., Neidhart, B., 2002. Evaporation rates of alkanes and alcohols from acoustically levitated drops. Anal. Bioanal. Chem. 372: 122–127. Weis, D. D., Nardozzi, J. D., 2005. Enzyme kinetics in acoustically levitated droplets of supercooled water: a novel approach to cryoenzymology. Anal. Chem. 77: 2558–2563. Yarin, A. L., Brenn, G., Keller, J., Pfaffenlehner, M., Ryssel, E., Tropea, C.,

1997. Flowﬁeld charateristics of an aerodynamic acoustic levitator. Phys. Fluids 9: 3300–3314. Yarin, A. L., Paffenlehner, M., Tropea, C., 1998. On the acoustic levitation of droplets. J. Fluid Mech. 356: 65–91. Yarin, A. L., Brenn, G., Kastner, O., Rensink, D., Tropea, C., 1999. Evaporation of acoustically levitated droplets. J. Fluid Mech. 399: 151–204.

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2 Near-Infrared Spectral Imaging for Visualization of Moisture Distribution in Foods Mizuki Tsuta

2.1 Introduction

Moisture distribution inside food products affects their quality, processing characteristics, drying efﬁciency and so on. Therefore, it is an important factor to be measured; there is not only an academic but also an industrial need for methods for the measurement of moisture distribution inside food products. Magnetic resonance imaging (MRI, see Chapter 3) is one of the possible methods. Several studies of the visualization of moisture distribution inside foods have been reported (Irie et al., 2004; Ramos-Cabrer et al., 2006). One of the advantages of the MRI technique is that it allows the internal structure of a sample to be measured non-destructively. However, expensive instruments and high maintenance cost are involved. In addition, only liquid water and related molecules can be measured and even ice cannot be easily detected by MRI. On the other hand, near-infrared (NIR) spectroscopy has been widely used for moisture content measurement. However, moisture distribution inside food is rarely measured in this way because every part of the food cannot be measured by the single point detector used in NIR spectroscopy. To overcome this limitation of NIR spectroscopy, NIR spectral imaging has been studied as an extension of NIR spectroscopy from single point detection to two- or three-dimensional measurement. Quantitative analysis of constituents and visualization of their distributions can be carried out concurrently by NIR spectral imaging. Visualization of sugar distribution in fruits (Martinsen and Schaare, 1998; Sugiyama, 1999; Tsuta et al., 2002), anthocyanin in vegetables (Nagata et al., 2006; Kobayashi et al., 2006) and detection of foreign substances in fruit material (Tsuta et al., 2006) can be listed as examples of NIR spectral imaging. Devices required for NIR spectral imaging are relatively inexpensive compared to those for MRI and several different constituents including water and ice can be visualized at the same time. Therefore NIR spectral imaging can be applied for visualization of moisture distribution even where MRI cannot be used.

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

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In this chapter, the principles of NIR spectral imaging and some examples of moisture distribution measurements using NIR spectral imaging are given.

2.2 Principles of Near-Infrared Spectral Imaging 2.2.1 Near-Infrared Spectroscopy

NIR spectroscopy (Iwamoto et al., 1994) is a spectroscopic method utilizing the NIR region of light. The constituents of a sample can be quantitatively or qualitatively analyzed by illuminating the sample and observing the absorption spectra, which reﬂect absorption of light by each constituent within speciﬁc wavelength ranges. NIR spectroscopy is based on molecular overtone and combination vibrations. Such transitions are forbidden by the selection rules of quantum mechanics. As a result, absorption of light in the NIR region is typically quite small and light can penetrate much farther into a sample than in the mid-infrared region. NIR spectroscopy is therefore not a particularly sensitive technique but it can be very useful in probing the bulk material with little or no sample preparation. NIR spectroscopy has been studied since the 1940s, but began to receive much attention in the 1960s when quantitative analysis of the moisture content of fruits (Norris and Butler, 1961) and grains (Ben-Gera and Norris, 1968) by NIR spectroscopy was reported. In the 1970s Hunt et al. (1977) developed a quantitative analytical method for protein in grains, which was much easier and faster than the conventional chemical analysis method and was thus adopted as an ofﬁcial method by the Canadian Grain Commission, the United States Federal Grain Inspection Service and so on. NIR spectroscopy therefore became highly regarded and its application expanded drastically along with improvement in accuracy by innovations in instrumentation, progress in the computer ﬁeld and development of modern statistical analysis methods in the 1980s. Nowadays, it is widely adopted as an easy and fast measurement method, replacing conventional chemical analysis in the food industry, the chemical industry, medical technology and so on. 2.2.2 Lambert–Beer Law

Suppose we have a sample of thickness d that contains a constituent with concentration c, as shown in Fig. 2.1. When light of wavelength l with an intensity of I0(l) illuminates the sample its intensity declines to It(l) as it passes through the sample. The absorbance, which is the extent of absorption of light by the constituent, can be calculated from the relationship AðlÞ ¼ log ðI t ðlÞ=I0 ðlÞÞ

ð2:1Þ

2.2 Principles of Near-Infrared Spectral Imaging Fig. 2.1 Absorption of light by a sample.

Fig. 2.2 Absorption spectrum of a fresh melon.

The absorbance spectrum shown in Fig. 2.2 can be acquired by using a spectrometer to measure the absorbance at each wavelength. In this ﬁgure, a higher absorbance value indicates that light is absorbed more strongly, and it can be seen that light is strongly absorbed at 444, 676 and 978 nm. Supposing that there is no reﬂection, scattering and ﬂuorescence except for absorption of light within the sample, the relationship between A(l), d and c can be described by AðlÞ ¼ cde

ð2:2Þ

Here, e is a constant called the absorption coefﬁcient. Equation 2.2 is called the Lambert–Beer law. It indicates that the absorbance is proportional to the constituent concentration and the thickness of the sample. This law is virtually applicable also in the case of diffuse reﬂection measurement by illuminating the sample and measuring the intensity of reﬂected light, as shown in Fig. 2.3. If there are multiple Fig. 2.3 Diffuse reflection measurement.

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constituents in the sample, the total light absorption by the sample is the sum of the absorbance of each constituent: AðlÞ ¼

n X

ci dei

ð2:3Þ

i¼1

This equation, on which NIR spectroscopy is based, indicates that the concentration of each constituent can be calculated by measuring only the total absorbance of the sample at the absorption band of every constituent. Practically, it is difﬁcult to measure I0(l) directly in order to calculate A(l), especially in the case of a diffuse reﬂection measurement. Therefore, a white reference board made of material without any speciﬁc absorption band in the NIR region is utilized as a standard in order to calculate the apparent absorbance A0 ðlÞ ¼ log ðI t ðlÞ=I s ðlÞÞ

ð2:4Þ

Here, A0 (l) is the apparent absorbance and Is(l) is the intensity of light that passes through or is reﬂected from the white reference board. Equation 2.4 can be expanded as follows: A0 ðlÞ ¼ log ðI t ðlÞ=Is ðlÞÞ ¼ log ðIt ðlÞ=I 0 ðlÞ I 0 ðlÞ=I s ðlÞÞ ¼ log ðI t ðlÞ=I 0 ðlÞÞðlog ðIs ðlÞ=I 0 ðlÞÞ ¼ AðlÞAs ðlÞ

ð2:5Þ

Here, A(l) and As(l) are real absorbance values of the sample and white reference board. Equation 2.5 shows that the apparent absorbance is acquired by subtracting As(l) from A(l). Since As(l) is constant regardless of constituent concentrations, linearity of Eq. 2.3 is maintained when A(l) is replaced by A0 (l). Because the apparent absorbance is usually measured in actual experiments, apparent absorbance is often called simply absorbance. In the practical application of NIR spectroscopy, calibration curves, from which constituent concentrations can be calculated from absorbance, are developed by measuring the absorbance spectra of samples with known constituent concentrations and calculating the product of dei of Eq. 2.3 for each constituent by statistical methods. Using these calibration curves, the constituent concentrations of unknown samples can be determined by measuring only the total absorbance. NIR spectroscopy therefore is a much easier and faster method than conventional chemical analysis. 2.2.3 Hyperspectrum

NIR spectral imaging is an extension of NIR spectroscopy from single point detection to two- or three-dimensional measurement. The spectrum is measured at one single

2.2 Principles of Near-Infrared Spectral Imaging

Fig. 2.4 Hyperspectrum.

point of the sample in conventional NIR spectroscopy, while one spectrum is acquired at every point of a surface of the sample in NIR spectral imaging. For example, when using a one-mega-pixel digital camera to acquire spectra of the surface area, the data volume is one million times larger than that measured by the conventional method. A series of data acquired during NIR spectral imaging is called a hyperspectrum and contains not only optical information from the sample, as in the case of the conventional method, but also spatial information, as shown in Fig. 2.4. Acquisition and analysis of a hyperspectrum enable quantitative analysis of a constituent and visualization of its distribution at the same time, which is a strong advantage of NIR spectral imaging. There are various techniques for acquisition of spectral and spatial information in NIR spectral imaging. The appropriate technique for the research objective should be selected by considering their characteristics. NIR spectral imaging will be classiﬁed by the type of spectral and spatial information acquisition techniques in the following two sections. 2.2.4 Classification by Spectral Information Acquisition Technique

The spectral information contained in a hyperspectrum can be acquired by placing a device working as a spectrometer in front of an illuminator or detector. The major devices used for spectral information acquisition are listed in Tab. 2.1. A bandpass ﬁlter is a device that lets light within a certain range of wavelength pass and rejects any other light. It is inexpensive and has high transmittance, which makes the data acquisition time shorter. However, the acquisition of sequential spectra is

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Tab. 2.1 Classification by spectral information acquisition technique.

Device

Wavelength

Advantages

Disadvantages

Bandpass ﬁlter

Fixed

High transmittance/ inexpensive

Multiple ﬁlters are necessary for sequential spectra

Grating

Tunable

Easy acquisition of sequential spectra

Low transmittance

Tunable ﬁlter

Tunable

Both of the above

Expensive

Examples

LCTF, AOTF

difﬁcult because multiple ﬁlters are necessary for data acquisition at different wavelengths. A grating is an optical device consisting of a surface with many parallel grooves that disperses a beam of light into its constituent wavelengths to produce its spectrum. It is commonly used in conventional NIR spectroscopy and sequential spectra can be easily acquired with it. The light intensity, however, is drastically attenuated by a slit placed in front of the grating so that it takes a long time to acquire the whole hyperspectrum. A tunable ﬁlter combines the high transmittance of a bandpass ﬁlter with the variability of wavelength of a grating. A liquid crystal tunable ﬁlter (LCTF), which is a typical tunable ﬁlter, consists of electrically controlled liquid crystal elements and birefringence ﬁlters to select a speciﬁc wavelength of light for transmission through the ﬁlter with the exclusion of all others. The transmission wavelength of a LCTF can be switched from one to another within 50 ms so that sequential spectra can be easily acquired. In addition, a LCTF has high maintainability because it has no moving parts. It is, however, much more expensive than a bandpass ﬁlter or grating. An acoustic optical tunable ﬁlter (AOTF), which is another example of a tunable ﬁlter, utilizes the phenomenon that ultrasound propagating through an acoustic optical element has a diffracting function like a grating and has almost the same characteristics as a LCTF. 2.2.5 Classification by Spatial Information Acquisition Technique

The major spatial information acquisition techniques are listed in Tab. 2.2. X–Y scanning is a technique to measure the spectrum of a point of a sample by a single point detector. Spatial information can be acquired by moving the sample or the detector in the direction of the X and Yaxes, which is different from the conventional method. Spectra are measured under the same conditions and there would be no shading caused by sensitivity variations between detectors and/or lighting variations. On the other hand, it takes a long time to acquire a hyperspectrum because repetition of the measurement for as many times as the number of pixels of the image to be acquired is necessary.

2.3 Image Processing Tab. 2.2 Classification by spatial information acquisition technique.

Method

Detector type

Mechanical scanning

Advantages

X–Y scanning

Single point

Necessary

No shading

Image acquisition

Disadvantages Example

Long time for measurement Not necessary Short time for Shading measurement correction is necessary

Multiple detectors aligned in plane Line scanning Multiple deNecessary (Pushbroom) tectors aligned in line

Confocal microscope CCD–camera, InGaAs– camera

Intermediate Intermediate Line sensor between above between above two two

Image acquisition is a technique to measure spatial information at once using an array of detectors aligned in a plane, such as a CCD array. Its advantage is quick data acquisition, while shading should be corrected in order to obtain proper data reﬂecting the optical characteristics of the sample. Line scanning, which is also called the pushbroom method (Mather, 1987), is a technique using an array of detectors, arranged in a line, to acquire a spectrum by means of combining the results from each detector during one measurement. Spatial information can be obtained by moving the sample or the detector in a direction perpendicular to the array. Line scanning is intermediate in characteristics between X–Y scanning and image acquisition; data with less shading than in the latter can be acquired in a shorter time than in the former.

2.3 Image Processing 2.3.1 Extraction of Spectral Images from a Hyperspectrum

A hyperspectrum is a three-dimensional data set that consists of two spatial coordinates and one spectral coordinate. It is difﬁcult to analyze the hyperspectrum as it is. Hence, spectral images, which are images of the sample taken at different wavelengths, are usually extracted from the hyperspectrum (Fig. 2.5b). Image processing and spectral analysis are then applied to these images. 2.3.2 Noise and Shading Correction

Acquired spectral images include (i) thermal noise due to dark current thermal electrons; (ii) bias signals to offset the detector slightly above zero A/D counts; (iii) sensitivity variations from pixel to pixel on the detector and (iv) lightingvariations on the

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Fig. 2.5 Image processing procedure.

samples surface. The noise and shading corrections shown in Fig. 2.5c are applied to each spectral image to compensate for the above (SBIG, 1998; Morita et al., 1992; Fukushima, 1996). This can be expressed by the relationship Corrected image ¼ ðoriginal imagedark frameÞ=ðflat fielddark frameÞ ð2:6Þ In Eq. 2.6, the dark frame is the image acquired under the same conditions as the original image except for the absence of lighting. Subtracting it from the original image allows corrections for (i) thermal noise and (ii) bias signals. On the other hand, the ﬂat ﬁeld is obtained as a reference image by taking an exposure of a uniformly lit planar object such as a ceramic board. After the dark frame has been subtracted from the ﬂat ﬁeld in the same way as in the numerator, the ratio between the two images is obtained. This procedure compensates the effect of (iii) sensitivity variations and (iv) lighting variations. 2.3.3 Conversion into Absorbance Image

The numerator and the denominator of Eq. 2.6 correspond to the intensity of the sample and white reference board in NIR spectroscopy. Therefore, the absorbance

2.3 Image Processing

image can be acquired as shown in Fig. 2.5d, according to the scheme Absorbance image ¼ log ððoriginal imagedark frameÞ= ðflat fielddark frameÞÞ ¼ log ðcorrected imageÞ ð2:7Þ Each pixel of the image indicates one value of absorbance. 2.3.4 Acquisition and Pretreatment of Spectral Data

In order to utilize spectral information, boundaries composed of closed curves are set surrounding the areas to be analyzed in the absorbance images, as shown in Fig. 2.5e. These boundaries deﬁne so-called regions of interest (ROIs). When the average absorbance values of the pixels within the ROIs of the spectral images at each wavelength are calculated, absorbance spectra can be acquired, as shown in Fig. 2.5f. Pretreatment methods such as smoothing and the derivative method are often applied to the spectra to remove noise effects and spectral shifts between the samples. Among various spectral pretreatment methods, the second derivative method is especially important and most often used in NIR spectroscopy because of the following features and merits (Katsumoto et al., 2001): 1. Positive peaks in a raw spectrum are converted into negative peaks in a second derivative spectrum. 2. The resolution is enhanced, resulting in a better separation of overlapping peaks and greater emphasis of small peaks. 3. The additive and multiplicative baseline shifts in a raw spectrum are removed. By applying the truncated Taylor series expansion, a second derivative spectrum can be calculated as follows (Morimoto et al., 2001): f 2 ðxÞ ¼ ð f ðx þ DxÞ2f ðxÞ þ f ðxDxÞÞ=Dx 2

ð2:8Þ

Here, f (x) is the spectral function at x, and f 2(x) is the second derivative function at x. Actual spectral data, however, take discrete values because of the limited wavelength resolution of NIR spectrometers. Therefore, a second derivative spectrum is calculated in NIR spectroscopy as d2 Aðli Þ ¼ Aðli þ k Þ2 Aðli Þ þ Aðlik Þ

ð2:9Þ

Here, A(li) is the absorbance at li, d2A(li) is the second derivative absorbance at li, and k is the distance between the neighboring wavelengths, which is called a derivative gap. Equation 2.9 shows that absorbance values at three wavelengths of li þ k, li, and li–k are sufﬁcient to calculate the second derivative absorbance at li. When Eq. 2.9 is applied to the absorbance at each wavelength, a second derivative spectrum can be acquired. Equation 2.9 also indicates that a second derivative

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absorbance image, where the value of each pixel expresses the second derivative of absorbance, can be obtained as 2Der: absorbance image at li ¼ absorbance image at li þ k 2 absorbance image at li þ absorbance image at lik :

ð2:10Þ

2.3.5 Analysis of Absorbance Spectra

The parts on which the ROIs are set are extracted from the sample for chemical analysis to measure the actual concentration of the target constituents. Statistical methods such as multiple linear regression or the partial least squares method are then applied to the acquired concentration data and the absorbance spectra of the ROIs to derive calibration curves for prediction of the concentration of an unknown sample, as shown in Fig. 2.5h. When chemical analysis of the speciﬁc parts of the sample is difﬁcult to conduct and no calibration curve can be obtained, absorbance spectra are examined to specify the absorption peaks of the target constituent. The magnitude of the peaks can be used for relative concentration images. 2.3.6 Visualization of Constituent Distribution

In general, a calibration curve utilized in NIR spectroscopy is a linear polynomial that contains several absorbance values at different wavelengths and can be written in the form c¼

n X

ai Aðli Þ þ b

ð2:11Þ

i¼1

Here, c is the concentration of the considered constituent, n is the number of wavelengths used in the calibration curve, A(li) is the absorbance at li, ai is the coefﬁcient of A(li) and b is a constant. In the same way, a constituent image, in which the value of each pixel indicates the concentration of the constituent, can be acquired by image arithmetic as Constituent image ¼

n X

ðai absorbance image at li Þ þ b

ð2:12Þ

i¼1

When a linear color or gray scale is applied to the constituent image, concentration of the constituent and its distribution can be visualized, as shown in Fig. 2.5j. If there is no calibration curve, then, by applying a linear color or gray scale to the absorbance image at the absorption peak of the target constituent, the relative concentration and distribution of the constituent can be visualized.

2.4 Applications of Near-Infrared Spectral Imaging for Visualization of Moisture Distribution

2.4 Applications of Near-Infrared Spectral Imaging for Visualization of Moisture Distribution

In the following sections, an application of NIR spectral imaging for determination of the absorption peaks of water and ice will be presented. Subsequently, visualization of moisture distribution inside soybean seeds utilizing the information from the absorption peaks of ice will be explained. 2.4.1 Specification of the Absorption Bands of Water and Ice 2.4.1.1 Imaging Apparatus The imaging apparatus utilized in this study is shown in Fig. 2.6. It was composed of a material cutting device called a Microslicer (AST-024s, Toshiba Machine Co., Ltd, Japan), a spectral illuminator and a NIR camera. The microslicer comprises a rotating microtome and a stepping motor. A sample is set in a sample holder above the motor and pushed up by the motor with a few micron increments. The increment can be adjusted from 1 to 30 mm with 1 mm accuracy. The top part of the sample is cut by the rotating microtome repeatedly so that cross sections at different depths are exposed serially. The sample holder can be maintained at about 15 C by an immersion cooler so that frozen samples can be measured. The spectral illuminator (S-10, Soma Optics Inc., Japan) comprises a xenon lamp box and a grating monochromater. It is connected to a germanium-doped light guide with a condensing lens (custom-made by Soma Optics Inc., Japan) and can illuminate the exposed surface of the sample at any wavelength from 400 to 1600 nm. The NIR camera (XEVA-USB-FP, XenICs, Belgium) is set on a ﬂuorescence microscope (BXFM, Olympus, Japan) with a ﬁve times objective lens for the NIR region (M Plan NIR 5 , Mitsutoyo Corp., Japan). The NIR camera has 320 256 pixels and its gradation is 12 bits (4096 steps). In addition, because its imaging sensor is made of an InGaAs array, it is sensitive in the wavelength region from 900 to 1600 nm, in which a normal CCD camera has little or no sensitivity. No ﬂuorescence

Fig. 2.6 Imaging apparatus.

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ﬁlter was installed in the microscope so that spectrometry by the spectral illuminator could work. 2.4.1.2 Acquisition of Hyperspectra of Water and Ice A white ceramic board, which was used as a ﬂat ﬁeld, was placed on the microslicer. Its images were taken by the NIR camera with changing wavelength of the spectral illuminator from 1400 to 1598 nm at 2 nm intervals with 12 ms exposure time. As a result, a hyperspectrum of 320 256 pixels 100 wavelengths was acquired. A pure water droplet with a volume of 1 ml was then added on a white ceramic board so that the droplet was in the view of the NIR camera. In the same way as for the white ceramic board, its hyperspectrum was acquired. After freezing the water droplet by using the cooler of the Microslicer, the hyperspectrum of the frozen droplet was obtained similarly. A dark frame was then taken with the lamp of the spectral illuminator switched off. 2.4.1.3 Spectral Analysis After noise/shading correction and conversion into absorbance images were carried out, an ROI was set surrounding the whole water droplet in the spectral images, as shown in Fig. 2.7. The average absorbance spectrum within the ROI was then calculated. This spectrum is depicted in Fig. 2.8. In the same way, the absorbance spectrum of the frozen droplet was acquired. In these working steps, image processing software (Image Pro Plus 5.0, Media Cybernetics Inc., USA) was utilized. Spreadsheet software (Excel 2003, Microsoft Corp., USA) was then used to calculate the second derivative absorbance spectra with a 20 nm gap and examine both the absorbance and the second derivative absorbance spectra. It was clariﬁed that the absorption peak of water was located at 1454 nm and that of ice at 1500 nm in the absorbance spectra. Furthermore, the negative absorbance peak of water was found to be at 1468 nm and that of ice at 1484 nm in the second derivative absorbance spectra (Fig. 2.9).

Fig. 2.7 Absorption images of water droplet and ROI.

2.4 Applications of Near-Infrared Spectral Imaging for Visualization of Moisture Distribution

Fig. 2.8 Absorbance spectra of water and ice.

2.4.2 Visualization of Moisture Distribution inside Soybean Seeds 2.4.2.1 Sample Six soybean seeds (Glycine max) were soaked in pure water for 0, 30, 60, 120, 240 min and 24 h, respectively. Immediately after the soaking process, the beans were embedded in freeze embedding agent (O. C. T. Compound, Sakura Finetechnical Co. Ltd., Tokyo, Japan), put into a deep freezer and kept for 1 h at 80 C to freeze free water and keep the moisture distribution inside them unchanged.

Fig. 2.9 Second derivative absorbance spectra of water and ice.

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2.4.2.2 Acquisition of Hyperspectra The frozen samples of soybean seeds were placed in the microslicer to be cut. The cutting process was repeated until the hypocotyl and the embryo were exposed. The hyperspectra of the exposed surface were acquired by the NIR camera under the same conditions as for the droplet except for an exposure time of 50 ms. The hyperspectra of a white ceramic board and a dark frame were also acquired in the same way as in the case of the water droplet. 2.4.2.3 Spectral Analysis After noise/shading correction and conversion into absorbance images had been carried out, the ROIs were set on the periphery and center parts of the soybean seeds in the absorbance images, as shown in Fig. 2.10. The average absorbance and second derivative absorbance spectra were then calculated with a gap of 20 nm within the ROIs, as shown in Figs. 2.11 and 2.12. In the absorbance spectra of the periphery of all soybean seeds (except those of the original sample without water soaking), absorbance peaks were observed at around 1500 nm, where the absorption peaks of ice were also observed in the case of the frozen droplet. Because the water inside the seeds was frozen, it was considered that light absorption at 1500 nm indicated the presence of ice resulting from water penetration during the water soaking process. However, no speciﬁc trend related to water soaking time was found. On the other hand, it was observed that the second derivative absorbance at 1484 nm, where negative absorbance peaks were located in the case of the frozen droplet, became smaller with soaking time. This trend is stronger at the periphery than in the center of the samples. Therefore, it was considered to indicate that an increase in moisture content takes place during the water absorption process. Image processing and spreadsheet software, as in the case of water droplet, were utilized in these derivations.

Fig. 2.10 Absorbance images of soybean seed (60 min sample) and ROI.

2.4 Applications of Near-Infrared Spectral Imaging for Visualization of Moisture Distribution

Fig. 2.11 Absorbance spectra of soybean seeds.

2.4.2.4 Visualization of Moisture Distribution Second derivative absorbance images of the soybean seeds at 1484 nm were developed as shown in Fig. 2.13 by applying Eq. 2.10 to the absorbance images at 1464, 1484 and 1504 nm. In these images, pixels with a low value of second derivative absorbance spread from the periphery towards the center of the soybean seeds as the soaking time increased. Because a lower value of second derivative absorbance at

Fig. 2.12 Second derivative absorbance spectra of soybean seeds.

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Fig. 2.13 Second derivative absorbance images of soybean seeds.

1484 nm indicates a larger moisture content, it may be concluded that water has penetrated deeper inside the sample seeds as the soaking time became longer, which is consistent with the water movement during the water soaking process. Therefore, these images seem to reﬂect the real moisture distribution in the samples.

2.5 Future Outlook

Not many applications of NIR spectral imaging for visualization of moisture distribution in foods have been reported yet and breakthroughs in various aspects can be expected. One possible progress would be the development of reliable calibration curves for the moisture content of small size foods such as grains and seeds. Utilization of a microtome to prepare cross-sections of a sample would be promising, because chemical analysis of a cross-section can be carried out after acquisition of its hyperspectrum. Accurate calibration curves can be developed from statistical analysis of several hundred hyperspectra and the actual moisture content data acquired by the chemical analysis. Three-dimensional visualization of moisture distribution inside foods can also be expected in the near future. It can be achieved by repetition of image acquisition at the absorbance peak of ice in combination with sample slicing by the microslicer. 3D visualization combined with a calibration curve covering a wide range of moisture content would be helpful in clarifying the effect of moisture distribution in foods, especially those with a moisture content so low that MRI cannot be applied. Finally, the development of a technique for the simultaneous visualization of the distributions of moisture and other constituents would greatly contribute to studies on changes in food properties during processing and optimization of unit operations, such as drying, in the food industry.

References

Additional Notation Used in Chapter 2

A A0 c d I k X, Y x

absorbance apparent absorbance concentration sample thickness light intensity derivative gap spatial coordinates general variable

— — mol m3 m W m2 m m various

Greek symbols

e l

absorption coefﬁcient wavelength

m2 mol1 m

Subscripts

s t 0

transmitted or reﬂected from white reference board transmitted or reﬂected incident light

References Ben-Gera, I., Norris, K. H., 1968. Determination of moisture content in soybeans by direct spectrophotometry. Israel J. Agric. Res. 18: 125–132. Fukushima, H., 1996. Reikyaku CCD Nyuumon. Seibundou Sinkousha, Tokyo, Japan. Hunt, W. H., Fulk, D. W., Elder, B., Norris, K. H., 1977. Collaborative study on infrared reﬂectance devices for determination of protein in hard red winter wheat, and for protein and oil in soybeans. Cereal Foods World 22: 534–536. Irie, K., Horigane, A. K., Naito, S., Motoi, H., Yoshida, M., 2004. Moisture distribution and texture of various types of cooked spaghetti. Cereal Chem. 81: 350–355. Iwamoto, M., Kawano, S., Uozumi, J., 1994. Kin-Sekigai Bunkouhou Nyuumon. Saiwai Shobou, Tokyo, Japan.

Katsumoto, Y., Jiang, J., Berry, R. J., Ozaki, Y., 2001. Modern pretreatment methods in NIR spectroscopy. Near Infrared Anal. 2: 29–36. Kobayashi, T., Nagata, M., Goto, Y., Toyoda, H., Tallada, J., 2006. Study on anthocyanin pigment distribution estimation for fresh fruits and vegetables using hyperspectral imaging part 2. Visualization of anthocyanin pigment distribution of strawberry (Fragaria X ananassa Duchesne). J. SHITA 18: 50–57. Martinsen, P., Schaare, P., 1998. Measuring soluble solid distribution in kiwifruit using near-infrared imaging spectroscopy. Postharvest Biol. Technol. 14: 271–281. Mather, P. M., 1987. Computer processing of remotely-sensed imagery. John Wiley & Sons, Ltd, New York, USA. Morimoto, S., McClure, W. F., Stanﬁeld, D. L., 2001. Hand-held NIR spectrometry: part I: an instrument based upon gap-second

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derivative theory. Appl. Spectrosc. 55: 182–189. Morita, K., Shiga, T., Taharazako, S., 1992. Evaluation of change in quality of ripening bananas using light reﬂectance technique. Memoirs of the Faculty of Agriculture Kagoshima University 28: 125–134. Nagata, M., Kobayashi, T., Tallada, J., Toyoda, H., Goto, Y., 2006. Study on anthocyanin pigments estimation for fresh fruit and vegetables using a hyperspectral imaging part 1. Visualization of anthocyanin pigments distribution of purple-ﬂeshed sweetpotato (Ipomoea batatas Poir). J. SHITA 18: 42–49. Norris, K. H., Butler, W. L., 1961. Techniques for obtaining absorption spectra on intact biological samples. IRE Trans. Bio-Med. Electron. 8: 153–157. Ramos-Cabrer, P., Van Duynhoven, J. P., Timmer, H., Nicolay, K., 2006. Monitoring

of moisture redistribution in multicomponent food systems by use of magnetic resonance imaging. J. Agric. Food Chem. 54: 672–677. SBIG 1998. Product Catalog. SBIG Astronomical Instruments, Santa Barbara, CA, USA. Sugiyama, J., 1999. Visualization of sugar content in the ﬂesh of a melon by nearinfrared imaging. J. Agric. Food Chem. 47: 2715–2718. Tsuta, M., Sugiyama, J., Sagara, Y., 2002. Nearinfrared imaging spectroscopy based on sugar absorption band for melons. J. Agric. Food Chem. 50: 48–52. Tsuta, M., Takao, T., Sugiyama, J., Wada, Y., Sagara, Y., 2006. Foreign substance detection in blueberry fruits by spectral imaging. Food Sci. Technol. Res. 12: 96–100.

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3 Magnetic Resonance Imaging for Determination of Moisture Profiles and Drying Curves Stig Stenstr€om, Catherine Bonazzi, and Loïc Foucat

3.1 Introduction

Moisture proﬁles which develop in the product during drying can have a high impact on the drying kinetics and the development of product quality parameters such as mechanical properties, porosity and shape. Drying of rice at high intensities results in ﬁssuring and subsequent breakage of the rice kernel which must then be rejected. The mechanical strength of a paper is established in the drying section; uneven drying of a paper web builds up stresses in the sheet which can result in surface wrinkles of cardboard material, poor printing properties and curl or twist of printing paper, and wavy copies from the laser printer. For clay products it is essential that the ﬁnal bricks all have the same size and shape after the drying and heat treatment processes. Knowledge of moisture proﬁles is also of importance for proposing drying mechanisms and determining rate limiting processes during drying as well as for validation of different modeling tools for the drying process. The techniques used to determine the moisture proﬁles can be classiﬁed as invasive or non-invasive. Invasive methods have the common feature that they disturb or interrupt the drying process. One example of an invasive method, which is also destructive, implies cutting the sample into a number of pieces and determining the moisture content in each sample (see Chapter 2). The method requires a sample large enough to be cut or sliced into at least ﬁve pieces and a drying process where the time for dividing the sample is signiﬁcantly less than the drying time. Suitable products for this method could be wood or larger fruits such as apples or pineapples. The moisture proﬁles as a function of time can be measured by repeating the process for different drying times. The method is based on a simple principle but has the disadvantages that the sample will be destroyed and for some products, such as fruits, it could be difﬁcult to ﬁnd samples that are identical in size and shape for a number of repetitive tests. It can also be questioned whether the cutting process has any inﬂuence on the measured moisture content. Another example of an invasive method is to build up the product from a number of slices from the same material, perform the drying process, separate the slices after

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

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a given time and determine the moisture content in each slice. This method has been used by a large number of investigators for studying the drying of paper but this method could also be suitable for textile materials. The advantage is again the rather simple experimental set-up which is needed and the possibility of performing both conductive and convective drying experiments. It could be questioned whether sandwiching a number of slices will produce one homogenous material. Pores in the material will be interrupted at the interfaces between the slices which will result in different capillary forces and thus also different liquid transport in the layered composite. Another drawback is that the resolution of the method is limited to the thickness of the individual layers. Non-invasive methods offer the possibility to obtain a large number of moisture proﬁles during the drying operation without destroying the product. The most common non-invasive methods are magnetic resonance imaging (MRI), neutron scattering and X- or g-ray attenuation methods. Dielectric and infrared techniques have also been proposed for some applications. MRI has developed into a standard instrument for medical applications but has also been used to measure moisture proﬁles in a large number of products, such as apples, corn, rice, model food gels, wood, plywood, cardboard, paper, concrete, cement and catalyst pellets (compare with Section 1.4.5). More data are given by Harding et al. (2001); Bucur (2003); Hills (1998). To obtain moisture proﬁles in the sample the instrument is set up to measure the concentration of hydrogen atoms in liquid water. Normally the concentration of gaseous water is too low to be detected by the instrument, and hydrogen atoms in solid matter (cellulose, proteins etc.) have very short relaxation times which cannot be recorded with standard MRI techniques. The sample is subjected to a strong magnetic ﬁeld inside a superconducting magnet so that the size of this magnet also limits the size of the sample. The magnetic resonance frequency depends on the magnetic ﬁeld, and by creating gradients in the magnetic ﬁeld in different directions a resolution in space can be obtained. The noninvasive, non-destructive principle makes MRI an attractive tool for obtaining moisture proﬁles for a large range of products. The method can be designed to give 1D, 2D or 3D images of the water distribution in the product with a resolution in space down to 10 mm and a temporal resolution down to about 1 s. Data on the mobility, the diffusion coefﬁcients of water within porous products and on the pore size distribution can also be measured. To obtain a high resolution the sample size is limited to about 10 mm so that great care is needed when designing the experimental set-up. This also limits the energy supply for the drying process to convective transport from air at a temperature of about 100 C, resulting in rather low drying rates. Some other drawbacks using this technique are that the instruments are expensive and require skilled personnel for operation and setting the machine parameters in an optimal way. g-Ray attenuation methods have been discussed by Bucur (2003) and used by Stammer and Schl€ under (1993) during microwave drying of two ceramic materials. Neutrons interact preferentially with protons, thus they are absorbed selectively by water in moist products. Neutron beam attenuation was used by Ketelaars et al. (1992)

3.2 Principles of MRI for Determination of Moisture Profiles

for the determination of moisture gradients during the drying of clay samples. The disadvantage with the g-ray method is a spatial resolution limited to around 1–2 mm. The neutron beam method requires a neutron source, normally only available at a nuclear reactor. In this chapter the principles, the advantages and the limitations of the MRI method for obtaining moisture proﬁles and drying curves will be presented. Applications and results of the method will be presented for paper, pulp, wood and for different food products. The measurement of diffusivities will be brieﬂy presented and the use of the resulting data discussed.

3.2 Principles of MRI for Determination of Moisture Profiles 3.2.1 General Considerations

Non-invasive assessment of moisture migration in multicomponent products can yield valuable data for the development and validation of transport models. One of the most outstanding non-invasive techniques available for studying the status of water in materials is MRI, as mentioned earlier. Contrast in MRI images is governed by the local physicochemical properties of the system. The ability of MRI to provide spatially resolved information non-invasively, and without the use of ionizing radiation or contrast agent, is especially attractive for the study of multicomponent systems. The different time scales of moisture transport require protocols where different compromises are made with respect to the acquisition time and the resolution of mobility regimes. Within applications of MRI, there is always a trade-off between the following requirements: . . . .

sensitivity spatial resolution temporal resolution the range of molecular mobility regimes that can be studied.

When one of these requirements is favored, this will always be at the expense of at least one of the other three. Hence, to yield valuable information, the development of an experimental MRI protocol involves a careful balance of these four requirements. The aim of this section is to introduce the basic concepts necessary for the understanding of MRI signal dependence upon intrinsic parameters of the sample (relaxation times, self-diffusivity etc.), and extrinsic parameters (magnetic ﬁeld strength, sequence parameters, temperature etc.). Here we deal with only one species: water protons (1 H). In order to heighten the awareness of the advantages but also the constraints of the MRI approaches, the limits of the technique are discussed. For more details on the theoretical principles of MRI, the reader is referred to the books by Hills (1998); Callaghan (1991).

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3.2.2 Basic NMR 3.2.2.1 Nuclear Magnetic Moment and Larmor Relation Nuclear magnetic resonance is based on the absorption and emission of energy in the radiofrequency (rf ) range of the electromagnetic spectrum. Many nuclear particles possess the property of spin, that is an intrinsic angular momentum. Magnetism is a phenomenon caused by electric charge in motion (like protons). NMR relies upon the ! fact that the elementary magnetic moment m thus created, which is collinear to the angular momentum and associated to the nucleus of the atom (such as the hydrogen proton 1 H), precesses at an angular frequency v0 when submitted to an external ! magnetic ﬁeld B0 , see Fig. 3.1. The angular frequency is directly proportional to the magnetic ﬁeld strength

v0 ¼ gB0

ð3:1Þ

In Eq. 3.1 g is the gyromagnetic ratio, a characteristic of the observed nucleus (for hydrogen, g ¼ 42.58 MHz T1). This relation is known as the fundamental Larmor relation.

Fig. 3.1 Precession of the magnetic moment in the static B0 magnetic field.

3.2.2.2 Net Magnetization and Radio Frequency Excitation The sum of the individual magnetic moments (or spins) of identical particles (such as water hydrogen) contained in a macroscopic sample gives a net magnetization ! M. At equilibrium, this net magnetization vector M lies along the direction of ! ! the applied magnetic ﬁeld B0 and is called the equilibrium magnetization M0 (Fig. 3.2a). Adopting the conventional NMR coordinate system, the external ! ! magnetic ﬁeld B0 and the net magnetization vector M 0 at equilibrium are both along the z axis. As in all spectroscopic techniques, signal receipt needs a prior perturbation of the system. For NMR, this perturbation is created by electromagnetic radiation, which consists of a radiofrequency excitation pulse at the appropriate frequency n0 ¼ v0/2p. ! This radiation is generated by an rf-coil placed around the sample, which creates a B1 ! ﬁeld perpendicular to B0 . The perturbation induces a resonant phenomenon that

3.2 Principles of MRI for Determination of Moisture Profiles

Fig. 3.2 The three basic states of an NMR experiment (a) M0 at equilibrium, (b) excitation by a radiofrequency pulse, (c) relaxation.

!

leads to a rotation of M0 at an angle u (Fig. 3.2b). The value of u depends on the rf-pulse duration tp: ð3:2Þ

u ¼ gB1 tp !

!

After the rf-excitation is turned off, M 0 precesses at a frequency n0 around B0 (Fig. 3.2c), and returns gradually to its thermodynamic equilibrium position along the z axis in the course of a relaxation process. To facilitate the vectorial description of this relaxation phenomenon, it is useful to deﬁne a frame of reference that rotates ! around the z axis at the Larmor frequency. Thus, the magnetization vector M 0 rotating at n0 in the laboratory frame appears stationary in the frame of reference and ! ! can be decomposed into two components: one longitudinal, ML , aligned with B0 , and ! ! another transversal, M T , in a plane perpendicular to B0 , see Fig. 3.3. 3.2.2.3 Relaxation and NMR Signal ! Figure 3.4 illustrates the return of M0 to equilibrium after an rf-pulse of 90 . The ! ! evolution of the two components ML and M T with time (in the rotating frame) is described by the following expressions:

ML ðtÞ ¼ M0 ð1exp ðt=T 1 ÞÞ

ð3:3Þ

MT ðtÞ ¼ M0 exp ðt=T 2 Þ

ð3:4Þ

We note that the two processes are exponential and separated. They are character! ized by the time constants T1 and T2. T1 related to the longitudinal component ML is called the longitudinal (or spin–lattice) relaxation time. It is due to energy exchange

Fig. 3.3 Magnetization vector in the rotating frame decomposed into longitudinal and transversal components.

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Fig. 3.4 Amplitude of the longitudinal and transversal components during T1 and T2 relaxation, given by Eqs. 3.3 and 3.4.

between the spins and surrounding lattice, re-establishing thermal equilibrium. T2, ! related to the transverse component MT is called the transverse (or spin–spin) relaxation time. It results from spins getting out of phase in the plane perpendicular ! to B 0 due to local interactions between spins. ! The electric signal induced by the decay of the transverse component M T during the relaxation is then detected with a receiver rf-coil (it is often the same as that used to generate the rf-pulse excitation) and constitutes the observed NMR signal (called a free induction decay (FID)). This time-dependent signal is then Fourier transformed (FT) to obtain the associated frequency signal (or frequency spectrum). Because all water protons contained in a homogeneous or heterogeneous sample have, theoretically, the same angular frequency, the frequency spectrum has only one peak, see Fig. 3.5. The natural line width at half maximum intensity n1/2 is related to T2 by: y 1=2 ¼

1 pT 2

ð3:5Þ

Often lines are broader. For example, in solids or for slowly tumbling molecules in liquids, magnetic dipole–dipole interactions between nuclei lead to appreciable line broadening, sometimes by several kHz. In a perfectly homogeneous ﬁeld B0, the time constant of the decay would be T2. However, this it is not the case in practice, because nuclei in different parts of the sample experience slightly different values of the ﬁeld B0. Hence, resonance takes places at slightly different frequencies. Thus, the free induction signal decays in a time T 2 < T 2 deﬁned by: 1 1 þ gDB0 ¼ pT 2 pT 2

Fig. 3.5 Envelope of the free induction decay and its Fourier transform.

ð3:6Þ

3.2 Principles of MRI for Determination of Moisture Profiles

Fig. 3.6 Different relaxation regimes as function of tc (v0 is given by the magnetic field strength, cf. Fig. 3.1).

This time includes contributions from both natural line width and magnetic ﬁeld inhomogeneity DB0. 3.2.2.4 Factors Influencing Relaxation Times Relaxation characteristics depend on the physicochemical properties of the system studied and more speciﬁcally on the molecular correlation time, t c, that can be deﬁned as the average time between molecular collisions for a molecule in some state of motion. One should note that t c is related to the viscosity and the temperature of the system by the proportionality relation t c / m/T. Figure 3.6 represents schematically the dependence of relaxation times on molecular correlation time and angular frequency via the product v0tc. Three main regimes can be distinguished: .

.

.

For v0tc 1, corresponding to non-viscous liquids (region A in Fig. 3.6), it is T1 T2 (typically 3 s for pure water at 25 C), and both relaxation times decrease with increase in tc or v0. In viscous liquids or non-rigid solids (v0t c > 1) T2 decreases and T1 increases with v0t c, and it is T1 > T2 (region B in Fig. 3.6). Such conditions typically prevail in the case of biological tissues, with T1 and T2 values about 1 s and a few tens of ms, respectively. The third region (region C at v0t c 1) concerns rigid lattices for which T2 is very short (<10 ms) and T1 T2 (T1 10 s).

Knowledge of the intrinsic parameters T1 and T2 is essential for the quantitative determination of water distribution in a heterogeneous sample. 3.2.3 Imaging Principles

As we have seen previously, the NMR frequency signal associated with the water protons contained in a sample appears as only one line. This line does not provide any information about the spatial variability of water distribution inside the sample. It is, therefore, necessary to encode the signal in space. To illustrate this space encoding, a

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Fig. 3.7 Principle of measurement of sample projection with the help of a magnetic gradient in the r-direction, Gr.

phantom constituted of two rectangular boxes ﬁlled with water at two different levels is used, see Fig. 3.7. 3.2.3.1 Projection of an Object (1D Imaging) ! The basic idea of MRI is to superimpose to the magnetic ﬁeld B 0 a magnetic gradient Gr, which varies linearly in the space direction r. The angular frequency then becomes dependent on the position r :

vðrÞ ¼ v0 þ gGr r

ð3:7Þ

This ﬁrst encoding step ( frequency encoding) allows one to obtain a relation between proton frequency and water localization. As illustrated in Fig. 3.7, after one-dimensional Fourier transformation (1D-FT) of the NMR signal created in this way, the projection of the object along the r direction is obtained. 3.2.3.2 Two-Dimensional Imaging ! ! After the rf-excitation of M0 , the created M T transverse magnetization, then submit! ted only to the ﬁeld B 0 , is dephased by an angle F expressed by the integral: ðt ð3:8Þ FðtÞ ¼ v0 dt 0

3.2 Principles of MRI for Determination of Moisture Profiles

Fig. 3.8 2D image resulting from frequency and phase spatial encoding after 2D-Fourier transformation. !

If a ﬁeld gradient Gp is superimposed to B 0 along a direction p, the combination of ! Eqs. 3.7 and 3.8 leads to a phase dependence of MT on the position p: ðt

ðt

Fðt; pÞ ¼ vðpÞdt ¼ ðv0 þ gGp pÞdt 0

ð3:9Þ

0

This permits a second spatial encoding step (phase encoding). The combination of frequency and phase encoding allows, after double Fourier transformation (2D-FT), a two-dimensional image to be obtained in the plane (r, p), see Fig. 3.8. 3.2.3.3 Slice Selection As mentioned above in Eq. 3.7, a ﬁeld gradient G induces an angular frequency dispersion of water protons, in relation to their position along the applied gradient direction. If an excitation rf-pulse of restricted frequency range (called a selective pulse) is applied simultaneously to this gradient, only one slice in the sample will be excited, see Fig. 3.9.

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Fig. 3.9 Principle of slice selection by use of a selective pulse of bandwidth Dvs and simultaneous application of a gradient Gs. This method selects spins which precess at the frequencies corresponding to the bandwidth of the selective pulse. These spins belong to a slice perpendicular to the s-gradient direction.

The slice thickness (Sthick) can be controlled by the choice of gradient strength (Gs) and/or frequency range selectivity (Dvs) of the rf-pulse: Sthick ¼ Dvs =gGs

ð3:10Þ

The applied Gs deﬁnes also the selected slice orientation, perpendicular to the gradient direction. Note that linear combinations of x, y, and z magnetic ﬁeld gradients allow oblique imaging to be performed. In this way, any image orientation in the object can be produced. 3.2.3.4 Three-Dimensional Imaging There are two main approaches to obtaining a 3D image of an object.

3.2 Principles of MRI for Determination of Moisture Profiles

The ﬁrst consists in repeating the slice selection process described previously over the sample. It can be thought of as collecting several contiguous slices through the imaged object. The second is based on two separate phase encodings and one frequency encoding. No slice selection is required. This latter encoding mode will not be detailed here; more information can be found in Brunner and Ernst (1979). 3.2.4 Imaging Sequences

An imaging sequence consists of interlaced rf-pulses and gradients. There is a great number of possible sequences, depending on what we want to see, but also on what we can see. Here, only the two basic spin-echo and gradient echo sequences will be introduced, to reveal the importance of the extrinsic and intrinsic parameters on the nature of the signal obtained, in particular on the quantitative aspects. Some others sequences such as parametric imaging and solid-like imaging could be of interest for particular applications in the context of this chapter, but will not be discussed in detail. 3.2.4.1 The Spin–Echo (SE) Sequence The spin–echo sequence is the basic MRI sequence described by Fig. 3.10. The amplitude of the signal in each voxel (v) of the image is given by the expression:

Av ðSEÞ ¼ krv ð1expðT R =T 1;v ÞÞexpðT E =T 2;v Þ

ð3:11Þ

where k is a constant which depends on the imager characteristics, TR and TE are the repetition and echo times which are the characteristic delays of the sequence, rv is the volumetric proton density, and T1,v and T2,v are the longitudinal and transverse relaxation times of water protons contained in each voxel.

Fig. 3.10 A typical spin–echo sequence.

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Fig. 3.11 A typical gradient–echo sequence.

3.2.4.2 The Gradient–Echo (GE) Sequence In a gradient echo sequence, a gradient is used instead of a 180 rf pulse to rephase the spins, see Fig. 3.11. The amplitude of the signal in each voxel of the image can now be expressed as

Av ðGEÞ ¼ krv ð1expðT R =T 1;v ÞÞexpðT E =T 2;v Þ

sin a 1expðT R =T 1;v Þcos a ð3:12Þ

For a ﬁxed TR/T1 ratio, the optimal a angle (Ernst angle), for which the signal amplitude is maximal, is extracted from the relation: cos a ¼ expðT R =T 1 Þ

ð3:13Þ

Imaging with a gradient echo is intrinsically more sensitive to magnetic ﬁeld inhomogeneities, and also to magnetic susceptibility differences that can exist in the sample (for example at air/water interfaces), because of the use of the refocusing gradient. On the other hand, use of a small ﬂip angle a and of a gradient for refocusing the magnetization vectors provide this sequence with a time advantage. Therefore it is widely used for fast scan images, including 3D acquisitions.

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples 3.3.1 Some General Data about the Materials

Paper is built up of a porous network of cellulose ﬁbers with typical diameters of 15–30 mm and lengths of 1–5 mm as well as some ﬁllers and chemical additives. The

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

ﬁbers are oriented in the plane of the paper with a preferred orientation in the machine direction (explained in the following). The paper is made on a paper machine as a continuous web 5–10 m wide by forming the paper structure from a suspension of 0.5–1% of cellulose ﬁbers. The water is subsequently removed in the forming, in the press and in the drying sections so that the ﬁnal paper contains 93–97% of dry matter. The basis weight of a paper is given by the total amount of dry matter content per square meter of paper. It varies from 40 g m2 for newsprint up to about 500 g m2 for high basis weight cardboard. This parameter is often used to deﬁne the experimental conditions and gives a clear indication of the thickness of the paper studied. Two different porosity scales exist in paper. The inter-ﬁber pores are pores that are formed between the ﬁbers with pore sizes of the order of 0.5–10 mm. The intra-ﬁber pores are pores in the walls of the cellulose ﬁbers with sizes below about 1 mm. Initially both inter- and intra-ﬁber pores are saturated with water. As the web dries, ﬁrst the inter-ﬁber water is removed, followed by removal of the water in the intraﬁber pores. The intra-ﬁber pores collapse during dewatering, so that essentially non-porous ﬁber walls are obtained. One parameter of importance for the discussion of water removal is the ﬁber saturation point (FSP), which is the total amount of water that can be contained in the intra-ﬁber pores. Typical values are in the range of 1–2 g water/g solid – depending on the type of trees used, the pulping process (chemical, mechanical etc.) and the treatment in different processing steps. In this context it should be noted that cellulose is a hygroscopic material with a maximum hygroscopic moisture content of about 30%. The properties of the web and the ﬁnal paper (such as basis weight, mechanical strength etc.) vary with the following directions: .

.

.

MD, machine direction; the direction in which the web moves in the paper machine; CD, cross-direction, across the width of the web and perpendicular to the machine direction; ZD, z-direction, the thickness direction perpendicular to the plane formed by MD and CD.

A pulp sheet is essentially a paper with a random or oriented distribution of ﬁbers in the plane and a basis weight of 750–1500 g m2, resulting in a thickness of about 1.5–3 mm. Moisture transport in cellulose structures is of high importance in a number of processing steps, in the retailing step as well as during ﬁnal consumer applications. During drying of paper most of the water is initially located in the intra-ﬁber pores. Water will either evaporate in these pores and diffuse in the gas phase to the surface of the paper or migrate as a liquid to the surface and evaporate there. Since the dry ﬁber is non-porous, the result is shrinkage in the CD and ZD of the web. This has a strong inﬂuence on a number of quality parameters such as tensile strength, sheet ﬂatness and surface smoothness. Another application that involves moisture transport is the coating process, where a coating color layer is applied to a dry base paper resulting in

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transport of water and chemicals into the base paper. Typical ﬁnal consumer applications of moisture transport are water uptake in baby diapers and soaking of water in corrugated packages resulting in loss of mechanical strength. 3.3.2 Overview of Previous Results 3.3.2.1 Pulp, Paper and Cellulose Samples The ﬁrst application of the MRI technique to study water distribution and transport in paper or pulp samples was reported by Nilsson et al. (1996). In their work the water distribution in a 4 mm thick cellulose cylinder was measured with a Bruker 24/30 MR imager with a magnetic ﬁeld strength of 2.4 T. The sample consisted of a 42 mm cylindrical plug of pulp which was prepared from dry commercial sulfate softwood pulp. The sample was dried by blowing room-temperature air over the sample holder, resulting in drying times of over 3 h, approximately 50 times longer than under industrial conditions. The instrument was used with a TR time of 2 ms and a TE time of 1.1 ms, and a spatial resolution of 0.39 mm was obtained. By using pulp slices with different known moisture contents a linear correlation between the moisture content of the pulp samples and the MRI signal was established. The experimental conditions resulted in an average drying rate of 8 105 kg m2 s1. It could be shown that the drying took place at a decreasing drying rate. Bell-shaped curves were obtained for the moisture distribution. The experiments were later improved by Bernada et al. (1998a,b), to reach a higher spatial resolution and a higher drying rate, that means conditions more representative of those employed in the industrial process. This was accomplished by increasing the drying air temperature and using industrial pulp sheets. The authors were able to measure the distribution of water with a spatial resolution of 0.15 mm during the drying of samples approximately 2.5 mm thick. The improvements in spatial resolution were brought about by improvement in imaging hardware, the use of a higher ﬁeld magnet and modiﬁcations of the imaging protocol. Evaporation could take place from both surfaces of the samples. Drying times were about 10 min for the highest temperature used (87.5 C), or about twice the time applied in an industrial dryer. The moisture proﬁles measured at this temperature are shown in Fig. 3.12. The curves are bell-shaped and somewhat shifted to one of the open surfaces, indicating that transport to this surface is enhanced by higher heat or mass transfer coefﬁcients. Leisen et al. (2001) studied in-plane moisture transport for a number of cellulose samples. The samples were handsheets, paperboard and a polyethylene-coated paperboard with thicknesses between 0.53 and 2.1 mm. The ratio of the sonic moduli MD/CD ranged between 1.7 and 6.8, showing a strong variation of the anisotropic ﬁber orientation of the samples. The samples were studied in a Bruker instrument with a magnetic ﬁeld strength of 9.4 T. The drying time was about 8 h, and the images showed annular patterns of reduced intensity as the samples dried from the outside edge. No anisotropy could be detected for the moisture proﬁles and, thus, the diffusional resistance should have been the same in all directions of the plane.

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

Fig. 3.12 Moisture profiles obtained by Bernada et al. (1998b) at an air temperature of 87.5 C and a relative humidity of 4 %. Drying times between 0 and 14 min.

In a subsequent work Leisen et al. (2002) studied diffusion in paper at moisture contents below 20%, thus in the hygroscopic range for the product. This is a more challenging task due to the lower amounts of water and the increased interactions with the solid phase. The paper samples used were prepared from southern pine bleached kraft and consisted of two sheets each with a basis weight of 468 g m2. The average sheet thickness of the dry sample was 1.2 mm. Samples with a diameter of 17 mm were analyzed in the instrument. Their moisture uptake was studied by placing them between a humid environment obtained from distilled water and a dry environment established by locating a dessicant on top of the paper sample. Because of the low moisture contents in the paper, the acquisition times were up to 68 min. The results show that quite long times are needed to establish equilibrium between the gas and the solid phases. When moisture could penetrate through only one surface, equilibrium was not established at the ﬁnal experimental time of about 55 h, while when moisture could penetrate through both surfaces some kind of equilibration could be seen after 3 h. Finally a model was developed, which was able to describe the gas diffusion in the inter-ﬁber pores and liquid diffusion in the solid cellulose. Harding et al. (2001) presented moisture proﬁles during drying of industrial cardboard samples at a resolution of 15 mm. These results will be discussed in more detail in Section 3.3.3.

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3.3.2.2 Wood A very good overview of NMR and MRI for wood applications is given by Bucur (2003). This includes not only measurements of moisture proﬁles and self-diffusivities during drying but also describes how the techniques have been used to study wood structure and decomposition processes taking place in this material. A relatively large number of publications deal with the interactions between water and wood and the determination of moisture content while the number of publications on applications of the technique to drying is rather limited. Some results have been presented by Lindgren (1994) with one-dimensional images of pine during drying from a moisture content of 27 to 11%. Other results for wood were communicated by Flibotte et al. (1990) and Olson et al. (1990). Menon et al. (1987) were one of the ﬁrst groups to use NMR for the quantitative measurement of water in wood materials. In this work fundamental data for the free induction decay were presented and these data, together with knowledge about the composition of the wood, were shown to give the same values for the total moisture content in the wood sample as is traditionally achieved from the oven-dry method. Drying was used as a means to change the average moisture content but no moisture proﬁles were measured in the samples. Rosenkilde (2002) investigated a number of different techniques (slicing, X-ray tomography, MRI) for measuring the distribution of moisture in wood samples during drying. Using X-ray the resolution was limited to 240 mm and, since this technique measures the overall density of the material, the solid density must be known in order to calculate the moisture content at different positions in the sample. This led the author to prefer the MRI technique for analyzing moisture gradients at small distances from the surface of a wood cylinder during drying (Rosenkilde and Glover, 2002; Rosenkilde et al., 2004). In the ﬁrst set of experiments, samples of Scots pine shaped as cylinders with a diameter of 14 mm and a length of 20 mm were used (Rosenkilde and Glover, 2002). The samples were sealed by means of plastic tape except on one end of the cylinder so that moisture transport took place through this surface. The initial moisture content was 1.16, and the samples were dried by blowing air with a velocity of 3 m s1, a temperature of 43–46 C and a relative humidity of 16–18% parallel to the open surface. The magnetic ﬁeld strength at the sample surface was 0.7 T and the ﬁeld strength normal to the wood surface was 17 Tm1 resulting in a very high resolution of 13 mm per pixel. The signal was converted to moisture content by comparing with the initial proﬁle in the sample which was assumed to be ﬂat. Some results for the moisture proﬁles are shown in Fig. 3.13. During the ﬁrst 4 h the proﬁles show a steep gradient in the ﬁrst 90 mm of the sample and are then almost ﬂat. Surface roughness was probably not the reason for the steep gradients at the surface. Other possibilities could be structural changes in the samples resulting in differences in the transport resistance for water or kinetics for the hygroscopic equilibrium between wood and the surrounding air. Hameury and Sterley (2006) used MRI to study the buffering capacity of wood materials to passively reduce the indoor humidity ﬂuctuations resulting from internal moisture loads and outside humidity ﬂuctuations. The moisture gradients were

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

Fig. 3.13 Normalized moisture profiles as presented by Rosenkilde and Glover (2002); 0.5 (o), 1 (x), 4 (), 19 (^), 24 ( þ ) h.

measured in a 12 mm cylinder fabricated from Scots pine. One surface of the cylinder was exposed to step changes in the relative humidity between 20 and 80% and the moisture was recorded in the sample with a resolution of 127 mm and a total ﬁeld of view of about 27 mm. Since the average moisture content of the sample was only 7–9%, the water bound to the solid matrix had very short transverse relaxation times. This problem was overcome by applying a method based on the single-point imaging sequence, also known as constant time imaging. This sequence is similar to the SPRITE sequence presented by MacMillan et al. (2002). Good data were presented showing that the moisture exchange between the wood and the environment is limited to a few mm below the surface of the material. The moisture buffering value could also be predicted with good accuracy from the moisture proﬁles. van Houts et al. (2004, 2006) investigated by means of MRI the water penetration into two different sizes of oriented strandboard (similar to plywood). In the ﬁrst paper a micro-imaging instrument was used allowing samples with dimensions of 11 15 mm2 to be studied. The second study was conducted in a body scan instrument where 152 152 mm2 samples could be investigated. In a specially designed glass tube the samples were initially soaked with water, the water was removed and the concentration of water in the samples was measured. This procedure was repeated for the required number of times up to a total soaking time of 180 min. Water penetration could be monitored quite well but for some reason only the water in the voids of strandboard was detected but not the free water within the solid wood. The self-diffusivities for water in Douglas ﬁr were reported by MacGregor et al. (1983) to be 1.2 109 m2 s1 in the longitudinal direction of the ﬁbers and 0.36 109 m2 s1 in the direction perpendicular to the ﬁbers. This indicates that water mobility along the ﬁbers is higher than that in the transverse direction. The reported data are close to the data reported for cellulose ﬁbers in paper samples, see Section 3.3.3.5.

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3.3.3 Determination of Moisture Gradients in Cardboard Samples

In this section the experiments performed by Harding et al. (2001) and Wessman et al. (2000) using MRI for determination of moisture proﬁles during drying of cardboard samples will be presented and discussed in detail. 3.3.3.1 Experimental Conditions A fresh, never previously dried composite cardboard sample taken after the press section from the production facilities of ASSI Dom€an Fr€ ovi was used in this study. It was stored in a cold room until the measurements were made. The storage time for the last piece of the sample was roughly 4 weeks. The cardboard is a three-layer composite with the composition described in Tab. 3.1. The CTMP (chemical thermo mechanical pulp) had undergone mild chemical and heat treatment as well as mechanical reﬁning which breaks up the lamellae in the ﬁber wall. The kraft pulp undergoes aggressive chemical and heat treatment during production which dissolves the lignin hence allowing the lamellae to separate and swell. Pulped broke refers to pulp from a bad batch that has been recycled – this could therefore contain pulp of any grade, with possibly smaller pores due to the initial drying process. The basis weight, dry thickness, density and initial water content of the complete composite sample and the three separated layers were determined by sample weighing and thickness measurements which were carried out in accordance with standard techniques (ISO 534). For the calibration, 3D imaging and diffusion experiments samples were slowly pre-dried to water contents of 1.0, 0.8, 0.6, 0.4, and 0.2. An additional sample was prepared by adding water to the cardboard sample to produce a water content of 2.0. The basis weight, dry thickness, density and initial water content of the complete composite sample and the three separated layers are given in Tab. 3.2. The error limits represent the standard deviation from measurements on four samples. The thickness of the composite sample is signiﬁcantly less than the sum of the thicknesses of the three individual layers once separated. This is due to the disruption of the ﬁber structure during the process of separating the layers. For this reason the thicknesses of the three layers after separation can only be taken as an indication of their relative thickness in the composite rather than as a measure of the absolute thickness of each layer in the sample. This result highlights the great advantage of non-invasive techniques such as NMR imaging that can monitor properties of the different layers without disrupting the ﬁber system. Tab. 3.1 Composition of the composite cardboard sample.

