Microfluidics Based Microsystems
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Microfluidics Based Microsystems Fundamentals and Applications edited by
S. Kakaç TOBB University of Economics and Technology Sögütözü, Ankara, Turkey
B. Kosoy State Academy of Refrigeration Odessa, Ukraine
D. Li University of Waterloo Waterloo, Ontario, Canada and
A. Pramuanjaroenkij Kasetsart University Chalermphrakiat Sakonnakhon Province Campus Sakonnakhon, Thailand
Published in cooperation with NATO Public Diplomacy Division
Proceedings of the NATO Advanced Study Institute on Microfluidics Based Microsystems: Fundamentals and Applications Çeşme-Izmir, Turkey August 23–September 4, 2009
Library of Congress Control Number: 2010930508
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CONTENTS Preface
ix
Convective Heat Transfer Correlations in Some Common Micro-Geometries O. Aydin and M. Avci
1
Convective Heat Transfer in Microscale Slip Flow A. Guvenc Yazicioglu and S. Kakaç Direct and Inverse Problems Solutions in Micro-Scale Forced Convection C. P. Naveira-Cotta, R. M. Cotta, H. R. B. Orlande, and S. Kakaç
15
39
Conjugated Heat Transfer in Microchannels J. S. Nunes, R. M. Cotta, M. R. Avelino, and S. Kakaç
61
Mechanisms of Boiling in Microchannels: Critical Assessment J. R. Thome and L. Consolini
83
Prediction of Critical Heat Flux in Microchannels J. R. Thome and L. Consolini
107
Transport Phenomena in Two-Phase Thermal Spreaders H. Smirnov and B. Kosoy
121
An Investigation on Thermal Conductivity and Viscosity of Water Based Nanofluids I. Tavman and A. Turgut
139
Formation of Droplets and Bubbles in Microfluidic Systems P. Garstecki
163
Transport of Droplets in Microfluidic Systems P. Garstecki
183
The Front-Tracking Method for Multiphase Flows in Microsystems: Fundamentals M. Muradoglu
v
203
vi
CONTENTS
The Front-Tracking Method for Multiphase Flows in Microsystems: Applications M. Muradoglu
221
Gas Flows in the Transition and Free Molecular Flow Regimes A. Beskok
243
Mixing in Microfluidic Systems A. Beskok
257
AC Electrokinetic Flows A. Beskok
273
Scaling Fundamentals and Applications of Digital Microfluidic Microsystems R. B. Fair
285
Microfluidic Lab-on-a-Chip Platforms: Requirements, Characteristics and Applications D. Mark, S. Haeberle, G. Roth, F. Von Stetten, and R. Zengerle
305
Microfluidic Lab-on-a-Chip Devices for Biomedical Applications D. Li Chip Based Electroanalytical Systems for Monitoring Cellular Dynamics A. Heiskanen, M. Dufva, and J. Emnéus
377
399
Perfusion Based Cell Culture Chips A. Heiskanen, J. Emnéus, and M. Dufva
427
Applications of Magnetic Labs-on-a-Chip M. A. M. Gijs
453
Magnetic Particle Handling in Microfluidic Systems M. A. M. Gijs
467
AC Electrokinetic Particle Manipulation in Microsystems H. Morgan and T. Sun
481
Microfluidic Impedance Cytometry: Measuring Single Cells at High Speed T. Sun and H. Morgan
507
CONTENTS
vii
Optofluidics D. Erickson
529
Vivo-Fluidics and Programmable Matter D. Erickson
553
Hydrophoretic Separation Method Applicable to Biological Samples S. Choi and J.-K. Park
577
Programmable Cell Manipulation Using Lab-on-a-Display H. Hwang and J.-K. Park
595
Index
615
PREFACE This volume contains an archival record of the NATO Advanced Study Institute on Microfluidics Based Microsystems – Fundamentals and Applications held in Çeşme-Izmir, Turkey, August 23–September 4, 2009. ASIs are intended to be high-level teaching activity in scientific and technical areas of current concern. In this volume, the reader may find interesting chapters and various microsystems fundamentals and applications. As the world becomes increasingly concerned with terrorism, early onspot detection of terrorist’s weapons, particularly bio-weapons agents such as bacteria and viruses are extremely important. NATO Public Diplomacy division, Science for Peace and Security section support research, Advanced Study Institutes and workshops related to security. Keeping this policy of NATO in mind, we made such a proposal on Microsystems for security. We are very happy that leading experts agreed to come and lecture in this important NATO ASI. We will see many examples that will show us Microfluidics usefulness for rapid diagnostics following a bioterrorism attack. For the applications in national security and anti-terrorism, microfluidic system technology must meet the challenges. To develop microsystems for security and to provide a comprehensive state-of-the-art assessment of the existing research and applications by treating the subject in considerable depth through lectures from eminent professionals in the field, through discussions and panel sessions are very beneficial for young scientists in the field. Microfluidics are great tools for security and anti-terrorism with many applications. New and better diagnostic technology must be developed in order to be prepared for an act of bio-terrorism. The subject will be treated through lectures by experts on biosensors, microsystems, bio micro-electromechanical devices, and nanofluidics. To establish the objectives of this Institute, important lectures by prominent expert on the field are presented and are included in this volume of the Institute. Basics of Electrokinetic Microfluidics, Lab-on-a-Chip Devices for Biomedical Applications, Microfluidic Biological Application Specific Integrated Circuits, Integrated Optofluidics and Nanofluidics, Cell Culture Revolution via Dynamical Microfluidic Controls, Fundamentals of droplet flow in microfluidics, Implementation of fluidic functions in digital microfluidics, Chip architecture and applications for digital microfluidics, Mixing in microfluidic systems are presented and discussed in detail. In addition more presentations such as Optofluidics – Fusing Nanofluidics and Nanophotonics, Programmable Matter – Micro and milliscale fluid dynamics of reconfigurable assembly for control of living systems, An Overview on Microfluidic
ix
x
PREFACE
Platforms for Lab-on-a-Chip Applications, Centrifugal Microfluidics for Lab-on-a-Chip Applications are also given. Transport of droplets and bubbles in microfluidic systems – from flow through a simple pipe to logic gates and automated chips for chemical processing, Analytical, Synthesis and Bio-Medical Applications of Microchip Technology, Hydrophoretic separation method for blood sample analysis, Magnetophoretic multiplexed immunoassays in a microchannel, programmable particle manipulation using lab-on-a-display are discussed in details with fundamentals and applications. During the 10 working days of the Institute, the invited lecturers covered fundamentals and applications of Microsystems in various fields including the security. The sponsorship of the NATO Science for Peace and Security Section (SPS) is gratefully acknowledged; in person, we are very thankful to Dr. Fausta Pedrazzini director of the ASI programs and the executive secretary, Ms Alison Trapp who continuously supported and encouraged us at every phase of our organization of this Institute. We are appreciative to TOBB University of Economics and Technology and International Centre of Heat and Mass Transfer for their sponsorships. We are also very grateful to Annelies Kersbergen, publishing editor of Springer Science; our special gratitude goes to Drs. Nilüfer Eğrican, Şepnem Tavman, Almıla Yazıcıoğlu, Ahmet Yozgatlıgil, Derek Baker, Selin Aradağ, Nilay S. Uzol for coordinating sessions and we are very thankful to Büryan Apaçoğlu, Gizem Gülben, Sezer Özerince, and Cahit C. Köksal for smooth running of the Institute. S. Kakaç B. Kosoy D. Li A. Pramuanjaroenkij
CONVECTIVE HEAT TRANSFER CORRELATIONS IN SOME COMMON MICRO-GEOMETRIES ORHAN AYDIN AND METE AVCI Department of Mechanical Engineering Karadeniz Technical University, 61080 Trabzon, Turkey,
[email protected]
Abstract. This work summarizes some of our recent theoretical studies on convective heat transfer in micro-geometries. Only pure analytical solutions are presented here. At first, forced convection is studied for the following three geometries: microtube, microchannel between two parallel plates and microannulus between two concentric cylinders. Constant heat flux is assumed to be applied at walls. Then mixed convection in a vertical parallel-plate microchannel with symmetric wall heat fluxes is investigated. Steady and laminar internal flow of a Newtonian is analyzed. In the analysis, the usual continuum approach is coupled with the two main characteristics of the microscale phenomena, the velocity slip and the temperature jump. In the forced convection problems, viscous dissipation is also included, while it is neglected for the mixed convection problem. Internal velocity and temperature distributions are obtained for varying values of governing parameters. Finally, fully analytical Nusselt number correlations are developed for the cases investigated.
1. Introduction Microelectromechanical systems (MEMS) have gained a great deal of interest in recent years. Such small devices typically have characteristic size ranging from 1 mm to 1 μm, and may include sensors, actuators, motors, pumps, turbines, gears, ducts and valves. Microdevices often involve mass, momentum and energy transport. Modeling gas and liquid flows through MEMS may necessitate including slip, rarefaction, compressibility, intermolecular forces and other unconventional effects [1]. The interest in the area of microchannel flow and heat transfer has increased substantially during the last decade due to developments in the electronic industry, microfabrication technologies, biomedical engineering, etc. In general, there also seems to be shift in the focus of published articles, S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_1, © Springer Science + Business Media B.V. 2010
1
2
O. AYDIN AND M. AVCI
from descriptions of the manufacturing technology to discussions of the physical mechanisms of flow and heat transfer [2]. Readers are referred to see the following recent excellent reviews related to transport phenomena in microchannels. Ho and Tai [3] summarized discrepancies between microchannel flow behavior and macroscale Stokes flow theory. Palm [2], Sobhan and Garimella [4] and Obot [5] reviewed the experimental results in the existing literature for the convective heat transfer in microchannels. Rostami et al. [6, 7] presented reviews for flow and heat transfer of liquids and gases in microchannels. Gad-el-Hak [1] broadly surveyed available methodologies to model and compute transport phenomena within microdevices. Guo and Li [8, 9] reviewed and discussed the size effects on microscale single-phase fluid flow and heat transfer. In a recent study, Morini [10] presents an excellent review of the experimental data for the convective heat transfer in microchannels in the existing literature. He critically analyzed and compared the results in terms of the friction factor, laminar-to-turbulent transition and the Nusselt number. It is shown that fluid flow and heat transfer at microscale differ greatly from those at macroscale. At macroscale, classical conservation equations are successfully coupled with the corresponding wall boundary conditions, usual no-slip for the hydrodynamic boundary condition and no-temperaturejump for the thermal boundary condition. These two boundary conditions are valid only if the fluid flow adjacent to the surface is in thermal equilibrium. However, they are not valid for gas flow at microscale. For this case, the gas no longer reaches the velocity or the temperature of the surface and therefore a slip condition for the velocity and a jump condition for the temperature should be adopted. The Knudsen number, Kn is the ratio of the gas mean free path, λ, to the characteristic dimension in the flow field, D, and, it determines the degree of rarefaction and the degree of the validity of the continuum approach. As Kn increases, rarefaction become more important, and eventually the continuum approach breaks down. The following regimes are defined based on the value of Kn [11]: (i) (ii) (iii) (iv)
Continuum flow (ordinary density levels) Kn ≤ 0.001 Slip-flow regime (slightly rarefied) 0.001 ≤ Kn ≤ 0.1 Transition regime (moderately rarefied) 0.1 ≤ Kn ≤ 10 Free-molecule flow (highly rarefied) 10 ≤ Kn ≤ ∞
Viscous dissipation is another parameter that should be taken into consideration at microscale. It changes temperature distributions by playing a role like an energy source induced by the shear stress, which, in the following, affects heat transfer rates. The merit of the effect of the viscous dissipation depends on whether the pipe is being cooled or heated.
CONVECTIVE HEAT TRANSFER CORRELATIONS
3
In this work, heat and fluid flow in some common micro geometries is analyzed analytically. At first, forced convection is examined for three different geometries: microtube, microchannel between two parallel plates and microannulus between two concentric cylinders. Constant wall heat flux boundary condition is assumed. Then mixed convection in a vertical parallel-plate microchannel with symmetric wall heat fluxes is investigated. Steady and laminar internal flow of a Newtonian is analyzed. Steady, laminar flow having constant properties (i.e. the thermal conductivity and the thermal diffusivity of the fluid are considered to be independent of temperature) is considered. The axial heat conduction in the fluid and in the wall is assumed to be negligible. In this study, the usual continuum approach is coupled with the two main characteristics of the microscale phenomena, the velocity slip and the temperature jump. Effects of the main governing dimensionless parameters on the momentum and heat flow transfer will be analyzed. Pure analytical correlations for Nusselt number as a function of the Brinkman number and the Knudsen number are developed for both hyrodynamically and thermally fully developed flow. In fact, this work will be a summary view of our recent studies [12–15]. 2. Nu Correlations In this part, three different geometries are considered and corresponding results for the Nusselt number these geometries are given respectively in the following. 2.1. FORCED CONVECTION IN A MICROPIPE
For this geometry, the fully developed velocity profile taking the slip flow condition at the wall is 2(1 − (r / r0 ) 2 + 4 Kn) u = um (1 + 8Kn)
(1)
where um is the mean velocity and Kn is the Knudsen number, Kn = λ / Dh . The Nusselt number correlation for this geometry is obtained as follows [12]: Nu =
Brq
2 Brq
1 + 16 Brq 1 ⎛ 16γ Kn ⎞ 1 1+ + + + + ⎜ ⎟ 4 3 4 ⎝ γ + 1 Pr ⎠ 3(1 + 8 Kn) (1 + 8 Kn) 24(1 + 8 Kn)2 6(1 + 8 Kn)
(2)
O. AYDIN AND M. AVCI
4
where Brq, represents the modified Brinkman number, whose value is determined from μ um2 (3) Brq = D qw′′
2.2. FORCED CONVECTION IN A MICROCHANNEL BETWEEN TWO PARALLEL PLATES
The fully developed velocity profile for this microchannel is: u 3 ⎡1 − ( y / w) 2 + 4 Kn ⎤ = ⎢ ⎥ um 2 ⎣ 1 + 6 Kn ⎦
(4)
where Kn is the Knudsen number, Kn = λ / 2w . In terms of the modified Brinkman number, Brq, the Nusselt number receives the following form [13]: Nu =
2 2Brq 11Brq 2(1 + 21Brq ) 1 ⎛ 12γ Kn ⎞ 2 + + + + 1+ ⎜ ⎟ 4 3 2 3 ⎝ γ + 1 Pr ⎠ 35(1 + 6Kn) 35(1+ 6Kn) 105(1 + 6Kn) 15(1+ 6Kn)
(5)
where Brq =
μ um2
w qw
(6)
2.3. FORCED CONVECTION IN A MICROANNULUS BETWEEN TWO CONCENTRIC CYLINDERS
The dimensionless velocity distributions is obtained as [14]: u = 2 (1 − R 2 + 2rm*2 ln ( R ) + A ) / B um
where A and B are, respectively:
(7)
CONVECTIVE HEAT TRANSFER CORRELATIONS
5
A = 4 Kn (1 − r * )(1 − rm*2 )
(8)
⎛ ⎞ ⎛1 ⎞ r *2 ln ( r * ) ⎟ + 8Kn (1 − r * )(1 − rm*2 ) ⎟⎟ B = ⎜⎜ 1 − r *2 − 4rm*2 ⎜ + *2 ⎝ 2 1− r ⎠ ⎝ ⎠
(9)
Here Kn is Knudsen number ( Kn = λ Dh ) and rm* designates the dimensionless radius where the maximum velocity occurs (∂u / ∂r = 0) . It is given by [14] 1/ 2
⎛ ⎞ ⎜ ⎟ 2 rm ⎜ ⎟ (1 − r * )(1 + 4 Kn) * rm = = ⎜ ⎟ 2 * ro ⎜ ⎛ r −1 ⎞ 2 ln(1 / r * ) − 4 Kn ⎜ * ⎟ ⎟ ⎜ r ⎟⎟ ⎜ ⎝ ⎠⎠ ⎝
(10)
For this geometry, two different forms of the thermal boundary conditions are applied, which are shown in Fig. 1. In the following, these two different cases are treated separately [14]: insulated
qw
ro
Flow
ri
r z
qw
insulated
(a) Case A
(b) Case B
Figure 1. Schematic of the problem [14].
For the Case A, the dimensionless temperature distribution is obtained as follows [14]:
O. AYDIN AND M. AVCI
6
θ (R) =
T − Ts qw′′ ro / k
*2 2 *2 2 a ⎛⎜ −3 − A + 2rm + R (1 + A − 2rm + R / 2) ⎞⎟ = ⎟ 2B ⎜ − ln R (1 + 2 A − 2rm*2 (1 + ln R ) ) ⎝ ⎠ Br 2 + 2 (1 − R2 )(1 + R2 − 8rm*2 ) + 4ln R (1 − 4rm*2 ) − 8rm*4 ( ln R ) + ln R B
(
where a=
(11)
)
−2 B 2 r * + 8Br ( r *2 − 1)(1 − 4rm*2 + r *2 ) + 32 Br rm*4 ln ( r * )
(
B (1 + 2 A − 2rm*2 − r *2 )( r *2 − 1) + 4 rm*2 r *2 ln ( r * )
)
(12)
and Br =
μ um2
(13)
qw′′ ro
Similarly, the dimensionless temperature distribution is obtained for the Case B as in the following [14]: θ ( R) =
T − Ts qw′′ ro / k
2 *2 *2 2 *2 * *2 a ⎛⎜ ( R − r )(1 + A − 2rm ) − ( R − r ) − ( ln R − ln r )(1 + 2 A − 2rm ) ⎞⎟ = ⎟ 2 B ⎜ +2rm*2 ( R 2 ln R − r *2 ln r * ) ⎝ ⎠ ⎛ ( R 2 − r *2 ) 8rm*2 − ( R 2 + r *2 ) + 4 ( ln R − ln r * )(1 − 4rm*2 ) ⎞ Br ⎜ ⎟ + 2⎜ ⎟ B ⎜ −8r *4 ( ln R )2 − ( ln r * )2 ⎟ ⎝ m ⎠
(
(
)
(14)
)
where a=
−2 B 2 r * + 8Br ( r *2 − 1)(1 − 4rm*2 + r *2 ) + 32 Br rm*4 ln ( r * )
(
B (1 + 2 A − 2rm*2 − r *2 )( r *2 − 1) + 4 rm*2 r *2 ln ( r * )
)
(15)
After performing necessary substitutions, the Nusselt number is obtained as follows [14]:
CONVECTIVE HEAT TRANSFER CORRELATIONS Nu =
7
qw Dh 2 = − * (1 − r * ) (Tw − Tm ) k θ m
(16)
2.4. MIXED CONVECTION IN A VERTICAL PARALLEL-PLATE MICROCHANNEL WITH SYMMETRIC WALL HEAT FLUXES
For this problem under the above mentioned assumptions, therefore, the dimensionless velocity profile is obtained as [15]:
U = C1eξ Y cos(ξ Y ) + C2 e−ξ Y cos(ξ Y ) + C3 eξ Y sin(ξ Y ) + C4 e−ξ Y sin(ξ Y )
(17)
where 1/ 4
⎡ Gr ⎤ ξ =⎢ qU⎥ ⎣ Re ⎦
(18)
By applying the boundary conditions given in Eq. (10), the four unknown constants C1, C2, C3 and C4 can be obtained. Some typical values of these constants for different values of Grq/Re and Kn are tabulated in Table 1. TABLE 1. Typical values of constants C1, C2, C3, and C4 [15].
Grq/Re 1
50
100
Kn 0.00 0.02 0.06 0.10 0.00 0.02 0.06 0.10 0.00 0.02 0.06 0.10
C1 2.87634 2.39220 1.82928 1.51201 0.82091 0.69563 0.55026 0.46847 0.59553 0.50312 0.39610 0.33599
C2 −2.87634 −2.19857 −1.41051 −0.96634 −0.82091 −0.49796 −0.12322 0.08763 −0.59553 −0.30136 0.03930 0.23064
C3 −8.90402 −7.16036 −5.13293 −3.99024 −0.42563 −0.30682 −0.16895 −0.09137 −0.11637 −0.05680 0.01218 0.05093
C4 15.15670 12.25113 8.87272 6.96858 3.39702 2.82999 2.17201 1.80179 2.88858 2.44242 1.92576 1.63556
After several steps of derivations, the Nusselt numbers is obtained as [15]: Nu1 = −
1
θ m*
(19)
O. AYDIN AND M. AVCI
8
where 0.5
T −T θ = m 1 = ( q Dh / k ) * m
∫ Uθ
*
dY
0 0.5
(20)
∫ UdY 0
and θ* = =
(T − Ts ,1 ) (Ts ,1 − T1 ) T − T1 = + q2 Dh / k q2 Dh / k q2 Dh / k
(
Re 2ξ 2 e −ξ Y ( (C4 − C3 )eξ Y + (C3e 2ξ Y − C4 ) cos(ξ Y ) + (C2 − C1e 2ξ Y )sin(ξ Y ) ) Grq
)
(21)
− β t Kn(q1 / q2 )
3. Results and Discussion
Here, only summary results are given for three different geometries considered separately. 3.1. FORCED CONVECTION IN A MICROPIPE
Figure 1 shows the variation of the Nusselt number with the Knudsen number for different values of the modified Brinkman number. For Brq = 0, an increase at Kn decreases Nu due to the temperature jump at the wall. Viscous dissipation, as an energy source, severely distorts the temperature profile. Positive values of Brq correspond to wall heating (heat is being supplied across the walls into the fluid) case (qw > 0), while the opposite is true for negative values of Brq. In the absence of viscous dissipation the solution is independent of whether there is wall heating or cooling. However, viscous dissipation always contributes to internal heating of the fluid, hence the solution will differ according to the process taking place. Nu decreases with increasing Brq for the hot wall (i.e. the wall heating case). As expected, increasing dissipation increases the bulk temperature of the fluid due to internal heating of the fluid. For the wall heating case, this increase in the fluid temperature decreases the temperature difference between the wall and the bulk fluid, which is followed with a decrease in heat transfer. When wall cooling is applied, due to the internal heating effect of the viscous dissipation on the fluid temperature profile, temperature difference is increased with the increasing Brq (Fig. 2). For more details, readers are referred to Ref. [12].
CONVECTIVE HEAT TRANSFER CORRELATIONS
9
8
7
Br q -----------0.1 -0.01 0.0 0.01 0.1
Pr=0.7
Nu
6
5
4
3
2 0,00
0,02
0,04
0,06
0,08
0,10
Kn
Figure 2. The variation of Nu with Kn at different values of Brq [12].
3.2. FORCED CONVECTION IN A MICROCHANNEL BETWEEN TWO PARALLEL PLATES
For this geometry, Fig. 3 illustrates the variation of the Nusselt number with the Knudsen number for different values Brinkman numbers. As seen, an increase at Kn decreases Nu due to the temperature jump at the wall. The effect of the viscous dissipation is discussed above. For more details, readers are referred to Ref. [13]. 5,6 5,2
Br q -------------
Pr=0.7 4,8
-0.1 -0.01 0.0 0.01 0.1
4,4
Nu
4,0 3,6 3,2 2,8 2,4 2,0 0,00
0,02
0,04
0,06
0,08
0,10
Kn
Figure 3. The variation of Nu with Kn at different values of Brq [13].
10
O. AYDIN AND M. AVCI
3.3. FORCED CONVECTION IN A MICROANNULUS BETWEEN TWO CONCENTRIC CYLINDERS
Figure 4 illustrates the variation of the Nusselt number with the aspect ratio of the annulus, r* for different values of the Knudsen number at Cases A and B without viscous dissipation (Br = 0), respectively. For the both cases, the influence of the increasing Kn is to decrease the heat transfer rates. As expected, for the Case A, an increase in r* increases Nu, while it decreases Nu for the Case B. However, this Nu-dependence on r* becomes negligible with increasing Kn. The variation of the Nusselt number with the Knudsen number for different values of the Brinkman number at r* = 0.2 for Cases A and B, respectively, is shown in Fig. 5. An increase at Kn decreases the Nu due to the temperature jump at the wall. Nu decreases with increasing Br for the hot wall (i.e. the wall heating case). For this case, the wall temperature is greater than that of the bulk fluid. Viscous dissipation increases the bulk fluid temperature especially near the wall since the highest shear rate occurs in this region. Hence, it decreases the temperature difference between the wall and the bulk fluid, which is the main driving mechanism for the heat transfer from wall to fluid. However, for the cold wall (i.e. the wall cooling case), the viscous dissipation increases the temperature differences between the wall and the bulk fluid by increasing the fluid temperature more. Therefore, increasing Br in the negative direction increases Nu. As seen from the figure, the behavior of Nu versus Kn for lower values of the Brinkman number, either in the case of wall heating (Br = 0.01) or in the case of the wall cooling (Br = −0.01) is very similar to that of Br = 0. In addition, as observed from the figure, Br is more effective on Nu for lower values of Kn than for higher values of Kn. For more details, readers are referred to Ref. [14]. 3.4. MIXED CONVECTION IN A VERTICAL PARALLEL-PLATE MICROCHANNEL WITH SYMMETRIC WALL HEAT FLUXES
For this problem, the variation of Nu with Grq/Re is plotted for different values of Kn in Fig. 6. As expected, increasing Grq/Re increases Nu while increasing Kn decreases Nu. Because of the lower values of the Grq/Re present at microscale, the aiding effect of the buoyancy forces on the inertia forces are not much. Therefore, increasing Grq/Re in this limited range will not have a profound effect on Nu. For example, at Kn = 0.02, increasing Grq/Re from 1 to 200 will lead to an increase of about 2% in Nu. For more details, readers are referred to Ref. [15].
CONVECTIVE HEAT TRANSFER CORRELATIONS
11
6 Br = 0.00 Pr = 0.71
5
Kn = 0.00
Nu
Kn = 0.02
4
Kn = 0.04 Kn = 0.06 Kn = 0.08
3
2 0.2
Kn = 0.10
0.3
0.4
0.5
0.6
0.7
0.8
r*
(a)
10 Br = 0.00 Pr = 0.71
8
Nu
Kn = 0.00
6 Kn = 0.02 Kn = 0.04
4
Kn = 0.06 Kn = 0.08 Kn = 0.10
2 0.2
0.3
0.4
0.5 r
0.6
0.7
0.8
*
(b) Figure 4. The variation of Nu with r* at different values of Kn for Br = 0.0, (a) Case A, (b) Case B.
O. AYDIN AND M. AVCI
12
7 Br = -0.10 Br = -0.01 Br = 0.00 Br = 0.01 Br = 0.10
6
5 Nu
r* = 0.2 Pr = 0.71
4
3
2 0.00
0.02
0.04
0.06
0.08
0.10
Kn
(a) 16 Br = -0.10 Br = -0.01 Br = 0.00 Br = 0.01 Br = 0.10
14 12
r* = 0.2 Pr = 0.71
Nu
10 8 6 4 2 0.00
0.02
0.04
0.06
0.08
0.10
Kn
(b) Figure 5. The variation of Nu with Kn at different values of Br for r* = 0.2, 0.5 and 0.8, (a) Case A, (b) Case B.
CONVECTIVE HEAT TRANSFER CORRELATIONS
13
9 Kn = 0.00
8
Nu (Nu1=Nu2)
7
Kn = 0.02
6
Kn = 0.04
5
Kn = 0.06 Kn = 0.08
4
Kn = 0.10
Pr = 0.7 rq = 1.0
3 0
50
100
150
200
Grq / Re
Figure 6. The variation of the Nu with the Grq/Re at different values of Kn.
Acknowledgment
The first author of this work is indebted to the Turkish Academy of Sciences (TUBA) for the financial support provided under the Programme to Reward Success Young Scientists (TUBA-GEBIT).
References 1. Gad-el-Hak, M., Flow physics in MEMS, Mec. Ind., vol. 2, pp. 313–341, 2001. 2. Palm, B., Heat transfer in microchannels, Microscale Thermophysical Engineering, vol. 5, pp. 155–175, 2001. 3. Ho, C.M. and Tai, C.Y., Micro-electro-mechanical systems (MEMS) and fluid flows, Annu. Rev. Fluid Mech., Vol. 30, pp. 579–612, 1998. 4. Sobhan, C.B. and Garimella, S.V., A comparative analysis of studies on heat transfer and fluid flow in microchannels, Microscale Thermophysical Engineering, vol. 5, 293–311, 2001. 5. Obot, N.T., Toward a better understanding of friction and heat/mass transfer in microchannels-A literature review, Microscale Thermophysical Engineering, vol. 6, pp. 155–173, 2002. 6. Rostami, A.A., Saniei, N. and Mujumdar, A.S., Liquid flow and heat transfer in microchannels: A review, Heat Technol., Vol. 18, pp. 59–68, 2000. 7. Rostami, A.A., Mujumdar, A.S. and Saniei, N., Flow and heat transfer for gas flowing in microchannels: A review, Heat Mass Transfer, vol. 38, pp. 359– 367, 2002.
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O. AYDIN AND M. AVCI
8. Guo, Z.Y. and Li, Z.X., Size effect on microscale single-phase flow and heat transfer, International Journal of Heat and Mass Transfer, vol. 46, pp. 59– 149, 2003. 9. Guo, Z.Y. and Li, Z.X., Size effect on single-phase channel flow and heat transfer at microscale, International Journal of Heat and Fluid Flow, vol. 24 (3), pp. 284–298, 2003. 10. Morini, G.L., Single-phase convective heat transfer in microchannels: a review of experimental results, International Journal of Thermal Sciences, vol. 43, pp. 631–651, 2004. 11. Beskok, A. and Karniadakis, G.E., Simulation of heat and momentum transfer in complex micro-geometries, J. Thermophysics Heat Transfer, vol. 8, pp. 355–370, 1994. 12. Aydın, O. and Avcı, M., Heat and Fluid Flow Characteristics of Gases in Micropipes, Int. J. Heat Mass Transfer, vol. 49, pp. 1723–1730, 2006. 13. Aydın, O. and Avcı, M., Analysis of Laminar Heat Transfer in MicroPoiseuille Flow, Int. J. Thermal Sci., vol. 46, pp. 30–37, 2007. 14. Avcı, M. and Aydın, O., Laminar forced convection slip flow in a micro-annulus between two concentric cylinders, Int. J. Heat and Mass Transfer, vol. 51, pp. 3460–3467, 2008. 15. Avcı, M. and Aydın, O., Mixed convection in a vertical parallel-plate microchannel with asymmetric wall heat fluxes, J. Heat Transfer, vol. 129, pp. 1091–1095, 2007.
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW A. GUVENC YAZICIOGLU1 AND S. KAKAÇ2 1
Orta Doğu Teknik Üniversitesi, Makine Mühendisliği Bölümü, Ankara, 06531 Turkey,
[email protected] 2 TOBB Ekonomi ve Teknoloji Üniversitesi, Makine Mühendisliği Bölümü, Söğütözü Cad.No:43, Söğütözü, Ankara, 06560 Turkey
Abstract. In this lecture, steady-state convective heat transfer in different microchannels (microtube and parallel plates) will be presented in the slip flow regime. Laminar, thermally and/or hydrodynamically developing flows will be considered. In the analyses, in addition to rarefaction, axial conduction, and viscous dissipation effects, which are generally neglected in macroscale problems, surface roughness effects, and temperature-variable thermophysical properties of the fluid will also be taken into consideration. Navier–Stokes and energy equations will be solved and the variation of Nusselt number, the dimensionless parameter for convection heat transfer, along the channels will be presented in tabular and graphical forms as a function of Knudsen, Peclet, and Brinkman numbers, which represent the effects of rarefaction, axial conduction, and viscous dissipation, respectively. The results will be compared and verified with available experimental, analytical, and numerical solutions in literature.