Layer

Pulp composition

Top Middle

Bleached kraft pulp birch/pine (70/30) þ 7% ﬁller material CTMP (Chemical Thermo Mechanical Pulp) 40%, unbleached kraft pulp 30%, pulped broke 30% Unbleached kraft pulp

Bottom

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples Tab. 3.2 Basis weight, thickness, density and initial moisture content for the separated layers and the composite cardboard sample.

Layer

Basis weight (g m2)

Thickness (lm)

Density (kg m3)

Initial moisture content

Top Middle Bottom Total for 3 layers Composite sample

78 2 116 2 50 1 244 5 239 2

174 14 365 15 142 8 681 16 559 33

449 58 319 12 352 11 358 13 428 20

1.63 0.05 1.33 0.03 1.62 0.20 1.49 0.06 1.45 0.06

All NMR imaging and diffusion measurements were carried out using a Bruker DRX 400 spectrometer, equipped with micro-imaging accessories and an 8 mm coil, unless otherwise stated. The data were then transferred to the program Matlab for further processing and analysis. 3.3.3.2 Drying Experiments and MRI Parameters One of the particular challenges encountered when using MRI to study water distribution in wood pulp cellulose ﬁbers is the short T2 (spin–spin) relaxation time of the water. The T2 relaxation time is typically between 1 and 6 ms and decreases with decreasing water content. Special attention was therefore paid to the choice of imaging procedure. A one-dimensional spin–echo method was chosen to allow fast acquisition times, maximize signal to noise and prevent susceptibility problems associated with gradient reversal methods. However, if the echo time employed in the imaging sequence is not less than about ﬁve times the T2 relaxation time, the signal recorded will be attenuated – and thus not directly a true representation of the water content in the sample. For this reason efforts were made to minimize the echo time. The effects of T2 attenuation were directly accounted for also by explicitly measuring the T2 relaxation time of the water across the proﬁles at each time point. The geometry of the cell and sample positioning was chosen to ensure onedimensional mass transport in the region of interest during drying and the imaging experiment was designed to yield one-dimensional water concentration proﬁles across the thickness of the cardboard sample. A specially designed Teﬂon sample holder was built to hold the cardboard sample in a vertical position within an open ended 8 mm glass tube, as shown schematically in Fig. 3.14. A section of the wet cardboard, approximately 30 mm by 7 mm, was cut and placed in the holder, positioned in the coil of the NMR probe. A small funnel was ﬁtted to the base of the tube to form a seal with the air supply outlet. The air temperature was controlled using a thermocouple and a heating element within the NMR imaging probe head. The sample was positioned across the diameter of the tube so that the drying air stream ﬂows evenly over the two faces of the cardboard allowing the sample to dry from both surfaces. The sample was positioned in a random orientation in the x–y plane (deﬁned in Fig. 3.14) so that any non-uniformity in the air ﬂow through the probe would not lead to systematic artifacts in the ﬂow pattern over the cardboard sample.

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Fig. 3.14 Cardboard sample holder showing imaging plane and region of selected profile.

Prior to the start of drying an initial horizontal 2D cross-sectional image of the cardboard sample was acquired to determine the orientation of the sample within the x–y plane. The direction of the 1D proﬁle was then set so that it was aligned perpendicular to the surface of the cardboard – across the thickness of the sample. The slice selection gradient was aligned parallel to the surface of the cardboard so as to selectively image only the central region of the cardboard sample. This eliminated the signal from the cardboard near the sample holder which may prevent evaporation from this region. The sample positioning procedure took approximately 4 min. After the air ﬂow was started the series of experiments were performed at regular intervals until the signal intensity had dropped below the noise level or no further signal intensity loss occurred. A spin–echo {90 (hard) – 180 (soft) – echo} pulse sequence was used for 1D proﬁling. Proﬁles containing 128 points were acquired across a ﬁeld of view of 2 mm giving a spatial resolution of 15.6 mm/pixel. The slice thickness of the proﬁle was 2 mm and slice selection was achieved by application of a 250 ms Gaussian soft pulse in combination with a 3 G cm1 gradient. A spectral width of 100 kHz was used for data acquisition and the read gradient strength was 178 G cm1, giving an echo time of 1.625 ms. A repetition time of 6 s was used and typically four scans were co-added giving a total acquisition time of 24 s. A long repetition time was used to minimize effects due to T1 attenuation. In addition, after the acquisition of each proﬁle a series of eight T2 weighted proﬁles were obtained by using a pre-conditioning Hahn echo module {90 (hard) – tT2/2 – 180 (hard) – tT2/2 – proﬁle} prior to the proﬁle acquisition with additional T2 delays, tT2 of 0.2, 0.4, 0.8, 1.2, 1.6, 2, 4 and 6 ms. The intensity of each point in the proﬁle, S, in the set of T2 weighted proﬁles acquired

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

with additional T2 delay tT2, was ﬁtted to the relationship S tT2 ¼ exp T2 Sð0Þ

ð3:14Þ

where S(0) is the signal intensity corrected for the effect of the delay tT2. The proﬁle of T2 relaxation times was then used to correct the signal intensity in the proﬁle for attenuation due to the echo time of 1.68 ms implemented in the proﬁling sequence. Before the start of drying and at regular intervals during drying at the slower drying rates studied, a set of T1 weighted proﬁles was also acquired using a pre-conditioning inversion recovery module {180 (hard) – tT1 – proﬁle} prior to proﬁle acquisition. The intensity of each pixel, S, in the set of T1 weighted proﬁles acquired with delay tT1, was ﬁtted to S tT1 ð3:15Þ ¼ 12exp T1 Sð0Þ where S(0) is the signal intensity corrected for the effect of the T1 weighting delay tT1. During drying at the slower drying rates studied two-dimensional slice selective images were also acquired with the help of a spin–echo slice selective imaging sequence. The read direction was oriented across the thickness of the cardboard. The ﬁeld of view was 2 and 8 mm in the read and phase directions, respectively. The image size was 128 16 providing a spatial resolution of 15.6 and 500 mm/pixel, respectively. The slice thickness was 8 mm. Typically, a repetition time of 4 s was used and 2 scans were co-added giving a total acquisition time of just over 2 min. Five different drying conditions were studied and the air temperatures, air ﬂow rates and air humidities used are given in Tab. 3.3. The air humidity was controlled by bubbling through a cylinder of water before passing the air into the imaging probe. Air moisture content was calculated from the wet and dry bulb temperatures. Three to six individual drying experiments were performed for each of the ﬁve drying conditions described in Tab. 3.3. By repeating the experiments, the reproducibility of results and the effects of sample variability could be assessed. 3.3.3.3 Calibration Procedure In order to test the quantitative nature of the proﬁling, experiments were carried out on samples prepared with water contents of 2.0, 1.0, 0.8, 0.6, 0.4, and 0.2 as well as on the original wetted sample (with a water content of 1.45). These samples were placed Tab. 3.3 Air temperatures, air flow rates and air humidities used in cardboard drying experiments.

Run

Temperature ( C)

Air flow rate (l h1)

Air moisture content (kg H2O/kg dry air)

Wet bulb temp. ( C)

A B C D E

60 20.5 60 20.5 20.5

400 400 135 135 135

0.0025 0.0025 0.0025 0.0025 0.0125

22.4 8.7 22.4 8.7 18.4

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in the cardboard holder and sealed using polymer ﬁlm to prevent drying during the measurement procedure. One dimensional proﬁles, T1 and T2 relaxation weighted proﬁles and slice selective images were acquired as described above for the drying experiments. A capillary containing water with a small amount of copper sulfate to reduce the T1 relaxation time to approximately 1 s was then placed adjacent to the cardboard sample. The imaging experiments were repeated using a ﬁeld of view of 4 mm (rather than 2 mm) across the sample thickness to allow the capillary to be simultaneously imaged. The use of the capillary as a reference sample allowed the water signal intensity from the cardboard to be directly quantiﬁed. By comparison of the directly quantiﬁed proﬁles with the proﬁles acquired without the reference capillary, using the same imaging scheme as applied in the drying experiments, a scaling factor was determined. This factor was then used to convert the signal intensity of the proﬁles acquired during drying into a water concentration. On some of the calibration samples relaxation weighted proﬁles were acquired using up to 32 variable delay times to test the assumption that the signal is characterized by a single relaxation time constant at each spatially resolved point. Water concentration proﬁles, and proﬁles of the water T1 and T2 relaxation constants for the calibration samples studied are shown in Fig. 3.15. In this and

Fig. 3.15 (a) Water concentration profiles, (b) T1 relaxation profiles, (c) T2 relaxation profiles for moisture contents of 0.2 (o), 0.4 (&), 0.6 (}), 0.8 (x), 1.0 ( þ ), 1.4 (~), 2.0 (.).

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

in all other comparable ﬁgures the cardboard proﬁles shown have been oriented such that the top layer described in Tables 3.1 and 3.2 is to the left-hand side of the proﬁle. For all the calibration samples studied the T1 and T2 weighted proﬁles showed a good ﬁt to Eqs. 3.14 and 3.15, which assume a single relaxation constant at each spatially resolved point. This was true even when up to 32 variable time delays were acquired and used in the ﬁtting procedure. The T2 relaxation time of the water in the cardboard decreased signiﬁcantly with water content, varying from around 4.8 ms for a sample a with water content of 2.0 to 2.1 ms for the sample with a water content of 0.2. The T2 relaxation time was fairly constant across the sample, but showed a slightly higher value in the lower layer. The T1 relaxation time showed a similar decrease with water content. However, for all calibration samples studied, the T1 relaxation time in the upper layer was signiﬁcantly longer than in either the middle or lower layers. This could be a consequence of the bleaching process – perhaps removing some impurities that act to reduce the T1 relaxation time of water in the other, nonbleached layers. The water concentration proﬁles shown in Fig. 3.15a have been extracted from two-dimensional cross-sectional images by averaging over the central 4 mm region of the cardboard sample in the image. The proﬁles were scaled to the intensity of the water from the capillary placed adjacent to the sample and corrected for the effects of relaxation contrast according to Eqs. 3.14 and 3.15. By scaling to the intensity of pure water the proﬁles could be made quantitative and expressed in terms of g cm3. The total amount of water in the calibration samples was calculated by summing across the water concentration proﬁles and dividing by the pixel resolution (15.6 mm). Figure 3.16 shows the calculated total water mass per area (in g m2) as a function of the water content of the calibration samples. Error bars represent standard deviation between proﬁles extracted at varying positions across the two-dimensional image of each sample. Linear ﬁt to the data gave a slope of 168 3 g m2 before correction for

Fig. 3.16 Total water determined from NMR profiles versus water content of samples before (&) and after (*) correction for relaxation effects.

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relaxation effects and 225 6 g m2 after correction. The data show that the total amount of water in the samples determined by the NMR imaging experiments is directly proportional to the water content determined by sample weighing. The gradient of the linear ﬁt is slightly lower than the measured basis weight of the cardboard (239 2 g m2), but this difference may be due to water loss during sample transportation, positioning in the magnet and general sample variability. Also shown in Fig. 3.16 is the total water that would be determined from the results if no correction were made for relaxation contrast effects. A linear ﬁt to this uncorrected data has a signiﬁcant non-zero intercept and a lower slope than the relaxation corrected data. This emphasizes the need to correct for relaxation contrast in order to obtain quantitative proﬁles during the whole of the drying process. The water concentration proﬁles of the calibration samples and the initial proﬁles acquired in the drying experiments clearly show a higher water concentration in the two outer layers than in the middle layer. Assuming that the thicknesses of the three layers are in the same proportion to each other in wet and dry samples, the relative concentration of water in the three layers can be calculated from the data shown in Tab. 3.2 to be 0.42 0.06, 0.24 0.02 and 0.33 0.02, respectively. This can be compared with the ratios determined by averaging all initial proﬁles acquired in the drying experiments. The water concentration in each layer was determined by dividing the total proﬁle into regions in the proportion of the dry layer thickness and then averaging across the central half of each layer. This gave relative water concentrations in the three layers of 0.38 0.02, 0.26 0.01 and 0.35 0.3, respectively. The errors quoted represent the standard deviation between samples and within these errors the ratios determined from the NMR imaging proﬁles are in agreement with those determined by standard weighing and measuring techniques. 3.3.3.4 Results for Drying Profiles Figure 3.17 shows typical results for the temporal evolution of the water concentration proﬁles across the thickness of cardboard samples drying under varying conditions. The proﬁles were corrected for T2 relaxation attenuation and then scaled to units of g cm3 using the scaling factor determined from the calibration experiments. Due to the variation in the time scale over which drying occurs the time interval between successive proﬁles is different for the different drying conditions. Clearly the outer layers of the cardboard initially contain more water than the middle layer. It should be pointed out again that the samples have been taken after the press section of an industrial machine and have been stored in a cold room for 1–4 weeks. The outer layers consist of bleached kraft pulp, most probably with a higher FSP than the middle layer where the main component is a mechanical pulp. The moisture distribution in the layers as the paper leaves the press section could not be measured and thus it is difﬁcult to argue if the proﬁles measured are the actual proﬁles on the machine or a result of moisture redistribution phenomena until the measurement took place. However, considering the FSP-values discussed above it seems reasonable that the proﬁles measured are also the proﬁles on the machine.

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

Fig. 3.17 Temporal evolution of water concentration (g m3) across the thickness of the cardboard samples during different drying conditions. (a) Run A: profiles shown at 30 s intervals, (b) run B: profiles shown at 1 min intervals, (c) run C: profiles shown at 1 min intervals, (d) and (e) run D (repeated experiment): profiles shown at 2 min intervals, (f) run E: profiles shown at 10 min intervals.

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Fig. 3.18 Cardboard thickness determined from NMR profiles for calibration samples (x) and for in situ drying experiments (.).

Initially more water is removed from the outer layers, resulting in a paper with relatively even moisture content. The bell-shaped proﬁles reported by Nilsson et al. (1996) and Bernada et al. (1998a,b) could be observed in run A but were not clearly seen in the other experiments. Instead moisture gradients appeared at the surfaces (considering shrinkage) while the moisture content inside the sample was close to constant. This indicates a rather rapid redistribution of water in the middle layer caused by high liquid diffusivities. These results were not conﬁrmed by the diffusion measurements, see Section 3.3.3.5. During drying the water concentration proﬁles decrease in intensity and width with time. Figure 3.18 shows that the width of the water proﬁle with an intensity above 0.1 of the maximum decreases approximately linearly with the water content, approaching the dry cardboard thickness in the limit of low water content. Moreover, the data follow the same trend as for the calibration samples in which the liquid distribution has fully equilibrated. There was no signiﬁcant variation in the relationship between sample thickness and overall water content for drying under the varying conditions studied. This implies that for all conditions studied the retreat of the water distribution is due to the shrinkage of the cardboard sheet during drying rather than to the evolution of a receding evaporation front inside the sample. Up to a water content of 1.45 there is a linear relationship between sample thickness and the water content, however, there appears to be only a slight increase in the sample thickness between a water content of 1.45 and 2.0 (data not shown in Fig. 3.18). A linear ﬁt to the data for the calibration samples up to a water content of 1.45 gives a slope of 0.21 0.02 mm and an intercept of 0.61 0.02 mm, which compares well with the dry sample thickness of 0.56 0.03 mm determined by standard thickness measurement techniques. Figure 3.19 shows the temporal evolution of T1 and T2 relaxation times. As expected, both relaxation rates decrease with decreasing water concentration and show similar trends with water concentration, as observed for the calibration samples in Figure 3.15a and b. By summing across the proﬁles the total amount of water in the samples can be evaluated as a function of time and from this the drying rate can be calculated. Such

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

Fig. 3.19 Temporal evolution of (a) T1 relaxation profiles and (b) T2 relaxation profiles during drying with conditions E. Profiles were acquired at 10 min intervals.

data are analogous to the drying kinetics as would be obtained, for example, by sample weighing. The effect of drying conditions on the drying kinetics is shown in Figs. 3.20 and 3.21. Figure 3.20 shows the variation in total water with time and Fig. 3.21 depicts the drying rate as a function of water mass per area in the sample. The drying rates increase with increasing temperature and air ﬂow rate and decrease with increasing

Fig. 3.20 Average total water mass per area as a function of drying time. Data are shown for drying conditions A (*), B (&), C (}), D (x), E ( þ ).

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Fig. 3.21 Average drying rate against water mass per area during drying. Same legends as for Fig. 3.20.

humidity. For the 60 C experiments the cardboard is ﬁrst heated, which results in an initial increase in drying rate. The constant drying rates that can be calculated based on the difference in dry and wet bulb temperatures and the heat transfer coefﬁcient between air and cardboard are close to the maximum values presented in Fig. 3.21. Further insight into the drying process can be gained by studying the evolution of shape of the drying proﬁles over time. Analysis and comparison of the shapes of proﬁles under varying drying conditions is, however, complicated by several factors. First, due to sample variability the initial proﬁles show some variation in water content. The initial water content is not evenly distributed across the sample thickness but changes signiﬁcantly between the different sample layers. During the drying process the sample shrinks and so the physical position of a particular region of ﬁbers in the proﬁle changes. It is also possible that the sample develops a slight curvature during the drying process so that it is slightly misaligned at the end of drying. The overall rate of drying varies signiﬁcantly with the drying conditions so for a fair comparison of the shape of the proﬁle the different time scales involved must be compensated for. Some of these issues are to a large extent unavoidable. However, efforts were undertaken to compensate for the initial distribution of water concentration, the sample shrinkage and the varying time scales of drying. First, attempts were made to convert the distance scale to the cardboard frame of reference. This was achieved by deﬁning the length of the proﬁle as the region of the proﬁle with intensity greater than 40% of the maximum intensity and then re-scaling each proﬁle so that the proﬁle covered the same number of points, using a nearest neighbor interpolation method. To compensate for the initially uneven distribution of water in the

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

Fig. 3.22 Temporal evolution of normalized moisture content against normalized thickness for drying under (a) condition A and (b) condition E.

sample, all proﬁles were divided by the initial proﬁle acquired prior to the start of drying. Finally, to compensate for the varying time scales of the drying process the temporal evolution at each position was re-scaled to give the same number of proﬁles up to the point when the overall drying rate fell below 0.02 g m2 s1. Typical results of this analysis are shown in Fig. 3.22 for the experiments with the fastest overall drying rate (run A) and the slowest drying rate (run E), respectively. The proﬁles for the fastest drying rate show the development of a clear gradient as drying progresses, indicating that proportionally more water is lost from the outer layers of the cardboard than from the inner layer. This can be compared with drying at the slowest drying rate where the normalized proﬁle remains much ﬂatter during the drying process. At small drying rates water loss appears to be more uniform over the entire thickness of the cardboard. 3.3.3.5 Diffusion Measurements Further insight into the self-diffusivity of water and the mean pore sizes of the considered materials can be achieved with the so-called pulsed gradient spin–echo (PGSE) techniques. Such measurements were performed for the cardboard samples with the equipment as before. PGSE NMR measurements were conducted on the calibration samples and the original wetted sample. A stack of 5 cardboard samples approximately 5 mm by 30 mm was wrapped in plastic ﬁlm and placed vertically in a sealed 8 mm NMR tube. An initial horizontal 2D cross-sectional image of the cardboard stack was acquired to determine the orientation of the thickness direction. The stimulated echo PGSE scheme developed by Stejskal and Tanner (1965) was used in the diffusion measurements. The diffusion was measured over a time interval D, which was varied between 15 and 100 ms, and the diffusion gradient duration d was 2 ms. For each value of D studied, the gradient strength was varied in 32 even increments up to a maximal value of 194 Tcm1. Experiments were carried out with the diffusion gradient applied either parallel or perpendicular to the thickness direction. In addition to the

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measurements on bulk samples, a set of diffusion weighted proﬁles was acquired for several calibration samples using the experimental set-up designed for the drying and calibration experiments. These experiments were used to test the similarity of the diffusion characteristics of the different layers in the composite sample. The diffusion weighted proﬁles showed no variation in the rate of signal intensity decay with increasing diffusion gradient strength across the sample thickness. This indicates that the three layers in the composite sample display similar diffusion behavior. The signal to noise ratio of these proﬁles was considerably poorer than in measurements on bulk samples due to the smaller sample size and extended T2 weighting involved in the diffusion proﬁling technique. For this reason, more detailed evaluation of the PGSE results was restricted to analysis of bulk, spatially unresolved measurements. Figure 3.23 shows typical signal intensity attenuation measured in the PGSE experiment for varying values of the observation time, D. If the water within the cardboard is characterized by a single self-diffusion coefﬁcient and the motion is not limited by any boundaries a plot of the logarithm of signal intensity log(S) against g2G2d2(D d/3), where g is the gyromagnetic ratio for protons, should be a straight line, the slope of which would give the diffusion coefﬁcient D, by ﬁtting to the relationship (Stejskal and Tanner, 1965) S d ¼ exp D g2 G2 d2 D Sð0Þ 3

ð3:16Þ

It can be seen in Fig. 3.23 that such a plot does not give a straight line and there is signiﬁcant variation in the signal attenuation with varying D. The water within the cellulose ﬁbers does not behave as a bulk liquid. Such curved log attenuation plots are

Fig. 3.23 Results from the PGSE experiments for cardboard with a water content of 1.45. Data are shown for D times of 15 (o), 30 (&), 50 (}), 75 (x) and 100 ( þ ) ms.

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

usually indicative of either multiple diffusion regimes in the system, the diffusing species experiencing boundaries to their motion over the time scale of the diffusion measurement, or anisotropic diffusion, where the molecule motion is restricted to one or two dimensions. Pore sizes within the ﬁbers have been estimated by Scallan (1987), from solute exclusion techniques, to be in the range 2–20 nm. The molecular mean displacement hr(t)2i over time due to diffusion is given by the Einstein relation hr(t)2i ¼ 6Dt. The molecular mean displacement over the observation time D is much greater than the pore size. A water molecule would, consequently, move through several hundred pores even at the lowest water contents studied. The restriction caused by such pores would, thus, not lead to an observation time dependent diffusion coefﬁcient – but rather to a decrease in diffusion coefﬁcient compared to the free liquid. A model was therefore sought that results in a diffusion coefﬁcient that is independent of the observation time. For this reason, models such as the two-component diffusion model proposed by Li et al. (1992) to rationalize PGSE results of water in cellulose ﬁbers with higher moisture content than that used in the present study were not thought to be physically appropriate. Addams and Gladden (1999) interpreted PGSE results of water sorbed in cotton ﬁbers by means of a two-component exchange model. This two-component exchange model accounts directly for the changing shape of the attenuation plot with changing observation time, D, without having to assume an observation time dependence of the diffusion coefﬁcient. The two-component exchange model assumes the existence of two diffusion regimes and allows for exchange of molecules between the two environments during the observation time. The signal attenuation between the two phases is described by the relationships S d d 0 0 2 2 2 0 0 2 2 2 þ ð1p 2 Þexp D 2 g G d D ¼ p 1 exp D 1 g G d D S0 3 3 ð3:17Þ 9 8 1 1 1 > > > > D1 þ D2 þ 2 2 2 þ > > > > g d G t1 t2 > > < = 1 0 0 1 D 2; D 1 ¼ " # 2 > 2> > 2> > > 1 1 1 4 > > > > D þ þ þ D 2 1 ; : g2 d2 G2 t1 t2 g4 d4 G4 t 1 t 2 ð3:18Þ p02 ¼

1 D02 D01

ðp1 D1 þ p2 D2 D01 Þ

ð3:19Þ

p01 ¼ 1p02

ð3:20Þ

p1 ¼ 1p2

ð3:21Þ

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t 1 p1 ¼ t 2 p2

ð3:22Þ

according to K€arger et al. (1981) and Callaghan (1991). D1 and D2 are the diffusion coefﬁcients, t 1 and t 2 are the mean life times of molecules, and p1 and p2 are the relative populations in the two regions, respectively. Equation 3.17 was ﬁtted simultaneously to all the data acquired on each sample at different observation times, D. The ﬁt of the data to Eq. 3.17 is shown with solid lines in Fig. 3.23. The coefﬁcient of determination R2 for the ﬁts for all water contents studied was between 0.992 and 0.9999. The component corresponding to the region with faster diffusion was found to account for typically over 95% of the total water content of the system. The diffusion coefﬁcient of the major component, measured across the paper thickness has a value of 0.45 109 m2 s1 at a water content of 1.45 falling to 0.038 109 m2 s1 at a water content of 0.2. The decrease in this diffusion coefﬁcient with the water content in the sample is shown in Fig. 3.24 and indicates the shrinkage of pores in the ﬁbers with decreasing saturation. The diffusion coefﬁcient of the major component was found to be larger when measured parallel to the surface of the cardboard compared to when the measure-

Fig. 3.24 Fit of the diffusion coefficient of the major component for the PGSE experimental data to the two-component exchange model given by Eqs. 3.17–3.22; along the thickness direction (o) and perpendicular to the thickness direction (.) of the sample.

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

ments were made across the thickness of the sample. This can, again, be explained by considering that the pores within the ﬁbers are elongated along the ﬁber axis, providing, on average, less hindrance to diffusion than across the ﬁber. The value of the diffusion coefﬁcient corresponding to the minor water fraction averaged over all water contents studied was 0.014 109 m2 s1, which is consistently over one order of magnitude smaller than the coefﬁcient of fast diffusion. This low diffusion coefﬁcient, as well as the fractional populations of the two components and the mean life time of molecules in the two components, showed no signiﬁcant or systematic variation with water content or direction of diffusion measurements. The average values of the mean life times for the major and minor components were 1.1 and 0.04 s, respectively, and the relative populations were on average 0.97 and 0.03, respectively. A physical interpretation of the results of this model could be that the bulk of the water in the ﬁber can be characterized by a single diffusion coefﬁcient which is independent of the observation time, while it is in exchange with a small fraction of the total water that has a much smaller diffusion coefﬁcient. This water could, for example, be the moisture sometimes described as non-freezing or, perhaps, water absorbed in the amorphous regions of the cellulose ﬁbers. Knowledge of the diffusion coefﬁcient of water within the ﬁbers and, in particular, of the concentration dependence of this diffusion coefﬁcient is useful for modeling studies and can also help to determine rate limiting steps for the drying process. It is instructive to compare the diffusion coefﬁcients measured by the PGSE technique with the effective liquid diffusivities used for modeling moisture transport through the porous cellulose network. Li et al. (1992) reported data for the self-diffusivity in pulp samples with moisture contents between 4.5 and 7. The diffusivity for the bulk water between the ﬁbers was in the range 1.12–1.47 109 m2 s1 and the diffusivity for the restricted water in the oderman (2002) pores was between 0.14 and 0.49 109 m2 s1. Topgaard and S€ communicated values ranging from 4 1011 m2 s1 at a moisture content of 0.1 to 0.9 109 m2 s1 at a moisture content of 0.7. At this moisture content it can be assumed that most of the water is within the intra-ﬁber pores. All the experimental self-diffusivities presented above are below the self-diffusivity for free water at 25 C, which was given by Topgaard (2003) to be 2.3 109 m2 s1. At high moisture loads the difference is a factor of 2 while at low moisture content the difference is a factor of about 50. The liquid self-diffusivities measured by Topgaard and S€ oderman (2002) were used in a modeling study by Baggerud (2004) to calculate the moisture and temperature gradients in a number of paper and pulp samples. Mass transfer could occur both by gas phase and liquid diffusion through the porous materials. The liquid diffusivity was calculated according to 8 3:7 > :D0 1e174ðX FSP Þ ebðXX FSP Þ if X > X FSP

ð3:23Þ

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Fig. 3.25 Function for liquid diffusivities as presented by Baggerud (2004).

At moisture contents below the ﬁber saturation point the function was determined from a best ﬁt to the experimental data presented by Topgaard and S€ oderman (2002), while at moisture contents above the ﬁber saturation point an exponential function was added. Both D0 and b were used as ﬁtting parameters to moisture and temperature gradients. One example for liquid diffusivity over the whole range of moisture contents is shown in Fig. 3.25 for XFSP ¼ 1.0, D0 ¼ 1.0 109 m2 s1 and b ¼ 2 kg dry substance per kg water. The curve at moisture contents above the ﬁber saturation point results in liquid diffusivities which are clearly above the self-diffusivity of free water. The reason for this could be that in this region the ﬁbers are, by deﬁnition, saturated with water and excess water exists in the inter-ﬁber voids of the sheet. The transport of this water can take place by capillary redistribution phenomena, which are more rapid than liquid diffusion. Thus, the liquid diffusivity needs to be increased dramatically to account for this phenomenon. The data were used to predict the moisture and temperature proﬁles measured with the help of MRI by Bernada et al. (1998a,b); Jones (1969) and Lee and Hinds (1982). The values ﬁtted for D0 were in the range 2.98 1010 to 4.2 109 m2 s1, and for b between 2.67 and 6.5. Using these data quite good agreement was presented between the experimental and calculated moisture proﬁles. Since the model for the liquid diffusivity is partially based on self-diffusivity data, it seems reasonable to conclude that such data could be used, at least as a starting point, for modeling moisture gradients during the drying of various materials.

3.4 MRI Applications to Drying of Agricultural and Food Samples

3.4 MRI Applications to Drying of Agricultural and Food Samples 3.4.1 MRI and Transport Phenomena in Agricultural and Food Products

Food and biological products are complex and heterogeneous in structure and composition. They are submitted to internal and external heat and mass (especially water) transport phenomena during processing and storage that make them unstable and affect their physical, chemical and microbiological properties. Water is probably the most important component in biological systems and it inﬂuences many product characteristics: rates of chemical reactions, enzyme activity, rheological behavior, physical state, nutritional content and so on. Water content is the most commonly used parameter for describing water in a food product, but it is insufﬁcient for predicting its stability. Water activity (aw) provides a better and more reliable measurement of the availability of water and, therefore, food and biological scientists and professionals have widely accepted it for safety and quality control. However, water activity is a thermodynamic equilibrium property whereas foods are usually non-equilibrium systems (multicomponent and multiphase systems with delayed crystallization, hysteresis etc.). Moreover, water exists in different states with different functions in a product and it is helpful to quantify the amount of each fraction of water in a certain state or of certain mobility in order to predict the chemical or physical phenomena likely to occur. Food processes and products are commonly characterized by measurement of average values, providing a single value of one variable measured at a speciﬁc time, for example average moisture content during drying. Such measurements are useful in characterizing a given process and are, in many cases, sufﬁcient for process design or product development. However, they do not provide signiﬁcant information on the phenomena responsible for controlling product properties (McCarthy and McCarthy, 1996). NMR and MRI provide powerful probes of the microscopic and macroscopic changes occurring in foods during processing and storage, without altering the phenomena being measured. NMR spectroscopy can be used for applications ranging from routine, such as on-line control of moisture and fat contents in food production facilities (low-resolution systems) (McCarthy, 1994) or on-line detection of bruised tissues in fruits (Zion et al., 1995), to advanced, such as the determination of the molecular structure of proteins and the dynamics of water in biological systems (high-resolution MRI). Many chemical and enzymatic reactions are diffusion controlled; many food processing operations involve removal or absorption of water; undesirable migration of water during storage may limit the shelf-life of products. It is therefore of primary importance to be able to predict water mobility in the products. MRI techniques are well suited for distinguishing between water molecules of different mobility and enable non-destructive and fast monitoring of water migration in food and biological

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materials. They provide access to water diffusion on the basis of the spatial distribution and migration of water in the system (transient moisture proﬁles) and allow one to characterize the dependence of the diffusion coefﬁcient on water content. MRI is also a very promising technique for fundamental understanding of the inﬂuence of water in foods and for the localization of water in tissues. MRI has long been recognized as a powerful diagnostic tool and used for functional studies in cognitive research and for medical applications. By comparison, the development of this technique for bioproducts and, especially, foods is rather limited. This is mainly due to the low moisture content of many products (inducing low signal to noise ratios), to the small size and/or complex structures and compositions (requiring high resolution), to the fast dynamic processes (requiring short acquisition times) and to the difﬁculty for food scientists to access MRI instruments (Ruan and Chen, 1998). Hesitation in the use of MRI in food engineering can also be explained by the need to extract quantitative information from gray level images, from T1 and T2, or from self-diffusion maps. This implies the need to validate the interpretation of MR images and to explain spatial variations in the NMR signal. Contrast can be explained by macroscopic variations in 1 H density, variations in the composition in moisture or lipids, and modiﬁcations of the microscopic structure or at the molecular level. A complete analysis of the relaxation signals obtained by NMR measurement is, however, necessary to validate the interpretation of the image (Mariette, 2004). 1 H density measured by NMR depends on the composition of the sample. 1 H density maps have been used to detect holes or cracks and to measure moisture or fat content (after applying a correcting term function of T2 values). Spin–spin relaxation times (T2) are very sensitive to the composition and structure of products. In highly hydrated food products, T2 is a faithful tracer for moisture content. The multi-exponential nature of T2 relaxation curves has also been interpreted in terms of different pools of water with different mobility or in terms of proton exchange and has been used to characterize the water retention properties in macromolecules or the microscopic structure of cellular tissues. 3.4.2 NMR for Characterization of Biological and Food Products

Low-resolution NMR spectroscopy (or time-domain NMR) is a fast and precise technique that has many applications in the food industry. Most of them are based on very simple NMR pulse sequences (FID or Hahn-echo acquisition) used to measure the relaxation times or to perform pulse ﬁeld gradient experiments for exploration of diffusion properties (Todt et al., 2006). As previously mentioned in Section 3.2, the rate of decay of the NMR signal depends very much on the surroundings of H atoms. In a solid environment the decay is very rapid (within a few hundreds of microseconds or less); in a liquid it is much slower (up to seconds). This allows a distinction to be made between solids, oils and water based on the different decay times (Isengard, 2001). Moisture content can be quantitatively measured using the signal amplitude. Hahn-echo NMR pulse sequences permit simultaneous oil and moisture analysis in

3.4 MRI Applications to Drying of Agricultural and Food Samples

Fig. 3.26 Hahn-echo NMR pulse sequence for the determination of moisture and fat content in low moisture products.

low-moisture food samples (typically below 15%) by measuring both FID amplitude (S1) and echo amplitude (S2); with a previous calibration, S2 represents the oils content and S1 – S2 is related to the moisture content (Fig. 3.26). Such an analysis is fast and requires no sample preparation (no previous extraction). Such a procedure can be applied to a large variety of low moisture foods (cocoa or milk powders, snacks, cereals, bread, nuts and almonds, beans, cookies, ﬂour, starch etc.) or agricultural products (all types of seeds and residues) (Todt et al., 2006). In high moisture products, the NMR signal from water would interfere with the oil signal and samples must therefore be pre-dried. However, the use of pulsed ﬁeld gradient (PFG) NMR experiments allows one to separate the signal contributions of water and oil and to measure directly and non-destructively the fat content in fresh products. This method has been applied to sauces, mayonnaises, margarines and dairy products with fat contents in the range 4 to 80% (Todt et al., 2006) or to minced meat (Sørland et al., 2004). It can also be used for selecting high yield seeds (Rutledge, 1990). The technique is a fast and accurate alternative to the use of drying and solvent extraction for the determination of fat content in a biological system. It requires a low-ﬁeld NMR spectrometer equipped with a gradient probe and a stable gradient power supply. Low-resolution pulsed NMR provides valuable information on the mobility of water molecules and can serve to deﬁne different water fractions. Monteiro-Marques et al. (1992) proposed a rapid low-resolution pulsed NMR method (<1 min per sample) for monitoring pseudo-relaxation times T1 and T2 during the drying of foodstuffs. Since T2 is relatively proportional to moisture content, T1 can be plotted in real-time vs. T2 and presents a minimum corresponding to a particular water mobility and to a water activity close to 0.7. The same procedure was applied to the monitoring of freeze-drying of potatoes in real-time inside the probe head of the NMR spectrometer (Monteiro-Marques et al., 1991). It allowed detection of the sublimation endpoint or any abnormal fusion of the frozen core. These experiments also showed that water desorption from the external dry part of the product begins during the sublimation of a remaining frozen core. Cornillon (2000) applied pulsed NMR to the osmotic dehydration process and developed a non-destructive method for kinetics analysis. T1 was measured by an inversion–recovery pulsed sequence and T2 was

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evaluated by the Carr–Purcell–Meiboom–Gill (CPMG) method. The acquisition time for T1 and T2 was about 4 min per sample. For apples soaked in a 60 Brix sugar solution, relaxation times were found to decrease dramatically in the ﬁrst 3 h and then to level off until the end of the experiment, revealing a strong decrease in water mobility as sucrose penetrates into the tissues and some physical alteration of the cells due to processing. 3.4.3 MRI for Measurement of Transient Moisture Profiles in Food and Biological Samples 3.4.3.1 General Data A rapid increase in the application of 1 H-MRI to foods has been observed since the 1990s. The true potential of MRI lies not in static structure determination but in following, non-invasively and in real-time, dynamic changes in products during processing, storage, packaging and distribution (Hills, 1995). The dynamic information emerging from MRI is contained in real-time changes in images (or maps) of NMR parameters causing image contrast. Depending on the protocols, these include spatial maps of spin number density, relaxation times or self-diffusion coefﬁcients, the intensity contrast caused by the value of the considered NMR parameter. With careful calibration, NMR parameter maps can be converted into maps of quantities such as moisture content. In some cases, MRI measurements can be made in realtime under conditions identical to those used in processing, directly inside the bore of the imaging coil using non-magnetic supports. In most experiments, a tube ﬁlled with CuSO4-doped water and placed within the probative zone serves as reference for signal intensity. Song and Litchﬁeld (1990) ﬁrst reported the feasibility of using MRI for measuring 3D transient moisture distribution in food products during drying. They compared 3D-FT and multi-slicing (10 adjacent slices of 1.394 mm) 2D-FT methods for obtaining 3D 1 H density images of an ear of corn during drying at 60 C. The second method allowed shorter acquisition times (11 min compared with 68 min for the ﬁrst one) and was therefore more valuable for following drying experiments. Transient moisture proﬁles extracted from NMR images at different times of drying were used to analyze moisture transfer between and inside kernels and structural changes (shrinkage). They showed that moisture distribution in grains prior and during drying is generally nonuniform. However, resolution was not sufﬁcient for mass transfer study within small particles during drying. Song et al. (1992) proposed to improve the resolution by using a Hahn spin–echo pulse sequence for acquisition in an NMR spectrometer equipped with a micro-imaging system. Image acquisition time for one set of 3D data was 4.8 min and the voxel size (spatial resolution) was 93 156 312 mm3. Moisture changes during drying were calculated from 1 H density images, taking into account the variations in T1 and T2 vs. drying time in each voxel according to: A 1 1 ð3:24Þ rðHÞ ¼ k 1eT R =T 1 1eT E =T 2

3.4 MRI Applications to Drying of Agricultural and Food Samples

where r(H) is the proton density, A the signal intensity, tR the repetition time (total sequence performing time, TR ¼ 73 ms) and TE the echo time (time between the 90 rf-pulse and the formation of the spin echo, TE ¼ 8 ms). The same type of measurements also permitted the observation of stress crack formation in the vitreous endosperm of the kernels as a function of moisture gradients, temperature and maize variety during drying (Song and Litchﬁeld, 1994). MRI is a very powerful tool for studying stress cracking in grains during drying because it allows the non-intrusive observation of both ﬁssures and moisture gradients at the same time. Zeng et al. (1996) used a multi-slice pulsed imaging technique to study the seed coat cracking of soybean kernels during drying in dependence on air temperature and initial moisture content. MRI is also an ideal technique for studying the non-uniformity of water distribution inside grains caused by structural heterogeneities of the tissues. Many authors brought this effect to light applying MRI measurements to corn (Song and Litchﬁeld, 1990; Song et al., 1992; Kovacs and Nemenyi, 1999), rice (Frias et al., 2002), wheat (Ghosh et al., 2006a, b), or soybean (Zeng et al., 1996). Using the technique described above, Song et al. (1992) distinguished between two main routes for moisture transfer in a corn kernel during drying, one to the glandular layer to the scrutellum (nutritive cells around the germ) and the other through the pericarp (seed coat). Ghosh et al. (2006a) showed that the moisture loss is faster from the pericarp and the endosperm compared to the germ and conﬁrmed the pattern of moisture migration inside the kernel from endosperm to germ during drying. Kovacs and Nemenyi (1999) used MR images of corn kernels during drying and performed a 1 H density gradient vector quantitative analysis to describe the pathways of moisture transfer from the exact positions in the grain. They showed that moisture content decreases more slowly in the germ and that the germ still contains free water after 4.5 h drying (biological mechanism for preserving the germ). Ghosh et al. (2006b) applied the same gradient vectors technique to analyze moisture removal pathways in wheat kernels during drying. For products with cylindrical symmetry, like spaghettis, Hills et al. (1997) proposed a protocol for radial imaging that allows one to obtain the radial moisture distribution by a single 1D transverse projection followed by Fourier transformation and inverse Abel transformation (spatial resolution: 36 mm). Note that the inverse Abel transformation transforms a projection to an image in a cartesian frame. The method removes the need for the phase encoding gradients used in 2D imaging and for calibration of relaxation time against the water content, therefore, it speeds up the acquisition process. To characterize the water mobility in solid foods that have low moisture contents, Cornillon and Salim (2000) and Troutman et al. (2001) reported the use of 1D, 2D or 3D SPRITE techniques. The SPRITE sequence is a rapid implementation of the CTI sequence described in Section 3.4.4.3 and is generally used for low hydrated products. Such detailed measurements of moisture distribution as described in this section are very interesting for testing or improving drying models. Schrader and Litchﬁeld (1992) measured 1D transient proﬁles in a model food gel (agar/MCC mix)

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submitted to drying at two different temperatures (18 and 30 C) in order to evaluate the accuracy of a Fickian description for moisture transport phenomena. 2D images were measured in the center of the gel cylinder using a standard spin–echo sequence with a short echo time and converted into moisture proﬁles after calibration in T1, T2 and signal intensity. Precise localization of the edge of the body was not possible so this position was extrapolated from each proﬁle. It should be noted that Ruiz-Cabrera et al. (2005) reported the same observation, but chose to eliminate the ﬁrst data near the surface from further diffusivity calculation. The transient proﬁles measured by MRI were compared to proﬁles calculated by the model for a cylinder. Fickian diffusion was found to be inaccurate for predicting moisture transport in the gel during drying at low temperature, but the proﬁles were more similar in shape to the measured ones at 30 C. Many authors (McCarthy et al. 1991; Song et al., 1992; Hills, Godward and Wright, 1997; Frias et al., 2002; Evans et al., 2002; Ruiz-Cabrera et al., 2005) have evaluated existing theories and methods for the calculation of diffusion coefﬁcients using transient moisture proﬁles measured by MRI. Many analogous uses of MRI measurements of water mobility and transient distribution have also been reported for foods submitted to other processes: for example steeping of grains (Ruan and Litchﬁeld, 1992), freeze-drying of potatoes (Rutledge et al., 1994), boiling of rice (Takeushi et al., 1997a, b), cooking of spaghetti (Horigane et al., 2006), engrossing and aging of jellybeans (Troutman et al., 2001), starch molding operations (Ziegler et al., 2003), post-harvest storage of pears (Nguyen et al., 2006). 3.4.3.2 Measurement of Moisture Profiles in a Gel during Drying Ruiz-Cabrera et al. (2005) have developed a well-described method for the precise measurement of water distribution in a gel sample during isothermal drying by MRI. Special attention was focused on .

.

The experimental set-up for realizing isothermal drying of the sample with almost unidirectional water migration and shrinkage. The validation of the procedure of converting signal amplitude proﬁles into moisture content proﬁles.

A special drying cell that ﬁtted exactly into the small micro-imaging probe head was designed and built in non-magnetic PVC. This device contained two cavities. The sample to be dried was poured into the ﬁrst cavity and subjected to drying at the upper face. The second cavity was ﬁlled with a gel protected from drying, used as a reference to check any drift in the measurements. The whole was thermostated by water circulating in a double-jacket insulation device around the samples. Special attention was also paid to the control of conditioned air characteristics for drying experiments: velocity (from 0.5 to 2 m s1), temperature (from 8 to 40 C), humidity (dew point temperature from 1 to 30 C). Measurements were performed on a NMR spectrometer using a 9.4 T superconducting magnet operating at 400 MHz for 1 H and equipped with a micro-imaging accessory with a 500 mm gradient coil. 2D images were recorded every 30 min on a

3.4 MRI Applications to Drying of Agricultural and Food Samples

Fig. 3.27 2D images of the gel before and after drying (Ruiz-Cabrera, 1999); the open face is at the left-hand side of the picture.

2 mm slice perpendicular to the air-ﬂow direction and to the drying surface, using a standard spin–echo sequence (acquisition time: 10 min). T2 was measured using CPMG sequences as a function of temperature, moisture content and pH. Calibration curves of T2 vs. moisture content were elaborated for calculating the true water content proﬁles extracted from the 2D images. Figure 3.27 presents 2D images obtained at t ¼ 0 and after drying for 7 h. The reference gel remained identical; the image recorded after drying shows clearly that only the central part of the gel can be considered to undergo unidirectional drying with homogeneous shrinkage. 1D proﬁles were then extracted from a central band of 3.9 mm (5 voxels) in width on the 2D images. The investigators demonstrated that the width of the band taken for extracting the 1D proﬁle has a large inﬂuence on the shape of the proﬁle. However, this procedure gave better results than a direct 1D acquisition procedure. Spatial inhomogeneities of the radiofrequency ﬁeld B1 were corrected and the ﬁrst seven points of the proﬁles were removed to avoid artifacts near the surface. The spatial resolution was 49 mm in the direction of water transfer. Moisture proﬁles were recorded for different drying rates and different initial moisture contents showing the impact of both parameters on drying. The Boltzmann transformation was then used to calculate water diffusivity as a function of moisture content without any assumption about the mathematical relationship between them. The same procedure was applied to the drying of pork meat samples by RuizCabrera et al. (2004) in order to calculate moisture diffusivity and to study the effect of lipid content, temperature and meat anisotropy on the diffusion of water.

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3.4.4 Non-Intrusive Measurement by MRI of Moisture Profiles in Paddy Rice Kernels during Drying

Water transport phenomena in paddy rice, as in any cereal that has to be dried after harvest for safe storage and further use, are essential for both the ﬁnal quality of the product and the economic beneﬁt of the producers. Mechanical damage of the rice, which is expressed by a decrease in the head rice yield (HRY), is closely related to the severity of the drying process and the moisture proﬁles developed in the grains (Kunze and Hall, 1965; Kunze and Prasad, 1978; Bonazzi et al., 1997; Kamst et al., 2002; Siebenmorgen et al., 2005; Schluterman and Siebenmorgen, 2007). Takeushi et al. (1997a, b) studied the boiling of rice by means of MRI techniques, showing the feasibility of the technique for measuring moisture proﬁles in a rice grain. However, application to low moisture contents (less than 20% on a dry basis) and to the processing times of real drying processes showed some additional difﬁculties. Such an application was reported by Frias et al. (2002) and will be described in the following. 3.4.4.1 Experimental Set-Up In order to perform drying experiments similar to those described by Ruiz-Cabrera et al. (2005), a sample carrier was designed that maintained a single rice grain in the center of the coil during drying (Fig. 3.28). A copper envelope acting as a radio frequency shield was added, in order to restrict excitation/detection to a 3 mm high central section of the grain. A capillary ﬁlled with doped water (50: 50) was placed next to the quartz tube in order to determine the proportionality coefﬁcient of the MRI signal to moisture content. The drying air ﬂux circulated through the MRI antenna to the sample carrier, with an approximate air velocity of 1 m s1. 3.4.4.2 NMR Preliminary Experiments The NMR equipment was a Bruker AMX 400 (Bruker Instruments GmbH, Germany) equipped with micro-imaging instrumentation. Preliminary measurements were performed on paddy and white (i.e. hulled and milled) grains pre-conditioned at different water contents in the range 0.19 to 0.03 g H2O per g dry matter. The grains were shaped in the form of a cylinder of 3 mm in height, cutting both top and bottom in order to eliminate the embryo. The dependence of T1 and T2 on moisture content was measured at 30 and 60 C using classical spectrometric inversion recovery and CPMG sequences. Only two peaks contributed to the Fourier transformed spectra signal (Fig. 3.29). The ﬁrst was identiﬁed as the signal coming from water 1 H by comparing spectra from kernels at different water contents (curves A and B); these spectra showed a decrease in the peak height correlated with the decrease in water content. The second was identiﬁed as the signal from the non-water 1 H, mainly lipids from the external aleurone layer, by analyzing spectra of white rice samples (obtained after removal of

3.4 MRI Applications to Drying of Agricultural and Food Samples

Fig. 3.28 Sample carrier for MRI measurements during drying of a single rice grain.

most of the bran protein and oil) which did not present any signiﬁcant second peak (curve C). The relaxation times T1 and T2 for the water and non-water peaks, together with their respective standard errors, were determined at six different moisture contents and two different temperatures (30 and 60 C) from a parametric estimation using a nonlinear time series model. Then, an inverse weighted linear regression was performed with the T1 data (using the inverse of the previously obtained T1 standard errors as weights in the regression) to obtain the dependence of T1 on moisture and temperature. The following results were obtained for the water 1 H peak T 1;w ¼

103 42:3X þ 0:014X 0:11X T 4:1

ð3:25Þ

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Fig. 3.29 Identification of the different peaks in FT-spectra.

and for the non-water 1 H peak T 1;nw ¼

103 20:2X þ 0:011T 0:053X T 4:8

ð3:26Þ

Here, X is the moisture content in kg water per kg dry matter, and T the temperature in C; T1 is obtained in ms. The spin–spin relaxation times for the same peaks were considered constant with average values of T 2;w ¼ 279 ms and T 2;nw ¼ 531 ms. Notice that these values have been corrected for magnetic ﬁeld heterogeneity according to Eq. 3.6. 3.4.4.3 NMR Imaging Experiments MRI experiments were developed using a constant time imaging (CTI) sequence. Such sequences have been used to follow the moisture migration in samples with low moisture content, where smaller image acquisition times than those obtained with spin–echo images are required (Beyea et al., 1998). CTI sequences were performed using a 2D gradient in the transversal direction of the paddy rice grain (x and y directions in the NMR coils integrating the whole height of the observed central slice of the grain). The sequence used a repetition time of TR ¼ 50 ms, a ﬂip angle of a ¼ 16 and an encoding time of tp,w ¼ 150 ms, which maximized the contrast of the water protons in the kernel (the water image). At the beginning of each experiment, another image (the fat image), with an encoding time tp,nw ¼ 1000 ms maximizing the contrast of the non-water protons of the kernel, was taken. The total acquisition time was 13 min 41 s, short enough compared to the total drying time (about 30 h).

3.4 MRI Applications to Drying of Agricultural and Food Samples

Four drying experiments were performed using paddy rice grains equilibrated at an initial moisture content of 0.19 kg water/kg dry. Two of them were performed with air at 30 C (w ¼ 30% and 27%, respectively), the two others with air at 60 C (w ¼ 7% and 6%, respectively). Twenty ﬁve images were collected during each experiment. The spatial resolution was 0.1 mm. 3.4.4.4 Conversion of the MRI Signal to Water Content The obtained signal Srice was a mixture of water and non-water 1 H contributions, due to the characteristics of both the MRI sequence and the relaxation times of the two FT spectra peaks. The qualitative analysis of the fat image showed that the lipid contribution to the proton signal was low and concentrated mainly in an annular section of the image, which presented too much noise to perform a quantitative procedure. Assuming that the non-water 1 H contribution was negligible, the water content for each pixel of the image was ﬁnally calculated with the help of the equation

Srice

rdry X ¼k 1 þ bX

T R

1eT 1;w ðX ;TÞ T R

tp;w T 2;w

sina e

ð3:27Þ

1cosa eT 1;w ðX ;TÞ

Here, rdry is the solid density of the dry matter, in kg m3. The coefﬁcient of proportionality k was calculated from the averaged signal of the central section of the doped water capillary tube, where the volumetric water concentration was known, neglecting any local inhomogenities of the magnetic ﬁeld. This procedure was validated by calculating the average moisture content using data of the images taken at the initial times and comparing it with the value measured according to the AFNOR standard procedure (AFNOR, 1976). An interactive root searching procedure was used in order to convert the MRI signal for each pixel into moisture content using Scilab from INRIA in France. 3.4.4.5 Imaging Results and Moisture Profiles Typical MR images at the beginning and the end of the drying process are shown in Fig. 3.30. These data show that it is possible to observe the evolution of moisture proﬁles during rice drying and the ﬁnal 1 H distribution by MRI using the CTI sequence. Two regions of interest were submitted to further treatment: the images of the doped water capillary and the images of the rice grain. Iso-moisture level curves extracted from the rice grain images are shown in Fig. 3.31. Image (a) in Fig. 3.31 shows that the initial moisture distribution in the grain is non-uniform, with a higher concentration in the center, despite a very long equilibration of the samples (>1 month). On both images in Fig. 3.30, and especially on (b), a sort of a crown can be observed at the surface of the grain, corresponding to the contribution of non-water 1 H to the NMR signal. Qualitative comparison with the corresponding fat image and the structure and composition of a rough rice grain indicates that it certainly reﬂects the external aleurone layer of the paddy rice grain, which is rich in lipids.

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Fig. 3.30 Typical 2D MR images obtained for moist (a) and dry (b) paddy rice grains. (a) was obtained at t ¼ 0 and (b) after 40 h drying at 30 C.

An example of moisture proﬁles calculated from elliptic images such as those of Fig. 3.31 along their short and long axes is shown in Fig. 3.32 for a drying experiment at 60 C. The proﬁles are bell-shaped with a slope that decreases gradually as drying proceeds. They show the importance of internal mass transport in high temperature drying of rice, and the sensitivity of the MRI sequence to the progress in drying.

Fig. 3.31 Water gradient developed in the rice grain at t ¼ 0 (a) and after 40 h (b) drying at 30 C. The smoothed contours correspond to iso-moisture levels.

Additional Notation Used in Chapter 3

Fig. 3.32 Drying at 60 C. 1D profiles extracted from the short (a) and long (b) axis of the MR image. The label of each line corresponds to the drying time in minutes.

3.5 Conclusion

Knowledge of moisture proﬁles is of importance for proposing drying mechanisms and determining rate limiting processes during drying as well as for validation of different modelling tools for the drying process. MRI is a technique that enables acquisition of such data and it has been used to measure moisture proﬁles in a large number of products, such as apples, corn, rice, model food gels, wood, plywood, cardboard, paper, concrete, cement and catalyst pellets. MRI has several advantages, one of the most important being that it is a noninvasive method with the potential of delivering a large number of data at high spatial resolution. However, if a high resolution is required a small sample size must be used. Even for small samples, long times may be necessary in order to obtain a sufﬁcient number of spectra. In this case it may be difﬁcult to follow the kinetics of the drying process. Additionally, rather extensive calibration work against liquid water or water bound to the solid matrix is required in order to obtain quantitative data. It is expected that these problems will be addressed in the research departments of companies manufacturing MRI instruments in the near future.

Additional Notation Used in Chapter 3

A (S) B G M p S (A)

amplitude, signal magnetic ﬁeld strength magnetic gradient magnetization relative population signal, amplitude

— T Tm1 A m1 — —

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S T

slice thickness relaxation times, other time constants

m s

Greek letters

a g D d u n r t F v

Ernst angle (ﬂip angle) gyromagnetic ratio time between onset of gradient pulses gradient pulse length angle frequency proton density molecular life or correlation time phase angle angular frequency

Subscripts

E dry L nw p p, r, s R T v w x, y, z 1 2

echo dry matter longitudinal non-water pulse gradient directions repetition transverse voxel water gradient directions spin–lattice spin–spin

Superscripts

corrected for magnetic ﬁeld heterogeneity

Abbreviations

CPMG CTI FID FSP FT GE HRY MCC

Carr–Purcell–Meiboom–Gill constant time imaging free induction decay ﬁber saturation point Fourier transform gradient echo head rice yield micro-crystalline cellulose

rad Hz T1 s s rad Hz m3 s rad Hz

References

MRI NMR PFG PGSE rf SE

magnetic resonance imaging nuclear magnetic resonance pulsed ﬁeld gradient pulsed gradient spin–echo radio frequency spin–echo

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4 Use of X-Ray Tomography for Drying-Related Applications Angelique Leonard, Michel Crine, and Frantisek Stepanek

4.1 Fundamentals and Principles 4.1.1 Introduction

X-ray tomography (from the greek: tom^e, section and graphein, to describe) refers to cross-sectional imaging of an object from transmission data collected by using an Xray beam to irradiate the object in many different directions. It is a non-intrusive technique giving access to the internal structure of the object. X-ray tomography was originally developed in the ﬁeld of diagnostic medicine. The impact of this technique has been revolutionary because it provided doctors with detailed views of internal organs (Oldendorf, 1961; Cormack, 1963). There are numerous non-medical applications in addition to those presented in the ﬁeld of this chapter on drying. X-ray imaging, or computed tomography, has been succesfully applied in geology (Ueta et al., 2000), hydrogeology (Wildenschild et al., 2002) and archaeology (Morton, 1995). Since the nineties, it has been extensively applied in chemical engineering in order to determine the phase saturation spatial distribution within a process vessel (Toye et al., 1998; Marchot et al., 1999). During the last decade, the development of microfocus and CCD camera technologies has allowed the achievement of much better resolution (around a few microns). This is the ﬁeld of microtomography which has opened the way to many applications in materials science (Sasov and Van Dyck, 1998; Salvo et al., 2003; Leonard et al., 2008a), biology (Steppe et al., 2004), biomedical science (Ritman, 2004; Jones et al., 2006) and food science (Lim and Barigou, 2003; Falcone et al., 2005). X-ray tomography and microtomography are powerful nondestructive evaluation (NDE) techniques, giving access to characteristics of the internal structure of an object such as dimensions, shape, internal defects, and density (Kim et al., 2006; Landis et al., 2007).

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

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4.1.2 Physical Principles

X-rays have the same wave-particle duality characteristics as those attributed to visible light, that is they can be described either as an electromagnetic wave with the frequency y¼

c l

ð4:1Þ

or as a particle (photon) with energy proportional to the frequency, E ¼ hy, where h is Plancks constant (h ¼ 6.6 1034 J s) and c is the speed of light (c ¼ 3.0 108 m s1). The photon energy is expressed either in J or eV (1 eV corresponds to 1.602 1019 J). X-rays are located at the high-energy side of the electromagnetic spectrum (Fig. 4.1). Their location is measured by either the wavelength l (m) or the frequency n (Hz) or the photon energy E (keV) of the radiation. The practical range of wavelengths for X-ray imaging is between 1012 and 108 m (0.01 and 100 A). This corresponds to a frequency range between 1016 and 1020 Hz and photon energy values between 1.2 keV and 1.20 MeV. Microfocus X-ray sources usually cover an energy range below 200–225 keV, whereas standard focus systems are limited to 450 keV. Higher energies are only reached with synchrotron-generated X-ray beams. The propagation of X-rays through matter is mostly affected in two ways, when the photon energy remains smaller than 1 MeV (Kak and Slaney, 1988). X-rays can either be completely absorbed (photoelectric absorption) or inelastically scattered (ineslastic scattering). Photoelectric absorption occurs when photons interact with electrons within the inner shell of the atoms. The photon energy is used to eject electron (see Fig. 4.2a). If this energy is larger than is required to eject the electron, the surplus will be transferred to the ejected electron in the form of kinetic energy. The photon energy is thus completely absorbed. Photoelectric absorption is the dominant process up to energies of about 200 keV.

Fig. 4.1 Electromagnetic spectrum (from http://earth.esa.int).

4.1 Fundamentals and Principles

Fig. 4.2 Interaction between photon and matter: (a) photoelectric absorption; (b) Compton scattering.

Inelastic scattering, also known as Compton scattering, occurs when photons interact with outer electrons of atoms. Inelastic interaction means the X-ray loses energy: the X-ray is scattered in a different direction with a lower energy (see Fig. 4.2b). Since the scattered X-ray photon has less energy, it has a longer wavelength and is less penetrating than the incident photon. The X-ray is not absorbed but is removed from the incident beam. Compton scattering prevails at high X-ray energies. For monoenergetic X-rays, the attenuation resulting from the above-mentioned interactions can be described by the Beer–Lambert law, which states that each layer of equal thickness of the material absorbs an equal fraction of the incident radiation. This is expressed by the following differential equation: dI ¼ m de I

ð4:2Þ

where I represents the local intensity of the radiation. dI represents the inﬁnitesimal intensity decrease experienced by the X-ray beam when traversing an inﬁnitesimal slice of material of thickness de. m is the linear attenuation coefﬁcient (cm1). It describes the fraction of X-rays that is absorbed or scattered per unit thickness of the material. The integrated and classical form of the Beer–Lambert equation is given by: I ¼ expðmeÞ I0

ð4:3Þ

where I0 represents the incident X-ray intensity, I represents the intensity of the transmitted X-ray after passing through a layer of material of thickness e. The thickness where half of the incident energy is attenuated is called the half-value layer (HVL). The HVL is expressed in units of distance (cm). It is inversely proportional to the attenuation coefﬁcient. Using the Beer–Lambert equation, it follows that: HVL ¼

ln2 0:693 ¼ m m

ð4:4Þ

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Although it does not bring any different information than the linear attenuation coefﬁcient, the HVL is often used because it is easier to remember values and perform simple calculations with length units. In shielding calculations, the necessary thickness of material is expressed as a number of HVL (e.g. 7 HVL allows for reduction of the transmitted intensity to less than 1% of the incident one). In the above Beer–Lambert equation, the linear attenuation coefﬁcient m is assumed to be constant and unique, that is, the material is assumed to be homogeneous. For composite materials, the intensity of transmitted X-rays is given by adding the individual contributions of each component: X I ¼ exp m i ei I0 i

! ð4:5Þ

If linear attenuation coefﬁcients mi are distributed continuously within the material, the addition has to be replaced by an integral 0 1 ð I ¼ exp@ mðeÞdeA ð4:6Þ I0 e

Ð

The line integral mðeÞde represents the contribution of local linear attenuation coefﬁcients at each point of the X-ray path. Measurements of the fractional transmitted intensity, I/I0, under a great number of directions will constitute the input used by reconstruction algorithms. The linear attenuation coefﬁcients are strongly dependent on the X-ray energy used. In the case of polychromatic X-rays, the intensity equation has to be rewritten to account for the energy distribution I0(E): ð

0

ð

1

I ¼ I 0 ðEÞexp@ mðe; EÞdeAdE E

ð4:7Þ

e

where E is the X-ray energy. The integration runs over the entire energy spectrum of the incident X-ray. The value of m(e,E) at any speciﬁc location within the material basically accounts for the number of atoms in a cubic centimeter volume of material at this location and the probability of a photon being scattered or absorbed from the nucleus or from an electron of one of these atoms. These mechanisms are dependent on the atomic number Z, the atomic weight A and the density r of the material as well as on the X-ray energy E. Experimental information and databases are widely available (see, e.g. Berger, 1961; Creagh and Hubbel, 1992; Chantler et al., 2005). Different correlations have been reported in the literature, to relate the linear attenuation m to E, Z, A and r (Pullan et al., 1981; Vinegar and Wellington, 1987; Duliu, 1999). These correlations have to account for contributions of photoelectric absorption mP and Compton scattering mC: mðe; EÞ ¼ mP ðe; EÞ þ mC ðe; EÞ

ð4:8Þ

4.1 Fundamentals and Principles

At low X-ray energies, photoelectric absorption prevails and this contribution is described by the following parametric equation mP ðe; EÞ ¼ a r

1 Zm En A

ð4:9Þ

the r, Z and A values are those prevailing at position e within the material. Values of the parametric exponents m equal to 3.8 and n equal to 3.2 have been reported in the literature (McCullough, 1975; Ketcham, 2005). At high X-ray energies, Compton scattering prevails and this contribution is described by the following equation: mC ðe; EÞ ¼ b r

Z A

ð4:10Þ

As the ratio Z/A does not vary signiﬁcantly (0.4–0.5) for most elements, one can conclude that mC is almost constant. Equation 4.9 describing the contribution of photoelectric absorption and Eq. 4.10 describing the contribution of Compton scattering show that the linear attenuation coefﬁcient m should be proportional to the material density r. This is conﬁrmed experimentally and led to the deﬁnition of the mass attenuation coefﬁcient m/r (cm2 g1), often used to characterize X-ray attenuation independently of the material density. The energy dependence of the mass attenuation coefﬁcient is illustrated in Tab. 4.1 for different elements. At high X-ray energies (E ﬃ 1 MeV), m/r values are almost identical (0.06 to 0.07 cm2 g1), that is independent of the atomic number Z. This conﬁrms that the attenuation phenomenon mostly depends on the Compton scattering contribution. At low X-ray energies (e.g. around 100 keV), the mass attenuation coefﬁcient depends on the atomic number Z. m/r is larger for Pb (Z ¼ 82) than for Al (Z ¼ 13) or C (Z ¼ 6). This means, at low X-ray energies, the mass attenuation coefﬁcient depends strongly on the chemical composition of the irradiated material. Tab. 4.1 Values of the mass attenuation coefficient m/r as a function of photon energy for different elements (data extracted from Hubbel and Seltzer, 2004).