1. Introduction Devices having the dimensions of microns have been used in many fields such as; biomedicine, diagnostics, chemistry, electronics, automotive industry, space industry, and fuel cells, to name a few. With the increase of integrated circuit density and power dissipation of electronic devices, it is becoming more necessary to employ effective cooling devices and cooling methods to maintain the operating temperature of electronic components at a safe level. Especially when device dimensions get smaller, overheating of microelectronic components may be a serious issue. Microchannel heat sinks, with hydraulic diameters ranging from 10 to 1,000 μm, appear to be the ultimate solution for removing these high amounts of heat. This pressing requirement of cooling of electronic devices has initiated extensive research in microchannel heat transfer. Many analytical and experimental studies have been performed to have a better understanding of heat transfer at the S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_2, © Springer Science + Business Media B.V. 2010
15
16
A. GUVENC YAZICIOGLU AND S. KAKAÇ
microscale. Both liquids and gases have been investigated. However, none of them has been able to come to a general conclusion. For example, there are controversial results in the literature about the boundary conditions, for liquids flows. It is not clear whether discontinuity of velocity and temperature exists on the wall or not. The pioneering conclusion drawn by Tuckerman and Pease in 1982 [1] that the heat transfer coefficient for laminar flow through microchannels may be greater than that for turbulent flow, accelerated research in this area. Many experimental [2–6], numerical [7–10], and analytical [11–14] studies have been performed, with some focusing on the effects of roughness [15–21] and temperature-variable thermophysical properties of the fluid [22–26]. Some of these works have been compiled in review articles such as those by Gad-El-Hak [27], Morini [28], Bayazitoglu [29], Hetsroni [30], Yener [31], Cotta [32], and Rosa [33]. The reader is also referred to excellent books by Karniadakis [34], Sobhan [35], and Yarin [36]. Several conflicting results may be drawn from the above-mentioned studies. First, some investigators reported laminar fully-developed friction factors and Poiseuille numbers lower than the conventional values, some reported higher values, while others reported agreement with conventional values. Another conflict occurs in laminar to turbulent transition Re values, varying between 3,000 and 6,000. A similar conclusion can be made about the laminar regime Nusselt number (Nu = hD/k, h being the convection heat transfer coefficient, and D the hydraulic diameter) and the effect of energy dissipation on heat transfer. However, it should also be noted that as the precision and reliability of the experimental set-ups and measurement devices increase, the deviation margin of theoretical and experimental results obtained from similar experiments conducted by different investigators reduces. In any case, future research is still needed for fundamental understanding, as pointed out in Refs. [28–33, 37, 38]. 2. General Considerations For the effective and economical design of microchannel heat sinks, some key design parameters should be considered and optimized. These are, the pressure required for pumping the cooling fluid, the mass flow rate of the cooling fluid, the hydraulic diameter of the channels, the temperature of the fluid and the channel wall, and the number of channels. In order to understand the effect of these parameters on the system, the dynamic behavior and heat transfer characteristics of fluids at the microscale must be well-understood. There are two major approaches to modeling fluid flow at the microscale: In the first model, the molecular model, the fluid is assumed to be a collection of molecules whereas in the second model, the continuum model, the fluid
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW
17
is assumed to be continuous and indefinitely divisible. In macroscale flows, the continuum approach is generally accepted. The velocity, density, pressure, etc., for the fluid are defined at every point and time in space. Conservation of mass, momentum, and energy are applied and a set of nonlinear partial differential equations (Navier–Stokes and energy equations) are obtained. These equations are solved to obtain the fluid flow and heat transfer characteristic parameters at the macroscale. However as the dimensions of the channels get smaller, the continuum assumption starts to break. For microscale slip flow regime, the continuum approach is still valid, and Navier–Stokes and energy equations may still be used, but with a modification of boundary conditions. One important dimensionless parameter characterizing the flow regime is the Knudsen number (Kn). Knudsen number, which signifies the degree of rarefaction in the flow and the degree of validity of the continuum model, is defined as the ratio of the mean free path of the molecules, λ, to the characteristic length, L (Kn = λ/L). The different Kn regimes are determined empirically and are therefore only approximate for a particular flow geometry. For example, for gases, below L ≈ 100 nm, the rarefaction effect seems to be significant, while for liquids, below L ≈ 0.3 nm, the interfacial electro-kinetic effects near the solid–liquid interface become important. In general, the following is a commonly used scale for Kn to differentiate flow regimes [34]: Kn < 0.001 0.001 < Kn < 0.1 0.1 < Kn < 10 Kn > 10
Continuum flow Slip-flow (slightly rarefied) Transition flow (moderately rarefied) Free-molecular flow (highly rarefied)
When the flow is in the higher Kn regime (transition and free-molecular), a molecular approach, such as direct simulation Monte Carlo method using the Boltzmann equation should be employed. For L λ, the continuum approach will be applicable with traditional no-slip, no-temperature jump boundary conditions. However as this condition is violated, the linear relation between stress and the rate of strain, thus the no-slip velocity condition will not be valid. Similarly, the linear relation between heat flux and temperature gradient, thus the no-temperature jump condition at the solid–fluid interface will no longer be accurate [39]. The fluid and solid particles cannot retain thermodynamic equilibrium at the surface, thus the fluid molecules close to the surface do not have the velocity and temperature of the surface. Therefore, the slip-flow regime may be modeled with classical Navier–Stokes and energy equations by making some modifications in the boundary conditions for velocity and temperature at the wall, because the rarefaction effect is not small enough to be negligible in the slip-flow regime. As a result, fluid molecules at the wall will have finite slip-velocity and temperature-jump at
18
A. GUVENC YAZICIOGLU AND S. KAKAÇ
the wall. These modified conditions depend on the Kn value, some thermophysical properties of the fluid, and accommodation factors. Besides the Knudsen number, some other dimensionless parameters become important in microscale flow and heat transfer problems. The first such number is the Peclet number (Pe), which is the product of Reynolds (Re) and Prandtl (Pr) numbers (Pe = Re·Pr), and signifies the ratio of rates of advection to diffusion. Peclet number enumerates the axial conduction effect in flow. In macro-sized conduits, Pe is generally large and the effect of axial conduction may be neglected. However as the channel dimensions get smaller, it may become important. Brinkman number is the dimensionless parameter representing the relative importance of heat generated by viscous dissipation (work done against viscous shear) to heat transferred by fluid conduction across the microchannel cross-section in the flow. Its definition varies with the boundary condition at the wall. For example, for constant wall temperature, Br = μum2/kΔT and for constant wall heat flux, Br = μum2/qwR, where μ is the fluid dynamic viscosity, um is the mean flow velocity, k is the fluid thermal conductivity, ΔT is the fluid inlet-to-wall temperature difference, R is the hydraulic radius of the channel, and qw is the wall heat flux. Br is usually neglected in lowspeed and low-viscosity flows through conventionally-sized channels of short lengths. However in flows through conventionally-sized long pipelines, Br may become important. For flows in microchannels, the length-to-diameter ratio can be as large as for flows through conventionally-sized long pipelines, thus Br may become important in microchannels as well. In this lecture, the effects of the abovementioned dimensionless parameters, namely, Knudsen, Peclet, and Brinkman numbers representing rarefaction, axial conduction, and viscous dissipation, respectively, will be analyzed on forced convection heat transfer in microchannel gaseous slip flow under constant wall temperature and constant wall heat flux boundary conditions. Nusselt number will be used as the dimensionless convection heat transfer coefficient. A majority of the results will be presented as the variation of Nusselt number along the channel for various Kn, Pe, and Br values. The lecture is divided into three major sections for convective heat transfer in microscale slip flow. First, the principal results for microtubes will be presented. Then, the effect of roughness on the microchannel wall on heat transfer will be explained. Finally, the variation of the thermophysical properties of the fluid will be considered. 3. Microtubes The geometry of the problem for microtubes is shown in Fig. 1. Steadystate, two-dimensional, incompressible, laminar, and single-phase gas flow is considered. An unheated section is provided, where the velocity profile
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW
19
develops. As mentioned before, in the slip flow regime, slip-velocity and temperature-jump boundary conditions should be applied to the momentum and energy equations. These are:
us = −
2 − Fm ⎛ du ⎞ λ⎜ ⎟ Fm ⎝ dr ⎠ r = R
Ts − Tw = −
(1)
2 − Ft 2γ λ ⎛ ∂T ⎞ ⎜ ⎟ Ft γ + 1 Pr ⎝ ∂r ⎠ r = R
Velocity entrance length
(2)
Tw or qw = constant u (η,Kn) R
r x
Tw or qw = constant Figure 1. The problem geometry for microtubes.
In Eq. (1), Fm is the momentum accommodation factor and has a value close to unity for the gas–solid couples used most commonly in engineering, and is also taken so in this work. In Eq. (2), Ts is the temperature of the fluid molecules at the wall, Tw is the wall temperature, γ is the ratio of the specific heats of the fluid, and Ft is the thermal accommodation factor. Ft may take a value in the range 0.0–1.0, depending on the gas and solid surface, the gas temperature and pressure, the temperature difference between the gas and the surface, and is determined experimentally. Using the slip-velocity boundary condition, the fully developed velocity profile may be written as [40]
(
)
u 2 1 − η2 + 8Kn = , um 1 + 8Kn
(3)
where η = r/R is the nondimensional radial coordinate. Figure 2 presents the variation of the nondimensional velocity along the radial distance as a function of rarefaction in the flow. As can be observed therein, for continuum (Kn = 0), the no-slip velocity is present at the wall while as the degree of rarefaction increases, so does the slip velocity at the wall [41].
A. GUVENC YAZICIOGLU AND S. KAKAÇ
20
3.1. CONSTANT WALL TEMPERATURE
For this boundary condition, the nondimensional energy equation and the boundary conditions for the flow inside a microtube, including axial conduction and viscous dissipation are
Dimensionless Radius (η= r/R)
1,0
Kn=0(continuum) Kn=0.02 Kn=0.04 0,5
Kn=0.06 Kn=0.08 Kn=0.10 0,0 0,0
0,5
1,0
1,5
2,0
Dimensionless Velocity (u/um)
Figure 2. Velocity profile variation with Kn along the radial direction. 2
⎛ ∂u * ⎞ u * ∂θ 1 ∂ ⎛ ∂θ ⎞ 1 ∂2θ ⎟⎟ , = ⎜⎜ η ⎟⎟ + 2 2 + Br ⎜⎜ 2 ∂ξ η ∂η ⎝ ∂η ⎠ Pe ∂ξ ⎝ ∂η ⎠
η = 0,
∂θ = 0, ∂η
⎛ ∂θ ⎞ η = 1, θ = −2κKn⎜⎜ ⎟⎟ , ⎝ ∂η ⎠ η=1 ξ = 0, θ = 1 .
(4)
(5) (6) (7)
In Eqs. (4–7), the following parameters have been used for nondimensionalization: T − Tw μu 2m x r u θ= , Br = , ξ= , η = , u* = , (8) Ti − Tw k (Ti − Tw ) PeR R um
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW
21
and κ is a parameter that accounts for temperature jump at the wall as κ=
2 − Ft 2 γ 1 . Ft γ + 1 Pr
(9)
The energy equation has been solved numerically [40] and analytically, using general Eigen functions expansion [42], and the details can be found in related references. Using the temperature distribution, the local Nusselt number may be determined as
Nu x =
hxD =− k
2
∂θ ∂η η=1
4 γ Kn ∂θ θm − γ + 1 Pr ∂η η=1
,
(10)
where θm is the nondimensional mean temperature defined by 1
∫
θ m (ξ) = 2 u * θ( η, ξ)ηdη .
(11)
0
3.2. CONSTANT WALL HEAT FLUX
In this case, the nondimensional energy equation and the boundary conditions become [40],
(
)
Gz 1 − η2 + 4 Kn ∂θ 1 ∂ ⎛ ∂θ ⎞ 1 ∂ 2θ 32 Br = η2 , ⎜⎜ η ⎟⎟ + 2 2 + 2(1 + 8Kn ) ∂ζ η ∂η ⎝ ∂η ⎠ Pe ∂ζ (1 + 8Kn )2 ∂θ η = 0, = 0, ∂η ∂θ η = 1, = 1, ∂η ξ = 0, θ = 1 .
(12) (13) (14) (15)
A. GUVENC YAZICIOGLU AND S. KAKAÇ
22
In Eqs. (12–15) the following additional parameters have been used for non-dimensionalization: θ=
k (T − Ti ) μu 2 2R , Br = m , Gz = Re Pr , qwR qwD L
(16)
The temperature profile is determined numerically, and using the temperature distribution, local Nusselt number may be determined as [40], Nu x =
hxD =− k
2 θs +
4 γ Kn − θm γ + 1 Pr
,
(17)
where θs is the nondimensional temperature of the fluid at the surface. 3.3. RESULTS
In this section, the results will be presented in tabular and graphical forms, for Nusselt number for both constant wall temperature and constant wall heat flux cases with variable Kn, Br, Pe values to investigate the effects of rarefaction, viscous dissipation, and axial conduction in the slip-flow regime for microtubes. Table 1 presents the effect of rarefaction on laminar flow fully developed Nu values for constant wall temperature (NuT) and constant wall heat flux (Nuq) cases, where viscous dissipation and axial TABLE 1. Laminar flow fully-developed Nu values for the present work for constant wall temperature (NuT) and constant wall heat flux (Nuq) cases, compared with analytical results from Ref. [43] (Pr = 0.6).
Kn
NuT [43]
NuT
Nuq [43]
Nuq
0.00
3.6751
3.6566
4.3627
4.3649
0.02
3.3675
3.3527
3.9801
4.0205
0.04 0.06 0.08 0.10
3.0745 2.8101 2.5767 2.3723
3.0627 2.8006 2.5689 2.3659
3.5984 3.2519 2.9487 2.6868
3.6548 3.3126 3.0081 2.7425
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW
23
conduction effects have been neglected. The table serves as a verification of the solution procedure, as comparisons with analytical solutions from literature [43] are also provided. To observe the effect of viscous dissipation on heat transfer, in Table 2, the fully developed Nusselt number is presented for constant wall temperature and constant wall heat flux cases with and without viscous dissipation. For all cases, the fully developed Nusselt number decreases as Kn increases. For Tw = constant, for the no-slip condition (Kn = 0), when Br = 0.01, Nu = 9.5985, while it drops down to 3.8227 for Kn = 0.1, a decrease of 60.2%. Similarly for qw = constant, for the no-slip condition, when Br = 0.01, Nu = 4.1825, while it drops down to 2.9450 for Kn = 0.1, with a decrease of 29.6%. This is due to the fact that the temperature jump, which increases with increasing rarefaction, reduces heat transfer, as can be observed from Eqs. (10) and (17). A negative Br value for the constant wall heat flux condition refers to the fluid being cooled, therefore Nu takes higher values for Br < 0 and lower values for Br > 0 compared with those for no viscous heating. TABLE 2. Laminar flow fully-developed Nu with and without viscous dissipation for Tw = constant and qw = constant cases (Pr = 0.7).
Kn 0.00 0.02 0.04 0.06 0.08 0.10
Tw = constant Br = 0.00 Br = 0.01 3.6566 9.5985 3.4163 7.4270 3.1706 6.0313 2.9377 5.0651 2.7244 4.3594 2.5323 3.8227
qw = constant Br = 0.00 4.3649 4.1088 3.8036 3.4992 3.2163 2.9616
Br = 0.01 4.1825 4.0022 3.7398 3.4598 3.1912 2.9450
Br = −0.01 4.5640 4.2212 3.8695 3.5395 3.2419 2.9784
In Fig. 3, the variation of local Nusselt number along the constant wall temperature tube is presented as a function of Peclet number, representing axial conduction in the fluid. For Pe = 50, which represents a case with negligible axial conduction, the solution of the classical Graetz problem, Nu = 3.66, is reached [44], while for Pe = 1, Nu = 4.03 [45] is obtained as the fully developed values of Nu. The temperature gradient at the wall decreases at low Pe values, thus the local and fully developed Nu values increase with decreasing Pe.
A. GUVENC YAZICIOGLU AND S. KAKAÇ
24 10
Kn = 0, Br = 0
Local Nu
8
Decreasing Pe (50, 10, 5, 1)
6
4.03 3.66
4
2 0.01
0.1
1.0
10
x = x / (R Pe) Figure 3. Variation of local Nu with Pe when Kn = 0 and Br = 0.
Figure 4 presents the local Nusselt number variation along the microtube for the constant wall temperature boundary condition for cases where both viscous dissipation and axial conduction effects have been considered. A positive Br for this boundary condition refers to the fluid being cooled as it flows along the tube. Local Nu value first decreases due to temperature jump at the wall, then increases to its fully-developed value because of the heating due to the viscous dissipation effect. Before the increase, the values of local Nu match those for the Br = 0 case presented in Fig. 3 [10, 42]. However, because of the definition of Pe, local Nu curves deviate from those for Br = 0 as the minima are approached. This effect results in the overall increase in the average Nu in the tube, thus we can conclude that average Nu increases as the effect of axial conduction is more prominent. Also, the amount of viscous dissipation does not affect the fully developed Nu value.
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW
25
Figure 4. Variation of local Nu with Pe when viscous dissipation is present (Br > 0, Kn = 0).
When the fluid is being heated along the tube, i.e., the fluid inlet temperature is less than that of the wall, for the constant wall temperature case, Br is negative and the local Nu variation is as shown in Fig. 5. As can be observed therein, local Nu reaches an asymptotic value when the fluid temperature is equal to the wall temperature, when viscous dissipation and axial conduction are included. Thermal development continues after this point, and the fully developed Nu is reached. Similar to positive Br cases, the amount of viscous dissipation effects the location where the sudden change in local Nu occurs, but the fully developed Nu is the same for all non-zero Br values. Table 3 summarizes a majority of the results for fully developed Nu for slip-flow in microtubes presented in this section for constant wall temperature boundary condition, and provides comparisons with available results from literature. Here, κ = 0 refers to no temperature jump while κ = 1.667 refers to temperature jump for air flow. The present results show excellent agreement with literature.
A. GUVENC YAZICIOGLU AND S. KAKAÇ
26 20
Br = - 0.1 Br = - 0.01
Decreasing Pe (10, 5, 2, 1)
Local Nu
15
10
Decreasing Pe (10, 5, 2, 1)
9.60
5
Br = 0, Pe Æ •
3.66
Kn = 0
0 0.01
0.1
1.0
10
x = x / (R Pe) Figure 5. Variation of local Nu with Pe when viscous dissipation is present (Br < 0, Kn = 0). TABLE 3. Comparison of fully developed Nu with results from literature.
Kappa (κ) 0 1.667 0 1.667 0 1.667
Pe = 1.0 Nu* Nu 4.028 4.030 4.028 4.030 4.358 – 3.604 – 4.585 – 3.093 –
Pe = 5.0 Nu Nu** 3.767 3.767 3.767 3.767 4.131 – 3.387 – 4.386 – 2.949 –
Nu: Present results Nu*: Results from Ref. [45]
Pe = 10 Nu Nu* 3.695 3.697 3.695 3.697 4.061 – 3.325 – 4.319 – 2.909 –
Pe → ∞ Nu Nu*** 3.656 3.656 3.656 3.656 4.020 4.020 3.292 3.292 4.279 4.279 2.887 2.887
Kn 0.00 0.04 0.08
Nu**: Results from Ref. [46] Nu***: Results from Ref. [9]
4. Roughness Effect
The effect of surface roughness may be particularly important in microchannel flows. Roughness characteristics of microchannels are strictly dependent on the manufacturing process. Since the random distribution and small size of the roughness peaks along a surface are quite difficult to define, most investigators neglect this effect in their studies. There is a limited number of publications in open literature compared to other effects in microscale. In one of the first experimental studies in this area water flow through rough
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW
27
fused silica and stainless steel microtubes was investigated, and deviations from theoretical predictions; such as higher friction factor, and early transition from laminar to turbulent flow, were found [15]. Later, heat transfer characteristics were also investigated and due to the surface roughness effect, smaller Nu values were determined [47]. Different models were proposed to represent the effects of surface roughness; such as roughness-viscosity model [15], porous medium layer model [48], and the explicit model [17, 18]. Roughness can reduce or increase Nu depending on the distribution, spacing, and geometry of the obstructions. However one common conclusion is that roughness is more effective at low Kn values. In this case, steady-state, laminar, developing air flow in a parallel-plate microchannel with one rough wall is considered. As shown in the channel schematic in Fig. 6, the roughness is modeled as two-dimensional equilateral triangular elements placed on the bottom wall surface. The relative surface roughness of the wall may be determined by ε = e/D, where e is the height of the roughness elements and D the hydraulic diameter of the channel. In most of the studies in literature, it is stated that silicon microchannels generally have a relative roughness value in the range 0–4%. Thus, in this work, ε = 1.325%, 2.0% are considered [49, 50]. Solid smooth wall, Tw = T u=Ui v=0 T=Ti
H=D/2
y x
e Solid rough wall, Tw = T
Figure 6. Schematic of the rough microchannel.
The equations to be solved are similar to those in the previous section with some minor differences due the change in geometry (parallel-plate microchannel versus microtube). In the solution, slip boundary conditions given in Eqs. (1) and (2) are applied and finite element method is used to solve for the velocity profile and the temperature distribution. Then, from the temperature profile, the local Nu is determined. For the continuum case (Kn = 0), without viscous dissipation, local Nu has a wavy pattern, as shown in Fig. 7, similar to the observations in Refs. [17, 20] for triangular roughness elements. Velocity and temperature gradients are higher at the peaks of the elements, thus local Nu is larger there, while at the bottom corners, the low gradients result in minimum local Nu.
A. GUVENC YAZICIOGLU AND S. KAKAÇ
28 25
Local Nu
20
(a)
smooth e = 1.325%
15 10 5 0 1.9 25
Local Nu
20
1.95
2 x
2.05
2.1
smooth e = 2.0%
(b)
15 10 5 0
1.9
1.95
2
x
2.05
2.1
2.15
Figure 7. Local Nu variation over the roughness elements for Kn = 0, Re = 100 and Br = 0 when (a) ε = 1.325%, (b) ε = 2.0%.
Graphical results are presented in Fig. 8 for the channel averaged Nu (including smooth inlet–outlet sections), including axial conduction and viscous dissipation (Br = 0.1). Without the rarefaction effect, roughness reduces heat transfer. However, with the rarefaction effect, an increase in the average Nu with respect to smooth channel values is observed. Due to the reduced interaction between the gas molecules and channel walls at high Kn values, the increase is less pronounced at high Kn values and more at low Kn values. Moreover, when rarefaction is considered, the average Nu values increase with increasing Pe and relative surface roughness height. In Table 4, average Nu values for the rough section of the channel (representing a channel with a completely rough wall from the inlet to the outlet) are presented for cases where axial conduction and viscous dissipation (Br = 0.1) are both included, compared to smooth channel values. For this case, average Nu takes higher values, except Kn = 0 cases, where the reduction in local Nu between roughness elements is dominant and cannot be compensated by the higher local Nu computed at the other parts of the channel. The
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW
29
general trend is similar to the channel averaged cases presented in Fig. 8; at low Kn, the effect of surface roughness is more prominent and average Nu increases with increasing roughness height. As the flow becomes more rarefied, the importance of relative surface roughness height is reduced and yields nearly the same average Nu values for the considered relative roughness heights. 25 21
21
19
19
17
17
15 13 11 9
smooth e = 1.325% e = 2.0%
23
Nu
Nu
25
smooth e = 1.325% e = 2.0%
23
15 13 11
Pe = 3.5 Br = 0.1
7 0.00
0.02
9 7 0.04
0.06
0.08
0.10
Pe = 70 Br = 0.1 0.00
0.02
Kn
0.04
0.06
0.08
0.10
Kn
Figure 8. Channel averaged Nu compared with fully developed smooth channel values when axial conduction and viscous dissipation (Br = 0.1) are included. TABLE 4. Rough section averaged Nu compared with fully developed smooth channel values when axial conduction and viscous dissipation are included (Br = 0.1).
17.484 13.680 16.450 12.289 9.782 8.090
Rough 1.325% 11.389 26.499 17.768 13.160 10.466 8.662
Rough 2.0% 11.175 29.783 16.450 12.289 9.782 8.090
17.547 13.775 11.298 9.563 8.280 7.295
11.585 28.354 18.330 13.820 11.062 9.184
11.384 32.332 20.324 15.345 12.340 10.295
Pe
Kn
Smooth
3.5
0.00 0.02 0.04 0.06 0.08 0.10
70
0.00 0.02 0.04 0.06 0.08 0.10
30
A. GUVENC YAZICIOGLU AND S. KAKAÇ
5. Temperature-Variable Thermophysical Properties
The earliest studies related to thermophysical property variation in tube flow conducted by Deissler [51] and Oskay and Kakac [52], who studied the variation of viscosity with temperature in a tube in macroscale flow. The concept seems to be well-understood for the macroscale heat transfer problem, but how it affects microscale heat transfer is an ongoing research area. Experimental and numerical studies point out to the non-negligible effects of the variation of especially viscosity with temperature. For example, Nusselt numbers may differ up to 30% as a result of thermophysical property variation in microchannels [53]. Variable property effects have been analyzed with the traditional no-slip/no-temperature jump boundary conditions in microchannels for three-dimensional thermally-developing flow [22] and two-dimensional simultaneously developing flow [23, 26], where the effect of viscous dissipation was neglected. Another study includes the viscous dissipation effect and suggests a correlation for the Nusselt number and the variation of properties [24]. In contrast to the abovementioned studies, the slip velocity boundary condition was considered only recently, where variable viscosity and viscous dissipation effects on pressure drop and the friction factor were analyzed in microchannels [25]. Because of the limited number of studies conducted in this area, simultaneously developing, steady-state, single phase gaseous flow and heat transfer in parallel plate microchannels in the slip flow regime (with slip-flow and temperature-jump boundary conditions) is studied numerically by taking into account the effects of rarefaction, viscous dissipation, and viscosity and thermal conductivity variation with temperature. The geometry is similar to the rough channel geometry, but without the roughness elements. Temperature dependent thermal conductivity is approximated by using a third-order polynomial function k(T ) = a 0 T 3 + a 1T 2 + a 2 T + a 3 ,
(18)
where ai are constants. Temperature dependent dynamic viscosity is modeled by using Sutherland’s formula μ( T ) = μ 0
T0 + C ⎛ T ⎞ ⎜ ⎟ T + C ⎜⎝ T0 ⎟⎠
3/ 2
,
(19)
where μ0 is the dynamic viscosity evaluated at the reference temperature T0 (273 K), and C is the Sutherland constant (111 K for air). Energy and momentum equations are solved in a coupled manner to account for the viscosity variation. Coupled solutions are made for pressure
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW
31
and velocity for investigating simultaneously developing flow. Variation of specific heat (Cp) and density (ρ) with temperature is not included, since these properties vary in negligible amounts within the studied temperature range (from 20°C, the inlet temperature, to 85°C, the wall temperature). The results, grouped into two categories as variable property (vp) and constant property (cp) are presented in Figs. 9–12. Both negative (fluid heating along the channel) and positive (fluid cooling along the channel) Brinkman values are analyzed, with Tinlet/Twall = 0.75 for heating and Tinlet/Twall = 1.5 for fluid cooling. Moreover Kn = 0.0 and 0.1, and Br = 0.001, 0.01, and 0.1 are considered [54]. An examination of Figs. 9–12 shows that the variation of Nu for cp and vp cases differ up to a certain distance in the channel and there is no significant difference in the fully developed Nu values. Both for the cooling and heating cases, the difference due to variable properties is non-negligible for part of the channel length. The difference in the cp and vp local Nu values decreases with increasing Br. An increase in Br, the nondimensional number representing viscous dissipation, results in the development of the flow in a shorter distance, and in return, the temperature gradients decrease. Since the temperature gradients directly affect the variation in properties, an increase in viscous dissipation reduces the difference due to variable properties. Moreover, the difference in the cp and vp local Nu values also decreases slightly with increasing Kn, representing the degree of rarefaction in the flow. As Kn increases, the flow is less affected by the wall conditions. As the heat transfer at the wall decreases, temperature gradients are reduced, and the difference due to variable properties decreases, as explained above. 17
17
15
15
Nu
13
13
Br � - - - - - - - constant properties variable properties
11 9 7
11 9 7
5
5 0
5
10 15 Dimensionless Length(x/H)
20
Figure 9. Local Nu variation with positive Br = 0.001, 0.01, 0.1 (fluid cooling) values along the microchannel for Kn = 0.01 (Tinlet/Twall = 1.5).
A. GUVENC YAZICIOGLU AND S. KAKAÇ
32 12
12
11
11 - - - - - - - constant properties variable properties
10
Nu
9
10 9
8
8
7
7 Br
6
6
5
5 0
5
10 15 Dimensionless Length(x/H)
20
Figure 10. Local Nu variation with positive Br = 0.001, 0.01, 0.1 (fluid cooling) values along the microchannel for Kn = 0.1 (Tinlet/Twall = 1.5).
25
25
Br
20
20 15
Nu
15
-------
10 5
Br
constant properties variable properties
10 5 0
0 0
5
10 15 Dimensionless Length(x/H)
20
Figure 11. Local Nu variation with negative Br = −0.001, −0.01, −0.1 (fluid heating) values along the microchannel for Kn = 0.01 (Tinlet/Twall = 0.75).
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW 12
12
Br
10
Nu
33
10
8
8
6
6
4
Br
- - - - - - - constant properties
4
variable properties
2
2 0
0
5
10 15 Dimensionless Length(x/H)
20
0
Figure 12. Local Nu variation with negative Br = −0.001, −0.01, –0.1 (fluid heating) values along the microchannel for Kn = 0.1 (Tinlet/Twall = 0.75).
6. Conclusions
In this lecture, a variety of results for convective heat transfer in microtubes and microchannels in the slip flow regime under different conditions have been presented. Both constant wall temperature and constant wall heat flux cases have been analyzed in microtubes, including the effects of rarefaction, axial conduction, and viscous dissipation. In rough microchannels the abovementioned effects have also been investigated for the constant wall temperature boundary condition. Then, temperature-variable dynamic viscosity and thermal conductivity of the fluid were considered, and the results were compared with constant property results for microchannels, with the effects of rarefaction and viscous dissipation. The conclusions drawn for microscale slip flow may be summarized as follows: 1. For high values of rarefaction (high Kn) and temperature jump (high κ), the effect of axial conduction is negligible. However for lower rarefaction and temperature jump values, as Pe decreases (axial conduction effect
34
2.
3.
4. 5.
6.
A. GUVENC YAZICIOGLU AND S. KAKAÇ
increases), the fully developed Nu increases more significantly. It may be concluded from these observations that the effect of axial conduction should not be neglected for low-rarefied flows and with low values of temperature jump. Regardless of the effect of axial conduction, for a given Kn and κ value, the flow reaches the same fully developed Nu value for all values of Br. When the fluid is cooled (Br > 0 for constant wall temperature and Br < 0 for constant wall heat flux) Nu takes higher values. The increase in fully developed Nu value with the added effect of viscous dissipation suggests that this effect should not be neglected for long channels. Since micro conduits have high length-to-diameter ratios, even for low values of Br, viscous dissipation effect must be considered. In general, for constant wall temperature and constant wall heat flux conditions, velocity slip and temperature jump affect the heat transfer in opposite ways: a large slip on the wall will increase the convection along the surface. On the other hand, a large temperature jump will decrease the heat transfer by reducing the temperature gradient at the wall. Therefore, neglecting temperature jump will result in the overestimation of the heat transfer coefficient. When viscous dissipation is neglected, the effect of axial conduction should be included for Pe < 100. When viscous dissipation is included in the analysis, axial conduction is significant for Pe < 100 for short channels. When surface roughness is considered, the fully developed Nu increases with respect to the smooth channel value for rarefied flows, but not for continuum, for all values of Peclet number. The increase in Pe increases Nu more for low values of rarefaction. It appears that, for the range Kn considered in this work, the maximum heat transfer is observed for Kn = 0.02. When viscous dissipation effect is included, in either fluid heating or fluid cooling, Nu increases, and more significantly with higher relative roughness values. The variation of thermophysical properties affects the temperature profile, but not the velocity field. For both fluid heating cooling cases, the variation in local Nu due to temperature-variable properties is significant in the developing region. However the fully developed Nu is almost invariant for constant and variable properties cases due to reduced temperature gradients in this region.
Acknowledgement
The authors would like to thank the Turkish Scientific and Technical Research Council, TUBITAK, Grant No. 106M076, for financial support.
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW
35
References 1. D.B. Tuckerman and R.F. Pease, Optimized convective cooling using micromachined structure, Journal of the Electrochemical Society 129, P. C 98 (1982). 2. P.Y. Wu and W.A. Little, Measurement of heat transfer characteristics of gas flow in fine channels heat exchangers used for microminiature refrigerators, Cryogenics 24, 415–420 (1984). 3. S.B. Choi, R.F. Barron, and R.O. Warrington, Fluid flow and heat transfer in microtubes, Micromechanical Sensors, Actuators, and Systems, ASME DSC 32, 123–134 (1991). 4. C.P. Tso and S.P. Mahulikar, Experimental verification of the role of Brinkman number in microchannels using local parameters, International Journal of Heat and Mass Transfer 43, 1837–1849 (2000). 5. J.Y. Jung and H.Y. Kwak, Fluid flow and heat transfer in microchannels with rectangular cross section, Heat Mass Transfer 44, 1041–1049 (2008). 6. H.S. Park and J. Punch, Friction factor and heat transfer in multiple microchannels with uniform flow distribution, International Journal of Heat and Mass Transfer 51, 4535–4543 (2008). 7. R.F. Barron, X.M. Wang, R.O. Warrington, and T.A. Ameel, The Graetz problem extended to slip flow, International Journal of Heat and Mass Transfer 40, 1817–1823 (1997). 8. T.A. Ameel, R.F. Barron, X.M. Wang, and R.O. Warrington, Laminar forced convection in a circular tube with constant heat flux and slip flow, Microscale Thermophysical Engineering 1, 303–320 (1997). 9. B. Cetin, H. Yuncu, and S. Kakac, Gaseous flow in microconduits with viscous dissipation, International Journal of Transport Phenomena 8, 297– 315 (2006). 10. B. Cetin, A. Guvenc Yazicioglu, and S. Kakac, Fluid flow in microtubes with axial conduction including rarefaction and viscous dissipation, International Communications in Heat and Mass Transfer 35, 535–544 (2008). 11. G. Tunc and Y. Bayazitoglu, Heat transfer in microtubes with viscous dissipation, International Journal of Heat and Mass Transfer 44, 2395–2403 (2001). 12. G. Tunc and Y. Bayazitoglu, Convection at the entrance of micropipes with sudden wall temperature change, Proceedings of IMECE, November 17–22, 2002, New Orleans, Louisiana. 13. S.P. Yu and T.A. Ameel, Slip-flow heat transfer in rectangular microchannels, International Journal of Heat and Mass Transfer 44, 4225–4235 (2001). 14. H.-E. Jeong and J.-T. Jeong, Extended Graetz problem including streamwise conduction and viscous dissipation in microchannel, International Journal of Heat and Mass Transfer 49, 2151–2157 (2006). 15. Gh.M. Mala and D. Li, Flow characteristics of water in microtubes, International Journal of Heat and Fluid Flow 20, 142–148 (1999). 16. C. Kleinstreuer and J. Koo, Computational analysis of wall roughness effect for liquid flow in micro-conduits, Journal of Fluids Engineering 126, 1–9 (2004). 17. G. Croce and P. D’Agaro, Numerical analysis of roughness effect on microtube heat transfer, Superlattices and Microstructures 35, 601–616 (2004).
36
A. GUVENC YAZICIOGLU AND S. KAKAÇ
18. G. Croce and P. D’Agaro, Numerical simulation of roughness effect on microchannel heat transfer and pressure drop in laminar flow, Journal of Physics D: Applied Physics 38, 1518–1530 (2005). 19. G. Croce, P. D’Agaro, and C. Nonini, Three-dimensional roughness effect on microchannel heat transfer and pressure drop, International Journal of Heat and Mass Transfer 50, 5249–5259 (2007). 20. G. Croce, P. D’Agaro, and A. Filippo, Compressibility and rarefaction effects on pressure drop in rough microchannels, Heat Transfer Engineering 28, 688– 695 (2007). 21. Y. Ji, K. Yuan, and J.N. Chung, Numerical simulation of wall roughness on gaseous flow and heat transfer in a microchannel, International Journal of Heat and Mass Transfer 49, 1329–1339 (2006). 22. Z. Li, X. Huai, Y. Tao, and H. Chen, Effects of thermal property variations on the liquid flow and heat transfer in microchannel heat sinks, Applied Thermal Engineering 27, 2803–2814 (2007). 23. S.P. Guidice, C. Nonino, and S. Savino, Effects of viscous dissipation and temperature dependent viscosity in thermally and simultaneously developing laminar flows in microchannels, International Journal of Heat and Fluid Flow 28, 15–27 (2007). 24. J.T. Liu, X.F. Peng, and B.X. Wang, Variable-property effect on liquid flow and heat transfer in microchannels, Chemical Engineering Journal 141, 346– 353 (2008). 25. M.S. El-Genk and I. Yang, Numerical analysis of laminar flow in micro-tubes with a slip boundary, Energy Conversion and Management 50, 1481–1490 (2009). 26. N.P. Gulhane and S.P. Mahulikar, Variations in gas properties in laminar micro-convection with entrance effect, International Journal of Heat and Mass Transfer 52, 1980–1990 (2009). 27. M. Gad-El-Hak, The fluid mechanics of microdevices, Journal of Fluids Engineering 121, 5–33 (1999). 28. G.L. Morini, Single-phase convective heat transfer in microchannels: A review of experimental results, International Journal of Thermal Sciences 43, 631–651 (2004). 29. Y. Bayazitoglu and S. Kakac, Flow regimes in microchannel single-phase gaseous flow, Microscale Heat Transfer – Fundamentals and Applications in Biological Systems and MEMS, edited by S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005). 30. G. Hetsroni, A. Mosyak, E. Pogrebnyak, and L.P. Yarin, Heat transfer in micro-channels: Comparison of experiments with theory and numerical results, International Journal of Heat and Mass Transfer 25–26, 5580–5601 (2005). 31. Y. Yener, S. Kakac, M. Avelino, and T. Okutucu, Single phase forced convection in microchannels – State-of art-review, Microscale Heat TransferFundamentals and Applications in Biological Systems and MEMS, edited by S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005). 32. R.M. Cotta, S. Kakaç, M.D. Mikhailov, F.V. Castellos, and C.R. Cardoso, Transient flow and thermal analysis in microfluidics, Microscale Heat TransferFundamentals and Applications in Biological Systems and MEMS, edited by
CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW
33. 34. 35. 36. 37.
38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.
37
S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005). P. Rosa, T.G. Karayiannis, and M.W. Collins, Single-phase heat transfer in microchannels: The importance of scaling, Applied Thermal Engineering 29, 3447–3468 (2009). G. Karniadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation (Springer, New York, 2005). C.B. Sobhan and G.P. Peterson, Microscale and Nanoscale Heat Transfer: Fundamentals and Engineering Applications (CRC Press, Florida, 2008). L.P. Yarin, A. Mosyak, and G. Hetsroni, Fluid Flow, Heat Transfer and Boiling in Micro-Channels (Springer, New York, 2008). Y. Bayazitoglu, G. Tunc, K. Wilson, and I. Tjahjono, Convective heat transfer for single phase gases in microchannel slip flow: Analytical solutions, Microscale Heat Transfer – Fundamentals and Applications in Biological Systems and MEMS, edited by S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005). N.T. Obot, Toward a better understanding of friction and heat/mass transfer in microchannels – A literature review, Microscale Thermophysical Engineering 6, 155–173 (2002). A. Beskok, G.E. Karniadakis, and W. Trimmer, Rarefaction, compressibility effects in gas microflows, Journal of Fluids Engineering 118, 448–456 (1996). W. Sun, S. Kakac, and A. Guvenc Yazicioglu, A numerical study of singlephase convective heat transfer in microtubes for slip flow, International Journal of Thermal Sciences 46, 1084–94 (2007). B. Cetin, Analysis of single phase convective heat transfer in microtubes and microchannels, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2005). M. Barisik, Analytical solution for single phase microtube heat transfer including axial conduction and viscous dissipation, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2008). G. Tunc and Y. Bayazitoglu, Heat transfer in microtubes with viscous dissipation, International Journal of Heat and Mass Transfer 44, 2395–2403 (2001). S. Kakac and Y. Yener, Convective Heat Transfer (CRC Press, Florida, 1994). R.K. Shah and A.L. London, Laminar flow forced convection in ducts, Advances in Heat Transfer, edited by T.F.Jr. Irvine, and J.P. Hartnett (Academic Press, New York 1978), pp. 78–152. J. Lahjomri and A. Oubarra, Analytical solution of the Graetz problem with axial conduction, Journal of Heat Transfer 121, 1078–1083 (1999). W. Qu, Gh.M. Mala, and D. Li, Heat transfer for water flow in trapezoidal silicon microchannels, International Journal of Heat and Mass Transfer 43, 3925–3936 (2000). J. Koo and C. Kleinstreuer, Analysis of surface roughness effects on heat transfer in micro-conduits, International Journal of Heat and Mass Transfer 48, 2625–2634 (2005). M.B. Turgay and A. Guvenc Yazicioglu, Effect of surface roughness in parallelplate microchannels on heat transfer, Numerical Heat Transfer 56, 497–514 (2009).
38
A. GUVENC YAZICIOGLU AND S. KAKAÇ
50. M.B. Turgay, Effect of surface roughness in microchannels on heat transfer, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2008). 51. R.G. Deisler, Analytical investigation of turbulent flow in smooth pipes with heat transfer, with variable fluid properties for Prandtl number of 1, NACA Technical Note 2242 (1950). 52. R. Oskay and S. Kakac, Effect of viscosity variations on forced convection heat transfer in pipe flow, METU Journal of Pure and Applied Sciences 6, 211–230 (1973). 53. H. Herwig and S.P. Mahulikar, Variable property effects in single-phase incompressible flows through microchannels, International Journal of Thermal Sciences 45, 977–981 (2006). 54. C. Gozukara, Heat transfer analysis of single phase forced convection in microchannels and microtubes with variable property effect, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2010).
DIRECT AND INVERSE PROBLEMS SOLUTIONS IN MICRO-SCALE FORCED CONVECTION C.P. NAVEIRA-COTTA1, R.M. COTTA1, H.R.B. ORLANDE1, AND S. KAKAÇ2 1
Laboratory of Transmission and Technology of Heat, LTTC Mechanical Engineering Department, COPPE & POLI, Cx. Postal 68503 CEP 21945-970, Universidade Federal do Rio de Janeiro, RJ, Brasil,
[email protected] 2 TOBB University of Economics & Technology, Ankara, Turkey
1. Introduction The analysis of internal flows in the slip-flow regime gained an important role along the last two decades in connection with micro-electromechanical systems (MEMS) applications and in the thermal control of microelectronics, as reviewed in different sources [1–5]. Several steady-state incompressible flow situations in laminar regime within simple geometries, such as circular micro-tubes and parallel-plate micro-channels, developed for the slip flow regime, have been employed in the heat transfer analysis of micro-systems [6, 7]. Also recently in Refs. [8–12], the analytical contributions were directed towards more general steady and transient problem formulations, including viscous dissipation, axial diffusion in the fluid and three-dimensional flow geometries. In this context, the first goal of this lecture is thus to illustrate the results obtained from a fairly general hybrid numerical–analytical solution for temperature distributions in a fluid flowing through two- or three-dimensional micro-channels, taking into account the velocity slip and temperature jump at the walls surfaces. For this purpose, a flexible approach was employed [13], based on formal solutions of the energy equation as obtained via the classical integral transform method [14], in association with the Generalized Integral Transform Technique, GITT [15–18], which was used for the solution of the required eigenvalue problem [19–21]. This method is here applied for illustration purposes in the integral transformation of the energy equation for thermally developing flow within parallel-plates micro-channels under the slip flow regime. This combination of solution methodologies provides a very effective eigenfunction expansion solution, through the fast converging analytical representation in all the space coordinates, together
S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_3, © Springer Science + Business Media B.V. 2010
39
40
C.P. NAVEIRA-COTTA ET AL.
with a flexible and reliable numerical–analytical approach for the Sturm– Liouville eigenvalue problem solution. The accuracy of such analytic-type solutions for the direct forced convection problem in micro-channels are however dependent on the also accurate determination of the momentum and thermal accommodation coefficients, as required by the slip and temperature jump boundary conditions inherent to the slip flow model that accounts for non-continuum effects at the fluid–surface interactions. Fundamental experimental work on rarefied gas dynamics have offered measurements of the tangential momentum accommodation coefficient, requiring, for instance, high vacuum and molecular beams impinging on carefully prepared substrates, such as recently reviewed in Ref. [22], but very few results are available for the actual conditions of the flow configuration within micro-channels and their actual bounding walls [23, 24]. The experiments indicate that the tangential momentum accommodation coefficient generally assumes values between 0.2 and 1.0, with the lower limit being associated with exceptionally smooth surfaces and the upper limit with very rough or highly oxidized surfaces [4]. Similar considerations are pertinent to the measurement of thermal accommodation coefficients [25], where an even more limited experimental database is available, and apparently no previous work seems to be available on the identification of this coefficient in actual heat and fluid flow conditions within specific pressure and temperature levels pertinent to MEMS applications, and in addition for actual morphology and finishing of the microchannel walls. Thus, we take advantage of the accuracy, robustness and efficiency of the direct problem solution, to tackle the associated inverse heat transfer problem analysis [26, 27] towards the simultaneous estimation of momentum and thermal accommodation coefficients in micro-channel flows with velocity slip and temperature jump. A Bayesian inference approach is adopted in the solution of the identification problem, based on the Monte Carlo Markov Chain method (MCMC) and the Metropolis–Hastings algorithm [28–30]. Only simulated temperature measurements at the external faces of the channel walls, obtained for instance via infrared thermography [30], are used in the inverse analysis in order to demonstrate the capabilities of the proposed approach. A sensitivity analysis allows for the inspection of the identification problem behavior when the external wall Biot number is also included among the parameters to be estimated. 2. Direct Problem Solution The approach here employed in the direct problem solution for forced convection in micro-channels, is borrowed from a recent work on diffusion in heterogeneous media, with arbitrarily space variable thermophysical
DIRECT AND INVERSE PROBLEMS SOLUTIONS
41
properties [13]. In this sense, the dimensionless velocity fields are mathematically equivalent to space variable thermal capacitances, and the solution procedure is here briefly described. For a general purpose automatic implementation, it is quite desirable to employ a flexible computational approach to handle eigenvalue problems with arbitrarily variable coefficients. Thus, the Generalized Integral Transform Technique (GITT) is here employed in the solution of the Sturm–Liouville problem via the proposition of a simpler auxiliary eigenvalue problem, and expanding the unknown eigenfunctions in terms of the chosen basis [19]. Also, the variable equation coefficients may themselves be expanded in terms of known eigenfunctions [13], so as to allow for a fully analytical implementation of the coefficients matrices in the transformed system. The equation coefficients of the auxiliary problem are simpler forms of the original coefficients, chosen so as to allow for an analytical solution of the auxiliary problem [13, 19]. Then, the resulting algebraic problem can be numerically solved to provide results for the eigenvalues and eigenvectors, which will be combined to provide the desired eigenfunctions of the original eigenvalue problem, as described in further detail in Ref. [13]. In order to illustrate both the direct and inverse problems solutions, we consider the two-dimensional situation of parallel-plates micro-channels, with steady thermally developing laminar flow under the slip flow regime. The fluid is assumed to enter the channel with a fully developed velocity profile and a uniform temperature, exchanging heat by convection with the surroundings with an external heat transfer coefficient that might not be known a priori in the inverse problem analysis. Thermophysical properties are assumed to be constant, while axial conduction and viscous dissipation are neglected. Although more involved formulations could be handled by the proposed approach, the direct problem solution is here illustrated for the parallel-plates channel incompressible flow case, previously solved in Ref. [6, 7] for the prescribed wall temperature boundary condition, and here written in a more general form including the external wall convection effect:
W (Y )
∂θ (Y , Z ) ∂ 2θ (Y , Z ) , 0 < Y < 1, Z > 0 = ∂Z ∂Y 2
θ (Y ,0) = 1, ∂θ (Y , Z ) ∂Y
Y =0
= 0,
∂θ (Y , Z ) ∂Y
Y =1
=−
0 ≤ Y ≤1 Bi θ (1, z ), Z > 0 1 + 2 Knβt Bi
where the corresponding dimensionless groups are given by
(1a) (1b) (1c,d)
C.P. NAVEIRA-COTTA ET AL.
42
Y=
αz T ( y , z ) − T∞ y ; Z= ; θ (Y , Z ) = ; 2 y1 uav y1 T0 − T∞ W (Y ) =
hy λ u( y) ; Bi = 1 ; Kn = 2 y1 uav kf
(2a–f)
and,
βt =
(2 − α t ) 2γ 1 α t (γ + 1) Pr
(2g)
is the wall temperature jump coefficient and αt is the thermal accommodation coefficient, λ is the molecular mean free path, γ=cp/cv, while cp is specific heat at constant pressure, cv specific heat at constant volume and Pr is the Prandtl number. The dimensionless velocity profile is given as [6]: W (Y ) =
6 Knβ v + 3(1 − Y 2 ) / 2 1 + 6 Knβ v
(3a)
where,
βv =
(2 − α m )
(3b)
αm
is the wall velocity slip coefficient and αm is the tangential momentum accommodation coefficient. The ratio of the boundary conditions coefficients is also of interest, and given as β = βt/βv. The solution of the dimensionless problem (1) is then a special case from the general solution given in Ref. [13], written as [6]: ∞
θ (Y , Z ) = ∑ f iψ% i (Y )e − μ Z , with f i = − 2 i
i =1
ψ% i' (1) μi2
(4a,b)
where ψi(Y) are eigenfunctions of the following Sturm–Liouville problem, with the corresponding normalization integral and normalized form of the eigenfunction: d 2ψ i (Y ) + μi2W (Y )ψ i (Y ) = 0, 2 dY
dψ i (Y ) dY
Y =0
= 0,
dψ i (Y ) dY
Y =1
=−
0 < Y <1 Bi ψ i (1) 1 + 2 Knβ t Bi
(5a) (5b,c)
DIRECT AND INVERSE PROBLEMS SOLUTIONS 1
N i = ∫ W (Y )ψ i2 (Y )dY ; ψ% i (Y ) = 0
ψ i (Y ) N i1/ 2
43
(6a,b)
The solution of problem (5) was obtained in Refs. [6, 7] in terms of the confluent hypergeometric function, also known as Kummer function, readily available in the Mathematica system [31]. Here, a more convenient path for the corresponding inverse problem analysis was chosen, in light of the intensive computational task required by the parameters identification algorithm, so as to provide a solution in terms of simpler functions. Thus, following the ideas in the Generalized Integral Transform Technique, GITT [13, 15, 19], the solution of problem (5) is provided as an eigenfunction expansion from a simpler eigenvalue problem, that retains the same boundary conditions of the original problem but avoids the variable coefficient corresponding to the dimensionless velocity field, in the form: d 2 Ω n (Y ) + λn2 Ω n (Y ) = 0, 0 < Y < 1 2 dY d Ω n (Y ) dY
Y =0
= 0,
d Ω n (Y ) dY
Y =1
=−
Bi Ωn (1) 1 + 2 Knβt Bi
(7a) (7b,c)
which is readily solved as Ω n (Y ) = cos(λn Y ), λn tan(λn ) =
Bi 1 + 2 Knβ t Bi
n = 1, 2,… ,
(8a,b)
Once the auxiliary eigenfunctions and eigenvalues have been obtained, we may express the desired eigenfunction of the original problem as an expansion of these simpler functions: ∞
% (Y )ψ , inverse ψ i (Y ) = ∑ Ω n i ,n
(9a)
1 % (Y )ψ (Y ) dY , transform ψ ii, n= ∫ Ω n i
(9b)
n =1
0
The integral transformation of the original eigenvalue problem is then 1 % (Y ) − dY , over Eq. (5a), which performed by employing the operator ∫ Ω n 0
results in the following algebraic eigenvalue problem for the original problem eigenvalues and corresponding eigenvectors:
( A − μ 2 B) ψ = 0 ψ = {ψ n ,m };
1
(10a)
% (Y )Ω % (Y )dY (10b,c) B = {Bn ,m }, Bn ,m = ∫ W (Y )Ω n m 0
44
C.P. NAVEIRA-COTTA ET AL.
An ,m = λn2δ n ,m , where δ n ,m = 1, for n = m, or δ n ,m = 0, for n ≠ m
(10d)
The algebraic problem (10a) can be numerically solved to provide results for the eigenvalues μ 2 and eigenvectors ψ from this matrix eigenvalue problem analysis [31], which will be combined within the inverse formula (9a) to provide the desired eigenfunctions of the original eigenvalue problem. The average temperature and the local Nusselt number along the channel length are then determined from: ∞
θ av ( Z ) = ∑ i =1
∞
Nu ( Z ) =
∑ i =1 ∞
∑ i =1
(ψ% i' (1)) 2
μ
4 i
(ψ% i' (1)) 2
μ
2 i
(ψ% i' (1)) 2
μi4
2
e − μi Z
(11a)
2
e− μi Z (11b)
e
− μi2 Z
3. Inverse Problem Solution
A variety of techniques is nowadays available for the solution of inverse problems [26, 27]. However, one common approach relies on the minimization of an objective function that generally involves the squared difference between measured and estimated variables, like the least-squares norm, as well as some kind of regularization term. Despite the fact that the minimization of the least-squares norm is indiscriminately used, it only yields maximum likelihood estimates if the following statistical hypotheses are valid: the errors in the measured variables are additive, uncorrelated, normally distributed, with zero mean and known constant standard-deviation; only the measured variables appearing in the objective function contain errors; and there is no prior information regarding the values and uncertainties of the unknown parameters. Although very popular and useful in many situations, the minimization of the least-squares norm is a non-Bayesian estimator. A Bayesian estimator [28] is basically concerned with the analysis of the posterior probability density, which is the conditional probability of the parameters given the measurements, while the likelihood is the conditional probability of the measurements given the parameters. If we assume the parameters and the measurement errors to be independent Gaussian random variables, with known means and covariance matrices, and that the measurement errors are additive, a closed form expression can be derived for the posterior probability density. In this case, the estimator that maximizes the posterior probability
DIRECT AND INVERSE PROBLEMS SOLUTIONS
45
density can be recast in the form of a minimization problem involving the maximum a posteriori objective function. On the other hand, if different prior probability densities are assumed for the parameters, the posterior probability distribution may not allow an analytical treatment. In this case, Markov Chain Monte Carlo (MCMC) methods are used to draw samples of all possible parameters, so that inference on the posterior probability becomes inference on the samples. In this work, we illustrate the use of Bayesian techniques for the estimation of parameters in micro-scale forced convection problems, via MCMC methods [28–30], as applied to the simultaneous identification of the momentum and thermal accommodation coefficients in slip flow modeling. The Metropolis–Hastings algorithm is employed for the sampling procedure, implemented in the Mathematica platform [31]. Consider the vector of parameters appearing in the physical model formulation as: PT ≡ [P1,P2, …, PNp]
(12a)
where Np is the number of parameters. For the solution of the inverse problem of estimating P, we assume available the measured temperature data given by:
r r r r r r (Y − T)T = Y1 − T1 , Y2 − T2 ,K , YN x − TN x
(
)
(12b)
r
where Yi contains the measured temperatures for each of the Nx sensors at time ti, i = 1, …, Nt, that is,
r r (Yi − Ti ) = Yi1 − Ti1 , Yi 2 − Ti 2 ,K , YiNt − TiNt for i = 1, …, Nx
(
)
(12c)
so that we have Nm = Nx. Nt measurements in total. In the present steady state estimation procedure, the sensors are assumed to be distributed along the channel wall length and the measurements are taken as an average in a time interval within the steady period (Nt = 1). Bayes’ theorem can then be stated as [28, 29]:
p posterior (P) = p(P Y) =
p(P) p(Y P) p(Y)
(13)
where pposterior(P) is the posterior probability density, that is, the conditional probability of the parameters P given the measurements Y; p(P) is the prior density, that is, a statistical model for the information about the unknown parameters prior to the measurements; p(Y|P) is the likelihood function, which gives the relative probability density (loosely speaking, relative probability) of different measurement outcomes Y with a fixed P, and p(Y)
46
C.P. NAVEIRA-COTTA ET AL.
is the marginal probability density of the measurements, which plays the role of a normalizing constant. In this work we assume that the measurement errors are Gaussian random variables, with known (modeled) means and covariances, and that the measurement errors are additive and independent of the unknowns. With these hypotheses, the likelihood function can be expressed as [28, 29]:
p ( Y P) = (2π ) − M /2 W
−1/2
⎧ 1 ⎫ exp ⎨ − [Y − T(P)]T W −1[ Y − T(P)]⎬ (14) ⎩ 2 ⎭
where W is the covariance matrix of the measurement errors. When it is not possible to analytically obtain the corresponding marginal distributions, one needs to use a method based on simulation [28, 29]. The inference based on simulation techniques uses samples to extract information about the posterior distribution p(P|Y). Obviously, as a sample is always a partial substitute of the information contained in a density, simulation-based methods are inherently approximate and should only be used when it is impossible to include the extraction of analytical information from the posteriori, as is the case in the present study. Unfortunately, for most problems of practical relevance it is complicated to generate the posteriori p(P|Y). Therefore, more sophisticated methods are required to obtain a sample of p(P|Y), for example, the simulation technique based on the Markov chains [29]. The numerical method most used to explore the space of states of the posteriori is the Monte Carlo approach. The Monte Carlo simulation is based on a large number of samples of the probability density function (in this case, the function of the posterior probability density p(P|Y)). Several sampling strategies are proposed in the literature, including the Monte Carlo method with Markov Chain (MCMC), adopted in this work, where the basic idea is to simulate a “random walk” in the space of p(P|Y)that converges to a stationary distribution, which is the distribution of interest in the problem. A Markov chain is a stochastic process {P0, P1, …} such that the distribution of Pi, given all previous values P0, …, Pi−1, depends only on Pi−1. That is, it interprets the fact that for a process satisfying the Markov property of Eq. (15), given the present, the past is irrelevant to predict its position in a future instant [29]:
p(Pi ∈ A P0 ,K, Pi −1 ) = p(Pi ∈ A Pi −1 )
(15)
The most commonly used Monte Carlo method with Markov Chain algorithms are the Metropolis–Hastings, here employed, and the Gibbs sampler [28, 29].
DIRECT AND INVERSE PROBLEMS SOLUTIONS
47
The Metropolis–Hastings algorithm uses the same idea of the rejection methods, i.e. a value is generated from an auxiliary distribution and accepted with a given probability. This correction mechanism ensures the convergence of the chain for the equilibrium distribution. That is, the algorithm now includes an additional step, where the transition mechanism depends on a proposal for a transition and a stage of assessing the equilibrium density, but this is represented by the global transition via the probability of acceptance. The Metropolis–Hastings algorithm uses an auxiliary probability density function, q(P*|P), from which it is easy to obtain sample values. Assuming that the chain is in a state P, a new candidate value, P*, is generated from the auxiliary distribution q(P*|P), given the current state of the chain P. The new value P* is accepted with probability given by Eq. (16) below, where the ratio that appears in this equation was called by Hastings [29] the ratio test, today called the ratio of Hastings “RH”:
⎡ p ( P* Y ) q ( P* P ) ⎤ ⎥ RH (P, P ) = min ⎢1, * ⎢⎣ p(P Y)q(P P ) ⎥⎦ *
(16)
where p(P|Y) is the a posteriori distribution of interest. An important observation is that we only need to know p(P|Y) up to a constant, since we are working with ratios between densities and such normalization constant is canceled. In practical terms, this means that the simulation of a sample of p(P|Y) using the Metropolis–Hastings algorithm can be outlined as follows [29]: 1. Boot up the iterations counter of the chain i = 0 and assign an initial value P(0). 2. Generate a candidate value P* of the distribution q(P*|P). 3. Calculate the probability of acceptance of the candidate value RH (P, P* ) by Eq. (16). 4. Generate a random number u with uniform distribution, i.e., u ~ U(0, 1). 5. If u ≤ RH then the new value is accepted and we let P(i+1) = P*. Otherwise, the new value is rejected and we let P(i+1) = P(i). 6. Increase the counter i to i + 1 and return to step 2. The transition core q(P*|P) defines only a proposal for a movement that can be confirmed by RH (P, P* ) . For this reason it is usually called the proposal or density distribution. The success of the method depends on not so low acceptance rates and proposals that are easy to simulate. The method replaces a difficult to generate p(P|Y) by several generations of the proposal q(P*|P). In this study we have chosen to adopt symmetrical chains, i.e., q(P*|P) = q(P|P*) for all (P*, P). In this case, Eq. (16) reduces to the ratio
48
C.P. NAVEIRA-COTTA ET AL.
of the posterior densities calculated at the previous and proposed chain positions, and does not depend on q(P*|P). Before addressing the estimation of the unknown parameters, the behavior of the determinant of the matrix JT J [27] needs to be analyzed in order to inspect the influence of the number of parameters to be estimated in the solution of the inverse problem. The sensitivity matrix J is defined as:
⎡ ∂T1 ⎢ ∂P ⎢ 1 ⎢ ∂T2 T T ⎢ ⎡ ∂T (P ) ⎤ = J(P) = ⎢ ⎢ ∂P1 ⎥ P ∂ ⎣ ⎦ ⎢ M ⎢ ⎢ ∂TI ⎢ ∂P ⎣⎢ 1 The sensitivity coefficients J ij =
∂T1 ∂P2
∂T1 ∂P3
∂T2 ∂P2
∂T2 ∂P3
M ∂TI ∂P2
M ∂TI ∂P3
∂T1 ⎤ ∂PN p ⎥ ⎥ ∂T2 ⎥ L ⎥ ∂PN P ⎥ M ⎥ ⎥ ∂TI ⎥ L ∂PN p ⎥⎥ ⎦ L
(17)
∂ Ti give the sensitivity of Ti (solution of ∂ Pj
the direct problem) with respect to changes in the parameter Pj. A small value of the magnitude of Jij indicates that large changes in Pj yield small changes in Ti. It can be easily noticed that the estimation of the parameter Pj is extremely difficult in such cases, because basically the same value for Ti would be obtained for a wide range of values of Pj. In fact, when the sensitivity coefficients are small, J T J ≈ 0 and the inverse problem is said to be illconditioned. It can also be shown that J T J is null if any column of J can be expressed as a linear combination of other columns [27]. Therefore, it is desirable to have linearly-independent sensitivity coefficients Jij with large magnitudes, so that the parameter estimation problem is not very sensitive to measurement errors and accurate estimates of the parameters can be obtained. The comparison of the magnitude of the sensitivity coefficients, as well as the analysis of possible linear dependence, is more easily performed by using the reduced sensitivity coefficients instead of the original ones. The reduced sensitivity coefficients are obtained by multiplying the original sensitivity coefficients, Jij, by the parameters that they refer to. Therefore, they have units of the measured variables, which is used as a basis of comparison.
DIRECT AND INVERSE PROBLEMS SOLUTIONS
49
4. Results and Discussion
The direct problem solution is first validated by direct comparison with the benchmark results provided in Ref. [6], as illustrated in Table 1 below, for the case of a parallel-plates under prescribed uniform wall temperature (Bi = ∞). TABLE 1. Results for the local Nusselt number, Nu(Z), for the parallel-plates case with Knβv = 0.1 and β = 1: Comparison against Ref. [6] for prescribed wall temperature (with asterisk), Bi = ∞, and reference results for Bi = 1.