Photon energy (keV) Element

Z

50

100

150

200

300

400

500

1000

Carbon Oxygen Aluminum Iron Copper Tungsten Lead

6 8 13 26 29 74 82

0.187 0.213 0.368 1.96 2.61 5.95 8.04

0.151 0.155 0.170 0.372 0.458 4.44 5.55

0.135 0.136 0.138 0.196 0.222 1.58 2.01

0.124 0.124 0.122 0.146 0.156 0.784 0.998

0.107 0.107 0.104 0.110 0.119 0.324 0.403

0.095 0.096 0.093 0.094 0.094 0.193 0.232

0.087 0.087 0.084 0.084 0.084 0.138 0.161

0.064 0.064 0.061 0.060 0.059 0.066 0.071

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Tab. 4.2 Values of the mass attenuation coefficient m/r as a function of photon energy for compounds and mixtures (data extracted from Hubbel and Seltzer, 2004).

Photon energy (keV) Material

50

100

150

200

300

400

500

1000

Bone (ICRU, 1989) Concrete, ordinary Glass (borosilicate) Polyethylene Polyvinylchloride Water, liquid

0.424 0.341 0.302 0.208 0.456 0.227

0.186 0.174 0.166 0.172 0.189 0.171

0.148 0.144 0.139 0.153 0.149 0.151

0.131 0.128 0.125 0.140 0.131 0.137

0.110 0.110 0.107 0.122 0.110 0.119

0.099 0.098 0.095 0.109 0.099 0.106

0.090 0.089 0.087 0.099 0.080 0.097

0.066 0.065 0.063 0.073 0.065 0.070

Examples of mass attenuation coefﬁcients for compounds and mixtures are provided in Tab. 4.2. Trends are similar to those observed with pure elements, that is almost identical values at high energies and a chemical composition sensitivity at low energies. Let us note that the mass attenuation coefﬁcient of mixtures can be estimated from the attenuation values of each element n m X m ¼ wi ð4:11Þ r r i i¼1 where wi is the mass fraction of the ith atomic constituent. 4.1.3 Reconstruction

X-ray tomography consists of reconstructing an image of the local attenuation coefﬁcients (related to local densities) within an object from signals of transmitted X-ray intensities recorded at a great number of angular positions. This is achieved numerically using reconstruction algorithms. All reconstruction algorithms rely on the concept of the line integral. We will use the coordinate system deﬁned in Fig. 4.3 to illustrate this concept.The intensity I of a single X-ray beam propagating through an object, following the straight line AB, is related to the incident intensity I0 by the Beer–Lambert law. Most reconstruction algorithms are based on the assumption of monochromatic X-rays. In this case, we have: ! ð I ¼ exp mðeÞde I0 e

or ð I0 ¼ mðeÞde Pu ðrÞ ¼ ln I e

ð4:12Þ

4.1 Fundamentals and Principles

Fig. 4.3 Line integral and projection function Pu(r).

Here, Pu(r) represents the line integral of a ray at position r, with an angle of incidence u. The X-ray intensity measured at one point of the detector (e.g. point B) contains the information on the attenuation inside the object integrated along the path of the corresponding X-ray beam. The equation of this line in the spatial domain (x, y) is given by: x cosu þ y sinu ¼ r The line integral can be expressed as ðð mðx; yÞdðx cosu þ y sinurÞdx dy Pu ðrÞ ¼

ð4:13Þ

ð4:14Þ

where d represents the Dirac delta function. It indicates that the integration is carried out only along the line deﬁned by Eq. 4.13. A projection is formed by combining a set of line integrals. The simplest situation corresponds to the case of a planar parallel beam, illustrated in Fig. 4.4. The line integral deﬁned above is known as the Radon transform (or sinogram) of m(x,y). It relates the Radon space (u and r: coordinates of the projection function) to the spatial domain (x and y: coordinates at which m has to be determined). If the number of projections from different incidence angles is inﬁnitely large, one could perfectly reconstruct the original object, m(x,y). So, to obtain an image of m(x,y) from X-ray transmission intensities Pu(r) means ﬁnding the inverse Radon transform. It is possible to ﬁnd an explicit formula for the inverse Radon transform, however, it appears to be extremely unstable, especially when dealing with noisy data. In practice, a more stable and discretized version of the inverse Radon transform is often used. It is known as the ﬁltered backprojection algorithm (Herman, 1980; Kak and Slaney, 1988). It is based on the Fourier slice theorem according to which the 1D Fourier transform of the projection function Pu(r) is equal to a slice of the 2D Fourier transform of the image of m(x,y). It follows that, given the Fourier transform of projection data at enough angles, it should be possible to estimate an image of the object by simply performing the 2D inverse Fourier transform.

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Fig. 4.4 Parallel beam projections and corresponding projection profiles at two different angles u1 and u2; (From Kak and Slaney, 1988).

The ﬁltered backprojection algorithm is used in almost all applications of X-ray tomography. It has been shown to be very accurate and easy to implement. In classical versions of ﬁltered backprojection algorithms, a ramp ﬁlter is used to compensate for the blur introduced by summing up the backprojections of all sinogram lines. More elaborate versions incoporate a ﬁltering technique optimizing both deblurring and noise reduction. Most X-ray sources do not produce a planar parallel beam (except for synchrotrongenerated X-rays). A possible way to achieve a parallel beam conﬁguration consists in using a collimated point source and moving it with the detector along the object. The source and detector are at opposite sites of the object and have parallel trajectories (Kak and Slaney, 1988). This is a rather time-consuming operation, which has by now been abandoned in most commercial tomographs. A much faster way to generate line integrals consists in using a slit-collimator producing a planar fan beam, as illustrated in Fig. 4.5. Simple ﬁltered backprojection algorithms cannot be applied directly to projection proﬁles obtained with a fan beam conﬁguration. Rebinning methods (i.e.

4.1 Fundamentals and Principles

Fig. 4.5 Fan beam projections and corresponding projection profiles at two different angles u1 and u2; (From Kak and Slaney, 1988).

interpolation) have to be applied in order to convert the fan beam data into parallellel projections. Further information on fan to parallel rebinning can be found in Hsieh (2003) or in Natterer (1993). The development of microtomographs equipped with 2D scan CCD cameras requires the adoption of a cone beam technology for the X-ray source. This gives access to 2D transmission images from which 3D images can be reconstructed. A possible way to have access to these 3D images consists in scanning the object slice by slice and recording a bunch of line projections. The reconstruction can be done by applying 2D methods to each line projection and putting together all the slices. Data acquisition can be much faster using a bunch of fan projections, forming a cone as illustated in Fig. 4.6 and rotating it around the object. The problem is that

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Fig. 4.6 Cone beam geometry: illustration of fan beam projections in the central part and the periphery of the object.

there is no exact solution to the reconstruction of 3D images obtained with this conﬁguration. This means that there will always be an error no matter how many projections are used and how high the spatial resolution of the detector can be. Only approximate methods can be used. The most popular one, the Feldkamp algorithm, was developed in the eighties by Feldkamp et al. (1984). Actually, the Feldkamp algorithm is an extension of the 2D ﬁltered backprojection algorithm. It produces an exact reconstruction in the central part of the object and approximate results in the peripheral parts. Despite several advances in the development of cone beam reconstruction algorithms, the Feldkamp method remains the most commonly used because it allows a straightforward implementation and it is applicable to most cone-beam tomography applications. Polychromatic X-ray sources are used in most tomographic devices. When a polychromatic beam passes through an object, low energy photons are preferentially absorbed. The beam becomes progressively harder: its residual energy increases. The harder a beam, the less it is further attenuated. The total attenuation is no longer a linear function of the material thickness. This can produce some artifacts in the reconstructed image, called beam-hardening, such as pronounced edges and streaks (Brooks and Di Chiro, 1976; Duerinck and Macovski, 1978). Different methods have been proposed to reduce the beam hardening effect (Ramakrishna et al., 2006). The easiest way to avoid beam hardening is by using ﬁlters. This hardware method is the most popular method (Jennings, 1988). By placing a ﬁlter between the source and the object, such as a thin aluminum foil, low energy X-rays are attenuated. A harder, more monochromatic beam is produced, reducing the beam hardening artifact. A disadvantage of the use of ﬁlters is, however, the reduction of the X-ray ﬂux, which implies an increase in the integration time of the detector or an increase in the signal/noise ratio.

4.2 Instrumentation

A second method is based on a software correction with the help of a linearization procedure (Hammersberg and Mangard, 1998). The Beer–Lambert equation holding for monochromatic beam (linear approximation) I ¼ exp½mðeÞ e

I0 is ﬁtted to the measured X-ray attenuation data versus the material thickness (e). The dependence of the apparent attenuation coefﬁcient m(e) versus e, is characteristic of the non-linearity of the phenomenon. m(e) can be ﬁtted with polynomials. The attenuation data are usually measured using a set of samples of different thicknesses. The polynomial order has to be determined for each individual case. For small beam hardening artifacts, as observed with soft materials, a second-order polynomial ﬁt is satisfactory, whereas for more severe artifacts, as observed in denser materials, polynomial orders as high as 8 or higher are required. In order to avoid the empirical nature of a polynomial ﬁtting, some authors proposed to use physical models based on a description of the X-ray source spectrum (Van de Casteele et al., 2002). A different approach for tomographic image reconstruction is based on assuming that the cross-section consists of an array of unknowns (pixel intensities) and then setting up algebraic equations for the unknowns in terms of the measured projection data. The algebraic reconstruction starts from an initial guess for the pixel intensity distribution and proceeds by a series of iterative projections and correction backprojections until the reconstruction has converged. Algebraic reconstruction was ﬁrst introduced in the 1970s (Gordon et al., 1970). Different algorithms were reported in the literature. More details are available in Kak and Slaney (1988). The disadvantage of using algebraic methods was their slow speed. This situation is progressively changing with the steadily increasing power of computers.

4.2 Instrumentation 4.2.1 Geometry of CT Systems

Since the ﬁrst X-ray computing tomograph built by the EMI Company in 1971, following Hounsﬁelds design (Petrik et al., 2006), numerous technical and technological improvements have led to the development of several generations of CT systems. The source, the detector and the object manipulation stage are the main components of each scanner. Depending on their geometrical conﬁguration, or the way the relative motion between the source, the detectors and the object to be scanned is realized, X-ray tomographs are usually classiﬁed into ﬁve generations (Michael, 2001), following the successive developments in the medical ﬁeld (Fig. 4.7). Most of the CT systems used in chemical engineering or in materials science belong

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Fig. 4.7 Five generations of X-ray tomographs (adapted from Thiery and Gerstenmayer, 2002).

to the third generation. Since the X-ray beam is able to cover the entire width of the object, they are often called rotate-only systems, in contrast to the ﬁrst and second generations which required the translation and the rotation of the X ray-source and the detector (Stock, 1999). Depending on the weight or the size of the object, either the source-detector assemblage (Toye et al., 1998) or the object (Jenneson et al., 2003) can be rotated during the acquisition of the projections. Two source conﬁgurations are usually encountered in commercial or home-built systems: fan beam (Fig. 4.8a) and cone beam (Fig. 4.8b). Parallel beam can only be obtained within synchrotron facilities (Fig. 4.8c). Depending on the source geometry, the detector can be an array of individual elements, that is one-dimensional, or a CCD camera, that is two-dimensional. The resolution of the reconstructed images will mainly depend on the spot size, the distance source–object–detector, and the deﬁnition of the detector. Depending on the maximum sample size they can accept and the resolution they can provide, X-ray computed tomography systems can be classiﬁed into the following categories: synchrotron radiation microtomography, microtomography, and macroor industrial tomography. Synchrotron X-ray microtomography measurements can only be performed within large facilities, requiring application for beamtime. Micro- or macrotomographs can be either commercial or home-built systems, the latter usually offering more user ﬂexibility. Nevertheless, for the time being, no X-ray tomography computed system has ever been built around a laboratory drying

4.2 Instrumentation

Fig. 4.8 Geometry of X-ray source (a) fan beam; (b) cone beam; (c) parallel beam.

equipment. Monitoring of the drying process thus requires the interruption of the process to scan the sample being dried. 4.2.2 X-Ray Macrotomography (or Industrial Tomography)

Even though some chemical engineering or earth science research work was realized using medical scanners (Petrovic et al., 1982; Vinegar and Wellington, 1987; Lutran et al., 2002) or modiﬁed medical systems (Kantzas, 1994), some limitations of these systems rapidly appeared, namely regarding the size or the geometry of the objects. As a consequence, industrial or macro-tomographs were specially designed to investigate large size objects for process control, non-invasive metrology, failure analysis and so on (Stock, 1999). In contrast to medical scanners, there are no patientrelated dose restrictions or immobility problems. This allows one to work at high energy and to use vertical systems. The ﬁrst large-scale X-ray tomographs were built at the end of the nineties. Toye et al. (1998) designed a 160 kV fan beam system to image gas–liquid ﬂow patterns in ﬁxed beds ﬁlled with plastic packings. In 2005, the same group built the ﬁrst European high energy (420 kV), large-scale (0.45 m in diameter, 4 m in height) X-ray tomograph (Fig. 4.9). The 420 kV source allows investigation of highly absorbing materials, such as thin metallic objects, and was used to study the structure of a packed bed during drying with a resolution of 0.4 mm (see Section 4.4.1). Other research groups developed large-scale X-ray CT systems for chemical engineering applications, namely those of R. B. Eldridge at the University of Texas

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Fig. 4.9 High-energy, large-scale X-ray tomography.

at Austin, D. Mewes at the Leibniz University of Hannover, and T. Heindel at the Iowa State University. Some scanners were also built for industrial applications within large companies such as SNECMA MOTORS, Vernon, France. 4.2.3 X-Ray Microtomography

The development of microfocus X-ray sources and high-resolution CCD detectors led to the birth of X-ray microtomography. The ﬁrst X-ray microtomograph seems to have been realized in 1982 (Stock, 1999). Since then, several groups, mainly active in material sciences (Clausnitser and Hopmans, 2000), or private companies (www. tomoadour.com) have developed their own systems (Jenneson et al., 2003; Steppe et al., 2004). Besides home-built mCT, several companies developed and put on the market commercial systems. The main providers of laboratory X-ray microtomographs are: Skyscan BV (Kontich, Belgium), GE Healthcare (Bucks, UK), Scanco Medical AG, (Bassersdorf, Switzerland), X-TEK (Herts, UK), Bio-Imaging Research Inc. (Lincolnshire, USA), Phoenix X-ray (Wunstorf, Germany), and Werth Messtechnik GmbH (Giessen, Germany). Nowadays, most of the systems can scan samples with volumes ranging from mm3 to cm3, producing images with a pixel size between 1 and 50 mm. Most of them use a cone-beam source, the energy typically varying between 20 and 150 kV.

4.3 Image Processing

In recent works, X-ray microtomography was used to characterize the structure of potatoes during frying (Miri et al., 2006), to evaluate the inﬂuence of the drying technique on the texture of banana slices (Leonard et al., 1983), to determine the shrinkage and moisture proﬁles during convective drying of sludge (see Section 4.4.1), to study the development of cracks during convective drying of resorcinol-formaldehyde xerogels (see Section 4.4.2), and to follow the liquid menisci during the drying of a particle packing (see Section 4.4.3). 4.2.4 Synchrotron X-Ray Microtomography

X-ray beams produced in a synchrotron are parallel, monochromatic and highly coherent. The parallel geometry leads to short reconstruction times. The main advantage of a monochromatic beam is the absence of beam hardening artifacts, resulting from preferential absorption of low energy X-rays in the periphery of the object. The high spatial coherence of the beam produces a phase contrast that can be exploited to detect material interfaces. A large energy range, typically from 6 to 150 kV, is available (Maire et al., 2004). For drying-related problems, the major drawback of synchrotron X-ray microtomography is the small sample size. With their high resolutions, close to the micron, these systems are rather dedicated to the characterization of the ﬁnal microstructure of dried materials than for following a drying process. Synchrotron X-ray microtomography was recently used to study the cellular structure of bread during prooﬁng and baking (Babin et al., 2006). The most well-known synchrotron radiation facilities allowing microtomography measurements are: European Synchrotron Radiation Facilities (ESRF, Grenoble, France), National Synchrotron Light Source (NSLS, New-York, USA), SPring8 (Harima Science Garden City, Hyogo, Japan), Advanced Photon Source (APS, Argonne, USA), Swiss Light Source (SLS, Villigen, Switzerland) and Pohang Accelerator Laboratory (PAL, Pohang, Korea).

4.3 Image Processing 4.3.1 Algorithms for 3D Image Filtering and Segmentation

As was stated in Sections 4.1.2 and 4.1.3 the outcome of a reconstruction algorithm is a three-dimensional map of local attenuation coefﬁcients. For multi-phase materials, where the pure-component attenuations are known, the local composition (mass or volume fractions) can be calculated using Eq. 4.11 under certain conditions, depending on the number of phases present in the system and the pure-component attenuations. In drying applications, at least three phases are present: gas, liquid, and solid. A necessary condition for X-ray tomography to be applicable to drying is, therefore, that the wet and the dry regions of the system under investigation have a

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sufﬁciently different X-ray attenuation, so that is it must be possible to relate local attenuation to the local moisture content. Let us rewrite Eq. 4.11 in terms of volume fractions, fi, speciﬁcally for a three-phase (gas–liquid–solid) system: X m¼ fi mi ¼ fs ms þ fl ml þ fv mv ð4:15Þ i

The vapor-phase attenuation coefﬁcient, due to the much lower density of the vapor phase, can usually be neglected compared to the solid- and liquid-phase ones, that is mv ﬃ 0. If the local solid phase volume fraction (which is equal to the porosity e) remains constant (fs ¼ const.) during drying (i.e. no de-swelling, porosity collapse, etc. takes place), then the overall local attenuation coefﬁcient m is only dependent on the liquid phase volume fraction, that is m ¼ m(fl) and X-ray tomography can be used to follow the moisture content proﬁle directly. On the other hand, for deformable solids where both fs and fl change during drying, it may not be possible to relate local X-ray attenuation to moisture content unambiguously. Depending on the spatial resolution of the X-ray tomography instrument in use and the characteristic length-scale of phase heterogeneities in the system being investigated, let us distinguish between two cases, represented schematically in Fig. 4.10: If the spatial resolution (voxel size, d) of the instrument is sufﬁciently smaller than the characteristic length-scale of phase heterogeneities in the system (the so-called feature length-scale, Lf), it is possible to explicitly resolve the singlephase regions within the system and the phase boundaries (interfaces) separating them. An example of this situation would be a porous solid with pore diameters in the range of 10s to100s of mm scanned with a spatial resolution of approximately 2 mm. In

Fig. 4.10 Schematic of a map of X-ray attenuation coefficients of a three-phase (gas–liquid–solid) system in situations where (a) the voxel size is smaller than the feature length-scale; (b) the feature length-scale is smaller than the voxel size.

4.3 Image Processing

this case, the local attenuation m will be equal to one of the single-phase attenuations (ms, ml, mv) in most voxels except the interfacial ones. If, on the other hand, the voxel size is larger than or comparable to the feature length-scale (Fig. 4.10b), it is not possible to explicitly resolve the heterogeneous structure of the system (individual constituent phases and phase boundaries) and the local value of the attenuation coefﬁcient is a reﬂection of the local volume-average composition, as given by Eq. 4.15. An example of this situation would be the use of an X-ray tomography instrument with about 2 mm spatial resolution to follow drying in a porous solid material with characteristic pore diameters in the 10s–100s of nm range. Only macroscopic gradients of the moisture content can be evaluated from the data, as indicated by the gray-scale gradient in Fig. 4.10b. The two cases shown in Fig. 4.10 can also occur simultaneously, for example if macroscopic cracks develop during the drying of a microporous solid, or in solids with bi-modal pore size distribution such that one mode is above and one below the spatial resolution of the X-ray tomography instrument. Let us now turn our attention to the case of Fig. 4.10a, that is a situation where the spatial resolution is sufﬁciently high to allow the heterogeneous material structure to be explicitly observed. In that case, the separation of the convoluted image of X-ray attenuation coefﬁcients into the individual phases requires certain image processing operations to be applied. The typical steps – thresholding, segmentation, and ﬁltering – will now be illustrated using an example from Kohout et al. (2006a). Figure 4.11a shows the typical attenuation coefﬁcient image of a three-phase system (solid particle packing partially saturated by a liquid), and the frequency distribution (histogram) of normalized attenuation coefﬁcient values evaluated from that image for several liquid phase volume fractions (Fig. 4.11b). The peaks on the histogram correspond – from left to right – to the gas, liquid, and solid phases, respectively. It can be seen that

Fig. 4.11 (a) X-ray attenuation image of a three-phase (gas–liquid–solid) system; (b) frequency distribution of attenuation coefficients evaluated from the image in course of drying (decreasing liquid-phase volume fraction, as indicated in the legend). The vertical lines indicate the chosen threshold values a1 and a2 (from Kohout et al., 2006a).

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the relative frequency of the solid phase remains more-or-less constant, while that of the liquid phase decreases with decreasing liquid volume fraction and the peak for the gas phase increases. In order to segment the image into the individual phases, two threshold values of the attenuation coefﬁcient have to be chosen: a1 at the local minimum of the frequency distribution between the gas and the liquid (a1 ¼ 0.16 for this example) and a2 at the local minimum between peaks corresponding to the solid and the liquid phases (a2 ¼ 0.42). The voxels representing the solid, the liquid and the gas phases are then identiﬁed as follows: (i) voxels with an attenuation coefﬁcient higher than the threshold a2 are assigned to the solid phase; (ii) voxels with an attenuation coefﬁcient between a1 and a2 are assigned to the liquid phase and (iii) remaining voxels with an attenuation coefﬁcient lower than the threshold a1 are assigned to the gas phase. The morphology of the sample after binarization (thresholding) of each phase is shown in Fig. 4.12a. As can be seen in Fig. 4.12a, the segmented image contains some artifacts that need to be ﬁltered out in order to obtain a realistic representation of the three-phase structure. There are two main types of artifacts: Isolated individual voxels (or small clusters of voxels) of either solid, liquid or gas phase that are surrounded by a continuum of another phase. These are generally the result of noise present in the original X-ray attenuation image and can be removed relatively easily. The second artifact consists of a thin artiﬁcial liquid ﬁlm covering most solid–gas interfaces. This thin layer is caused by the nature of the thresholding algorithm and therefore it appears even in a completely dry sample. Its explanation can be found in Eq. 4.15 – the X-ray attenuation coefﬁcient of a voxel at the solid phase boundary that contains no liquid can happen to be the same as that of a liquid-only voxel if it contains such proportion of the solid phase that m = fsms. The thresholding algorithm then wrongly

Fig. 4.12 Segmented image of a three-phase (gas–liquid–solid) system: (a) after thresholding of X-ray attenuation image from Fig. 4.11a; (b) after filtering and removal of artifacts.

4.3 Image Processing

assigns this voxel to the liquid phase, and a ﬁlm of single-voxel thickness is formed on the gas–solid interface. The liquid ﬁlm artifact can be removed by the following ﬁltration algorithm, proposed by Kohout et al. (2006a): (i) Morphological closing and opening is ﬁrst applied to the solid and the liquid phases individually; (ii) Voxels that were occasionally assigned to both the liquid and the solid phases after step (i) are reassigned to the solid phase only; (iii) the gas phase is then deﬁned as the complement of the solid and the liquid phases; (iv) ﬁnally, a morphological opening and closing is applied to the gas phase in order to ﬁll any gaps that may have formed between the solid and the liquid phase. A cross-section of the three-phase morphology of the sample after ﬁltration is shown in Fig. 4.12b. Note that morphological closing means the application of the dilation followed by erosion operations using the same structuring element (the N6 structuring element in 3D was used throughout); morphological opening is the application of the erosion operation ﬁrst, followed by dilation (Gonzalez and Woods, 2008). Simply speaking, erosion has the effect of removing a layer of voxels from the surface of a cluster, while dilation means the addition of a layer of voxels onto the surface of each cluster. Morphological closing tends to remove small holes present in a continuous domain of a single phase, while morphological opening tends to remove isolated speckles as well as any thin (one to two voxels) sections. The image segmentation and ﬁltration algorithm described above is by no means the only possible one, although it has been developed and tested speciﬁcally for drying applications. Several other algorithms can be found in the literature – mainly focusing on making the image thresholding and segmentation steps automatic, thus minimizing manual intervention or a priori knowledge about the correct morphology of the system. Prodanovic et al. (2006) used X-ray tomography to investigate the spatial distribution of multi-phase ﬂuid systems (oil, water, air) in porous polyethylene cores. The three-dimensional images were obtained with a spatial resolution of 4.1 mm using a synchrotron source. In order to allow the water and oil phases to be segmented, the X-ray attenuation coefﬁcient of the oil phase was modiﬁed by doping it with 15% of bromohexadecane. While this makes the segmentation between the oil and the water/polyethylene phases possible, the non-oil phases still have too close X-ray attenuation coefﬁcients to be segmented. Therefore, the location of the solid phase was obtained independently by ﬁrst scanning an oil-saturated core and this was then used to infer the location of the aqueous phase in the partially saturated cores (after an appropriate image alignment). In order to apply this method to drying, the fully water-saturated medium would be scanned ﬁrst in order to obtain the exact boundaries of the solid phase (i.e. water would play the role of the doped oil phase), and drying – that is the ingress of the gas phase – would then represent the analogy of water imbibition in the case of the oil–water multiphase system. Even in that case a robust algorithm for segmenting a two-phase image is required. In a recent work by Rajagopalan et al. (2005), no less than 12 different segmentation algorithms were compared and the porosity of a porous tissue engineering scaffold evaluated from the segmented image was compared with experimentally measured values. The algorithms gave vastly different results, as can be seen in

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Fig. 4.13 Comparison of 12 different segmentation algorithms applied to an X-ray tomography image of a porous tissue engineering scaffold. Algorithm no. 12 is the indicator kriging method. (Reproduced from Rajagopalan et al., 2005, with permission.)

Fig. 4.13. The best agreement between experimentally measured and calculated porosity was obtained by the so-called indicator kriging algorithm (panel no. 12 in Fig. 4.13), which is based on a combination of global (frequency distribution of attenuation coefﬁcients) and local (spatial correlation) criteria. According to Oh and Lindquist (1999), the basic indicator kriging algorithm for binary segmentation can be described as follows: 1. Thresholding step. Let Z(x) be the histogram of X-ray attenuation coefﬁcients obtained from the original (un-segmented) image. We are seeking to assign each voxel into one of two phases, P0 and P1 (e.g. gas and solid, etc.). Let T0 and T1 be two threshold values such that voxels whose X-ray attenuation coefﬁcients are below T0 fall into phase P0 without any doubt and those with attenuation

4.3 Image Processing

coefﬁcients above T1 fall clearly into phase P1. Points whose X-ray attenuation coefﬁcients are between T0 and T1 will be called unassigned voxels. (The choice of T0 and T1 can be automated, however, it is neither too time-consuming nor too error-prone to make this choice manually.) 2. Kriging step. Let x0 be the spatial location of an unassigned voxel and let xa, a ¼ 1, . . ., n be the spatial locations of voxels in the neighborhood of x0. The set of neighborhood points is termed the kriging window and it should be large enough to contain voxels already assigned to both phases in step 1. The kriging step assigns voxel x0 to one of the two phases according to 8Y < if PðT 0 ; x 0 jnÞ>1PðT 1 ; x 0 jnÞ Zðx0 Þ 2 Y0 ð4:16Þ : otherwise 1 where P(T0;x0|n) represents a probability that an unassigned voxel belongs to phase P0 and 1 P(T1;x0|n) represents a probability that it belongs to P1. The probabilities are estimated by PðT i ; x 0 jnÞ ¼

n X

la ðT i ; x 0 ÞiðT i ; x a Þ;

i ¼ 0; 1

ð4:17Þ

a¼1

The indicator variables i(Ti;xa) are deﬁned by ( 1 if Zðx a Þ T i iðT i ; x a Þ 0 otherwise

ð4:18Þ

and the weights la(Ti;x0) are obtained as a solution of a linear system of (n þ 1) equations for (n þ 1) variables: n X lb ðT i ; x 0 ÞCI ðT i ; x a x b Þ þ mðT i ; x 0 Þ ¼ CI ðT i ; x a x 0 Þ b¼1 n X

a ¼ 1; . . . ; n ð4:19Þ

lb ðT i ; x 0 Þ ¼ 1

b¼1

In Eq. 4.19, m(Ti;x0) is a Lagrange multiplier introduced in order to satisfy the constraint of the sum of the weights being equal to 1, and CI(Ti;h) is the spatial covariance of the indicator variables. 4.3.2 Calculation of Morphological Characteristics

Once the raw 3D image of X-ray attenuation coefﬁcients is segmented into the appropriate number of phases, it is usually desirable to evaluate some quantitative morphological descriptors that characterize the spatial distribution of the phases, their characteristic dimensions, interface areas, curvatures, percolation and connectivity, and so on. Such morphological descriptors are relevant in the context of drying – the phase volume fraction is related to the moisture content, interface area and curvature

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to the drying rate, percolation to the capillary transport as well as thermal conductivity and effective diffusivity. Before discussing some of the most commonly used morphological descriptors let us ﬁrst deﬁne the phase function fp(x) as ( f p ðxÞ ¼

1 if x 2

Y p

ð4:20Þ

0 otherwise

where x is a point on a three-dimensional Cartesian grid of N3 voxels with spatial resolution d (the voxel size). The phase function is the direct result of image segmentation, as described in the previous section. 4.3.2.1 Phase Volume Fraction The phase volume fraction is a measure of the composition of the sample or its subregion, and it is deﬁned by

fp ¼

Sx fp ðxÞ N3

ð4:21Þ

It follows that the sum of all phase volume fractions must be equal to 1. In the context of drying, the ratio fl/fs is the moisture content expressed on a volume basis, and its time derivative is the drying rate of the region under investigation. The phase volume fractions can also be evaluated on a sub-set of the entire sample, for example a horizontal layer of given thickness, in order to follow moisture content evolution within the sample. 4.3.2.2 Cluster Volume Distribution If the liquid or gas phase does not form a single continuous region within the sample, it is of interest to measure the distribution of isolated volumes (clusters) of each phase. Such distribution is of interest for example to follow the emergence and growth of vapor bubbles in a liquid-saturated porous medium, or the distribution of residual moisture during the later stages of drying from a capillary porous medium. Let Np be the number of isolated clusters of the p-th phase in the sample per unit of volume. This number is a sensitive indicator of qualitative changes in the liquid phase distribution that may not be visible on the phase volume (or moisture content) proﬁles due to their appearance in the later stages of drying. When a single liquid phase domain remains in the system throughout drying, this is indicative of a relatively sharp drying front; on the other hand, the emergence of a large number of clusters indicates a diffuse drying front with potentially many dead-end pores in the material structure. As drying proceeds, the number of clusters tends to go through a maximum as a function of moisture content: initially, the number increases sharply as the originally single liquid cluster breaks up into residual liquid regions but then, as individual clusters begin to dry up, the total number of clusters decreases, eventually reaching zero in a dry medium.

4.3 Image Processing

Fig. 4.14 Illustration of site percolation on a two-dimensional square lattice. The fraction of occupied sites is 10, 24, 43, and 59%, from left to right. Above the percolation threshold, a path through occupied sites can be found.

4.3.2.3 Percolation The phase volume fraction and the cluster size distribution are closely related to another important quantity – the percolation threshold (Sahimi, 1994). The concept of percolation is illustrated in Fig. 4.14. Consider a square lattice on which the sites can be in two states: unoccupied (white) or occupied (gray). Starting from a fully unoccupied lattice, let us gradually increase the fraction of occupied sites by randomly selecting an unoccupied site in each iteration and turning it into an occupied one, as is shown in Fig. 4.14. Initially only isolated occupied sites will exist. As the fraction of occupied sites increases, some larger clusters consisting of two or more adjacent occupied sites will emerge. Finally, when the fraction of occupied sites is increased even further, the so called domain-spanning cluster will be formed. As the name suggests this cluster has the property of reaching over the entire lattice, that is it is possible to ﬁnd a path between opposite sides of the lattice that leads only through the occupied sites. The fraction of occupied sites for which the domainspanning cluster ﬁrst emerges is called the percolation threshold. On a two-dimensional square lattice, reaching the percolation threshold of one phase automatically means the loss of connectivity of the other phase (the unoccupied sites). However, on a three-dimensional lattice bi-continuous structures can exist. Percolation has been shown to underline macroscopic properties of multiphase materials, notably transport properties such as permeability, thermal conductivity and effective diffusivity (Sahimi, 1994), all of which are directly relevant for drying. The loss of percolation of the liquid phase has also been related to the transition from the constant to the falling rate period of drying in vacuum contact drying of a static powder bed (Kohout et al., 2006b). The loss of percolation of the liquid phase means

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that wall re-wetting by capillary ﬂow was no longer possible, which in turn gives rise to a receding drying front propagating from the heated walls towards the interior of the powder bed. On the other hand, the loss of percolation of the vapor phase during the initial state of drying means that evaporation is only possible from pores near the surface of the bed. 4.3.2.4 Interfacial Area The total interfacial area (or the interfacial area per unit volume) between two phases within a multiphase structure is another parameter that can be estimated from X-ray tomography images and that has direct relevance to drying. By plotting the measured liquid evaporation rate against the available liquid–vapor interface area, the rate-limiting step of the drying process can be identiﬁed (diffusion- or heat-transfer limitations, etc.). The solid–liquid interfacial area is also an important parameter, for example in situations where the deposition of a solute occurs simultaneously with drying, such as during the impregnation of catalysts and other applications. The interfacial area between two phases, p and q, can be estimated from the phase functions as X ap ðxÞ ð4:22Þ Ap;q ¼ x2Vp;q

where Vp,q is a set of voxels belonging to phase p and having at least one nearest neighbour from phase q; ap is the contribution of a single voxel to the interfacial area, normally d2. Due to the binary nature of thresholded and segmented images, the calculation of surface area is not as accurate as, for example when using the volume of ﬂuid (VOF) method, however, the correct scaling is preserved. 4.3.2.5 Interface Curvature The mean curvature of a liquid–vapor interface is important when calculating the equilibrium vapor pressure from the Kelvin equation (capillary condensation/ evaporation) or the capillary pressure – for ﬂuid ﬂow – from the Young–Laplace equation. From the phase function, the interface curvature at a given point can be calculated according to:

kp ðxÞ ¼ r ~ np ðxÞ

ð4:23Þ

where the interface normal vector is obtained as ~ np ðxÞ ¼

rf^p ðxÞ jjrf^p ðxÞjj

ð4:24Þ

The so-called molliﬁed phase function is used in the evaluation of the interface normal vector. The molliﬁed phase function is obtained from fp(x) by the application of the 1-6-1 smoothing ﬁlter – that is, the new value of fp(x) is the weighted average of its old value (with a weight of 6) and its six face-nearest neighbors, each with a weight of 1. Since the local curvatures can ﬂuctuate due to noise originally present in the X-ray attenuation coefﬁcient image, it is usually more representative to evaluate the

4.4 Applications

mean interface curvature for all liquid–vapor interfaces belonging to the same liquidphase cluster.

4.4 Applications 4.4.1 Convective Drying of Sludge

Because of stringent environmental regulations, the production of sludge from wastewater treatment plants has been continuously increasing worldwide for several years. The management, preferably the valorization, of the growing amounts of sludge has become a key issue. When taking a look at recent legislation around the world, it appears that two major options prevail for sludge disposal after mechanical dewatering: energy valorization and landspreading (Spinosa, 2001). It is now well established that a thermal drying operation, after dewatering, is an essential step. It can indeed lower the water content below 5% on a dry basis. This obviously reduces the mass and volume of waste and, consequently, the cost for storage, handling and transport. The removal of water to such a low level increases drastically the lower caloriﬁc value, transforming the sludge into an acceptable combustible. Furthermore, the dried sludge is a pathogen-free, stabilized material because of the high temperature treatment. Despite the industrial and economic importance of such a process, rather few studies have been carried out in order to geta better understanding of thekey– rate controlling – mechanisms. Sludge drying behavior remains extremely difﬁcult to predict because it depends greatly on its origin and on the way it is processed (Leonard et al., 2006). The application of X-ray tomography is illustrated at two scales: the individual extrudate and the packed bed. At the extrudate level, a methodology is developed in order to follow the shrinkage and the development of moisture proﬁles during drying. At the packed bed level, tomography is used to evaluate the packed bed properties for several initial sludge moisture contents. 4.4.1.1 Sludge Individual Extrudates The drying behavior of any type of material is usually evaluated in terms of drying curves. The drying data are processed to obtain the so-called Krischers curves, that is _ kg m2 s1) vs. the moisture content the evolution of the mass ﬂux (or drying rate, m, on a dry basis (X, -) (Kemp et al., 2001). For non-shrinking materials, the mass drying ﬂux can be directly obtained from the mass evolution and the initial surface area (A, m2). For shrinking materials, it is necessary to determine the surface area evolution during the course of drying. In their work, Perre and May (2002; 2007) clearly showed the importance of considering exchange area reduction, in the particular case of food drying. X-ray tomography coupled with image analysis is a suitable technique for an accurate determination of the drying shrinkage. In addition to its accuracy, X-ray microtomography is non-destructive and constitutes

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a modern alternative to traditional methods such as calliper or volume displacement methods which have been largely used in the drying literature (Lozano et al., 2000; Lewicki and Witrowa, 1992; Ratti, 1994; Moreira et al., 2000; Mayor and Sereno, 2004). The measurement of internal moisture proﬁles developing during drying is rather complicated. Up to now, moisture proﬁles have been mainly determined either by destructive techniques such as slicing (Chapter 2, see also Couturier et al. (2000)) or by sophisticated non-destructive methods such as nuclear magnetic resonance (Chapter 3, see also Ruan et al. 1991; Frias et al. 2002). These technical difﬁculties have limited the ability of validating drying models by the comparison of actual and predicted moisture proﬁles (Waananen et al., 1993). Moreover, the ﬁnal internal moisture distribution can be of high importance for the quality of some speciﬁc materials. By using X-ray microtomography together with a calibration method, it is possible to determine accurately internal moisture proﬁles, provided that the attenuation properties of the solid matrix and water are sufﬁciently different. Residual urban sludge was collected after the thickening step and it was conditioned and dewatered in the laboratory (Leonard, 2003). Individual sludge extrudates with initial diameter and height of 12 mm and 15 mm, respectively, were made from the dewatered sludge cake and then were dried in a classical convective drying rig with controlled air temperature, velocity and humidity (Leonard et al., 2004b). Since desktop microtomographs are closed systems, the measurement of shrinkage and moisture proﬁles required interruption of the drying process several times to remove and scan the sample. In this example, the acquisition parameters were chosen such as to shorten the acquisition time to about 3 min. It was proved that repeated interruptions had no effect on the drying kinetics. For each interruption, the height and the equivalent diameter of the sample were obtained from image analysis of the radiographs and the cross-sections, respectively (Figs. 4.15 and 4.16, see Leonard et al. (2005a). The shrinkage curves are then easily determined. Figure 4.17 shows the results obtained following a 33 experimental design including 27 experimental trials (Leonard et al., 2005b). It shows ﬁrst a period of ideal shrinkage characterized by the linear change in volume with the water content. The material remains bi-phasic

Fig. 4.15 (a) Grey level and (b) binary radiograph of the sludge extrudates.

4.4 Applications

Fig. 4.16 (a) Gray level image of reconstructed sludge crosssection; (b) binary image of reconstructed sludge cross-section; (c) concentric rings used for moisture content profile determination.

during this period. Ideal shrinkage is followed by a plateau corresponding to a triphasic rigid medium. The internal moisture content proﬁle determination is based upon the differential X-ray attenuation properties of water and sludge. In a cross-section, the gray value of each pixel corresponds to a local moisture content that can be obtained through the establishment of a calibration curve (Leonard, 2003). The mean gray value and the corresponding moisture content are determined in successive concentric rings for each reconstructed sample cross-section (Fig. 4.16a). The rings are not circular but follow the external shape of the extrudate (Leonard et al., 2005a). The results are then averaged along the height of the samples. Figure 4.18 shows typical internal moisture

Fig. 4.17 Shrinkage curve obtained from 27 drying experiments at different conditions (Leonard, 2003).

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Fig. 4.18 Internal moisture profiles obtained at 160 C, 1 m s1 and ambient humidity.

proﬁles obtained during convective drying at 160 C, 1 m s1 and ambient humidity. The moisture content is uniform at the beginning of drying, then gradients develop towards the outer surface of the extrudate because of internal diffusional limitations. From a knowledge of both the moisture content gradients and the mass drying ﬂux, the effective diffusion coefﬁcient can be obtained. For sludges, Deff typically ranges from 1011 to 7 1010 m2 s1 (Leonard et al., 2008a). This methodology, based on X-ray microtomography and image analysis, could be successfully applied to a large variety of materials, in order to get an accurate determination of drying shrinkage and of the internal moisture proﬁles. 4.4.1.2 Sludge Packed Bed Belt dryers are largely used to dry wastewater sludges (ADEME and CETIAT, 2000). In these systems, the wet material is fed on the belt in a divided form, for example through an extrusion process, in order to increase the exchange area. The stiffness of the material must be sufﬁcient to keep the structure of a packed bed consisting of individual extrudates on the belt, otherwise the drying process will not be efﬁcient and the pressure drops across the bed will increase. When the texture of the sludge is too soft to produce separated pellets, a pre-conditioning of the feed by mixing with recycled dried material can be realized. The so-called backmixing operation leads to an increase in the sludge layer height, together with an increase in the total exchange area. With X-ray tomography, it is possible to study the impact of backmixing on the sludge bed properties. Sludge collected after mechanical dewatering was extruded through a 12 mm diameter circular die. The bed of sludge extrudates was dried in a discontinuous pilot scale dryer reproducing most of the operating conditions prevailing in a full scale

4.4 Applications

Fig. 4.19 Extrudate sludge bed in the drying chamber.

continuous belt dryer (Leonard and Crine, 2004a). The drying experiments were performed with ambient air heated at 105 C, crossing the bed at a velocity of 1 m s1. The mass was recorded throughout the drying process. To illustrate the backmixing effect, two sludge beds having the same total amount of water but different initial moisture contents were dried. The ﬁrst bed was made from 1 kg of fresh sludge (water and solids), while the second bed was obtained by adding 0.4 kg of dried product to the fresh sludge before extrusion. The bed was cylindrical in shape with an initial diameter of 12 cm, the height depending on the amount of sludge lying on the grid (Fig. 4.19). Figure 4.20 shows the drying curves obtained for both sludges. Backmixing induced an acceleration of the drying process, due to an increase in the drying rate. The total drying time dropped from 88 to 59 min. The drying rate increase is related to the expansion of the bed, which leads to an enhancement of the exchange area. X-ray tomography is a useful technique to evaluate the effect of backmixing on the bed properties. Because of the dimensions of the sludge bed, a tailor-made high energy tomograph allowing the scanning of large materials was used (Toye et al., 2005). Figures 4.21a and b show cross sections of each bed. An increase in the porosity is clearly observed in Fig. 4.21b. Sludge extrudates present a more individual character while they were stuck together before backmixing. The 3D reconstructed images of the two sludge beds, Fig. 4.21c and d, conﬁrm the bed expansion, leading to the increase in the external exchange area available for heat and mass transfer. Image analysis was performed to determine the total porosity and the exchange area of both beds. Table 4.3 indicates an increase of 10% for the porosity, together with the doubling of the exchange area when backmixing is realized. This factor of two is in

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Fig. 4.20 Drying curves obtained at 105 C, 1 m s1 and ambient humidity, for two sludge beds.

rather good agreement with the values of maximum mass ﬂow rates of drying indicated in Fig. 4.20. Indeed, for identical drying conditions, the same drying ﬂux was supposed to be obtained for both sludges when heat and mass transfer are externally controlled, that is during the constant drying period.

Fig. 4.21 Cross-section of the bed (a) without and (b) with backmixing; 3D view of the bed (c) without and (d) with backmixing (a quarter of the bed was numerically cut in order to have a better view of the internal structure) (Leonard et al., 2008b).

4.4 Applications Tab. 4.3 Properties of the sludge extrudate beds.

Initial height (cm) Porosity (%) Exchange area (m2) 1 kg fresh sludge 7.8 1 kg fresh sludge þ 0.4 kg dried product 13.5

31 41

0.13 0.26

The expansion of the bed can be explained by the rigidiﬁcation of the sludge when its moisture content decreases. However, for the same level of backmixing, the gain in porosity and exchange area will greatly depend on the rheological properties of the material. The use of a backmixing step must rely on rigorous experimental studies for which tomography can be an efﬁcient characterization technique (Leonard et al., 2004). 4.4.2 Drying Optimization of Resorcinol-Formaldehyde Xerogels

Carbon xerogels obtained by subcritical drying and pyrolysis of resorcinolformaldehyde resins are promising synthetic materials. Their pore texture can be tailored so that micro-macroporous, micro-mesoporous, microporous, or nonporous carbon materials can be obtained by adjusting the synthesis solution (Job et al., 2004; Leonard et al., 2008). Potential applications are: adsorbents for gas separation, catalyst supports, electrode material for double layer capacitors, energy storage devices, column packing materials for chromatography, and so on. The drying step is a particularly critical step when carbon monoliths are required, for example for electrodes or supercapacitors, especially when the sample undergoes a large volume reduction. When the drying conditions are too severe, the mechanical stresses caused by differential shrinkage may lead to cracking of the sample (Izumi and Hayakawa, 1995; Colina and Roux, 2000; Pourcel et al., 2006). The detection and quantiﬁcation of cracks during the drying process turns out to be essential for quality criteria purposes or model validation. Until recently, the production of resorcinol-formaldehyde based carbon materials usually involved a supercritical drying step (Al Muhtaseb and Ritter, 2003), following the original process developed by Pekala (1989). Supercritical conditions were used to suppress capillary tensions at the liquid–vapor interface, in order to avoid shrinkage and cracking. Since the required solvent exchanges are time consuming and the supercritical drying process difﬁcult to apply on an industrial scale, the search for solvent removing alternatives was of great interest. Convective drying presents many advantages because it is a well-known process, largely used in the industry, that offers many design possibilities. The only issue was to verify that it is possible to maintain the porous properties of the dried gels without structure collapse or cracking during drying. The suitability of convective drying for the production of porous carbon xerogel was recently assessed (Leonard et al., 2008). This investigation concluded that convective drying is possible, but the drying conditions have to be carefully controlled

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Fig. 4.22 (a) Monolithic and (b) totally broken resorcinol-formaldehyde xerogel.

in order to avoid the cracking or total rupture of the samples, as illustrated by Fig. 4.22. X-ray microtomography can be efﬁciently used to follow the crack formation (Leonard et al., 2005b) and help in optimizing the drying process. Since the gel texture and its shrinkage behavior depend greatly on the synthesis conditions (Al Muhtaseb and Ritter, 2003; Job et al., 2006), so also does the propensity of the sample to crack. Two extreme situations are illustrated in the following, correspondinng to almost no shrinkage and to a volume reduction of circa 60% during drying. Hydrogels were obtained by polycondensation of resorcinol (R), solubilized in water, with formaldehyde (F) in the presence of Na2CO3, usually called catalyst (C). The resorcinol to Na2CO3 molar ratio was ﬁrst ﬁxed at 1000, which corresponds to no shrinkage, and then set to a value of 300, which leads to a volume reduction after drying close to 60%. The molar ratio R/F and the dilution ratio D, that is the solvent/(R þ F) molar ratio, were ﬁxed at 0.5, (the stoichiometric ratio), and 5.7, respectively. Cylindrical samples with diameters of 23 mm were obtained by casting 5 ml solution into glass molds and putting them for gelation and aging at 70 C for 24 h under a saturated atmosphere. After removal from the mold, the monoliths were convectively dried. Several air temperatures and velocities were tested to ﬁnd the drying conditions that allow the fastest solvent removal without any sample cracking. The samples were periodically removed from the dryer to be scanned in the microtomograph. The temperature was found to have a critical inﬂuence on the cracking behavior, while air velocity had almost no effect. Samples undergoing a negligible volume reduction during drying, that is for R/C ¼ 1000, remained monolithic up to the maximum drying temperature the system can reach, that is 160 C. The situation was totally different with the other samples obtained with R/C ¼ 300. The drying temperature had to be reduced to 30 C in order to avoid cracking in this case (Fig. 4.23, see also Job et al., 2006). With X-ray tomography, it is possible to determine the drying time and the location corresponding to crack onset. This is particularly interesting for the validation of

4.4 Applications

Fig. 4.23 Cross-section of a sample synthesized with R/C ¼ 300 (a) before drying; (b) after drying at 30 C and 2 m s1; (c) after drying at 70 C and 2 m s1.

thermo-hygro-mechanical models (see Chapters 3 and 4 in Vol. 1 of Modern Drying Technology) and the development of cracking criteria, which remains a ﬁeld to be deeply explored. For RF xerogels, cracks appear quite early in the drying process, indicating that they correspond to the mechanical response to hydrous strains due to differential shrinkage. Figure 4.24 shows how the temperature has a large inﬂuence on the sample stress state during drying. For samples obtained with R/C ¼ 300, the maximal von Mises stress developed around crack initiation is multiplied by a factor of 4 when the drying temperature increases from 30 to 110 C.

Fig. 4.24 Influence of the drying temperature on the evolution of simulated Von Mises stress vs. drying time – RC ¼ 300.

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4.4.3 Contact Drying of a Packed Bed

Drying kinetics is usually observed on a volume-averaged basis, that is the mass loss of a wet material as a function of time is recorded, without explicitly measuring the internal distribution of the liquid phase within the porous medium being dried. Although in some cases the moisture distribution proﬁles can be determined a posteriori by taking samples of a material from different depths before drying is complete, or by inserting probes into the material, these methods are generally destructive, in the sense that they irreversibly modify the microstructure of the system. Moreover, they are applicable to bulk quantities of mechanically robust materials (e.g. a layer of sand) but not to small amounts of fragile particles, such as a sample of a new pharmaceutical ingredient whose drying kinetics needs to be determined. In a study by Kohout et al. (2006a) X-ray microtomography was used as a non-invasive technique for the direct observation of evolution of moisture proﬁles in a sample of a porous material (packed particle layer) during contact drying. By the measuring of the 3D distribution of X-ray attenuation, which is proportional to the local density, it is possible to identify the solid, liquid and gas phases in a cylindrical vacuum contact dryer (heat is applied through the walls and the headspace above the particle layer is connected to a vacuum source). 4.4.3.1 Experimental Set-Up A model system consisting of alumina extrudate particles (Criterion Catalysts and Technologies, USA) with two different shapes – spherical (1 mm diameter) and cylindrical (1 mm diameter and length of 3–5 mm) – as the solid phase and water as the solvent has been investigated experimentally. The particles of both shapes were packed in a small cylindrical plastic container with diameter 12 mm, forming a packed bed of 10 mm height. After packing the sample was completely saturated by water and dried in vacuum (150 or 250 mbar). The heat was supplied by conduction from the bottom of the container at a constant temperature of 65 C. Every 15 min (one drying step) the sample was weighed in order to determine the amount of solvent evaporated during this drying step and its morphology was analyzed by an X-ray microtomography scanner. Even if great care was taken during the manipulation of the container in order to minimize the movement of the solid phase due to small shakes, it was not possible to completely avoid small dislocations of particles between scans. The dislocations became more pronounced near the end of experiment when the liquid content was very low and the cohesive forces of capillary liquid bridges between particles disappeared. A portable X-ray microtomograph Skyscan 1074HR (SkyScan, Belgium) equipped with a 40 kV, 1 mA X-ray tube and a 768 576 pixels X-ray camera with pixel size of 22 mm was used. The volume of the sample that can be analyzed is about 1 cm3. After scanning, each three-dimensional image of X-ray attenuation coefﬁcients was segmented, as described in Section 4.3.1. An example of the original X-ray attenuation coefﬁcient maps and the resulting segmented 3D rendering of the three-phase

4.4 Applications

Fig. 4.25 2D cross-sections of a source image of X-ray attenuation coefficients (a); final 3D rendering of a segmented three-phase image (b).

image is shown in Fig. 4.25. The actual samples of two particle shapes (cylindrical and spherical) are shown in Fig. 4.26. 4.4.3.2 Spatio-Temporal Evolution of the Drying Front First, the packing of hydrophilic spherical particles dried at 250 mbar and 65 C was studied experimentally by X-ray microtomography. The solid-phase microstructure and the evolution of the liquid phase during drying is shown in Fig. 4.27. The solid phase volume fraction is fs ¼ 0.587. The solid phase is only shown for the initially

Fig. 4.26 3D view of a partially wet packing of (a) cylindrical and (b) spherical extrudates.

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Fig. 4.27 Morphology of the packing of spherical hydrophilic particles dried in vacuum – tomographic visualization. Only the liquid phase is shown in all columns except the first one for the purpose of better readability; liquid-phase volume fractions are: (a) fl ¼ 0.365, (b) fl ¼ 0.145, (c) fl ¼ 0.089, (d) fl ¼ 0.019.

nearly saturated sample in order not to obscure the 3D view of the liquid phase in subsequent panels. For a better quantitative understanding of the drying dynamics at the particle level, the relative liquid-phase fraction was averaged over the cross-sections along the r- and z-directions. The evolution of these proﬁles in the r- (a) and the z-direction (b) is plotted in Fig. 4.28. A drying front propagating from the top of the unit cell and at the same time becoming more diffuse can be clearly identiﬁed. On the other hand, the proﬁles in the r-direction are relatively homogeneous (within the small ﬂuctuations caused by the microstructure of the solid phase) and the drying front is moving only in the z-direction. This can be expected as the sample was heated from the bottom of the container. The solid-phase microstructure and the evolution of the liquid phase during the drying of a random packed layer of hydrophilic cylindrical particles at 150 mbar and 65 C is shown in Fig. 4.29. Due to the application of the vacuum, a cavity was formed in the packed layer of particles. The solid phase volume fraction fs is 0.474. As in the case of spherical particles, the results suggest the existence of a drying front that propagates along the z-direction and at the same time becomes more diffused. However, there are two such drying fronts due to the cavity. The dispersion of the

4.4 Applications

Fig. 4.28 Evolution of averaged relative liquid-phase volume fraction during drying of a packed layer of spherical particles at 250 mbar and 65 C; (a) experimental data averaged in the r-direction, (b) experimental data averaged in the z-direction.

front (Fig. 4.30) appears to be somewhat stronger in these experiments, probably due to the capillary action of the smallest pores that are responsible for the retention of the liquid in the otherwise dry upper sections of the particle packing. It should also be noted that the formation of a diffuse drying front is characteristic of an invasion

Fig. 4.29 Morphology of the packing of cylindrical hydrophilic particles dried in vacuum forming a macroscopic cavity. Only the liquid phase is shown in all columns except the first one for the purpose of better readability; liquid-phase volume fractions are: (a) fl ¼ 0.241, (b) fl ¼ 0.146, (c) fl ¼ 0.070, (d) fl ¼ 0.004.

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Fig. 4.30 Evolution of xy-averaged (i.e. in z-direction) relative liquid-phase volume fraction during drying of a packed layer of cylindrical particles with a cavity at 150 mbar and 65 C.

percolation process, whereby larger pores empty preferentially while small ones retain the liquid. This leads to the dispersion of the drying front. Due to the relatively small size of our sample, the asymptotic width of a drying front that would develop in an inﬁnite porous medium may be larger than our unit cell, hence the observed liquid phase proﬁles.

4.5 Future Outlook

Future trends in the application of X-ray tomography to drying are likely to be inﬂuenced by several factors, mainly connected with the continuing improvement of the instruments available for X-ray tomography (both large-scale and micro-CT). Improved spatial resolution achievable in desktop systems means that it will be increasingly possible to visualize pore-level phenomena that occur during drying, by explicitly resolving the solid phase and capillary liquid in a porous medium at the micron level. This may bring new fundamental insights to the theory of drying of porous solids, in particular in combination with computational models based on reconstructed porous media (Stepanek et al., 2007) or pore network approximation (Metzger et al., 2007). Such pore-level visualization of drying will be particularly important in situations where drying is not used simply as a means of removing moisture from a material, but as a method for material structuring on the microscale. It will also be beneﬁcial for situations where a strong coupling between moisture content and solid transport properties exists (deformable materials, drying with deposition of a dissolved phase, etc.). Another development that we may see in the not-too-distant future is the customization of X-ray tomography instruments speciﬁcally for drying

Additional Notational used in Chapter 4

applications. The applications described in this chapter were all based on the use of general-purpose X-ray tomography instruments, and the drying process had to be modiﬁed (e.g. by stop–go operation, see Section 4.3) in order to allow scanning. However, the full dynamics of drying could be better observed if X-ray tomography instruments designed speciﬁcally for drying applications were built, for example including an environmentally controlled specimen chamber (temperature, pressure, humidity). Instrument and applications development often go hand-in-hand, thus the availability of an X-ray tomograph with environmental control would be likely to spur new creative applications of tomography, not only in drying research, but also in other areas where there is a need for real-time observation of physicochemical transformations inside a porous medium.

Additional Notational used in Chapter 4

A a (T) c e f h I Lf P T(a) w xl Z

atomic weight threshold value speed of light thickness coordinate phase function Plancks constant intensity feature length scale line integral (projection function) threshold value mass fraction relative liquid-phase volume fraction atomic number

kg k mol1 —, m1 m s1 m — Js various m — —, m1 — — —

voxel size wave length attenuation coefﬁcient frequency volume fraction

m m m1 s1 —

Greek Letters

d l m n f Subscripts

C P p

Compton scattering photoelectric absorption phase

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Abbreviations

C CT F HVL NDE R

catalyst computed tomography formaldehyde half-value layer non-destructive evaluation resorcinol

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microstructure of banana slices: an illustrative use of x-ray microtomography in microstructural evaluation of a food product. J. Food Eng. 85: 154–162. Leonard, A., Meneses, E., Le Trong, E., Salmon, T., Marchot, P., Toye, D., Crine, M., 2008. Inﬂuence of back mixing on the convective drying of residual sludges in a ﬁxed bed. Water Resour. 42(10–11): 2671–2677. Lim, K. S., Barigou, M., 2004. X-ray micro-computed tomography of cellular food products. Food Res. Int. 37(10): 1001–1012. Lozano, J. E., Rotstein, E., Urbicain, M. J., 1983. Shrinkage, porosity and bulk density of foodstuffs at changing moisture contents. J. Food Sci. 48: 1497–1553. Lutran, P. G., Ng, K. M., Delikat, E. P., 1991. An experimental study using computedassisted tomography. Ind. Eng. Chem. Res. 30: 1270–1280 McCullough, E. C., 1975. Photon attenuation in computed tomography. Med. Phys. 2(6): 307–320. Maire, E., Salvo, L., Cloetens, P., Di Michel, M., 2004. Tomographie a rayons X appliquee a letude des materiaux. Techniques de lIngenieur, Paris, France. Marchot, P., Toye, D., Crine, M., Pelsser, A. M., LHomme, G., 1999. Investigation of liquid maldistribution in packed columns by x-ray tomography. Chem. Eng. Res. Des. 77(A6): 511–518. May, B. K., Perre P., 2002. The importance of considering exchange surface area reduction to exhibit a constant drying ﬂux period in foodstuffs. J. Food Eng. 54(4): 271–282. Mayor, L., Sereno, A. M., 2004. Modelling shrinkage during convective drying of food materials: a review. J. Food Eng. 61(3): 373–386. Metzger, M., Irawan, A., Tsotsas, E., 2007. Inﬂuence of pore structure on drying kinetics: a pore network study. AIChE J. 53: 3029–3041. Michael, G., 2001. X-ray computed tomography. Phys. Educ. 36(6): 442–451.