Z 0.01
Bi = ∞ Nu(Z) Z 2.70290 2.70289
0.02
2.33112 2.33111
0.03 0.04
0.07 0.08
2.00027
0.09
2.00027* 0.05
1.90676 1.90676
*
0.01
2.81057
0.06
1.96128
0.02
2.45481
0.07
1.90338
0.03
2.25900
0.08
1.85615
0.04
2.12882
0.09
1.81694
0.05
2.03406
0.1
1.78394
*
1.73627 1.73627
Nu(Z)
*
1.78071 1.78071
*
Z
1.83608 1.83608
*
2.13091 2.13090
0.06
*
Nu(Z)
Bi = 1.0 Nu(Z) Z
*
1.69996 1.69996*
0.1
1.66993 1.66992
*
The results in Ref. [6] were obtained from the classical integral transform method as well, but utilizing the exact solution of the related eigenvalue problem in terms of confluent hypergeometric functions, as obtained from a symbolic computation platform [31]. The numerical results for the local Nusselt number along the channel length obtained from the two approaches are practically coincident to the six significant digits presented. The Nusselt number results for the case of Bi = 1 here computed are also presented for reference purposes. The constructed algorithm for the inverse analysis was then also validated for this same benchmark problem with Bi = ∞, from a theoretical perspective, assuming the fluid temperature at the wall to be measurable. Simulated experimental results were produced with 50 terms in the eigenfunction expansion provided in Ref. [6], and the direct problem solution in the inverse analysis was implemented with just 10 terms in the expansion here proposed to avoid the so called inverse crime [28]. A total of 1,000 measurements are provided, with white noise considered normally distributed
C.P. NAVEIRA-COTTA ET AL.
50
with averages at the simulated values and 1% standard deviation. Table 2 summarizes the employed initial values, search steps, search limits, estimated values and the 95% confidence intervals. Non-informative uniform distributions were employed as priors, so as to test the algorithm in the worst situation, with knowledge only of the admissible minimum and maximum limits of the parameters. Only 10,000 states were necessary in the MCMC chains for reaching converged estimates, as evident from Fig. 1 that illustrate the chains evolution for each of the parameters, βv and βt, broadly bounded by the prescribed search limits. It can be seen from Table 2 that the estimated results are quite accurate, without inverse crime and white noise in the simulated data, and with the confidence intervals encapsulating the exact parameter values. Finally, Table 3 presents results of the local Nusselt number, as obtained from the exact eigenfunction expansion [6] and as recovered from the estimated parameters values, from Table 2. The estimated Nusselt numbers are then reproduced to three significant digits throughout the range of the dimensionless axial variable. TABLE 2. Inverse analysis of test case [6]: Exact values of parameters, search steps, initial guesses, lower and upper limits, estimated values and 95% confidence intervals.
0.6
Lower limit 0.5
Upper limit 1.5
1.4
0.5
2
P
Exact
Step
Initial
βv
1
0.05
βt
1
0.05
(a) βv
0.989
Min. w/95% 0.903
Max. w/95% 1.087
1.014
0.917
1.114
Estimated
(b) βt
Figure 1. (a, b) Markov chain evolution for parameters (a) βv and (b) βt for a total of 100 temperature measurements.
Next, the inverse problem solution is illustrated, by adopting the governing parameters as indicated in Ref. [24], related to N2 flow in a silicon channel, with the representative values βv = 1.5, βt = 2.0, Kn = 0.025, and Bi = 1.0. Only wall temperature measurements, obtained from simulated data, are employed in this work, which may be obtained for instance through infrared thermography [30].
DIRECT AND INVERSE PROBLEMS SOLUTIONS
51
A total of 1,000 uniformly distributed points along the dimensionless channel length, Zf = 5, was initially adopted. The simulated measurements were considered normally distributed with averages at the simulated values and 1% standard deviation. They were obtained with 50 terms in the eigenfunction expansions, while the direct problem solution within the inverse problem procedure was handled with 20 terms only, again in order to avoid the inverse crime. TABLE 3. Results for the local Nusselt number, Nu(Z), for the parallel-plates case with Bi = ∞, Knβv = 0.1 and β = 1: Comparison of exact results, Ref. [6], and recovered results from estimated parameters. Exact
Estimated
Z 0.01
Nu(Z) 2.70290
Z 0.06
Nu(Z) 1.83608
Z 0.01
Nu(Z) 2.698
Z 0.06
Nu(Z) 1.833
0.02
2.33112
0.07
1.78071
0.02
2.327
0.07
1.778
0.03
2.13091
0.08
1.73627
0.03
2.127
0.08
1.734
0.04
2.00027
0.09
1.69996
0.04
1.997
0.09
1.697
0.05
1.90676
0.1
1.66993
0.05
1.904
0.1
1.667
Based on possible experimental setups, we consider three different orders of magnitude of the Biot number (Bi = 0.1, 1 and 10) for the analysis of the determinant of the information matrix (Fig. 2a). Clearly, by increasing the Biot number to Bi = 10, markedly decreases the value of the determinant. Also, for the two lower values of Bi, it has been observed that the determinants are indeed larger, with a still increasing value for the lower value Bi = 0.1, and an almost stabilized value for the intermediate Biot number, Bi = 1.0, at the end of the channel at Zf = 5. Figure 2b illustrates the reduced sensitivity coefficients for each of the three parameters obtained with Bi = 1.0. This figure indicates that the estimation of the Biot number should not pose difficulties, because its sensitivity coefficient is large and linearly independent with respect to the others. On the other hand, the sensitivity coefficients with respect to the two accommodation coefficients are small and linearly dependent, so that the simultaneous estimation of these two parameters may not be possible, unless an informative prior is provided for at least one of them. In fact, an initial attempt of estimating the three parameters was performed by providing a priori information in the form of uniform probability distribution functions for all three parameters, within the admissible minimum and maximum values intervals for each parameter. It was then observed that, especially for the parameter βv, more informative prior would be required for achieving convergence in the estimation procedure. Fortunately, a priori information for both βv and Bi can in principle be obtained for most experimental conditions, by utilizing pressure and mass flow rate measure-
C.P. NAVEIRA-COTTA ET AL.
52
ments to approximate the slip coefficient and by employing classical correlations for estimating the external heat transfer coefficient, respectively. We have then proceeded to the analysis of the inverse problem by providing normal probability distributions as priors for these two parameters (βv and Bi), while maintaining the uniform probability distribution as prior for βt in the interval [1, 5]. The Gaussian priors for βv and Bi were initially assumed with means at the exact values and 10% standard deviations. However, larger standard deviations were also examined in order to further challenge the convergence behavior of the Markov chains, as described below. det [JTJ] 40 30
Bi=1 Bi=0.1
20 10
Bi=10 200
400
600
800
1000
No.Measurements
Figure 2. (a) Influence of Biot number on the sensitivity matrix determinant in terms of the number of measurements along the channel for the simultaneous estimation of the three parameters.
bv
J
−0.05 −0.1
200
i 400
600
No.Measurements 800
1000
bt
−0.15 −0.2
Bi
−0.25
Figure 2. (b) Comparison of reduced sensitivity coefficients in terms of the number of measurements along the channel, Bi = 1.
We first illustrate the Markov chains for each of the three parameters for the base case, involving Gaussian priors for βv and Bi with 10% standard
DIRECT AND INVERSE PROBLEMS SOLUTIONS
53
deviations. In this case, the chains were started from the average values between the admissible minimum and maximum limits (Table 4). Figure 3a–c illustrate the evolution of the Markov chains (up to 50,000 states) for the estimation of the three parameters, βv, βt, and Bi, respectively. Also shown in these figures are the straight lines that correspond to the admissible minimum and maximum limits for each specific parameter, while the initial values were taken as the averages of these two values. One may clearly observe that the Markov chain for the parameter Bi has a distinguished behavior of a very fast convergence, in comparison to the other two parameters, requiring less than 1,000 states. The slip boundary condition coefficient, βv, appears to be the worst one to estimate in the present situation, as also indicated by the respective sensitivity analysis (Fig. 3b). Table 4 below summarizes the input data and illustrates not only the estimated values, after neglecting the first 10,000 states in each chain, but also the minimum and maximum values of the 95% confidence intervals for such estimated parameters. Even for the least sensitive parameter, βv, the exact value lies within the confidence intervals, though it presents the widest interval among the three estimated parameters. TABLE 4. Estimated parameters values with 50,000 states in Markov chains (neglecting first 10,000 states for the chains burn in) and the corresponding 95% confidence intervals for the base case. Parameter βv
Exact 1.5
Initial 3
Interval [1, 5]
Estimated 1.52
Min. with 95% 1.31
Max. with 95% 1.79
βt
2.0
3
[1, 5]
2.01
1.89
2.14
Bi
1.0
5.05
[0.1, 10]
1.000
0.996
1.003
Then, we attempt to illustrate the effect of increasing the standard deviation on the average values informed as priors for the two coefficients βv and Bi, now markedly increased to 20%, with the initial guesses provided by the average values of the admissible limits as for the base case. It has been noticed that the convergence of the Markov chains have been affected, especially for the slip coefficients βv and βt. For βv it is apparent that the burn in period seems to require a larger number of states (around 25,000 in this example). This behavior is also evident from the worst estimated values in Table 5, together with the wider confidence intervals, especially for the slip boundary condition coefficients.
C.P. NAVEIRA-COTTA ET AL.
54
Figure 3. (a) Markov chain evolution for parameter βv for the base case.
Figure 3. (b) Markov chain evolution for parameter βt for the base case. Bi
1
10 8 6 4 2
1000
2000
3000
4000
5000
states
Figure 3. (c) Markov chain evolution for parameter Bi for the base case.
DIRECT AND INVERSE PROBLEMS SOLUTIONS
55
TABLE 5. Estimated parameters values with 50,000 states in Markov chains (neglecting first 10,000 states for the chains burn in) and the corresponding 95% confidence intervals for 20% standard deviation in the priors distributions. Parameter
Exact
Initial
Interval
Estimated
Min. with 95%
Max. with 95%
βv
1.5
3
[1, 5]
1.63
1.19
2.11
βt
2.0
3
[1, 5]
2.05
1.85
2.23
Bi
1.0
5.05
[0.1, 10]
1.000
0.997
1.003
Another variation of the base case is considered now by increasing the uncertainty on the simulated temperature measurements to 5%, while returning to the Gaussian priors for βv and Bi with means at the exact values and 10% standard deviations. The estimation of βv is not markedly affected by increasing the measurement errors. On the other hand, the convergence behavior of the chain for βt is clearly altered, with larger amplitudes of oscillation, though still showing a convergence pattern. The Biot number is again the least sensible parameter to the uncertainty on the measurements, with an excellent convergence behavior in its Markov chain. Table 6 reflects such observations, with a larger confidence interval for the temperature jump coefficient, βt. TABLE 6. Estimated parameters values with 50,000 states in Markov chains (neglecting first 10,000 states for the chains burn in) and the corresponding 95% confidence intervals for 5% uncertainty in temperature measurements. Parameter
Exact
Initial
Interval
Estimated
Min. with 95%
Max. with 95%
βv
1.5
3
[1, 5]
1.48
1.22
1.78
βt
2.0
3
[1, 5]
2.00
1.43
2.56
Bi
1.0
5.05
[0.1, 10]
1.001
0.983
1.019
Finally, we examine the influence of reducing the number of experimental measurements by one order of magnitude, bringing the total number down to 100 points along the channel wall, as might be eventually required by resolution limitations of the specific thermographic equipment with respect to the micro-channel length. In this case, it has also been assumed Gaussian priors for βv and Bi, with 10% standard deviations. From Fig. 4a–c, one may conclude that the βt Markov chain convergence is the one most noticeably affected, in comparison to the base case where a total of 1,000 measurement points have been made available. Clearly, larger amplitudes on the βt Markov chain oscillations can be observed, while the Markov chains for the other two parameters do not present an evident variation with respect to
C.P. NAVEIRA-COTTA ET AL.
56
those presented in Fig. 4a–c. The reduced number of measurement points similarly affects the width of the confidence interval for the parameter βt, but again the estimated value remains quite reasonable, as observed from Table 7. The estimation of the other two parameters is less affected by the reduction on experimental observations. TABLE 7. Estimated parameters values with 50,000 states in Markov chains (neglecting first 10,000 states for the chains burn in) and the corresponding 95% confidence intervals for a total of 100 temperature measurements.
1.47
Min. with 95% 1.21
Max. with 95% 1.76
[1, 5]
1.97
1.53
2.40
[0.1, 10]
1.000
0.989
1.011
Parameter
Exact
Initial
Interval
Estimated
βv
1.5
3
[1, 5]
βt
2.0
3
Bi
1.0
5.05
Figure 4. (a) Markov chain evolution for parameter βv for a total of 100 temperature measurements.
Figure 4. (b) Markov chain evolution for parameter βt for a total of 100 temperature measurements.
DIRECT AND INVERSE PROBLEMS SOLUTIONS
57
Figure 4. (c) Markov chain evolution for parameter Bi for a total of 100 temperature measurements.
5. Conclusions
Inverse problem analysis of laminar forced convection within micro-channels has been undertaken, focusing on the identification of the momentum and thermal accommodation coefficients for gas flow within the slip flow regime, together with the usually unknown Biot number for the walls heat exchange with the external environment. The aim is to demonstrate the simultaneous estimation of these parameters in actual operating conditions of the associated micro-systems. Also, the idealized experimental setup is based solely on temperature measurements of the external wall surface, as obtainable by infrared thermographic measurements. The Integral Transform method was employed in the direct problem solution, avoiding cumbersome functional representations in the original eigenfunction expansions by adopting a hybrid numerical–analytical solution for the related eigenvalue problem, implemented via the Generalized Integral Transform Technique (GITT). A Bayesian approach of parameter estimation is applied that permits to rigorously take into account a priori information available for the parameters, such as from previous experimental runs, or even from other experimental setups or theoretical predictions. Thus, a priori information usually available for the slip flow boundary condition coefficient and for the Biot number are employed in the proposed estimation procedure, here considered in the form of Gaussian distributions. For the other parameter, the temperature jump boundary condition coefficient, a non-informative uniform distribution was used as prior. The results obtained with simulated measurements containing Gaussian random errors revealed the accuracy and robustness of the present estimation approach.
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Acknowledgements
The authors would like to acknowledge the partial financial support provided by CNPq, CAPES and FAPERJ, Brazilian agencies for the fostering of sciences.
References 1. P. Tabeling, Introduction a la Microfluidique, Belin, Collection Échelles, Paris (2003). 2. G. Karniadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation, Springer, NY (2005). 3. Y. Yener, S. Kakaç, M.R. Avelino, and T. Okutucu, Single-phase Forced Convection in Micro-channels – a State-of-the-art Review, in: S. Kakaç, L.L. Vasiliev, Y. Bayazitoglu, Y. Yener. (Eds.), Microscale Heat Transfer – Fundamentals and Applications, NATO ASI Series, Kluwer Academic Publishers, The Netherlands, pp. 1–24 (2005). 4. R.W. Barber and D.R. Emerson, Challenges in Modeling Gas-Phase Flow in Microchannels: From Slip to Transition, Heat Transfer Eng., V. 27, no. 4, pp. 3–12 (2006). 5. C.B. Sobhan and G.P. Peterson, Microscale and Nanoscale Heat Transfer: Fundamentals and Engineering Applications, CRC Press, FL (2008). 6. M.D. Mikhailov and R.M. Cotta, Mixed Symbolic-Numerical Computation of Convective Heat Transfer with Slip Flow in Microchannels, Int. Comm. Heat & Mass Transfer, Vol. 32, Issues 3–4, pp. 341–348 (2005). 7. R.M. Cotta, M.D. Mikhailov, and S. Kakaç, Steady and Periodic Forced Convection in Microchannels, NATO Science Series II: Microscale Heat Transfer: Fundamentals and Applications, V. 193, S. Kakaç et al. (eds.), pp. 49–74 (2005). 8. S. Yu and T.A. Ameel, Slip Flow Heat Transfer in Rectangular Microchannels, Int. J. Heat Mass Transfer, Vol. 44, pp .4225–4234 (2001). 9. G. Tunc and Y. Bayazitoglu, Heat Transfer in Microtubes with Viscous Dissipation, Int. J. Heat Mass Transfer, Vol. 44, pp. 2395–2403 (2001). 10. G. Tunc and Y. Bayazitoglu, Heat Transfer in Rectangular Microchannels, Int. J. Heat Mass Transfer, Vol. 45, pp. 765–773 (2002). 11. F.V. Castellões and R.M. Cotta, Analysis of Transient and Periodic Convection in Micro-channels via Integral Transforms, Progress in Computational Fluid Dynamics, Vol. 6, 321–326 (2006). 12. F.V. Castellões, C.R. Cardoso, P. Couto, and R.M. Cotta, Transient Analysis of Slip Flow and Heat Transfer in Microchannels, Heat Transfer Engineering, Vol. 28, 549–558 (2007). 13. C.P. Naveira-Cotta, R.M. Cotta, H.R.B. Orlande, and O. Fudym, Eigenfunction Expansions for Transient Diffusion in Heterogeneous Media, Int. J. Heat and Mass Transfer, Vol. 52, pp. 5029–5039 (2009).
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14. M.D. Mikhailov and M.N. Ozisik, Unified Analysis and Solution of Heat and Mass Diffusion, John Wiley, NY (1994); also, Dover Publications (1993). 15. R.M. Cotta, Integral Transforms in Computational Heat and Fluid Flow, CRC Press, USA (1993). 16. R.M. Cotta and M.D. Mikhailov, Heat Conduction: Lumped Analysis, Integral Transforms, Symbolic Computation, Wiley-Interscience, NY (1997). 17. R.M. Cotta, The Integral Transform Method in Thermal and Fluids Sciences and Engineering, Begell House, New York (1998). 18. R.M. Cotta and M.D. Mikhailov, Hybrid Methods and Symbolic Computations, in: W.J. Minkowycz, E.M. Sparrow, and J.Y. Murthy (Eds.), Handbook of Numerical Heat Transfer, 2nd ed., Wiley, NY, pp. 493–522 (2006). 19. M.D. Mikhailov and R.M. Cotta, Integral Transform Method for Eigenvalue Problems, Comm. Num. Meth. Eng., Vol. 10, pp. 827–835 (1994). 20. M.C. Oliveira, R. Ramos, and R.M. Cotta, On the Eigenvalues Basic to the Analytical Solution of Convective Heat Transfer with Axial Diffusion Effects, Comm. Num. Meth. Eng., Vol. 11, pp. 287–296 (1995). 21. L.A. Sphaier and R.M. Cotta, Integral Transform Analysis of Multidimensional Eigenvalue Problems Within Irregular Domains, Num. Heat Transfer, Part BFundamentals, Vol. 38, pp. 157–175 (2000). 22. A. Agrawal and S.V. Prabhu, Survey on Measurement of Tangential Momentum Accommodation Coefficient, J. Vac. Sci. Technol. A, Vol. 26, Issue 4, pp. 634–645 (2008). 23. E.B. Arkilic, K.S. Breuer, and M.A. Schmidt, Mass Flow and Tangential Momentum Accommodation in Silicon Micromachined Channels, J. Fluid Mech., V. 437, pp. 29–43 (2001). 24. S.S. Hsieh, H.H. Tsai, C.Y. Lin, C.F. Huang, and C.M. Chien, Gas Flow in a Long Micro-channel, Int. J. Heat & Mass Transfer, Vol. 47, pp. 3877–3887 (2004). 25. D.J. Rader, W.M. Trott, J.R. Torczynski, J.N. Castañeda, and T.W. Grasser, Measurements of Thermal Accommodation Coefficients, Report SAND20056084, Sandia National Laboratories, Albuquerque (2005). 26. J. Beck and K. Arnold, Parameter Estimation in Engineering and Science, Wiley Interscience, New York (1977). 27. M.N. Ozisik and H.R.B. Orlande, Inverse Heat Transfer: Fundamentals and Applications, Taylor and Francis, New York (2000). 28. J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, Springer-Verlag (2004). 29. D. Gamerman and H.F. Lopes, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman & Hall/CRC, 2nd edition, FL (2006). 30. O. Fudym, H.R.B. Orlande, M. Bamford, and J.C. Batsale, Bayesian Approach for Thermal Diffusivity Mapping from Infrared Images Processing with Spatially Random Heat Pulse Heating, Journal of Physics. Conference Series (Online), V. 135, p. 012–042 (2008). 31. S. Wolfram, The Mathematica Book, version 7.0, Cambridge-Wolfram Media (2008).
CONJUGATED HEAT TRANSFER IN MICROCHANNELS J.S. NUNES1,2, R.M. COTTA1, M.R. AVELINO3, AND S. KAKAÇ4 1
Laboratory of Transmission and Technology of Heat, LTTC Mechanical Engineering Department, COPPE & POLI, Cx. Postal 68503 CEP 21945-970, Universidade Federal do Rio de Janeiro, RJ, Brasil,
[email protected] 2 INPI, Rio de Janeiro, RJ, Brasil 3 Universidade do Estado do Rio de Janeiro, UERJ, Rio de Janeiro, Brasil 4 TOBB University of Economics & Technology, Ankara, Turkey
1. Introduction Energy conservation and sustainable development demands have been driving research efforts, within the scope of thermal engineering, towards more energy efficient equipments and processes. In this context, the scale reduction in mechanical fabrication has been permitting the miniaturization of thermal devices, such as in the case of micro-heat exchangers [1]. More recently, heat exchangers employing micro-channels with characteristic dimensions below 500 μm have been calling the attention of researchers and practitioners, towards applications that require high heat removal demands and/or space and weight limitations [2]. Recent review works [2, 3] have pointed out discrepancies between experimental results and classical correlation predictions of heat transfer coefficients in micro-channels. Such deviations have been stimulating theoretical research efforts towards a better agreement between experiments and simulations, through the incorporation of different effects that are either typically present in micro-scale heat transfer or are effects that are normally disregarded at the macro-scale and might have been erroneously not accounted for in micro-channels. Our own research effort was first related to the fundamental analysis of forced convection within micro-channels with and without slip flow, as required for the design of micro-heat exchangers in steady, periodic and transient regimen [4, 5]. Also recently in Refs. [6–11], the analytical contributions were directed towards more general problem formulations, including viscous dissipation, axial diffusion in the fluid and three-dimensional flow geometries. Then, this fundamental research was extended to include the effects of axial fluid heat conduction and wall corrugation or roughness on heat transfer enhancement [12]. The work of Maranzana et al. [13] further motivated the S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_4, © Springer Science + Business Media B.V. 2010
61
62
J.S. NUNES ET AL.
present analysis, dealing with longitudinal wall heat conduction effects in symmetric micro-channels. Conjugated conduction–convection problems are among the classical formulations in heat transfer that still demand exact analytical treatment. Since the pioneering works of Perelman (1961) [14] and Luikov et al. (1971) [15], such class of problems continuously deserved the attention of various researchers towards the development of approximate formulations and/or solutions, either in external or internal flow situations. For instance, the present integral transform approach itself has been applied to obtain hybrid solutions for conjugated conduction–convection problems [16–21], in both steady and transient formulations, by employing a transversally lumped or improved lumped heat conduction equation for the wall temperature. The present work then illustrates theoretical–experimental research efforts on forced convection in micro-channels, trying to focus on the fundamental aspects that are required to play some role in matching the classical heat transfer models to available or produced experimental results in laminar forced convection. The first aim was to address the walls conjugation effects for a parallel-plates micro-channel, micro-machined from metallic plates, subjected to asymmetric thermal boundary conditions. The typical low Reynolds numbers in such micro-systems may lead to low values of the Peclet number that bring up some relevance to the axial heat diffusion along the fluid stream, especially for regions close to the inlet. Thus, both the bounding walls and the fluid axial diffusion may participate in the overall heat transfer process, and yield different predictions than those reached by making use of conventional macro-scale relations for ordinary liquids. All the theoretical work was performed by making use of mixed symbolicnumerical computation via the Mathematica 7.0 platform [22], and a hybrid numerical–analytical methodology with automatic error control, the Generalized Integral Transform Technique – GITT [23–26], in handling the governing partial differential equations. An experimental setup was designed and built for the determination of Nusselt numbers in a parallel plates channel made of brass and copper inside a PMMA (poly-methyl methacrylate) prism, with Joule effect heating on the brass side. Experimental runs for different Reynolds numbers allowed for obtaining a significant set of experimental results for a microchannel height of 270 μm. Experimental results are then briefly discussed and presented to verify the proposed models.
CONJUGATED HEAT TRANSFER IN MICROCHANNELS
63
2. Theoretical Analysis The objective of this research was to theoretically and experimentally analyze the conjugated heat transfer problem in micro-scale for laminar flow, involving the simultaneous determination of the temperature fields in the liquid and solid regions of a rectangular micro-channel formed by parallel plates made of distinct materials and subjected to asymmetric thermal conditions. The methodology that has been applied in the modeling and solution of this problem consists in the application of the Lumped System Approach to the solid boundaries adjacent to fluid, which are then transformed into boundary conditions for the convection problem and, subsequently, applying the Generalized Integral Transform Technique (GITT) [23–26] to obtain an ordinary differential formulation for the transformed fluid temperatures, solved by an adequate routine in the Mathematica computational platform [22]. An experimental setup was designed and built for the determination of Nusselt numbers in a parallel plate channel made of brass and copper, with Joule effect heating on one side and adjustable distance between the plates, offering comparisons and validation of the proposed model. We thus consider thermally developing forced convection of a Newtonian fluid in the continuum regimen, under fully developed laminar flow inside a rectangular micro-channel formed by parallel layers of different materials and/or thicknesses, and subjected to an inlet temperature Te. The walls are assumed to participate in the heat transfer process within the fluid along the channel length, and to exchange heat with the external environment with the temperature Text and a heat transfer coefficient hext, according to Fig. 1. In addition, the walls are allowed to uniformly generate heat. LZ Text, hext ¶T2 =0 ¶z
Te
y ¶T1 =0 ¶z
¶T2 ¶z
g2
=0
L2
Lf
u(z) z ¶T1 ¶z
g1
=0
L1
Text, hext
Figure 1. Geometry and coordinates system for asymmetric conjugated heat transfer in micro-channels.
J.S. NUNES ET AL.
64
The thermophysical properties of all the materials are taken as constant and the conjugated problem can be written in dimensionless form as follows: ∂ 2θ1 1 ∂ 2θ1 + + Q1 = 0; ∂η 2 ( 2Pe )2 ∂ζ 2
− lη1 < η < 0; 0 < ζ < lξ
2 2 ⎛ dU (η ) ⎞ U (η ) ∂θ f ∂ θ f 1 ∂ θf + +Br ⎜ = ⎟ 2 2 2 4 ∂ζ ∂η ⎝ dη ⎠ ( 2Pe ) ∂ζ
(1a)
2
∂ 2θ 2 1 ∂ 2θ 2 + + Q2 = 0; ∂η 2 ( 2Pe ) 2 ∂ζ 2
0 <η <1
1 < η < lη 2
ζ >0
0 < ζ < lζ
(1b) (1c)
where the three energy equations above refer, respectively, to the lower wall, to the fluid and to the upper wall in Fig. 1. The following boundary and inlet conditions are proposed:
−
∂θ1 =0 ∂ζ
ζ = 0,
∂θ1 =0 ∂ζ
ζ = lξ
(2a,b)
∂θ 2 =0 ∂ζ
ζ = 0,
∂θ 2 =0 ∂ζ
ζ = lζ
(2c,d)
∂θ1 + Biη 1θ1 = 0 ∂η
∂θ 2 + Biη 2θ 2 = 0 ∂η
η = −lη1 ,
θ f (η , ζ ) = 1
∂θ f
ζ = 0,
η = lη 2
(2e,f)
=0
ζ = lζ
(2g,h)
=
∂θ1 ∂η
η =0
(2i,j)
=
∂θ 2 ∂η
∂ζ
besides the interface conditions θ f = θ1 θ f = θ2
η =1
η = 0, 0 < ζ < lζ ,
k1* k2*
∂θ f ∂η ∂θ f ∂η
η =1
0 < ζ < lζ
The following dimensionless relations were here employed:
(2k,l)
CONJUGATED HEAT TRANSFER IN MICROCHANNELS
θi =
Ti − T∞ , where i = 1, 2, f ; T0 − T∞
Dh =
ζ =
z ; Pr Re Dh
η=
y ; Lf
4( L f * Lw ) 4S ⇒ , since Lw >> L f ⇒ Dh = 2 L f ; P 2( L f + Lw )
U (η ) =
u ( y) u
Pe = Re Pr;
dζ 1 = ; dz Pr Re Dh
; Re =
uDh
ν
65
(3a–k)
dη 1 = ; dy L f
u ( y ) = 3 y (1 − 2 y )
;
and, Q1 =
g1 L2f k1ΔT
, W (η ) =
k1* =
kf
;
k1
U (η )
, Q2 =
4
k2* =
kf k2
lη1 =
;
g 2 L2f k 2 ΔT
and Br =
μ u k ΔT
L2 + L f L1 , lη 2 = Lf Lf
(3l–o) (3p–s)
where the indexes 1 and 2 denote the lower and upper solid layers, and f refers to the fluid. The Classic Lumped System Analysis is applied to the energy equations of the two solid layers that define the walls of the channel. This reformulation and simplification strategy is feasible once the temperature gradients across both walls are sufficiently smooth, a behavior governed by the magnitudes of the Biot numbers at each face of the two walls. For instance, considering the thermally thin-walled hypothesis for layer 1 above, the lumping procedure assumes that θ1 ( −lη 1 , ζ ) ≅ θ1 ( 0, ζ ) ≅ θ av ,1 (ζ )
(4a)
where θ av ,1 (ζ ) is calculated by the transversally averaged temperature definition: θ av ,1 (ζ ) =
1 lη1
∫
0
− lη 1
θ1 (η , ζ ) dη
(4b)
Equation (1a) for θ1 (η , ζ ) is thus integrated in the η direction, applying the integral operator
1 lη 1
∫
0
− lη 1
in both the energy equation and required
___ dη
boundary conditions, providing after some manipulation: −
∂θ f ∂η
+ Biη*1θ f =
∂ 2θ f (η , ζ )
lη1
( 2Pe )
2
∂ζ 2
+ Q1* η =0
η =0
(5a)
J.S. NUNES ET AL.