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5 Measuring Techniques for Particle Formulation Processes Stefan Heinrich, Niels G. Deen, Mirko Peglow, Mike Adams, Johannes A.M. Kuipers, Evangelos Tsotsas, and Jonathan P.K. Seville

5.1 Introduction

Particulate products become more and more important in many industries such as ﬁne chemicals, food or pharmaceuticals. Solid products are mostly better than liquid products because their properties are not only inﬂuenced by the chemical composition but also by the structure and size of the particles. Thus particles of the same composition but with different particle size and/or moisture content may have different properties with regard to ﬂowability, release and dissolution behavior as well as afﬁnity to generation of dust and breakage. Since particulate products have numerous applications, the processes of particle formulation are very important. One of such processes is the ﬂuidized bed spray granulation process, in which a solution, suspension or melt is injected into a ﬂuidized bed. The primary particles grow in the ﬂuidized bed due to layering or agglomeration under intense heat and mass transfer characteristics (M€orl et al., 2007). The objective of this chapter is to present a survey of the measuring techniques for particle formulation processes. The available measuring techniques are grouped into four categories. Category 1 (Section 5.2) includes techniques for in-line particle size analysis during granulation in a ﬂuidized bed and off-line measurements of the particle size distribution, which is probably the main criterion characterizing granulation processes. Category 2 (Section 5.3) comprises modern measurement techniques for solid concentration proﬁles and particle velocities in ﬂuidized beds, which can be non-intrusive or intrusive in nature. Detailed investigations of the ﬂuid dynamics, especially of the solids movement in ﬂuidized beds, have improved the understanding of phenomena occurring in ﬂuidized bed processes (Werther, 1999). In particular, investigations of injection processes into ﬂuidized beds enhance the understanding of coating, granulation or agglomeration. Knowledge of the change of local solids concentration and particle velocities with changing process parameters provides the basis for improved modelling of droplet deposition on the particles, particle–particle collisions,

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

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humidity distribution and chemical reactions in ﬂuidized beds. Category 3 (Section 5.4) is related to the mechanical stability of particles during treatment in ﬂuidized beds, by measuring solids attrition under dry and wet conditions as well as on-line analysis of overspray from non-deposited liquid droplets. Both nucleation phenomena inﬂuence particle properties and the population balance. Finally, category 4 (Section 5.5) includes basic characterization methods of the mechanical properties of partially and fully saturated wet granular media. Some of these measuring techniques, for example the in-line particle size measurement, can also be used for a predictive control of granulation processes, especially in combination with mathematical models. Some other techniques, for example near infrared (NIR) spectroscopy for analysis of components within the particles or confocal laser scanning microscopy (CLSM) for determination of the coating quality of granules are not discussed at all. Additional literature on experimental techniques for particle formulation processes can be found in Salman et al. (2007). Furthermore, the physical properties of particles and particle systems will be discussed in Chapter 6.

5.2 Measurement of Particle Size 5.2.1 In-Line Particle Size Measurement

In-line measurement of particle size may improve our understanding of the dynamics of particle systems, leading to better process control and, thus, to improvement of process stability and product quality, and reduction of waste and costs. Based on a modiﬁed spatial ﬁltering technique, Petrak et al. (1996) have presented a new optical probe for the simultaneous measurement of size and velocity of individual particles. Fiber optical spatial ﬁltering velocimetry was modiﬁed by ﬁber optical spot scanning in order to determine the particle size. Meanwhile an in-line measuring device with the probes IPP-30, IPP-50 and IPP-70 based on a modiﬁed spatial ﬁltering technique is available from PARSUM GmbH (2006). The advantages of this in-line measuring device are low hardware requirements, user friendly handling, long time stability and robust design at reasonable cost (Aizu and Asakura, 1987; Petrak, 2001). 5.2.1.1 Measuring Principle Spatial ﬁltering velocimetry is a method for determining the velocity of an object by observing the object through a spatial ﬁlter in front of a receiver. The modiﬁed spatial ﬁltering technique enables one to measure particle size and velocity simultaneously (Petrak et al., 1996; Petrak, 2001, 2002). Spatial ﬁltering velocimetry is used to determine the unknown particle velocity vp. As mentioned above, the basic operation of spatial ﬁltering velocimetry is to observe the image of a moving object through a ﬁber optical spatial ﬁlter placed in front of a

5.2 Measurement of Particle Size

Fig. 5.1 Measurement principle of the modified spatial filtering technique.

photodetector. The output signal (burst) of the photodetector contains a frequency f0 related to the object velocity vp: vp ¼ f 0 g

ð5:1Þ

where g is the interval of the spatial ﬁlter. Fiber optical spot scanning is an addition to spatial ﬁltering velocimetry. The basic operation of the ﬁber optical spot scanning is to observe the shadow image of a moving particle through a single optical ﬁber with a small diameter d. When the shadow image passes through the single optical ﬁber, an impulse is generated, the width (pulseor tp) of which depends on the particle size xp and the particle velocity vp. The particle size is equal to x p ¼ vp tp d

ð5:2Þ

The probe with the modiﬁed spatial ﬁltering technique uses a ﬁber optical conﬁguration, as demonstrated in Fig. 5.1. The single ﬁber for spot scanning and a ﬁber optical spatial ﬁlter are arrayed together. 5.2.1.2 Instrumentation The PARSUM probe determines the speed and size of particles as they pass through the measurement zone. Simplistically, this is achieved by measuring for how long the particle interrupts a light beam, and how quickly it sequentially blocks a series of detectors. The technique measures particle chord lengths (chord length of the particle shadow), from which particle size distributions (number distribution Q 0 and volume distribution Q 3) can be determined. Software provided with the instrument allows calculation of alternative representations of particle size, so that the data produced can be compared easily with analogous measurements using, for example, laser diffraction or sieving techniques. In addition, because particle velocity is also measured, the results can be conﬁgured to include ﬂow rate, mass throughput and particle concentration data. Results presentation is, therefore, easily customized to the individual monitoring application for which the probe is being used.

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The IPP-70 probe is constructed from stainless steel and has sapphire windows with a wear-resistant coating. It is suitable for measurement of particles in the size range 50–6000 mm, with velocities of between 0.01 and 50 m s1. It has an operating temperature range of 20 to 100 C. An internal air supply in combination with various accessories allows the instrument to be conﬁgured to meet the demands of different applications. This supply is used to purge the optics, ensuring that they remain clean. Additionally, it can be used to dilute and disperse the sample ﬂow if particle loading is too high. Alignment of particle movement is required for applications with chaotic particle motion, such as ﬂuidized beds, and accessories are available to achieve this. In the basic system conﬁguration the IPP-70 particle size probe is connected to a PC running under MS Windows. Particle size information from up to four probes can be processed using a single PC installed up to 200 m from the probes. Particle size data are transferable to a control system in the form of 4 to 20 mA signals, whilst an integrated TCP–server interface allows data transfer over greater distances. 5.2.1.3 Applications The ﬂuidized bed spray granulation process plays an important role in many special chemical, food industry (life sciences) and mineral processing applications. It is used for the production of high quality, free-ﬂowing, low-dust and low-attrition granular solids with applications as particle catalysts or adsorbents, waste water treatment granules, organic or inorganic salts, pharmaceuticals, and so on. The actual particle size distribution of the granules is one of the main parameters determining the product quality, because it has an effect on, for example, drying behavior, solubility and afﬁnity for agglomerate formation. Currently, particle size distribution is usually determined by sieving, laser diffraction or image processing of granules in the laboratory. On the basis of such discontinuous, off-line measurements continuous processes can only be controlled with large time delays, and batch processes cannot be controlled at all. On the contrary, in-line measurement enables real-time process visualization. This will be illustrated in the following by four examples of the use of IPP probes from PARSUM in ﬂuidized bed granulation of detergents and pharmaceuticals (Eckardt and Untenecker, 2005; Dietrich, 2006/2007). Continuous Granulation of Detergents A manufacturer of detergents uses several continuous ﬂuidized bed granulators with a hold-up of 1.5 t each. The ﬁnal product granulates are discharged via classifying discharge tubes with an average particle size of x50,3 ¼ 700 mm. The goal of the manufacturer is low residence times of the product in the granulator and low recycle ﬂow rates to keep the product quality constant. Figure 5.2 depicts particle sizes x10,3, x50,3, x90,3 measured with a PARSUM probe IPP-50 under dust-EX-conditions over a period of 5 h. The process starts with the feeding of particles into the granulator (point A), the beginning of liquid injection (point B), and the achievement of steady-state operation (point C). During the process the particle size increases due to a reduced bed height (D, error status due to external inﬂuences) and a process correction occurs (points E and F) until the steady-state is reached again (point G).

5.2 Measurement of Particle Size

Fig. 5.2 Monitoring of particle size during continuous fluidized bed granulation of detergents.

Another manufacturer of detergents used a similar ﬂuidized bed granulator and recorded the process behavior shown in Fig. 5.3 during a period of 4 days. The process was operated close to the stability limit, which results in a permanent oscillation of the particle size. Comparison of the in-line measurement with off-line image analysis shows good agreement. Batch Granulation of Pharmaceutical Products Active pharmaceutical ingredients are often granulated in ﬂuidized beds to improve their ﬂowability and compressibility. In contrast to ﬁne chemicals, the pharmaceutical industry is dominated by batch processes. Figure 5.4 shows two PARSUM probes IPP-50 installed in a laboratory granulator for measuring tasks in galenics (Schmidt-Lehr et al., 2007). In the example of Fig. 5.5 a pharmaceutical product with an initial mass of 300 kg was granulated batchwise in a ﬂuidized bed. The aim of the measurements was to test the reproducibility of the measured data. To this purpose particles were sampled 40 cm above the gas distributor. Comparison between off-line laser diffraction measurements with a HELOS probe and the in-line PARSUM probe data show good agreement. The whole granulation process is characterized by the following time periods: (i) the granulator is ﬁlled with hold-up particles; (ii) granulation with 100% injection rate; (iii) granulation with reduced injection rate; (iv) shut down of the ﬂuidized bed granulation. For the same production process, Fig. 5.6 depicts the progression of the particle sizes x10,3, x50,3 and x90,3 of three batches during a period of 14 h. The mean initial diameter of the hold-up of 50 mm was granulated to 220 mm. The time segments A to

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Fig. 5.3 Monitoring of particle size during continuous fluidized bed granulation of detergents during a period of 4 days.

D are according to Fig. 5.5. The periods E to G describe the post-drying, the coating and the discharge of particles. The trials indicate that the probe can be used effectively for in situ monitoring of the granulation process. The measured data allow the effect of operating parameters on

Fig. 5.4 Two in-line particle probes IPP-50 installed in a laboratory fluidized bed granulator for pharmaceutical products.

5.2 Measurement of Particle Size

Fig. 5.5 Development of particle size in batch fluidized bed granulation of 300 kg lactose with active pharmaceutical ingredients.

Fig. 5.6 Progression of particle size during fluidized bed granulation of three batches of lactose.

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particle size to be closely monitored and more clearly understood and can, therefore, support the development of increasingly effective control strategies. These, in turn, will result in optimal operation of ﬂuidized bed granulation units. 5.2.2 Off-Line Particle Size Measurement

In 1999 Retsch Technology introduced the CAMSIZER for particle size and shape analysis. This dynamic image analysis system uses digital image processing for free ﬂowing particles in a range from 30 mm to 30 mm. The CAMSIZER achieves particle size analysis with a very high resolution for all kinds of bulk solids. Particle projections are scanned in all possible directions and size distributions are saved in 1000 size classes. Additionally, the analysis of particle shape, transparency, counting of particles and the determination of sample density are possible with this device. The CAMSIZER was developed in cooperation with Jenoptik L.O.S. GmbH and has been constantly improved ever since. Digital image processing for particle analysis uses optical components that record and evaluate images of the particles to be analyzed. One should differentiate between static and dynamic image analysis. Static image processing works with images that are taken from stationary particles that are oriented in a preferred position. Dynamic image analysis captures the shadow projections of randomly oriented free falling particles. The CAMSIZER works with the dynamic method. In contrast to static image processing, this has the advantage that a large number of particles can be analyzed. Thus the measurement statistics are very reliable, while the measured particle size distribution is both representative and reproducible. 5.2.2.1 Measuring Principle The measuring set-up of the CAMSIZER – two digital cameras as an adaptive measuring unit – records, digitizes and processes the shadow projections of particles (Fig. 5.7). The sample is fed in from the feed channel with a vibrating chute so that all particles fall through the image ﬁeld within the measurement shaft uniformly. For a reliable measurement it is necessary that the light source is shadowed by the ﬂow of

Fig. 5.7 Measuring set-up of the Camsizer.

5.2 Measurement of Particle Size

single particles at a constant and low level. This is achieved by dosing the sample with the feed chute that can be controlled to optimally feed the different samples. On the left side of the CAMSIZER there is an LED strobe light source with a diffuser and a collimator to create a consistent and strong light intensity over the whole area. The light beam is spread homogeneously and parallel to the particles and cameras. The particle images are recorded as shadow projections by the two full-frame CCD cameras with a frequency of about 60 images per second. The basic camera (CCD-B) records large particles, the zoom camera (CCD-Z) records the smaller ones. The high number of camera pixels results in a very high resolution and the use of two cameras results in a wide dynamic range. The two-camera construction is patented for the CAMSIZER, providing a unique beneﬁt in comparison to other devices working with dynamic image analysis. Detection of Particles The particle images are recorded by the matrix cameras using a pixel raster of a CCD camera chip. The analog brightness values are digitized into 256 gray scale values by an A/D transducer and afterwards put into binary codes by the software (see also Section 6.2.1). Pixel – a made-up word from Picture and Element – is the synonym for the smallest presentable dot of a picture. One pixel is an element of a particle projection when at least half of it is covered. The size and number of presented pixels determine the resolution. One pixel of the basic camera (CCD-B) has a size of 75 mm, one pixel of the zoom camera (CCD-Z) has a size of 15 mm. Determination of the Outline of Particles For the correct analysis of particles it is necessary that the CAMSIZER software is able to differentiate whether a pixel belongs to a particle projection or not (Fig. 5.8). For this purpose digitized gray tones from the background are deducted from those of the camera image. If a certain threshold is exceeded after the deduction, the pixel group is considered to be part of the particle. For the determination of the outline of a particle, the CAMSIZER uses dynamic threshold values. These are calculated from each individual transition from the light background to the dark particle area. At the point where the value reaches 50% the edge of the particle is deﬁned. This method bears some advantages to deﬁne (ﬁx) threshold values for the deﬁnition of the particle edges: Even blurry or transparent particles or those that appear with different color or brightness are deﬁned correctly in terms of size and shape.

Fig. 5.8 Principle of the dynamic threshold values used for the determination of the particle edge.

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Fig. 5.9 Edge error correction according to ISO 13322-1 and ISO 13322-2.

With a measuring set-up containing only one full frame camera, the factor between the smallest detectable particle (limited by the resolution of the camera) and the largest one would merely be around 100. The upper measuring limit is determined by the edge error correction for particles that touch the edges of the measuring ﬁeld and thus exclude themselves from the analysis (Fig. 5.9). This is consistent with the ISO 13322-2, afﬁx B. Only particles that are inside the frame completely are detected. Particles which intersect the edge are not analyzed. The high resolution and the size overlapping of the two cameras of the CAMSIZER enables precise frame taking (frame-grabbing) within a dynamic range of 1000. For the correct determination of the volume-related particle size distribution that is measured by the CAMSIZER, the number and volume share of the zoom camera measurement needs to be weighted. For this purpose a volume factor is determined from the number and volume share of the basic camera to the number and volume share of the zoom camera in an overlap range of 0.625 to 1.25 mm. The overlap range is chosen in such a way that both the zoom and the basic camera are able to record a sufﬁciently high number of particles with good statistics and high resolution. The combination of the two cameras in the CAMSIZER provides a large dynamic measuring range between 30 mm and 30 mm. 5.2.2.2 Measurement Results: Size and Shape Due to the high information content of the digital images of each measurement process, the particle projections can be analyzed in many different ways. Speciﬁc to the application, the CAMSIZER measures various area-, perimeter- and lengthdimensions. For that purpose, every particle projection is scanned in high resolution and the data are compressed in 64 measuring directions. The results obtained can be, for example: chord length, Feret diameter, width/length aspect ratio, symmetry, Martin diameter, straight length, sphericity, convexity. Size Particle size distributions can be analyzed with many different size parameters, see Fig. 5.10 and compare with Section 2.6.1, Fig. 6.1.

5.2 Measurement of Particle Size

Fig. 5.10 Different size parameters.

The parameter xc,min is a measure of the width of the particle projection. It is deﬁned as the minimum of all maximal chords in the particle area out of all possible measuring directions. xF,max is the maximal Feret diameter and complies with the length of the particle. For this measurement the particle is also scanned in all directions. Finally, xarea is an equivalent diameter that is very common in particle sizing. It is the diameter of a coextensive circle that is derived from the area of the particle image (Chapter 6, Eq. 6.4). For ideally globular particles all size parameters have the same value, but for irregular particle shapes there will be a difference in the particle size distributions (Fig. 5.11). All size parameters have a practical relevance: For a good comparability of the CAMSIZER results with results from a sieve analysis, the width of a particle projection (xc,min) is relevant (Fig. 5.12). With this parameter, the CAMSIZER provides a volume-

Fig. 5.11 Different size parameters deliver different results if particles are not spherical.

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Fig. 5.12 Calculation of the volume of particles and volume-related particle size distribution Q3.

related particle size distribution that is very similar to the results obtained by sieve analysis. The size parameter xarea is well suited for comparison of CAMSIZER results with results from a laser light scattering device, since laser scattering analyzers calculate particle size distributions from scattered light spectra assuming globular particles. The length of a particle projection, xF,max, is used to describe, for example, the length distribution of rods and cylinders. In order to determine the volume-based particle size distribution from the measured sizes of single particles (equivalent to the mass-related size distribution of a sieve analysis), both its speciﬁc size and volume need to be assigned to every particle. Systems of dynamic image analysis mainly use the sphere model for this calculation. In contrast, the volume of the particle measured by the CAMSIZER is approximated by calculating the volume of an ellipsoid from xF,max and xc,min. This calculation of the volume has the decisive advantage of delivering a volume-related particle size distribution that is highly comparable with the mass-related particle size distribution of a sieve analysis. A precondition for that is, of course, a uniform density of the sample particles. Sieve Correlation and Fitting An important application of the CAMSIZER is the replacement of sieve analyses for the determination of particle size distributions. Sieve analysis is a widespread but labor-intensive and time-consuming analytical method with limited resolution. Nevertheless, it is often important for communication between suppliers and purchasers in terms of quality standards and product speciﬁcations. A fast and powerful alternative needs, therefore, to generate comparable measurement results with algorithms that simulate sieve analyses. In this way, users can substitute time-consuming sieve analyses without losing the familiar quality characteristics. The description of particle size deﬁnitions and the calculation of particle volumes in the previous section have already suggested that the examination of particle width, xc,min, should deliver good results for this purpose. Figure 5.13 shows a typical example of the comparability of sieving results and CAMSIZER measurements regarding xc,min. In spite of the general agreement with sieving results in Fig. 5.13, in the range above 0.8 mm the CAMSIZER delivers somewhat different, in this case larger,

5.2 Measurement of Particle Size

Fig. 5.13 CAMSIZER results compared to sieving results for sand.

results. The differences are due to the evaluation of xc,min and particle shape. Figure 5.14 illustrates that ﬂat particle shapes can cause differences to sieving results because of the width measurement. Flat particles can, when falling, be recorded by the CAMSIZER in various orientations, ranging from xs to xm. With their maximal diameter xm they can still pass a square sieve mesh in its diagonal (see Fig. 5.14b). The particle size result that is obtained by sieving is, however, assigned to the mesh width xsieve and can, therefore, be smaller than the result obtained with the CAMSIZER. Deviations of this kind are speciﬁc to the particle shape and, therefore, systematic. Consequently, ﬁtting algorithms that are included in the evaluation software can allow for complete conformity between the results of both measurement methods. In the latest generation of this instrument, a

Fig. 5.14 Reasons for deviations between CAMSIZER and sieving results.

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new method for such ﬁtting was introduced. A narrow single class that is close to the mode of the entire particle size distribution is screened. From the CAMSIZER measurement of this single class and the comparison of the CAMSIZER results from the entire sample with the sieving results, a speciﬁc ﬁtting is created for the product under consideration. Shape While sieving only captures the particle size, the described dynamic image analysis allows the simultaneous determination of both particle size and shape. In contrast to manual analytical methods by, for example a microscope, it can generate a statistically relevant data volume within a short measurement time. All particle shape parameters are usually normalized to take unity as the value for a perfectly globular particle. The more unshaped the particle, the lower becomes the value of the shape parameter. The following four parameters are most commonly used: .

.

Width/length, aspect ratio xc;min =xF;max This parameter describes the ratio between the width and the length of the particle projection by means of the already mentioned values of xc,min and xF,max (Fig. 5.15). As described above, globular particles will have a ratio near unity while spicular, uneven, jagged particle projections will have a ratio tending to lower values. pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Convexity Areal =Aconvex The convexity is calculated by dividing the real area of a particle projection by the area of the convex shell. The convex shell can be described best as an imaginary rubber band that is tied around the particle and ﬁlled up inside (Fig. 5.16).

.

Sphericity/circularity 4pA=P2 The sphericity describes the ratio between the area of the particle image and its perimeter, see also Section 6.2.1. The sphericity is a very important parameter when the ﬁnal product needs to be as globular as possible.

.

Symmetry ð1 þ minðr 1 =r 2 ÞÞ=2 To determine symmetry it is ﬁrst of all necessary to ﬁnd the center point of the particle (C). In every measurement direction lines from edge to edge are applied through the center point C. The center point thus divides every such line in two parts. Then the ratio of these two sections (r1 and r2) is determined. The symmetry is calculated from the smallest measured ratio between r1 and r2. For highly symmetrical shapes close to perfect circles, squares or rectangles, the symmetry will be near unity.

Fig. 5.15 Definition of the aspect ratio.

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

Fig. 5.16 Definition of convexity.

Fig. 5.17 Definition of sphericity.

Fig. 5.18 Definition of symmetry.

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability 5.3.1 Introduction

Several experimental techniques have been developed and used to map the behavior of spout-ﬂuid beds, spouted beds and bubbling ﬂuidized beds and to supply the experimental data required for validation. A non-intrusive method is presented that obtains whole-ﬁeld particle concentration proﬁles in a pseudo-2D set-up from digital images. This technique uses differences in light intensity levels to distinguish between particles and bubbles. The light intensity level is not merely a function of the presence of particles and bubbles but also varies with position and time. The manner in which the quality of the images is enhanced, along with the methods that were used to compensate for the inﬂuence of time and position, are described. The digital images were also used to obtain whole-ﬁeld particle concentration proﬁles in a pseudo-2D set-up using particle image velocimetry (PIV). The method requires two images separated by a short time interval and subsequently uses crosscorrelation analysis to determine the spatially-averaged displacement of the particle images between the ﬁrst and second image. The displacement and the time interval are used to obtain the average velocity of a group of particles. The methods that were used to ensure and enhance the quality of the results are explained.

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Spectral analysis of pressure drop ﬂuctuations is a non-intrusive measurement technique, which supplies information about the dynamic behavior of the particles in a spout-ﬂuid bed, in a spouted bed and in a bubbling ﬂuidized bed through the pressure drop ﬂuctuations. The characteristics of the dynamic behavior are captured by applying a Fourier transformation to a recording of the ﬂuctuations of the pressure drop over the entire bed. The result of this transformation is rendered into a frequency spectrum, which characterizes the dynamic behavior of the bed. A scaling method is described that can be used to compare results obtained with recordings of different duration. Positron emission particle tracking(PEPT) is a non-intrusive measurement technique, which supplies detailed information about the particle motion by tracking the position of a single activated particle in the interior of a three-dimensional bed. The activated particle emits positrons which are annihilated when they encounter electrons, producing back-to-back gamma rays. These gamma rays are simultaneously detected by a pair of detectors. The position of the particle emitting the positrons is reconstructed by calculating the point of intersection of several pairs of gamma rays. The method that was used to reduce the amount of noise that was present in the signal is described and the manner in which the particle circulation time was extracted from the signal is explained. Finally, a ﬁber optical measurement system was used to determine the solid concentration proﬁles and particle velocities in a freely bubbling ﬂuidized bed and in a ﬂuidized bed with a jet, with and without the presence of droplets. 5.3.2 Particle Detection

Particle detection is an optical measurement technique that can, amongst others, be used to instantaneously produce the spatial distribution of the particles. The technique uses digital images, which can be recorded without inﬂuencing the behavior of the particles. In the images, the particle is distinguished from the background based on the intensity. Subsequently, the local particle fraction can be calculated. The main advantages of the particle detection technique are that it is a non-intrusive measurement technique and that the images supply instantaneous information about a large spatial area. A drawback of using an optical technique in a ﬂuidized bed is that ﬂuidized beds are predominantly opaque due to the presence of particles. Consequently, only the particle behavior in the vicinity of the wall can be captured. To capture the particle behavior in the interior of a ﬂuidized bed, alternative techniques, like positron emission particle tracking, which will be discussed in Section 5.3.5, are required. Agarwal et al. (1997) were the ﬁrst to use digital image analysis to study a ﬂuidized bed. In their work they positioned a light source behind the bed to visualize the bubbles. The light source was only visible to the camera when a bubble was present. This type of bubble, which extends from the front wall to the back wall, is termed a deep bubble and is illustrated in Fig. 5.19. Goldschmidt et al. (2003) did not detect the bubbles, but the particles. They illuminated the bed from the front with a diffuse light

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

Fig. 5.19 An illustration of the illumination of shallow and deep bubbles.

source. Consequently, the particles in the vicinity of the wall were adequately lit and are termed bright particles. Bright particles block part of the incoming light and may consequently prevent the proper illumination of particles further away from the wall, as illustrated in Fig. 5.19. Particles that are not properly illuminated are termed shaded particles. The presence of a shaded particle implies the presence of a bubble located between this particle and the wall. Shaded particles are therefore indicative of bubbles. Since these bubbles do not extend from wall to wall, they are termed shallow bubbles. Goldschmidt et al. (2003) distinguished deep bubbles by using a different color for the background of the bed, which they detected by means of a color camera. In the present study a monochromatic camera is used. In combination with a background of low intensity (black), the particles can be distinguished from both types of bubbles solely on intensity information. The quality of the results of the image analysis obviously depends on the quality of the individual images. An overview of the set-up that has been used to record the images is presented in Fig. 5.20. The quality of the images is negatively affected by reﬂections, movement of the particles during the exposure time, that is motion blurring, and varying illumination conditions. Reﬂections are avoided by lighting the bed directly under a small angle (<45 ) and by covering the surroundings of the set-up with black curtains. Motion blurring can

Fig. 5.20 Overview of the digital image analysis set-up.

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be prevented by minimizing the exposure time, which reduces the amount of lighting. This needs to be compensated for to ensure that the bed is sufﬁciently illuminated. For this reason two 500 W halogen lamps along each side of the camera were used to illuminate the bed. Furthermore, the amount of lighting can be increased by increasing the aperture of the camera. The spatial variation of the illumination can be prevented by minimizing the aperture of the camera and by using diffuse lighting. The temporal variation of the illumination is caused by the alternating current of the power supply of the lamps and needs to be compensated for. The conﬂicting requirements for the prevention of motion blurring and the spatial variation of the illumination have been reconciled to obtain a reasonably homogeneous, but strong illumination. Consequently, the spatial variation of the illumination needs to be compensated for. The manner in which the temporal and spatial variation of the illumination is handled is discussed below. In the particle detection algorithm, the intensity of each pixel (I) is compared with a threshold value (IT): I>I T Y I 2 particle

ð5:3Þ

I < I T Y I 2 bubble

ð5:4Þ

The determination of the threshold value is, unfortunately, not straightforward since, as stated before, the intensity depends not only on the distance between the particle and the wall, but also varies with time and position: I ¼ f ðx; z; tÞYIði; j; tÞ

ð5:5Þ

The intensity of the light emitted by the lamps is affected by the alternating current and therefore varies with time. The temporal correction that is required to compensate for these ﬂuctuations is determined by using the difference between the average illumination of the entire bed, IðtÞ, and its local time-average, hIi: I ¼ f ðx; z; tÞYIði; j; tÞDIðtÞ ¼ c t ðI ðtÞhIiÞ

ð5:6Þ

where ct is the temporal correction constant and where the spatial average is deﬁned as: IðtÞ ¼

N X M 1 X Iði; j; tÞ N M i¼1 j¼1

ð5:7Þ

and the temporal average around time t as: hIði; jÞi ¼

n 1 X Iði; j; tÞ 2n þ 1 t¼n

ð5:8Þ

Furthermore, the intensity of the illumination depends on the orientation of the lamps and the aperture of the camera, and consequently is a function of the position. Both of these disturbances are constant in time and can be compensated for by using a method proposed by Goldschmidt et al. (2003). They calculated correction factors

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

Fig. 5.21 Illustration of the spatial correction of the illumination.

for each pixel by evaluating the variation of the intensity with position for a timeaveraged recording of a uniformly white sheet: c x ði; jÞ ¼

hIi hIði; jÞi

ð5:9Þ

Applying both corrections results in: I0 ði; j; tÞ ¼ c x ði; jÞIði; j; tÞDIðtÞ

ð5:10Þ

After the spatial correction has been applied to the images, which is illustrated in Fig. 5.21, the threshold value and ct are determined by examining several situations. First, a stagnant bed, illustrated in Fig. 5.22, is studied. In a stagnant bed all particles are, in principle, within the ﬁeld of view (FOV). Therefore, the solids volume is known. Furthermore, the width and depth of the bed are known. The height of the bed within the ﬁeld of view, hFOV, can be determined from the snapshot. Consequently, the volume-averaged solids fraction can be determined: es;3D ¼

NpV p W D hFOV

ð5:11Þ

The height of the bed occupied by solids, hs, can also be determined from the snapshot. Consequently, the packed bed solids fraction, which is considered to be the maximal solids fraction, can be determined: emax s;3D ¼

NpV p W D hs

ð5:12Þ

Subsequently a series of images of an operating regime for which all particles remain within the ﬁeld of view is analyzed. These images are divided into areas of N

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Fig. 5.22 Illustration of the analysis of a snapshot of a stagnant bed.

times M pixels, termed interrogation areas. The solids fraction in each of these areas is determined as follows: es;2D ¼

N X M 1 X dði; jÞ; N M i¼1 j¼1

where

dði; jÞ ¼ 1 if I0 ði; j; tÞ>IT dði; jÞ ¼ 0 if I0 ði; j; tÞ < I T

ð5:13Þ

By assuming that the particle conﬁguration in the third dimension, the depth, is equivalent to the two-dimensional particle conﬁguration in the interrogation area, the three-dimensional solids fraction of the interrogation volume can be obtained: es;3D ¼ ðes;2D Þ3=2

ð5:14Þ

When all particles are within the ﬁeld of view, es;3D is known. The threshold value for each image can now be set in such a way that the measured value is in correspondence with the calculated value: NX X NZ 3=2 NpV p 1 X ¼ ðes;2D ði; jÞÞ W D hFOV N X N Z i¼1 j¼1

ð5:15Þ

where NX and NZ are, respectively, the number of interrogation areas in the horizontal and vertical directions. With the following condition: ðes;2D ði; jÞÞ3=2 ¼ emax s;3D

if

ðes;2D ði; jÞÞ3=2 > emax s;3D

ð5:16Þ

the effect of spurious results is reduced. Example input and output images of the particle detection, including the solids fraction distribution, are displayed in Fig. 5.23.

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

Fig. 5.23 An example result of the particle detection algorithm.

Fig. 5.24 Each point shows the spatially averaged intensity and the corresponding threshold of a single image.

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When a series of images is evaluated, the same pixels are attributed to particles in a stagnant part of the bed. On the other hand, when a ﬁxed threshold is used, the number of pixels representing a particle ﬂuctuates with the intensity of the light emitted by the lamps. Consequently, the inﬂuence of time on the images is successfully compensated for. as The temporal correction constant, ct, can be determined from a plot of IT versus I, shown in Fig. 5.24. Since the images can be corrected for the inﬂuence of position and time, a single threshold value, which is equal to the average threshold value in Fig. 5.24, can be used for all subsequent experiments, even in cases where some particles leave the ﬁeld of view. 5.3.3 Particle Image Velocimetry

Particle image velocimetry (PIV) is an optical, non-intrusive measurement technique that produces instantaneous two-dimensional ﬂow velocity data for a whole plane in a three-dimensional ﬂow ﬁeld. The initial groundwork for the PIV technique was laid down by Adrian (1991). Keane and Adrian (1990) used the PIV technique to obtain experimentally ﬂow velocity ﬁelds from photographs. Willert and Gharib (1991) were the ﬁrst to use images that were recorded with digital cameras. Westerweel (1993) extended the theory to evaluate digital PIV images and developed a method to estimate the displacement at sub-pixel level. Digital PIV has already been used extensively in the ﬁeld of experimental ﬂuid dynamics, for example to study twophase ﬂows in dilute systems (Deen et al., 2002). The PIV technique that was used in this work will be discussed in this section and is based on the method developed by Westerweel (1997), to which the interested reader is referred for further details. In traditional PIV, the ﬂow is visualized by seeding it with small tracer particles that closely follow the ﬂow. As was demonstrated by Link et al. (2004) and Bokkers et al. (2004), in gas–particle ﬂows the discrete particles can readily be distinguished, so no additional tracer particles are required to visualize the particle movement. The image acquisition is illustrated in Fig. 5.25.

Fig. 5.25 Illustration of the image acquisition.

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

Fig. 5.26 Illustration of PIV analysis.

The PIV analysis is illustrated in Fig. 5.26. Two subsequent images of the particle ﬂow, separated by a short time delay, dt, are divided into small interrogation areas with a size DI, consisting of N times M pixels. The particle velocity within each of the interrogation areas is assumed to be approximately constant. Cross-correlation analysis is used to determine the spatiallyaveraged displacement of the particle images, s(x, t), between the interrogation areas in the ﬁrst and second image: RðsÞ ¼

N X M X

I 1 ði; jÞI2 ði þ sx ; j þ sy Þ

ð5:17Þ

i¼1 j¼1

This can be split into three contributions: RðsÞ ¼ RC ðsÞ þ RF ðsÞ þ RD ðsÞ

ð5:18Þ

where RC is the correlation of the mean intensity, RF the correlation of the mean with the ﬂuctuating image intensity, and RD the correlation of the intensity ﬂuctuations. The terms RC and RF vanish by subtracting the mean intensity from the image ﬁelds. The particle image displacement, sD, is determined by measuring the location of the tallest peak in RD. An illustration of a cross-correlation diagram is given in Fig. 5.26. The velocity in the interrogation area is then easily determined by dividing the measured displacement by the image magniﬁcation, M, and the time between two images, dt: vp ðx; tÞ ¼

sD ðx; tÞ Mdt

ð5:19Þ

provided that dt is sufﬁciently small. An example result is displayed in Fig. 5.27. To apply PIV successfully, a few conditions need to be met. First, PIV requires the spatial and temporal scales of the ﬂow to be large with respect to DI and dt. The former can be expressed by considering the velocity gradient within the interrogation area

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Fig. 5.27 An example of the input and the result of the PIV analysis.

(Du), which needs to be small: MjDujdt dp < DI DI

ð5:20Þ

This can be achieved by using small interrogation areas. On the other hand, PIV requires a certain effective number of particle image pairs per interrogation area to produce reliable results. This topic has been addressed by Keane and Adrian (1990). They examined the inﬂuence of the effective number of particle image pairs per interrogation area on the accuracy of the measurement. The effective number of particle image pairs per interrogation area can be expressed as NIFIFO, where NI is the initial number of particle images present in the interrogation area. The factor FI is a measure for the in-plane displacement, that is particles that move out of the interrogation area in the plane of measurement. FI represents the fraction of particle images remaining in the interrogation area. The factor FO is a measure of the out-of-plane displacement, that is particles that move out of the plane of measurement. FO represents the fraction of particle images remaining in the measuring plane. The relative height of the tallest peak in RD, and consequently the accuracy of the measurement of the particle displacement, sD, scales linearly with NIFIFO: RD ðsD Þ N I F I F O

ð5:21Þ

Keane and Adrian (1990) have shown that the following design rule needs to be satisﬁed in order to have an accuracy greater than 95%: N I FIFO > 7

ð5:22Þ

Westerweel (1997) assessed the effect of using digital images for the PIV analysis. In a digital image, a particle image consists of a limited number of pixels. As a

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

consequence, the particle displacement can only be determined in an integer number of pixels, which severely limits the accuracy of the measurement. By applying a peakﬁt to the displacement correlation peak, he was able to determine the displacement of the particle images on sub-pixel level. He tested several peak-ﬁt functions of which a Gauss curve was most suitable for the conditions encountered in this study. He found that a minimum of only two pixels was required to represent the diameter of each particle image in order to determine the displacement on sub-pixel level with good precision. He even concluded that increasing the number of pixels per particle image beyond two did not improve the results. A number of procedures have been developed to improve the results of the PIV analysis. Keane and Adrian (1992) introduced a procedure to reduce the loss of particle images due to in-plane displacement, that is to increase the value for FI. This was achieved by using a window offset, which means that each interrogation area of the ﬁrst image is not cross-correlated with the same interrogation area of the second image, but with an interrogation area that is shifted by the particle displacement: RðsÞ ¼

N X M X

Iði; jÞIði þ ishift þ sx ; j þ jshift þ sy Þ

ð5:23Þ

i¼1 j¼1

This procedure implies that the displacement is determined in two steps. In the ﬁrst step the overall displacement is determined, while this result is reﬁned in the second step. Westerweel et al. (1997) concluded that this procedure can also be used to increase the precision and the accuracy of the determination of the displacement. Even when the design rules are met and window-shifting is applied, the particle velocity ﬁeld produced by the PIV analysis contains spurious vectors. These are vectors that signiﬁcantly deviate from the ﬂow pattern of the particle phase, which should be reasonably continuous. Westerweel (1994) found that a local median test is the most effective method to eliminate these spurious vectors. In this test, each vector is compared with the median of the eight surrounding vectors. The whole PIV analysis procedure is summarized in a ﬂow diagram displayed in Fig. 5.28. The PIV analysis was also applied to a novel spouted bed apparatus with a gas distributor which consists of two adjustable chopped cylinders, developed by M€ orl et al. (2001) and brought to the market by Glatt GmbH (ProCell module). By rotating the cylinders, the free cross-sectional area of the gas inlet can be varied. Thus, the opening ratio of the gas distributor and, consequently, the gas inlet velocity can be regulated during the operation. This is an advantage when the gas distributor tends to get clogged with bed material. By varying the gas inlet area, clogging and dead zones within the apparatus are eliminated without interrupting the process. For this kind of spouted bed, Gryczka et al. (2008) measured instantaneous as well as time-averaged particle velocity distributions by means of PIV experiments at a transparent acrylglass set-up. Figure 5.29 shows such instantaneous velocity vector maps and Fig. 5.30 displays time-averaged velocity vector maps obtained by the PIV measurements at different inlet gas volume ﬂow rates.

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Fig. 5.28 Flow diagram of the particle image velocimetry analysis procedure.

A circulating particle motion can be recognized in both ﬁgures (Figs. 5.29 and 5.30). By analysis of the velocity vector maps, several regions of different particle motion can be identiﬁed. Clearly recognizable is the jet zone characterized by a vertical particle motion from the bottom to the top and by high particle velocities (see, e.g. Figs. 5.29 or 5.30b and c). In the fountain zone, where the particles are separated towards the apparatus walls, and also in the annulus zone, where they slide downwards on the slope due to gravity, the particle velocities are much lower. The ﬁrst basic conclusion which can be extracted from the PIV measurements is that the particle velocity is not approximately equal to the gas velocity in the jet zone (20–30 m s1), but is much less (1–2 m s1). So, particle attrition might presumably not be higher than in conventional ﬂuidized bed apparatuses. Furthermore, the instantaneous velocity vector map in Fig. 5.29a shows that particles in the jet zone are not conveyed straightforwardly in a vertical direction, but are slightly deﬂected to the left or to the right. So it can be assumed that the ﬂuidization is unstable at a gas throughput of V_ g;in ¼ 0:022 m3 s1 . Compared with that unstable operation, the particles in Fig. 5.29b and c at gas volume ﬂow rates of 0.026 m3 s1 and 0.029 m3 s1, respectively, are conveyed straightforwardly from the bottom to the top of the apparatus. In those cases the process is stable. These observations can be used to determine the stable operation range. It was asserted that the transition between unstable and stable spouting operation is at a gas volume ﬂow rate of about V_ g;in ¼ 0:025 m3 s1 .

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

Fig. 5.29 Instantaneous velocity vector maps at different inlet gas volume flow rates V_ g;in obtained by PIV measurements (material: 1.0 kg g-Al2O3-particles, d50,3 ¼ 1.75 mm).

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Fig. 5.30 Time-averaged velocity vector maps at different inlet gas volume flow rates V_ g;in obtained by PIV measurements (material: 1.0 kg g-Al2O3-particles, d50,3 ¼ 1.75 mm).

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

From the time-averaged velocity vector maps of Fig. 5.30, general conclusions on the ﬂuidization with respect to mean particle velocities and bed expansion at different gas volume ﬂow rates can be drawn. In Fig. 5.30a, at a gas volume ﬂow rate of V_ g;in ¼ 0:016 m3 s1 , one can hardly recognize any velocity vectors. A narrow jet zone and a little roof of particles on the top of the bed can be observed. Consequently, particles move very slowly (less than 1 m s1) in the jet zone, resulting in a marginal bed expansion. The ﬂuidization process is, thus, unstable. In Fig. 5.30b, at a gas throughput of 0.022 m3 s1, a wider jet zone can be discerned, which becomes more pronounced with increasing distance from the gas inlet. The bed expansion is larger and a distinct roof of particles has formed on the top of the bed. These phenomena are caused by the higher inlet air volume ﬂow. Particles move faster, so that particle velocity vectors can be identiﬁed in Fig. 5.30b. One can see that particles in the jet zone move upwards at about 1 m s1. In the fountain zone (roof) the particle velocity decreases to about 0.5 m s1. In the annulus zone particle velocity vectors are not visible, indicating that the particle velocities are much lower than, for example, in the fountain zone (less than 0.5 m s1). Thus, a good particle mixing is not accomplished at a gas volume ﬂow rate of 0.022 m3 s1 and the process is unstable. In Fig. 5.30c, at a gas throughput of 0.028 m3 s1, a pronounced bed expansion with a large fountain zone can be recognized. The particle velocity is between 1 and 2 m s1 in the jet zone and about 0.5 to 1.0 m s1 in the fountain zone. Particle velocity vectors are visible even in the annulus zone, indicating that the particles move downwards on the slope faster than in the previous two cases (0.016 and 0.022 m3 s1). By analyzing the magnitude as well as the direction of the particle velocity vectors, one can assert that the particles perform a continuous circulating motion and conclude that the process operates stably. By increasing the inlet gas volume ﬂow rate to 0.038 m3 s1 (see Fig. 5.30d) the bed expansion increases further. The particle velocities are higher in all zones than in the previous case (0.028 m3 s1). The amount of particles in the annulus zone decreases enormously because more particles are entrained by the gas jet. The velocity vector of Fig. 5.30d also shows a continuous circulating particle motion pattern so the ﬂuidization regime can be considered as stable. In the following, the results of PIV measurements in the novel spouted bed will be presented in the form of time-averages and ﬂuctuations of particle velocity. Figure 5.31 shows the proﬁles of the horizontal (x-component) and vertical (z-component) time-averaged particle velocity (left-hand side of the diagram) as well as the associated ﬂuctuations (root mean square RMS – right-hand side of the diagram) at a height of 0.09 m above the base plate. During the bubbling spouting state at an inlet air volume ﬂow rate of 0.015 m3 s1 (Fig. 5.31a), the particles are almost stationary. Only when gas bubbles rise through the bed are some particles entrained upwards. Thus, the time-averaged particle movement is nearly zero (see Fig. 5.31a left) and the ﬂuctuating motion is also very low. This spouting state is similar to the ﬁxed bed state. Increasing the inlet air volume ﬂow rate to 0.022 m3 s1, the gas bubble size increases and particles are accelerated more intensively in a vertical direction in the jet zone (between 0.09 and 0.16 m in the x-position) resulting in a distinct peak in the time-averaged z-component velocity proﬁle in Fig. 5.31b left. A small peak in the

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5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

time-averaged x-component particle motion is observable, indicating the presence of some lateral movement due to growing or coalescing bubbles. Also the ﬂuctuating velocity plots in the x- and z-directions (Fig. 5.31b right) show higher peaks in the jet zone compared to the previous case (0.015 m3 s1), indicating that the particles are accelerated due to the passage of gas bubbles. In the annulus zone (from 0 to 0.08 m and from 0.17 to 0.25 m in the x-direction) the particles hardly move at the considered height of 0.09 m above the base plate. This observation can be made for all four inlet air volume ﬂow rates depicted in Fig. 5.31 during the series of PIV measurements. From video recordings and from PIV images one can see that the particles move downwards very slowly in the annulus zone (highest time-averaged velocity is about 0.2 m s1 at V_ g;in ¼ 0:035 m3 s1 , in both, the x- and the z-directions, due to the inclination of the side wall). Increasing the gas throughput from 0.022 m3 s1 to 0.028 m3 s1 (Fig. 5.31c), the ﬂow undergoes the transition from unstable to stable spouting. A large peak occurs in the time-averaged particle velocity distribution in the z-direction in the jet zone, with a maximum of about 1.1 m s1 (Fig. 5.31c left). This means that particles in the jet zone are accelerated more intensively, resulting in a periodic formation of large, elongated gas bubbles. Positive and negative values of the time-averaged x-component velocity emphasize that particles are slightly deﬂected from the center during the spouting process, but not in such an extreme manner as one can observe beyond the stable spouting range. In the plots of the velocity ﬂuctuations of Fig. 5.31c right, one can see that the maximal value of the z-component is three times larger than in the previous case. This underlines that gas bubbles rise through the bed periodically causing an intermittent particle motion. Moreover, the x-component of the velocity ﬂuctuation has doubled. This shows that the gas jet does not pass the bed straightforwardly, but is slightly deﬂected from the center. Further increase in the inlet air volume ﬂow rate to 0.035 m3 s1 (Fig. 5.31d) does not change the main features of the plots of time-averaged and ﬂuctuating particle velocities. The peak shapes and maximal values of the time-averaged z-component particle velocities are approximately equal at around 1.0 m s1. Positive and negative values of the time-averaged x-component particle velocities (Fig. 5.31d left) still indicate the slight deﬂection of particles when being entrained upwards by the air jet. Also the maximal values of the z- and x-component of the velocity ﬂuctuation are nearly equal to the previous ones at about 0.3 and 0.1 m s1, respectively. However, the shape of the distribution of the z-component of ﬂuctuating velocity, shown in Fig. 5.31d, has changed. In Fig. 5.31d, two pronounced peaks can be seen, which can be attributed to a more intensive deﬂection of the gas jet to the left and right. In this way, two main particle stream lines are created, which are located somewhat left and 3 Fig. 5.31 Profiles of the horizontal (x-component) and vertical (z-component) time-averaged particle velocity (left) and associated RMS fluctuations (right) at a height of 0.09 m above the base plate at different inlet air volume flow rates (material: 1.0 kg g-Al2O3-particles, d50,3 ¼ 1.75 mm).

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right of the center of the jet zone. From this, one can conclude that the ﬂow pattern at the gas inlet volume ﬂow rate of 0.035 m3 s1 is near to the upper boundary of stable spouting, where the deﬂections are even more intense. This interpretation is conﬁrmed by the results of investigations of gas phase pressure ﬂuctuations in Section 5.3.4. According to these results, the upper boundary of stable spouting occurs at a gas throughput of around 0.040 m3 s1. 5.3.4 Spectral Analysis of Pressure Drop Fluctuations

Spectralanalysis ofpressuredropﬂuctuations(SAPDF)isa non-intrusivemeasurement technique, which supplies information about the dynamic behavior of the particles in all kinds of ﬂuidized beds (e.g. spout-ﬂuid bed, spouted bed, bubbling ﬂuidized bed). Fluidized, spout-ﬂuid and spouted beds display dynamic behavior caused by the presence of heterogeneous ﬂow structures. Consequently, the particle conﬁguration changes continuously. Since the particle conﬁguration affects the pressure drop, the dynamic behavior involves pressure drop ﬂuctuations. To capture the characteristics of the dynamic behavior, a Fourier transformation is applied to a recording of the ﬂuctuations of the pressure drop over the entire bed. This results in a frequency spectrum that characterizes the dynamic behavior of the bed. Van der Schaaf et al. (1998) studied the contribution to the pressure drop ﬂuctuations of both local, that is in the vicinity of the pressure probe, and global changes in the particle conﬁguration. They concluded that global ﬂuctuations originated from the bottom part of the bed, caused by bubble formation or coalescence, while the local ﬂuctuations originated from gas bubbles passing the sensor. These authors observed that the local ﬂuctuations can mainly be discerned at high frequencies and are overpowered by the global ﬂuctuations at intermediate frequencies (1–10 Hz). Global ﬂuctuations are more easily observed near the bottom of the bed. The global pressure drop ﬂuctuations contain most of the information about the dynamic behavior of the entire bed that is of main interest for, for example, a spout-ﬂuid bed. The pressure drop ﬂuctuations are therefore recorded just above the gas distributor. An exemplary pressure drop signal is displayed in Fig. 5.32. Furthermore, the spectral analysis will focus on the intermediate frequency range (1–10 Hz). The Fourier transformation decomposes a periodic function into sinusoids of different frequency, which sum to the original function. It identiﬁes the sinusoids of different frequency and their respective amplitudes. The coefﬁcients of the Fourier transformation of f (t) are deﬁned as: 1 ð

FðuÞ ¼

f ðtÞ ei2ptu dt

ð5:24Þ

1

pﬃﬃﬃﬃﬃﬃﬃ where i ¼ 1, t is time and u is termed the frequency variable. The Fourier transform can be converted with: eiu ¼ cos u þ i sin u

ð5:25Þ

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

Fig. 5.32 A typical recording of the pressure drop over a spout-fluid bed.

into its sinusoidal form: 1 ð

FðuÞ ¼

f ðtÞðcos ð2putÞi sin ð2putÞÞ dt

ð5:26Þ

1

The complex function F(u) can be decomposed into a real and an imaginary part according to: FðuÞ ¼ RðuÞ þ iIðuÞ

ð5:27Þ

The magnitude of F(u) increases with the number of times the period associated with frequency u is observed in the signal and with its amplitude in the signal. Therefore, F(u) represents the contribution of the function with frequency u to the original signal. The contribution of each frequency is usually represented by its power, which is the square of the magnitude of F(u): PðuÞ ¼ jFðuÞ2 j ¼ R2 ðuÞ þ I2 ðuÞ

ð5:28Þ

In practice, the pressure is not available as a continuous signal, like f (t), but is measured at regular time intervals at N discrete points in time, which are indicated by j. Consequently, only N frequencies can be discerned, which are indicated by k. Therefore, a discrete Fourier transformation, the fast Fourier transfer (FFT) algorithm available in Matlab 6.5, was applied to the pressure drop ﬂuctuations: FðkÞ ¼

N X

i2p f ð jÞeð N Þð j1Þðk1Þ

ð5:29Þ

j¼1

Note that k ¼ 1 produces the sum of all inputs and consequently contains no information about the periodicity of the signal and is therefore discarded. Furthermore, k and (N k þ 2) produce the same results, which means that the second half of F(k) is the same as the ﬁrst half and therefore redundant.

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Since the magnitude of F is a linear function of N, N was used to normalize P: jFðkÞj 2 ð5:30Þ PðkÞ ¼ N=2 Note that since the ﬁrst element of Fand the second half of F were discarded, P only consists of N/2 elements. Each element of P(k) is associated with the following frequency: freq ðkÞ ¼

f sample N

k

ð5:31Þ

where fsample is the sampling rate. The frequency spectrum consists of a plot of P versus the frequency. Equation 5.31 shows that the maximum number of frequencies that can be distinguished per Hz depends on N/fsample, that is on the period over which the pressure drop signal is recorded. Consequently, pressure drop signals that are recorded over different periods of time can only be appropriately compared when the frequency spectra are scaled. The scaling procedure can be explained using the analogy with a histogram. A larger number of frequencies per Hz is analogous to a smaller bin size in a histogram. When two data sets recorded over different periods of time are considered, the frequency spectra that are based on pressure drop signals recorded over the longest period of time consist of a larger number of smaller bins. The contributions, that is powers, to several smaller bins can be added to result in bins that have the same size as the bins encountered in the pressure drop signal recorded over the shortest period of time. Example frequency spectra, both scaled and unscaled, are displayed in Fig. 5.33. The unscaled frequency spectrum after a period of 7 s does not seem to correspond

Fig. 5.33 Example frequency spectra of pressure drop fluctuations measured over different time intervals.

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

with the unscaled frequency spectrum obtained after a period of 63 s. However, when the frequency spectrum obtained after a period of 63 s is scaled to match the number of bins present in the unscaled frequency spectrum after a period of 7 s, it resembles the frequency spectrum obtained after a period of 7 s much more closely. In addition to the work discussed in the previous section, where different operation ranges of a novel slit-shaped spouted bed apparatus with two horizontal and adjustable gas inlets were analyzed by means of PIV-technique, Gryczka et al. (2008) also carried out gas pressure drop ﬂuctuation measurements by means of a high speed pressure detector. This sensor was used to record a total of 10 000 pressure samples over the entire bed (overpressure) during a period of 10 s. By subtracting the overpressure values of the empty apparatus from the overpressure values measured with bed material, the bed pressure drop values were obtained. A representative bed pressure drop value was obtained by averaging. Subsequently, the Fourier tranformation was applied to these measured spectra. The typical evolution of the bed pressure drop of a spouted bed with gas throughput is characterized by a high initial bed pressure drop, a nearly constant pressure drop in the stable operation range and a slightly decreasing pressure drop at high inlet gas volume ﬂow rates (Gryczka et al., 2008). As an example, some results of the measurement of the gas-phase pressure ﬂuctuations and of the Fourier transformation are presented in Fig. 5.34 for experiments with g-Al2O3-particles (d50,3 ¼ 1.75 mm), a bed mass of 1.0 kg and an opening angle of the gas inlet cylinders w ¼ 0 . The graphs of the bed pressure drop show only the ﬁrst 3 s of the recordings. In this way, characteristic ﬂuctuations can be recognized more accurately. The amplitudes of the gas pressure ﬂuctuations indicate the existence of pressure impulses that originate from gas bubbles bursting on the bed surface. From the upper plot of Fig. 5.34a it can be extracted that about 4 to 5 main ﬂuctuations of different amplitudes were detected per second at a gas volume ﬂow rate of 0.021 m3 s1. Also the Fourier tranformation (lower plot) indicates the existence of a commanding frequency of about 5 Hz. However, there are further frequencies between 2 and 4.5 Hz as well as between 5.5 and 7 Hz which cannot be neglected. This means that rising gas bubbles burst on the bed surface at irregular time intervals. The corresponding PIV analysis shows a series of images of this spouting state (Gryczka et al., 2008). One can see that bed expansion is very low and that big and small bubbles move upwards through the bed causing more or less powerful pressure impulses, which are recorded by the pressure detector when the bubbles burst on the bed surface. The total bed movement is more similar to a ﬁxed bed state, that is particle mixing caused by the ﬂuidization gas is very low. This operation range is referred to as the bubbling state and is instable by deﬁnition as was reported earlier by Piskova (2002); Piskova et al. (2003). An increase in the inlet gas volume ﬂow rate to 0.023 m3 s1 does not change this unstable spouting state. However, when the gas throughput is increased to 0.025 m3 s1 (Fig. 5.34b) a serious change occurs compared to the previous graphs. Now, the main ﬂuctuations are equal and have nearly the same amplitude, which results in a large dominant peak in the Fourier transformation. The position of this peak on the abscissa reﬂects the frequency of the main ﬂuctuation. This spouting

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Fig. 5.34 Measured bed pressure drop fluctuations (top) and Fourier transformation of the frequency spectra of these fluctuations (bottom).

operation is called stable. Hence, the turnover between instable bubbling and stable operation takes place somewhere between the gas volume ﬂow rates of 0.023 and 0.025 m3 s1 (Gryczka et al., 2008). The stable spouting range is characterized by a circulating particle motion and good particle mixing without dead zones. The PIV images by Gryczka et al. (2008) illustrate the stable spouting operation. Only one large, elongated gas bubble is observed, which moves uniformly upwards just above the gas distributor element. Only one pressure impulse will be detected when this bubble bursts on the bed surface, which in this case is found at around 6 Hz. When the gas ﬂow rate is further enhanced, the process remains stable. The main ﬂuctuations are uniform in period and amplitude. However, from a gas ﬂow rate of 0.035 m3 s1 peaks of other frequencies start to occur in the Fourier transformation due to slight instabilities of the bed movement. The core jet does not pass the bed straightforwardly in a vertical direction, but is slightly deﬂected to the left or to the right due to increased gas ﬂow turbulence. However, from visual observation and because these peaks are

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

much smaller in amplitude than the main frequency peak, one can conclude that the ﬂuidization process is still stable. At a gas volume ﬂow rate of 0.042 m3 s1 (Fig. 5.34c), the main ﬂuctuations are no longer uniform and exhibit different amplitudes. The upper boundary of the stable operation range has been reached and the process is, thus, unstable. The irregular main ﬂuctuations in Fig. 5.34c illustrate these instabilities. The gas jet no longer passes the bed straightforwardly but is heavily deﬂected to the left or to the right. This results in the formation of arbitrary bubble sizes and shapes causing the irregular gas phase pressure ﬂuctuations. The described spouting operation state is called slugging ﬂuidization. In total, the plots of the time-averaged as well as of the ﬂuctuating particle velocities from PIV (Section 5.3.3) conﬁrm the results of the determination of the stable spouting range obtained by analysis of the gas phase pressure ﬂuctuations in Section 5.3.4. 5.3.5 Positron Emission Particle Tracking

Positron emission particle tracking (PEPT) is a non-intrusive measurement technique, which supplies detailed information about the particle motion by tracking the position of a single activated particle. PEPT was ﬁrst applied to engineering equipment by Parker et al. (1993) and Parker and McNeil (1996). Stein et al. (1997, 2000) and Hoomans et al. (2001) were among the ﬁrst to apply PEPT to ﬂuidized beds. The latest review paper on the use of PEPT is from Seville et al. (2005). Contrary to other non-intrusive measurement techniques, like PIV, PEPTsupplies information about the particle behavior in the interior of the bed. This allows an experimental study of a three-dimensional spout-ﬂuid bed, where the spout is located at the geometrical center. PEPTsupplies very detailed information about the behavior of a single particle, which makes it a very useful technique to validate discrete particle models. A drawback of the technique is that it only allows the study of a single particle and therefore requires a long measuring time to produce results that are representative for the entire bed. PEPT takes advantage of a particular class of radioisotopes, which decay through the emission of positrons. When the positrons encounter electrons they are annihilated, converting matter into two back-to-back 511 keV gamma rays. These gamma rays are simultaneously detected by a pair of detectors. The position of the particle emitting the positrons is reconstructed by calculating the point of intersection of several pairs of gamma rays, as illustrated in Fig. 5.35. The three-dimensional spout-ﬂuid bed was placed in between two PEPTdetectors. Depending on the amount of radiation emitted by the single tracer particle that was present in the bed, the space between the detectors and the bed was varied. The tracer particle was produced by exposing one of the glass particles used in the experiments to a 3 He beam generated by a cyclotron to produce the positron emitter 18 F from reactions involving 16 O in the glass. The primary output of the PEPTmeasurements consisted of the particle position as a function of time in three directions, as illustrated in Fig. 5.36. The PEPT output contained a certain amount of noise. The amount of noise observed in each direction

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Fig. 5.35 Illustration of the detection of a particle based on successive back-to-back g-ray pairs emerging from a particle.

differed signiﬁcantly and also depended on the location of the particle within the bed. The noise was most profound in the horizontal plane near the bottom of the bed, which was close to the edge of the PEPT detectors. At the edge of the detectors, the differences in the slopes of the intersecting g-ray pairs in one or more directions is small. Therefore the accuracy of the point of intersection in those directions, which represents the location of the tracer particle, is reduced. Consequently, the amount of noise is increased. In order to suppress the noise, a cubic smoothing spline ﬁlter was applied to the PEPT output data. Since the PEPT detectors only covered the lower 0.47 m of the bed, the tracer particle occasionally left the detectable range. In that case, the readings directly before exit and after return of the particle were discarded. To diminish the effect of the remaining noise on the time-averaged particle velocities, all instantaneous particle velocities are calculated using the average particle velocity over six subsequent particle locations. The velocity is subsequently assigned to the cell containing the average position over six particle locations. An example velocity ﬁeld is presented in Fig. 5.37. 5.3.5.1 Particle Circulation Time The particle position versus time resulting from the PEPT analysis was also used to determine the amount of time a particle requires to move from the bottom of the bed, up the spout, and back down through the annulus towards the bottom, which is termed the particle circulation time. The particle circulation time can be used to assess differences in the behavior of small and large particles, to compare the extent of circulation for different operating regimes and to study the distribution of particle circulation times within a single experiment. The detection of a cycle in a spout-ﬂuid bed differs from the methods used for spouted beds, see for example Larachi et al. (2003). This is necessary, since, contrary to spouted beds, the spout-ﬂuid bed is not necessarily operated in a steady state, that is due to the inﬂuence of bubbles in the annulus, the spout channel does not necessarily

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

Fig. 5.36 Particle trajectories in three directions originating from the PEPT measurements and their xz-, yz- and xy-projections along with the associated smoothing splines.

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Fig. 5.37 Example of the time-averaged particle velocities including the RMS-component in the vertical direction determined using PEPT.

continuously display the same angle with the bottom plate. Furthermore, the bubbles in the annulus of a spout-ﬂuid bed disturb the regular ﬂow patterns generally observed in the annulus of spouted beds. An example of a cycle is presented in Fig. 5.38. A cycle is determined by analyzing the location of the particle in the z-direction, that is the particle height. In this case, a cycle starts with a local maximum in the particle height (point A), followed by a local minimum (point B), which is at least 0.05 m below point A. If no point B is found, point A can be adjusted, when a new local maximum is found with a higher value than the current local maximum. After a proper point B is found, the cycle is completed when the next local maximum (point C), which is at least 0.05 m above the local minimum, is found. If no point C is found, point B can be adjusted, when a new local minimum is found with a smaller value than the current local minimum. The minimum increase or decrease in height of 0.05 m was used to avoid spurious cycles caused by noise in the measurement and by small bubbles, which drag the particle upwards when they pass. After the analysis, pictures of the particle trajectory

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

Fig. 5.38 Typical particle circulation time distribution for a spout-fluid bed.

of each cycle were examined. Virtually all cycles were valid cycles. Rejected valid cycles, which would have been portrayed in these pictures if they existed, were scarcely observed. The obtained cycles are subsequently validated by evaluating the minimum and maximum z-position of each cycle. An example overview of the minimum and maximum z-position of each cycle in a typical experiment is presented in Fig. 5.39. The ﬁgure shows that most of the minima are below a certain height (0.18 m) and

Fig. 5.39 Overview of the minimum and maximum particle heights in a cycle for a typical experiment in a spout-fluid bed.

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Fig. 5.40 Histogram of particle circulation times for a typical experiment in a spout-fluid bed.

most maxima can be found above this height. The height dividing the minima and the maxima is virtually the same for all experiments. This implies that the particle needs to pass a certain height to complete a proper cycle. Most spurious cycles can be easily discerned in Fig. 5.39 and are subsequently checked manually and eliminated. Figure 5.40 presents the resulting particle circulation time distribution in the form of a histogram. The ﬁgure shows that the distribution of the particle circulation times is quite wide. Since the particle takes more time to pass through long cycles, the impact of these cycles on the overall result should be larger. Therefore the particle circulation time itself is used as a weight factor in the histogram. The horizontal axis of the histogram has a logarithmic scale, as does the bin size used on the x-axis. 5.3.6 Fiber Optical Probe Measurement Technique

A ﬁber optical measurement system was used to determine the solid concentration proﬁles and particle velocities in a ﬂuidized bed with a jet. The ﬁber optical measurement system consists of a ﬁber optical probe, an infrared light source, two infrared light detectors with integrated ampliﬁer, an A/D conversion card and a notebook. The infrared light emitted by an infrared LED is in the range 800–1400 nm. The light is conducted over optical ﬁbers from the light source to the tip of the ﬁber optical probe. The light conduction is subjected to refraction if a light beam goes from an optically dilute medium to an optically denser medium. In this case the refraction angle of the light e0 is always less than the incoming angle e (Fig. 5.41). The refraction is described by the refraction law of Snell (1618): sin e n0 ¼ sin e0 n

ð5:32Þ

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

Fig. 5.41 Refraction of a light beam on an interface.

which describes that the sine function of the angle of incidence and the angle of refraction are inversely proportional to the refraction indices of both media. At the intersection from the optically dense to the optically dilute medium, an incoming angle larger than eg leads to total reﬂection. Following Eq. 5.32, this happens if the angle of refraction in the optically dilute medium is 90 . The value of eg can be obtained from sin eg ¼

n n0

ð5:33Þ

This effect is exploited in the case of the use of optical ﬁbers as light conductors. The optical ﬁbers consist of glasses with different refraction indices made by doping the glasses with germanium oxide. The annulus of the optical ﬁbers is made of the glass with the lower refraction angle and the core of the ﬁber is made out of the glass with the higher refraction angle. The refraction indices are chosen in such a way that total reﬂection occurs at the intersection area of the two glasses. This leads to the conduction of light through the optical ﬁber. To avoid damage the ﬁbers are generally covered with a plastic coating. The sensor used in this work consists of seven optical ﬁbers. Three of these ﬁbers are emitting light and are arranged in a line through the center of the probe. The other four ﬁbers are arranged as pairs on the left and the right, parallel to this center line. Fluidized particles passing the probe reﬂect a part of the light emitted by the three center line ﬁbers. This reﬂected light is detected by the four receiving ﬁbers and conducted back to two infrared light detectors with integrated operation ampliﬁers. Each of these ampliﬁers is connected to one of the light detecting ﬁber lines. The light signals are converted to a voltage. The voltage signals are recorded by a data acquisition system comprising an A/D-converter card and a portable PC. The intensity of the light reﬂected back to the probe by the ﬂuidized particles is a measure of the solids volume concentration. The velocity of particles crossing the probe perpendicularly to the optical ﬁber lines can be calculated from the signals of the two detecting ﬁber lines, which are at a distance of 240 mm from each other (Fig. 5.42).

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Fig. 5.42 Fiber optical probe: (a) schematic, (b) photo.

The velocity of the particles is calculated from the time difference between the signals of the two detecting ﬁber optical lines. This is done by a cross-correlation function: 1 R1;2 ðt; TÞ ¼ T

t¼T=2 ð

U 1 ðtÞ U 2 ðt þ tÞdt

ð5:34Þ

t¼T=2

where U1(t) and U2(t þ t) are the voltage signals of the detecting lines and t is the time difference between the signals. The cross-correlation function has a maximum, when the time that a particle needs for passing the probe and the time t are equal. With this time and the distance between the two detecting lines the velocity of a particle passing the probe can be calculated as follows: vp ¼

t x fiber

ð5:35Þ

In order to be able to measure the high velocities expected in the jet zone of ﬂuidized beds the measurement acquisition system is equipped with an A/Dconverter with a maximum sampling frequency of 5 MHz.

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

5.3.6.1 Calibration The calibration of ﬁber optical probes is one of the main difﬁculties in the measurement of solids volume concentrations (solids fractions) because it is nearly impossible to produce a homogenous gas–solid ﬂow. This is especially true for measurements in bubbling ﬂuidized beds, because the calibration method must be suitable for a wide range of solids concentrations from very low up to those of a packed bed. Hartge et al. (1989) propose a calibration method which is suitable for the whole range from zero volume concentration up to the packed bed condition. It is shown, that the calibration function of ﬁber optical probes can be described by the correlation

U ¼ U 0 þ k eas

ð5:36Þ

where U is the measured voltage signal in the gas-solid ﬂow and U0 is the voltage signal in the absence of particles (i.e. in an empty tube). The constants k and a can be derived from calibration experiments in different gas–solids and liquid–solids ﬂows. In the investigations of Hartge et al. (1989), water and glycol were used as liquids and quartz sand and FCC-catalyst were used as solids. The investigations show that the constant k depends mainly on the properties of the light source, reﬂection and ampliﬁcation properties, the efﬁciency of the measuring section and, most importantly, on the reﬂection properties of the solid particles. The exponent a only depends on particle properties like size and shape. Additionally, it was pointed out that only the constant k changes, if one compares measurements in liquid–solid ﬂows and in gas–solid ﬂows. The exponent a does not depend on the suspending agent. The measurements of gas–solid ﬂows were performed in a circulating ﬂuidized bed. By variation of the process parameters it was possible to produce solids concentrations in the range from 0 to 50 vol.%. As a reference, time-averaged X-ray absorption measurements were used to compare with the measurements of the ﬁber optical probes. Because the exponent a does not depend on the suspending agent it is possible to determine the constant k by calibration of the measuring system in a homogeneous stirred liquid suspension of known solids volume concentration. By measuring the voltage signal as a function of solids concentration the constants a and k of the calibration function (Eq. 5.36) can be determined by means of non-linear regression. The calibration in this work was carried out in a homogeneous stirred suspension of Al2O3-particles in water. To enhance the stirring, bafﬂes were mounted on the wall of the vessel. The rotational speed of the stirrer was adjusted so as to avoid the formation of bubbles in the suspension. Because the exponent a determined by calibration in the liquid–solid suspension does not depend on the suspending agent, it can also be used for gas–solid ﬂows. The calibration constant k for the gas–solid ﬂow can be determined by measuring two voltage signals at deﬁned solids volume concentrations of the gas–solid ﬂow. The empty bed and the packed bed are the only conditions where the solids volume concentrations of the gas–solid ﬂow are clearly deﬁned. For this reason, two points were used to determine the calibration constant k during this investigation. Whereas the voltage signal in an empty bed can be easily determined, it must be ensured that

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Fig. 5.43 Calibration functions of the fiber optical probe.

the signal for the packed bed is not falsiﬁed by particles which are very close to the probe tip. These particles would lead to too high voltage signals. In order to avoid this, the measurements of the signal of the packed bed were conducted in a very slowly rotating vessel with a packed bed of the particles. Figure 5.43 shows the calibration for the Al2O3-particles in both water and air. 5.3.6.2 Experimental Results In order to see the inﬂuence of the injection of gas jets on the particle movement in ﬂuidized beds, experiments with and without injection were carried out in a cylindrical ﬂuidized bed at pilot-plant scale with a diameter of 400 mm (Link et al., 2008). For the ﬁber optical probe measurements of the time-averaged particle volume concentrations the measurement cycle time was adjusted to 60 s at a sampling frequency of 1 kHz. Thus, both the measurement of a time-averaged particle volume concentration and analysis of ﬂuctuations of the particle volume concentration and of the bubble formation during a measurement cycle are possible. For the measurement of particle velocities the measurement cycle time was adjusted to 0.1 s with a sampling rate of 1 MHz. Because of the arrangement of the ﬁber optical rows in the probe, only the measurement of velocities in one direction is possible. The use of a cross-correlation allows only for measurement in directed particle ﬂows, such as in the injection zone into the ﬂuidized bed. Figure 5.44a depicts the time-averaged porosity distribution of a bubbling ﬂuidized bed without any injection. The bed porosity distribution is characterized by a region of high volume concentrations near the bottom plate. With increasing distance from the gas distributor the particle concentrations decrease in the center of the ﬂuidized

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

Fig. 5.44 Measured time-averaged porosity in a fluidized bed.

bed. This is due to the movement of small bubbles, generated near the gas distributor plate, from the circumference of the ﬂuidized bed to the center and their subsequent coalescence to larger bubbles. Due to the downward movement and recirculation of the particles, the particle volume concentrations are increased and, thus, the bed porosities are decreased near the wall. In Fig. 5.44b it can be seen clearly that the injection of atomization air into the ﬂuidized bed strongly affects the local particle volume concentrations. The injection zone is characterized by low particle volume concentrations that increase at the borders of this zone. The injection region is surrounded by a region of nearly constant particle volume concentration and regular ﬂuidization. At the wall a signiﬁcant increase in the particle volume concentration can be seen, which is again due to the downward movement of particles and the particle circulation typical for ﬂuidized beds. With increasing distance from the bottom plate the particle volume concentration in the injection zone increases steadily until it reaches nearly the same value as in the ﬂuidized bed region. Due to particle entrainment in the jet and particle acceleration, the momentum of atomization air and its inﬂuence on the ﬂuidized bed decrease with increasing height. At larger distances from the bottom plate the particle volume concentrations in the center of the ﬂuidized bed decrease because of bubble coalescence and growth in the upper region of the bed. For coating, granulation and agglomeration tasks the deposition of the atomized liquid droplets on the ﬂuidized particles is mainly

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inﬂuenced by the local particle volume concentrations in the injection region. The particle volume concentrations themselves are inﬂuenced by the momentum of the atomization air. Figure 5.45 shows the particle velocity distribution in the injection zone at different atomization air ﬂow rates at different heights above the bottom plate. The particle

Fig. 5.45 Particle velocity distribution at different atomization air flow rates.

5.3 Measurement of Particle Concentrations, Velocities, and Hydrodynamic Stability

velocities depend strongly on the atomization air ﬂow rate and, thus, on the momentum of the atomization air. With increasing distance from the gas distributor the momentum of the atomization air is reduced due to the particles that are sucked into and accelerated in the injection zone. The measured particle volume concentrations and particle velocities show very clearly the inﬂuence of the atomization air ﬂow rate on the local ﬂuid dynamics in the injection region and, thus, also on the deposition of coating or binding material on the ﬂuidized particles. Consequently, the atomization air ﬂow rate is a powerful parameter to control and achieve desired product qualities. Besides the measurement of local particle volume concentrations and particle velocities the ﬁber optical probe enables detection of liquid injected into the ﬂuidized bed. The injected water droplets lead to a higher measured voltage signal compared to experiments without injection of water. Because in regions where no water droplets are present the measured voltage signal with and without water injection is the same, it is possible to detect the size of the region where water droplets are present (Fig. 5.46). The size of the injection region in experiments with only a gas jet is, on the one hand, deﬁned by the region of high particle volume concentrations which surrounds the injection region. On the other hand, the penetration depth of the gas jet is determined by comparison of the measured particle volume concentrations in the center of the ﬂuidized bed with those in the annulus, around the injection region. The position where the measured particle volume concentrations in the center are the same as in the annulus is deﬁned as the injection depth. In Fig. 5.47 the measured sizes of the injection regions with and without spraying are compared. As can be seen, the injection region with water injection is signiﬁcantly larger than the injection region without spraying. Thus, injected water droplets are also present in regions of high particle volume concentration, where the atomization air has no signiﬁcant inﬂuence.

Fig. 5.46 Measured voltage signals with and without injection of water at a height of 125 mm above the gas distributor.

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Fig. 5.47 Size of the injection zone with and without injection of water.

5.4 Measurement of Mechanical Stability of Particles during Fluidized Bed Processing 5.4.1 Introduction

Particles are subjected to various stressing conditions (for example, interparticle collisions, granule–apparatus wall collisions) during spray granulation in a ﬂuidized bed. As a result, particle attrition and breakage may occur (compare with Section 6.3.6). Attrition and breakage affect granule growth and nucleus formation, inﬂuencing both the residence time distribution and the population balance. During pneumatic transportation the granules are also mechanically stressed due to particle–particle and particle–internal tube wall impacts, which change the particle size distribution, cause deterioration in the product quality and sometimes may form harmful toxic dust. The breakage mechanism depends considerably on whether the granules show elastic or plastic deformations before fracture as well as on the micro- and macrostructures of the granules (Antonyuk et al., 2005a, b, 2006). The mechanical stability of particles during ﬂuidized bed processing depends on particle properties (density, form, composition), apparatus geometry (distributor plate), operation regime (bubbling or circulating ﬂuidized bed) and process parameters (ﬂuidization velocity, temperature, humidity). In the literature one can ﬁnd measurements of integral attrition coefﬁcients which are related either to the mass (Merrick and Highley, 1974; Rangelova, 2002; Rangelova et al., 2002; Seville et al., 1992; Werther and Xi, 1993; Werther and Reppenhagen, 1999; Xi, 1993) or to the surface of all particles (Rangelova, 2002; Rangelova et al., 2004). Therefore, the goal of this section is to present modern measuring techniques that enable one to quantify attrition and overspray (non-deposited droplets during liquid injection) in ﬂuidized beds.

5.4 Measurement of Mechanical Stability of Particles during Fluidized Bed Processing

Fig. 5.48 Fluidized bed plant for measurement of attrition.

5.4.2 Measurement of Attrition Dust with an Isokinetic Sensor

In order to detect attrition of particles in a ﬂuidized bed of 150 mm diameter (Fig. 5.48), the particle concentration in the exhaust gas was measured with a gravimetric method. For this purpose a fraction of the exhaust gas leaves the granulator via a ﬁlter by means of isokinetic suction. The dust concentration can be derived according to the standardized gravimetric methods VDI 2066 (2006) and EN 13284-1 (2001) from the weight increase of the ﬁlter and the sucked gas volume. To avoid the necessity of determining the velocity of the exhaust gas over the whole apparatus cross-section, an isokinetic dust sensor was used which measures the static pressure inside and outside the exhaust gas pipe. The pressure difference can be adjusted to zero by control of the exhaust gas ﬂow rate. A scheme of the experimental set-up is depicted in Fig. 5.49. 5.4.2.1 Theory The time-dependent decrease in the bed mass due to attrition can be calculated from the data measured by means of the described sensor system. Correspondingly to Fig. 5.49 the following deﬁnitions and equations can be used: .

Volume ﬂow rate of dry sample gas (subscript: sample) at standard conditions (subscript: n): _ sample;dry ðtÞ M V_ sample;n;dry ðtÞ ¼ ð5:37Þ rsample;n;dry

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Fig. 5.49 Schematic of the isokinetic dust sensor system for dust concentration measurements.

_ sample;dry ðtÞ is the mass ﬂow rate of the dry sample gas, which can be measured M with the mass ﬂow sensor in the pump unit, and rsample,n,dry is the density of the dry sample gas under standard conditions (input parameter in the electronic unit). .

Volume of dry sample gas (standard conditions): ð

tsample

V sample;n;dry ðtÞ ¼ 0

V_ sample;n;dry ðtÞdt

ð5:38Þ

5.4 Measurement of Mechanical Stability of Particles during Fluidized Bed Processing

This value is calculated automatically in the electronic unit and appears as an indication at the end of the sampling time tsample, which is an input value. .

Volume of wet sample gas (standard conditions): V sample;n ¼ V sample;n; dry

1 1cH2 0 ðtÞ

ð5:39Þ

This value is calculated manually taking into account the average volumetric water vapor concentration (cH2 0 in m3 m3) during the sampling time. For the determination of c H2 0 the Antoine equation can be used to calculate the saturation pressure according to the ambient temperature. Subsequently, the water concentration can be calculated from the humidity and density of the air and the density of water vapor. .

Volume of wet sample gas (operating conditions): V sample ¼

T Pn V sample;n Tn P

ð5:40Þ

This value must be calculated manually, whereby the temperature T and pressure P in the investigated cross-section must be measured separately during the sampling time. Velocities of sample gas at the entry of the sucking nozzle – Velocity related to the dry sample gas volume ﬂow rate (standard conditions):

.

vnozzle;n;dry ðtÞ ¼

V_ sample;n;dry ðtÞ Anozzle

ð5:41Þ

with the cross-sectional area of the sucking nozzle Anozzle from the input value dnozzle. The velocity according to Eq. 5.41 is displayed automatically in the electronic unit. – Velocity related to the wet sample gas volume ﬂow rate (operating conditions) follows from the respective volume, the cross-sectional area of the nozzle and the sampling time: vnozzle ¼ .

V sample Anozzle tsample

ð5:42Þ

Average particle concentrations in the sample volume (manual calculation)

– Particle concentration in the dry sample gas (standard conditions): cdust;dry ¼

Mdust V sample;n;dry

¼

M 0 M

00

V sample;n;dry

ð5:43Þ

with M0 as the mass of the dried and empty ﬁlter socket before sampling and M00 as the mass of the dried and particle loaded ﬁlter socket (drying: 1.5 h at 105 C, weighing in the laboratory). The value of cdust;dry is needed for comparison with

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the compulsory limits, which are related to the volume of dry sample gas at standard conditions. – Particle concentration in the wet sample gas (standard conditions): 00

cdust ¼

M dust M M 0 ¼ V sample V sample

ð5:44Þ

is the particle concentration in the considered cross-section of the apparatus needed for the calculation of dust emissions. .

Velocities of gas in the measuring section: Placement of the sucking nozzle of the pressure sensor in the center of the measuring section means that the nozzle is located at the maximum of the proﬁle of gas velocity in the cross-sectional area of the apparatus. Because of automatically controlled isokinetic suction, the velocity of the wet sample gas in the nozzle is: vnozzle ¼ vcross-section;max

ð5:45Þ

The average velocity in the entire measuring section is: vcross-section ¼ vnozzle f

ð5:46Þ

with factor f, which relates the average to the maximal velocity in the ﬂow proﬁle and depends on the Reynolds number for turbulent ﬂow. .

Volume ﬂow rate of exhaust gas in the measuring section (manual calculation): V_ cross-section ¼ vcross-section Across-section

.

ð5:47Þ

Particle mass ﬂow rate in the measuring section (manual calculation): _ dust ¼ cdust V_ cross-section M

ð5:48Þ

5.4.2.2 Experimental Results Experiments were performed in a ﬂuidized bed of 150 mm diameter (Fig. 5.48). The bed material consisted of porous monodisperse g-Al2O3-particles (d32 ¼ 1.77 mm) and was ﬂuidized at different superﬁcial velocities over a period of more than 200 h. In Fig. 5.50a the average dust concentration according to Eq. 5.44, measured with the isokinetic sensor, is illustrated. The ﬂuidized bed was operated batch-wise and the complete bed material was discharged at certain time intervals and weighed. Figure 5.50b compares the total mass of all particles in the bed Mbed(t) ¼ Mbed,0 – Mdust(t) obtained from the isokinetic sensor measurement with the weighed bed masses at different times. Both plots show an increased attrition at larger superﬁcial gas velocities. Now, a time-dependent attrition coefﬁcient can be calculated by reference to either the mass or the surface of the particles. Werther and Xi (1993), Werther and Reppenhagen (1999) and Xi (1993) assume a mass-related attrition coefﬁcient,

5.4 Measurement of Mechanical Stability of Particles during Fluidized Bed Processing

Fig. 5.50 (a) Dust concentration in the exhaust gas and (b) bed mass by variation of the superficial gas velocity.

whereby Rangelova et al. (2004) postulated the surface dependence of attrition. In Fig. 5.51 both attrition coefﬁcients Rm;i ¼

DMattrition;i DM dust;i ¼ Dti Mi1 Dti Mi1

½kg kg1 h1

ð5:49Þ

RA;i ¼

DMattrition;i DMdust;i ¼ Dti Ai1 Dti Ai1

½kg m2 h1

ð5:50Þ

are compared at various times i for a superﬁcial gas velocity of 3 m s1. It is obvious that both attrition coefﬁcients decrease at the beginning and then reach constant values of Rm ¼ 0.001 293 9 kg kg1 h1 and RA ¼ 0.000 395 3 kg m2 h1. Additionally, Fig. 5.52 shows the particle size distributions at 24 h time intervals, which were measured off-line with the CAMSIZER system (see Section 5.2). It is obvious that ﬂuidization with a superﬁcial gas velocity of 3 m s1 leads to an appreciable decrease in particle size. The Sauter diameter after 208 h is reduced to a value of 1.59 mm.

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Fig. 5.51 Comparison of mass and surface-related attrition coefficients at u ¼ 3 m s1.

Fig. 5.52 Measured time-dependent mass-related sum distribution of the size of the bed particles at u ¼ 3 m s1.

Merrick and Highley (1974) and Seville et al. (1992) derived empirical correlations from their experiments, whereby a mass-related attrition coefﬁcient in a bubbling ﬂuidized bed is proportional to the excess gas velocity (u–umf ). Linear correlations based on the constant, steady-state values of both attrition coefﬁcients from our experiments are depicted in Fig. 5.53. Since bed mass affects the power of the fan, both attrition coefﬁcients can be illustrated according to Fig. 5.54 as functions of fan power Pfan ¼

V_ g DPtot h

ð5:51Þ

whereby the efﬁciency of the fan was assumed to be h ¼ 0.75, and the total pressure loss is DPtot ¼ DP bed þ DPgas distributor . Attrition coefﬁcients can be calculated by simple linear dependences according to Fig. 5.54.

5.4 Measurement of Mechanical Stability of Particles during Fluidized Bed Processing

Fig. 5.53 Comparison of mass and surface-related attrition coefficients as functions of excess gas velocity.

Fig. 5.54 Comparison of mass and surface-related attrition coefficients as functions of fan power.

5.4.3 Measurement of Attrition Dust and Overspray with an On-Line Particle Counter 5.4.3.1 Lorentz–Mie Theory as Measuring Principle The measurement procedure of optical aerosol spectrometers is based on the Lorentz–Mie theory, see Section 6.2.2. If light with wavelength l meets a spherical particle with diameter x and refractive index n, then the light is strewn in different directions (Fig. 5.55). The scattering of light at the particle is caused by diffraction, refraction and reﬂection. The polarization plane of the incident light wave is also turned. The intensity I of light scattered at single particles depends on the incident light intensity I0, the polarisation angle w, the detection angle of the scattered light q, the refractive index n, the light wavelength l and the particle diameter x

I ¼ I 0 f ðw; q; n; l; xÞ

ð5:52Þ

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Fig. 5.55 Light diffraction principle for optical aerosol spectrometers.

By means of the scattering parameter z introduced by Mie (1908) z¼

px l

ð5:53Þ

the relation between the sphere circumference px and the wavelength l is used in Eq. 5.52 to obtain I ¼ I 0 f ðw; q; n; zÞ

ð5:54Þ

One can differentiate between three ranges regarding the dependence of I on particle diameter or scattering parameter: Rayleigh-range, z 1: Here the intensity of scattered light rises with the sixth power of the particle diameter (Friehmelt et al., 1998; Friehmelt, 1999), being proportional to x6/l4. This means that in the Rayleigh-range 64-times stronger light is necessary in order to measure half so large particles (lower detection limit). Mie-range, 0.1 z 10: Here the correlation between scattered light intensity and particle size is not straightforward, but depends on the other involved parameters in a complicated way, see Figs. 5.56 and 5.57. Fraunhofer or geometrical range, z 1 (from z 10): Here a quadratic correlation between scattering power and particle diameter is valid. To be able to determine the particle size distribution with an optical aerosol spectrometer (OAS) as exactly as possible, a clear calibration curve, as shown in Fig. 5.57 is essential. Usually, OAS are calibrated by the manufacturer with monodisperse latex aerosols with a refractive index of n ¼ 1.59. Other suitable calibration procedures as, for example, the aerodynamic calibration, have been described by Friehmelt (1999). 5.4.3.2 Measurement in High Concentrations with Small Optical Measuring Volume To directly apply the above, only one particle should be available for analysis in the measuring volume. If more than one particle is present in the measuring volume, then the particle size is measured too large and the number of particles is measured too small. To fulﬁll the condition of one single particle, the measuring volume should have a linear dimension of 1 mm or 100 mm for particle concentrations of 103 particles cm3 or 106 particles cm3, respectively. In the instrument PCS-2010 of Palas GmbH, which has been developed by Umhauer (Umhauer, 1983; Umhauer and Bottlinger, 1989; Umhauer and Bottlinger, 1991), the measuring volume has edge

5.4 Measurement of Mechanical Stability of Particles during Fluidized Bed Processing

Fig. 5.56 Relative intensity of scattered light for monochromatic incident light (e.g. laser light) and 45 scattering angle from a spherical single particle, receiver aperture 14 , light wave length 0.436 mm (VDI 3489, 1990).

lengths of approximately 100 mm, so that concentrations up to 105 particles per cm3 can be measured without signiﬁcant coincidence errors. Figure 5.58 shows the principle of optical measuring volume limitation. Due to its small dimensions, the measuring volume is evenly illuminated. If a particle ﬂies through the core of the measuring volume, then a scattered light impulse of a certain height is generated. However, if the same particle ﬂies through the edge of the measuring volume, 50% within and 50% outside the measuring volume, then the height of the scattered light impulse will amount to only 50% of the previous one. Due to this so-called border zone error, particle sizes are measured too small. The bigger the particles, the bigger the error, as demonstrated in Fig. 5.59. Due to the ﬁndings of Helsper (1981), a new measuring volume with border zone error correction was developed and implemented in the instrument PCS-2010. Figure 5.60 shows that PCS-2010 has two measuring volumes. The inner and smaller measuring volume is produced with the aperture L and aperture 1. The outer and larger measuring volume is produced with the apertures L and 2. The light scattered by the single particleisdetectedbyboth photomultipliersPM1 and PM2 andapulseamplitude comparison is accomplished. It can be seen in the detail drawing that the particles 1 and 2, provided that they are of equal size and single in the measuring volume, deliver the same pulse amplitude with PM1 as with PM2. Particle 3 of the same size delivers with

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Fig. 5.57 Relative intensity of scattered light for white incident light and 90 scattering angle from a spherical single particle, receiver aperture 24 (VDI 3489, 1990).

PM1 only a pulse amplitude half as high as with PM2. Due to the different pulse amplitudes the signal of particle 3 is rejected. Particle 4 is rejected anyway, since the signal of PM1 is zero. Consequently, the criterion for rejection of particles is the amplitude difference of the two scattered light impulses. For a quantitative determination, the particles correctly measured with PM1 are counted. It can be seen in the detailed drawing of Fig. 5.60, that with this technology only two sides of the measuring volume are corrected and thus the border zone error is reduced by 50%. Since 2003, Palas GmbH has offered a new white light aerosol spectrometer system, registered under the name welas, which has a still smaller border zone and coincidence detection error. This is achieved by new aperture technology. Computer control and evaluation can take place, due to optical ﬁbers, far away from the small sensor. Environmental parameters, such as pressure, relative humidity and temperature can be measured. The sensors can be used in a highly combustible environment, at temperatures from 90 up to 120 C and at 10 bar overpressure. 5.4.3.3 Calibration and Evaluation Due to the white light source and the 90 scattered light detection, a clear calibration curve (Fig. 5.57) can be obtained, depending on the particle sizes to be measured. All optical aerosol spectrometers are calibrated with latex particles according to

5.4 Measurement of Mechanical Stability of Particles during Fluidized Bed Processing

Fig. 5.58 Measuring principle: optical volume limitation, 90 scattered light detection.

Fig. 5.59 Border zone error with optical measuring volume limitation: Sum distribution of different monodisperse aerosols (Helsper, 1981).

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Fig. 5.60 Measuring principle of PCS-2010.

international convention. The measured scattered light pulse amplitudes are assigned to a certain particle size by means of the calibration curve. The particles are directly assigned to size classes in order to compute the following representations of the particle size distribution (see also Section 6.1): .

Sum distribution Q r ðxÞ ¼

Quantity q of measured particles x qtotal for all measured particles

ð5:55Þ

with n P

Q r ðx i Þ ¼

i¼1

qi

ð5:56Þ

qtotal

where x: particle size, r: considered quantity. . Density distribution qr ðxÞ ¼

Quantity Dq of particles measured in the interval Dx Total measured quantity qtotal interval range Dx

ð5:57Þ

In differential terms: dQ r ðxÞ qr ðxÞ ¼ dx

Q r ðx 0 Þ ¼

ðx0 qr ðxÞdx

ð5:58Þ

x min

Depending on the type of considered quantity then: r ¼ 0: number, r ¼ 1: length, r ¼ 2: area, r ¼ 3: volume.

5.4 Measurement of Mechanical Stability of Particles during Fluidized Bed Processing

5.4.3.4 Experimental Results During ﬂuidized bed spray granulation the injection of liquid (solution, suspension, melt, emulsion) affects the attrition of particles. Additionally to the dry state, nondeposited liquid droplets (overspray) may create new solid particles. This nucleation inﬂuences the growth kinetics of particles as well as the population balance of the total system. Therefore, additionally to the experiments of Section 5.4.2, the optical aerosol spectrometer PCS-2010 has been used in a pilot-plant scale ﬂuidized bed with a diameter of 0.2 m. By using the isokinetic sensor (Fig. 5.49) an exhaust gas bypass fraction has been analyzed under dry conditions, as well with injection of water and solid solution, with regard to the dust mass ﬂow. As bed material sodium benzoate particles were used (d32 ¼ 1.2 mm, rs ¼ 1440 kg m3) with a hold-up mass at the beginning of 2 kg. First, the particles were ﬂuidized for 34 min under dry conditions without any injection. Then, a nozzle pressure of 1.5 bar was adjusted, which corresponds to a nozzle gas volume ﬂow rate of V_ g;nozzle ¼ 5:2 m3 h1 . During this period the nozzle, which is placed for side spray, is operated without liquid. The operating values were increased after 14 min to 3 bar and V_ g;nozzle ¼ 9:4 m3 h1 and decreased again after an additional 14 min to 1.5 bar and V_ g;nozzle ¼ 5:2 m3 h1 . Then, at this constant nozzle gas pressure the injection of pure water was started and was changed stepwise _ w ¼ 5:4 kg h1 and, again, to M _ w ¼ 3 kg h1 . The _ w ¼ 3 kg h1 up to M from M same schedule was repeated with a higher nozzle gas volume ﬂow rate of V_ g;nozzle ¼ 9:4 m3 h1 at 3 bar. After the water injection, a 35 mass% sodium benzoate solution was atomized with the same variation of nozzle gas pressure and liquid injection rate. At the end of the experiment the injection was stopped and a post-drying process took place. Figures 5.61 and 5.62 show the measured number and mass ﬂow rates of dust in the exhaust gas by variation of nozzle pressure and liquid injection rate of water and solution. It is obvious that the number of dust particles increases at the beginning of the experiment even without any injection. Operation with a gas jet causes a rapid increase in the attrition due to higher particle velocities and, thus, larger energy input. Although the number of attrited particles decreases after doubling of the nozzle _ dust increases due pressure from 1.5 bar to 3 bar (Fig. 5.61), the dust mass ﬂow rate M to the increased diameter of the eluted dust particles (Fig. 5.62). The reason for this is the larger fraction of particle breakage. In the second phase of the experiment, water was injected at different pressures and injection rates. The rapid transition from dry to wet conditions leads to a decrease in the dust mass ﬂow rate (Fig. 5.62). The latter is intensiﬁed by increasing the liquid injection rate. During the injection of liquid, overspray is formed. These droplets are eluted together with pieces of attrited particles, leading to a larger number of dust particles (Fig. 5.61). The subsequent increase in nozzle pressure produces smaller droplets and thus a larger number of droplets, which leads to a larger number of dust particles. At constant liquid injection rate, an increased number of droplets results in a decreased dust mass ﬂow. A larger amount of atomized liquid and smaller droplets may lead to a higher agglomeration probability. In the third period a sodium benzoate solution was injected, which

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Fig. 5.61 Dust particles per second measured in the exhaust gas for dry and spray operation at different nozzle pressures and liquid injection rates of water or solution.

promotes the particle growth. Droplets with dissolved solid are deposited on the particles. After evaporation of the solvent solid bridges can be formed. Small attrited particles will be absorbed by the droplets and generate agglomerates. The larger agglomerate formation results in a decreased dust mass ﬂow. The number of eluted droplets (overspray) decreases because the solvent contains less water. After shutdown of the injection, the dust mass ﬂow decreases again.

Fig. 5.62 Dust mass flow rates for the same experiment as in Fig. 5.61.

5.5 Characterization of the Mechanical Properties of Partially and Fully Saturated Wet Granular Media

5.5 Characterization of the Mechanical Properties of Partially and Fully Saturated Wet Granular Media 5.5.1 Introduction

The introduction of relatively small quantities of a liquid into a powder results in dramatic changes to the mechanical properties such that free ﬂowing particles are eventually transformed to a cohesive solid; a sandcastle is a common example. Provided that the phase volume of the liquid is sufﬁciently small so that there is signiﬁcant interstitial voidage between the particles, such a cohesive solid is likely to be relatively fragile and will tend to fragment under loading, particularly if the particles are coarse. Mixtures of powders and liquids in this partially saturated state are sometimes referred to as wet granular solids but it should be emphasized that many of the terms used for powder/liquid mixtures are not universal across different subject areas. For certain mixtures of ﬁne powders and liquids, the addition of liquid to completely replace the air phase results in a much more plastically deforming state. Clays are a notable example in which the plasticity is aided by the electrostatic repulsion between the clay platelets that results in effective interparticle lubrication due to water ﬁlms between the platelets. Such fully saturated mixtures are commonly termed soft solids or pastes. A further increase in the liquid content results in the mixture behaving as a non-Newtonian ﬂuid, which is often termed a concentrated suspension/slurry/dispersion or sol; a particulate suspension is referred to as a dispersion if the particles are colloidal in nature and consequently do not sediment (diameter < 1 mm). In practice, there will be gradual changes in the mechanical characteristics, rather than discrete transitions, as the phase volume of the liquid is increased. Wet granular media are common intermediate states in a wide range of processing operations such as granulation, extrusion, molding and coating. The operational performance is critically dependent on the mechanical behavior of the particulate feed materials, which may necessarily involve formulations that compromise downstream processes or the speciﬁcation of the ﬁnal product. For example, the particle phase volume of a ceramic sol may be less than the maximum packing value in order to achieve ﬂow in a coating process but this may increase the susceptibility of the coating to shrinkage cracks on drying. In the case of granulation, for which the drying processes commonly involve mechanical forces such as those imposed by a ﬂuidized bed, granule attrition and breakage may lead to unacceptable recycle. However, a liquid binder that is optimized for a certain size distribution may not necessarily result in sufﬁcient damage resistance (Nieuwmeyer et al., 2007). Another factor that may be of considerable importance, particularly for pharmaceutical granules, is the extent of migration of functional materials in the drying process because of the development of a non-uniform concentration distribution (Kapsidou et al., 2001). In industrial processes it is common to use simple measures of the deformation and ﬂow behavior, such as the slump test and indentation hardness, that experience has

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shown provide a reasonable correlation with processability. However, to employ computer simulation techniques, for example ﬁnite element analysis, phenomenological material models are necessary in order to represent the constitutive behavior. Examples of some measurement procedures and data analysis schemes will be summarized later. Schemes have been developed for this purpose based on analyzing the industrial assessment techniques such as the slump test (e.g. Pashias et al., 1996). This is also the case for indentation hardness, which will be considered later. It may be difﬁcult to obtain material models for some particulate systems that satisfactorily describe the mechanical behavior in all processing environments, for example cyclic rather than monotonic loading. Consequently, there has been an enormous effort in developing discrete computational techniques such as the distinct element method which has been employed to study wet agglomerates, see for example Lian et al. (1998). Discrete ﬁnite element analysis (many-body ﬁnite elements) is likely to become more routinely applied as computing power becomes increasingly accessible (Gethin et al., 2006), since it is possible to incorporate more complex material behavior and particle geometries. These methods rely on analytical expressions or closed-form approximations to describe the interactions between the particles. In principle, homogenization may be applied to the results of such simulations in order to derive continuum material models, as is possible with more analytical approaches (e.g. Hicher and Chang (2007), Volume 1 of Modern Drying Technology). Interparticle interactions will be considered in the next section and the measurement of the mechanical properties of wet granular solids and pastes will be described subsequently. 5.5.2 Interparticle Forces

In this section, the interactions between particles will be described in terms of those arising from mechanical, adhesive, cohesive and also frictional and lubrication mechanisms. Particles have a wide range of shapes and surface topographies. To develop general principles they are generally treated as smooth spheres, particularly in discrete simulation procedures, otherwise there would be an inﬁnite set of stochastic systems to consider. This is a reasonable approximation for angular particles as there will be an effective curvature at contact points, which may deviate somewhat from that of a volume equivalent sphere. Given the acute radii of curvature of small rough particles, contact may occur between single or a few asperities. In such cases, the effective contact radius may be considerable less. The introduction of a liquid in such contacts leads to a number of regimes of behavior that will be discussed later. 5.5.2.1 Mechanical Interactions A major proportion of particles in industrial processes are inorganic with relatively large Youngs moduli and consequently may be subject to only small elastic deformations. However, there is a growing interest in softer particles such as organic encapsulates that may be subject to greater elastic deformations or may

5.5 Characterization of the Mechanical Properties of Partially and Fully Saturated Wet Granular Media

deform plastically. In any case, even for hard particles, the elastic deformation is critical in controlling such mechanical properties as the friction and coefﬁcient of restitution. The possibility of particle fracture or fragmentation will be ignored here although there will be some discussion of failure processes in the context of wet agglomerates. The Youngs modulus of a smooth spherical particle may be measured using diametric compression between parallel platens. For large particles (>200 mm in diameter) it is possible to use conventional mechanical testing equipment. Parallelism of the platens can be achieved by ﬁxing one of the platens with an adhesive such as an epoxy resin and allowing it to set while the platens are in contact. Smaller particles require special micromanipulation equipment (Zhang et al., 1992). The data are analyzed using the Hertz equation (Johnson, 1985) which may be written in a general form for two spherical particles under an applied normal load, W, as: 4 W ¼ R1=2 E d3=2 3 The mean radius, R, for the particles is deﬁned by the expression: 1 1 1 þ R ¼ R1 R2

ð5:59Þ

ð5:60Þ

where R refers to the radii of the particles and the subscripts 1 and 2 refer to the two particles. In the case of diametric compaction, 1/R for the platens is equal to zero so that R ¼ R. The composite Youngs modulus, E, for two particles is given by: 1 1n21 1n22 E ¼ þ ð5:61Þ E1 E2 where E and n are the Youngs modulus and Poissons ratio of the particles. For a deformable particle being compressed by much more rigid platens, it may be assumed that the ﬁrst term on the right-hand side of Eq. 5.61 is negligible given that the subscript 1 refers to the platens and the subscript 2 refers to the particle ~ The parameter d in Eq. 5.59 refers to the center-to-center viz., E ¼ E=ð1n2 Þ ¼ E. approach of the particles and thus for diametric compression, the total platen displacement is given by D ¼ 2d in order to account for the two contact points (compare with Section 6.3.6.2). There are two practical difﬁculties with diametric compression. The ﬁrst is that the displacements are small and it is essential to correct for the compliance of the equipment; the main source is usually the load transducer. Essentially at any given load, the applied displacement will be partitioned between the sample deformation and that of the equipment. The compliance can be determined by making load measurements without a sample particle present between the platens, although this has to be carried out at very low speeds to avoid damaging the load transducer. The second problem is the uncertainty in accurately identifying the position of the moving platen that corresponds to ﬁrst contact. This is particularly the case for soft or small particles since the loads may be very small. It is therefore useful to introduce

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a zero error displacement parameter, j. For diametric compression, Eq. 5.59 becomes: pﬃﬃﬃ pﬃﬃﬃ 2 1=2 ~ 2 1=2 ~ _ 3=2 R EðD þ jÞ3=2 ¼ R ED W¼ ð5:62Þ 3 3 ~ and j are obtained by a multivariate ﬁt of Eq. 5.62 to the data. The values of E Having obtained a value for j, a plot of the load as a function of the corrected displacement to the power 3/2 should be linear. However, the Hertz is ﬃﬃﬃﬃﬃﬃ

pequation applicable to values of a/R that are approximately <0.4 where a ¼ Rd is the maximum contact radius. At greater deformations it will be observed that the loads are less than the predicted Hertzian values, either due to a breakdown of the theory or to material factors such as the onset of non-linear elastic deformation or plastic deformation. It is also possible to verify that a particle is behaving elastically by ensuring that the unloading curve is identical to that in loading. Moreover, the load should remain constant at a ﬁxed displacement. If the load decays it could be due to viscoelastic creep. In this case the Youngs modulus will increase with the displacement velocity. More complex analytical treatments are available to derive viscoelastic material laws (Attard, 2001), which may be important in the case of particles formed from organic polymers, for example, that show pronounced viscoelasticity. For rough particles with asperity curvatures that are small compared to the gross radii, there may be many asperity contacts in the circular contact region. As a result, the load is a linear function of the displacement (Johnson, 1985; Adams et al., 1987a) and it is not possible to obtain a value for the Youngs modulus using diametric compression. It may be possible to use indentation in such cases by employing an atomic force microscope (AFM) or nanoindenter provided that the asperity heights are small compared with the indentation distance. is equal to the When a particle deforms plastically, the mean contact pressure, P, mechanical hardness, H, which is about a factor of three greater than the uniaxial yield stress, Y, thus (Johnson, 1985): W ð5:63Þ P ¼ 2 ¼ H ¼ 3Y pa pﬃﬃﬃﬃﬃﬃﬃﬃ _ where a ¼ R D is the contact radius. Thus the yield stress may be obtained from the gradient of the load as a function of the corrected displacement, which is linear and is given by the following expression: dW _ ¼ 3pRY dD

ð5:64Þ

Elastoplastic particles deform elastically at small strains so that the displacement may be corrected using the parameter j obtained from the Hertz analysis. 5.5.2.2 Adhesive Interactions Molecular interaction forces operate between dry particles due to van der Waals, polar and, for metal powders, metallic interactions. They are important for small particles because, as discussed below, these interactions scale with the radius of the particles

5.5 Characterization of the Mechanical Properties of Partially and Fully Saturated Wet Granular Media

while the gravitational force scales as the cube of the radius (see Section 6.3.4). Talcum powder is a common example. It has a low bulk density in the untapped state since the adhesive forces are large compared with those arising from gravity. Particle adhesion is usually measured against a ﬂat counter surface by attaching a particle to the probe tip of an AFM, which may be specially modiﬁed (Toikka et al., 2001). This is acceptable if the composition of such a surface is identical to that of the particle, for example, silica may be readily obtained in the form of particles and ﬂat sheets. Otherwise it is necessary to attach identical particles to the counter surface as a coating (Jones et al., 2003). However, the tip of an AFM probe is spherical and many studies have been undertaken that may be usefully applied to understanding particle interactions. The pull-off force, FA, depends on the surface free energy of the particles, gS, and is given by an expression that was derived by Johnson et al. (1971) known as JKR theory: F A ¼ 3pR gS

ð5:65Þ

or that derived by Derjaguin et al. (1975) known as DMT theory: F A ¼ 4pR gS

ð5:66Þ

The applicability of these theories depends on a non-dimensional parameter (Tabor, 1977): 1=3 4R gS ð5:67Þ u¼ E z0 where z0 is the equilibrium spacing between the solid surfaces (0.2 nm). The parameter u is a measure of the relative magnitudes of the surface forces (the numerator) and the elastic deformation (the denominator). Essentially, the surface forces are resisted by the elastic deformation. For small hard low surface energy particles when u < 0.1, DMT theory is applicable, while for large soft high surface energy particles when u > 5, JKR theory is applicable. Between the two regimes there is a gradual transition (Maugis, 1992). The pre-factors obtained with JKR and DMT theories are relatively similar for the pull-off forces but there are more signiﬁcant differences in the values of the contact areas at a given normal load. Measurements of particle adhesion are difﬁcult in practice (Drelich et al., 2004) and are likely to lead to a wide distribution of values between different pairs of particles. This may arise from a non-spherical geometry, surface roughness and/or contamination. If the relative humidity is not controlled there could be capillary condensation. If the particles are not perfectly elastic (e.g. plastic or viscoelastic) then more complex interaction laws would have to be employed. The inﬂuence of partially or fully wetting liquids on the pull-off force between particles has not been measured directly. In Eqs. 5.65 and 5.66, the solid surface free energy is replaced by the solid–liquid surface free energy. The adhesion is eliminated if the liquid completely wets the particles since the solid surface free energy is then zero. This has been discussed in more detail elsewhere in a study of ﬁber adhesion in liquids (Adams et al., 1983) and the strength of binderless granules (Cheong et al., 2007).

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5.5.2.3 Cohesive Interactions Generally the cohesive interactions are considerably greater than those arising from adhesion and result from the presence of liquid and solid junctions. The main contributions in the case of liquid bridges are the capillary and viscous forces. However if a non-Newtonian liquid phase is involved, such as one containing a polymer as a binder for ceramic slip casting, there may be a contribution from viscoelastic forces. These forces are difﬁcult to measure directly and a more practical approach is to calculate the values involved, since the theories for the capillary and viscous forces are well established, for spherical particles at least. The capillary forces are the direct consequence of the surface tension of the liquid and are present even when the particles are static. A detailed review of the capillary forces between particles has been published recently (Willett et al., 2007) and here only a brief summary will be given. A pendular capillary bridge between two particles will have a concave meridional curvature provided that the contact angle is sufﬁciently small, which is commonly the case (Fig. 5.63). The capillary force between two particles is

F c ¼ 2pr N gl pr 2N DP

ð5:68Þ

where gl is the surface tension of the liquid and rN is the radius of the neck of the capillary bridge. The ﬁrst term arises from the axial component of the surface tension acting at the liquid–air interface and the second corresponds to the Laplace hydrostatic pressure difference, DP, between the interior of the bridge and the atmosphere. It may be calculated by the expression: 1 1 ð5:69Þ þ DP ¼ gl rN rM

Fig. 5.63 A schematic diagram of a capillary bridge between two spherical particles.

5.5 Characterization of the Mechanical Properties of Partially and Fully Saturated Wet Granular Media

where rM is the meridional radius of curvature at the neck. For a concave meridional curvature, the origin of rM is located outside the bridge and therefore takes a negative value. Consequently, the term in brackets is often negative, so that the Laplace pressure component of the capillary forces is attractive as is always the surface tension term. Equation 5.68 ignores the buoyancy force due to the partial immersion of the particles in the liquid and also any gravitational distortion of the liquid bridge. These are second-order effects for relatively small particles (Adams et al., 2002). The calculation of the meridional proﬁle involves a cumbersome integration of the Laplace–Young equation. However, closed-form approximations have been developed. For example, the following expression may be used for identical particles and for ﬁlling angles of <20 (Willett et al., 2000): Fc ¼

2pRgl cos w 1 þ 2:1S þ þ 10:0ðS þ Þ2

ð5:70Þ

where w is the contact angle that the liquid makes with the particles and S þ ¼ SR1/2/2V where S is the separation distance between the particles and V is the volume of the liquid bridge. A more complex expression is available for greater liquid volumes (Willett et al., 2000). Equation 5.70 shows that the capillary force decreases with increasing separation distance and increases with increasing liquid volume at ﬁnite separation distances. At very small liquid volumes, the denominator in Eq. 5.70 should be replaced by the exact expression (1 þ tan(x/2)) where x is the half-ﬁlling angle. Thus at contact, the cohesive force decreases with the liquid volume. At a critical separation distance, Scr, a capillary bridge will rupture at a ﬁnite value of the neck diameter. For an inviscid liquid bridge, it has been predicted that this distance is related to the cube root of the volume of the bridge, V (Lian et al., 1993): w 1=3 Scr ¼ 1 þ V 2

ð5:71Þ

This relationship has been found by direct measurement to be applicable to even nanoscopic liquid bridges with volumes as small as 104 nm3 (Sirghi et al., 2006). The energy required for rupture, E, increases with the square of the liquid volume (Simons et al., 1994): E ¼ k1 gl

V2 R4

ð5:72Þ

where k1 is a system constant. Relatively large particles are required for exact measurements of the capillary forces such as those reported by Willett et al. (2000) and Rossetti et al. (2003). While AFM is capable of measuring these forces for small particles, it is difﬁcult to directly observe the liquid bridge and consequently determine the bridge volume and geometry. Consequently, for volatile ﬂuids, such as water, the mean radius (given

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by the term in brackets in Eq. 5.69) is calculated using the Kelvin equation which for water may be written as (Sirghi et al., 2006): rk ¼

0:54 nm lnðP=PS Þ

ð5:73Þ

where rk is equal to the mean bridge radius, P is the vapor pressure and PS is the saturated vapor pressure. Thus the term P/PS is equal to the relative humidity in the case of water. There is a viscous resistance when two particles approach each other or are separated along the axis joining their centers. This arises from the radial pressure ﬂow of the liquid resulting in a velocity ﬁeld that is similar to that for Poiseuille ﬂow in a pipe. For a Newtonian ﬂuid, it is possible to derive (Adams and Perchard, 1985) a simple expression for the viscous force: 3 1 dS F V ¼ pml R2 2 S dt

ð5:74Þ

where ml is the viscosity of the liquid. This relationship is based on the lubrication approximation which is valid for S R and assumes that the radius of the bridge, b, which is treated as cylindrical, is equal to that of the particles. If b < R, the following expression is applicable (Mattewson, 1988): ! 3 S 1 dS 2 F V ¼ pml R 1 2 2 S dt S þ b =R

ð5:75Þ

More complex expressions are available for power law ﬂuids (Lian et al., 2001). To a good approximation it has been shown by direct measurement that the total force between two particles with a pendular liquid junction is given by the sum of the capillary and viscous forces (Pitois et al., 2000). However, the stability of a liquid bridge increases with increasing viscosity. Instead of rupturing at S ¼ Scr the neck forms a ﬁlament and the rupture distance, SR, increases with the square of the _ thus separation velocity, S, SR ¼ Scr þ k2 S_

1=2

ð5:76Þ

where k2 is a system constant (Pitois et al., 2000). In the context of capillary bridges, it has been argued, for rough particles, that there are three regimes of behavior corresponding to different ranges of liquid volume (Halsey and Levine, 1998). In the asperity regime, the maximum radius of the bridge is equal to that of the asperity contact zone and the meridional radius is of the order of twice the mean heights of the asperities. In the roughness regime, the bridge radii are larger than the asperity contact zone but the maximum gap in the bridge is still comparable to the surface roughness of the particles. In the spherical regime, the gap is much larger than the asperity heights and the cohesion is controlled by the gross curvature of the particles. These arguments were based on rigid particles, but could be extended to deformable particles under load and also to the viscous forces.

5.5 Characterization of the Mechanical Properties of Partially and Fully Saturated Wet Granular Media

Measurements of the adhesive forces for small particles using an AFM have revealed a number of complexities. For example, it has been found that the distributions of capillary forces in repeated measurements arise from relatively small changes in the contact geometry (Farshchi-Tabrizi et al., 2006). Measurements involving aluminum oxide particles resulted in a maximum in the cohesive force with increasing humidity that was ascribed to the formation of strongly bound water or icelike junctions (Assay and Kim, 2006). 5.5.2.4 Frictional and Lubrication Interactions Most particles will be contaminated by an organic deposit and the sliding frictional force is equal to the product of the real area of contact and the interfacial shear strength of the contaminant layer t w ð¼ t 0 þ aPÞ where t 0 is the intrinsic interfacial shear strength and a is the associated pressure coefﬁcient. This is known as the adhesion component of friction (Bowden and Tabor, 1954). For Hertzian particles, the corresponding frictional force is given by the following expression (Adams et al., 1987a): 3R 2=3 2=3 W þ aW ð5:77Þ F int ¼ pt 0 4E

This equation has two load-dependent terms with indices of 2/3 and unity. It can be conveniently written in the following form (Adams et al., 1997): F int ¼ k3 W n

ð5:78Þ

where k3 is equal to the coefﬁcient of friction at unit load and n is termed the load index. These parameters may be related to the quantities in Eq. 5.77 by the expressions: n

1=3 2 þ 3bW 1=3 3 þ 3bW

2=3 n 1

ð5:79Þ

and k3

c 1n 1=3 þ a W W

ð5:80Þ

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ W min W max is the where c ¼ pt 0(3R/4E )2/3 and b ¼ a/c. The parameter W geometric mean of the range of normal loads over which Eq. 5.78 is applied such that Wmin and Wmax are the minimum and maximum values of this load range. It may be Þ and k ¼ kðW Þ so that these parameters will depend on the load noted that n ¼ nðW range being considered; viz., they are not material parameters. For rough particles, the friction is given by Eq. 5.77 with a reduced radius of curvature for single asperity contact or the coefﬁcient of friction, m, is independent of the load for multiple asperity contacts viz. Fint ¼ mW. The above treatment of friction describes the dynamic frictional force after sliding has been initiated. For the soft particle discrete element method, particle–particle interactions are calculated over a ﬁnite time interval rather than instantaneously as in

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the case of hard particle schemes. It is then necessary to consider the evolution of the tangential forces (Thornton, 1988) which involves the application of the theory developed by Mindlin and Dereswiewicz (1953) to describe the details of the tangential failure process. Thus far only solid interactions have been considered. Boundary lubricants act to reduce the interfacial shear strength. A typical example is magnesium stearate, which is used in the production of pharmaceutical tablets. For particles with a loadindependent coefﬁcient of friction, the coefﬁcient will be about 0.1. Much smaller values are possible if the particles are hydrodynamically lubricated such that they are separated by a ﬂuid ﬁlm. This arises from liquid ﬂow in the convergent geometry in the region between particles, causing a hydrostatic pressure to be developed in this region. An analysis for two rigid particles and a power law lubricating ﬂuid has been carried out (Huang et al., 2006). If the elastic deformation of the particles is taken into account (elastohydrodynamic lubrication), the central ﬁlm thickness, hc, for a Newtonian ﬂuid is given by the following expression (Hamrock and Dowson, 1978): hc ¼ 1:43

ðml vrel Þ0:64 R0:80 m E 0:42 W 0:22

ð5:81Þ

where ml and vrel are the viscosity of the ﬂuid and the relative sliding velocity between the particles. For particles with a 1 mm diameter and a Youngs modulus of 20 GPa, a ﬂuid viscosity equal to that of water and a sliding velocity of 1 m s1, the ﬂuid ﬁlm thickness would be 0.1 mm if the normal force was only 0. nN. Thus under normal circumstances, ﬂuid ﬁlm lubrication is unlikely. However, there is an intermediate lubrication regime known as mixed lubrication in which small regions of ﬂuid ﬁlm lubrication are developed in the contact area. The various regimes of lubrication are best represented in the form of a Stribeck curve (Williams, 1994), which involves a double logarithmic plot of the coefﬁcient of friction as a function of the group (mlvrel/W) as shown in Fig. 5.64.

Fig. 5.64 Schematic Stribeck curve showing the various regimes of lubrication.

5.5 Characterization of the Mechanical Properties of Partially and Fully Saturated Wet Granular Media

The friction and lubrication of particles have been most commonly measured with an AFM in a sliding mode (lateral force microscopy or LFM) using a similar approach to that described in Section 5.5.2.2. Usually, for ﬁne particles, it is necessary to account for the adhesive force that has to be added to the applied normal load. This is simple in the DMTregime since the effective normal load is the sum of the applied load and the pull-off force. When JKR theory is applicable, a more complicated expression is required. This has been applied to LFM data and found to provide an excellent ﬁt (Carpick et al., 1996). For particles attached to an LFM tip, a range of linear and nonlinear and also adhesive behavior has been found, depending on the roughness of the particles (Jones et al., 2004). There is a considerable literature on the study of boundary lubrication using an AFM that will not be considered here. Nominally clean particles may be subject to damage or wear during sliding and tribochemical ﬁlms may be formed in the presence of water, for example hydrated alumina layers have been observed for an alumina ceramic, which acts as a soft lubricating ﬁlm (Ziebert and zum Gahr, 2004). In addition, the friction between inorganic particles is sensitive to the pH and ionic strength of an aqueous immersion solution, which is important for some ceramic sols. Normally, particles are negatively charged and an electrical double layer is generated at pH values greater than the isoelectric point. At small normal loads, this repulsion is sufﬁcient to generate a ﬂuid ﬁlm between the particles and hence lead to a large reduction in the friction (Feiler et al., 2000), as discussed previously in the context of clays. Such interactions are also critical in controlling the transition from plastic to brittle behavior in ceramic slurries (Franks and Lange, 1999). 5.5.3 Mechanical Properties of Wet Granular Media

At small liquid phase volumes, the particles in a granular material may only be connected by pendular liquid junctions; this is known as the pendular state (Newitt and Conway-Jones, 1958). The funicular state is developed at greater phase volumes in which some of the interstitial space is saturated by the liquid and other local regions retain air. In the capillary state, the voids are completely ﬁlled by liquid and the concave menisci at the external surface result in a negative suction pressure. The slurry state is formed at greater liquid contents when there is no suction pressure due to the capillary action. The development of material models depends on being able to measure the relationship between the principal stresses and strains in terms of absolute values, increments or time derivatives. In the saturated state, the total mean stress (s ¼ s0 þ sf ) is partitioned between the effective stress, s0 , acting on the network of particles and the hydrostatic pressure due to the pore water, sf (Terzaghi, 1943). In the unsaturated state, it has been proposed that sf should be replaced by the gas pressure, suction pressure and/or the interparticle capillary stress (cf. Hicher and Chang, 2007). Rigorous mechanical measurements on granular media are extremely difﬁcult, particularly because of the sensitivity to densiﬁcation in compressive loading and to contraction or dilatancy in shear loading. If the volume increases (dilatancy), the granular medium is said to be overconsolidated and to be normally consolidated or

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underconsolidated if there is a reduction in the volume. Dilatancy arises from the particles sliding over each other and thus causing a reduction in the bulk density. The mechanical properties of wet granular media are extremely sensitive to the pore volume as it is closely related to the number density and magnitudes of the interaction forces between the particles. For example, it is possible to induce a ductile–brittle transition in ceramic slurries by consolidation under a hydrostatic stress, which could cause problems in forming operations (Franks and Lange, 1999). Instabilities in extrusion of a concentrated suspension can result from the removal of entrained air by vacuum imposition due to a critical change in the rheological properties (Aral and Kalyon, 1995). A range of common measurement procedures will be considered for both the deformation and failure characteristics of granular media. At small liquid contents, granular media tend to be elastoplastic and they may strain harden or soften due to the change in bulk density, as discussed previously. This will be considered in the next section in the context of the deformation properties of granular media at the continuum length scale. In the subsequent section, the measurement of failure properties will be considered. In the ﬁeld of soil mechanics, it is common not to distinguish between yield, damage, shear bands and shear failure, since they may be represented by surfaces in stress space that deﬁne a critical combination of principal stresses. These surfaces are represented by yield or failure criteria, which are able to describe phenomenologically the pressure dependence such as those due to Mohr– Coulomb and Drucker–Prager (Sundaresan, 2001). In the simplest case of the Mohr–Coulomb criterion, yielding is considered to occur on a failure plane on which the shear stress, t, is related to the normal stress, s, by the following linear relationship: t ¼ mi ðs þ sC Þ

ð5:82Þ

where mi is the internal coefﬁcient of friction and sC is the normal cohesive stress. Saturated granular media such as pastes tend to show rate-dependent mechanical properties. They can be treated as elastoviscoplastic, which means that the yield surface expands with increasing strain rate. The Herschel and Bulkley (1926) relationship is commonly used to describe such behavior (e.g. Huang et al., 2002): s ¼ Y þ kC e_ m

ð5:83Þ

where s is the uniaxial stress, kC, is the extensional ﬂow consistency, m is the extensional ﬂow index and e_ is the viscoplastic strain rate. This model is appropriate for some processing operations but it ignores elastic or viscoelastic deformation at small strains that may be important if elastic recovery is a signiﬁcant factor, for example, in the dimensional stability of a formed shape. Generalized non-linear viscoelastic models can be used but this involves more complexity in terms of determining a greater number of material parameters. 5.5.3.1 Elastoplastic Measurements The procedures for measuring the deformation properties of granular media that are described in this section will not include conventional rheological techniques

5.5 Characterization of the Mechanical Properties of Partially and Fully Saturated Wet Granular Media

suitable for relatively ﬂuid granular systems. There are a wide range of such techniques that are described in rheological texts and include, for example, the vane method (Dzuy and Boger, 1985), which has the particular advantage that wall slip (see below) does not occur. Sphere indentation is one of the simplest types of measurement. A sphere of known radius, RS, is indented into the test material and the load is measured as a function of the penetration depth, d. This may be carried out by ﬁtting a ball-bearing, for example, to the compression load cell of a universal test machine usually via a rod. The equivalent measurements may be made on spherical granules by diametric compression of the granules. The initial response is Hertzian for an elastoplastic material and, as described in Section 5.5.2.1 for single particles, the data may be analyzed using Eq. 5.59. In the plastic region, Eq. 5.64 may be used for the diametric compression of a granule or, for sphere indentation, the numerical pre-factor 3 has to be replaced by the pre-factor 6. However, strain hardening is likely to occur in the unsaturated state. For example, the hardness of wet granules was found to increase as the displacement was increased with a strain hardening index equal to about 0.5 (Mangwandi et al., 2007). Densiﬁcation of the primary particles in the contact regions was considered to be the likely cause. This is consistent with the values of the Youngs modulus measured from the unloading data. For an elastoplastic material, unloading is elastic (Fig. 5.65) and the force–displacement relationship for sphere indentation is as follows (Thornton and Ning, 1998; Adams et al., 2004): 1 d þ 1=4 RS E u3=2 ðdd0 Þ3=2 Y 1=2 2 1=4

F¼

1=2

ð5:84Þ

where d þ is the maximum indentation depth, d0 the permanent plastic deformation after unloading and Eu is the Youngs modulus corresponding to unloading. The equivalent relationship for the diametric compression of spherical granules is given by Mangwandi et al. (2007) and it was reported that the loading modulus for the wet

Fig. 5.65 A schematic diagram of data for the indentation of a sphere into an elastoplastic solid showing the elastic Hertzian and plastic loading regions and the elastic unloading.