66
where Biη*1 =
Biη 1
lη1
and Q1* =
k
* 1
k1*
(5b,c)
Q1
The same procedure is then applied to layer 2, Eq. (1c), which results in: ∂θ f ∂η
+ Biη* 2θ f =
(l
η2
− 1) ∂ 2θ f (η , ζ )
k2* ( 2Pe )
η =1
+ Q2*
∂ζ 2
2
(5d)
η =1
where Biη*2 =
Biη 2 k
and Q2* =
* 2
(l
− 1)
η2
k
* 2
Q2
(5e,f)
Thus, application of the lumping procedure to the original formulation leads to the extended Graetz problem described by the equation and boundary conditions below: W(η)
∂θ f ∂ζ
=
−
∂2θ f ∂η2
∂θ f ∂η
∂θ f ∂η
+
1
2
∂2θ f
⎛ dU(η) ⎞ + Br ⎜ ⎟ , 0 <η < 1, ζ > 0 ⎝ dη ⎠
2 2 ( 2Pe) ∂ζ
∂ 2θ f (η , ζ )
+ Biη*1θ f = Cj1
∂ 2θ f (η , ζ )
+ Biη* 2θ f = Cj2
θ f (η , ζ ) = 1
∂ζ 2
∂ζ 2
ζ = 0,
∂θ f ∂η
(6a)
+ Q1* ,
η =0
(6b)
+ Q2* ,
η =1
(6c)
=0
ζ = lζ
(6d,e)
where Cj1 and Cj2 are the conjugation coefficients, respectively, in the lower and upper walls, as: Cj1 =
lη 1 (2Pe) k 2
* 1
; Cj2 =
lη 2 − 1 (2Pe) 2 k2*
(6f,g)
Equations (6) are now solved by the Generalized Integral Transform Technique, GITT, starting with the choice of an appropriate filtering solution that eliminates the non-homogeneous terms in the equation and boundary conditions: θ f (η , ζ ) = θ H (η , ζ ) + θ P (η )
(7)
A fairly simple filter in terms of a purely diffusive formulation in the transversal direction is proposed:
CONJUGATED HEAT TRANSFER IN MICROCHANNELS
67
2
d 2θ P (η ) ⎛ d (U (η ) ⎞ +Br ⎜ ⎟ =0 dη 2 ⎝ dη ⎠
−
0 <η <1
dθ P (η ) + Biη*1θ P (η ) = Q1* dη dθ P (η ) + Biη* 2θ P (η ) = Q2* dη
ζ >0
(8a)
η =0
(8b,c) η =1
The filtered problem formulation is then given by: W (η )
∂θ H (η , ζ ) 1 ∂ 2θ H (η , ζ ) ∂ 2θ H (η , ζ ) − = ∂ζ (2Pe)2 ∂ζ 2 ∂η 2
θ H (η , ζ ) = 1 − θ P (η ), ζ = 0; −
∂θ H (η , ζ ) ∂η
∂θ H (η , ζ ) ∂η
+ Biη*1θ H (η , ζ ) = Cj1
+ Biη 2θ H (η , ζ ) = Cj2 *
0 <η <1
∂θ H (η , ζ ) ∂η
ζ >0
(9a)
= 0, ζ = lζ
(9b,c)
∂ 2θ H (η , ζ ) ∂ζ 2 ∂ 2θ H (η , ζ ) ∂ζ 2
η =0
(9d,e) η =1
The auxiliary problem that forms the basis for the eigenfunction expansion is then proposed: d 2ψ i (η ) dη 2
−
dψ i (η ) ∂η
+ β i2W (η )ψ i (η ) = 0,
+ Biη*1ψ i (η ) = 0, η = 0;
dψ i (η ) ∂η
0 <η <1
+ Biη* 2ψ i (η ) = 0, η = 1
(10a) (10b,c)
Then, the integral transform pair is constructed for application of the GITT: ⎧θ (ζ ) = 1W (η )ψ (η )θ (η , ζ ) dη i H ∫0 ⎪⎪ i ∞ ψ η ⎨ ( ) ⎪θ H (η , ζ ) = ∑ i θ i (ζ ) N ⎪⎩ i =1 i
transform
(11a,b) inverse
where the norm is given by: 1
Ni = ∫ W (η )ψ i (η ) dη 0
2
(11c)
Using the integral operator in Eq. (11a) and applying the 2nd Green’s formula, the transformed system is given by:
J.S. NUNES ET AL.
68 dθi (ζ ) dζ
+ βi2θi (ζ ) = Cj1ψ i ( 0)
∂2θH ∂ζ 2
+ Cj2ψ i (1) η =0
∂2θH ∂ζ 2
+ η =1
1
( 2Pe)
1
ψ i (η ) 2 ∫ 0
∂ 2θH dη (12a) ∂ζ 2
Employing the inverse formula in the axial diffusion term, 1 ∂2θH ψ η dη , we find: ( ) i 2 ∂ζ 2 ( 2Pe) ∫0 1
∞
∑ j =1
1
( 2Pe )
2
2 ∞ d 2θ j (ζ ) 1 1 1 d θ j (ζ ) Iψ ij ψ η ψ η d η = ( ) ( ) ∑ j 2 ∫0 i 42444 d ζ 2 N j 144 dζ 2 N j 3 j =1 ( 2Pe )
(12b)
Iψ ij
Replacing directly into Eq. (12a) the relations found in the modified boundary conditions, Eq. (9d,e), we have: dθi (ζ ) dζ
⎛ ∂θ + βi2θi (ζ ) = ψ i ( 0) ⎜ − H ⎜ ⎝ ∂η
⎞ ⎛ ∂θ ⎞ + Biη*1θw1 (ζ ) ⎟ +ψ i (1) ⎜ H + Biη*2θw2 (ζ ) ⎟ + ⎟ ⎜ ⎟ η =0 ⎠ ⎝ ∂η η =1 ⎠ (12c) 2 ∞ 1 d θ j (ζ ) Iψ ij +∑ 0 <η < 1 ζ > 0 2 dζ 2 N j j =1 ( 2Pe )
where θ w1 (ζ ) = θ f ( 0, ζ ) and θ w 2 (ζ ) = θ f (1, ζ ) . After substitution of the inverse formulae in the remaining terms, and some rearrangement, the transformed ODE system is written as: ∞
∑ aaij j =1
d 2θ j (ζ ) dζ 2
∞
− ∑ δ ij
dθ j ( ζ ) dζ
j =1
∞
− ∑ aijθ j (ζ ) =
(13a)
j =1
− ⎡⎣ g1iθ w1 ( ζ ) + g 2iθ w 2 (ζ )i ⎤⎦
0 <η <1
ζ >0
where ⎧ dψ 1 ⎛ ⎪ βi2 − ⎜ψ i (1) i ⎜ N dη ⎪⎪ j ⎝ A = {aij } ⎨ dψ j ⎪ 1 ⎛ ⎜ψ i (1) ⎪ − ⎜ Nj ⎝ dη ⎩⎪
⎞ ⎟ ⎟ η =0 ⎠
i≤N j≤N i= j
⎞ ⎟ −ψ i ( 0 ) dη η = 0 ⎟⎠ η =1
i≤N j≤N i≠ j
−ψ i ( 0 ) η =1
[ AA] = {aaij } =
dψ i dη dψ j
Iψ ij
1
( 2Pe )
2
Nj
(13b,c)
⎧i ≤ N ∀i, j ⎨ ⎩j≤ N
(13d)
CONJUGATED HEAT TRANSFER IN MICROCHANNELS g1 = { Biη*1ψ i ( 0 )} , g 2 = {Biη*2ψ i (1)} ,
69
i≤N
(13e,f)
The equations that govern the wall temperatures are then rewritten as: dθ w' 1 1 N 1 ∂ψ j =− ∑ dζ Cj1 j =1 N j ∂η dθ w' 2 1 = dζ Cj2
1 ∂ψ j ∑ N j =1 j ∂η
θ j (ζ ) + η =0
N
θ j (ζ ) + η =1
Biη*1 Cj1
Biη* 2 Cj2
θ w1 (ζ )
(14a,b)
θ w 2 (ζ )
The boundary conditions for the transformed temperatures and wall temperatures are given by: θ i (ζ ) = f i dθ w1 dζ
=0; ζ =0
ζ = 0 , θ i ' (ζ ) = 0 dθ w1 dζ
=0; ζ = lζ
dθ w2 dζ
ζ = lζ , =0; ζ =0
i = 1, 2,K, N (14c,d) dθ w 2 dζ
= 0 (14e–h) ζ = lζ
where 1
fi = ∫ W (η )ψ i (η )(1 − θ P (η ) ) dη
(14i)
0
Due to the slower convergence rates expected from the above formal solution once the inverse formula is substituted back into Eq. (12c), as noted in Refs. [17, 18], the energy equation is integrated across the transversal domain, as described in Refs. [23, 24] and named as the integral balance scheme, in order to reach an improved convergence behavior in the representation of the derivatives and temperatures at the boundary positions. Thus, the fluid energy equation is integrated across the channel, and the inverse formula is substituted for the bulk temperature within the convection term, providing alternative expressions for the boundary derivatives. This procedure can be found in detail in Ref. [11]. Thus, the following ODE system truncated to order N is to be solved:
{Y ' (ζ )} = [C ]{Y (ζ )}
{
(15a)
}
Y = θ1 (ζ ) ,θ2 (ζ ) ,K,θN (ζ ) ,θ1' (ζ ) ,θ2' (ζ ) ,K,θN' (ζ ) ,θw1 (ζ ) ,θw2 (ζ ) ,θw'1 (ζ ) ,θw'2 (ζ )
T
(15b)
which requires the computation of the eigenvalues and eigenvectors of matrix C to yield the solution vector Y, or:
J.S. NUNES ET AL.
70
(C − I λ )ξ = 0 ,
N +4
∑c ξ e
Y (ζ ) =
k
k =1
k
λk ζ
(15c,d)
It should be noticed that the averaged wall temperatures, θ ( ζ ) and θ ( ζ ) , are directly obtained from the solution vector Y ( ζ ) as positions N + 1 and N + 2, as well as their longitudinal derivatives (positions N + 3 and N + 4). The fluid bulk temperature is given by the working expression below: w1
w2
θ (ζ ) ∑ ∫ W (η )ψ (η ) dη N ∫ W (η )θ (η ) dη + (ζ ) = η η W d ( ) ∫ ∫ W (η ) dη N
θ av
i =1
1
i
0
i
1
i
P
0
1
1
0
0
(16)
For the computation of the associated local Nusselt numbers, the derivatives at the walls of the fluid temperature are obtained by making use of the expressions previously derived with the integral balance scheme, or simply in the more direct form illustrated below for wall 1: ⎛ ∞ dψ (η ) θ i (ζ ) dθ p (η ) ⎞ i ⎟ −2 ⎜ ∑ + ⎜ i =1 dη η = 0 N i dη η = 0 ⎟⎠ ⎝ Nu1 = θ w1 (ζ ) − θ av (ζ )
(17)
3. Experimental Analysis Before obtaining the experimental results for the proposed covalidation effort, two prior steps were required, namely, the design and fabrication of the microchannels, and the assembly of an experimental platform that would allow for the easy exchange of different microchannel setups. A PMMA (poly-methyl methacrylate) prism of low thermal conductivity was employed as the structural support of the metallic plates that form the microchannels, chosen to be made of electronic grade copper (upper plate) and brass (lower plate). Micro-machining of the PMMA block and of the metallic plates was accomplished and the setup was assembled according to Fig. 2 below. Figure 3 show the assembled microchannel setup, within the PMMA block, and the installed thermocouples at both the lower (Fig. 3a) and the upper (Fig. 3b) plates. The employed technique allowed for the fabrication of microchannels up to 20 μm of plates spacing and uncertainty of ±2.0 μm. The complete experimental platform is shown in Fig. 4 below, which is fully automated, both in the data acquisition and on the control of the flow and heating parameters. The concept was that of allowing for straightforward interchanges of the microchannel setups without modifications of the remaining of the platform.
CONJUGATED HEAT TRANSFER IN MICROCHANNELS a plenum de entrada
furos para os termopares
entrada do fluido
71
saída do fluído plenum de saida tomada de pressão de saida
tomada de pressão de entrada microcanal terminais eletricos
b
(a)
cobre
canal blocos de
(b)
latão
Figure 2. (a) Schematic representation of the microchannel assembly, (b) cross section view of the assembly.
Figure 3. Details of the lower and upper plates of the microchannel setup with installed thermocouples.
Figure 4. General view of the experimental platform.
72
J.S. NUNES ET AL.
The microchannel wall was heated by Joule effect through an alternate current circuit of 220 V and 33 A. Temperature measurements were taken with type E (chromel-constantan) and type K (chromel-alumel) thermocouples, with uncertainty to within 0.3°C. Pressure difference measurements were obtained with membrane type pressure tranduscers, model S10 from WIKA Alexander Wiegand GmbH & C.KG, 0–10 bar (4–20 mA). Mass flow rate was determined with the aid of an electronic scale MARTE model AS 2,200 (0–2,000 g, ±0.0001 g). The acquisition system was based on a microcomputer Pentium IV with 2Gb of RAM, HD of 80 Mb, and RS 232 and USB connections, also functioning as a “data logger”. The system employed was the Compact Field Point of National Instruments, model CFP 2000, with one module for acquisition of temperature through resistance, two modules for temperature acquisition through thermocouples, and one module for acquisition with current, as can be observed in Fig. 5. The software LabView 8.0 was utilized in the construction of the control and acquisition computer code, including the data statistical treatment and the uncertainty analysis of the incorporated measurements (Fig. 6). Figure 5 below shows a schematic representation of the experimental apparatus, where each one of the constructive elements is identified. An additional computational code was developed on the Mathematica 7.0 system for determining the propagation of uncertainties up to the evaluation of the local and mean Nusselt numbers, based on the measurements of temperature, mass flow rate, channel dimensions, and the power generated by Joule effect in the copper bar at the bottom of the channel, through the
Figure 5. Schematic representation of the experimental apparatus.
CONJUGATED HEAT TRANSFER IN MICROCHANNELS
73
Figure 6. (a) CFP2000 acquisition system with the acquisition and signal processing modules, (b) screen of the software constructed with LabView 8.0 for control and acquisition.
resistance and potential difference measurements on the bar. Table 1 below shows uncertainties associated to the each experimental measurement, used to calculate the uncertainty of the experimental Nusselt numbers. The average uncertainty estimated for the local Nusselt number experimental results was around 11.6%. 4. Results and Discussion The first step in the present implementation of the conjugated heat transfer problem in microchannels was to compare and validate the obtained results with published ones for the symmetric case [16, 19], also obtained through GITT but not accounting for heat generation within the walls and the fluid and for axial heat conduction along the fluid. In both sets of results the observed agreement was quite good, and the present implementation reproduces slightly more closely the more recent implementation in Ref. [19]. It should be noted that truncation orders of up to N = 30 were employed in the present simulation.
J.S. NUNES ET AL.
74
TABLE 1. Uncertainties associated to each individual measurement that compose the uncertainty of the Nusselt number. Parameter
Uncertainties
Meter
Reading
Time Mass Pressure
0.01% 2.0% 1.0%
clock/CPU Scale Transmitter pressure
LW R-232/LW cFP-22/LW
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PT-100 Thermocouple E Thermocouple K Digital micrometer Digital multimeter Digital multimeter
cFP-22/LW cFP-22/LW cFP-22/LW Manual Manual Manual
Next, the proposed asymmetric model was verified through experimental measurements on the parallel plates micro-channel micro-machined from metallic plates of copper and brass, with adjustable spacing. The lower plate is heated by Joule effect and the whole set was encapsulated in the acrylic casing, being cooled by distilled water. Temperature measurements were then taken within both plates, and compared with the simulation results for the lumped wall temperatures along the channel length. The range of Reynolds number analyzed was approximately from Re = 10 to 250. Sample graphs of such comparisons are shown in Fig. 7 below, for a parallel plates spacing of 270 μm, and Re = 13, 64, 122, and 224, and in Fig. 8 for Re = 15, 47, 64 and 151. The two sets of curves were taken in different runs, so as to provide a repeatability analysis as well. The curves to the left refer to the measurements at the heated bottom wall, while the curves to the right are temperatures measured at the top wall. The agreement between theoretical and experimental wall temperature values is indeed quite reasonable, except at the last set of curves in each figure, related to the very low values of Reynolds number. One may also observe the marked influence of the Reynolds number on the heat transfer behavior throughout this range, with the noticeable loss of adherence of the theoretical results for lower values of Re (Re = 13 in Fig. 7 and Re = 15 in Fig. 8). Also, the model here proposed does not account for heat losses at the walls ends and for axial heat flow towards the entry tubing of the channel, beyond the heat transfer section,
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which start playing some role for such lower values of Peclet number and reducing the temperature gradients along the walls. Figure 9 provides the theoretical predictions of the dimensionless walls temperature distributions along the channel length, for the same values of Reynolds numbers as considered in Fig. 7. Clearly, the present model predicts that the temperature differences between the entrance and exit are less marked for the higher values of Re, while more significant temperature variations along the channel are observable at the lower values of Re, towards the channel exit. In fact, the proposed formulation does not account for heat losses at the fluid and walls ends, and also the structure, which are seen to be significant when the temperature differences increase at low Re. Table 2 brings a comparison of theoretical and experimental local Nusselt numbers at the middle of the channel length (x = L/2) and at the end (x = L), together with the corresponding values of Reynolds and Prandtl numbers, and conjugation parameters at the bottom and top walls. It can be seen that the conjugation parameters grow from around 10–4 for the higher values of Re, to almost 1 at the lower value of Re around 10. The model seems to account reasonably well for the physical effects, predicting the Nusselt numbers at both axial positions to within a maximum deviation of 3% in the range of parameters here investigated, with a slightly higher deviation for decreasing Reynolds number. TABLE 2. Comparison of simulation and experiments for local Nusselt numbers in microchannel (x = L/2 and x = L). Re 242.2 206.1 151.2 122.2 102.4 79.47 65.34 47.45 15.44 10.82
Pr 6.48 6.27 6.25 6.33 5.94 5.76 6.18 5.33 5.52 5.01
Cj1 2.86 × 10–4 4.26 × 10–4 7.86 × 10–4 1.18 × 10–3 1.89 × 10–3 0.00332 0.00429 0.00947 0.0954 0.234
Cj2 1.17 × 10–3 1.74 × 10–3 3.21 × 10–3 4.80 × 10–3 7.71 × 10–3 0.0136 0.0175 0.0386 0.389 0.955
Nuth(L/2)
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5.072 4.926 4.755 4.675 4.615 4.576 4.569 4.554 4.509 4.473
5.068 4.987 4.823 4.738 4.656 4.580 4.553 4.485 4.380 4.385
4.683 4.628 4.581 4.566 4.561 4.556 4.555 4.547 4.488 4.440
4.715 4.672 4.587 4.545 4.503 4.466 4.453 4.485 4.499 4.374
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The experimental results for the local Nusselt numbers may also be examined over Fig. 9 below, where the results are encapsulated by the theoretical values of the limiting situations of prescribed wall temperatures and prescribed wall heat fluxes. It can be noticed that for lower values of Re, when the conjugation parameters also markedly grow (see Table 2), the obtained Nusselt numbers approach the limiting solution of a prescribed uniform wall temperature, due to the longitudinal wall heat conduction effect. As the Reynolds number increases, the Nusselt number starts migrating towards the prescribed wall heat flux condition, with the progressive reduction of the conjugation effects. It should also be observed that for the higher values of Re, the Nusselt number values at x = L/2 and x = L deviate significantly, since at the middle of the channel (and eventually even at the end) one has not yet reached a fully developed condition, such as for the lower values of Re where they practically coincide. In conclusion, the influence of conjugated convection–conduction heat transfer in microchannels was investigated, considering an asymmetric parallel-plates configuration, with heat generation within the walls, besides axial heat diffusion and viscous dissipation in the fluid. An experimental setup was built to measure the wall temperatures and evaluate Nusselt numbers along a brass–copper microchannel with 270 μm spacing between the parallel plates, heated at the bottom brass plate. In the range of parameters analyzed (10 < Re < 250), the relevance of wall conjugation was verified, and the simulated results provided an agreement within 3% against the experimental local Nusselt numbers along the channel (Fig. 10). Conjugation deviates the thermal boundary condition from the expected simplified model of applied uniform heat flux, and at limiting situations brings the system behavior to that of a prescribed uniform temperature case. Thus, the simplified uniform wall heat flux modeling can induce an erroneous interpretation of heat transfer augmentation once conjugation effects are not accounted for in the interpretation of experimental results, which might aid in partially explaining discrepancies observed among experimental results in microchannels and classical correlations for internal forced convection built for macroscale situations [3, 13].
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Figure 10. Comparison of measured (dots) local Nusselt numbers for parallel-plates microchannel against limiting fully developed values for prescribed wall temperature (solid line) and heat flux (dashed line) (rearranging from 10 to 242).
Acknowledgements The authors would like to acknowledge the financial support provided by CNPq, Brasil, RJ.
References 1. C.B. Sobhan and G.P. Peterson, Microscale and Nanoscale Heat Transfer: Fundamentals and Engineering Applications, CRC Press, Boca Raton, FL (2008). 2. Y. Yener, S. Kakaç, M. Avelino, and T. Okutucu, Single-phase Forced Convection in Micro-channels – a State-of-the-art Review, in: S. Kakaç, L.L. Vasiliev, Y. Bayazitoglu, Y. Yener (Eds.), Microscale Heat Transfer – Fundamentals and Applications, NATO ASI Series, Kluwer Academic Publishers, The Netherlands, pp. 1–24 (2005). 3. G.L. Morini, Single-Phase Convective Heat Transfer in Microchannels: a Review of Experimental Results, Int. J. of Thermal Sciences, 43, 631–651 (2004). 4. M.D. Mikhailov and R.M. Cotta, Mixed Symbolic-Numerical Computation of Convective Heat Transfer with Slip Flow in Microchannels, Int. Comm. Heat & Mass Transfer, 32, 341–348 (2005). 5. R.M. Cotta, S. Kakaç, M.D. Mikhailov, F.V. Castellões, C.R. Cardoso, Transient Flow and Thermal Analysis in Microfluidics, in: S. Kakaç, L.L.
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6. 7. 8. 9. 10. 11.
12.
13. 14. 15. 16. 17. 18. 19. 20. 21.
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Vasiliev, Y. Bayazitoglu, Y. Yener (Eds.), Microscale Heat Transfer – Fundamentals and Applications, NATO ASI Series, Kluwer Academic Publishers, The Netherlands, pp. 175–196 (2005). S. Yu and T.A. Ameel, Slip Flow Heat Transfer in Rectangular Microchannels, Int. J. Heat Mass Transfer, 44, 4225–4234 (2001). G. Tunc and Y. Bayazitoglu, Heat Transfer in Microtubes with Viscous Dissipation, Int. J. Heat Mass Transfer, 44, 2395–2403 (2001). G. Tunc and Y. Bayazitoglu, Heat Transfer in Rectangular Microchannels, Int. J. Heat Mass Transfer, 45, 765–773 (2002). F.V. Castellões and R.M. Cotta, Analysis of Transient and Periodic Convection in Micro-channels via Integral Transforms, Progress in Computational Fluid Dynamics, 6, 321–326 (2006). F.V. Castellões, C.R. Cardoso, P. Couto, and R.M. Cotta, Transient Analysis of Slip Flow and Heat Transfer in Microchannels, Heat Transfer Engineering, 28, 549–558 (2007). J.S. Nunes, P. Couto, and R.M. Cotta, Conjugated Heat Transfer Problem in Rectangular Micro-channels under Asymmetric Conditions, Proc. of 5th National Congress of Mechanical Engineering, CONEM 2008, ABCM, Paper no. CON08-0739, Salvador, BA, August 2008. F.V. Castellões and R.M. Cotta, Heat Transfer Enhancement in Smooth and Corrugated Microchannels, Proc. of the 7th Minsk Int. Seminar on Heat Pipes, Heat Pumps, Refrigerators, Invited Lecture, Minsk, Belarus, 8–11 September 2008. G. Maranzana, I. Perry, and D. Maillet, Mini- and Micro-channels: Influence of Axial Conduction in the Walls, Int. J. Heat and Mass Transfer, 47, 3993– 4004 (2004). Y.L. Perelman, On Conjugate Problems of Heat Transfer, Int. J. Heat and Mass Transfer, 3, 293–303 (1961). A.V. Luikov, V.A. Aleksashenko, and A.A. Aleksashenko, Analytical Methods of Solution of Conjugated Problems in Convective Heat Transfer, Int. J. Heat and Mass Transfer, 14, 1047–1056 (1971). R.O.C. Guedes, R.M. Cotta, and N.C.L. Brum, Conjugated Heat Transfer in Laminar Flow Between Parallel – Plates Channel, 10th Brazilian Congress of Mechanical Engineering, Rio de Janeiro, Brazil, 1989. R.O.C. Guedes, R.M. Cotta, and N.C.L. Brum, Heat Transfer in Laminar Tube Flow with Wall Axial Conduction Effects, J. Thermophysics & Heat Transfer, 5 (4), 508–513 (1991). R.O.C. Guedes and R.M. Cotta, Periodic Laminar Forced Convection within Ducts Including Wall Heat Conduction Effects, Int. J. Eng. Science, 29 (5), 535–547 (1991). F.G. Elmor, R.O.C. Guedes, and F.N. Scofano, Improved Lumped Solution for Conjugate Heat Transfer In Channel Flow with Convective Boundary Condition, Int. J. Heat & Technology, pp. 78–88 (2005). C.P. Naveira, M. Lachi, R. M. Cotta, and J. Padet, Hybrid Formulation and Solution for Transient Conjugated Conduction-External Convection, Int. J. Heat & Mass Transfer, 52, 112–123 (2009). C.P. Naveira-Cotta, M. Lachi, M. Rebay, and R.M. Cotta, “Comparison of Experiments and Hybrid Simulations of Transient Conjugated Conduction–
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J.S. NUNES ET AL. Convection–Radiation, ICCHMT International Symposium on Convective Heat and Mass Transfer in Sustainable Energy, CONV-09, Yasmine Hammamet, Tunisia, April 2009. S. Wolfram, The Mathematica Book, version 7.0, Cambridge-Wolfram Media (2008). R.M. Cotta, Integral Transforms in Computational Heat and Fluid Flow, CRC Press, USA (1993). R.M. Cotta and M.D. Mikhailov, Heat Conduction: Lumped Analysis, Integral Transforms, Symbolic Computation, Wiley-Interscience, NY (1997). R.M. Cotta, The Integral Transform Method in Thermal and Fluids Sciences and Engineering, Begell House, New York (1998). R.M. Cotta and M.D. Mikhailov, Hybrid Methods and Symbolic Computations, in: W.J. Minkowycz, E.M. Sparrow, and J.Y. Murthy (Eds.), Handbook of Numerical Heat Transfer, 2nd ed., Wiley, New York, pp. 493–522 (2006).
MECHANISMS OF BOILING IN MICROCHANNELS: CRITICAL ASSESSMENT J.R. THOME AND L. CONSOLINI EPFL-STI-IGM-LTCM Ecole Polytechnique Fédérale de Lausanne (EPFL) Lausanne CH-1015, Switzerland,
[email protected]
Abstract. Numerous characteristic trends and effects have been observed in published studies on two-phase micro-channel boiling heat transfer. While macro-scale flow boiling heat transfer may be decomposed into nucleate and convective boiling contributions, at the micro-scale the extent of these two important mechanisms remains unclear. Although many experimental studies have proposed nucleate boiling as the dominant micro-scale mechanism, based on the strong dependence of the heat transfer coefficient on the heat flux similar to nucleate pool boiling, they fall short when it comes to actual physical proof. A strong presence of nucleate boiling is reasonably associated to a flow of bubbles with sizes ranging from the microscopic scale to the magnitude of the channel diameter. The bubbly flow pattern, which well adapts to this description, is observed however only over an extremely limited range of low vapor qualities (typically for x <0.01–0.05). Furthermore, at intermediate and high vapor qualities, when the flow assumes the annular configuration and a convective behavior is expected to dominate the heat transfer process, the experimental evidence yields entirely counter intuitive results, with heat transfer coefficients often decreasing with increasing vapor quality rather than increasing as in macro-scale channels, and with a much diminished heat flux dependency as would be expected. In summary, convective boiling in micro-channels has revealed to be much more complex than originally thought. The present review aims at describing and analyzing the boiling mechanisms that have been proposed for two-phase microchannel flows, confronting them with the available experimental heat transfer results, while highlighting those questions that, to date, remain unanswered. 1. Introduction The initial purpose of the studies on two-phase heat transfer in micro-channels was (and still is, to a certain extent) aimed at understanding the mechanisms controlling the flow boiling process. The earliest results of Lazarek and Black [1] showed values for the heat transfer coefficient that were unaffected S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_5, © Springer Science + Business Media B.V. 2010
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by vapor quality, but were a function of heat flux, leading them to conclude that nucleate boiling was the dominant heat transfer mechanism as in macroscale flow boiling. While others confirmed this trend and adopted their explanation, new trends arose as the amount of experimentation in the sector grew. A significant number of studies found decreasing curves in the α–x plane rather than flat ones (with α the heat transfer coefficient and x the thermodynamic vapor quality), and even some increasing trends in α versus x, giving rise to a rather puzzling scenario with respect to the macro-scale knowledge base (these were documented, for instance, in Ref. [2]). The relative importance of nucleate boiling, thin film evaporation and convective boiling in the individual flow patterns that are characteristic to a micro-channel flow is thus still unclear. The studies directed specifically to flow patterns (see, for example, [4, 5]), many of which are for air–water flows, found general agreement as to the four main regimes: (i) bubbly flow, at very low mass fractions of air or vapor, (ii) slug flow, describing the passage of long bubbles separated by liquid slugs, (iii) churn flow, a transition mode between slug flow and fully annular flow, and (iv) annular flow, occurring at the highest gas superficial velocities (see Fig. 1). Recently, similar flow patterns have also been reported for the flow of refrigerants (cf. [6]), confirming the absence of any stratified regime in the micro-scale. Cornwell and Kew [7] coupled flow patterns and heat transfer, by arguing that different flow regimes presented different heat transfer mechanisms, varying from essentially nucleate boiling, to confined bubble boiling, and finally to purely convective evaporation for annular flows. Jacobi and Thome [8] and Thome et al. [9] postulated that during slug flow, nucleate boiling is completely suppressed and heat is transferred primarily by conduction through the thin evaporating film surrounding the elongated bubbles, while heat transfer to the liquid slug and any dry zone are only of second and third importance depending on their respective residence times. An added element to the discussion concerns the possibility of periodic dry-out of the channel wall (see [7, 9, 10]). This mechanism however was not entirely understood, and very few gave a clear opinion as to how and when it occurred. The work presented in Ref. [9] was among the few that attempted to address this issue, suggesting the development of a dry-zone at the tail of an evaporating bubble. In recent years, a number of studies provided evidence to the sensitivity of two-phase micro-channel systems to flow instabilities. Oscillating pressure drops and wall temperatures, and visualizations showing cyclical backflow, were encountered in many experiments. Unfortunately, many of these data have been mingled in with stable data and thus create a confusing situation.
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Figure 1. From top to bottom: bubbly, slug, churn, and annular flows for R-134a in a 510 μm tube at a mass velocity of 500 kg/m2s (Taken from Ref. [12]).
Bergles and Kandlikar [11] classified these flows as compressible volume instabilities, relating them to the presence of compressibility prior to the heated channels. Relative to a stable mode, an unstable system presents entirely different flow features, and may bring about substantial differences in the heat transfer mechanisms (see [12]). The discussion that follows is aimed at providing a critical review of the main conclusions that may be drawn to date on the mechanisms of heat transfer for boiling in micro-channels, focusing primarily on the characteristics of stable two-phase flows. 2. Experimental Heat Transfer Among the first studies on flow boiling heat transfer in a single channel was the one by Lazarek and Black [1] who reported experimental heat transfer coefficients for flow boiling of R-113 in a vertical tube with an inner diameter of 3.1 mm (Fig. 2). Their heat transfer coefficients had a strong dependency on the applied heat flux, but were essentially independent of vapor quality. Similar results were obtained by Tran et al. [13] and Bao et al. [14]. Tran et al. performed experiments on R-12 in circular and rectangular
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channels with sizes ranging from 2.40 to 2.92 mm. Their data showed that for a sufficiently high wall superheat (above 2.75 K) the values of the heat transfer coefficient were unaffected by vapor quality and mass velocity, but increased significantly with heat flux. The flow boiling experiments of Bao et al. again confirmed these trends and presented additional data showing the improvement in heat transfer with increasing saturation pressure, further promoting the view that nucleate boiling was dominating (no visualization of the flow was possible in their setup). More recently, Lihong et al. [15] performed experiments on a 1.3 mm circular channel for refrigerant R-134a, yielding similar results.
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Added trends in heat transfer were reported in the work by Lin et al. [16] (Fig. 3). In their study on R-141b (1.1 mm tube), they observed three distinct responses in the heat transfer coefficient to changes in heat flux and vapor quality: (1) at low heat fluxes, heat transfer improved with increasing vapor quality, (2) for intermediate values from 30 to 53 kW/m2 in Fig. 3 and vapor qualities within 0.40, the heat transfer coefficient increased with heat flux, much like what was observed in the investigations cited previously, and (3) at the highest heat fluxes, heat transfer gradually fell with x and tended to heat flux independent values. While further heating increased the heat transfer coefficient for vapor fractions up to 0.40, the correspondence was much less clear beyond this threshold.