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granules was less than 50% of that measured in unloading. In principle, it would be possible to determine the relationship between the applied strain and the Youngs modulus using this method. Conical indentation is an alternative method for studying strain hardening (Huang et al., 2002) since the uniaxial strain, e(¼tan b), may be varied by changing the cone angle, b, (Fig. 5.66). The hardness is given by H ¼ W/pd2 cot2b where W is the applied load and d is the indentation depth. In addition, the method is useful for investigating viscoplastic materials since the strain rate may be varied by changing the indentation velocity, vi , as e_ ¼ vi cot b=d (Bower et al., 1993). It is especially difﬁcult to determine the contact position for conical indentation since the contact force is small and, moreover, there may be a defect at the tip of the probe. Consequently, it is advisable to introduce a zero error displacement parameter, as described in Section 5.5.2.1. In addition, the data will be affected by wall slip (Adams et al., 1996), which is a more serious problem than for spherical indenters because they are inherently blunter. In Fig. 5.66, the resistive force due to wall friction is shown as the product of the interfacial shear strength and the area of contact, A, between the indenter and sample. This is a general complication in the measurement of the mechanical properties of granular media and is best avoided by using rough walls (Meeten, 2004). For concentrated dispersions, it arises from the transport of particles away from the walls leaving a depleted lubricating layer; this is apparent rather than the true slip that would occur at smaller liquid contents. In such suspensions, the slip velocity is often linearly related to the wall shear stress, which is known as the Navier boundary condition. It has been directly quantiﬁed, for example, by torsional measurements between parallel circular plates (Kalyon et al., 1993). Liquid migration can be a critical factor in the measurement of wet granular media and is sufﬁciently important that it is explicitly accounted for in methods developed

Fig. 5.66 Schematic diagram of a conical probe indenting a granular solid at an applied load W and a displacement velocity vi.

5.5 Characterization of the Mechanical Properties of Partially and Fully Saturated Wet Granular Media

by soil mechanists (see below). For example, it has been observed in squeeze ﬂow and ram extrusion measurements of pastes provided that the ﬂow rate is less than some critical value (Mascia et al., 2006); at large ﬂow rates the characteristic time of the experiment is short compared to that for liquid transport. Squeeze ﬂow involves the compression of cylindrical specimens between parallel platens of greater radii. In the absence of liquid migration and wall slip, the mean compressive pressure,P, is related to the gap, S, by the following relationship for a Herschel–Bulkley paste (Adams et al., 1994): m 2 Rp 2 2m þ 1 m Rp m þ 1 S_ P ¼ Y 1 þ pﬃﬃﬃ þ kc ð5:85Þ S S mþ3 m 3 3 S where Rp is the radius of the sample. The velocity ﬁeld corresponds to a radial pressure ﬂow in which the material is subject to shear only. In the work of Mascia et al. (2006), the platens were lubricated which results in biaxial extension and the liquid migration was ascribed to dilation; it is reasonable to expect a similar result for no slip boundary conditions. In the case of ram extrusion, Mascia et al. (2006), argued that the migration was the result of both dilation and densiﬁcation. This is a more convenient technique for pastes since samples can be equilibrated to a particular temperature while effectively sealed from the environment, thus reducing the evaporation of the ﬂuid phase. Mascia et al. (2006) used conical entry dies. However, there is an advantage in using sharpedged oriﬁces (Fig. 5.67) as there is no sensitivity to the wall boundary conditions. This involves extrusion at different velocities and measuring the pressure, P, which is related to the Herschel–Bulkley parameters by the following expression: 3m ! D 2vr D 1 þ Ak4 ð5:86Þ P ¼ 2Y ln D D0 D0 where D0 is the barrel diameter, D is the oriﬁce diameter, vr is the mean velocity in the oriﬁce and A ¼ ð2=3 mÞðsinzð1 þ cos zÞÞm . The angle z corresponds to shear bands formed prior to the oriﬁce and may be taken as 45 to a close approximation. The ﬂow into an oriﬁce is extensional and thus is complementary to squeeze ﬂow under no-slip boundary conditions, which results in shear, as mentioned above. For Newtonian ﬂuids, the ratio between the extensional viscosity and shear viscosity is known as the Trouton ratio with a constant value of 3. Similarly, for perfectly plastic

Fig. 5.67 Ram extrusion through a sharp-edge orifice showing shear bands at an angle z.

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pﬃﬃﬃ solids, there is a constant ratio between the uniaxial and shear yield stresses ( 3 if von Mises yield criterion applies). However, there are likely to be deviations from these ratios for granular materials due to anisotropies being developed in the force networks between load carrying particles. These networks are the subject of intensive research (e.g. Richefeu et al., 2006). Taking a simple example of an array of Hertzian particles, the Youngs modulus in compression may be accounted for by percolating linear force chains acting in the direction of the major principal stress with a spacing of a few particle diameters (Adams et al., 1997). Nevertheless, interesting comparative data can be obtained from these types of procedures. For example, the ﬂow stress determined from squeeze ﬂow measurements of pastes formed from glass ballotine and liquids of different viscosity were shown to be described by an expression that could be written in the form of the Herschel–Bulkley model with the rate-dependent term expressed as a capillary number (Iveson et al., 2003). Thus at small rates and viscosities, the stress was controlled by the capillary forces and vice versa for the viscous forces. 5.5.3.2 Failure Properties The focus of this section will be the measurement of the failure properties. In soil mechanics, shear and triaxial testing are commonly carried out and details about the procedures involved are described in soil mechanics texts. A more rigorous technique is based on the true triaxial apparatus (Matsuoka et al., 2002) but is less commonly used and will not be considered here. Direct shear testing is carried out at a critical void ratio for which the shear stress is independent of the strain. This is best achieved using a ring shear apparatus which is based on two ring cells containing the sample in an annulus geometry (Bishop et al., 1971), see Section 6.4. The torque required to rotate the lower cell against the ﬁxed upper cell is measured to obtain the shear stress at a given applied normal stress. The advantage of this conﬁguration is that large strains may be applied continuously to establish the critical void ratio. The original design was based on a horizontally split box and the force required to move one of the boxes relative to the other provides a measure of the shear stress; this limits the strains that may be applied in a single direction. Direct shear measurements of wet systems are usually carried out slowly to determine the drained strength of the sample and the results are presented in terms of the shear strength as a function of the normal stress, which should be linear in the ideal case (Eq. 5.82). In the pendular state it is possible to determine the shear strength as a function of the liquid content (Pierrat et al., 1998). The results suggest that the effective stress is the sum of the applied and the interparticle capillary stresses, since the data may be superimposed on a single curve by shifting them horizontially. The internal coefﬁcient of friction is not affected on this basis, which indicates that the liquids do not act to lubricate the particles. Similar behavior is exhibited in the capillary state involving measurements made as a function of the suction pressure (Mitarai and Nori, 2006). There is clearly some scaling of the internal friction and the interparticle friction since the friction between single particles will depend on the effective normal force (sum of the applied and adhesive/cohesive forces) as discussed previously when the contacts are not hydrodynamically lubricated.

5.5 Characterization of the Mechanical Properties of Partially and Fully Saturated Wet Granular Media

For triaxial tests, the sample is contained in a cylindrical rubber membrane, which is submersed in water that may be pressurized (Bishop and Henkel, 1962). It is compressed by a platen to induce a major principal stress in the axial direction. The minor principal stresses act laterally and are equal to the pressure acting on the rubber membrane. The shear stress is obtained from the deviatoric stress, which is the difference between the major and minor principal stresses. Drainage is made possible by the insertion of ﬁlter paper between the sample and rubber membrane that connect to a porous disc located at the base of the sample. In an undrained test on a saturated powder, the stress is carried by the liquid phase and hence the measured shear stress is independent of the normal stress. However, if the sample is partially saturated, the deviatoric stress will increase with increasing normal stress due to the reduction in pore voidage. As in the case of the direct shear test results described above, the data will be described by Eq. 5.82 although it is quite common for the data to be non-linear with an index of <1. The pore space will also decrease in drained tests so that again the deviatoric stress will increase with the normal stress. Triaxial measurements will not be considered further here as they are laborious to carry out and require specialized equipment. In the absence of discrete simulation, it is difﬁcult to categorize the nature of the failure process in direct shear tests in terms of internal frictional sliding or mode II fracture (in plane shear). However, experiments involving crack opening (mode I) unambiguously involve fracture. The tensile strength is an important parameter to characterize for investigating shrinkage cracks. This is a problem in fracture mechanics and introductions to this subject in the context of granular systems are given in a number of publications for example Adams et al. (1987b). Cracks initiate at ﬂaws that act to concentrate the applied stress at the crack tip. The fracture stress corresponds to the value when crack growth is initiated. Provided that the body and ﬂaw geometry are well deﬁned it is possible to obtain the fracture toughness (termed the critical stress intensity) from the fracture stress. One method is to use the three-point bend method in which a rectangular sample is supported on two lower rollers (Fig. 5.68). A load is applied on the upper surface of the sample by a third upper roller with a notch cut on the lower surface of the sample directly below the upper roller. This has been carried out, for example, with bars formed from sand and a polymeric binder (Adams et al., 1989). Such measurements are limited to samples that are self-supporting and that do not bend plastically rather than fracturing. The fracture of all granular materials is non-linear because of frictional or micro-cracking processes that occur in the region ahead of the crack tip known as the process or plastic zone.

Fig. 5.68 The three-point bend configuration for fracture measurements.

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Fig. 5.69 Cantilever configuration for fracture measurements of fragile samples in which the weight of the over-hanging sample provides the fracture force.

An alternative to measuring the fracture stress from the applied force, is to determine the fracture energy by integrating the load–displacement curve to fracture. The fracture energy per unit of crack surface is termed the strain energy release rate. However, for soft samples care must be taken to avoid signiﬁcant indentation of the rollers (note that this affects only the displacement and not the force). It can be minimized by a suitable choice of sample and notch dimensions. If this is not possible, an alternative conﬁguration has been developed that relies on the sample fracturing by allowing a fraction of it to overhang a supporting surface (Adbel-Ghani et al., 1991). Figure 5.69 shows how this may be achieved by indenting a wedge into a sample; in practice a sharp blade is more appropriate. For materials that are too soft or fragile for this method, wire cutting is an option (Goh et al., 2005). The wire can be gripped tautly in a frame such that it is horizontially above the sample. The frame can be attached to the compression cell of a universal testing machine and the cutting force measured as a function of distance. This is only suitable for samples that are sufﬁciently brittle that fracture rather than plastic indentation occurs in front of the wire. It is also possible to use tension tests in which the sample is formed into a dumbbell geometry or cylindrical pellet and a side notch introduced. Again the sample must be capable of fracture rather than undergoing plastic deformation and necking. In practice, most studies of granular media involve nominal measurements of tensile strength in which notches are not used. Such an approach does not provide material (fracture) parameters, which by deﬁnition are independent of the sample geometry and loading. However, the methods are simpler to implement and provide a means of comparing the behavior of different samples. For example, tensile measurements of cylindrical moist limestone agglomerates have shown that both the fracture stress and the strain at fracture increase with moisture content (Schubert et al., 1975). For agglomerates, diametric compression is commonly used where the nominal fracture stress, sF, is given by the following expression (Hiramatsu and Oka, 1966): sF ¼ 0:7

FF pRg

ð5:87Þ

5.6 Conclusions

where FF is the fracture force and Rg is the radius of the granule. Such measurements have been applied to dry granules but they could be used for those in the wet state. There are a number of models that attempt to relate the tensile strength of granular media to the adhesive or cohesive interactions between the particles. The mostly widely used is due to Rumpf (1970) who developed an expression for the fracture stress based on summing the adhesive forces in the failure plane. This expression is an upper bound since it does not account for the stress concentration at the tip of a crack. In one study involving model dry binderless agglomerates, it was found that the overestimate was about a factor of four (Cheong et al., 2007). Kendall et al. (1986) developed a model in which the fracture energy was related to the sum of the adhesive forces between the particles using JKR theory. This is theoretically correct but it ignores frictional work in the process zone, as mentioned previously, that can lead to a large underestimate of the fracture energy (Abdel-Ghani et al., 1991).

5.6 Conclusions

Monitoring of process variables and control of particle formulation processes are very important in maintaining product quality. The gas–solid ﬂuidized bed system with liquid injection of solutions, suspensions or melts for granulation of particles is one of the main particle formulation processes and a multiphase ﬂow system which is characterized by high solids volume concentrations. In this work two different techniques are distinguished to measure local solids concentrations and particle velocities in such ﬂuidized beds, non-intrusive and intrusive methods. The former are characterized by the fact that the measurement is taken from outside the ﬂuidized bed. Whereas the other are characterized by the fact that a probe is introduced into the ﬂuidized bed. In the present chapter an overview is given of available measuring techniques for solids concentrations and particle velocities in ﬂuidized beds. The focus is also on the analysis of the hydrodynamic stability of ﬂuidized beds. To assess the various aspects of spout-ﬂuid bed behavior, several measurement techniques have been employed. Two image analysis techniques have been used to obtain quantitative information on the particle behavior: (i) particle detection has been used to obtain instantaneous and time-averaged porosity ﬁelds; (ii) particle image velocimetry has been used to obtain instantaneous and time-averaged particle velocity ﬁelds. Spectral analysis of pressure drop ﬂuctuations produced information on the overall dynamic behavior of the spout-ﬂuid bed. Positron emission particle tracking has been applied to study the bed behavior by tracking an individual particle. Finally, with a ﬁber optical probe technique, solids concentration proﬁles and particle velocities were measured inside a ﬂuidized bed with a jet with and without additional droplet injection. A further topic is the measurement of attrition and overspray in ﬂuidized beds by means of an isokinetic dust sensor and an optical aerosol spectrometer. The spectrometer uses scattered light to measure the number and size of small particles.

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Our last topic is related to the mechanical characterization of wet granular media which involves considerable complexity in order to account for such behavior as dilatency, densiﬁcation, ﬂuid migration, wall slip and mechanically induced stress anisotropy. Experimental procedures are available for deriving useful material descriptions but rigorous phenomenological material models that are able to account for behavior under all processing environments are unlikely to be achievable. In the context of shrinkage cracks in drying, it is possible to measure well-deﬁned fracture parameters for many systems. The major developments in understanding the micromechanics of wet granular materials are likely to come from new simulation procedures that are capable of addressing multiscale multiphysics problems such as drying. In particular, short term developments in combining discrete particle with meshless ﬂuid methods will provide a much more detailed description of the ﬂuid behavior. The limitation of mesh-based techniques is that mesh merging is still not routinely available and this is necessary to simulate the transport of a ﬂuid. Developments will also occur in the use of discrete ﬁnite elements embedded in a ﬂuid mesh, which has the advantage of being able to describe complex particle shapes. Finally, laws need to be developed that are able to represent the complex interactions that can occur between particles, especially in aqueous environments.

Additional Notation Used in Chapter 5

a a c c D, d E F F, f f f, F g H h, H H I N n P q Q R

contact radius maximal contact radius volumetric concentration, mass concentration correction factor for the intensity of a pixel diameter, size, depth Youngs modulus force correction factor, factor frequency functions in Fourier transform spatial interval (gap) mechanical hardness height, thickness mechanical hardness intensity number of particles, pixels, frequencies refraction index perimeter density distribution function sum distribution function attrition coefﬁcient

m m m3 m3, kg m3 — m Pa N — s1 — m Pa m Pa — — — m — — kg kg1 h1, kg m2 h1

Additional Notation Used in Chapter 5

R r, R S S_ s U u W W x Y z0

cross-correlation function radius, radial coordinate separation distance separation velocity displacement voltage frequency variable width normal force, load particle size uniaxial yield stress equilibrium spacing

— m m m s1 m V s1 m N m Pa m

Greek Letters

b, e, z, j, w gl gs d, D e e e_ z y l m ml n x t tW j

various angles liquid surface tension solid surface free energy displacement, deformation, indentation volume fraction uniaxial strain strain rate scattering parameter Tabor parameter, angle of scattering wavelength coefﬁcient of friction liquid viscosity Poissons ratio zero error displacement parameter shear stress shear strength liquid–solid contact angle

Subscripts and superscripts

A, area A App c F F M m N

surface area based adhesion apparatus chord fracture Ferret meridional mass-based neck

rad J m2 J m2 m — — s1 — —, rad m — Pa s — m Pa Pa rad

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n r r T 2D 3D

standard or normal conditions distributed quality index reﬂection threshold two-dimensional three-dimensional

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6 Determination of Physical Properties of Fine Particles, Nanoparticles and Particle Beds Werner Hintz, Sergiy Antonyuk, Wolfgang Schubert, Bernd Ebenau, Aimo Haack, and J€ urgen Tomas

6.1 Introduction to Common Particle Properties

Process design in particle technology is closely connected to the physical behavior of disperse systems. Knowledge of the physical properties is of vital importance for understanding and optimization of processes and operations. A disperse system consists of individual particles whose physical properties have to be characterized as precisely as necessary. In process engineering such properties are called granulometric properties. Considering particulate solids as the material most commonly produced in particle technology, there is in many cases a very complex inﬂuence of the individual particle characteristics on the behavior of the population as a whole, for example ﬂow, compression and permeation behavior of particle beds. In this context, particle size analysis is an important issue in particle processing and product handling of ﬁne (d < 100 mm), ultraﬁne (d < 10 mm) and nanosized (d < 0.1 mm) particles. Experimental determination appears to be easy, but especially for ultraﬁneand nanosized dispersed systems one should take into account critical aspects arising, for example from shape, surface interactions, concentration, and homogeneity of the particles. Likewise, experimental techniques available for particle sizing, for example image analysis, electron microscopy, light scattering, laser diffraction, and ultrasonic methods, use different physical theories as their basis (see Section 6.2). Assemblies of individual particles with a diameter d (spherical shape is often the basic assumption of the measurement method) can be described mathematically with the help of cumulative particle size distributions dð max

Q r ðdÞ ¼

qr ðdÞdðdÞ

ð6:1Þ

dmin

Herein, qr ðdÞ ¼

dQ r ðdÞ dðdÞ

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

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is the particle size frequency distribution, and the index r denotes the quantity measured (e.g. number- or mass-based distributions). The cumulative particle size distribution Qr (d) is normalized to a maximum value of 1, but the particle size frequency distribution has to be determined in the unit per length, for example mm1. Physical properties, such as speciﬁc surface area, internal particle porosity, and pore size distributions of particles and agglomerates, are closely related to the particle size. The most commonly used experimental technique is the gas (nitrogen, helium) adsorption method (BET method). There is a series of other physical properties which depend on particle size, for example probability of particle breakage, strength and the elastic–plastic contact behavior. Here, impact tests are used to determine the particle restitution coefﬁcient. Other properties result from the interaction between the surface and volume forces, for example adhesion and dispersion or the tendencies to agglomerate and to disperse. Related experimental techniques are the centrifuge method or atomic force microscopy (AFM). Granulometric properties also include the determination of different particle densities, for example solid particle density measured by helium pycnometry, as well as pore size distributions by porosimetry (Section 6.3). The physical properties of packed and moving beds of particulate solids are not only connected to the characteristics of the individual particles, but also to the properties of the particle assembly as a whole. In practice, the behavior of particle beds can be very complex, that is there is a variety of interactions, and complicated because of the extremely large particle number of ﬁne powders. The main features of particle beds are, for example bulk and tapping density, rheological behavior of suspensions, ﬂow and compression behavior of powders. These properties should be understood as material or constitutive functions, which depend on other material properties, such as particle size, surface interactions, ﬂuid properties within voids, and ambient conditions like pressure. Examples are the elasticity, yield stress, internal friction, ﬂowability, compressibility and ﬂuidizability of powders, but also the viscosity of suspensions and pastes, and the mechanical ﬂow behavior of ﬁlter cakes. The main experimental techniques to investigate these constitutive functions are various shear tests presented in Sections 6.4 and 6.5.

6.2 Analysis of Particle Size Distribution 6.2.1 Image Analysis by Optical and Scanning Electron Microscopy

The most important feature of particulate systems is the particle size. Obvious tools to measure size are optical, electron and scanning probe microscopes. In optical and electron microscopy the principles of diffraction, reﬂection and refraction of radiation are used; the goal is to produce a magniﬁed visual image of an object too small to be

6.2 Analysis of Particle Size Distribution

seen with the naked eye. Concerning optical microscopy there are many modiﬁcations in addition to the ordinary light microscope, for example ﬂuorescence microscopy, polarized light microscopy, near-ﬁeld optical microscopy, and so on. 6.2.1.1 Optical Microscopy The ability to resolve ﬁne sample details is most relevant for the performance of a microscope. In this connection, the physical properties of light and the materials used for lenses are important. The resolution ability is the minimum distance at which two features of an object can be separated optically. According to Eq. 6.3 the minimal distance ls depends on the wave length of the incident light l and the numerical aperture A of the optical system:

ls ¼

0:61l 0:61l ¼ A n sin w

ð6:3Þ

A is a function of the refractive index n of the media between the object and objective as well as of the half opening angle of the objective w. Resolution is usually evaluated for the wavelength of green light, l ¼ 550 nm, that corresponds to the maximum sensitivity of the human eye. Thus, due to diffraction, an optical microscope is limited physically to a resolution of around 0.2 mm. Generally, the technique of optical microscopy is applied down to a resolution of about 1.0 mm. Visual methods offer major advantages for users since the particles can actually be seen. However, sample preparation is one of the critical steps involved. The samples must be dispersed to create clear images of the particles. Visual techniques are often more convenient for particle shape analysis than for particle size determination (Davidson and Abramowitz, 1999). 6.2.1.2 Electron Microscopy If nanoscaled particles need to be visualized (size is about from 1 to 100 nm), transmission electron microscopy (TEM) can be used effectively. In general, the conventional TEM is quite similar to a light microscope. A beam of electrons is transmitted through the sample; an image is formed, magniﬁed, and directed to a screen, or is detected by a sensor such as a CCD camera. As the de Broglie wavelength of an electron is much smaller than the wavelength of visible light, the resolution limit of TEM is much smaller than 1 nm. In scanning transmission electron microscopy (STEM), an electron beam is focused on a small spot and is scanned over the sample surface. At each spot, the transmitted signal is recorded to build up an image. Problems with TEM microscopy arise from difﬁculties in getting a sample into a highly evacuated chamber, and from changes in the sample structure caused by interactions with the electrons and the vacuum. In scanning electron microscopy (SEM), an electron beam is also passed pointby-point across the sample surface. In contrast to conventional TEM, scanning electron microscopy produces images by detecting secondary electrons which are emitted from the surface due to excitation by the primary electron beam (Amelinckx et al., 1997).

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6.2.1.3 Image Analysis Image analysis offers the possibility to measure both the size and the shape of particles using their two-dimensional projections. This approach is often considered as an ideal reference technique to validate other particle size distribution characterization methods, however, one should pay attention to practical limitations due to sample preparation and theoretical problems concerning the deﬁnition of particle size and shape. Image analyzing systems capture a two-dimensional image of three-dimensional particles. The digital process requires the deﬁnition of gray tone limits to detect particles electronically in an 8-bit gray tone image, followed by conversion of the gray tone into a binary image (binarization). In this way, a value is assigned to every pixel of the original image between 0 (black) and 255 (white). The last step is particle sizing. For simplicity, often only one single length is used to describe the particle size. However, there are many methods to deﬁne this length, unless the particle is a perfect sphere. To represent particles that are not perfect spheres, the following geometrical characteristics are commonly used (compare with Section 5.2.2):

1. main dimensions of the particle, 2. statistical lengths, for example Feret, Martin and maximum chord length, 3. other geometrical features, for example equivalent circle diameter, projected areas, shape factors. To get the statistical lengths, Fig. 6.1, the outline of the projection area of randomly orientated particles, is analyzed. Due to the variable particle orientation, it is necessary to deﬁne a direction of measurement. The Feret chord length dF is the distance between two parallel tangents to the particle outline perpendicular to the measurement direction. The Martin chord length dM is deﬁned as the length of the line which bisects the projection area; the maximum chord length dS is the greatest distance inside the particle projection area in the measurement direction. Further frequently used geometrical characteristics are the equivalent circle diameter d and the sphericity cU. The equivalent circle diameter pﬃﬃﬃﬃﬃﬃﬃﬃﬃ d ¼ 2 A=p ð6:4Þ

Fig. 6.1 Characterization of particle geometry by statistical lengths.

6.2 Analysis of Particle Size Distribution

is the diameter of a circle with an area that is equal to the projected area A of the particle in a stable position. The sphericity cU ¼ 4 p

A U2

ð6:5Þ

compares the projection area A of the real particle relative to the projection area of an ideally spherical particle; U is the circumference of the real particle. Equation 6.5 is the transformation of a more general, three-dimensional shape factor according to Wadell (1932) to planar, two-dimensional particle images. More and more, particle structures are characterized by using the concept of the fractal structure to describe the contour as a characteristic of the shape and the roughness of particle. The particle outline can be reshaped by a polygon. The total length of the polygon L correlates with the length of a single polygon element l according to the relationship L ¼ kl1D

ð6:6Þ

For two-dimensional images, the fractal dimension D is a non-integer number with 1 D 2. In this context, a line has the fractal dimension D ¼ 1, a square the fractal dimension D ¼ 2. Finally, the particle shape can be speciﬁed in terms of a Fourier series. In the relationship N X rðwÞ ¼ lim Ak sinðkw þ dk Þ N !1 R k¼0

ð6:7Þ

the distance r from particle edge points to the center of the area can be described in dependence on the angle w, running from 0 to 360 . R is the radius of a circle with an area equal to the projected area. Ak are Fourier series coefﬁcients that have to be calculated (Rumpf, 1990). 6.2.2 Laser Light Scattering and Diffraction for Dilute Particle Dispersions

The scattering phenomenon is based on the fact that electromagnetic radiation interacts with matter. This effect appears when a light ray hits an atom, molecule or particle. Different mechanisms of interaction are possible, dependent on size, wavelength of the incident light as well as other physical particle properties. Generally, the term scattering covers reﬂection and refraction as well as diffraction. A well known example of light scattering is the Tyndall effect occurring when white polychromatic light passes through a solution of colloidal particles. Here, light scattering is observed at a right angle to the incident light as a blue shining light. Another example in nature is the blue color of the sky. An exact theoretical treatment of the light scattering phenomenon is not simple (compare with Section 5.4.3). Only the Mie theory (Mie, 1908) gives a complete analytical solution of the Maxwell equations for spherical particles. Consequently, the Mie theory is widely used when dealing with scattering problems on the basis of the

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exact Maxwell equations. It embraces all possible ratios of particle size to the wavelength of incident light. Several approximate approaches are described in the literature (Van de Hulst, 1981; Kerker, 1988), which are applicable, in contrast to the Mie theory, only for certain ranges of particle size in relation to the wavelength l of incident light. 1. The Rayleigh theory (Rayleigh, 1871) is valid for particle sizes ranging from about 0.5 nm to l/20. It is assumed that an isotropic particle has only one scattering center; the scattered light is independent of this center. Electromagnetic waves polarize the scattering center thus inducing a Hertz dipole moment inside the particle. These oscillating electrons cause a secondary light emission. 2. The Rayleigh–Gans–Debye theory (Gans, 1925) is an extension of the Rayleigh approximation. Here, the electromagnetic wave of the scattered light is a superposition of single contributions resulting from inﬁnitesimal volume elements of scattering centers inside the particle. The Rayleigh–Gans–Debye theory can be used for larger particles with sizes up to l/6. 3. If the particle size is from about 4l up to several mm, the application of the Fraunhofer theory is possible. Here, the interaction of the particle with light can be explained with the help of the classical laws of optics. The scattering of light in gases was ﬁrst treated quantitatively by Rayleigh (Rayleigh, 1871) to explain the blue color of the sky and the red color of the sunset. He observed that the intensity I of the scattered light correlates with the wavelength l (I proportional to l4). A shorter wavelength – blue light – gives a more intense scattered light. The intensity I of the scattered light depends on the scattering angle u, the interaction between particles, and the possibility to polarize them. For one small isotropic particle that scatters light of incident intensity I0 and wavelength l, the scattering intensity I at a distance ls from the scattering source and the angle u between the incident and detected intensity will be given for polarized light by I sin2 u 16p4 ¼ 2 4 a2 ; I0 l ls

ð6:8Þ

and for non-polarized light by I 1 þ cos2 u 8p4 2 ¼ 4 a I0 l l2s

ð6:9Þ

Here, a is the polarizability of the particle; it is assumed that a is proportional to the particle volume, with the consequence that the intensity I of scattered light is proportional to d6, d being the particle size. Note, that every particle generates scattered light. Strictly speaking, Eqs. 6.8 and 6.9 are only valid for ideal gases. However, it is possible to modify both equations in a way that scattering in dilute suspensions of particles can be speciﬁed in detail. Here, it is not the polarizability a of the particle that is important for the scattering phenomenon, but local and temporal density

6.2 Analysis of Particle Size Distribution

ﬂuctuations of the polarizability a in a volume element of the suspension, caused by ﬂuctuations in the particle concentration Cs (theory of Einstein and Smoluchowski about density ﬂuctuations; Smoluchowski, 1908; Einstein, 1910). In the static light scattering experiment, the physical framework is represented by the Rayleigh–Debye equation (Einstein, 1910; Rayleigh, 1910) KCs 1 1 ¼ þ 2BC s þ . . . ð6:10Þ Ru MW PðuÞ Here, MW denotes the weight averaged or apparent molecular mass of the particles that characterizes their sizes, Cs the particle mass concentration, and B the so-called second virial coefﬁcient reﬂecting the particle–particle interactions for non-ideal systems. Ru is the so-called Rayleigh ratio (from Eq. 6.9 for non-polarized light) Ru ¼

I 1 l2s I 0 V 1 þ cos2 u

ð6:11Þ

The Rayleigh ratio includes the scattered light intensity of the suspension I, the incident light intensity I0 (here, both intensities are excess intensities reduced by the background scattering of the suspension medium) as well as the scattering geometry (distance from scattering source to detector ls, scattering volume V for the instrument). The optical constant K 2p2 n20 qn 2 ð6:12Þ K¼ N A l4 qCs embeds the scattering ability of the particle suspension; K includes the wavelength of the incident light l, the refractive index of the suspension medium n0 as well as the differential refractive index increment ðqn=qCs Þ – the change in the refractive index n of the suspension as a function of the change in particle concentration Cs. NA is Avogadros number. For many systems the differential refractive index increment is available in the literature (Brandrup and Immergut, 1999); while for new combinations it can be measured by the use of a differential refractometer. Note that a difference in the refractive indices of the suspension medium and the particle is a prerequisite for scattering. Small particles (d < l/20) have an isotropic scattering behavior, the form factor is P (u) ¼ 1. The graphical plot of Eq. 6.10 is KCs/Ru vs. Cs, the so-called Debye plot. Here, the y-axis intercept is the reciprocal apparent molecular mass MW; the slope of the graph, 2 B, gives the second virial coefﬁcient B. For larger particles (d > l/20) having an anisotropic scattering behavior, the form factor or intraparticle structure factor P(u) has to be used to correct the angular scattering dependence of the scattering intensity of the sample. Thus, Eq. 6.10 represents a function of the particle mass concentration Cs and the scattering angle u. In Fig. 6.2, a commonly used evaluation approach – the so-called Zimm plot – is shown, plotting KCs/Ru against sin2(u/2) þ kCs, where k is an arbitrary constant chosen to spread the experimental data and make graphical extrapolations easier (Zimm, 1948). The reciprocal of the apparent molecular mass MW can be determined from the intercept point on the y-axis. From the grid in Fig. 6.2, two types of curves are

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Fig. 6.2 Zimm plot to determine (i) the apparent molecular mass MW; (ii) the diameter of gyration dg and (iii) the second virial coefficient B from static light scattering experiments.

obtained, one by connecting the experimental points with the same scattering angle u by extrapolating to Cs ! 0, and the other by connecting the experimental points at the same concentration and by extrapolating to u ! 0. Extrapolation at the scattering angle u ¼ 0 to Cs ! 0 generates a line with a slope 2B yielding the second virial coefﬁcient B; extrapolation at the particle concentration Cs ¼ 0 to u ! 0 generates a line with a slope yielding the form factor P(u) (Guinier, 1939) with 2 2 1 1 4pn dg 2 u ¼ 1þ ð6:13Þ sin PðuÞ 3 2 l2 P(u) is connected to the square of the diameter of gyration, dg, where dg is deﬁned as twice the radius of gyration rg. Thus, the following set of parameters is accessible through static light scattering: (i) the apparent molecular mass MW; (ii) the radius of gyration rg and (iii) the second virial coefﬁcient B. The prerequisite of the scattering processes already considered here is that the frequencies of the incident and the scattered light are the same (elastic scattering process). However, when observing scattering particles in liquids, it is found that there is a remarkable frequency broadening of the scattered light compared to the incident monochromatic laser beam. The mean frequency has been unchanged. These are so-called quasi-elastic scattering processes; line broadening results from Brownian diffusion of the scattering particles due to collisions with liquid molecules. Quasi-elastic light scattering (QELS) is a commercially well established laser light scattering method, widely used in the single particle scattering regime to observe the dynamic behavior of nanoscaled systems (Pecora, 1985). Synonyms used are photon correlation spectroscopy (PCS) or dynamic light scattering (DLS). The quasi-elastic frequency line broadening results, as mentioned above, from thermal ﬂuctuations of the nanoparticles. Simply considered, this corresponds to a so-called Doppler shift. On the one hand, it is possible to measure the frequency

6.2 Analysis of Particle Size Distribution

Fig. 6.3 (a) Fluctuation of scattered light intensity I(t) versus time t for a small and a large particle, (b) autocorrelation function G2(t) versus t.

broadening by interferometry. The quasi-elastic scattering signal matches a Lorentz curve; the width of the curve correlates with the self-diffusion coefﬁcient of the particles. The experimentally possible frequency resolution is about 1011 Hz, compared with a smaller line broadening for slower diffusion processes in pure liquids of about 106 Hz. On the other hand, modern instruments measure intensity ﬂuctuations of the scattered light. These intensity ﬂuctuations are the result of interferences of scattered light coming from the particle diffusion; ﬂuctuation time ranges from about microseconds to milliseconds. The applied measurement procedure ﬁrst aims to gain the intensity of ﬂuctuations quantitatively and secondly for result interpretation, to calculate the particle size. One option is to use an autocorrelation function. The intensity ﬂuctuations with time for a small and a large particle, respectively for a fast and a slowly diffusing particle, are shown in Fig. 6.3a; Fig. 6.3b shows the autocorrelation function G2(t). The autocorrelation function correlates the scattered light intensity I(t þ t) with the intensity I(t): ðt G ðt; t þ tÞ ¼ hIðtÞ I þ ðt þ tÞi ¼ lim

IðtÞ Iðt þ tÞdt

2

t!1

ð6:14Þ

0

Simply speaking, the correlation of the local particle arrangement at a starting time t is compared with that arrangement at a later time t þ t. Here, the brackets h i mean a summation (integral) of the intensity products measured at different times; t is the correlation or sample time. As dynamic light scattering has a stochastic nature G2(t) represents an exponential decay. For interpretation, G2(t) has to be normalized to g2(t) g 2 ðt; t þ tÞ ¼

hIðtÞ Iðt þ tÞi hIðtÞi2

ð6:15Þ

and converted into the autocorrelation function of the electrical ﬁeld, g1(t), g 2 ðt; t þ tÞ ¼ 1 þ jg 1 ðt; t þ tÞj2

ð6:16Þ

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Assuming an idealized monodisperse particle size, g1(t) is a simple e-function, g 1 ðt; t þ tÞ ¼ expðGtÞ

ð6:17Þ

where G represents the characteristic decay rate; G is related to the translational diffusion coefﬁcient D and scattering vector q, ð6:18Þ

G ¼ D q2

q¼

4pn0 u sin 2 l

ð6:19Þ

The reciprocal value of G is the characteristic decay time t C. The scattering vector q is the difference between the wave vectors of the scattered and the incident light. The value of q is constant for a given system, depending only on scattering angle u, the wavelength of the incident light l, and the refractive index n0 of the liquid. The hydrodynamic particle diameter dH can be obtained by applying the Stokes–Einstein equation to dH ¼

kB T 3pmD

ð6:20Þ

where kB is the Boltzmann constant, T is the Kelvin temperature and m is the dynamic viscosity of the liquid. Note, that the particle size dH is assumed as sphere equivalent. For practically relevant products, particle sizes are distributed. Since every particle size has its own characteristic decay rate, the auto correlation function g1(t) represents an integral function 1 ð

g 1 ðt; t þ tÞ ¼

expðGtÞGðGÞdG

ð6:21Þ

0

Here, G(G) is a normalized distribution function of the decay rates. The term G(G)dG is proportional to the fraction of the light intensity scattered by particles with decay rates in the range G to G þ dG. Consequently, G(G)dG is related to the particle size frequency distribution q0(d). A problem arising here is to calculate the correct particle size distribution. A small change in the autocorrelation data leads to a dramatic change in the particle size distribution. Several mathematical approaches have been developed to solve this ill-posed numerical problem: 1. A simple algorithm is the cumulant method (Koppel, 1972). Here, a cumulant generating function has to be calculated in terms of the logarithmic autocorrelation function for a monodisperse particle size, leading to a linear graph. For a particle size distribution experimental data are ﬁtted to a polynomial function. This leads to an average particle diameter (ﬁrst moment of light intensity correlated particle size distribution) and to a polydispersity index, assuming a Gauss distribution.

6.2 Analysis of Particle Size Distribution

2. In the multiexponential sampling analysis the autocorrelation function represents a sum of discrete exponential functions in a logarithmic distance with related amplitudes that can be ﬁtted, for example by a non-linear least-square (NLLS) algorithm (Lawson and Hansen, 1974). 3. Likewise, the Contin analysis (Provencher, 1982) is an iterative method to solve the inverse Laplace transform. Here, the best particle size distribution is selected from a set of solutions assuming the best ﬁt as well the simplest distribution. The dynamic light scattering is an excellent method for spherical particles with narrow distributions. Difﬁculties arise when both conditions are not fulﬁlled. Sample preparation is most important, because nanoparticles, liquid convection and coarse particle sedimentation may disturb the measuring procedure. For concentrated suspensions that show a multi-scattering behavior, an alternative approach is the NIBS (non-invasive back scattering) technology. The scattering volume of the sample is near the wall of the test cell to shorten the laser path through the suspension and to avoid multi-scattering behavior. Laser diffraction spectroscopy is a widely used technique in scientiﬁc and industrial applications to determine particle sizes from about 4 l to several millimeters. The investigation of suspensions as well as of dry powders is of interest, sampling is possible off-line as well as on-line. Here, application of the Fraunhofer theory is possible, explaining the particle interaction with light by classical laws of optics. That means, diffraction occurs at the interphase of the particle and leads to interferences of the diffracted waves (see the principle of Huygens). For Fraunhofer diffraction on a spherical, absolutely opaque single particle, the relationships 2 I A 2J 1 ðjÞ 2 ¼ ð6:22Þ I0 lls j j

pd sinu l

ð6:23Þ

can be deduced; I is the intensity of the diffracted laser light, I0 the intensity of the incident light, ls the distance of the diffracting particle from the screen, A the projection surface area of the particle, l the wavelength of the incident light, J1(j) the ﬁrst order Bessel function, u the diffraction angle, and d the particle size. Due to the Bessel function in Eq. 6.22, about 84% of the intensity of the diffracted light is found at the interference maximum of zeroth order (u ! 0) of the diffraction pattern; the intensity I is proportional to d4/ls2. Otherwise, at interference maxima of higher order intensities I are proportional to d2/ls2. By analogy to diffraction at an optical slit, a diffraction pattern is generated behind particles. If diffraction occurs at spherical particles, concentric circles are observed. Near the particle, Fresnel diffraction occurs. The interference pattern is distance dependent, but far from the particle (ls d2/l) application of the Fraunhofer approximation is possible; these interference patterns become distance independent (for a particle of 1 mm this distance from the particle is about 1.6 m). For an assembly

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of particles there is a superposition of diffraction light from each particle. This leads to uncertainty in the diffraction pattern. To overcome these problems, in the instrumental implementation the diffracted as well the transmitted light is focused on a plane. Using a lens with a focal width f it is possible to transform the angle-dependent Fraunhofer diffraction of each particle into a local distance on the screen by the relationship D ¼ uf

ð6:24Þ

Here, D is the distance from the light axis on the screen and u the diffraction angle. This means that the image of the diffraction pattern of all particles is radially symmetric. Inserting Eqs. 6.23 and 6.24 into Eq. 6.22, with sin u u for small diffraction angles, the intensity of the diffracted light I(D,d) is obtained as 2 2 IðD; dÞ pd 2J 1 ðjÞ 2 ¼ ð6:25Þ 4lf I0 j with j

pdD lf

ð6:26Þ

Considering now an assembly of N particles, there is a superposition of the Fraunhofer diffraction pattern I(D,d) of each particle; intensity I(N,D,d) is proportional to N, where q0(d) is the particle size frequency distribution, dmax ð

IðN; D; dÞ ¼ N

IðD; dÞ q0 ðdÞdðdÞ

ð6:27Þ

dmin

In the instrumental implementation, the experimental intensity distribution I(N,D,d) has to be transformed into a particle size frequency distribution q0(d). For particle systems not meeting the Fraunhofer approximation (d > 4 l), Mie theory is implemented in modern laser diffraction instruments. Mie theory can predict scattering intensities for all particles, small or large, transparent or opaque. It allows phenomena of primary scattering from the surface of the particle and secondary scattering caused by light refraction within the particle to be included. However, extra data of material properties are needed, for example light absorption coefﬁcient, difference of refractive indices of particle and ﬂuid. According to ISO 13320, Mie theory offers the best general solution for particles smaller than 50 mm (Born and Wolf, 1993). For very ﬁne particles the forward diffraction is quite low, with the consequence that it is impossible to detect the diffracted light by ring detectors. Modern instruments, for example Mastersizer 2000 (Malvern Instruments Inc.), have additional detectors, see Fig. 6.4. Thus, diffracted light can be measured by so-called forward and large angle detectors. In addition, the back-scattered light intensity is used to determine particle size distributions. A further improvement of resolution for very ﬁne particles is possible by using lasers with a blue light source (l ¼ 466 nm) instead of a red light source (l ¼ 633 nm).

6.2 Analysis of Particle Size Distribution

Fig. 6.4 Arrangement of optical components of Mastersizer 2000 (Reproduction by courtesy of Malvern Instruments Inc.).

6.2.3 Ultrasonic Methods for Dense Particle Dispersions

Ultrasonic techniques give an extraordinary tool to characterize concentrated particle dispersions. An acoustic spectrometer measures the attenuation of ultrasound, the propagation velocity of this sound and/or acoustic impedance, depending on the instrument. The acoustic signal contains information about the particle size distributions, volume fraction and structural and thermodynamic particle properties. 6.2.3.1 Acoustic Attenuation Spectroscopy Acoustic spectroscopy uses sound wavelengths in the range from 15 mm to 1.5 mm, corresponding to frequencies from 1 to 100 MHz. The acoustic behavior of dispersions is based on several attenuation phenomena. Besides material-speciﬁc contributions of the particles and the liquid (inner absorption loss), interactions between liquid and solid phases have to be taken into account. An important reason for attenuation is scattering; this phenomenon includes diffraction and reﬂection on particles that disturb the straight propagation of sonic waves. Other reasons for attenuation are thermal and viscous effects caused by pulsation and oscillation of particles. The pulsation effect is due to local pressure ﬂuctuations in the ﬂuid leading to local dispersion density and particle concentration changes. Viscous losses are due to relative movement between oscillating particles and ﬂuid. Additionally, at high particle concentration there are structural losses as a result of interactions of the dispersed particles (adhesion and electrostatic double layer repulsion), water dipoles and directional hydrogen bonds (cluster formation). Viscous attenuation is dominant. For the experimental determination of particle sizes, the main input parameters needed are the density of the suspension and the volume fractions of each phase. For systems which have a low density difference between particles and ﬂuid, thermophysical properties, for example thermal conductivity, speciﬁc heat capacity, thermal expansion coefﬁcient, are required additionally. Usually, attenuation is more sensitive to particle size than the propagation velocity of sound. Currently approximations used for calculating the particle size from attenuation data are based on scattering or

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coupled phase approaches. A comparison of these theories is quite complex, the validity of different models depends on the investigated system. Generally, the determination of the attenuation spectrum as well as the calculation of particle size distributions is quite sophisticated, however, today it can be conducted with a high precision and accuracy. In many cases, it is now possible to determine particle sizes in suspensions experimentally for particle volume fractions ws 50% (Dukhin and Goetz, 2004). 6.2.3.2 Electrokinetic Sonic Amplitude Spectroscopy Electro-acoustics is another ultrasound-based technique, applied for colloidal particles having, normally, electrochemical double layers. Here, it is possible to obtain information about the particle size as well as about the zeta-potential. In electroacoustics, acoustic and electric ﬁeld effects are coupled. There are two ways to generate this phenomenon, depending on which ﬁeld is the driving force and what the response is. In the electrokinetic sonic amplitude (ESA) technique, the electrical ﬁeld is the driving force, followed by an acoustic response; in the colloid vibration potential (CVP) or colloid vibration current (CVI) techniques the acoustic ﬁeld is the driving force, followed by an electric response. The ESA effect arises because the colloidal particles are driven away from or towards the electrodes, causing a local compression wave of the liquid around them. The strength of the resulting ESA signal is inﬂuenced by the density difference between the particle and the ﬂuid and by the volume fractions. It also depends on the zeta-potential, since this affects the particle velocity in the electrical ﬁeld. The particle velocity has a time lag to the electrical signal, indicating the inertia or mobility of the particle and thus the size of the particle. Consequently, determination of the particle size and the zeta-potential from the ESA signal requires the calculation of the dynamic mobility spectrum,

ESA ¼ AðvÞ ws

Dr Z mD r

ð6:28Þ

Here, ESA denotes the measured ESA signal, mD the dynamic particle mobility. A(v) is the calibration function depending on the frequency v of the electrical ﬁeld; ws is the particle volume fraction, Dr the density difference between particle and ﬂuid, r the ﬂuid density and Z the acoustic resistance. According to OBrien et al. (1995) the dynamic mobility mD is related to the zeta-potential and the particle size, mD ¼

2ez Gðd; vÞ ð1 þ f Þ 3m

ð6:29Þ

This correlation is valid for a spherical particle with a thin double layer. In Eq. 6.29, e refers to the permittivity of the ﬂuid; m is the dynamic viscosity and z the zetapotential. The G(d,v) factor represents the effect of the inertia on the dynamic mobility. The (1 þ f ) factor in Eq. 6.29 is proportional to the tangential electrical ﬁeld at the particle surface. It depends on, for example the permittivity of the particle and the surface conductance of the double layer.

6.3 Measurement of the Physical Properties of Particles

For a particulate system with N particles the experimental dynamic mobility represents an averaged or mean value of all particles (ﬁrst statistical moment), herein referred to as hmDi. It can be written formally in an integral equation dð max

hmD i ¼

mD ðd; z; wÞ q0 ðdÞ dðdÞ

ð6:30Þ

dmin

q0(d) being the particle size frequency distribution. Here, again, the problem is the numerically poorly conditioned equation. A small error in the measurements leads to a substantial error in the particle size frequency distribution. But, nevertheless, in our opinion, it seems that the ESA technique gives more accurate results for higher concentrations than ultrasonic attenuation spectroscopy.

6.3 Measurement of the Physical Properties of Particles 6.3.1 Solid Density Analysis by He-Pycnometry 6.3.1.1 Introduction In technical processes the density of the material provides not only a feature of quality that keeps a process under control but also reveals important information about the nature and structure of the ﬁnal product. The true or solid density of a powder equals the mass of a quantity of the solid material divided by the volume that this material occupies

rs ¼

ms Vs

ð6:31Þ

Thus, the density can be determined by measuring both the mass and the volume of the particles (Webb and Orr, 1997). The mass can be measured by using a balance with suitable accuracy. However, the measurement of the volume is the actual problem because shapes and geometrical structures of particles frequently differ. According to both surface shape and internal structure, there are different deﬁnitions of the solid volume of a powder. Only for a non-porous and perfect sphere can the volume be calculated easily and directly after measuring its diameter. In many cases, coarse and ﬁne particles have both manifold irregularities of the surface and their internal structure like slits, ﬁssures and pores. The solid density (also termed true, absolute or skeletal density) is then characterized by the mass and the volume of the solid after exclusion of all pores. This means that all internal voids (pores, cracks, slits etc.) connected to the surface should be excluded to fulﬁll the typical volume deﬁnition as the space occupied by an object. In the case of pores enclosed by solid matter that have no access to the surface, the pore volume is

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Fig. 6.5 Effect of the thermal treatment.

included because there is no realistic chance to detect it. The accuracy and precision of the volume determination depend strongly on the sample preparation. Especially, the sample should be free of moisture and volatile substances. This can be ensured by intensive desorption, for example by heating under vacuum (Fig. 6.5). 6.3.1.2 Volume Determination Using Gas Pycnometry There are several methods to detect the volume of irregularly shaped particles. In this section the most common method, namely gas pycnometry, is explained. In gas pycnometry, no open pores or other open internal cavities will count to the volume of solids, so that the experimental volume determination leads to the true or solid density, which is a property of the material of the particles. There is no inﬂuence of the structure of the particles. The method is based on the fact that the used gas is displaced by the solid object. In a gas pycnometer the displacement is detected by a pressure change. As already pointed out, the volume of solid matter can be determined independently of the surface structure and the existence of open pores of any size or shape. A pycnometer has a chamber of precisely known volume that is used to determine an unknown volume of matter. Though pycnometers can operate using different media, the gas pycnometer is the most commonly applied instrument. If using helium, the gas penetrates into open pores larger than 0.1 nm. Thus, almost all pores will be detected. If a liquid is used it can happen that only a fraction of the pores will be ﬁlled by penetration of the liquid, depending on the particle and liquid properties (Fig. 6.6).

Fig. 6.6 Incomplete wetting of the matter (pores and slits are only partially filled with liquid).

6.3 Measurement of the Physical Properties of Particles

Fig. 6.7 Set-up of gas pycnometer.

Incomplete wetting leads to a wrong skeletal volume determination. Hence, in order to ﬁnd the true value of the solid volume helium is preferred. The principle of gas pycnometry (Micromeritics Instrument Corporation, 1992) is based on volume measurement by using the ideal gas law, so that the displacement of gas by a solid matter can be detected by the pressure change. Sample and reference chambers (Fig. 6.7) are pre-calibrated to quantitatively determine the volume of an unknown sample. The volumes of the sample and reference chambers must be known. The measurement procedure of the unknown sample volume is performed in the following way. After weighing, the sample is placed into the sample chamber. Then: 1. A helium atmosphere is created inside the instrument to rinse the sample intensively. 2. After pressurizing the sample chamber, the attained stabilized pressure P1 is measured. 3. Subsequently, by expansion of this gas into a precisely calibrated volume (reference chamber) the pressure drops to pressure P2. Both pressure P1 and pressure P2 have to be monitored in an equilibrated state. Assuming a constant temperature, the calculation of the sample volume is performed by P1 ðV SCh V Sample Þ ¼ P2 ðV SCh þ V Ref V Sample Þ;

ð6:32Þ

(S-Ch: sample chamber, Ref: Reference chamber) which leads to calculation of the volume of the sample, as V Ref V Sample ¼ V SCh P1 P 2 1

ð6:33Þ

The accuracy of gas pycnometry in the determination of solid volume is at least 0.2% of the respective sample chamber volume. Moisture and volatile substances in the sample can contribute to pressure change and, thus, cause errors and instabilities. Pressure instabilities lead to a wrong determination.

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6.3.2 Specific Surface Area by Gas Adsorption Method 6.3.2.1 Physical Principles Gas adsorption on the outer surface and the pore walls of solids is a common phenomenon (Webb and Orr, 1997; Lowell and Shields, 1991). Adsorption on the outer surface is inﬂuenced by surface imperfections and irregularities. In the case of porous particles, these effects are superposed by effects of their internal structure, that is the shape and dimensions of the pores. Surface molecules interact with gas molecules by molecular interaction forces (Van der Waals forces), resulting in adhesion of gas molecules onto the solid surface. This is called physical adsorption. Physical adsorption is inﬂuenced by the interaction potential U between the gas (adsorbate) and the surface (adsorbent), absolute temperature T and pressure P (see Fig. 6.8). Pressure means total pressure in a pure gas atmosphere and the partial pressure of the considered component in the case of a gas mixture. The number or amount of adsorbed gas molecules can be expressed as

N ads ¼ f ðP; T; UÞ

ð6:34Þ

which reduces to N ads ¼ f ðP; UÞ

ð6:35Þ

at constant temperature, and to N ads ¼ f ðPÞ

ð6:36Þ

with a particular vapor at constant temperature (U ¼ const., T ¼const.). Equation 6.36 is a general representation of the so-called sorption isotherm. Frequently, the amount of adsorbed species is expressed as a mass content related to the mass of the adsorbent, and it is plotted as a function of the relative pressure P/P of the vapor phase. The adsorbate equilibrium pressure P is normally related to the saturation pressure P. The gas is considered to be below its critical temperature and,

Fig. 6.8 Phases involved in gas adsorption.

6.3 Measurement of the Physical Properties of Particles

Fig. 6.9 Exemplary shape of an adsorption isotherm.

therefore, condensable. Alternatively, the volume of adsorbed gas under standard conditions VSTP (0 C, 1.013 bar), can be plotted on the ordinate (Fig. 6.9). It has been found that measured adsorption isotherms can usually be divided into ﬁve different types (Fig. 6.10). Each of them reﬂects a typical adsorption behavior of the solid that may be correlated with the size of the pores (see Section 6.3.3). .

The type 1 curve is encountered with particles that are microporous (see Section 6.3.3). Their pore sizes are of the order of magnitude of the adsorbate molecule diameter (smaller than 2 nm). Overlapping potential forces in the pores result in condensation of the adsorbate that will ﬁll up the pores. The adsorbed gas is essentially inﬂuenced by the geometrical shapes of the pores, especially at very low relative pressures.

.

Type 2 isotherms are encountered for mesoporous particles with pore sizes from 2 to 50 nm. The adsorption of gas molecules takes place on the pore surfaces in

Fig. 6.10 Basic adsorption isotherm types according to IUPAC recommendation 1994.

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multiple layers. The number of adsorbed layers can increase at higher relative pressures and tend ultimately to apparent inﬁnity. .

Type 3 curves indicate a behavior when the adsorbate interaction with an already adsorbed layer is stronger than the interaction between the solid surface and the adsorbate. The isotherm shape is convex with increasing relative pressure.

.

Type 4 isotherms reﬂect in their upper part adsorption that occurs on particles with meso- or macro-pores (Section 6.3.3). With increasing relative pressure the elevated adsorbate uptake is caused by capillary condensation in such pores.

.

Type 5 curves are encountered for particles that exhibit a small adsorbate–adsorbent interaction like in type 3 isotherms. Furthermore, the particles possess meso- or macro-pores that result in similar adsorption behavior to type 4 isotherms.

The well-established and standardized method of gas adsorption can contribute to the detection of surface irregularities and internal pore structures. In this way, it represents a powerful tool to characterize any powders. Especially, techniques have been developed that enable generation of important information about surface area, total pore volume and pore size distribution. 6.3.2.2 Surface Area Determination using the BET-Model The BET-theory was developed by Brunauer, Emmett and Teller (Brunauer et al., 1938; Lowell and Shields, 1991). It provides the basis for a well-established method to calculate the surface area of powdered particles from measured adsorption data by using nitrogen gas at a temperature of 77 K. BET theory describes the adsorption of molecules on surfaces in multiple layers as a function of the relative pressures of the adsorbate in the gas phase. A major model parameter is the amount of molecules needed to cover the surface completely by a monomolecular layer, corresponding to the gas volume Vmono. The second parameter C describes the adsorption behavior of the ﬁrst layer of molecules; it increases exponentially with their adsorption enthalpy (bond energy of adsorbate molecules) and may be considered as constant for constant temperature. The model uses the strong assumption that subsequent molecular layers do not interact with the solid surface. With increasing relative pressure, more and more of these layers will form (typically, none of them will be fully occupied). For an inﬁnite number of possible layers, the relationship between relative pressure P/P and adsorbed amount of gas can be given in a linear form (Brunauer et al., 1938)

P 1 ðC1Þ P ¼ þ V ads ðP PÞ V mono C V mono C P

ð6:37Þ

which is typically valid for moderate relative pressures from 0.05 to 0.30. (For higher values of P/P the theory needs to be extended to account for the ﬁnite size of the pores.) The straight line corresponding to Eq. 6.37 is plotted in Fig. 6.11.

6.3 Measurement of the Physical Properties of Particles

Fig. 6.11 Linearized form of the BET equation.

From this plot, the axis intercept a¼

1 V mono C

ð6:38Þ

C1 V mono C

ð6:39Þ

and slope b¼

can be determined to calculate the monolayer capacity. Equations 6.38 and 6.39 lead to: V mono ¼

C¼

1 aþb

b þ1 a

ð6:40Þ

ð6:41Þ

Based on the known cross-sectional area of nitrogen molecules (AN2 ¼ 0.162 nm2), the so-called BET-surface area, ABET ¼

V mono N A AN2 ~ mol V

ð6:42Þ

can be calculated from the monolayer volume Vmono, Avogadros constant (NA ¼ ~ mol ¼ 22:4 l mol1 ). 6.022 1023 mol1) and the molar volume (V For calculation of the BET surface area the adsorption isotherm needs to be measured as described above (multipoint BET method) to determine the quantity of nitrogen adsorbed in the monolayer. In some cases if the adsorption constant C exceeds 100, and therefore b 6¼ f (C ) a, the experimental effort can be reduced by measuring the adsorbed amount only at a P/P value of 0.3 (single-point method) to get the monolayer volume. Based on Eq. 6.41 for relatively high values of C the intercept a may be neglected as compared to the slope a¼

b C1

ð6:43Þ

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It is (C 1)/C 1 so that Eq. 6.37 becomes P P V ads ðP PÞ V mono P

ð6:44Þ

which leads to the following equation for calculation of the monolayer volume P V mono V ads 1 ð6:45Þ P By using the single-point method the surface area is calculated again by Eq. 6.42. Strictly speaking, the BET method is best applicable to particles whose adsorption isotherm is of type 2. Nevertheless, the approach can provide useful orientation and a basis for comparison between different products, even if the prerequisites of the BET theory are not fulﬁlled completely, that means also for other isotherm types. 6.3.3 Pore Size Distribution by Gas Adsorption Method 6.3.3.1 Introduction In general, porosity is deﬁned as the ratio of the volume of cavities to the total volume (that means the volume plus pore volume). According to the IUPAC convention (International Union of Pure and Applied Chemistry) pores of solids are classiﬁed depending on their diameter into micropores (< 2 nm), mesopores (from 2 to 50 nm) and macropores (> 50 nm), see Rouquerol et al. (1994). Porous materials can also be distinguished by the structure of their pores. Various types of often encountered pores are illustrated in Fig. 6.12 (Rouquerol et al., 1994), namely:

a) b) c) d) e) f)

Closed pores, totally isolated in the solid, without connection to the surface, shallow pores resulting from irregularities of the outer surface of the particle, open, bottle neck pores that may cause hysteresis of the adsorption curve, open pores with only one end, described as blind, funnel-shaped pores, open pores that go through from one side of the particle to the other.

Fig. 6.12 Different types of pores in a solid particle.

6.3 Measurement of the Physical Properties of Particles

The condensation of adsorbed gas molecules in pores is thermodynamically preferred. This effect is based on the overlap of attractive interaction potentials of the pores that leads to a stronger adsorbate bonding and gas condensation compared to the adsorption on plane surfaces. Speciﬁcally, condensation occurs ﬁrst in small pores and proceeds in the larger pores as the amount of gas molecules in the environment increases or, in other words, as the gas pressure increases. Vice versa, desorption starts at large pores down to small pores which have a high bond capacity for condensed gas molecules. 6.3.3.2 Assessment of Microporosity Generally it is observed that the adsorption behavior of gases is modiﬁed in micropores as compared to adsorption on a plane surface since the closeness of the pore walls is associated with an increase in the strength of the adsorbent–adsorbate interaction, especially at very low P/P. Additionally, condensation effects are encountered which lead to complete ﬁlling of the pores at somewhat higher P/P. This results in an adsorption according to the classical Langmuir isotherm (type I). For calculation of the micropore volume it is hence assumed that the micropores are completely ﬁlled with liquid adsorbate. A frequently used method for calculation of the micropore volume was developed by Dubinin and Radushkevich (Webb and Orr, 1997). Their approach is based on the potential theory of Polanyi that describes the adsorption of pure gases in microporous materials. According to Polanyi theory each adsorbent possesses a characteristic adsorption potential E or adsorption enthalpy, that is bond energy of the adsorbate molecules. Consequently, the micropore volume ﬁlled by liquid adsorbate at the relative pressure P/P is a function of the molar adsorption potential E, which is equivalent to the energy needed to transfer the molecules from the adsorbed to the gaseous state. In the case of T < Tcritical, Dubinin uses for the adsorption potential the expression P E ¼ R T ln ð6:46Þ P

that represents the characteristic property of the adsorbate and the adsorbent and reﬂects the so-called bond strength or afﬁnity behavior of the particle surface–condensed gas interactions. Further, an afﬁnity coefﬁcient b¼

E E0

ð6:47Þ

is introduced that is a measure of adsorbability of different adsorbates to the adsorbent. Here, E0 is the characteristic molar adsorption bond potential of standard vapor. Dubinin and Radushkevich assumed that the dependence of the adsorbed volume on the adsorption potential can be expressed by the characteristic function RT P 2 ln ð6:48Þ V ads ¼ V micro exp bE 0 P

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Fig. 6.13 Evaluation of adsorption data by the method of Dubinin–Radushkevich.

which can be transformed into RT 2 2 P ln lnV ads ¼ lnV micro P bE 0

ð6:49Þ

When plotting measured values of the adsorbed volume as lnVads versus ln2(P/P), as in Fig. 6.13, often a linear segment of the curve with slope (RT/bE0)2 can be observed. From this segment the micropore volume Vmicro can be estimated by extrapolation. For evaluation of Vmicro, adsorption data in the relative pressure range 104 < P/P < 0.1 should be used. 6.3.3.3 Assessment of Mesoporosity Capillary condensation is observed especially in so-called meso- and macro-pores (Fig. 6.14). By steadily increasing the relative pressure capillary condensation takes place ﬁrst in relatively small pores and then proceeds to larger ones. If the adsorbent contains no macropores, it is observed that the isotherm comes to a plateau at high relative pressure P/P. This state corresponds to a completely ﬁlled state of the mesopores. Thus, the calculation of the total meso-pore volume is based on the fact that the

Fig. 6.14 Scheme of capillary condensation.

6.3 Measurement of the Physical Properties of Particles

vapor adsorbed at the plateau (at P/P 1) has ﬁlled the meso-pores in the normal liquid state. Mesopore volume calculation is usually performed by means of the Kelvin equation in its general form rc ¼

~ mol cosd 2 slg V ~ lnðP=P Þ RT

ð6:50Þ

where rc is the radius of the meniscus, slg is surface tension (i.e. bond potential per ~ mol is the molar volume of the liquid unit surface), d is the contact angle and V condensate. When using nitrogen, Eq. 6.50 can be transformed to rc ¼

0:9573 nm lnðP=P Þ

ð6:51Þ

If we assume that the surface of the pore is covered by a layer of adsorbed molecules before capillary condensation proceeds, the radii from Eqs. 6.50 and 6.51 have to be corrected by the thickness t of the adsorbed layer in order to obtain the pore radius, with the assumption that the contact angle d is set to zero: r pore ¼ r c þ t

ð6:52Þ

This postulates that an adsorbed ﬁlm with thickness t remains on the pore wall when desorption occurs. When using nitrogen as adsorbate, de Boer et al. (1965) developed for t the expression vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u 13:99 t ¼ 0:1 nm u t P 0:0340:4343 ln P

ð6:53Þ

Barrett, Joyner and Halenda (BJH) have implemented the above described model into a procedure for the assessment of pore size distribution by stepwise calculation on the basis of measured adsorption data (Webb and Orr, 1997). This method is strictly valid only for the determination of cylindrical pores within the mesopore range (>2 nm); it assumes a sorption isotherm of type 4. Condensation occurs in the pores, with a relative pressure corresponding to the Kelvin radius rc. Furthermore, it is assumed that a multilayer with surface area Apore and thickness t exists and is changing by evaporation or condensation. The method is applicable on either desorption or adsorption isotherms. The relationship DVpore;i ¼

X rpore;i 2 DVl;i Dti Apore;i rc;i

ð6:54Þ

between the mean pore radius rpore mean Kelvin radius rc and the corresponding pore volume DVpore,i is based on a relative pressure change DPi/P which has to be performed stepwise downwards in the relative pressure range from 0.99 to 0.3 (Lowell and Shields, 1991).

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Fig. 6.15 Cumulative pore volume plot.

The liquid volume DVl,i can be calculated using the standard volume DVSTP obtained directly from the isotherm by DV l ¼

~ DV STP M ¼ 1:545 103 DV STP ~ rl V mol

ð6:55Þ

~ is the molar mass and rl is the density of the liquid; (for nitrogen: Here, M ~ ¼ 28 g mol1 , rl ¼ 809 kg m3). M In Eq. 6.54 the pore volume DVpore,i is calculated from the evaporated part of the liquid volume plus the volume remaining adsorbed on the walls of the pores. This volume can be determined from the surface area Apore,i (surface area previously created by desorption, see Fig. 6.14) multiplied by the change in ﬁlm depth Dt. In the case of assumed cylindrical pores with the radius rpore,i the fraction area can be calculated with V pore;i : Apore;i ¼ 2 r pore;i

ð6:56Þ

By summation of the incremental DVpore,i depending on the pore radius rpore the cumulative pore volume plot can be obtained (see Fig. 6.15). 6.3.3.4 Simplified Assessment of Pore Volume The total pore volume of particles Vtotal can be estimated approximately in a very simple way by measuring the adsorbed volume in a relative pressure range from a minimum of 103 up to a value near to unity and assuming that the adsorbed amount ﬁlls up all pores completely in the form of liquid condensate. In the ﬁrst part of the curve at relative pressures P/P smaller than 0.3, the measured isotherm has a relatively steep slope. This behavior is caused by the presence of micropores. In the second part, at relative pressures greater than 0.3, further slopes are encountered. This region can be attributed to the existence of meso- and macro-pores with a volume of (Vtotal – Vmicro). In Fig. 6.18 a simple tangent method is used to ﬁnd characteristic points of the isotherm and the volumes Vmicro and Vtotal.

6.3 Measurement of the Physical Properties of Particles

Fig. 6.16 General shape of an isotherm for pore volume assessment.

To convert the adsorbed volume VSTP estimated from the isotherm curve at standard conditions to liquid volumes corresponding to pore volumes such as Vtotal and Vmicro Eq. 6.55 can be used. However, it should be noted that measured adsorption isotherms of different materials may have similar characteristics to those presented in Fig. 6.16. Especially for ﬁne compact powders, that means materials with large surface area without any presence of pores, adsorption isotherms show, in the relative pressure range below 0.3, comparable trends to isotherms of porous materials. Thus, the above-described method should be considered with care and applied only to materials which are known to be microporous. 6.3.3.5 Measurement Set-Up and Test Method There are different methods for determining adsorption data. Both, the volumetric and gravimetric methods aim to measure the quantity of gas condensed on a solid surface at equilibrated vapor pressure. Depending on the measurement set-up, the amount of adsorbed gas is determined as a volume or mass (weight). When using the gravimetric method, the accuracy of measurement depends essentially on the sensitivity of the balance. Usually, the sample mass has to be conﬁned to very small amounts that must be representative. The accuracy of volumetric instruments depends on the quality of pressure gauges. It has to be noted that the equilibration of gas pressure is achieved after numerous cycles. In the following, a volumetric measurement set-up of Porous Materials Inc., Ithaca, is exemplarily presented (Fig. 6.17). The principle of operation is comparable with that of pycnometry. The sequential steps are as follows:

1. Placement of a known sample mass in the sample chamber, 2. pre-treatment of the sample at elevated temperature under vacuum to remove adsorbed gases and moisture,

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Fig. 6.17 Measurement set-up of a volumetric instrument (Porous Materials Inc.).

3. immersion of the sample chamber in a Dewar vessel containing liquid nitrogen, 4. stepwise pressurization of the reference chamber, gas expansion to sample chamber until the relative pressure point is reached, 5. calculation of the adsorbed gas amount using the ideal gas law. The reference volume is pressurized with adsorbate gas and is then isolated, so that the resulting gas pressure (Pi) can be measured. This gas is then allowed to expand into the sample chamber where adsorption at the sample takes place. When the pressure has equilibrated, the ﬁnal gas pressure (Pf) is measured. The molar amount of gas adsorbed at the sample can be calculated stepwise (subscript n corresponds to one step) by: N ads ¼

N X

ðN ads;n N ads;n1 Þ

ð6:57Þ

n¼1

with incremental steps N ads;n N ads;n1 ¼ ðPi;n P f ;n Þ ðPf ;n P f ;n1 Þ

V Ref ~ T inst R

V test V sample V inst þ ~ T inst ~ T test R R

ð6:58Þ

The volumes of the instrument (reference volume VRef, instrument volume at instrument temperature Vinst, test volume Vtest at liquid nitrogen temperature) are determined by a calibration test, while Vsample can be calculated from the mass of the sample via gas pycnometry.

6.3 Measurement of the Physical Properties of Particles

6.3.4 Measurement of Particle Adhesion 6.3.4.1 Particle Adhesion Effects Particle adhesion can occur by one or more of the following bonding effects, Fig. 6.18 (Rumpf, 1958, 1974, 1975; Schubert, 1979, 2003; Borho et al., 1991; Tomas, 1991, 2007a, b): .

Surface and ﬁeld forces at direct contact: – Van der Waals forces (all dry powders consisting of polar, induced polar and non-polar molecules, for example minerals, chemicals, plastics, pharmaceuticals, food), – Electrostatic forces, – electric conductor (metal powders), – electric non-conductor (polymer powders, plastics), – Magnetic force (iron powder);

.

Material bridges between particle surfaces: – Hydrogen bonds of adsorbed surface layers of condensed water (powders), – Organic macromolecules as ﬂocculants in suspensions (in waste water); – Liquid bridges of

Fig. 6.18 Particle adhesion and micro-processes of bonding of particles in contact.

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– Low viscosity wetting liquids by capillary pressure and surface tension (moist sand, moist soil), – Highly viscous bond agents (tar sand, resins); – Solid bridges by – Recrystallization of liquid bridges which contain solvents (salt), – Solidiﬁcation of swelled ultraﬁne sol particles (starch, clay), – Freezing of liquid bridge bonds (frozen soil), – Chemical reactions with adsorbed surface layers (cement hydration by water) or cement with interstitial pore water (concrete), – Solidiﬁcation of highly viscous bond agents (asphalt), – Contact fusion by sintering (aggregates of nanoparticles, ceramics), – Chemical bonds by solid–solid reactions (glass batch, activated metal alloys); .

Interlocking by macromolecular and particle shape effects: – Interlocking of chain branches at macromolecules (proteins), – Interlocking of contacts by overlaps of surface asperities (rough particles), – Interlocking by hook-like bonds (ﬁbers).

6.3.4.2 Comparison between Different Adhesion Forces The strengths of different adhesion effects are compared in Fig. 6.19. Disregarding the solid bridge bonds, the liquid bridge is the dominant adhesion force (Rumpf, 1974), as

Fig. 6.19 Adhesion forces between stiff particle and smooth surface according to Rumpf (1974), calculated with a0 ¼ 0.4 nm minimum molecular separation (at interaction force equilibrium), a ¼ 20 bridge angle, u ¼ 0 wetting angle, slg ¼ 72 mJ m2 surface tension of water, CH ¼ 19 1020 J Hamaker constant according

to Lifshitz (1956), qmax ¼ 16 1018 As mm2 surface charge density, U ¼ 0.5 V contact 0:5 2 potential, C H;sls ¼ ðC 0:5 H;ss C H;ll Þ , Hamaker constant for particle–water–particle interaction. Instead of the plate one can also consider a coarse particle with a large radius of surface curvature.

6.3 Measurement of the Physical Properties of Particles

long as a liquid bridge is formed, see for example Tomas (1983); Schubert (1982); Ennis et al. (1990). In the absence of a liquid bridge, the van der Waals force of a dry contact dominates. The van der Waals force decreases considerably in a wet environment because of the reduction of the Hamaker constant by the interstitial water. This effect is widely used in washing processes. For charged particles such as toner particles the Coulomb force becomes important. The surface-charge density is assumed to be qmax ¼ 16 1018 A s mm2, which is the maximum value decided by the electric ﬁeld limit for discharge. Sometimes the Coulomb force may be larger than the van der Waals force because the maximum surface-charge density is determined by the voltage limit rather than the ﬁeld limit (Masuda and Gotoh, 1997). In the above discussion, the effects of the atmospheric conditions are not taken into consideration. Because of the humidity of the ambient air water is adsorbed at particle surfaces. These surface layers of condensed water markedly increase the effective contact zone. By molecular bonds between these condensed liquid molecules (known as surface tension), these surface layers may additionally form small liquid bridges, which results in the alternation of the adhesive force (Rumpf, 1958; Chigazawa et al., 1981). The humidity also changes the adsorbed water layer thickness (Chigazawa et al., 1981; Tomas, 1991), and hence also affects the adhesion force. Thus, the adhesion is inﬂuenced by mobile adsorption layers due to molecular rearrangement and development of additional hydrogen bonds (Schubert, 2003). As long as the liquid bridge is stable, the critical separation for rupture is about acrit ¼ V1/3, where V is the volume of the bridge (Lian et al., 1993). The separation hardly inﬂuences the bond force. Van der Waals forces and Coulomb forces (for a conductor) have similar long-range force-separation (distance) curves FH0(a), Fig. 6.19b. The Coulomb forces of a non-conductor do not depend on separation. This principle is widely used to precipitate dust particles in an electric ﬁeld. The effect of van der Waals forces depends strongly on the roughness of a surface, Fig. 6.19c. A minimum van der Waals force is seen versus roughness height hr for different particle sizes d. The inﬂuence of roughness for liquid bridge bonds and adsorption layers (humidity) is comparatively small. The adhesion will also be affected by temperature (Masuda and Gotoh, 1997). It is worth noting here that the particle weight for d < 100 mm is very small compared to the adhesion forces, which dominate particle interaction in the gravitational ﬁeld. Recently, the force–displacement behavior of elastic, elastic–adhesion, plastic– adhesion, elastic–plastic, elastic–dissipative, and plastic–dissipative contacts has been discussed in detail in review papers by Tomas (2007a,b). 6.3.4.3 Survey of Adhesion Force Test Methods The principles of various methods used to measure the adhesion force are shown in Fig. 6.20. All these methods involve application of an external force on the particles. The interacting force between two microscopic bodies is measured by the spring balance method as a function of the elongation of the spring when the bodies are separated. In the centrifugal method, the plate on which particles are deposited is put on a centrifuge to press particles on the surface by a compressive force FC and, after

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Fig. 6.20 Methods for testing the adhesion force between particle and surface as collected by Masuda and Gotoh (1997).

this so-called contact preconsolidation, to detach the particles (Krupp, 1967). The centrifugal force that is necessary to remove half of the deposited particles is measured to evaluate the average adhesion force (Graichen et al., 1974; Sch€ utz and Schubert, 1976, 1980; Schmidt, 1998). When the plate is turned perpendicularly to the axis of revolution, the tangential or shear force distribution of the contacts can be measured by the cumulative mass fraction of detaching particles. The vibration method, ﬁrst described by Derjaguin and Zimon (1961), is based on particle detachment from a vibrating surface caused by its inertia at a certain acceleration. Thus, the vibration not only yields a detachment or pull-off force to compensate the adhesion force, but also causes compressive normal forces between particles and surface of the same order. For example, these alternating contact compression and detachment forces are frequently used during the dynamic stressing of cohesive powders as ﬂow promotion in the practice of process engineering (Kollmann and Tomas, 2002). The impact separation method uses an acceleration generated by the bullet (Derjaguin et al., 1968) or hammer impact (Otsuka et al., 1983). When a ﬂuid ﬂow ﬁeld is applied to particles adhered on a plate, the particles suffer a force caused by the ﬂow. At a certain ﬂow velocity, particles start to detach from the plate. Then, the adhesion force can be obtained as a function of ﬂow velocity and/or stress (Matsusaka et al., 1994). Vibration and the hydrodynamic method were recently combined. Particle detachment events are continuously recorded and correlated with acting acceleration, particle mass and ﬂow conditions, which allows calculation of the pull-off force (Hucke et al., 2002). 6.3.4.4 Particle Interaction Apparatus According to Butt In a direct force–separation measurement the atomic force microscope (AFM) can be used. The particle is stuck at a cantilever in the so-called colloid probe technique (Butt et al., 1995), Fig. 6.21. The sample is moved up and down against the ﬁxed

6.3 Measurement of the Physical Properties of Particles

Fig. 6.21 Measurements of adhesion force – separation function by particle interaction apparatus (PIA) according to Butt et al. (1995).

cantilever by applying a voltage to the piezoelectric translator. The cantilever deﬂection DaC is measured versus the position of the piezo Dap normal to the surface. To obtain a force distance curve, DaC and Dap have to be converted into normal force and separation (distance). The normal force FN ¼ kC DaC is obtained by multiplying the deﬂection of the cantilever by its spring constant kC, and the tip–sample separation a ¼ DaC þ Dap is calculated by adding the deﬂection DaC to position Dap. The deﬂection of the cantilever is normally measured using the optical lever technique. A beam from a laser diode is focused onto the end of the cantilever and the position of the reﬂected beam is monitored by a position sensitive detector array (photodetector). The backside of the cantilever is usually covered with a thin gold layer to enhance its reﬂectivity. When a force is applied to the probe, the cantilever bends and the reﬂected light beam moves through a certain angle. pﬃﬃﬃﬃﬃ The resolution of the optical lever technique is roughly 1013 Dw= Dt (Dw pixel width at the photosensor, Dt the time for measuring a pixel of the force curve). With, typically, Dt ¼ 0.1 ms the height-position resolution is 0.01 nm. But, in practice, the position sensitivity is often limited by thermal cantilever vibrations, which are p ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 4 kB T=3 kC (kB Boltzmann constant, T temperature and kC spring constant of the cantilever). With typical spring constants between 0.01–1 N m1 the amplitude of thermal noise is 0.7–0.07 nm at room temperature. The primary result of AFM measurements is a plot of the deﬂection of the cantilever DaC versus the height position of the sample, Dap. A cycle in the force

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Fig. 6.22 Force-separation-curve at AFM-testing.

measurement starts at a large tip–surface separation. At large distances no force acts between tip and sample; the cantilever is not deﬂected. In the scheme of Fig. 6.22 it was assumed that at smaller distances a repulsive force acts between tip and sample. Hence, when the sample approaches the tip the cantilever bends upwards. Since tip and sample are not in contact, this region is often referred to as the non-contact region. At a certain point the tip often jumps onto the sample surface. This jump-in occurs when the gradient of attractive force exceeds the spring constant plus the gradient of repulsive forces. Further sample movement generates a deﬂection of the cantilever by the same amount as the deﬂection of the sample. The nearly vertical force–separation curve represents this contact region, which includes contact loading. Then the sample is withdrawn at point U and moves to the detachment point A. Finally, its starting position is reached. During retraction the tip often sticks to the surface up to large distances due to adhesion. To obtain force–separation curves the original deﬂection-position curves have to be converted (Butt et al., 1995). Cantilevers for AFMs are usually V-shaped to increase their lateral stiffness. They are typically 100–200 mm long, each arm is about 20 mm wide and 0.5 mm thick. The spring constant of V-shaped cantilevers is often approximated by that of a rectangular bar of twice the width of each arm, for details see Butt et al. (1995). Friction forces as a function of normal forces can also be measured by AFM equipment (Schwarz et al., 1997; Carpick et al., 1996; Ecke and Butt, 2001; Jones, 2003). 6.3.5 Measurement of Particle Restitution Coefficient

Particles (raw materials, intermediate and ﬁnal products) are subjected to a lot of mechanical stressing during their processing sequence. During testing of the particles (compare with Section 5.5), stressing methods (impact) and their frequencies must be set equivalent to the conditions occurring in processing equipment such as dryers, conveyors, granulators or mixers. The restitution coefﬁcient is a very important material parameter to describe the particle dynamics in particle and particle–ﬂuid ﬂows. The restitution coefﬁcient is needed to describe the damping force and energy

6.3 Measurement of the Physical Properties of Particles

Fig. 6.23 Contact normal force versus (a) time and (b) displacement for different types of deformation behavior.

in numerical discrete modeling of particles, see for example Kruggel-Emden et al. (2006), and depends on many parameters, such as impact velocity, material behavior of impact bodies, their particle size, shape, roughness, moisture content, adhesion properties and process conditions, for example temperature. An impact between solid bodies (particle–particle or particle–wall) occurs in a very brief period of time. The impact period can be divided into two phases, compression and restitution. The contact force versus time and displacement during the impact between a soft spherical particle and a stiff wall by different types of deformation behavior is shown in Fig. 6.23. During the initial period of impact the contact partners are compressed and their kinetic energy is transformed into internal energy of deformation, friction and adhesion. The reaction force deforms the particle contact, which leads to the contact displacement or overlap as response. With increasing indentation the contact force increases and the relative velocity of contact partners decreases. If the deformation is rate-independent (elastic and plastic behavior), the maximum indentation and maximum contact force occur when the normal component of relative velocity vanishes (Stronge, 2000). The elastic part of the impact energy absorbed during the compression is released during restitution and leads to the elastic force that separates the contact partners during the restitution phase of impact. The dissipation of the kinetic energy of the partners during the impact can be described by the restitution coefﬁcient. The coefﬁcient of restitution is a ratio of impulse during the restitution phase of impact (tC t tR) to that during the compression phase (0 t tC) ÐtR e¼

tC ÐtC 0

Fdt Fdt

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ E kin;R E diss vR ¼ ¼ ¼ 1 E kin E kin v

ð6:59Þ

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Moreover, the impulse ratio in Eq. 6.59 gives the square root of the ratio of elastic strain energy Ekin,R released during the restitution to the impact energy that is initial kinetic energy Ekin. Both contributions of impact energy can be obtained from the force–displacement curve, Fig. 6.23b. Hence, the restitution coefﬁcient is the square root of the ratio of the area below the curve during unloading (restitution) to that during loading (compression). In the case of elastic impact the impact energy absorbed during compression is fully restored during the rebound and so the relative velocity of contact partners before impact is equal to that after the impact, e ¼ 1 in Eq. 6.59 (Hagedorn, 1995). In the case of full dissipation of initial kinetic energy due to plastic deformation, adhesion, friction in the contact as well as propagation of the stress waves, the impact bodies are not separated after the unloading (restitution), e ¼ 0 in Eq. 6.59. The force–displacement curve of perfectly plastic contact partners does not show elastic restitution as illustrated in Fig. 6.23b. For elastic–plastic behavior during the impact, the restitution coefﬁcient is in the range 0 < e < 1, see examples in Hunter (1957); Goldsmith (1960); Walton and Braun (1986); Foerster et al. (1994); Hagedorn (1995); Labous et al. (1997); Lorenz et al. (1997); Iveson and Litster (1998); Huang et al. (1998); Stronge (2000); Kharaz et al. (2001); Louge and Adams (2002); Fu et al. (2004); Coaplen et al. (2004); Chandramohan and Powell (2005); Stevens and Hrenya (2005); Seifried et al. (2005); Weir and Tallon (2005); Dong and Moys (2006); Antonyuk (2006); Kantak and Davis (2006); Mangwandi et al. (2007). Different types of equipment have been developed to measure the restitution coefﬁcient. These can be divided into free-fall, particle–particle and pendulum tests. The typical experimental set-up for the free-fall experiments used by many authors, for example Goldsmith (1960); Walton and Braun (1986); Kharaz et al. (2001); Louge and Adams (2002); Fu et al. (2004); Dong and Moys (2006); Antonyuk (2006); Mangwandi et al. (2007), is shown in Fig. 6.24. Before the fall, a particle is held at a height h from the target with the help of vacuum tweezers. The particle falls freely onto a target and reaches a rebound height hR after the impact. The movement of the particle near the contact point, before and after the impact, is recorded by a high-speed video camera. From video analysis the impact and rebound velocities of the particle can be obtained to calculate the restitution coefﬁcient. From the ratio of energies in Eq. 6.59, it follows that the coefﬁcient of restitution is a ratio of rebound relative velocity vR (by t ¼ tR) to that before impact v (by t ¼ 0). Two different types of impact, that is normal and oblique, are described by normal and tangential restitution coefﬁcients. The vectors of the velocity before and after the impact can be decomposed into normal vN and tangential vT components as shown in Fig. 6.24. The ratio of the normal component before and after the impact determines the normal restitution coefﬁcient: pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð6:60Þ eN ¼ v N;R =vN ¼ hR =h Similarly, the tangential restitution coefﬁcient is obtained by: eT ¼ v T;R =v T

ð6:61Þ

6.3 Measurement of the Physical Properties of Particles

Fig. 6.24 The principle of a free-fall device.

To describe the oblique impact the measurements are carried out at different angles of incidence (u in Fig. 6.24) in the range 0 to 90 . Additional information about the impact behavior can be obtained from the measured angle uR and the angular speed of rotation vR created during rebound (Kharaz et al., 2001; Dong and Moys, 2006). Neglecting the ﬂuid drag force acting upon the particle during free fall and rebound, the normal coefﬁcient of restitution can also be determined as a ratio of heights after and before impact, Eq. 6.60. In this case, only the rebound height of the particle hR needs to be measured during the fall experiments. In several publications (Goldsmith, 1960; Walton and Braun, 1986; Kharaz et al., 2001; Louge and Adams, 2002; Fu et al., 2004) the restitution coefﬁcient was measured without any initial spin of particles. In fact, the vacuum nozzle prevents initial rotation. To release the particle with a predeﬁned initial spin, the particle can be wrapped with a strip of paper that unwraps during the fall under gravity (Dong and Moys, 2006). The angular velocity of the particle can be varied using strips with different unwrapping length. A disadvantage of this method is the possible slip of the particle during the unwrapping. In many cases, the same material is chosen for the target of fall experiments as the material of the walls of the apparatus that is going to be used in the investigated process. However, some authors have investigated the impact of particles on targets covered with a speciﬁc layer. The knowledge of respective impact characteristics is necessary for the description of particle-collisions in the presence of solid or liquid layers that occur in some processes such as wet comminution, ﬂuidized bed spray granulation, ﬁltration and so on. Kantak and Davis (2006) performed impact tests of steel and Teﬂon balls with wet or dry porous layers placed on the quartz wall. In the

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work of Huang et al. (1998) the inﬂuence of milling conditions, including impact velocity, ball size and powder thickness was studied by fall tests. During these experiments a steel ball fell onto steel powder particles located in a shallow recess in the hardened steel plate. The elastic stress waves arising in the contact area can have signiﬁcant effects on the restitution coefﬁcient. At the beginning of contact deformation, the spherical elastic wave expands away from the contact region into the target. After reﬂection from the target borders, the wave comes back towards the contact area. If the contact time is longer than the period of wave propagation in the wall, then the wave front will reach the contact partners and lead to loss of kinetic energy, which was ﬁrst calculated by Hunter (1957). Thus, the thickness of the wall to be used must be sufﬁciently large to exclude the energy dissipation due to reﬂected elastic waves, according to the condition d>

vl tR 2

ð6:62Þ

The speed vl of the longitudinal wave propagating through the target (wall) can be calculated from the modulus of elasticity E, Poissons ratio u and the density r of the target (Landau and Lifschitz, 2001): v1 ¼

12 E ð1uÞ r ð1uÞ ð12uÞ

ð6:63Þ

The duration of the impact tR in Eq. 6.62 can be estimated using Hertzs theory of elastic impact: "

tR;el

m2 ð1u2 Þ2 ¼ 2:87 v r E2

#15 ð6:64Þ

where m is the mass and r the radius of the particle. For particle–particle impact experiments, in contrast to the above category of devices, two particles are brought to collision with each other without any rigid tool involved (Foerster et al., 1994; Labous et al., 1997; Lorenz et al., 1997; Chandramohan and Powell, 2005). This type of stressing occurs in ﬂuidized bed granulation and comminution. The experimental device consists of two vacuum tweezers that are placed on top of each other to release the particles. The top particle is dropped ﬁrst and reaches, in a deﬁnite time, the bottom particle, which is released second. After the release of the top particle, the bottom vacuum nozzle must be quickly taken out of the way of the top particle. A high-speed camera records the collision. To achieve a central impact, the release mechanisms of these devices must be accurately centered. Pendulum-based experiments are also performed to measure the restitution coefﬁcient of particle–wall, particle–particle and particle–beam impacts. The pendulum experiments are shown schematically in Fig. 6.25. The two particles are attached with ﬁne wires to a horizontal overhead plate at a certain distance from each other. During the experiment the particles are simultaneously released and collide in the

6.3 Measurement of the Physical Properties of Particles

Fig. 6.25 A schematic of pendulum experiments.

normal direction. The relative impact velocity can be calculated from the distance between the overhead plane and the impact point. The velocity of the particles after the impact can be calculated by measuring the time between two points on the path of the particles using high-speed video recording or photodiodes (Iveson and Litster, 1998; Coaplen et al., 2004; Stevens and Hrenya, 2005; Weir and Tallon, 2005; Seifried et al., 2005). The coefﬁcient of restitution can decrease with increasing impact velocity, as was shown in many experimental studies (Goldsmith, 1960; Kharaz et al., 2001; Fu et al., 2004; Stevens and Hrenya, 2005; Kantak and Davis, 2006; Mangwandi et al., 2007). If the behavior of the particles during impact is not viscous or if the impact force value is below the yield point, the restitution coefﬁcient can be constant. This behavior is illustrated in Fig. 6.26 for some granules examined by Antonyuk (2006). It is evident that all three granules produce an elastic–plastic impact. The increase in the impact velocity in the examined range did not change the coefﬁcient of restitution. As revealed by repeated compression tests of these granules, the loading force level does not affect the ratio of plastic strain energy to the elastic strain energy.

Fig. 6.26 Normal restitution coefficient of different granules versus impact velocity.

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Fig. 6.27 Coefficient of restitution of cylindrical tungsten carbide impacted on a PVC target versus the carbide temperature for four different impact velocities (Pouyet and Lataillade, 1975).

Under the assumption that the force–displacement behavior during slow stressing is approximately the same as during dynamic stressing, this fact can give a rational explanation for the constant restitution coefﬁcient. An increase in material temperature can change the contact behavior of particles from predominantly elastic to elastic–plastic or viscoplastic. In this case the restitution coefﬁcient is decreased. The results of impact tests between carbide and PVC at different temperatures are shown in Fig. 6.27. For a given impact velocity the decrease of the restitution coefﬁcient with temperature is relatively small from 20 to 70 C (in the glassy state) while a severe decrease can be observed at a temperature of approximately 70 C and above, as PVC begins to behave as a viscoplastic material (Pouyet and Lataillade, 1975). 6.3.6 Particle Abrasion and Breakage Tests 6.3.6.1 Survey of Test Methods and Principles During production, transportation and handling particles are mechanically stressed due to particle–particle and particle–apparatus wall impacts (Fig. 6.28). These can lead to the breakage and attrition of particles. Attrition is deﬁned here as the partial breakage of particles resulting in the formation of ﬁne fragments due to friction or low normal forces. Repeated interparticle and particle–wall interactions lead to breakage of sharp edges, roughness and defects on the surface of the particles. Attrition tests in ﬂuidized beds (see Section 5.4) show that the surface of the particles becomes smoother (Fig. 6.29). The formed fragments are much smaller than the initial particles. The mass and size of the fragments depend on the intensity (stress level, velocity, conﬁguration of impact partners) and the frequency of the impact events (Pouyet and Lataillade, 1975; Joost and Schwedes, 1996; Rangelova, 2002; D€ uck et al., 2003; Seifried et al., 2005). The particle size and morphology (shape and texture) also have signiﬁcant effects on the

6.3 Measurement of the Physical Properties of Particles

Fig. 6.28 Typical stressing of particles during (a) rotation in a drying drum; (b) granulation in fluidized bed; (c) transportation and (d) discharge.

amount of ﬁnes, since these factors determine the coordination number (mean number of contact points) and so the force transfer between colliding partners. High normal forces during compression or impact loading lead to breakage when the particle is crushed into several big fragments. Factors affecting the breakage mechanism are intensity and frequency as well as material behavior and the microstructure of the particles. The basis of breakage phenomena has been studied using spherical particles, see for example Rumpf (1965); Sch€ onert (1966); Kiss (1979); Beekman et al. (2003); Sheng et al. (2004); Samimi et al. (2005); Antonyuk et al. (2006). In general, particulate products should not form dust and fragments during transportation, storage and handling. For example, particle attrition and breakage during spray granulation in a ﬂuidized bed affect granule growth, nucleus formation and, therefore, residence time distribution and product quality. The strength of

Fig. 6.29 SEM of surface of sodium benzoate granule (a) before and (b) after abrasion test in the fluidized bed: 1 – visible roughness, 2 – defects (Heinrich and M€ orl, 1999).

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particles deﬁnes the maximal stress conditions to which they can be subjected without damage. On the other hand, the particles should be soft enough in order to retain their solvability, dispersibility, moisturizing properties and to avoid complications during further processing. For example in the production of high performance ceramics, powders that have been granulated ﬁrst so that they do not break during transport, may fail during further press agglomeration (Agniel, 1992). In order to optimize production processes and minimize the product quality losses during transportation and handling, the mechanical behavior and breakage mechanisms of particles are investigated by different testing methods (Fig. 6.30, see also Section 5.5). The necessary method is chosen depending on the stressing conditions of particles in the investigated industrial process and the probable failure mechanisms, that is attrition or breakage.

Fig. 6.30 Testing methods for investigation of deformation and breakage behavior of particles according to Antonyuk (2006).

6.3 Measurement of the Physical Properties of Particles

All testing methods can be categorized into two groups: stressing of particles in a bed (Fig. 6.30a–f ) and single particle tests (Fig. 6.30g–n). The behavior of particles in the bed regarding their attrition resistance, compression and impact strengths is studied using the stressing in rotating drums, ﬂuidized beds, shear and press cells, vibration chamber and air gun. The rotating drum is a standard device for measurement of particle attrition in the chemical and pharmaceutical industries (Grant and Kalman, 2001). In this test, the particle size distribution of the examined sample is analyzed after a predeﬁned time of rotation and compared with an initial distribution to obtain the attrition mass fraction. The rotation speed, duration of operation, weight and temperature of the sample can be varied. The behavior of a single particle can be tested by compression, tension, bending and impact tests (Fig. 6.30g–n). With these experiments the inﬂuence of single particle properties such as size, porosity and roughness on the mean behavior in the bed can be determined. One of the most important tests, the simple uniaxial compression of a single particle, will be introduced in the following section. 6.3.6.2 Compression Test The compression test of a single particle up to the point of primary breakage determines the minimum energy requirement for the breakage, as shown ﬁrst by Carey and Bosanquet (1933). The losses of stressing energy are much higher in particle bed crushing than in compression of a single particle, because of friction and plastic deformation of the particles at the contacts. Due to the comparatively low deformation rate (from mm min1 to cm min1) the secondary breakages that take place after the primary breakage can be separately observed in the compression test. In a pioneering publication of Rumpf (1965) the deformation and breakage behavior of solid particles was described by force–displacement curves measured by compression tests. In recent works, various granules have been investigated using the compression test, namely: Al2O3 produced by ﬂuidized bed-spray granulation (Agniel, 1992), enzyme (Beekman et al., 2003), polymer-bound Al2O3 granules (Sheng et al., 2004), detergents (Samimi et al., 2005), calcium carbonate (Mangwandi et al., 2007). The principle of the uniaxial compression test is shown in Fig. 6.31. During the movement of the punch towards the ﬁxed upper plate, a contact between the particle and the ﬁxed plate is created. During the stressing period, displacement and force values are measured. Compression tests are carried out either with strain control (constant stressing velocities) or stress control (ﬁxed stress or load rate). Force–Displacement Behavior The typical force–displacement curve of a spherical zeolite granule with elastic–plastic properties is presented in Fig. 6.32 (Antonyuk et al., 2005). At the beginning of punch–particle contact the micro-asperities on the particle surface are deformed due to micro-plastic yielding. On further stressing, elastic contact deformation of the granule takes place. The contact force FN,el in the normal

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Fig. 6.31 Principle of single particle compression test (Antonyuk et al., 2005).

direction during the elastic deformation s of the granule with diameter d compressed between two walls can be described by the Hertz contact theory (Hertz, 1882) as 1 pﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð6:65Þ F N;el ¼ E d s3 6

Fig. 6.32 Typical force-displacement curve for a zeolite 13X granule (d ¼ 1.2 mm) during compression test at the stressing velocity of 0.02 mm s1.

6.3 Measurement of the Physical Properties of Particles

The effective modulus of elasticity E of both granule (without index) and punch (index w) is given by: 1 1u2 1u2w þ E ¼2 ð6:66Þ E Ew where u and uw are the Poisson ratios of the granule and the punch (wall). The contact stiffness measured by the compression test can be evaluated from part II of the curve in Fig. 6.32. Due to the parabolic curvature of the function FN,el(s), the contact stiffness in the normal direction increases with increasing deformation and particle diameter: 2 2 1 kN dF N;el 1 pﬃﬃﬃﬃﬃﬃﬃ ð6:67Þ kel ¼ þ ¼ ¼ E ds 2 ds k kw 4 Based on Eqs. 6.66 and 6.67, Youngs modulus and the stiffness of the particle during elastic deformation can be obtained. For the case of zeolite 13X granules it is: E ¼ 2.3 GPa, kN ¼ 295 N mm1 (at the yield point F that marks the beginning of plastic deformation). When the yield point F in Fig. 6.32 is reached, plastic deformation begins. This is conﬁrmed by the increasing deviation of the experimental curve F–B from the theoretical Hertz curve. The breakage of the particle follows at point B, then the multiple stressing leads to failure of the fragments. Cyclic Stressing Tests Because of fatigue of particles during cyclic loading, their breakage can occur at stress levels that are substantially lower than the failure stress during static loading. The reduction of fracture strength occurs because of the formation and propagation of shear zones and micro-cracks during each cycle. This effect can be described with the W€ohler curve (Riehle and Simmchen, 2002). Investigations of solid particles and agglomerates demonstrate the considerable effect of repeated loading on the breakage point. Tavares and King (2002) described a decreasing elastic–plastic stiffness of solids during repeated impact and explained the breakage behavior by the formation and propagation of damages. On the contrary, the stiffness of spherical granules was found to increase with increasing number of loading/unloading compression cycles as long as the saturation of the plastic deformation is not reached (Antonyuk, 2006). The intensity and the frequency of stressing, the particle size and the microstructure have an inﬂuence on the resistance of the material against the cyclic loading. Beekman et al. (2003); Pitchumani et al. (2004) have also conﬁrmed this effect for granules. During a repeated compression test, the punch moves towards the upper plate and presses the particle up to a deﬁned force. Then, the punch moves downwards, thus the unloading of the particle takes place. A typical force–displacement diagram for the repeated compression of zeolite granule (Antonyuk, 2006) is shown in Fig. 6.33. During the measurement, a zeolite granule was repeatedly loaded and unloaded with a velocity of 0.02 mm s1 up to the force Fcyc 0.7FB, which is called the stressing amplitude. At this load a large displacement due to plastic deformation (O–E1 in Figure 6.33) is observed. The area between unloading (U1–E1) and reloading curves

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Fig. 6.33 Typical loading-unloading force–displacement curves for compression of a zeolite 13X granule (d ¼ 1.7 mm, Fcyc ¼ 7 N).

(E1–U2) characterizes the energy dissipation or the damping behavior of the particle during one compression cycle. This inelastic deformation work is reduced with each cycle. During the ﬁrst cycle, the maximum plastic deformation and the highest breakage limit can be observed. The number of cycles to breakage depends on the stressing intensity and material properties. The cyclic stiffening or hardening generates changes in the structure of the material at the contact points, where the internal stresses are very high. Material density and contact stiffness are increased. With the increase in cycle number, microcracks propagate inside the specimen. The granule stores cyclic loading energy during every elastic–plastic deformation, so that fatigue develops and a lower breakage force than for single loading is obtained. The fracture stress (ﬁrst breakage point) is not constant for a given size of granule. The mechanical characteristics of the primary particles and the bonding agents are randomly distributed within the granule volume. The porosity and shape of the particles and the orientation and size distribution of defects have a large effect on the breakage behavior. The pores can be regarded as crack-release zones. The pores and structural defects in granulated particles are similar to imperfections, inhomogeneities or micro-cracks in compact solid materials. The highest local tensile stress is generated at these defective zones in the granules, so that the fracture starts from these zones. Breakage Probability The probability that a particle will fracture depends on the applied stressing intensity and frequency, material properties and particle size. May (1975); Klotz and Schubert (1982) describe fragment size distribution and

6.3 Measurement of the Physical Properties of Particles

Fig. 6.34 Breakage probability P for zeolite 13X granules of different size versus mass-related breakage energy Wm.

breakage probability for glass particles, clay pellets and cement clinkers by three and four parametric log-normal distributions; they also calculate the speciﬁc surface of fragments. During compression-shear tests of various materials, Hess (1980) observed a reduction of breakage force and energy because of the additional shear stress. Kerber (1984) showed that there is a strong inﬂuence of shape and roughness of the stressing tools on the mass-related breakage energy for gypsum, limestone and quartz bulk materials. Traditionally, the breakage probability is measured versus the mass-related breakage energy, which can be obtained from the area below the force–displacement curve up to the primary breakage point B in Fig. 6.32. The results for zeolite 13X granules are shown in Fig. 6.34. For increasing particle size the curve is shifted to the left. That means, to initiate the fracture at the same probability level a higher mass-related energy is required for smaller granules than for larger granules. An overview of models to describe the breakage probability of granules and to calculate functions such as those of Fig. 6.34 can be found in Antonyuk (2006). 6.3.6.3 Impact Test Different experimental equipment has been developed to conduct single particle impact tests. Based on the impact geometry, this equipment can be categorized into three groups:

1. Particle–wall impact; 2. double impact between two rigid plates; 3. particle–particle impact. In air guns, particles are accelerated in a long tube towards a target by means of air pressure. This type of device enables one to realize single particle–wall impacts at different velocities, impact angles and target materials. The test conditions can be set equivalent to the stressing conditions of particles during pneumatic conveying, drying or mixing. Therefore, important information about the breakage processes during

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impacts with, for example bends of a pneumatic conveyor or ﬂash dryer tube, can be obtained by this testing method. Air guns have been used for impact experiments with single particles and agglomerates – press agglomerates of cement matrix and quartz particles, brown coal, concrete ball, alumina, glass, polystyrene, wood, carbide, calcium carbonates powder, acrylic resin and polymethyl methacrylates (Tschorbadjiski, 1969; Kiss, 1979; Tomas et al., 1999; Salman et al., 2002, 2004; Chaudhri, 2004). During the double plate stressing experiment, a particle is loaded between two rigid plates. The impact velocity can be adjusted, and the impact force and deformation can be measured in these devices. This type of equipment has been used to study the breakage behavior of quartz, apatite, limestone, cement clinker, marble, acrylic resin, polymethyl methacrylate, plaster spheres, concrete ball and sodium benzoate granules (Tavares and King, 2002; Chaudhri, 2004; Pitchumani et al., 2004; Wu et al., 2004; Khanal, 2005; Antonyuk et al., 2006). In contrast to the above two categories of devices, two particles are mutually stressed without use of any rigid tool in particle–particle impact tests (Labous et al., 1997; Weir and Tallon, 2005). This type of stressing occurs in ﬂuidized bed granulation and comminution. A typical device for particle–wall impact tests is shown in Fig. 6.35 (Antonyuk et al., 2006). The particles are fed with the help of a vibrating feeder (1) into the hopper of the injector (2). The vibrating feeder is installed in a sealed chamber, connected to the feed hopper of the injector, in order to avoid false air entrainment from the environment and reverse ﬂow from the injector.

Fig. 6.35 Impact test rig according to Antonyuk et al. (2006).

6.3 Measurement of the Physical Properties of Particles

The particles are further fed into an air stream of deﬁned velocity in the acceleration tube (3). Air pressure is generated in the compressed air tank (5) by means of a compressor (4). The control valve (6) is installed between two nozzles, which are connected by means of two check valves, so that air velocity in the acceleration tube can be adjusted. The air velocity can be measured at the attached Pitot tube (7). The particles collide horizontally with a hardened steel target (8) in the impact chamber (9). After the impact, fragments and unbroken particles fall into a ﬁlter (12). The velocity of this fall is increased by means of two aspirators (13) placed in parallel at the outlet of the test rig. The removal of the fragments from the impact chamber in vertical directions at high velocity helps to avoid additional impacts of the particles with internal walls and other fragments. The particle size distribution of the fragments is measured on-line with a laser diffraction spectrometer (11) before entering the ﬁlter. Video recording can be performed through the glass window of the impact chamber by means of a high-speed digital video camera (10). For example, the images from the high-speed video recording in Fig. 6.36 show the impact breakage of three different granules: g-Al2O3, zeolite 13X and sodium benzoate at an impact velocity of 23 m s1 (Antonyuk, 2006). The g-Al2O3 granules behave in an elastic–brittle way during impacts. The granule is separated into several meridian fragments due to meridian cracks. The zeolite and sodium benzoate deform plastically during the contact. At high granule velocity, secondary cracks are formed in a direction perpendicular to the direction of impact. Many ﬁne particles are produced during crack propagation and crack branching. Because of the various mechanical properties of the particles, their microstructures and different stressing conditions, the deformation and breakage behavior of

Fig. 6.36 Images from high-speed video recording of the impact of granules at 23 m s1 (13 600 frames per second): (a) g-Al2O3; (b) zeolite 13X; (c) sodium benzoate.

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solid particles and granules during impact and compression is still not completely understood, but is an area of continuing research.

6.4 Testing of Particle Bed Properties

In particle processing and product handling, the well-known ﬂow problems of dry cohesive powders in process apparatuses or storage and transportation containers include bridging, channeling, widely spread residence time distribution associated with time consolidation or caking effects, chemical conversions and deterioration of bioparticles. Avalanching effects and oscillating mass ﬂow rates in conveyors lead to feeding and dosing problems. Finally, insufﬁcient apparatus and system reliability of powder processing plants are also related to these ﬂow problems of particle beds. Thus, it is essential to understand the fundamentals of particle adhesion with respect to product quality assessment and process performance in particle technology. Generally, compressible and cohesive powders are considered here. However, only the non-rapid frictional ﬂow with shear rates vS << 1 m s1 and, consequently, a small shear stress contribution of t << rb.vS2 1 kPa is described. The shear stress contribution by particle–particle collisions or a turbulent-equivalent momentum transfer is negligible. Thus, the shear resistance of a cohesive powder is dominated by Coulomb friction between the adhering particles. In terms of ﬂuid dynamics, this frictional powder ﬂow is characterized by the independence of shear rate. 6.4.1 Bulk Density and Tapping Density

In contrast to liquids, particle beds such as powders and bulk solids are more or less compressible, like gases. Thus, the density of bulk solids depends strongly on the effect of external forces in the form of stresses, impacts or vibrations. Therefore, one can distinguish between different types of bulk density depending on the strains occurring during the corresponding process. The density is measured using a vessel of known total volume, V, by weighing the solid mass, ms, that exactly ﬁlls this vessel: rb ¼

ms V

ð6:68Þ

The vessel is provided with a cap in order to be able to ﬁll in a larger volume ﬁrst, which will then be reduced accurately with a stripper to the real measuring volume after removal of the cap. For the determination of the bulk density, rb,0, of a loosely packed bulk solid the vessel is ﬁlled as carefully as possible without any preconsolidation. A shear cell can also be used as the reference vessel. To measure the tapping density, rb,t, the loosely ﬁlled measuring tank with the cap is placed on an eccentric driven desk and exposed to vertical drop impacts of low frequency (DIN-EN ISO 787-11, 1995). During this process the bulk solid will be compressed to the tapping density, which is also determined by weighing after

6.4 Testing of Particle Bed Properties

stripping. The degree of compression depends on the elasticity of the vessel and the height of fall (drop delay) as well as the number of drop impacts. 6.4.2 Angle of Repose of a Moving Particle Bed

Several empirical methods are commonly used to assess the ﬂow properties of freeﬂowing bulk solids or granular materials, for example to determine the angle of repose, wr (Fig. 6.37). However, these simple test methods result in different angles of repose. A conical heap, Fig. 6.37a, will yield a different angle of repose, wr, compared to a wedgeshaped heap. For a hopper that is discharged from a central outlet, Fig. 6.37b, the angle of repose is higher, but in a rotating drum still another (smaller) angle of repose will prevail. To measure the angle of repose correctly, the DIN ISO 4324 (1983) should be used. The determination of the angle of repose of a bulk solid takes place by outﬂow of a given bulk volume through a hopper with a certain geometry on an even plate at a given gap between the hopper and the plate. The discussed methods can be applied with acceptable scattering and errors only for cohesionless and free-ﬂowing bulk solids. 6.4.3 Flow Behavior of Cohesive and Compressible Bulk Solids

A bulk solid represents either an inactive and stable or an unstable and moving (ﬂowing) particle packing whose pores are ﬁlled with gas and/or liquid. Despite inhomogeneities, bulk solids can be treated as a continuum over a length scale of D > 25 d (Tomas, 1983). A ﬂuidized bulk solid behaves like a Newtonian liquid (like a dilute suspension). With an increase in the bulk density, the bulk solid behaves more and more like an elastic–plastic frictional material. After time consolidation, a comparatively rigid solid state of the powder bed is often obtained (Tomas and

Fig. 6.37 Methods to measure the angle of repose for free-flowing bulk solids.

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Tab. 6.1 Survey of different frictional failure limits (yield loci) in powder mechanics.

Yield locus

Characteristic friction angle

Process

yield locus, t ¼ 0 time yield locus, t > 0 stationary yield locus effective yield locus wall yield locus

angle of internal friction ji angle of internal friction jit stationary angle of internal friction jst effective angle of internal friction je wall friction angle jW

incipient ﬂow, internal friction ﬂow after a storage time cohesive steady-state ﬂow cohesionless steady-state ﬂow powder wall friction

Schubert, 1981, 1982; Tomas, 1983, 1991, 1997). However, a cohesive powder can also show compressibility like a gas (Tomas, 2004a, b; Grossmann et al., 2004; Grossmann and Tomas, 2006). To describe the stress states of the non-rapid frictional ﬂow of cohesive and compressible bulk solids a couple of different material characteristics are needed, Tab. 6.1. An essential problem in powder mechanics is to measure that stress state at which ﬂow (breakage or failure) of the bulk solid is initiated within a processing apparatus. Consequently, a ﬂow criterion should give a statement about the stress which leads to ﬂow connected with irreversible plastic deformation or to yield. This failure limit, called yield locus, cannot be crossed. The yield locus shows the dependence of the shear stress t on the normal stress s, whereby the slope of the yield locus line is a measure of the internal friction of the bulk solid. Table 6.1 gives an overview of different friction angles of the yield loci. In Fig. 6.38 the ﬂow characteristics of cohesive bulk solids are shown. The yield locus is characterized by its slope tanwi and the intersection with the t-axis, the so-called cohesion t c. It ends on the Mohr-circle of cohesionless steady-state ﬂow

Fig. 6.38 Flow characteristics of bulk solids on a phenomenological basis (Jenike, 1964).

6.4 Testing of Particle Bed Properties Tab. 6.2 Classification of powders according to Jenike (1964); Tomas (1991)

Flow function

Characteristic behavior

Examples

10< ffc 4< ffc <10 2< ffc <4 1< ffc <2 ffc <1

free ﬂowing easy ﬂowing cohesive very cohesive non-ﬂowing, hardened

dry sand moist sand dry cement moist powders aged cement

that is determined by the minor and major principle stresses s2 and s1. The position of the yield locus depends on the bulk density, rb, so that it is shifted upwards with increasing bulk density. This results in a family of yield loci (not shown in Fig. 6.38). To determine the strength properties of cohesive powders the uniaxial compressive strength sc is signiﬁcant; this applies to a powder that has been exposed to the major consolidation stress s1. The uniaxial compressive strength is the stress that leads to a failure or breakage of a bulk solid cylinder consolidated with the stress s1 by uniaxial pressure. This means that a powder can ﬂow more easily with a smaller sc at a given s1. To characterize the ﬂowability of cohesivepowders theratio of the major principle stress s1 to the uniaxial compressive strength sc is used. According to Jenike (1964) this ratio is denoted here by ﬂow function (in the sense of a dimensionless number), Tab. 6.2. ffc ¼

s1 sc

ð6:69Þ

A scheme to better understand the meaning of the ﬂow function is shown in Fig. 6.39. Free-ﬂowing powders have practically no uniaxial compressive strength (sc ¼ 0), so that the ﬂow function tends to inﬁnite. The category hardened is deﬁned by the fact that the major principle stress s1 is smaller than the uniaxial compressive strength sc.

Fig. 6.39 A scheme to explain the flow function ffc; (a) Generation of a bulk solid cylinder by applying the major principal stress s1, (b) measurement of the uniaxial compressive strength sc of the preconsolidated cylinder until failure.

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6.4.4 Flow Criteria of Preconsolidated Cohesive Powders on a Physical Basis

The microscopic failure conditions of particle contacts can be formulated using the elastic–plastic and frictional particle contact model (Tomas, 2000a, b, 2001a, b, 2004a, b, 2007a). Macroscopically, it is worth noting here that the stressing prehistory of a cohesive powder ﬂow is in most practical cases stationary (steady-state) and results signiﬁcantly in a cohesive stationary yield locus in the t–s diagram of Fig. 6.40, according to the equation t ¼ tanwst ðs þ s0 Þ:

ð6:70Þ

This steady-state ﬂow is characterized by a dynamic equilibrium of simultaneous contact shearing, unloading and failing, followed by the creation of new contacts, loading, reloading, unloading and shearing again. The isostatic tensile strength s0 ¼ (1 e0)/e0FH0/d2 of an unconsolidated powder without any particle contact deformation is microscopically referred to the adhesion force FH0 and to the initial porosity e0 of a very loose packing, see Section 6.4.1. The stationary angle of internal friction wst determines the slope of the stationary yield locus (SYL) for elastic–plastic frictional contacts and is related to the angle of internal friction wi for incipient contact failure (slope of yield locus) as (Tomas, 2001b): tanwst ¼ ð1 þ kÞ tanwi

ð6:71Þ

The dimensionless, elastic–plastic contact consolidation coefﬁcient k determines the slope of the adhesion force FH inﬂuenced by predominant plastic contact failure: k¼

kp P VdW ¼ kA kp Pf

1 2 3

þ

1 3

Apl AK

PPVdW f

:

Fig. 6.40 Yield characteristics of a cohesive powder in the t–s diagram on a physical basis. In general, the steady-state flow of a powder is cohesive. Hence, the total normal stress consists of an external contribution, s, plus (by absolute value) an internal contribution by the preconsolidation dependent isostatic tensile stress sZ, Eq. 6.77. The diagram ends with the consolidation locus and its isostatic pressure siso.

ð6:72Þ

6.4 Testing of Particle Bed Properties

Thus, the softer the particle contacts, the larger the differences between these friction angles and, consequently, the more cohesive is the macroscopic powder response after preconsolidation. For these poorly ﬂowing cohesive and compressible powders, Tomas (2000a, b, 2001a, 2003a, b, 2004a, b) has developed a constitutive equation to describe the linear increase in adhesion force FH for elastic–plastic contact deformation by the model stiff particles with soft contacts: FH ¼

kp kA F H0 þ F N ¼ ð1 þ kÞ F H0 þ k F N kA kp kA kp

ð6:73Þ

The adhesion force FH0 without additional consolidation (FN ¼ 0) can be approached as a single rigid sphere–sphere contact. However, if this particle contact is soft enough the contact is microscopically ﬂattened by an external normal force FN to a plate–plate contact. The elastic–plastic contact area coefﬁcient kA represents the ratio of plastic particle contact deformation area Apl to total contact deformation area AK ¼ Apl þ Ael and includes a certain elastic displacement (Tomas, 2000a, b): kA ¼

2 1 Apl þ 3 3 AK

ð6:74Þ

The solely elastic contact deformation Apl ¼ 0, kA ¼ 2/3, has only minor relevance for cohesive powders in loading, but for the completely plastic contact deformation (Apl ¼ AK) the coefﬁcient kA ¼ 1 is obtained. For the plate–plate model of the ﬂattened contact, the plastic repulsion coefﬁcient kp describes a dimensionless ratio kp ¼

CH;sls P VdW 4 ssls ¼ ¼ : 3 Pf 6 p a0 P f a0 P f

ð6:75Þ

of the attractive van der Waals pressure PVdW ¼

C H;sls 4 ssls ¼ a0 6 p a30

ð6:76Þ

to a constant repulsive particle micro-hardness Pf (or micro-yield strength) as response. The surface tension solid–liquid–solid amounts to ssls 0.25–50 mJ m2 and, consequently, PVdW 3–600 MPa. For rigid (ideally hard) contact this plastic repulsion coefﬁcient is inﬁnitely small, that is kp 0 and for a soft or compliant contact kp ! 1. The Hamaker constant (Hamaker, 1937) CH,sls ¼ (0.2–40) 1020 J for solid–liquid–solid interaction (subscript sls) according to the continuum theory of Lifshitz (1955, 1956) is related to continuous media and depends on their permittivities (dielectric constants) and refractive indices, for details see Krupp (1967); Israelachvili and Tabor (1973) or Israelachvili (1992). The characteristic adhesion separation for the direct contact of spheres is of a molecular scale (atomic center-to-center distance) and can be estimated for the total force equilibrium F ¼ dU/da ¼ 0 of molecular attraction and repulsion potentials. This separation of the interaction potential minimum amounts to about a0 ¼ 0.3–0.4 nm. With respect to large speciﬁc surfaces of ultraﬁne particles, this separation a0 depends on the properties of liquid-equivalent packed adsorbed water layers (Tomas, 2007a).

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The linear yield locus, Fig. 6.40, is obtained from resolution of a general square function and Taylor expansion series (Tomas, 2001b, 2004b) to sR;st sM;st ð6:77Þ t ¼ tanwi ðs þ sz Þ ¼ tanwi s þ sinwi and is quite simple to use (sM,st, sR,st: center and radius stresses of cohesive steadystate ﬂow, respectively). Using the mentioned radius and center stresses, the essential ﬂow parameters can be calculated as one set of linear constitutive equations (Tomas, 2004a, b). They describe for instantaneous consolidation the so-called consolidation locus (CL) sR ¼ sinwi ðsM sM;st Þ þ sR;st ;

ð6:78Þ

for incipient yield the yield locus (YL) sR ¼ sinwi ðsM sM;st Þ þ sR;st ;

ð6:79Þ

and for the cohesive steady-state ﬂow the stationary yield locus (SYL) sR;st ¼ sinwst ðsM;st s0 Þ

ð6:80Þ

The consolidation locus and the instantaneous yield locus describe the limits of incipient plastic deformation during consolidation and ﬂow. The stationary yield locus is the envelope of all stress states (Mohr circles) for steady-state ﬂow with a certain negative intersection of the abscissa s0. From the cohesionless steady-state ﬂow, that is s0 0, the effective yield locus can be obtained (Tomas, 2004a, b), see Fig. 6.38. The effective angle of internal friction is the slope of the effective yield locus. This depends on the average pressure sM,st: s0 ð6:81Þ sinwe ¼ sinwst 1 þ sM;st With the derivation of the linear yield locus, Eq. 6.77 and Fig. 6.40, the uniaxial compressive strength or unconﬁned yield stress, sc, results in a linear function of the major principal stress, s1, for details see Tomas (2004a, b), Fig. 6.41: sc ¼

2 ðsinwst sinwi Þ 2 sinwst ð1 þ sinwi Þ s1 ¼ s0 ð1 þ sinwst Þ ð1sinwi Þ ð1 þ sinwst Þ ð1sinwi Þ

ð6:82Þ

Equivalent to this linear function of the major principal stress, s1, the absolute value of the uniaxial tensile strength, sZ,1, also results in a linear function of the major principal stress, s1: sZ;1 ¼

2 ðsinwst sinwi Þ 2 sinwst s1 þ s0 ð1 þ sinwst Þ ð1 þ sinwi Þ 1 þ sinwst

ð6:83Þ

Again, it should be noted that both sc and sZ,1 depend on the preconsolidation level of the shear zone which is expressed by the consolidation stress, s1, applied during steady-state ﬂow. After one day of storage under this major principal stress, s1, a considerable time consolidation occurs, as shown in Fig. 6.41. Equivalent linear functions can be used to describe these very problematic time consolidation effects in powder processing and handling (Tomas, 1991, 1997, 2000a, 2001b, 2003a).

6.4 Testing of Particle Bed Properties

Fig. 6.41 Straight line regressions for the constitutive consolidation functions of limestone powder, d50 ¼ 1.2 mm, surface moisture X ¼ 0.5% (by Karl Fischer titration). Additional flow properties are the averaged angle of internal friction wi ¼ 37 , the stationary angle of internal friction wst ¼ 43 and the isostatic tensile strength of the unconsolidated powder s0 ¼ 0.62 kPa. The subscript 1 in sZ,1 denotes uniaxial tensile strength.

In Fig. 6.41 the time dependence of the uniaxial compressive strength sc and the uniaxial tensile strength sZ,1 can be seen. Both sc and sZ,1 have higher values after a time consolidation of 24 h compared to the respective values without any time consolidation. 6.4.5 Translational Shear Cell according to Jenike

The most common device to determine the ﬂow behavior and ﬂow properties of cohesive bulk solids is the translational shear cell according to Jenike. In 1964 Jenike published his fundamental work on silo and bulk solids technology and introduced a translational shear tester. This tester was the ﬁrst one designed for the purposes of powder technology (e.g. measurement at small stresses s < 50 kPa).

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Fig. 6.42 Modern arrangement of the Jenike shear cell by pulling shear force.

The shear cell of the Jenike shear tester consists of a bottom ring (also called mold ring), an upper ring of the same diameter lying above the bottom ring, and a shear lid (Fig. 6.42). At the shear lid the normal force FN is centrally applied. The upper ring is displaced horizontally against the ﬁxed bottom ring by a motor driven stem. In a modern arrangement of the translational cell, the shear force FS is applied by pulling the stem instead of pushing (Jenike, 1964) to improve the homogeneity of the normal stress distribution within the cell (to avoid a bending moment of the lid). This shear force is recorded versus time or shear displacement. Due to the displacement of the upper ring and the shear lid against the bottom ring, the bulk solid incurs a shear deformation. The normal stress s and shear stress t acting in a horizontal plane between bottom and upper ring are determined by dividing the normal force FN and the shear force FS by the cross-sectional area of the shear cell A. To measure one point of a yield locus, the shear cell is loosely ﬁlled with a sample of the bulk solid. A manual preconsolidation (The Institution of Chemical Engineers, 1989) of the powder follows and afterwards the sample is presheared. Finally, the sample is sheared to failure, as explained in the previous paragraph. For the next point of the yield locus, a new bulk solid sample has to be prepared and sheared again. Although the Jenike shear tester is widely accepted, a disadvantage might be the time needed for one test (1–2 h per yield locus, depending on the powder and the skills of the operator). During this time the operator must be present. In addition, the manual preconsolidation of each material sample can be a source of measurement errors. Due to the limited shear displacement (maximum: twice the thickness of the wall of the upper ring), very elastic bulk solids can hardly be tested, because these powders need too much shear displacement to reach steady-state ﬂow. The Jenike shear tester in the laboratory of the present authors has been supplemented with a system to determine accurately the vertical movement of the shear lid, Fig. 6.43. Four laser sensors were mounted to measure the distance between shear lid and sensor position. From the vertical movement of the shear lid the dilatancy in the shear zone can be determined. The dilatancy reﬂects an expansion in the bulk volume and, consequently, a decrease in the bulk density in the shear zone during shear ﬂow. The vertical movement of the shear lid is measured by the single point optical triangulation method. This method uses a laser light source, a lens and a linear lightsensitive sensor. The light source (typically a laser or LED) illuminates a point on the object. An image of this light spot is then formed on the sensor surface. When the object is moved, the image moves along the sensor area. By measuring the location of

6.4 Testing of Particle Bed Properties

Fig. 6.43 (a) Laser distance measurement mounted at the Jenike shear tester (Mechanical Process Engineering Laboratory, Magdeburg); (b) principle of the single point optical triangulation method.

the light spot image, the distance of the object from the instrument can be determined, provided that the baseline length and the angles are known. In Magdeburg the sensor is a position sensitive detector (PSD). Such detectors are often chosen for devices measuring over a small range. They provide an analog output, which is ideal for use with pass–fail applications. 6.4.5.1 The Shear Testing Technique SSTT according to ICE The determination of the yield locus with a Jenike shear tester is standardized in the translational shear test according to SSTT (The Institution of Chemical Engineers: European Federation of Chemical Engineering, 1989). The technique involves three steps: preconsolidation, preshear and shear. With the ﬁrst two steps a reproducible initial state with a stress and strain history corresponding to the conditions of steadystate ﬂow is created. This means that ﬂow under a constant shear force is reached at a normal stress, spre, during the preshear, Fig. 6.45. Because of the limited shear displacement of the Jenike shear cell, this initial stress state can be reached only with a preconsolidation of the powder. The conditions of preconsolidation must be varied until a critical consolidation level is reached at about scrit ¼ 3 mm (Fig. 6.44a). At the beginning of the preshear, the bulk solid is deformed elastically (point A in Fig. 6.44b). This is also the beginning of frictional plastic deformation of the sheared powder. In the further process the sample is consolidated (point B in Fig. 6.44b) until a constant shear force value is reached. Here the stationary ﬂow starts. During this shearing a shear force–displacement curve corresponding to the behavior of an overconsolidated bulk solid can bee seen in Fig. 6.44b. Such a curve has a shear force maximum (point C). The material volume inside the shear zone expands (dilates) depending on the applied normal load and the shear velocity. Measurements with the translational shear cell according to Jenike provide during preshearing the maximal value of the shear stress t corresponding to the applied normal stress s, Fig. 6.45. Because of the unknown dimensions of the shear zone, the

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Fig. 6.44 (a) Possible shear force–displacement curves during preshear; (b) Shear force–displacement curves for preshear and shear.

deformation and the change in volume cannot be determined exactly. The bulk solid starts to ﬂow if the acting shear stress is sufﬁcient to destroy the interparticle adhesion force. Then, the yield limit is reached. The acting shear and normal stresses correspond to the maximum stresses that the bulk solid can endure. After the preshear, the procedure is continued with reduced normal load s in order to obtain one shear point. This is repeated at least two times for each of four different values of s with fresh samples. For cohesive powders, a shear force maximum can be obtained during the shear, Fig. 6.45a. For cohesionless powders the material sample starts to ﬂow stationary at a lower shear force level. One point of the yield locus results directly from the shear stress t and the normal stress during shear s, Fig. 6.45b. Several shear points are combined to a yield locus that can be approximated by a straight line in the stress range s ¼ (0.25–0.8) spre. By variation of the normal stress during preshear, spre, a family of yield loci is obtained with the parameters preshear stress spre, center stress during steady-state ﬂow sM,st, bulk density rb or porosity e.