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Saitoh et al. [17] obtained heat transfer data for boiling of R-134a in a 0.51 mm tube (550 mm long) at 15 and 29 kW/m2 for qualities extending to almost unity. Their heat transfer coefficients showed an inverted “U” shape in the α–x plane. The heat transfer data increased up to a quality of 0.60, beyond which the coefficients declined monotonically. In another study on R-134a, Martin-Callizo et al. [18] presented results for a vertical 0.64 mm stainless steel micro-channel, finding that once again the dominant effect was that of heat flux while mass velocity was less important. They found that their heat transfer coefficients were rather insensitive to vapor quality until reaching the higher range of their heat flux test range, whereupon the heat transfer coefficients then decreased monotonically from vapor qualities of about 0.01–0.02 down to values of about 0.6–0.8 without going through any maximum or minimum. As for the effect of mass velocity, a number of investigations have shown heat transfer coefficients to remain unchanged when varying the fluid flow rate, as in the data from Tran et al. [13] (see Fig. 4). Tran et al. reported an improvement in heat transfer with mass velocity only for wall superheats lower than 2.75 K. The experiments from Bao et al. [14] on R-11 and R-123, and from Lihong et al. [15] on R-134a, also showed no change in heat transfer with flow rate, with the latter observing mild differences only at the lowest heat flux tested. One of the few studies on a single
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channel that presented a different outcome was that of Sumith et al. [19] for flow boiling of water in a 1.45 mm vertical tube, reporting heat transfer coefficients that often decreased when increasing the flow, even at high heat fluxes. 12000
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At present, there is general agreement among the studies that addressed the effect of saturation conditions on heat transfer, that a higher saturation pressure/temperature yields higher heat transfer coefficients (see for example [14, 15, 18]). Similar results have also been recently reported in flow boiling heat transfer experiments on multi-micro-channel systems, as in the case of Agostini et al. [20, 21] who tested refrigerants R-134a and R-236fa in a 67 parallel micro-channel evaporator (rectangular channels, 0.223 mm wide, 0.680 mm high and 20.0 mm long, separated by 0.80 mm wide fins). It can be seen from Fig. 5 that their heat transfer data at low heat fluxes tend to increase with vapor quality until intermediate heat fluxes where they first increase and then show nearly no influence of vapor quality. At higher heat fluxes, the heat transfer coefficients start to decline with increasing vapor quality. While the heat transfer coefficients rise sharply with increasing heat flux, at the highest values (starting at 178.4 W/cm2 relative to the surface area of the heating element) a peak is reached and the heat transfer coefficients begin to decrease with increasing heat flux as the critical heat flux is approached (but not reached) in this data set.
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Figure 5. Flow boiling data of Agostini et al. [20] for R-236fa in a silicon multi-microchannel test section at a mass velocity of 810.7 kg/m2s, a nominal pressure of 2.73 bar and saturation temperature of 25°C. The silicon test section without its cover plate is shown in the inset photograph.
3. Heat Transfer Mechanisms The heat transfer mechanisms that are active in boiling in micro-channels can be summarized as follows: (i) in bubbly flow, nucleate boiling and liquid convection would appear to be dominant, (ii) in slug flow, the thin film evaporation of the liquid film trapped between the bubble and the wall and convection to the liquid and vapor slugs between two successive bubbles are the most important heat transfer mechanisms, also in terms of their relative residence times, (iii) in annular flow, laminar or turbulent convective evaporation across the liquid film should be dominant, and (iv) in mist flow, vapor phase heat transfer with droplet impingement will be the primary mode of heat transfer. For those interested, a large number of two-phase videos for micro-channel flows from numerous laboratories can be seen in the e-book of Thome [22]. Notably, many experimental papers conclude without proof that nucleate boiling is dominant in their data only because they find a substantial heat flux dependency; a heat flux dependency however does not prove that nucleate boiling is dominant or even present. For instance, Jacobi and Thome [7] and Thome et al. [8] have argued that the heat flux effect can be explained and predicted by the thin film evaporation process occurring around elongated bubbles in the slug flow regime without any nucleation sites. Their model shows that the heat flux dependency comes mainly through its effect on the bubble frequency and the thin film evaporation process. Thus, simply labeling
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micro-channel flow boiling data as being nucleate boiling dominated is misleading since this seems to only be the case for the bubbly flow regime, which occurs at very low vapor qualities (typically for x < 0.01–0.05 depending on the mass velocity, etc.). Some experimental flow boiling studies that report that nucleate boiling was dominant at low vapor qualities also report that the flow regime observed at these conditions was elongated bubble flow without any bubbly flow observed. These two conclusions thus seem to be contradictory. One should further contemplate that a nucleate boiling correlation does not actually model the nucleate boiling process, but is only an empirical relationship relating the heat transfer coefficient to the heat flux, and hence the actual mechanism is not actually addressed in the correlation. Hence, in flow boiling in a micro-channel in elongated bubble (slug) flows, the heat flux dependency in such a correlation most likely is coming in through the bubble frequency and thin film effects, not that of nucleate boiling. To date, many types of non-circular micro-channels have been tested: for instance results for square, rectangular, parallel plate, triangular, and trapezoidal geometries are currently available in the literature. Besides the problems associated with characterizing the channel size (e.g., a hydraulic diameter of a non-circular channel has no physical relationship to an annular film flow), the rectangular channels tested sometimes have very high aspect ratios whose effect on heat transfer is not well understood. Recalling the wedge flows observed by Cubaud and Ho [23] for air–water, a partially wetted perimeter along and around elongated bubbles will have an influence on heat transfer whilst the wet corners may tend to better resist complete dry-out. 4. Empirical Prediction Methods The variety of trends in heat transfer data and the inherent difficulties in performing experimental work on these small systems have made it very challenging to develop a well-established understanding of boiling in micro-channels. Several authors have correlated their experimental results through different sets of generally non-dimensional groups. Others, on the other hand, have attempted to either extend methods previously developed for conventional macro-scale systems to the micro-scale, or define new approaches specifically for micro-channel two-phase flows. 4.1. LAZAREK AND BLACK CORRELATION
From their heat transfer experiments on R-113, Lazarek and Black [1] proposed the following non-dimensional correlation for the flow boiling Nusselt number (Nul = αD/kl):
MECHANISMS OF BOILING IN MICROCHANNELS
Nu l = 30 Relo0.857 Bo 0.714
91
(1)
with Relo = GD/μl, the all-liquid Reynolds number, Bo = q/(Ghlv) the Boiling number and G the mass velocity of the total flow of liquid and vapor. Equation (1) expresses no dependence of the heat transfer process on the local vapor quality. 4.2. TRAN ET AL. CORRELATION
As mentioned earlier, in their experiments on R-12 and R-113 Tran et al. [13] observed that for wall superheats above 2.75 K their heat transfer data expressed a strong α versus q behavior, assigning this to the macro-scale mechanism of nucleate boiling. The authors therefore modified the correlation of Lazarek and Black, Eq. (1), by replacing the Reynolds number with the Weber number, Welo = G2D/(ρlσ), removing viscous effects in favor of surface tension. The liquid to vapor density ratio was added to further account for variations in fluid properties, so that
⎛ρ ⎞ α = (8.4 × 10 ) Bo We ⎜ l ⎟ ⎝ ρv ⎠ 5
0.6
−0.4
0.3 lo
(2)
The 8.4 × 105 factor in Eq. (2) is dimensional, with units of W/(m2K). Equation (2) removes any dependence of the heat transfer coefficient on mass velocity. Furthermore, Eq. (2) also yields the following proportionality between the heat transfer coefficient and the channel diameter: α ∝ D0.3, which seems to be the opposite of experimental trends found in later studies. 4.3. KANDLIKAR AND BALASUBRAMANIAN CORRELATION
Kandlikar and Balasubramanian [24] extended the correlation proposed by Kandlikar for conventional tubes, where the local two-phase heat transfer coefficient was determined according to the value of the dominant mechanism between nucleate boiling (nb) and convective evaporation (cv):
⎧α α = larger of ⎨ nb ⎩ α cv
(3)
The original correlations for the two coefficients in Eq. (3) were developed for all-liquid Reynolds numbers, Relo, above 3,000, and presented the following functional dependencies:
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⎡⎛ ρ ⎞0.5 ⎛ 1 − x ⎞0.8 q ⎤ α nb G2 ⎥ x , , , = f nb ⎢⎜ v ⎟ ⎜ ⎟ 2 αl ⎢⎣⎝ ρl ⎠ ⎝ x ⎠ Ghlv ρl gD ⎥⎦ ⎡⎛ ρ ⎞ 0.5 ⎛ 1 − x ⎞ 0.8 q ⎤ α cv G2 , 2 , x⎥ = f cv ⎢⎜⎜ v ⎟⎟ ⎜ ⎟ , αl ⎢⎣⎝ ρ l ⎠ ⎝ x ⎠ Ghlv ρ l g D ⎥⎦
(4)
The non-dimensional groups in Eq. (4) are respectively the Convection number, Cv, the Boiling number, Bo, the all-liquid Froude number, Frlo, and the vapor quality. For Relo > 3,000, Kandlikar suggested using transition (Gnielinski) and fully turbulent (Petukhov and Popov) correlations for the single-phase liquid heat transfer coefficient, αl, based on the all-liquid Reynolds number. However, for smaller channels the authors argued that the value of the Reynolds number was generally lower than 3,000, making the above single-phase correlations inconsistent. Furthermore, the reduced effect of gravity in micro-channels justified the removal of the Froude number from Eq. (4). In view of both these considerations, Kandlikar and Balasubramanian proposed the following modified correlations for αnb and αcv:
α nb = 0.6683 Cv − 0.2 (1 − x) 0.8 + 1058.0 Bo 0.7 (1 − x) 0.8 Fsf αl α cv = 1.136 Cv − 0.9 (1 − x) 0.8 + 667.2 Bo 0.7 (1 − x) 0.8 Fsf αl
(5)
with Fsf a constant that was used to fit the expressions to each particular surface material–fluid combination. For Reynolds numbers in the range 1,600 ≤ Relo < 3,000, the authors suggested interpolating between laminar and transition correlations for αl. On the other hand, for Relo < 1,600 the flow was considered laminar, and a laminar correlation of the form Nu = αlD/kl = constant was deemed applicable. Finally, for Relo ≤ 100 Eq. (3) was modified to α = αnb, with αnb given by Eq. (5). Interestingly, their nucleate boiling and convective boiling heat transfer correlations in Eq. (5) are identical, except for values of the two lead constants and one of the exponents. Thus, it is not clear how one represents nucleate boiling and the other convective boiling. 4.4. ZHANG ET AL. EXTENSION OF CHEN’S CORRELATION
Zhang et al. [25] analyzed thirteen separate databases, confronting them with some of the most widely quoted correlations for two-phase heat transfer in conventional systems. Chen’s superposition model gave the best
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outcome. However, the authors observed that for micro-channels, the values of the liquid Reynolds numbers, Rel = G(1 – x)/μl, were mostly lower than 2,000, i.e. lower than the laminar-transition threshold, and argued that this was inconsistent with the original form of Chen’s model (similar to the reasoning of Cubaud and Chih-Ming [23]). Chen’s superposition model for convective boiling states that heat is transferred by two competing mechanisms, namely nucleate boiling and convective vaporization. The overall heat transfer coefficient is given by an additive law that combines these different contributions,
α = α nb + α cv
(6)
The nucleate boiling term in Eq. (6) is expressed as the product of the nucleate pool boiling value (αnpb) computed at the corresponding wall superheat through the Forster-Zuber (1955) correlation [26], and a boiling suppression factor, S, that accounts for the suppression of bubble nucleation due to the convective nature of the two-phase system. On the other hand, the convective contribution depends on the flow properties and is given as an all liquid heat transfer coefficient multiplied by a two-phase correction factor, F. That is:
α nb = S α npb
and α cv = F α l
(7)
For the all liquid heat transfer coefficient in Eq. (7), Zhang et al. suggested using a laminar or turbulent expression according to the value of the liquid Reynolds number, Rel. For the two-phase factor, F, they proposed using the larger value of 1 and an expression, F′, based on the general form of the Martinelli parameter, X:
1 ⎞ ⎛ C F ′ = 0.64 ⎜1 + + 2 ⎟ ⎝ X X ⎠
(8)
where C is Chisholm’s constant. For the suppression factor, S, they presented a similar form to the one given by Chen:
S=
1 1 + 2.53 × 10−6 Rel1.17
(9)
(with a liquid Reynolds number in the place of the two-phase Reynolds number as originally proposed by Chen), justifying their choice by assuming the nucleate boiling suppression mechanism to remain the same as in the macro-scale.
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4.5. FURTHER REMARKS
Some further comments about the above methods are in order. All of the above methods are essentially modifications of macro-scale flow boiling methods, and thus assume that nucleate boiling is an important heat transfer mechanism without proof of its existence for the two principal micro-channel flow regimes: slug (elongated bubble) flow and annular flow. Furthermore, using a tubular single-phase flow correlation to predict convective heat transfer in an annular flow is not physically realistic since an annular flow is a film flow and is thus governed by its film Reynolds number rather than by a tubular Reynolds number. Similar to Nusselt’s (1916) laminar film condensation theory, as long as there are no interfacial waves, the local laminar annular flow heat transfer coefficient is dependent on heat conduction across the liquid film thickness and it is thus not appropriate to calculate its value in terms of the tubular solution of Nul = 4.36. For instance, no one applies the tubular flow solution to predict laminar falling film condensation on a vertical plate so it does not seem to be appropriate to apply it to an evaporating laminar annular film flow either. For that matter, turbulent falling film condensation on a vertical plate is correlated based on its local liquid film Reynolds number in which the film thickness is the active characteristic dimension and hence turbulent annular film evaporation should be correlated in the same manner, not using a tubular flow Reynolds number. Not withstanding the above comments, wholly empirical methods can be fit to experimental databases for prediction purposes. On the other hand, none of the above correlations is able to predict the diverse trends in the heat transfer coefficient versus vapor quality described earlier. 5. Mechanistic Prediction Method: Thome et al. Three Zone Evaporation Model for Slug Flow
Thome et al. [8] developed a phenomenological method to describe heat transfer for a purely convective micro-channel slug flow (no nucleate boiling), based principally on the following assumptions: 1. The vapor and liquid travel at the same velocity. 2. The heat flux is uniform and constant with time along the inner wall of the micro-channel. 3. All energy entering the fluid is used to vaporize liquid. Thus, the temperatures of the liquid and vapor remain at the saturation value, i.e. neither the liquid nor the vapor is superheated. 4. The local saturation pressure is used for determining the local saturation temperature.
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5. The liquid film remains attached to the wall. The influence of vapor shear stress on the liquid film is assumed negligible, so that it remains smooth without ripples. 6. The thickness of the film is very small with respect to the inner radius of the tube. 7. The thermal inertia of the channel wall can be neglected. Slug flow was modeled as a cyclical passage of a “three zone” sequence, comprising a liquid slug, an elongated bubble surrounded by an evaporating liquid film, and an all-vapor dry-zone at the bubble tail (see Fig. 6), respectively referred to by subscripts L, F and D. The first assumption yields an equal velocity, W, for the vapor and liquid, given by the homogeneous expression
⎛ x 1− x⎞ ⎟ + W = G ⎜⎜ ρ l ⎟⎠ ⎝ ρv
(10)
with G the total mass velocity and x the thermodynamic vapor quality. The residence times of the vapor, ΔtV, intended as the elongated bubble plus the dry-zone (ΔtV = ΔtF + ΔtD), and the liquid slug, ΔtL, were derived from the definition of vapor quality and through Eq. (10) as
Gx Δt = ρ vW
Δt ρ 1− x 1+ v ρl x G (1 − x) Δt Δt L = Δt = ρ x ρ lW 1+ l ρv 1 − x ΔtV =
(11)
with Δt the passage period of the three-zone structure, and having neglected the liquid mass within the film. The local film behavior was modeled as the evaporation of a stagnant liquid layer; from an energy balance at given axial position, z:
2πR qdz = −2π ρ l ( R − δ) Therefore,
dδ = −
dδ hlv dz dt
q R dt ρ l hlv ( R − δ)
(12)
(13)
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with δ the thickness of the film, q the uniform wall heat flux and R the channel radius. In view of Eq. (13), the film thickness will vary from an initial value, corresponding to the liquid film thickness at the bubble nose, δn, to a value given by the bubble residence time. From assumption 6, and by integration of Eq. (13):
δ (t , z ) = δ n ( z ) −
q t ρ l hlv
(14)
uniform heat flux
D
vapor slug
liquid slug
bubble
flow direction
liquid film
Figure 6. Image of an elongated bubble (top) and a schematic diagram of the three-zone evaporation model (bottom).
Assuming the condition for dry-out of the liquid film to occur at a finite value of the film thickness, δ = δmin, equivalent to the surface roughness (a representative value of 0.3 μm was recommended for δmin), the dry-zone will be present when the time required for film dry-out,
Δt DO =
ρ l hlv [δ n ( z ) − δ min ] q
(15)
is such that ΔtV > ΔtDO. Their eighth-order asymptotic expression for the bubble nose film thickness was derived from two prior correlations of Moriyama and Inoue [27]:
⎛ δn νl ⎞ ⎟ = 0.29 ⎜ 3 ⎜ WD ⎟ D ⎝ ⎠
0.84
[(0.07We
)
0.41 −8
+ 0.1−8
]
−1 8
(16)
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with νl the fluid’s kinematic viscosity and We the Weber number (= ρlDW2/σ). In terms of heat transfer, the authors suggested a transient behavior of the heat transfer coefficient, determined by the local flow conditions: (1) single phase convection during the passage of a liquid slug or a dry-zone (vapor slug in Fig. 6), and (2) conduction of heat through the liquid film during the passage of an elongated bubble. The local time-averaged heat transfer coefficient was thus
α( z ) =
Δt L ( z ) α L ( z ) + Δt F ( z ) α F ( z ) + Δt D ( z )α D ( z ) Δt
(17)
with ΔtL the residence time of the liquid slug given by Eq. (11), and ΔtF and ΔtD the residence times of the bubble and dry-zone, respectively, are:
Δt F = ΔtV Δt F = Δt DO
and and
Δt D = 0
for
Δt D = ΔtV − Δt DO
for
ΔtV ≤ Δt DO ΔtV > Δt DO
(18)
The single-phase heat transfer coefficients in Eq. (17) were determined by asymptotic interpolation of standard correlations, i.e. Shah and London (SL) for Re ≤ 2,300 and Gnielinski (G) for Re > 2,300. Thus,
(
4 Nu L , D = Nu SL + Nu G4
)
14
(19)
with
Nu SL = 0.91 3 Pr
ReD L
and
f 23 ( Re − 1, 000) Pr ⎡ ⎛D⎞ ⎤ NuG = 8 1 + ⎢ ⎜ ⎟ ⎥ f ⎝ L ⎠ ⎥⎦ 23 1 + 12.7 ( Pr − 1) ⎢⎣ 8
(20)
These are the average laminar and transition to turbulent Nusselt numbers over the respective single-phase lengths L. In Gnielinski’s correlation the friction factor is taken as f = (1.82 log10 Re − 1.64) −2 . The bubble heat transfer coefficient, αF, was determined by applying simple conduction theory through the liquid film:
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1 α F ( z) = Δt F
Δt F
∫ 0
kl 2 kl dt ≅ δ(t , z ) δ n + δt
(21)
with δt the minimum local film thickness (the subscript t stands for the bubble tail) given from Eq. (14) as:
δt ( z) = δ n ( z) − δ t ( z ) = δ min
q ΔtV ρ l hlv
for
for
ΔtV ≤ Δt DO ΔtV > Δt DO
(22)
The final equation that provided closure to the model was for the passage period, Δt, of the liquid–bubble–vapor triplet. The authors correlated Δt with the wall heat flux and the fluid properties represented by the reduced pressure, proposing the following dimensional correlation (q in W/m2 and Δt in s):
⎛ 1 ⎞ pr0.5 q ⎟ Δt = ⎜ ⎝ 3,328 ⎠
−1.74
(23)
where pr is the reduced pressure (pr = psat/pc). The above mechanistic type of model is only strictly for describing the heat transfer process in the elongated bubble flow regime. Significantly, it explicitly explains the influence of heat flux on the flow boiling heat transfer coefficient while empirical correlations do not. Due to lack of an appropriate flow pattern map to classify the existing boiling database as such at the time of its development, the authors used all of the database they put together from seven independent studies for its development, irrespective of the flow regimes involved. It is recommended that a general flow pattern based model be developed in the future to cover all three principal flow regimes, not just one. Furthermore, the model highlights the sensitivity of the slug flow regime heat transfer process to the frequency, the nose film thickness and the onset of dry-out thickness of elongated bubbles. Hence, future experimental studies should address these features of the flow to better understand and model them. For example, the recent mechanistic flow pattern map of Revellin and Thome [28], based on the rate of collision of elongated bubbles to define the flow pattern transitions and predict the bubble frequencies and bubble length distributions (see also [29]), may be a starting point for such a model.
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6. Comparing Prediction Methods
Figure 7 depicts a comparison of four empirical methods and the lone mechanistic method described above for R-134a boiling in a 0.5 mm microchannel by Consolini [30]. As can be seen, the Lazarek and Black [1] and the Tran et al. [13] correlations predict no influence of vapor quality and hence give a fixed value at all values of x, even at very high values of x. The Zhang et al. [25] correlation depicts a slight increase in heat transfer at low vapor quality, nearly no effect of vapor quality at intermediate values and then a slight downward tendency, all trends which are reasonable according to some data sets, but extrapolation of this method to high vapor qualities is clearly not appropriate. The Kandlikar and Balasubramanian [24] correlation shows a tendency to decrease with vapor quality before flattening off at the present simulated conditions. Meanwhile, the Thome et al. [8] three-zone model for elongated bubble flows depicts a monotonic decrease in the heat transfer coefficient when extrapolating it to low vapor qualities characterized by bubbly flow and to high vapor qualities characterized by annular flow. Notable in this simulation is the large discrepancy in the predicted values, which range from about 4,000 to 11,000 W/m2K. Furthermore, it is evident that reliable application of heat transfer prediction methods requires use of a diabatic flow pattern map, such as that in Ref. [28], to determine the critical vapor quality and hence the location where the postdry-out heat transfer regime begins with much lower heat transfer coefficients. Some of the methods presented above have been recently been compared to independent heat transfer databases. For instance, Shiferaw et al. [31] measured local flow boiling data for R-134a in a 2.01 mm stainless steel tube at 8 bar. The three-zone model predicted most of their data within ±20% while their other data at 12 bar were less well predicted, yielding a spread of ±30% while showing a tendency to under predict with increasing pressure. Agostini et al. [21] compared their multi-micro-channel database obtained in collaboration with IBM to selected methods. Utilizing only the data at vapor qualities above 5% to eliminate the inlet effects of the 90° turn in the flow and the orifice at the entrance to each channel, their database used for the comparison consisted of 1,438 data points for R-245fa and R-236fa and accounted for the fin efficiency effects. The three-zone model using the measured surface roughness (0.17 μm for their silicon channels) in place of the original value of 0.3 μm predicted 90% of these data within ±30% (only 31% were predicted within ±30% using the original value, just to indicate the sensitivity of the surface roughness in the model and on the heat transfer process). The Kandlikar and Balasubramanian [24] correlation captured 58% and the Zhang et al. [25] correlation yielded 19% of the data within ±30%.
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100 16000
Lazarek Tran Zhang Kandlikar Thome
heat transfer coefficient (W/m2K)
14000 12000 10000 8000 6000 4000 2000 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
vapor quality
Figure 7. Predicted two-phase heat transfer coefficients. Values for R-134a at 7 bar, with q = 50 kW/m2, G = 500 kg/m2s, in a D = 0.5 mm circular, stainless steel channel (Taken from Ref. [30]).
Consolini and Thome [12] compared their extensive database for R-134a, R-236fa and R-245fa for stable flow conditions for 0.510 and 0.790 mm stainless steel test sections at near ambient saturation temperatures to five of the methods presented earlier. Using the Revellin and Thome [28] diabatic flow pattern map described earlier in this chapter to eliminate the annular flow data from the comparison, they found that 77% of the remaining data were predicted within ±30% by the three-zone model (but still including the bubble flow data). In comparison, the Lazarek and Black [1] correlation captured 88% of the entire database within ±30%, while the Tran et al. [13] correlation captured only 4% within this range, the Kandlikar and Balasubramanian [24] correlation captured 21% and the Zhang et al. [25] correlation yielded 58%. 7. Conclusions
Current experimentation on micro-channel two-phase flows has provided some evidence of the heat transfer mechanisms that govern the micro-scale flow boiling process: (i) at low vapor qualities, when bubbly flow is the dominant flow pattern, thermal transport is primarily associated to nucleate boiling, (ii) at intermediate vapor qualities, with the intermittent passage of elongated bubbles and slugs of liquid, heat is transferred by single phase
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convection in the all liquid and vapor zones, and by conduction/convection through the thin films surrounding the elongated bubbles, and is also highly dependent on the bubble frequency, and (iii) at the high vapor quality characteristic of annular flows, the heat transfer process is expected to be governed by the convective and conductive mechanisms involved in evaporation of the annular film. The presence of nucleate boiling, which many have suggested to be the dominant heat transfer mode, even at high vapor qualities, without physical or theoretical proof, is not substantiated by flow visualizations that report an extensive presence of small bubbles (relative to the channel size) only at the very low vapor qualities. The strong dependency of the boiling heat transfer coefficients on the heat flux is instead mechanistically explainable by the thin film evaporation process and the cyclical heat transfer process occurring in elongated bubble flows, whose elongated bubble frequency and transient heat conduction process are strong functions of heat flux. In addition, the experimental heat transfer coefficients for annular flow pose additional questions, since in this region the values of α do not exhibit the expected increase with x, but rather remain constant or even decrease as evaporation progresses. Future investigations should better address the issues of the heat transfer mechanisms in micro-channel flow boiling, the effect of surface roughness and flow regimes, rather than just continue to add new heat transfer data to the literature. NOMENCLATURE
Latin Bo C Cv D F Fr f G h g k L Nu p Pr q
Boiling number, dimensionless Chisholm parameter, dimensionless Convection number, dimensionless diameter, m two-phase factor, dimensionless Froude number, dimensionless friction factor, dimensionless mass velocity, kg/m2s specific enthalpy, J/kg gravitational acceleration, m/s2 thermal conductivity, W/m/K length, m Nusselt number, dimensionless pressure, Pa Prandtl number, dimensionless heat flux, W/m2
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R Re S T t W We X x z
radius, m Reynolds number, dimensionless boiling suppression factor, dimensionless temperature, °C time, s mean axial velocity direction, m/s Weber number, dimensionless Martinelli parameter, dimensionless vapor quality, dimensionless axial coordinate, m
Greek α δ μ ν ρ σ
heat transfer coefficient, W/m2/K liquid film thickness, m dynamic viscosity, Pa s kinematic viscosity, m2/s density, kg/m3 surface tension, N/m
Subscripts c cv D DO F G L l lam lo lv min n nb npb r SL sat sf t tt
critical convective vaporization dry-zone dry-out elongated bubble/evaporating film Gnielinski liquid slug liquid laminar liquid-only liquid–vapor minimum bubble nose nucleate boiling nucleate pool boiling reduced Shah and London saturation surface-fluid bubble tail turbulent–turbulent
MECHANISMS OF BOILING IN MICROCHANNELS
V v
103
elongated bubble + dry zone vapor
References 1. Lazarek, G. M., and Black, S. H., Evaporative Heat Transfer, Pressure Drop and Critical Heat Flux in a Small Vertical Tube with R-113, Int. J. Heat and Mass Transfer, 25(7), 945–960 (1982). 2. Agostini, B., and Thome, J. R., Comparison of an Extended Database for Flow Boiling heat transfer Coefficients in Multi-Microchannel Elements with the Three-Zone Model, ECI Heat Transfer and Fluid Flow in Microscale, Sept. 25–30, 2005, Castelvecchio Pascoli, Italy. 3. Tripplett, K. A., Ghiaasiaan, S. M., Abdel-Khalik, S. I., and Sadowski, D. L., Gas-Liquid Two-Phase Flow in Micro-Channels Part I: Two-Phase Flow Patterns, Int. J. Multiphase Flow, 25, 377–394 (1999). 4. Serizawa, A., Feng, Z., and Kawara, Z., Two-Phase Flow in Microchannels, Experimental Thermal and Fluid Science, 26, 703–714 (2002). 5. Revellin, R., Dupont, V., Thome, J.R., and Zun, I., Characterization of diabatic two-phase flows in micro-channels: flow parameter results for R-134a in a 0.5mm channel, Int. J. Multiphase Flow, 32, 755–774 (2006). 6. Cornwell, K., and Kew, P. A., Boiling in Small Parallel Channels, in Energy Efficiency in Process Technology, Elsevier Applied Science, 624–638, London, 1993. 7. Jacobi, A. M., and Thome, J. R., Heat Transfer Model for Evaporation of Elongated Bubble Flows in Microchannels, Journal of Heat Transfer, 124, 1131–1136 (2002). 8. Thome, J. R., Dupont, V., and Jacobi, A. M., Heat Transfer Model for Evaporation in Microchannels. Part I: presentation of the model, Int. J. Heat and Mass Transfer, 47, 3375–3385 (2004). 9. Kew, P. A., and Cornwell, K., Correlations for the Prediction of Boiling Heat Transfer in Small-Diameter Channels, Applied Thermal Engineering, 17, 705– 715 (1997). 10. Kandlikar, S. G., Heat Transfer Mechanisms During Flow Boiling in Microchannels, Journal of Heat Transfer, 126, 8–16 (2004). 11. Bergles, A. E., and Kandlikar, S. G., On the Nature of Critical Heat Flux in Microchannels, Journal of Heat Transfer, 127, 101–107 (2005). 12. Consolini, L., and Thome J. R., Micro-Channel Flow Boiling Heat Transfer of R-134a, R-236fa, and R-245fa, J. Microfluidics and Nanofluidics, doi: 10.1007/ s10404-008-0348-7 (2008). 13. Tran, T. N., Wambsganss, M. W., and France, D. M., Small Circular- and Rectangular-Channel Boiling with Two Refrigerants, Int. J. Multiphase Flow, 22(3), 485–498 (1996).