Fig. 6.45 (a) Results of translational shear test and (b) evaluation of the yield locus. The shear displacement, s, is directly related to the recorded time, s ¼ vst, at a constant shear rate vs.

6.4 Testing of Particle Bed Properties

The discussed test method is used to calibrate the simulations of shear dynamics by the discrete element method (DEM) with physically realistic material data, Tykhoniuk et al. (2007). 6.4.6 Ring Shear Tester according to Schulze for Dry Powder

Ring shear testers (rotational shear testers) have been used in soil mechanics since the 1930s (Hvorslev, 1939). In the 1960s Walker designed a ring shear tester for bulk solids (Carr and Walker, 1967/68), where lower stresses than those used in soil mechanics are of interest. In the following decades different ring shear testers have been built and investigated (e.g. M€ unz, 1976; Gebhard, 1982). In 1992 a ring shear tester (type RST-01.01) was developed by Schulze (Schulze, 1994), followed by a computer-controlled version in 1997 (type RST-01.pc). With the control software yield loci, wall yield loci, time consolidation, and so on, can be measured automatically. The principle of the shear cell of a ring shear tester is shown in Fig. 6.46. The ring-shaped (annular) bottom of the shear cell contains the bulk solid sample. The (annular) lid is placed on top of the bulk solid specimen. The lid is ﬁxed at a crossbeam. A normal force FN is exerted on the crossbeam in the rotational axis of the shear cell and transmitted through the lid to the bulk solid specimen. Thus, a normal stress s is applied to the bulk solid sample. The counterbalance force FA also acts in the center of the crossbeam. FA is directed upwards and is created by counterweights. It counteracts the gravity forces of the lid, the hanger, and the crossbeam. To shear the bulk solid, the lid and the bottom ring of the shear cell must rotate relative to each other. This is accomplished by rotating the bottom ring in the

Fig. 6.46 Shear cell of a ring shear tester (here: Schulze ring shear tester type RST-01, Schulze (1994)).

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direction of the arrow v (v is the angular velocity), whereas the lid and the crossbeam are prevented from rotation by two tie-rods connected to the crossbeam. Each of the tie-rods is ﬁxed at a load beam, so that the forces, F1 and F2, acting in the tie rods can be measured. Both forces ensure that the lid is self-centered during the measurement, which is necessary for correct results. The bottom of the shear cell and the lower side of the lid are rough in order to prevent the bulk solid from sliding relative to these surfaces. Therefore, rotation of the bottom ring relative to the lid creates a shear deformation within the bulk solid. Through this shearing the bulk solid is deformed and, thus, a shear stress t prevails. The forces acting in the tie rods (F1 and F2) are directly proportional to the shear stress t acting in the bulk solid. The test procedure is quite similar to the test procedure recommended for the Jenike tester (preshear and shear, see Section 6.4.5). However, the test procedure for the ring shear tester is less time-consuming, easier to perform, and, hence, less inﬂuenced by the operator who accomplishes the test. This, in combination with the principle of the ring shear tester, results in a good reproducibility compared to other testers (Verlinden, 2000). With the ring shear tester a complete set of yield loci is usually measured with only one bulk solid sample. In order to measure another point of the yield locus with the same sample, after every shear period the normal stress is increased to the preshear stress spre (the normal stress applied during the ﬁrst preshear period), and the bulk solid is presheared again until steady-state ﬂow is reached. Thus, the bulk solid is again critically consolidated. Afterwards, the same sample can be sheared again under another normal stress s to obtain the next point of the yield limit in the s–t diagram. This succession of shear and preshear at spre continues until a sufﬁcient number of points of the yield limit are known. 6.4.7 Press Shear Cell according to Reichmann for Wet Filter Cake

The increasing amount of nanodisperse (d < 100 nm) to ultraﬁne (d < 10 mm) particles from sol–gel, crystallization or precipitation processes and the increasing amount of ﬁnest sludges in waste water treatment, mineral and chemical processing lead to problems in dewatering processes. The particulate solids of these suspensions form very compressible cakes with extremely low permeability in ﬁltration processes. However, the mechanical expression of as much liquid as possible out of compressible cakes can reduce the water content signiﬁcantly and, thus, minimize the energy demand of subsequent thermal drying. For applied pressures of DP ¼ 0.5 to 5 MPa the ﬁltrate-related speciﬁc energy consumption of mechanical dewatering amounts only to Wm,l ¼ DP/rl ¼ (0.5–5) kJ kg1. This is very favorable in comparison with the speciﬁc energy consumption of thermal drying, which follows in the processing sequence. On the other hand, the ﬂow and storage behavior of these ﬁnest particulate solids has a large inﬂuence on the reliability of handling and storing equipment. Cohesion, shear strength and uniaxial

6.4 Testing of Particle Bed Properties

Fig. 6.47 Flow of dilute and saturated solid–liquid dispersions, yield of wet and moist particle packings (Tomas and Reichmann, 2002).

compressive strength are important parameters for design purposes (Reichmann and Tomas, 2001). The mentioned nanoparticle dispersions are not easy to handle, because their ﬂow behavior is at the transition between concentrated particle suspension, paste rheology dominated by viscous ﬂow, and powder mechanics of compressed, liquid saturated particle packings. For the latter, contact deformations with interparticle Coulomb friction (wi > 0) are dominant (Fig. 6.47). Generally, in a volume element of wet paste with closed boundaries, a closed system, no ﬂuid is able to penetrate through the boundary walls. An external total pressure P loads both, the liquid (with pressure Pl) and also the particle phase (with pressure Ps), where P ¼ Pl þ Ps

ð6:84Þ

and both pressure increments are dP ¼ dP l þ dPs

ð6:85Þ

The compressibility of the liquid phase dV l =ðV l dPl Þ ¼ kl

ð6:86Þ

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increases if gas is dissolved or gas bubbles are dispersed in the liquid (softening effect). In contrast, capillary pressure within the ﬁne pores causes a stiffening of the liquid. Long-range ionic liquid–particle and van der Waals particle–particle interactions enhance additionally the stiffening and shear-thickening effects. Shear-thinning can be observed as well (Tomas and Reichmann, 2002). However, if the walls of the volume element are semi-permeable membranes the liquid can leave the process chamber and the dispersion is compressed to form a particle packing (ﬁlter cake) that is drained to the equilibrium of capillary pressure in the pores. The attractive capillary pore pressure can only be compensated by a large overpressure to drain the packing. This gives rise to a capillary pressure distribution due to the pore size distribution in a random packing. During short-term expression, the permeability of the packing is not sufﬁciently high and the liquid remains in the ﬁne pores. The behavior of the packing is equivalent to that of a closed system. But if the liquid in the porous packing is given enough time to penetrate and drain, then the pressure drop, –dPl, of the pores creates simultaneously an increasing loading of the particle contacts of the packing, dPs; (if P ¼ const then dP ¼ 0 and dPl þ dPs ¼ 0). Now, the particles are able to approach each other. Direct contacts are formed and deformed by normal forces. The shear strength depends on normal stress, friction angles and particle contact deformation characteristics. Additionally, liquid permeation kinetics, packing density, pore size distribution and pressure drop inﬂuence the shear and normal stress level. The expression process can be distinguished into ﬁltration and consolidation subprocesses, Fig. 6.48. In the ﬁltration stage (index F) a ﬁlter cake builds up. The compressible cake consists of ﬁne particles, which are more or less compressible, mainly dependent on particle contact stiffness. Thus, the cake may be consolidated after ﬁltration by applying a mechanical pressure. This second stage of the process is the consolidation stage (subscript c). The decreasing volume of the cake leads to a

Fig. 6.48 Two-stage expression characteristics (filtration and consolidation) of a suspension with particle volume concentration ws (Reichmann and Tomas, 2001).

6.4 Testing of Particle Bed Properties

Fig. 6.49 Principle of the press shear cell according to Reichmann (Reichmann and Tomas, 2001).

minimal amount of water in the pores. A dense particle packing saturated with liquid is obtained. During the expression process the liquid ﬂows through a compressed packing and there, the ﬂow rate difference between solid and liquid has to be taken into account. The dynamic cake formation (Fig. 6.48), with cake height ﬁrst increasing to h(tF) and then decreasing to h(tc), causes a liquid drag force acting on the particles. This leads to an axial particle stress, Ps, transmitted to the particle contacts. To obtain material properties such as packing porosity, permeability, wall friction angle and lateral stress ratio a test apparatus that can imitate in situ the expression process and measure the parameters of constitutive models has been developed by Reichmann. This apparatus is a combination of laboratory ﬁlter, compression-permeability-cell and high pressure ring shear cell, Fig. 6.49 (Reichmann and Tomas, 2001). To determine the material properties of a compressed cake, the feed suspension is ﬁlled into the ring chamber. The ring piston above the ring chamber is moved towards the suspension. An open valve removes the air between the piston and the suspension until the piston touches the upper suspension level. After this touch the valve is closed. Then a constant piston pressure is applied to drain the suspension. A sensor built in the piston surface indicates this isostatic pressure. Filtrate ﬂows through the supported ﬁlter medium; the piston velocity is equal to the ﬁltrate volume ﬂow rate per unit ﬁlter area. To prevent suspension losses, Teﬂon double-lip seals are ﬁxed at the inner and outer circumference of the ring piston. As the ﬁltrate runs dry the cake is consolidated, dV < 0, with a nearly isostatic stress. The packing porosity or density can be easily determined from the cake height h(tc) obtained from the piston position and the initial solid mass per ﬁlter surface area in the suspension. The solid density rs is obtained with a helium pycnometer (see Section 6.3.1). The permeability can be calculated by applying Darcys law. The ﬁltrate mass ﬂow rate is recorded by means of a balance. To measure the ﬂow behavior of the cake, the ring cell rotates, driven by a motor, with a variable number of revolutions. The two lever arms ﬁx the piston. They are connected with force sensors to determine the required force to ﬁx the piston, which is the shear force. To avoid a sliding of the material at the wall, the bottoms of the

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piston and ring chamber are covered with small ﬂight plates. Applying additionally a preshear stress at a certain normal pressure between the plates, the particle packing structure is destroyed, so that the cake is either compressed and drained (dV < 0) or ﬂows with expanding shear zone (dilatancy dV > 0) (Tomas and Reichmann, 2002). This compression and ﬂow behavior can be determined with the shear procedure according to Schulze (1994), as already described in Section 6.4.6. 6.4.8 Survey of Selected Direct and Indirect Shear Testers 6.4.8.1 The Biaxial Shear Tester according to Schwedes Another device to determine the ﬂow behavior of bulk solids is the biaxial shear tester (Schwedes, 2002). In the biaxial shear tester the bulk solid sample is conﬁned in lateral x- and y-directions by four steel plates. Vertical deformations of the sample are avoided by stiff top and bottom plates. The material sample can be loaded by the four lateral plates, which are linked by guides so that the horizontal cross-section of the sample may take rectangular shapes. In deforming the sample, the stresses sx and sy can be applied independently of each other in both the x- and y-directions. To avoid friction between the material sample and the steel plates, the plates are covered with thin rubber membranes. Silicon grease is placed between the steel plates and the rubber membranes. Thus, it is ensured that no wall shear stresses can occur on the x-, y- and z-planes, and that sx and sy are the principal stresses. The biaxial shear tester can also be used to obtain a yield locus corresponding to Figs. 6.38 and 6.45. The minor principal stress s2, for example acting in the y-direction, is kept constant during a test (Fig. 6.50). In the x-direction, a positive strain rate e_ 1 is applied, resulting in an increasing major principal stress s1. The value of s1 increases continuously up to the point of steady-state ﬂow. After this preshear, the stress state is reduced to a smaller s2 value and the second step of the shear process is performed by applying again a positive strain rate e_ 1 in the x-direction. 6.4.8.2 The Uniaxial Tester according to Enstad The uniaxial tester is an indirect shear tester, where the compressive failure strength can be determined immediately as a function of the previous consolidation. The powder sample is uniaxially consolidated in a die by pressing down a piston (Fig. 6.51). The boundary between the sample and the die is made nearly frictionless by means of a lubricated ﬂexible rubber membrane. After consolidation to a

Fig. 6.50 Shear at constant s2 in the biaxial shear tester (Schwedes, 2002).

6.4 Testing of Particle Bed Properties

Fig. 6.51 Consolidation and failure test by the uniaxial tester (Nysæter and Enstad, 2006).

pre-decided consolidation stress, the axial stress is removed and the die taken away. Then, the unconﬁned sample is loaded again until it fails and the compressive strength is measured (Nysæter and Enstad, 2006). Several features of the uniaxial tester are shown in Figs. 6.51 and 6.52. A ﬂexible membrane is stretched between the outer periphery of the piston and the inner periphery of the lower part of the conﬁning die (see Fig. 6.51). A ring is mounted on the lower part of the die to protect and keep the membrane in a locked position. This concept will ensure that the membrane and the powder sample always have a matching strain. To minimize the friction that develops on the interface between the membrane and the die wall, the die wall is highly polished and lubricated. As the sample is deformed by the vertically moving piston, the membrane will come into full contact with the die wall. Air conﬁned in the sample leaks out of a ﬁlter

Fig. 6.52 (a) Consolidation and (b) failure measurement (Nysæter and Enstad, 2006), see also Fig. 6.39.

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in the cup covering the bottom part of the sample. The die is mounted on a lower bearing, while the piston is mounted on a rod that is placed on an upper bearing. Mounted correctly, this will ensure coaxiality of the piston and the die. When ﬁlling the sample into the die, the die is turned upside down, the bottom cup is removed, and the die is ﬁxed in a special frame, which can vibrate the die during ﬁlling with adjustable frequency and amplitude. A suction system in the frame sucks air from the space between the membrane and the die wall, which is formed because of the stretching of the membrane. By use of the suction the membrane is brought back towards the die wall. The powder is then ﬁlled into the die either with a spoon or with a vibration feeder. In the uniaxial tester (see Fig. 6.52) a cylindrical sample is compressed by an axial consolidation stress, s1, that causes a deformation, e1. A cylindrical die encloses the sample and hinders radial expansion (e3 ¼ 0). The sample will, therefore, be compacted. The axial consolidation stress will cause a radial consolidation stress, s3, against the die wall. The radial consolidation stress will be smaller than the axial consolidation stress (s1 < s3). This type of consolidation is called uniaxial consolidation. When the sample has been consolidated at the chosen consolidation stress s1 for a certain time, the axial consolidation stress is reduced to zero. The strength of the powder is measured by removing the cylindrical die, so that the sample can expand in a radial direction, before the axial stress is increased again until the sample collapses (at sc). 6.4.8.3 Couette Device by Tardos In a Couette device (Tardos et al., 2003) the powder is sheared between two vertical cylinders by rotating the inner cylinder at different rotational rates. The instrument is similar to devices used to characterize ﬂuids, except that the walls of the device are covered with sandpaper of a coarseness similar to the particle diameter of the powder. A schematic representation of the device is shown in Fig. 6.53. Inner and outer cylinders of different sizes are used to obtain different sizes of the shear gap as well as different overall heights. The device is equipped with sensors to measure normal stresses in both horizontal and vertical directions at a given height in the powder bed. The advantage of this unit is that coarse and ﬁne powders from millimeter down to micron size can be tested. The torque on the rotating inner cylinder can be checked from the current drawn by the electric motor. The unit is equipped with a small observation window on the outer wall, at a piston not covered by sandpaper. Both stress sensors and the torque measurement are connected to a data acquisition system that enables the measurement of stresses and their ﬂuctuations at high sampling rates. The experimental Couette device can be mounted on a bench with feeding systems for ﬁlling and emptying the instrument. A computer-controlled camera can be used to image the ﬂow. 6.4.8.4 Powder Flow Analyzer ShearScan TS12 by AnaTec The ShearScan TS12 (AnaTec, 2001) measures automatically the ﬂow characteristics of powders and granular materials (Fig. 6.54). The shear tests are accomplished

6.4 Testing of Particle Bed Properties

Fig. 6.53 (a) Principle and (b) top view of Couette device.

Fig. 6.54 Principle of the powder flow analyzer ShearScan TS12 (AnaTec, 2001).

similarly to the Jenike (1964) method. All samples are automatically consolidated to the same point. This improves the reproducibility of analysis, as compared to traditional tests, by eliminating operator errors due to over-twisting or undertwisting.

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Tab. 6.3 Rough comparison between different shear testers.

Measuring of Yield loci Wall friction Time yield loci Compressibility Abrasion Pressure range new sample needed?

Jenike shear tester

Ring shear tester

Press shear cell

Biaxial box

Couette device

Yes Yes Yes Yes No low (<50 kPa) Yes

Yes Yes Yes Yes No low (<50 kPa) No

Yes Yes No Yes Yes middle (50–1 MPa) No

Yes No No Yes No low (<50 kPa) Yes

Yes No No No No low (<50 kPa) No

At the beginning of the experiment, the material sample is placed inside the shear cell. After the start of the measurement the upper piston drives automatically downwards and consolidates with a certain number of twistings the material sample at a given pressure. During the measurement the lower ring of the shear cell moves. The shear force is measured by a pressure sensor. After reaching stationary ﬂow, the normal load is reduced stepwise, then the material sample is sheared again. 6.4.8.5 Survey of Different Shear Testers Normally, the ﬂow behavior of cohesive bulk solids is determined with the translational shear cell according to Jenike in a low pressure range (1–50 kPa), with a small shear velocity (1–2 mm min1), and a shear displacement of about 6 mm. Li and Puri (2003) carried out experiments in the middle pressure range (< 690 kPa) and in the high pressure range (< 21 MPa). They found a relationship between loose bulk density and compressibility of bulk solids. If the initial bulk density is low, then the bulk solid is highly compressible, and vice versa. Thepress shear cell ofTomasandReichmann(2002) can determine theﬂowbehavior of wet cohesive bulk solids after press ﬁltration (Section 6.4.7). This press shear cell can also be used to determine yield loci of dry cohesive powders in the medium pressure range at shear velocities of up to 0.042 m s1 (2520 mm min1) which are much higher than those attainable with the Jenike shear tester (Grossmann et al., 2004). To investigate the ﬂow properties of bulk solids several devices are available, for example Jenike shear tester, ring shear tester and biaxial box. These shear testers have been evaluated and compared with each other by Schwedes (2000); Kamath et al. (1993). Table 6.3 summarizes the comparison between different shear testers.

6.5 Measurement of Particle Bed Movement in Rotary Drums by High-Speed Camera

Various processes, such as grinding, sieving, mixing and drying, are conducted in rotary drums. Usually, particles move in a more or less diluted bed that is

6.5 Measurement of Particle Bed Movement in Rotary Drums by High-Speed Camera

characterized by a collisional ﬂow regime with shear rates vS > 1 m s1. They contact each other and transfer impact forces, momentum or heat over their contacts. The shear stress contribution by particle–particle collisions or a turbulent-equivalent momentum transfer, see Section 6.3.5, is no longer negligible. During their motion in these drums, particles change their physical properties, especially their size, mixing state and moisture content. The following factors control the motion of a particle bed in a rotating drum (Sch€onert, 2003): . . . .

Diameter and circumferential velocity of the drum, type, size and ﬂow properties of the particles, number of particles in the drum, material, proﬁle and geometry of the interior coating of the drum.

Depending on the process, the drum is partially ﬁlled with a deﬁnite number of particles. This ﬁlling can be characterized by the particle load or particle charge, which is the ratio of the volume of the particle bed ﬁlling the drum, Vb, to the net volume of the drum, V: w¼

Vb ms ¼ V rp ð1eb ÞV

ð6:87Þ

Special motion patterns appear when the drum rotates at different circumferential velocities. This velocity determines the height to which particles can be lifted by the rotary motion of the drum before they start moving down. At lower circumferential velocities, particles roll and slide from the top to the bottom of the heap, not losing contact with their neighbors. This pattern is called cascading (Fig. 6.55a). At higher speeds, particles lose their contacts and fall in a parabolic curve to the toe of the heap, producing a pattern named cataracting (Fig. 6.55b). Centrifuging occurs above a critical speed and lets the particles permanently stick on the inner wall of the drum (Fig. 6.55c). Naturally, every transition from one state to another goes smoothly. The speed of a rotating drum can be given as a percentage of its critical speed. This concept assumes that at the highest point of the drum, at a distance R from the center of rotation, two forces, the radial force and weight, act on a particle of mass mp and are

Fig. 6.55 Motion patterns generated by particles at different drum speeds: (a) Cascading, (b) cataracting, (c) centrifuging (Sch€ onert, 2003).

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in balance when the particle starts to centrifuge: mp

v2 ¼ mp g R

ð6:88Þ

Provided that the drum is much larger than the particle, which is normally the case, and provided that the particle is in direct contact with the drum wall and follows its rotation without any slip, the speed of this particle meets that of the drum. This speed is called theoretical critical circumferential speed, pﬃﬃﬃﬃﬃﬃﬃﬃﬃ vcrit ¼ R g ð6:89Þ R and g are the radius of the drum and the gravitational acceleration, respectively. This speed can be converted into revolutions per second by dividing by 2pR. To compare drums of varying sizes, it is customary to give a percentage of the critical speed (Sch€onert, 2003; Perry and Green, 1999; Bernotat and Sch€ onert, 2005): c¼

v vcrit

ð6:90Þ

Motion patterns can also be characterized by the angle between the vertical and the radius drawn to the point of change from circular to parabolic motion, shown in Fig. 6.56a. The measurement of the angle of repose of granular materials in rotating drums is described in detail by Liua et al. (2005a, b). During uniform rotation, a particle bed develops typical velocity zones characterized by particles that move in the same direction at similar speeds. Four zones can be distinguished (Fig. 6.56, Sch€onert, 2003): the climbing zone, where the drum lifts the particles to a higher position; the falling zone, where particles lose contact with the drum, falling down fast; the rolling zone, where layers of particles slide on each other; and the placing zone, representing the tail of the particle bed, where particles, hit by other falling particles, take positions from which they are lifted. Common ranges of drum speeds are given in Tab. 6.4. In drums used in industry, particles do not normally reach the centrifugal state.

Fig. 6.56 A particle bed in a drum rotating at 70% of critical speed, shown (a) schematically (Sch€ onert, 2003) and (b) photographically. The zone labels mean: a, climbing, b, falling, c, rolling, and d, placing.

6.5 Measurement of Particle Bed Movement in Rotary Drums by High-Speed Camera Tab. 6.4 Industrial applications of rotary drums and their typical operating speeds.

Process

Equipment

Percentage Dominant of critical speed motion pattern Reference

Drying Grinding

rotary dryer ball mill

5–20 60–80

autogenous mill

70–90

cascading cascading– cataracting cataracting

Perry and Green (1999) Sch€onert (2003); Perry and Green (1999); Bernotat and Sch€onert (2005)

Screening drum screen 25–45 Agglome- drum granulator 25–50 rating disc granulator 60–75

cascading cascading cataracting

H€ofﬂ (2005); Schubert (2003) Schubert (2003)

Fig. 6.57 (a) Photographs taken at a shutter speed of 1/1000 s; (b) photographs taken at a shutter speed of 1/12 s; and (c) DEM simulations showing a particle bed of 10-mm glass spheres moving at different drum speeds.

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The inner wall of rotary drums is often lined by replaceable liners, which are usually made of steel or rubber. These lifters help to raise the particles and minimize the slip between wall and particles. The effect of bar lifters is shown in Fig. 6.57. A drum of 300 mm in diameter, packed with 10-mm glass spheres at w ¼ 30%, rotates at different circumferential velocities, producing different motion patterns. Flashlight reﬂections mark the path of the balls, especially at a shutter speed of 1/12 s. Different lengths of the luminous trails indicate here different ball velocities. Computer simulations using the discrete element method(DEM) (Cundall and Strack, 1979; Cundall et al., 2005) are capable of producing realistic motion patterns (Fig. 6.57). In Fig. 6.58, they give additional information about the velocity distribution of the balls, whose graytones change with their velocity, and about the mass center of the particle bed, marked by the black cross, whose position alters with drum speed. Centrifuging does not necessarily start at exactly 100% of critical speed. Projecting liners as well as large particle loads cause particles to centrifuge at lower speeds, whereas slippery liners and small particle loads inhibit the onset of centrifuging (Perry and Green, 1999; Bernotat and Sch€ onert, 2005). No example given above refers to wet operation. However, wet operation is similar in principle to dry operation. In wet operation, the motion patterns occur at higher drum speeds because liquid reduces the friction between drum and particles, and enlarges forces that resist particle motion.

Fig. 6.58 DEM simulation of a ball mill rotating at 72% of critical speed.

Additional Notation Used in Chapter 6

6.6 Conclusions

The experimental methods and the physical models shown in this chapter can be used for the determination of the properties of powder products of different particle size (nanoparticles to granules), moisture content (dry, moist and wet) and material (minerals, chemicals, pigments, waste, plastics, food etc.). For example, data from compression and impact tests of granules have been evaluated. The presented methods are powerful in describing the frictional shear ﬂow of cohesive and compressible powders. By modelling the single particle adhesion and by suitable micro–macro interaction rules, constitutive equations were shown to describe the preconsolidation-dependent mechanical behavior of cohesive powders and to simulate the dynamics of packed particle beds in powder processing, that is agglomeration, disintegration, size reduction, powder storage and ﬂow. With this knowledge and the respective tools, improved apparatus design (process chambers, feed hoppers, silos and conveyors) can be accomplished for process industries.

Additional Notation Used in Chapter 6

A A A a B Cs D D dS E E ESA e F f f ffc G2 g1 g2 h

I J1

aperture area (surface, cross-sectional) calibration function molecular separation distance second virial coefﬁcient particle mass concentration fractal dimension distance from the light axis on the screen maximum chord length modulus of elasticity molar adsorption potential ESA (electrokinetic sonic amplitude) signal restitution coefﬁcient force focal width factor ﬂow function (ffc ¼ s1/sc) autocorrelation function of the scattered light intensity normalized autocorrelation function of the electrical ﬁeld normalized autocorrelation function of the scattered light intensity height intensity of light ﬁrst order Bessel function

m m2 — m mol m3 kg2 kg m3 — m m N m2 J mol1 Pa m V1 — N m — — W2 m4 — — m W m2 —

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K kB k k ls Mw NA n n0 P P(u) Q q q q Ru r, R S s t U U U ~ mol V W Wm w Z

optical constant Boltzmann constant spring constant, stiffness compressibility distance between macroscopic objects weight averaged or apparent molecular mass Avogadros number refractive index refractive index of suspension medium breakage probability form factor cumulative sum distribution function scattering vector surface charge density frequency distribution function Rayleigh ratio radial coordinate, radius saturation displacement adsorbed ﬁlm thickness contact potential circumference interaction potential molar volume work mass-related energy consumption width acoustic resistance

mol m2 kg2 J kg1 N m1 Pa1 m kg mol1 mol1 — — — — — m1 As m2 various m1 m — m m V m J mol1 m3 mol1 J J kg1 m kg m2 s1

Greek letters

a a b G g_ d d e e_ z u k kA kp

bridge angle polarizability of particle afﬁnity coefﬁcient decay rate shear rate contact angle wall (target) thickness strain strain rate zeta-potential angle (scattering, wetting, diffraction, impact, rebound) elastic–plastic contact consolidation coefﬁcient elastic–plastic contact area coefﬁcient plastic repulsion coefﬁcient

rad m3 — s1 s1 rad m — s1 V rad — — —

Additional Notation Used in Chapter 6

l l mD u s sc sM,st spre sR,st sZ sZ,1 s0 s1,2 t t tc w w ws c c v

wavelength length of a single polygon element dynamic particle mobility Poissons ratio normal stress uniaxial compressive strength center stress of the Mohr circle for steady-state ﬂow preshear normal stress radius stress of the Mohr circle for steady-state ﬂow isostatic tensile strength uniaxial tensile strength isostatic tensile strength of the unconsolidated powder principle stresses (major, minor) correlation or sample time shear stress cohesion volumetric particle load friction angle in powder mechanics particle volume fraction ratio of actual to critical speed sphericity frequency of the electrical ﬁeld

m m m2 V1 s1 — Pa Pa Pa Pa Pa Pa Pa Pa Pa s Pa Pa — rad — — — s1

Subscripts and superscripts

A ads B b C c crit ct cyc diss e el F F f g H H H0 i

area related adsorbed breakage bulk, bed cantilever compressive critical compressive for time consolidation cyclic dissipation effective elastic Feret chord length ﬁltration ﬁnal gyration hydrodynamic Hamaker, adhesion single rigid contact without deformation internal friction

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it inst K K kin l M micro mono N p pl R R Ref r r r S S-Ch STP s s st T t U VdW 0

internal friction for time consolidation instrument contact, sum of plastic and elastic deformations piston kinetic longitudinal Martin chord length micropores monolyer in normal direction piezo plastic rebound (restitution) impact duration reference disctributed quantity index repose roughness shear sample chamber standard conditions (273.15 K, 1.013 bar) maximum chord length solids (particle), solid matter steady-state, stationary tangential tapping circumferential van der Waals reference (incident, loosely packed, molecular etc.) effective, combined

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Index 1D imaging, NMR 98 2D imaging, NMR 98–99 3D image ﬁltering and segmentation, algorithms 157–163 3D imaging, NMR 100–101 90 scattered light detection 247

a absorbance image 80–81 absorbance spectra, analysis 82 absorption, total light, deﬁnition 76 absorption bands – imaging apparatus 83 – spectral analysis, soybean seeds 86–87 – water and ice 83–85 absorption spectrum, fresh melon 75 acoustic attenuation spectroscopy 291 acoustic ﬁeld, characterization 42 acoustic levitation 41–66 – force, one-dimensional 46 – interactions of a droplet with the sound pressure ﬁeld 47–55 – pure water droplets, evaporation rates 61–63 – single droplet drying 55–66 – solvent droplets, drying rate 58 – standing acoustic waves 43–47 acoustic levitator – typical 60–61 – ventilation gas stream 52 acoustic optical tunable ﬁlter (AOTF) 78 acoustic streaming, primary and secondary 48–53 acoustic wave, forces 43–47 adhesion, particle 307–312 adhesion force test methods 309–310 adhesive interactions, wet granular media 254–255 aerosol spectrometers, optical 243–244

AFM see atomic force microscopy agricultural samples – MRI 125–137 – transport phenomena 125–126 Anatec powder ﬂow analyzer 346–348 angle of repose, moving particle bed 329 angular frequency, deﬁnition 42 AOTF see acoustic optical tunable ﬁlter apparent absorbance, deﬁnition 76 aqueous mannitol solution, single droplet drying 63–66 aspect ratio – effect of droplet size 53 – width/length 200 aspect ratio method, sound pressure level 47 asperity regime, capillary bridges 258 atomic force microscopy (AFM), adhesion force measurement 310–312 atomization air ﬂow rates 234 attenuation coefﬁcients – X-ray 147–148, 158–163 attrition coefﬁcients, mass and surfacerelated 241–243 attrition dust measurements – isokinetic sensor 237–243 – on-line particle counter 243–250 average moisture content, measurement 1–67

b backprojection algorithm, ﬁltered 149–150 balance, magnetic suspension see magnetic suspension balance bandpass ﬁlter, spectral information acquisition 78 batch drying, ﬂuidized beds 21–23 beam-hardening, X-rays 152 beam projections, X-ray image reconstruction 149–152

Modern Drying Technology, Vol. 2: Experimental Techniques Edited by Evangelos Tsotsas and Arun S. Mujumdar Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31557-4

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bed dryer, continuous ﬂuidized 25–27 Beer-Lambert law, X-rays 145 belt dryers, wastewater sludges 170–171 BET see Brunauer-Emmett-Teller biaxial shear tester, Schwedes 344 biological samples – NMR spectroscopy 126–128 – transient moisture proﬁles 128–131 bonding effects, particle surfaces 307–312 boundary layer, sound pressure 50 breakage, testing methods 320–321 breakage probability, zeolite granules 324–325 bridges, material 307–308 Brunauer-Emmett-Teller model (BET-model) – surface area determination 298–300 – see also gas adsorption method bubbles, optical particle detection 203 bulk density, particle bed 328 bulk solids – ﬂow behavior 329–331 Butt particle interaction apparatus 310–312

c calibration – infrared spectrometer 14–20 – MRI 111–114 calibration curves, NIR spectroscopy 82 CAMSIZER 194–200 capillary condensation 302–303 capillary forces, between particles 256–258 capillary state, wet granular media 261 cardboard samples – calibration procedure 111–114 – diffusion measurements 119–124 – drying experiments and MRI parameters 109–111 – drying proﬁles 114–119 – moisture gradients 108–124 CCD camera, CAMSIZER 195 CD, cross-direction, cellulose ﬁbers 103 cellulose ﬁbers 102–103 cellulose samples, MRI, previous results 104–105 centrifugal method, adhesion force testing 309–310 chemical thermo mechanical pulp (CTMP) 108 chord length 282 – particle 189 circularity/sphericity, particle shape 200 cluster volume distribution 164–165 cohesive bulk solids, ﬂow behavior 329–331 cohesive interactions, wet granular media 256–259

cohesive powders, ﬂow criteria 332–335 colloid probe technique 310–312 compressible bulk solids, ﬂow behavior 329–331 compression test, particle breakage 321–325 Compton scattering, X-rays 145 concentrated suspension/slurry/dispersion see sol concentration see particle concentration condensation, capillary 302–303 cone beam geometry, X-ray sources 155 conical indentation, wet granular media 264 consolidation and ﬁltration expression characteristics 342 constant-rate drying period 59 constant time imaging (CTI) sequence, NMR 134 constituent distribution, visualization 82 constituent image, deﬁnition 82 constitutive functions, particle properties 280 contact drying – experimental set-up 176–177 – spatio-temporal evolution 177–180 contact preconsolidation 310 Contin analysis 289 continuous ﬂuidized bed dryer, moisture distribution, modeling 25–27 convective drying, sludges 167–173 convexity, particle shape 200 cotton ﬁbers, water sorbed in 121 Couette device, Tardos 346 coulometry – advantages 32–33 – and NMR, combination 37 – moisture measurement 28–33 critical stress intensity 267 critical time, deﬁnition 26 cross-correlation analysis, particle image velocimetry 209 CTI see constant time imaging CTMP see chemical thermo mechanical pulp cumulant method, particle size distribution 279–280, 288–289 cumulative number distribution, particle moisture 26–27 cumulative pore volume plot 304 cyclic stressing test, zeolite granules 323–324 cylindrical hydrophilic particles, morphology of packing 179

d d2-law 56 DCC see dynamic contamination control Debye plot 285

Index deformation – droplet shape 48 – testing methods 320–321 DEM see discrete element method dense particle dispersions, ultrasonic methods 291–293 desorption curves, SIC 8 dew point measurement – experimental set-up 12 – infrared spectrometer 13–14 – infrared spectroscopy 10–24 – particle systems 10–11 dew point mirror 14–17 – calibration device 16 diametric compression, smooth spherical particles 253–254 diffraction, laser light, particle dispersions 283–291 diffuse reﬂection measurement 75 diffusion coefﬁcients 122–123 diffusion measurements, MRI 119–124 digital image analysis set-up 203 dilute particle dispersions, laser light scattering and diffraction 283–291 direct shear testing 266, 344–348 discharge, particle stress 319 discrete element method (DEM), simulation of rotating particles 351–352 dispersions, solid-liquid 341 DMT theory 255 drop ﬂuctuations, spectral analysis 218–223 drop-out method, sound pressure level 47 droplet drying kinetics, ﬁlm theory 57 droplet shape, deformation 48 droplet size, effects of changing 53–55 droplet surface, pressure difference across 53 droplets – acoustic levitation 41–66 – aqueous mannitol solution 63–66 – drying rate, solutions or suspensions 58–59 – interactions with the sound pressure ﬁeld 47–55 – mean moisture mass fraction 59 – mean particle porosity 59 – particle density 59 – spherical solvent, drying rate 55–57 dry powder, ring shear tester 339–340 dry sample gas – volume 238 – volume ﬂow rate 237 drying air – ﬂow rates 62 – temperature 65 drying curves, MRI 91–137

drying drum, particle rotation 319 drying front, spatio-temporal evolution 177–180 drying kinetics – ﬁlm theory 57 – measurement 1–67 – single particle 2–4, 20–24 drying optimization, xerogels 173–175 drying proﬁles, cardboard samples 114–119 drying rate – acoustically levitated solvent droplet 58 – droplets of solutions or suspensions 58–59 – ﬁrst period 39 – normalized 25 – spherical solvent droplet 55–57 Dubinin-Radushkevich method 301–302 dust mass ﬂow rate 249–250 dynamic contamination control (DCC), dew point measurement 15

e effective amplitude, deﬁnition 45–46 elastic impact 313–318 elastohydrodynamic lubrication 260 elastoplastic measurements, wet granular media 262–266 electrokinetic sonic amplitude (ESA) spectroscopy 292–293 electrolysis current, moisture distribution 30–32 electrolytic cell, coulometry 29 electromagnetic spectrum 145 electron microscopy, particle size distribution 281 Enstad uniaxial tester 344–346 equilibrium moisture content 39 ESA see electrokinetic sonic amplitude evaporation rate 11, 17 – acoustically-levitated pure water droplets 61–63 – aqueous mannitol solution droplets 63–66 extrudates, sludge 167–170

f failure properties, wet granular media 266–269 falling-rate drying period 59 fan beam geometry, X-ray sources 155 fan beam projections 151–152 Feldkamp algorithm 152 Feret chord length 282 ﬁber optical probe measurement technique – calibration 231–232

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366

– particle concentration and velocity 203, 228–236 – results 232–236 ﬁber saturation point (FSP) 103 ﬁbers – cellulose 102–103 – pore sizes within 121 FID see free induction decay ﬁeld of view (FOV) 205 ﬁlm theory, droplet drying kinetics 57 ﬁltered backprojection algorithm 149–150 ﬁltration and consolidation expression characteristics 342 ﬁne particles, physical properties 279–283 ﬁrst period drying rate 39 ﬁtting algorithms, sieve correlation 198–200 ﬂow behavior, bulk solids 329–331 ﬂow criteria, preconsolidated cohesive powders 332–335 ﬂow diagram, particle image velocimetry 212 ﬂow rates – atomization air 234 – drying air 62 – dust 249–250 ﬂuidized beds – attrition measurement 237–243 – batch drying 21–23 – continuous drying 25–27 – dew point measurement 11 – experimental set-up 12 – granulation 319 – parameters of drying experiments 21 – particle stability 236–250 – porosity 232–233 – spray granulation 190–194 food samples – moisture distribution 73–88 – MRI 125–137 – NMR spectroscopy 126–128 – transient moisture proﬁles 128–131 – transport phenomena 125–126 force-displacement behavior, zeolite granules 321–323 force-separation measurement 310–312 forces – adhesion 308–309 – capillary 256–258 – in a standing acoustic wave 43–47 – interparticle 252–261 FOV see ﬁeld of view fracture, granular materials 267–268 Fraunhofer range 244 Fraunhofer theory 284, 289–290

free-fall device, impact measurement 315–316 free induction decay (FID) 96 frequency, sound pressure wave 43–44 frequency encoding, NMR 98 frictional force, Hertzian particles 259 frictional interactions, wet granular media 259–261 FSP see ﬁber saturation point fully and partially saturated wet granular media, mechanical properties 251–269 funicular state, wet granular media 261

g g-Al2O3 – desorption curves 7–8 – pore diameter 6 g-ray attenuation methods, moisture proﬁles 91 gas adsorption method 280 – pore size distribution 300–307 – speciﬁc surface area 296–300 – see also Brunauer-Emmett-Teller model gas particle displacement, deﬁnition 42 gas particle velocity, deﬁnition 42 gas-phase pressure ﬂuctuations, spectral analysis 221–222 gas pycnometry 294–295 GE see gradient-echo gels, moisture proﬁles 130–131 geometrical range see Fraunhofer range Glycine max, moisture distribution 85 gradient-echo (GE) sequence, NMR 102 granular materials – fracture 267–268 – underconsolidated 262 granulation, in ﬂuidized bed 319 grating, spectral information acquisition 78

h Hahn-echo NMR pulse sequences 126–127 half-value layer (HVL) 145 Hamaker constant 333 HE-pycnometry 293–295 Helmholtz equation 46 Herschel-Bulkley parameters 265 Hertzian particles, frictional force 259 high-speed camera, particle bed movement 348–352 HVL see half-value layer (HVL) hydrodynamic method, adhesion force testing 310 hydrodynamic stability see particle stability hyperspectra

Index – soybean seeds 86 – water and ice 84 hyperspectrum – image processing 79 – near-infrared spectral imaging 76–77

i ice – absorption bands 83–85 – hyperspectra 84 – shear testing technique SSTT 337–339 illumination, spatial correction 204–205 image acquisition – particle image velocimetry 208 – spatial information acquisition 79 image analysis – by optical and scanning electron microscopy 280–283 – set-up, digital 203 image ﬁltering and segmentation, algorithms 157–163 image processing 79–82 – acquisition and pretreatment of spectral data 81–82 – analysis of absorbance spectra 82 – conversion into absorbance image 80–81 – hyperspectrum 79 – noise and shading correction 79–80 – visualization of constituent distribution 82 – X-ray tomography 157–166 image reconstruction, X-ray tomography 148–153 imaging apparatus, water and ice absorption bands 83 imaging principles, NMR 97–101 – 1D imaging 98 – 2D imaging 98–99 – 3D imaging 100–101 – slice selection 99–100 imaging sequences, NMR 101–102 impact, between solid bodies 313–318 impact separation method, adhesion force testing 310 impact test, particle breakage 325–328 in-line particle size measurement 188–194 – batch granulation of pharmaceutical products 191–194 – continuous granulation of detergents 190–191 – instrumentation 189 indicator Kriging algorithm 162–163 indirect shear testers 344–348 industrial tomography 155–156 information acquisition techniques 77–79

infrared (IR) spectrometer – calibration of 14–17 – linearization 17 – testing the calibration 10–24 infrared (IR) spectroscopy, dew point measurement 10–24 Institution of Chemical Engineers (ICE), shear testing technique 337–338 integral moisture balance 19–20 inter-ﬁber pores, paper 103 interface curvature, liquid-vapor interface 166 interfacial area, liquid-vapor interface 166 interparticle forces, wet granular media 252–261 interrogation areas, particle image velocimetry 209 intra-ﬁber pores, paper 103 invasive methods, moisture proﬁles 91 ipp-70 probe 190 IR see infrared isokinetic sensor, attrition dust measurements 237–243

j Jenike translational shear cell 335–339 JKR theory 255

k Kelvin equation 258 Kings equation 43 Kriging algorithm 162–163

l Lambert-Beer law 74–76 Laplace-Young equation 257 large-scale X-ray tomography 155–156 Larmor relation 94 laser light scattering and diffraction, dilute particle dispersions 283–291 lateral force microscopy (LFM) 261 LCTF see liquid crystal tunable ﬁlter levitation, acoustic see acoustic levitation LFM see lateral force microscopy light scattering and diffraction, dilute particle dispersions 283–291 line integral concept, X-ray image reconstruction 148–149 line scanning, spatial information acquisition 79 linear attenuation coefﬁcient, X-rays 146 linearization, IR spectrometer 17–18 liquid crystal tunable ﬁlter (LCTF) 78 liquid self-diffusivities 123–124

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368

longitudinal relaxation time 95–97 Lorentz-Mie theory 243–244 low-resolution NMR spectroscopy 126–127 lubrication, elastohydrodynamic 260 lubrication interactions, wet granular media 259–261

m macrotomography, X-ray 155–156 magnetic resonance imaging (MRI) – calibration procedure 111–114 – conversion of signal to water content 135 – diffusion measurements 119–124 – drying of agricultural and food samples 125–137 – drying of paper, pulp and wood samples 102–124 – general data 102–104 – moisture proﬁles and drying curves 91–137 – net magnetization 94–95 – paddy rice kernels 132–137 – parameters and drying experiments 109–111 – principles 93–102 magnetic suspension balance (MSB) 2–10 – conﬁguration and periphery 4–6 – experimental results 6–10 – experimental set-up 5 – single particle drying kinetics 2–4 Martin chord length 282 mass attenuation coefﬁcient, X-rays 147–148 mass ﬂow rate, dust 249–250 mass-related attrition coefﬁcients 241–243 material bridges, between particle surfaces 307–308 maximum chord length 282 MD, machine direction, cellulose ﬁbers 103 mean moisture mass fraction, droplets 59 mean particle porosity, droplets 59 mean residence time, deﬁnition 26 measuring volume, small optical 244–246 mechanical interactions, wet granular media 252–254 mechanical stability, particles 236–250 melon, absorption spectrum 75 mesoporosity, measurement 302–304 microbalance see magnetic suspension balance microporosity, measurement 301–302 microslicer 83 microtomography, X-ray 156–157 Mie range 244 mixed lubrication 260 moisture – quantitative analysis, procedure 30

– see also water moisture balance, integral 19–20 moisture content – and volume concentration 14 – change 11 – equilibrium 39 – measurement for justiﬁcation of linearization 17 moisture distribution – at the outlet of a continuous ﬂuidized bed dryer 25–27 – experimental 37–41 – food, near-infrared spectral imaging 73–88 – particle systems 24 – soybean seeds 85–88 – visualization 83–88 moisture gradients, in cardboard samples 108–124 moisture proﬁles – g-ray attenuation methods 91 – in a gel 130–131 – invasive an non-invasive methods 91 – MRI 91–137 – paddy rice kernels, non-intrusive measurements 132–137 – transient, food and biological samples 128–131 molliﬁed phase function 165 morphological characteristics, X-ray attenuation coefﬁcients 163–167 morphology of packing – cylindrical hydrophilic particles 179 – spherical hydrophilic particles 178 moving particle bed, angle of repose 329 MRI see magnetic resonance imaging MRI signal – and moisture proﬁles 135–137 – conversion to water content 135 MSB see magnetic suspension balance multiexponential sampling analysis 289 multiple detectors, spatial information acquisition 79

n nanoparticles, physical properties 279–283 near-infrared (NIR) spectral imaging 74–79 – hyperspectrum 76–77 – Lambert-Beer law 74–76 – moisture distribution in foods 73–88 – spatial information acquisition technique 78–79 – spectral information acquisition technique 77–78 – spectroscopy 74

Index – visualization of moisture distribution 83–88 near-infrared (NIR) spectroscopy 74 – calibration curves 82 – second derivative spectrum 81 NIR camera 83 NMR – and coulometry, combination 37 – basic 94–97 NMR spectroscopy – biological and food products 126–128 – low-resolution 126–127 – moisture measurment 33–37 – rice kernels 132–134 noise correction, image processing 79–80 non-intrusive measurements – moisture proﬁles in paddy rice kernels 132–137 – NMR preliminary experiments 132–134 – particle concentration measurements 201–208 non-invasive methods, moisture proﬁles 91 normalized drying rate, single particle 25 normally consolidated media, granular 261 nuclear magnetic moment 94 nuclear magnetic resonance see NMR Nusselt number, thin ﬁlm 57

o OAS see optical aerosol spectrometers off-line particle size measurement 194–200 – detection of particles 195 – outline of particles 195–196 – shape 200 – sieve correlation and ﬁtting 198–200 on-line particle counter, attrition dust and overspray measurements 243–250 one-dimensional acoustic levitation force 46 optical aerosol spectrometers (OAS) 243–244 optical microscopy, particle size distribution 281–283 optical particle detection 202–208 – bubbles 203 – digital image analysis set-up 203 – ﬁeld of view 205 – illumination 204–205 – solids fraction 205–206 – see also ﬁber optical probe measurement technique optical volume limitation 247 overconsolidated media, granular 261 overspray measurements, with an on-line particle counter 243–250

p packed beds – contact drying 176–180 – dew point measurement 11 – sludge 170–173 paddy rice kernels, MRI 132–137 paper, porosity scales 103 paper samples, MRI – general data 102–104 – previous results 104–105 parallel beam geometry, X-ray sources 155 PARSUM probe 189 partially and fully saturated wet granular media, mechanical properties 251–269 particle abrasion, measurement 318–328 particle adhesion 254–255 – adhesion force test methods 309–310 – comparison of adhesion forces 308–309 – measurement 307–312 particle bed movement, in rotary drums 348–352 particle bed properties 328–348 – angle of repose 329 – bulk density and tapping density 328 – cohesive and compressible bulk solids 329–331 – direct and indirect shear testers 344–348 – physical 279–283 – preconsolidated cohesive powders 332–335 – press shear cell 340–344 – ring shear tester 339–340 – translational shear cell 335–339 particle breakage – measurement 318–328 – testing methods 320–321 particle chord lengths 189 particle circulation time 224–228 particle concentration – ﬁber optical probe measurement technique 203, 228–236 – non-intrusive measurements 201–207 particle deformation, testing methods 320–321 particle density, droplets 59 particle detection – off-line measurement 195 – optical 202–207 particle dispersions – laser light scattering and diffraction 283–291 – ultrasonic methods 291–293 particle drying kinetics, comparison of measurment methods 3 particle edge

j369

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370

– correction according to iso 196 – determination 195 particle ﬂow rate variation, parameters 38 particle formation, aqueous mannitol solution droplets 63–66 particle formulation processes, measuring techniques 187–270 particle image velocimetry (PIV) 201, 208–218 – cross-correlation analysis 209 – ﬂow diagram 212 – image acquisition 208 – interrogation areas 209 – velocity vector maps 212–215 particle interaction apparatus, Butt 310–312 particle moisture – as a distributed property 24 – cumulative number distribution 26–27 particle outline, off-line measurement 195–196 particle properties, physical see physical particle properties particle restitution coefﬁcient, measurement 312–318 particle shape – deﬁnition 283 – off-line measurement 200 – parameters 200 particle size – measurement 188–200 – parameters 197 – volume-related 198 – see also in-line particle size measurement; off-line particle size measurement particle size distribution – analysis 280–293 – cumulative 279–280, 288–289 – density 248 – sum 248 particle stability – during ﬂuidized bed processing 236–250 – hydrodynamic 218–223 particle stresses 319 particle surfaces, bonding effects 307–312 particle systems, dew point measurement 10–11 particle tracking, positron emission 223–228 particle velocity 208–218 – ﬁber optical probe measurement technique 228–236 particles – acoustic levitation 41–66 – ﬁne 279–283 – gas 42

– Hertzian 259 – morphology of packing 178–179 – rotating 351–352 – single see single particle drying – spherical see spherical particles – stiff, with soft contacts 333 pastes see soft solids PCS-2010, measuring principle 248 pendular state, wet granular media 261 pendulum experiments, impact measurement 316–317 PEPT see positron emission particle tracking percolation 165 PFG see pulsed ﬁeld gradient (PFG) NMR PGSE, pulsed gradient spin-echo phase encoding, NMR 99 phase segmentation, X-ray tomography 163–167 phase volume fraction 164 photoelectric absorption, X-rays 144–145 physical particle properties 279–352 – measurement 293–328 – mesoporosity 302–304 – microporosity 301–302 – particle abrasion and breakage 318–328 – particle adhesion 307–312 – particle bed see particle bed properties – particle restitution coefﬁcient 312–318 – pore size distribution 300–307 – pore volume 304–305 – solid density analysis 293–295 – speciﬁc surface area 296–300 – volume determination 294–295 PIV see particle image velocimetry plastic zone, fracture of granular materials 267 platinum resistance thermometer (PRT) 15 Polanyi theory 301 pore size distribution – gas adsorption method 300–307 – measurement set-up 305–307 pore sizes, within ﬁbers 121 pore volume, measurement 304–305 pore volume plot, cumulative 304 porosity – ﬂuidized bed 232–233 – mean particle 59 – paper 103 positron emission particle tracking (PEPT) 202, 223–228 powder ﬂow analyzer, Shearscan TS12 346–348 powders – classiﬁcation 331

Index – cohesive 332–335 – single particle drying kinetics 20–24 preconsolidated cohesive powders, ﬂow criteria 332–335 press shear cell, Reichmann 340–344 pressure difference, across droplet surface 53 pressure drop ﬂuctuations – spectral analysis 202, 218–223 pressure nodes, effect of droplet size 54–55 primary acoustic streaming 48–53 process zone see plastic zone projections – fan beam 151–152 – X-ray image reconstruction 149–152 PRT see platinum resistance thermometer pulp samples, self-diffusivity 123–124 pulsed ﬁeld gradient (PFG) NMR 127 pulsed gradient spin-echo (PGSE) technique 119–124 pure water droplets, acoustically-levitated 61–63 pushbroom method, spatial information acquisition 79

q quasi-elastic light scattering (QELS) 286–287

r radio frequency excitation, MRI 94–95 Radon transform 149–150 ram extrusion 265 rate constant, deﬁnition 26, 40 Rayleigh-Debye equation 285 Rayleigh-Gans-Debye theory 284 Rayleigh range 244 Rayleigh theory 284 refraction, Snells law 228–229 regions of interest (ROIs), spectral information acquisition 81, 84, 86 Reichmann press shear cell 340–344 relaxation, and NMR signal 95–97 repose angle, moving particle bed 329 resorcinol-formaldehyde xerogels, drying optimization 173–175 rice kernels, moisture proﬁles 132–137 ring shear tester, Schulze 339–340 ROI see regions of interest rotary drums, particle bed movement 348–352 rotating particles, discrete element method 351–352 roughness regime, capillary bridges 258 Ruiz-Cabrera method 130–131

s SAPDF see spectral analysis of pressure drop ﬂuctuations scanning electron microscopy (SEM), particle size distribution 281–283 scattered light detection, 90 247 scattering, laser light, particle dispersions 283–291 Schulze ring shear tester 339–340 Schwedes biaxial shear tester 344 SE see spin-echo second derivative spectrum – NIR spectroscopy 81 – soybean seeds 87–88 secondary acoustic streaming 48–53 segmentation algorithms, X-ray attenuation 161–162 self-diffusivity, pulp samples 123–124 shading correction, image processing 79–80 shear cell – Jenike translational 335–339 – Reichmann 340–344 shear force-displacement curves 338 shear testers – direct and indirect 344–348 – Schulze 339–340 – survey 348 shear testing technique SSTT 337–339 Shearscan TS12 346–347 Sherwood number 51 SIC – desorption curves 8 – pore diameter 6 sieve analysis, off-line particle size measurement 198–200 signal intensity, MRI in cardboard samples 111 simulation of rotating particles, discrete element method 351–352 single droplet drying – aqueous mannitol solution 63–66 – drying rate 55–57 – water 59–63 single particle drying – general remarks 2–4 – normalized drying rate 25 – powdery material 20–24 single point detectors, spatial information acquisition 79 sinogram see Radon transform slice selection, NMR 99–100 sludges – convective drying 167–173 – individual extrudates 167–170

j371

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372

– packed bed 170–173 slump test 251–252 slurry state, wet granular media 261 small droplets, acoustic levitation 41–66 small optical measuring volume 244–246 Snells law 228–229 sodium benzoate granules 319 sol 251 solid bodies, impact 313–318 solid density analysis, HE-pycnometry 293–295 solid-liquid dispersions, ﬂow characteristics 341 solids – soft 251 – wet granular 251 solids fraction, stagnant bed 205–206 solvent droplets – acoustically levitated, drying rate 58 – spherical, drying rate 55–57 sound pressure – deﬁnition 42 – inﬁnite levitator 45 sound pressure boundary layer 50 sound pressure ﬁeld – change of droplet size 53–55 – deformation of droplet shape 48 – interactions with droplets 47–55 – primary acoustic streaming 48–53 sound pressure level (SPL) – deﬁnition 42 – effect of droplet size 54 – effective 47 sound pressure wave, frequency 43–44 sound velocity level (SVL), deﬁnition 42 soybean seeds 86–87 – moisture distribution 85–88 – second derivative spectrum 87–88 Spalding transfer number 57 spatial ﬁltering velocimetry 188–189 spatial information acquisition technique 78–79 spatio-temporal evolution, contact drying 177–180 speciﬁc surface area – BET-model 298–300 – gas adsorption method 296–300 spectral analysis – absorption bands – of pressure drop ﬂuctuations (SAPDF) 202, 218–223 spectral data – acquisition 81–82 – pretreatment 81–82

spectral illuminator 83 spectral imaging, near-infrared see near-infrared spectral imaging spectral information acquisition technique 77–78 sphere indentation, wet granular media 263 spherical particles – capillary forces 256–258 – diametric compression 253–254 – morphology of packing 178 – Youngs modulus 253 spherical regime, capillary bridges 258 spherical solvent droplets, drying rate 55–57 sphericity/circularity, particle shape 200 spin-echo (SE) sequence, NMR 101–102 spin-lattice relaxation see longitudinal relaxation time spin-spin relaxation see transverse relaxation time SPL see sound pressure level spout-ﬂuid bed – particle circulation time 227–228 – spectral analysis 219 spraying rate 17–18 spring balance method, adhesion force testing 309–310 squeeze ﬂow, wet granular media 265 SSTT, shear testing technique 337–338 stagnant bed, solids fraction 205–206 standing acoustic wave, forces 43–47 Stefan ﬂow 57 stiff particles with soft contacts, model 333 strain energy release rate 268 surface area – BET-model 298–300 – gas adsorption method 296–300 surface-related attrition coefﬁcients 241–243 surfaces – bonding effects 307–312 – pressure difference across 53 SVL see sound velocity level symmetry, particle shape 200 synchrotron X-ray microtomography 157

t tapping density, particle bed 328 Tardos Couette device 346 temperature, drying air 65 temperature protocols, moisture distribution 30–32 tension tests 268 test methods – adhesion force 309–310

Index

ultrasonic levitation see acoustic levitation ultrasonic methods, dense particle dispersions 291–293 unassigned voxels, X-ray attenuation 163 underconsolidated media, granular 262 uniaxial tester, Enstad 344–346

– single droplet drying 59–63 – sorbed in cotton ﬁbers 121 water concentration proﬁles, MRI calibration 112–113 water content – conversion of NMR signal 135 – see also moisture water droplets, acoustically-levitated 61–63 web, cellulose ﬁbers 103 wet ﬁlter cake, press shear cell 340–344 wet granular media – adhesive interactions 254–255 – cohesive interactions 256–259 – elastoplastic measurements 262–266 – failure properties 266–269 – frictional and lubrication interactions 259–261 – interparticle forces 252–261 – mechanical interactions 252–254 – mechanical properties 251–269 wet granular solids 251 wet sample gas – particle concentration 240 – velocity 239–240 – volume 239 width/length aspect ratio, particle shape 200 wire cutting 268 wood samples, MRI, general data 102–104

v

x

van der Waals forces 309 velocimetry – particle image see particle image velocimetry – spatial ﬁltering 188–189 velocity see particle velocity velocity vector maps 212–215 ventilation gas stream, acoustic levitator 52 vibration method, adhesion force testing 310 viscous force 258 visualization – constituent distribution 82 – moisture distribution 83–88 volume concentration, and moisture content 14 volume determination, using gas pycnometry 294–295

X-ray attenuation coefﬁcients 147–148, 158–163 – morphological characteristics 163–167 X-ray macrotomography 155–156 X-ray microtomography 156–157 – synchrotron 157 X-ray sources, geometry 154–155 X-ray tomography 143–181 – applications 167–180 – fundamentals and principles 143–153 – geometry of CT systems 153–155 – image processing 157–166 – image reconstruction 148–153 – instrumentation 153–157 – large-scale 155–156 – packed bed, contact drying 176–180 – physical principles 144–148 – resorcinol-formaldehyde xerogels, drying optimization 173–175 – sludge, convective drying 167–173 x-y scanning, spatial information acquisition 79 xerogels, drying optimization 173–175

– breakage 320–321 – pore size distribution 305–307 thin ﬁlms, Sherwood number 57 thin layer method (TLM), packed beds 11 three-point bend method 267 time-domain NMR see low-resolution NMR spectroscopy TLM see thin layer method total amount of water, MRI calibration 113 total light absorption, deﬁnition 76 transient moisture proﬁles, food and biological samples 128–131 translational shear cell, Jenike 335–339 transport phenomena, agricultural and food products 125–126 transportation, particle stress 319 transverse relaxation time 96–97 triaxial tests 267 Trouton ratio 265 tunable ﬁlter, spectral information acquisition 78

u

w wastewater sludges see sludges water – absorption bands 83–85 – hyperspectra 84

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374

y Youngs modulus, smooth spherical particles 253

z ZD, z-direction, cellulose ﬁbers 103 zeolite 4A – adsorption 9

– desorption curves 7–8 – mass determination 10 – pore diameter 6 zeolite granules – breakage probability 324–325 – cyclic stressing test 323–324 – force-displacement behavior 321–323 Zimm plot 285–286