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14. Bao, Z. Y., Fletcher, D. F., and Haynes, B. S., Flow Boiling Heat Transfer of Freon R11 and HCFC123 in Narrow Passages, Int. J. Heat and Mass Transfer, 43, 3347–3358 (2000). 15. Lihong, W., Min, C., and Groll, M., Experimental Study of Flow Boiling Heat Transfer in Mini-Tube, ICMM2005, 2005. 16. Lin, S., Kew, P. A., and Cornwell, K., Two-Phase Heat Transfer to a Refrigerant in a 1mm Diameter Tube, Int. J. Refrigeration, 24, 51–56 (2001). 17. Saitoh, S., Daiguji, H., and Hihara, E., Effect of Tube Diameter on Boiling Heat Transfer of R-134a in Horizontal Small-Diameter Tubes, Int. J. Heat and Mass Transfer, 48, 4973–4984 (2005). 18. Martin-Callizo, C., Ali, R., and Palm, B., New Experimental Results on Flow Boiling of R-134a in a Vertical Microchannel, UK Heat Transfer 2007 Proceedings, Edinburgh, 2007. 19. Sumith, B., Kaminaga, F., and Matsumura, K., Saturated Flow Boiling of Water in a Vertical Small Diameter Tube, Experimental Thermal and Fluid Science, 27, 789–801 (2003). 20. Agostini, B., Thome, J. R., Fabbri, M., Calmi, D., Kloter, U., and Michel, B., High Heat Flux Flow Boiling in Silicon Multi-Microchannels: Part I – Heat Transfer Characteristics of R-236fa, Int. J. Heat Mass Transfer, doi:10.1016/ j.ijheatmasstransfer.2008.03.006 (2008). 21. Agostini, B., Thome, J. R., Fabbri, M., Calmi, D., Kloter, U., and Michel, B., High Heat Flux Flow Boiling in Silicon Multi-Microchannels: Part II – Heat Transfer Characteristics of R-245fa, Int. J. Heat Mass Transfer, doi:10.1016/ j.ijheatmasstransfer.2008.03.007 (2008). 22. Thome, J. R., Wolverine Engineering Databook III, at www.wlv.com/products, 2007. 23. Cubaud, T., and Chih-Ming, H., Transport of Bubbles in Square MicroChannels, Physics of Fluids, 16(12), 4575–4585 (2004). 24. Kandlikar, S. G., and Balasubramanian, P., An Extension of the Flow Boiling Correlation to Transition, Laminar, and Deep Laminar Flows in Mini-Channels and Micro-Channels, Heat Transfer Engineering, 25(3), 86–93 (2004). 25. Zhang, W., Hibiki, T., and Mishima, K., Correlation for Flow Boiling Heat Transfer in Mini-Channels, Int. J. Heat and Mass Transfer, 47, 5749–5763 (2004). 26. Forster, H. K., and Zuber, N., Dynamics of vapor bubbles and boiling heat transfer, AIChe J., 1, 531 (1955). 27. Moriyama, K., and Inoue, A., Thickness of the liquid film formed by a growing bubble in a narrow gap between two horizontal plates, J. Heat Transfer, 118, 132–139 (1996). 28. Revellin, R., and Thome, J. R., A New Type of Diabatic Flow Pattern Map for Boiling Heat Transfer in Microchannels, J. of Micromechanics and Microengineering, 17, 788–796 (2006). 29. Revellin, R., Agostini, B., and Thome, J. R. Elongated Bubbles in Microchannels Part II: Experimental Study and modeling of Bubble Collisions, Int. J. Multiphase Flow, doi:10.1016/j.ijmultiphaseflow.2007.07.006 (2008).
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30. Consolini, L., Convective boiling heat transfer in a single micro-channel, Ph.D. dissertation, École Polytechique Fédérale de Lausanne, Switzerland. Available at: http://library.epfl.ch/theses/?nr=4024, 2008. 31. Shiferaw, D., Huo, X., Karayiannis, T. G., and Kenning, D. B. R., Examination of Heat Transfer Correlations and a Model for Flow Boiling of R-134a in Small Diameter Tubes, Int. J. Heat and Mass Transfer (2007), 50, 5177–5193 (2007).
PREDICTION OF CRITICAL HEAT FLUX IN MICROCHANNELS J.R. THOME AND L. CONSOLINI EPFL-STI-IGM-LTCM Ecole Polytechnique Fédérale de Lausanne (EPFL) Lausanne CH-1015, Switzerland,
[email protected]
Abstract. An overview of the state-of-the-art of predicting critical heat flux during saturated flow boiling in microchannels is presented. First, a selection of experimental results is described for single channels and for multichannels in parallel, including non-circular channel shapes. Next, the various empirical methods for predicting CHF are presented and discussed. Then, the theoretically based model of Revellin and Thome for microchannels, including prediction of CHF under hot spots, is described and discussed. Finally, some overall comments on the status of CHF modeling and experimentation are provided.
1. Introduction For critical cooling applications using flow boiling in multi-microchannel evaporator plates, a significant research effort is underway. As example of emerging applications, the cooling of microprocessors, power-electronics, microreactors, digital displays, etc. can benefit from the high cooling rate and uniform temperature resulting from forced flow boiling in a multitude of parallel channels to dissipate the heat using the heat of evaporation of the coolant. Among the parameters to be resolved in such a design, the critical heat flux (CHF) in saturated flow boiling conditions represents a very important operational limit. It signifies the maximum heat flux that can be dissipated at the particular operating conditions. Surpassing CHF means that the heated wall becomes completely and irrevocably dry, instigating a very rapid and sharp increase in the wall temperature as the two-phase flow regime passes into the mist flow (post-dryout) heat transfer regime. Figure 1, for example, illustrates the onset of CHF in a single microchannel in a test by Wojtan, Revellin and Thome [1], on R-134a at a saturation temperature of 30°C and a mass velocity of 1,000 kg/m2s (0.509 mm tube, with a heated length of 70 mm). It shows the temperature excursion that occurs during small steps of increasing heat flux. Upon reaching CHF at an imposed heat flux of about 164 kW/m2, the wall temperature takes off and S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_6, © Springer Science + Business Media B.V. 2010
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within about a second surpasses 75°C and proceeds to exceed 120°C (not shown) soon afterwards, at which point the electric heater of the test section is shut off by a control system to keep the heater from reaching the failure temperature of the circuit. For most applications, this temperature excursion would result in irreparable damage to the device being cooled. Thus, the critical heat flux is a particularly important design parameter. Physically speaking, CHF in an annular flow is reached by drying out the liquid film flowing on the channel wall (or destabilizing the film via interfacial waves to create a stable dry spot) and is followed by the complete entrainment of the liquid-phase into the high speed vapor flow. The heat transfer process then occurs through the much less effective vapor-phase heat transfer on the wall that requires a very large temperature to dissipate the imposed heat flux. Regarding macroscale CHF, the Katto and Ohno [2] method is usually considered the most accurate and reliable one. Below, first some experimental results are presented to illustrate typical trends and then several leading empirical CHF prediction methods are described. Next, a recently proposed theoretical microchannel CHF model is presented. The topic of modeling of local CHF under hot spots for computer chip cooling is then addressed.
Figure 1. Heat flux versus wall superheat measurements during a critical heat flux experiment by Wojtan, Revellin and Thome [1].
2. Flow Pattern Effects on CHF Pribyl, Bar-Cohen and Bergles [3] have studied the effect of flow pattern on CHF, based on water data obtained in three independent test facilities with a total number of experimental points of 4109. The tube diameters ranged from 1.0 to 37.0 mm, heated lengths from 31 to 3,000 mm and mass
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velocities from 10 to 18,580 kg/m2s. The database was sorted by regime using Taitel and Dukler [4] flow pattern map to identify annular, intermittent and bubble flows. They found that CHF varied linearly with quality in distinct segments, with a relatively sharp discontinuity and change in slope at low vapor qualities, where the Taitel–Dukler map predicts a regime transition. The most apparent difference in slope was observed between bubbly flow and annular flows. They concluded that a change in flow regime might affect the mechanism of CHF and that within each flow regime a similar but distinct CHF mechanism could be expected to apply. Bergles and Kandlikar [5] reviewed the existing studies on critical heat flux in microchannels. They concluded by saying that few single-tube CHF data were available for microchannels at the time of their review. For the case of parallel multi-microchannels, they noted that all the available CHF data at that time were taken under unstable conditions, where the critical condition was reached as the result of a compressible volume instability upstream or the excursive Ledinegg instability. As a result, the unstable CHF values reported in the literature were expected to be lower than they would be if the channel flow were kept stable by an inlet restriction. 3. Experiments and Correlations for CHF in Microchannels Some early CHF data for saturated CHF (that is, where CHF is surpassed where the local condition is in the saturated liquid–vapor region, not in a subcooled liquid) in small diameter tubes were obtained by Lazarek and Black [6]. They obtained a limited number of measurements for R-113 in a single 3.15 mm bore, stainless steel tube with a heated length of 126 mm. Shah [7] proposed a general CHF correlation for uniformly heated vertical channels created from a database covering 23 fluids (water, cryogens, organics and liquid metals) for tube diameters varying from 0.315 to 37.5 mm and heated length to diameter ratios from 1.2 to 940, taking data from 62 independent sources. His correlation is given as follows:
⎛L qcrit = 0.124 ⎜⎜ h m& hLG ⎝ di
⎞ ⎟⎟ ⎠
−0.89
⎛ 10 4 ⎜ ⎜Y ⎝ Shah
n
⎞ ⎟ (1 − xinlet ) ⎟ ⎠
(1)
In this expression, xinlet is the inlet vapor quality, which can be negative when considering a subcooled inlet condition, i.e. the inlet subcooling enthalpy relative to the latent heat. As CHF normally occurs at the outlet, the heated length Lh is taken as the channel length. The parameter YShah is:
YShah = m&
1.8
c pL
⎞⎛ μ L ⎞ ⎟⎜ ⎟⎟ 0.8 0.4 ⎟⎜ ⎝ k L ρ L g ⎠⎝ μG ⎠
⎛ d i0.6 ⎜⎜
0.6
(2)
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This parameter is evaluated as follows. When YShah ≤ 104, n = 0. When YShah ≥ 104, n is calculated using one of the two expressions:
YShah
⎛d ≤ 10 , n = ⎜⎜ i ⎝ Lh 6
YShah > 10 6 , n =
⎞ ⎟⎟ ⎠
0.54
(3)
0.12 (1 − xinlet )0.5
(4)
For parallel multi-microchannels, Bowers and Mudawar [8] obtained perhaps the first CHF data. Their tests were for R-113 in two test sections, one with 0.510 mm channels and the other with 2.54 mm channels, both circular, with a heated length of 10 mm made of copper and nickel. Qu and Mudawar [9] then obtained CHF data for water in a multi-microchannel heat sink with 21 parallel rectangular channels of 0.215 mm width by 0.821 mm height. They found that as CHF was approached, flow instabilities induced vapor backflow into the heat sink’s upstream plenum as shown in Fig. 2, resulting in mixing vapor with the incoming subcooled liquid. The backflow negated the usual advantage of inlet subcooling, resulting in a CHF virtually independent of inlet subcooling. Using these data together with the previously mentioned CHF data of Bowers and Mudawar [8], they proposed a Katto–Ohno style empirical correlation with CHF occurring in saturated flow, with a new leading constant and exponents, as follows:
⎛ρ qcrit = 33.43 ⎜⎜ G m& hLG ⎝ ρL
⎞ ⎟⎟ ⎠
1.11
⎛ WeL−0.21 ⎜⎜
Lh ⎝ di
⎞ ⎟⎟ ⎠
−0.36
(5)
The liquid Weber number, based on the uniformly heated length Lh, is defined as:
We L =
m& 2 Lh
ρ Lσ
(6)
This correlation predicted their experimental database for water and R-113 with a very small mean absolute error of 4%.
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Figure 2. Qu and Mudawar [9] diagram of flow instabilities observed near CHF.
Zhang et al. [10] analyzed the existing CHF correlations available for water versus a very large international experimental database for small diameter channels (0.33 ≤ di ≤ 6.22 mm). They proposed the following correlation for CHF of saturated water in small channels:
⎡ ⎛L q crit = 0.0352 ⎢We d i + 0.0119 ⎜⎜ h m& hLG ⎢⎣ ⎝ di 0.170 ⎡ ⎤ ⎛ ρG ⎞ ⎜ ⎟ ⋅ ⎢ 2.05 ⎜ − xinlet ⎥ ⎟ ⎢⎣ ⎥⎦ ⎝ ρL ⎠
⎞ ⎟⎟ ⎠
2.31
⎛ ρG ⎜⎜ ⎝ ρL
⎞ ⎟⎟ ⎠
0.361
⎤ ⎥ ⎥⎦
−0.295
⎛ Lh ⎜⎜ ⎝ di
⎞ ⎟⎟ ⎠
−0.311
(7)
The liquid Weber number, based on the channel diameter rather than its length, is defined as:
We d i =
m& 2 d i
ρ Lσ
(8)
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Qi et al. [11, 12] have measured cryogenic CHF data for saturated liquid nitrogen for 0.531, 0.834, 1.042 and 1.931 mm circular microchannels. The tests were done for mass velocities from about 400 to 2,800 kg/m2s at saturation pressures of about 6.8 bar. They found that the macroscale correlation of Katto and Ohno [2] and that of Zhang et al. [10] for water and extrapolated to liquid nitrogen, tended to severely under predict their data by 65–80%. Therefore, they proposed a new correlation based on the Weber number and the Confinement number as follows for CHF of liquid nitrogen:
⎛ρ qcrit = (0.214 + 0.140 Co )⎜⎜ G m& hLG ⎝ ρL
⎞ ⎟⎟ ⎠
0.133
⎛ ⎞ 1 ⎟⎟ (9) Wed−i0.333 ⎜⎜ ⎝ 1 + (0.03 Lh / d i ) ⎠
This method fit their nitrogen data with a mean average error of about 7.4%. Wojtan, Revellin and Thome [1] ran CHF tests in 0.509 and 0.790 mm internal diameter stainless steel microchannel tubes as a function of refrigerant mass velocity, heated length, saturation temperature and inlet liquid subcooling for R-134a and R-245fa. The heated lengths varied from 20 to 70 mm. The results showed a strong dependence of CHF on mass velocity, heated length and microchannel diameter but no measurable influence of small levels of liquid subcooling (2–15 K). An example of their results is shown in Fig. 3. To put these values in perspective, the departure from nucleate boiling using the expression of Lienhard and Dhir [13] yields a value of qDNB = 384 kW/m2, which is similar to the maximum value in the graph. All their CHF results corresponded to annular flow conditions at the exit of the microchannel based on flow pattern results obtained separately in the same test sections. Their experimental results were compared to the CHF single-channel correlation of Katto and Ohno [2] and the multichannel CHF correlation of Qu and Mudawar [9]. The correlation of Katto and Ohno predicted their microchannel data better with a mean absolute error of 32.8% but with only 41.2% of the data falling within a ±15% error band. The correlation of Qu and Mudawar [9] significantly over predicted their data. Based on their own experimental data, a new microscale version of the Katto–Ohno correlation for the prediction of CHF during saturated boiling in microchannels was proposed by Wojtan, Revellin and Thome [1] as:
⎛ρ qcrit = 0.437 ⎜⎜ G m& hLG ⎝ ρL
⎞ ⎟⎟ ⎠
0.073
⎛ We L−0.24 ⎜⎜
Lh ⎝ di
⎞ ⎟⎟ ⎠
−0.72
(10)
PREDICTION OF CHF IN MICROCHANNELS 500
113
0.790 mm 0.509 mm
450 400
CHF [kW/m2]
350 300 250 200 150 100 50 0 0
200
400
600 800 1000 1200 Mass velocity [kg/m2s]
1400
1600
1800
Figure 3. Wojtan, Revellin and Thome [1] CHF data for R-134a at a saturation temperature of 35°C, a heated length of 70 mm and inlet subcooling of 8 K.
WeL is determined using the expression above based on channel length. The experimental points are predicted with the mean absolute error of 7.6% with 82.4% of data falling within a ±15.0% error band. The database covered: two fluids (R-134a and R-245fa), two diameters (0.509 and 0.790 mm), numerous mass velocities (400–1,600 kg/m2s), four heated lengths (20–70 mm), two saturation temperatures (30°C and 35°C) and small subcoolings (2–15 K). Regarding the dimensionless ratios, they ranged as follows: 293–21044 for WeL, 0.009–0.041 for ρG/ρL, and 25–141 for Lh/di. More recently, additional multi-microchannel CHF data have become available. For example, Agostini et al. [14] measured CHF for R-236fa in a silicon test section with a special inlet header to provide stable flow and good flow distribution (the joining of the inlet liquid distributor to the microchannels created a rectangular orifice at the inlet of each channel). Boiling was in a silicon multi-microchannel element with a heated length and width of 20 mm, with 67 channels of 0.223 mm width, 0.680 mm high and 0.080 mm thick fins. Figure 4 depicts some of their test results. Small inlet subcoolings (0.8–18 K) had essentially no effect on the results, primarily because the inlet orifices had a beneficial flashing effect of triggering flow boiling without passing through the onset of nucleate boiling. The wetted wall heat fluxes accounting for the fin efficiency are plotted (not including the top glass plate used for viewing of the process), which ranged from about 219 to 522 kW/m2. These values correspond to cooling rates 1,120– 2,500 kW/m2 in terms of the footprint of the test section (i.e. at these conditions, 112–250 W/cm2 could be dissipated from a microprocessor chip
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for example). The CHF correlation of Wojtan, Revellin and Thome [1] described above and the Revellin and Thome [15] theoretical CHF model (to be described below) were both found to predict all their 26 CHF data points within ±20%. For a uniformly heated circular channel, the critical vapor quality can be obtained from a simple energy balance as follows:
⎛ q x crit = ⎜⎜ crit ⎝ m& hLG
⎞⎛ 4 Lh ⎟⎟⎜⎜ ⎠⎝ d i
⎞ ⎛ hsub ⎞ ⎟⎟ ⎟⎟ − ⎜⎜ h ⎠ ⎝ LG ⎠
(11)
In this expression, qcrit is calculated with the correlation of choice, while hLG is the latent heat of vaporization and hsub in the enthalpy change necessary to bring the incoming subcooled liquid to saturation. Thus, from a design point of view, once the critical heat flux is known, the maximum exit vapor quality to avoid CHF can be calculated. It should be pointed out that xcrit is not often the same value as xdi, which is the onset of dryout, since the latter can occur from a hydrodynamic effect (vapor shear) at low heat flux. 600 550 500
CHF [kW/m2]
450 400 350 300 250
∆Tsub = −0.8K ∆Tsub = −5K
200
∆Tsub = −11K
150 100 200
∆Tsub = −15K
300
400
500 600 700 Mass velocity [kg/m2s]
800
900
1000
Figure 4. Agostini et al. [14] CHF data for R-236fa at an inlet saturation temperature of 26°C.
4. Mechanistic Model for CHF in Microchannels Revellin and Thome [15] proposed a mechanistic type of method for predicting CHF in microchannels, based on the premise that CHF is triggered in annular flow at the location where the height (trough) of the interfacial waves equals that of the annular film’s mean thickness. To implement their model, they first solve the one-dimensional conservation equations for
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mass, momentum and energy by assuming annular flow from the inlet of the channel at x = 0. This yields the variation of the annular liquid film thickness δ ignoring any interfacial wave formation along the channel. Then, based on the slip ratio and a Kelvin–Helmoltz critical wavelength criterion (assuming the film thickness to be proportional to the critical wavelength of the interfacial waves), the wave height Δδ is predicted with the following expression:
⎛ d ⎞⎛ u Δδ = 0.15 ⎜ i ⎟ ⎜⎜ G ⎝ 2 ⎠ ⎝ uL
⎞ ⎟⎟ ⎠
−
3 7
⎛ g (ρ L − ρ G )(d i 2 )2 ⎞ ⎜ ⎟ ⎜ ⎟ σ ⎝ ⎠
−
1 7
(12)
Then, when δ equals Δδ at the outlet of the microchannel, CHF is reached. The leading constant and two exponents were determined empirically using a database including three fluids (R-134a, R-245fa and R-113) and three circular channel diameters (0.509, 0.790 and 3.15 mm) taken from the CHF data of Wojtan, Revellin and Thome [1] and Lazarek and Black [6]. Figure 5 shows the profiles from the channel centerline to the wall for an example simulation. 250
Radius [mm]
200
150
100
50 Wave height Film thickness 0
0
5
10 Heated length [mm]
15
20
Figure 5. Revellin and Thome [15] CHF model showing the annular film thickness variation along the channel plotted versus the wave height with respect to the channel centerline. The simulation is for R-134a at a saturation temperature of 30°C in a 0.5 mm channel of 20 mm heated length without inlet subcooling for a mass velocity of 500 kg/m2s, yielding a CHF of 396 kW/m2.
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Their model also satisfactorily predicted the R-113 data of Bowers and Mudawar [8] for circular multi-microchannels with diameters of 0.510 and 2.54 mm of 10 mm length. Furthermore, taking the channel width as the characteristic dimension to use as the diameter in their 1-d model, they were also able to predict the rectangular multi-microchannel data of Qu and Mudawar [9] for water. All together, 90% of the database was predicted within ±20%. This model also accurately predicted the R-236fa multimicrochannel data of Agostini et al. [14], utilizing the hydraulic diameter of the heated perimeter. Furthermore, in a yet to be published comparison, this model also predicts microchannel CHF data of liquid nitrogen and also CO2 data from three independent studies. 5. Modeling of CHF at Hot Spots in Microprocessor Cooling Elements Microprocessors in computers can have very high, local heat dissipation rates that are ten times or more the chip’s average heat flux, thus leading to the creation of so-called “hot spots”. Similar situations can also occur in cooling of power electronics and other devices. Thus, it is interesting to know if a local hot spot heat flux will trigger the onset of CHF when applying a multi-microchannel evaporator cooling element. Implementing the mechanistic CHF model of Revellin and Thome [15] described above, but now for a non-uniform heat flux boundary condition along the channel, Revellin et al. [16] simulated the effects of hot spots on triggering of CHF. Figure 6 shows the effect of a small hot spot (0.4 mm long around the perimeter of the channel) on the variation of the annular liquid film thickness with respect to the channel centerline and the liquid film wave height, and its triggering of CHF at their point of intersection. At the conditions shown, CHF at the hot spot occurs at 3,000 kW/m2 for the otherwise uniform heat flux of 218 kW/m2. Hence, in this case, a local heat flux 13.8 times the mean value can be sustained. The value of CHF without a hot spot (that is, with the hot spot heat flux set equal to that of the rest of the channel) for these same conditions is 396 kW/m2 as noted above, and hence the hot spot value is still over seven times that. For cooling of microprocessors and power electronics, this means that very high local hot spot heat fluxes can be sustained as long as they are not located near the exit of the flow channel. In their paper, Revellin et al. [16] also simulated the effects of the location, size and number of hot spots on CHF for various channel sizes, lengths and mass velocities.
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250
Radius [mm]
200
150
100
50 Wave height Film thickness 0
0
5
10 Heated length [mm]
15
20
Figure 6. Revellin et al. [16] simulation of a hot spot of 0.4 mm length located half way along a heated channel of 20 mm length for R-134a at a saturation temperature of 30°C in a 0.5 mm channel without inlet subcooling for a mass velocity of 500 kg/m2s.
6. Additional Comments For those interested in further reading on recent work on CHF in microchannels, refer to: Revellin and Thome [17] for a parametric study using their mechanistic CHF model, Park and Thome [18] for test results with three refrigerants (R-134a, R-236fa and R-245fa) in two copper multimicrochannel test sections, Revellin et al. [19] for CHF in constructal treeshaped microchannel networks, and Revellin et al. [20] on some special CHF effects observed for CO2. For multi-microchannel elements with “fins” separating the channels, the fin efficiency effect should be taken into account in calculating the effective heated perimeter. Furthermore, it is best to use the hydraulic diameter based on the heated perimeter as the “diameter” to implement these methods while the actual mass velocity (that is mass flow rate through the actual cross-sectional area) is also the best to use (thus not the mass velocity calculated using the heated perimeter hydraulic diameter). This choice has been confirmed by Park and Thome [18] to be the best for all the leading methods against their database for three refrigerants and two multimicrochannel test sections with rectangular shapes.
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7. Summary An overview of the state-of-the-art of predicting critical heat flux during saturated flow boiling in microchannels has been presented. Based on our own experience in comparison to published data for small channels, it appears that the best method for predicting CHF for water as the working fluid is obtained using the method of Zhang et al. [10]. For non-aqueous fluids, the two most accurate methods are those of Wojtan, Revellin and Thome [1] and Revellin and Thome [15]. NOMENCLATURE Latin CHF Co c d g h k L m& q u We x
critical heat flux, W/m2 Confinement number specific heat, J/kg/K diameter, m gravity acceleration, m/s2 specific enthalpy, J/kg thermal conductivity, W/m/K length, m mass velocity, kg/m2/s heat flux, W/m2 mean axial velocity, m/s Weber number vapor quality
Greek
δ μ ρ σ
film thickness, m dynamic viscosity, Pa s density, kg/m3 surface tension, N/m
Subscripts
crit di L G
critical Weber number based on diameter liquid phase, or Weber number based on length vapor phase
PREDICTION OF CHF IN MICROCHANNELS
h i sub
119
heated internal subcooled enthalpy difference
References 1. Wojtan, L., Revellin, R. and Thome, J.R., Investigation of Critical Heat Flux in Single, Uniformly Heated Microchannels, Experimental Thermal and Fluid Science, 30, 765–774, (2007). 2. Katto, Y. and Ohno, H., An Improved Version of the Generalized Correlation of Critical Heat Flux for the Forced Convective Boiling in Uniformly Heated Vertical Channels, Int. J. Heat Mass Transfer, 27, 1641–1648, (1984). 3. Pribyl, D.J., Bar-Cohen, A. and Bergles, A.E., An Investigation of Critical Heat Flux and Two-Phase Flow Regimes for Upward Steam and Water Flow, Proc. of the 5th International Conference in Boiling Heat Transfer, May 4–8, 2003, Jamaica. 4. Taitel, Y. and Dukler, A.E., A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow, AIChE J., 22, 47–55, (1976). 5. Bergles, A.E. and Kandlikar, S.G., On the Nature of Critical Heat Flux in Microchannels, J. Heat Transfer, 127, 101–107, (2005). 6. Lazarek, G.M. and Black, S.H., Evaporating Heat Transfer, Pressure Drop and Critical Heat Flux in a Small Vertical Tube with R-113, Int. J. Heat Mass Transfer, 25, 945–960, (1982). 7. Shah, M.M., Improved General Correlation of Critical Heat Flux during Upflow in Uniformly Heated Vertical Tubes, Int. J. Heat Fluid Flow, 8, 326– 335, (1987). 8. Bowers, M.B. and Mudawar, I., High Flux Boiling in Low Flow Rate, Low Pressure Drop Mini-Channel and Micro-Channel Heat Sinks, Int. J. Heat Mass Transfer, 37, 321–332, (1994). 9. Qu, I. and Mudawar, W., Measurement and Correlation of Critical Heat Flux in Two-Phase Micro-Channel Heat Sinks, Int. J. of Heat and Mass Transfer, 47, 2045–2059, (2004). 10. Zhang, W., Hibiki, T., Mishima, K. and Mi, Y., Correlation for Critical Heat Flux for Flow Boiling of Water in Mini-Channels, Int. J. Heat Mass Transfer, 49, 1058–1072, (2006). 11. Qi, S.L., Zhang, P., Wang, R.Z. and Xu, L.X., Flow Boiling of Liquid Nitrogen in Micro-Tubes: Part I – The Onset of Nucleate Boiling, Two-Phase Flow Instability and Two-Phase Pressure Drop, Int. J. Heat Mass Transfer, 50, 4999–5016, (2007). 12. Qi, S.L., Zhang, P., Wang, R.Z. and Xu, L.X., Flow Boiling of Liquid Nitrogen in Micro-Tubes: Part II – Heat Transfer Characteristics and Critical Heat Flux, Int. J. Heat Mass Transfer, 50, 5017–5030, (2007). 13. Lienhard, J.H. and Dhir, V.K., Extended Hydrodynamic Theory of the Peak and Minimum Pool Boiling Heat Fluxes, NASA CR-2270, July, 1973.
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14. Agostini, B., Revellin, R., Thome, J.R., Fabbri, M., Michel, B., Kloter, U. and Calmi, D., High Heat Flux Flow Boiling in Silicon Multi-Microchannels: Part III – Saturated Critical Heat Flux of R236fa and Two-Phase Pressure Drop, Int. J. Heat Mass Transfer, 41, 5426–5442, (2008). 15. Revellin, R. and Thome, J.R., A Theoretical Model for the Prediction of the Critical Heat Flux in Heated Microchannels, Int. J. Heat Mass Transfer, 51, 1216–1225, (2008). 16. Revellin, R., Moreno Quiben, J., Bonjour, J. and Thome, J.R., Effect of Local Hot Spots on the Maximum Heat Transfer during Flow Boiling in a Microchannel, IEEE Trans. on Components and Packaging Technologies, 31, 407– 416, (2008). 17. Revellin, R. and Thome, J.R., Critical Heat Flux during Flow Boiling in Microchannels: A Parametric Study, Heat Transfer Engineering, 30, 556–563, (2009). 18. Park, J.E. and Thome, J.R., Critical Heat Flux in Multi-Microchannel Copper Elements with Low Pressure Refrigerants, Int. J. Heat Mass Transfer, 52, in press, (2009). 19. Revellin, R., Thome, J.R., Bejan, A. and Bonjour, J., Constructal Tree-Shaped Microchannel Networks for Maximizing the Saturated Critical Heat Flux, Int. J. of Thermal Sciences, 48, 342–352, (2009). 20. Revellin, R., Haberschill, P., Bonjour, J. and Thome, J.R., Conditions of Liquid Film Dryout during Saturated Flow Boiling in Microchannels, Chem. Engng. Sci., 63, 5795–5801, (2009).
TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS H. SMIRNOV1 AND B. KOSOY2* 1
Odessa Academy of Food Technologies, Odessa, Ukraine Odessa State Academy of Refrigeration, Odessa, Ukraine,
[email protected] 2
1. Introduction According to the second law of thermodynamics, the entire world is moving towards maximum entropy: “heat cannot of itself pass from a colder to a hotter body”. By definition, “heat transfer is a basic science that deals with the rate of transfer of thermal energy” [1]. There are three basic mechanisms of heat transfer: conduction, convection, and radiation. Conduction is based on energy transfer between two adjacent particles of a substrate with different energy levels, whereas in convection, the heat transfers between a solid and an adjacent moving fluid. The mechanism of heat transfer through the emission of electromagnetic waves (or photons) from a matter is called radiation. Enhanced heat transfer in the industrial applications, such as electronics cooling, is often required. One of the most common methods of heat transfer enhancement is the use of enhanced surfaces, e.g. fins. Moreover, for a constant size and heat exchange rate, a lower temperature gradient shows a more efficient heat transfer. Enhanced heat transfer techniques can be classified as active and passive. Passive techniques do not require any external power and employ surface and fluid treatments to enhance heat transfer. Surface treatment techniques consist of surface coating or surface extension. Surface coating techniques use metallic or non-metallic coating. As an example of nonmetallic coating, Teflon promotes dropwise condensation, while hydrophilic coatings promote the condensate drainage in evaporator. Fine-scale porous coatings enhance heat transfer by enhancing nucleate boiling [2]. Surface extension techniques use offset strip fins, segmented fins, integral strip-finned tubes. These techniques decrease the thermal resistance by increasing the heat transfer coefficient or the surface area. Fluid treatment techniques typically
______
* Boris Kosoy, Odessa State Academy of Refrigeration, 1/3 Dvoryanskaya St, Odessa, 65082, Ukraine e-mail:
[email protected]
S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_7, © Springer Science + Business Media B.V. 2010
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contain a number of geometrical arrangements to create a secondary flow. Some examples of fluid treatment techniques include the use of twisted-tape inserts, helical vane inserts and static mixers. Surface tension is typically employed to drive the working fluid in heat pipes. A wick structure in the heat pipe helps the capillary pressure to transport liquid films from the condenser to the evaporator. Active techniques require external power, such as electronic or acoustic fields and vibration sources. In the electrostatic field technique, both direct current and alternative current can be applied to a dielectric fluid. That causes a better bulk mixing of the fluid in the vicinity of the heat transfer surface [2]. Vibration techniques are classified as surface vibration and fluid vibration techniques. Surface vibration impinges small droplets onto a heated surface to promote spray cooling. Both low and high frequencies are used in surface vibration, especially for single-phase heat transfer. However, fluid vibration is a more practical vibration enhancement, due to the mass of most heat exchangers. Surface vibration covers the frequency range from 1 Hz to ultrasound. Besides, modern technology is characterized by the tendency to package larger power conversion or transfer devices in smaller volumes. Ranging from the largest to the smallest, examples of such devices abound in microelectronics, nuclear technology, and aerospace. The heat transfer objectives can usually be stated as either (i) removing large rates of energy generation through small surface areas with moderate surface temperatures rises or (ii) reducing the size of a boiler for a given rating. Both objectives involve higher heat fluxes. This desire to accommodate or promote high heat fluxes has been a major driving force for the study of boiling heat transfer, in general, and the development of methods to enhance boiling heat transfer, in particular. Liquid cooling with boiling has been extensively studied in the past, starting with the pioneering work of Bergles and his group [3, 4] and continuing with Incropera [5], Bar-Cohen [6] and other researchers. The main issues investigated are the critical heat flux (CHF) levels that can be attained, temperature overshoot and incipient excursion, bubble growth and departure as well as the effect of surface enhancement. Microfluidics, fluid mechanics at the micro scale, has received more attention in the past years due to ever-increasing applications. The adaptability of microfluidic devices has been a key factor in their wide range of applications. Thermal microfluidic chips employ the micro scale fluid flow for thermal applications. They have been considered for special applications such as electronics cooling and bio microelectromechanical systems. In microelectronics, thermal microfluidic chips provide attractive solutions for the thermal management in highly compacted integrated circuits. Increasing the compaction of electronic components requires tremendous amount of heat dissipation, i.e. in the order of 100 W/cm2. Traditional techniques of
TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 123
heat removal, such as using cooling fans, cannot meet the thermal requirements of the new electronic chips. For cooling fans, further heat can be removed from a chip by increasing the fan’s RPM. However, the frequencies of the noises generated by these fans pass the threshold of human hearing, and it disturbs the users. Microfluidic chips demonstrated very promising performances for heat removal applications. One very important benefit of using microfluidic chips for electronic cooling is the ability of manufacturing integrated microelectronic/microfluidic chips. Both active and passive techniques are used for different types of thermal microfluidic chips. Micro heat pipe, micro capillary pumped loop, micro loop heat pipe, micro gravitational heat pipe, and micro heat pips heat spreader are some examples of thermal microfluidic chips used in the various applications. During the past two decades, the significant growth of microfluidic systems demonstrated promising capabilities for a wide range of applications. From drug delivery and biosensors in BioMEMS, to heat removal in microelectronic systems, microfluidic devices have proven their high efficiency and versatility. Microscale energy transport is an emerging science with a large number of potential applications [7]. More than 25 years ago, Tuckerman and Pease [8] presented the use of microchannels for electronics cooling. They investigated the thermal removal from planar integrated circuits, and used water as the working fluid in microchannels etched in a silicon substrate. The result was a heat transfer rate of 105 W/m2K that was almost two orders of magnitude higher than state-of-the-art commercial technologies for cooling Integrated Circuits [9]. Since then, experimental and theoretical investigations were conducted to address thermal behavior of microfluidic chips. Research was carried out on single-phase flow microfluidic systems that are employing either gas or liquid [9, 10]. However, it was shown that the latent heat in a vaporization process can highly improve the efficiency of thermal microfluidic chips; hence, extensive research was carried out on two-phase flow thermal microfluidic devices [9–11]. According to the literature, typical passive techniques were used in various microfluidic chips, such as micro heat pipes, micro heat spreaders, micro loop heat pipes, etc. Different investigations on fluid flow and heat transfer in microfluidic devices were compared analytically [12]. Figure 1 presents the basic types of thermal spreaders’ designs. Number of researchers reports the liquid forced convection inside narrow channels is a most valuable form of heat removal from heat sinks [13–16]. However, the respective key issues are the maximum attainable heat flux by using liquid forced convection, and its value in comparison with the preeminent alternatives of boiling critical heat fluxes. We believe that maximum heat flux could be accomplished by using the “inverted meniscus” principle of evaporation coupled with excluding of vapor
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hydraulic losses and minimizing liquid hydraulic losses. Such an approach was discussed in the papers [17–20]. Present paper is devoted to the current state of the art of the “reverse meniscus” concept.
Figure 1. Design of thermal spreaders: A – horizontal two-phase thermosyphon with internal PIN-structure; B – horizontal two-phase heat pipe with internal PIN-structure; C – horizontal liquid TS with internal PIN-structure; D – horizontal liquid TS with internal PIN-structure and spray cooling.
2. Theoretical Analysis of the “Reverse Meniscus” Model As it is known, the principle of vapor and liquid transport lines separation together with using capillary porous structure primarily as a locking wall that provide pumping of working fluid, was first realized in Loop Heat Pipes (LHP) [21]. Modern designs of LHP and CPL evaporators allow transferring of thermal power ~1 kW or even higher, heat flux density up to 100 W/cm2, heat transfer coefficients in the range of 5 × 104…105 W/m2K, vapor and liquid lines length more than 10 m, etc. Development of reliable models of the LHP and CPL evaporators requires special accounting for the following peculiarities: – – – –
Low heat and mass transfer intensity at small heat flux density Noticeably non-monotonous variation of thermal resistance for some evaporators designs and existence of a wide zone of constant thermal resistance for other ones Experimental data on heat transfer coefficients inside the LHP and CPL evaporators Correlation between the heat transfer intensity inside evaporators and saturation temperature
TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 125
–
Influence of the evaporator’s location, its place with respect to the condenser, transport lines geometry and lengths on the heat and mass transfer inside evaporator, etc.
Physical principles and experimental data presented by LHP and CPL researchers proved a capability to apply such technological designs, where the system of vapor removal channels is located right close to the evaporator wall, providing effective vapor generation process. It is a so-called “reverse meniscus” thermal regime. The behavior of the liquid–vapor boundary surface meniscus in the LHP evaporator microporous capillary structure has a critical significance for the start-up and reliable operation of LHP devices. Heat transfer through thin liquid film (microfilm) formed in the root of vapor bubbles determines a scale and peculiarities of the vaporization process. The thinner this film, the higher intensity of heat transfer. However at the break or complete dryout of a film, the heat transfer intensity goes down sharply. Thus, the problem of securing of “micro-film evaporation” consists in providing such conditions when time of survival of this form of vaporization exceeds the characteristic duration of the process. For this purpose, a liquid supply must be provided in the places of micro-film formation. For example, imposition of a porous structure on the vaporization surface provides a necessary liquid input due to the action of capillary forces. The smaller size of the channels through which the medium moves, the higher heat transfer intensity. Consequently, secure heat transfer requires providing a liquid movement near the wall in microchannels. Besides, using of the surface finning reduces the entire thermal resistance. Therefore, creation of systems with the micro-finned surfaces (PIN-structures) contributes to the significant heat transfer augmentation. Technology of the “reverse meniscus” consists in imposition of microporous layer to the PIN-structure that provides high intensity of heat transfer. Using of bidisperse wick structure is also instrumental in intensification of heat transfer. Typical schematics of the LHP evaporators and corresponding heat transfer regimes are shown in Figs. 2 and 3. Hence, the following thermo-hydraulic modes occur inside circumferential channels: 1. Channels and porous structure are filled with a thermal fluid and heat transfers from the wall of LHP evaporator to the surface of compensation chamber and to the edge of the vapor generating surface of the evaporator primarily due to effective heat conduction (Fig. 3, mode 1). This thermal regime occurs when the initial boiling is impossible even inside the near-wall circumferential channels, i.e. temperature drop is less than 4σTs/(rρ″Rch) =ΔTmin, where Rch is an inscribing radius of corresponding near-wall channel.
H. SMIRNOV AND B. KOSOY
126 B
1
1
2 5 3
1
5 3
B 5
B-B-1 1
3 1
B-B-2
3
4 B-B-3
3 B-B-4
A-A Figure 2. Design schematics of the LHP evaporators. A-A is a cross-section of the cylindrical LHP evaporator; B-B-1…B-B-4 are typical circumferential vapor generation channels: 1 – evaporator wall; 2 – axial vapor removal channels; 3 – main porous structure; 4 – compensation chamber; 5 – circumferential vapor generation channels.
2. Wall temperature drop increase causes small vapor bubbles coming out inside the channel and expansion of initial boiling. The boiling regularities are similar to case of boiling inside narrow slits of the identical size. Thus, such thermal mode is similar to boiling in narrow slits and it continues until wall superheat will attain a temperature drop sufficient for the vapor appearance inside the porous structure, i.e. 4σTs/(rρ″Ref)=ΔTmin2. 3. Porous structure counting the contact surface between the porous insert and evaporator wall is saturated with a liquid. Vaporization occurs only on those porous structure elements, which are liquid-free due to heat transfer through the contact surface to the vapor–liquid interface (Fig. 3, mode 2). Curvature of the vapor–liquid interface is reliant on the vapor–liquid pressure drop determined for each steady state mode as the entire hydraulic resistance of LHP or CPL. The value of curvature remains constant within single elementary cell of circumferential channel (Fig. 2, mode 2). 4. Further rise in heat load maintains increasing of the abovementioned entire hydraulic resistance, and if it exceeds 2σ/Rmax; a local deformation of the interface happens at some decreasing of thermal resistance in the evaporation zone. When heat load keeps on increasing and the entire hydraulic resistance exceeds 2σ/Ref, (Rmin < Ref < Rmax) then edging between the wall and the liquid in the porous structure will be destroyed and two-phase boundary layer will appear between the evaporator wall and vapor–liquid interface (Fig. 3, mode 3). This mode exists until the whole porous structure around the circumferential channels is occupied by the two-phase layer. Then vapor phase filtration through the porous
TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 127
structure occurs in the radial direction and the balance between the capillary pressure and the entire hydraulic resistance is irreversibly broken. vapor liquid liquid 1
q ≥ q0 ΣΔpi ≤ 2σ/Reff
2
0 ≤ q ≤ q0
vapor
vapor
3
δ′′
h
Two-phase border
h
δ′′
liquid Two-phase border
ΣΔpi≥ 2σ/Ref, δ′′< h
liquid 4
δ′′> h, ΣΔpi > 2σ/Ref Tw↑
Figure 3. Typical heat transfer modes inside the LHP evaporator.
5. The next thermal mode occurs when the major part of the porous structure remains in superheat state, vapor occasionally enters the compensation chamber, and capillary pressure becomes steady-state. Present mathematical model is not valid for these operating conditions (Fig. 3, mode 4). When thermal mode matches the temperature drop in range of ΔTmin ≤ ΔT ≤ ΔTmax, where ΔTmin ≅
2σ Ts 4σ Ts ; ΔTmax ≅ ; R0 is a pore radius; r ρ ′′R0 r ρ ′′Def
and Def is a channel effective diameter, boiling heat transfer intensity inside narrow slits is prescribed as α ≈ Cq m s − n p k , where 0 < m < 2; 0 < n < 1; and 0 < k < 1. The exact values of C, m, n, and k should be determined experimentally. In case of intensive vaporization, recommendations presented in the papers [22, 23] and approximation performed by Krukov [24] allow determining dependency of specific mass flow rate jz on coordinate z. Therefore, if
jz = 0.6 2 RдTs (ρ s − ρ0 )
ρ0 , ρs
(1)
H. SMIRNOV AND B. KOSOY
128
then
j z = 0.84ε
dPs ΔT0 ( z ) , RдTs dT 1
(2)
where ΔT0(z)=Ts − T0=(ΔT(z) − ΔT*)/(1 + 2σ/rρ″R); and ΔT* = 2σTs/rρ″R. Specific superheat of the evaporator wall υ could be determined by solving the heat conduction equation: ϑ = ϑ0 +
⎡ 2σTs q0 ( a + b) B0 ⎤ 2σTs , = exp ⎢ − z ⎥+ rρ ′′R λeff b ⎥⎦ rρ ′′R λeff bB0 ⎢⎣
where B0 = 0.84rε
dPs dTs
1 RдTs
; at z = 0, ϑ =
q0 ( a + b )
λeff bB0
+
2σTs rρ ′′R
(3)
(4)
Superheat of evaporator wall is required for providing certain heat flux through the porous structure saturated with liquid. The total superheat of evaporator wall can be determined by treating the heat transferred to edge surface between the evaporator wall and porous structure through a sequence of thermal resistances. Assigning the entire specific thermal resistance of the edge as Rk0 yields the following correlation for the overall average superheat of the evaporator wall in the mode 2:
ΔT0 =
q0 (a + b) 2σTs q0 (a + b) 3 q0 a3 + b3 + ab2 + + Rk 0 + 32 λM δ M a+b b λeff bB0 rρ ′′R
(5)
Comparison between the Eqs. (3) and (5) gives
jz =
⎡ B0 q0 ( a + b) B0 ⎤ exp ⎢ − z ⎥ λeff b ⎥⎦ r λeff bB0 ⎢⎣
(6)
One-dimensional filtration equation is −dp/dz = (ν′/Kf)jz, consequently, −
dp ν ′ = dz rK f
⎡ B0 ⎤ ⎥ q0 (a + b) exp ⎢− z λeff b λeff b ⎥⎦ ⎢⎣ B0
(7)
TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 129
Then, the pressure drop in capillary structure is ⎡ B0 ⎤ ν ′q (a + b) ′ Δpm = 0 exp ⎢− z ⎥ + c1 , and if z = 0 → Δpm = ν q0(a + b)/rKf (8) rK f b λ ⎥ eff ⎦ ⎣⎢ In the thermal mode 2, a value Δpm can be considered as auxiliary hydraulic resistance due to concentration of heat and mass fluxes in the zone of vapor generation according to the “reverse meniscus” principle. When specific design of the LHP allows assumption that all hydraulic resistances (excluding Δpm) are much smaller than capillary potential developed by porous structure 2σ/Ref; it is feasible a correlation for the maximum heat flux (q0)max attained in dependence from certain type of the working fluid, saturation pressure and core design parameters of the nearwall capillary structure: (q0)max < 2σrKf /Refν′(a + b)
(9)
As seen from the Eq. (9), accomplishment of the value (q0)max requires both increasing the near-wall zone permeability Kf , and decreasing the radius of pores involved in the vaporization process. It is known that bidisperse pore structures provide maximum heat flux densities at the highest efficiency [25]. Decrease of circumferential channel dimensions (a and b) also causes increasing of (q0)max, however, it also escalating the entire hydraulic resistance inside the LHP. In certain conditions, it plays the major role in heat flow Q and heat flux q0 limitations before the value (q0)max is attained. Thus, besides the Eqs. (4), (5) and (8), the known steady-state thermohydrodynamic correlations of the LHP should be also implemented to the model. The necessity of such mutual consideration appears obvious in case of determining transition conditions from the thermal mode 2 to the thermal mode 3, and in the analysis of heat transfer regularities of the thermal mode 3. Assuming that vapor channel length Lvch is independent on the heat supply, the following equation yields a dependency between the curvature radius and surface area of the vapor–liquid interface: 2σ 1 Ri+1 ⎫⎪ Q ⎧⎪ Π n (a + h)2 (a + b) ≥ + 0.16ν ′∑ ln ⎨4ν ′′ ⎬+ 2 3 R rLvch ⎪⎩ K fi Ri ⎪⎭ n0 (ah) 2 −3 −2 ⎛ Q ⎞ 1 ⎡ 8.1⋅ 10 Lvch 3.2 ⋅ 10 Lvch ⎤ ν ′Q(a + b) +⎜ ⎟ + ⎢ ⎥+ 2 5 Dk5 ⎝ r ⎠ ρ′′ ⎣ n0 d0 ⎦ Πn LvchrK f
The substitution of following terms in the Eq. (10)
(10)
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130
4ν ′′Π vch ( a + h ) 2 ( a + b ) ν ′ i=n 1 Ri+1 = A ; 0.16 1 ∑ ln = A2 ; n 02 r ( ah ) 3 L vch rLvch i=1 K fi Ri
ν ′(a + b) 1 ⎡ 8.1⋅10−3 Lvch 3.2 ⋅10−2 Lk ⎤ = A4 (11) + = A ; ⎢ ⎥ 3 Π L rK r 2 ρ ′′ ⎣ n02 d 05 Dk5 vch vch f ⎦ gives the next correlation ( 2σ / R ≥ { A1 + A2 + A3Q} × Q + A4Q
(12)
Simultaneous consideration of the Eqs. (12) and (5), and introducing the specific thermal resistance of the LHP evaporation section as ΔT0 / q 0 = Rvch in the thermal mode 2, yields
Rvch =
ΔT0 Π L T a +b Πvch Lvch = + vch vch s × Q r ρ ′′ λeff bB0
a+b 3 1 a3 + b3 + ab2 Rk 0 + ×{[ A1 + A2 + A4 ] + A3Q} + b a+b 32 λmδ m
(13)
As seen from the Eq. (13), in the thermal mode 2 the specific thermal resistance (heat transfer coefficient) is practically autonomous of heat supply value. It is also justified by existing experimental data. Thus, the Eq. (13) provides proper description of interrelations of the following parameters: − − −
Decreasing dimensions a and b causes reduction of Rvch, i.e. increasing heat transfer coefficients Increasing the heat transfer parameters of evaporator wall, δm and λm, maintains decrease of Rvch When the LHP is operating in the gravity field, the extra term, ρ′gL0 sinϕ should be added to the right-hand side of the Eq. (12). The angle ϕ accounts for the LHP evaporator location in relation to the condenser. If ρ′gL0 sinϕ > 0, the value Rvch is increased, while the negative values of this term uphold reliable operation of the LHP at low heat supply until the Eq. (12) is valid.
Transition from the thermal mode 2 to the thermal mode 3 is defined by the Eq. (12). Thus, if Eq. (12) is not true at increasing heat supply and R → Rmin in the edge between the evaporator wall and porous structure saturated with liquid, it creates conditions encouraging vapor–liquid interface displacement from the evaporator wall and generation of vapor layer between
TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 131
the evaporator wall and vapor–liquid interface inside the porous structure. As shown by Smirnov [26], a real geometric shape of the interface is quite complex. Appearance of the vapor layer causes vaporization over the whole surface of the vapor–liquid interface separating the porous structure saturated with the liquid from the evaporator wall. It means both possibility to neglect with the first term of the right-hand side of the Eq. (13), and increasing value of Rk0 in the third term; i.e. vaporization of liquid in the edge zone requires introducing an extra thermal resistance term δ/λef corresponded to the heat transfer from the evaporator wall to the vapor–liquid interface through the porous structure occupied by the vapor layer with thickness, δ. Depending on hydraulic resistances ratio, the rate of increasing of the vapor layer thickness changes with respect to the increase in the heat supply, but as a rule dδ/dQ > 0. Available experimental data justify increasing specific thermal resistance when heat supply rises in the thermal mode 3. Thus, the following correlation is valid for the thermal mode 3:
Rn = +
{
}
Π vch LvchTs A1 + A2′ + A3Q + A5 + r ρ ′′
a+b 3 1 a3 + b3 + ab2 δ Rk′ 0 + + b a+b 32 λmδ m λef
(14)
Vapor layer thickness δ could be determined by solving corresponding hydrodynamic equation with boundary condition based on the Eq. (12). When R = Rmin, the transition between the thermal modes 2 and 3 (Q = Q0) could be determined. Irreversible failure of the LHP operation occurs during further displacement of the vapor–liquid interface in the case when Q = Qmax and thickness δ becomes equal to h, i.e. increase of vapor filtration hydraulic resistance is not balanced by the decrease of hydraulic resistance of liquid filtration inside the porous structure anymore. The value Qmax corresponding to equality of δ = h determines the maximum heat supply allowing reliable operating of the LHP. 3. Strategy of Thermal Spreader’s Optimization The geometry of thermal spreader could be optimized to match one of the following criteria: − −
Minimum entire thermal resistance Minimum weight
H. SMIRNOV AND B. KOSOY
132
− −
Minimum heat losses Maximum efficiency
Optimization of the heat spreader involves determining the combination of internal geometric parameters with respect to following constraints: heat removal surface geometry (rectangular (length a and width b are given), cylindrical (radius R and length L are given), spherical (radius R and angle Θ are given), semi-spherical, semi-cylindrical, etc.; feasible thermal regimes (temperature constraint on the heat input surface T0, partial or transient thermal regimes T1, T2, and corresponding heat input scales Q0, Q1, Q2, location change connected with the thermal regimes); temperatures of the heat removal surfaces TA1, TA2; fixed heat removal conditions (radiation, contact heat transfer, convection, etc.). The principal view of the goal function is J = g1 ×
N M1 M M M + g 2 × 2 + ... + g n × n = ∑ g i i , M 01 M 02 M 0 n i =1 M 0i
(15)
where M1, M2, …, Mn and M01, M02, …, M0n are values of variables with different dimensions and physical nature, and they values under some reference state, correspondingly; g1, g2, …, gn are weight factors of these variables. Assuming M1 = R1, M2 = V1 or H1, where R1, V1, and H1 are entire thermal resistance in the main heat spreader’s volume, and its real volume or its height (thickness), the key issue of the method appears as determination of the values R1, and H1. Suppose that cooled chip is located in such a way that the heat carrier returns to the heating zone under the gravity action, i.e. the heat is transferred from the horizontal plate with known power Qi at given temperature level Ti. Heat is removed at given temperature Tj or the heat removal mode is known, i.e. Qi = f(Tj). Then, optimization algorithm appears as following: Step 1. Determine the most extended thermal regime having the temperature T1b. Preliminary select the heat carrier with respect to the condition: T1b − δ t ≥ T S , where δt is a temperature drop on the internal surface of the heat input zone, TS is a saturation temperature. Validate the condition: TS T0, (T0 a triple point temperature). Step 2. Estimate the temperature drop for the simple design of heating surface (without any enhancements) by calculating a heat flux as qJmax = QJmax/F, where QJmax is a given value of the heat input, and F=a ⋅ b, (a and b are given dimensions of the heat output surface).
TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 133
For selected heat carrier by iterations assume δt, and determine TS. Calculate the critical heat flux by the Kutateladze formula
qCR ≅ const × r × 4 g × σ ( ρ ' − ρ " )
(16)
Validate the condition qCR ≤ qJmax. In case when this condition is false, proceed with the subsequent iteration. Step 3. Select a surface material with respect to its compatibility with the heat carrier, and nature of the finned surface (rectangular, PIN-structure, cylindrical, grooves, porous coating, etc.) Determine the local temperature drop on the lateral part of the finned surface as
⎡q ⎢ J max ⎢ μ1r δ T = C0 × r × (Pr1 )1.7 × ⎣
⎡ ⎤ σ ⎢ ⎥ ⎣ g ( ρ ′ − ρ ′′) ⎦ C1
0.5 0.33
⎤ ⎥ ⎥ ⎦
,
(17)
where: r, Pr1, σ, μ, C1, ρ′, ρ″ are the latent heat of evaporation; liquid Prandtl Number; surface tension; liquid dynamic viscosity, specific heat capacity; liquid and vapor densities, correspondingly. C0 is an empirical constant accounting the effect of heat carrier – surface arrangements on the boiling heat transfer augmentation. Local heat transfer coefficient at boiling on the fin lateral surface is
α = qJ max / δ T
(18)
Determine the effectiveness of finned surface as
E f = tanh(mh) / mh; m = (αU f ) /(λ f S f ) ,
(19)
where Uf, λf, and Sf are perimeter, specific thermal conductivity of fins and its cross section area, correspondingly. The entire internal thermal resistance of the heat input zone is
Rb =
1 , α × E f × U f × h + α × F0
(20)
where h and F0 are the fins’ height and the edge surface area without fins. Consequently, the simplest form of the goal function appears as
H. SMIRNOV AND B. KOSOY
134
J = g f × ( Rb / Rb 0 ) + g h × ( h / h0 ) ,
(21)
where gf and gh are the weight factors corresponding to the entire thermal resistance of the finned surface and the consequent occupied. Step 4. Determine the optimal geometric parameters for the condensation zone with respect to the following assumptions of the model: − − −
Calculations for the plane condensation surface has no sense. Primary heat transfer occurs at the lateral surfaces of fins. Part of condensate is collected at the top inside fin’s gap under the action of surface forces; consequently, the entire calculated condensation heat transfer area should be reduced.
Thus, corresponding equation for calculation of condensation heat transfer coefficient is
⎧ ⎫ μ1 × (h − hC ) α C = const × ⎨ ⎬ 3 ⎩ ρ ′ × ( ρ ′ − ρ ′′) × λ1 × r × g ⎭
−1/ 3
× (q)−1/ 3 , (22)
where (h − hc) is a reduction of the heat transfer surface due to condensate gathering at the fins’ edge under the action of surface tension forces; q is an average heat flux from the fins’ lateral surfaces; and const is a constant parameter determined by solving conventional problem of the condensation heat transfer at the vertical surface. In such a case, the effectiveness of the finned surface is
E fC = tanh{m(h − hC )} /{m(h − hC )}; m = (α CU C ) /(λ S C )
(23)
Here SC = ( h − hC ) × U C × N C , where Nc is a fins’ density (their number related to the given surface area). Hence, the entire internal thermal resistance of the condensation zone appears as RC =
hC δ 1 + × ( 0 + 1) , α C × E fC × SC λ × ( N C × U C × δ C ) δ C
where δ0 and δC are fin’s gap and thickness, correspondingly.
(24)
TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 135
In order to validate the present approach, the experimental sample of two-phase thermal spreader was designed and manufactured for cooling of high thermal power chip placed in the horizontal position. With respect to the thermal regime constraint, ammonia was selected as the heat carrier and stainless steel was used as the core material. The following optimal geometric parameters of the experimental sample were determined: − −
Evaporation zone – h = 5 mm; s = 1 mm; δb = 1 mm. Condensation zone – h = 10 mm; s = 2.5 mm; δC = 6 mm. Figure 4 presents design of the experimental sample of thermal spreader. Temperatures were measured in heat input and heat output zones. 32
f 88 f4
2
32
f80
Y 6
x
5
1
63
10
2,5
30
74
1 63
Figure 4. The real two-phase thermal spreader with finned surfaces in the heat input and heat output zones.
Corresponding temperature sensors’ locations are shown in Figs. 5 and 6.
Figure 5. Locations of experimental temperature sensors in the heat input zone (T2, T3, and T4).
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Figure 6. Locations of experimental temperature sensors in the heat output zone.
Representative experimental data shown in the Figure 7.
Figure 7. The effect of heat input on the entire temperature drop in the two-phase thermal spreader.
4. Conclusions
The present approach cannot be considered as the completed theory or the perfect model given accurate values of the corresponding thermal and flow resistances. A number of improvements can be made to theoretical descriptions used at different stages of heat and mass transfer process modeling as well as more accurate two-dimensional or three-dimensional models of heat and mass transfer could be applied. However, the current concept represents a source for further researches committed with such issues as: − −
Determination of optimal geometrical and technological parameters (a, b, h, d0, etc.) by treating the minimum thermal resistance ΔT0/Q under the given heat input Calculation of value Qmax in constraint of ΔT0/Q (aopt, bopt, Lvch, etc.)
TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 137
− −
Determination of the LHP optimal parameters at given value of Q0 with respect to minimization of the weight and maximization of the reliability factor, etc. Study of the physical nature of various heat and flow instabilities
Using the current concept, especially in modeling the LHP dynamics, requires paying special attention to conditions of transition between thermal modes, uncertainty of hydraulic parameters due to the flow mode changing; position of the vapor–liquid interface and its stability, as well as inconsistency of factors determining a structure’s geometry. Further studies in the field of geometric optimization for two-phase thermal spreaders can be classified into two categories: modeling investigations, and validation studies. The future modeling issues worth addressing include: − −
Modeling of more complex geometries (e.g. polygonal, curved sided, or combined cross-sections, as well as interconnected geometries Geometric optimization of three-dimensional networks, using twophase flow simulations maintaining the proper operation and accurately captured the detailed phenomena
References 1. Cengel, Y.A., Heat Transfer: a practical approach. (Second ed., New York: McGraw-Hill, 2003). 2. Webb, R.L. and N.-H. Kim, Principles of enhanced heat transfer (Second ed., New York: Taylor & Francis, 2005). 3. Park, K.A., and Bergles, A.E., Boiling Heat Transfer Characteristics of Simulated Microelectronic Chips with Detachable Heat Sinks, Eighth International Heat Transfer Conference, Vol. 4, Hemisphere Publishing Corporation, Washington, DC, pp. 2099–2104, 1986. 4. Bergles, A.E. and Bar-Cohen, A., Direct Liquid Cooling of Microelectronic Components, Advances in Thermal Modeling of Electronic Components and Systems, Eds., Bar-Cohen, A. and Kraus, A.D., Vol. 2, pp. 233–250, ASME Press, New York, 1990. 5. Incropera, F.P., Liquid Immersion Cooling of Electronic Components, Heat Transfer in Electronic and Microelectronic Equipment, Ed. A. E. Bergles, pp. 407–444, Hemisphere Publishing Corporation, 1990. 6. Bar-Cohen, A., Thermal Management of Electronic Components with Dielectric Liquids, International Journal of JSME 36(1), 1–25 (1993). 7. Tien, C.-L., A. Majumdar, and F.M. Gerner, Microscale energy transport. Series in chemical and mechanical engineering (Washington, DC: Taylor & Francis, 1998).
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8. Tuckerman, D.B. and R.F.W. Pease, High-performance heat sinking for VLSI. IEEE Electron Device Letters, 1981. ED-2(5): p. 126. 9. Zohar, Y., Heat convection in micro ducts. Microsystems, ed. S. Senturia (Norwell, MA: Kluwer Academic Publishers. 2003). 10. Kandlikar, S.G., et al., Heat transfer and fluid flow in minichannels and microchannels., (Oxford: Elsevier, 2006). 11. Zhang, L., T.W. Kenny, and K.E. Goodson, Silicon microchannel heat sinks. Microtechnology and MEMS, ed. H. Baltes, H. Fujita, and D. Liepmann, (New York: Springer-Verlag, Berlin-Heidelberg, 2004). 12. Sobhan, C.B. and S.V. Garimella, A comparative analysis of studies on heat transfer and fluid flow in microchannels. Microscale Thermophysical Engineering, 5(4), 293–311 (2001). 13. Leslie, S.G., Cooling options and challenges of high power semiconductors modules, Electronics Cooling, 12(4), 20–27 (2006). 14. Copeland, D., Fundamental Performance of Heatsinks, ASME Journal of Electronic Packaging, 125(2), 221–225 (2003). 15. Copeland, D., Review of Low Profile Cold Plate Technology for High Density Servers, Electronics Cooling, 11(2), (2005). 16. Clemens J.M. Lasance and R.E. Simons, Advances In High – Performance Cooling For Electronics, Electronic Cooling, http://electronics-cooling.com/ articles/ 2005/2005_nov_article2.php 17. North, M.T., Shaubach R.M., Rosenfeld, J.H., Liquid Film Evaporation From Bidisperse Capillary Wicks in Heat Pipe Evaporators, Proceedings of 9th IHPC, May 1995, Albuquerque NM. 18. Rosenfeld, J.H., Anderson, W.G., North, M.T., Improved High Heat Flux Loop Heat Pipes using bidisperse evaporators wicks, Proceedings of 10th IHPC, September 1997, Stuttgart. 19. H.F. Smirnov and K.A. Goncharov, Physical and Mathematical modelling of loop heat pipes evaporators, Proceedings of 11th IHPC, September 1999, Tokyo. 20. Altman, E.I., Mukminova, M.Ja., Smirnov, H.F., Loop Heat Pipe Evaporators’ Theoretical Analysis, Proceedings of 12th IHPC , May 2002, Moscow. 21. Maidanik, Yu.F., Fershtater, Yu.G., Pastukhov, V.G., Loop Heat Pipes: Working out, Investigations, Engineering calculations’ elements, The Scientific reports of USSR Academy of Sciences, Ural Branch, 1989, Sverdlovsk. 22. D.A. Labuntzov and A.P. Krukov, Intensive evaporation processes, Teploenergetika, 4, 8–11 (1977). 23. D.A. Labuntzov and A.P. Krukov, Analysis of intensive evaporation and condensation, International Journal of HMT, 22, 989–1002 (1979). 24. Krukov, A.P., Kinetic analysis of evaporation and condensing processes on the surface, International Seminar of Belarus Academy of Science, 1991, Minsk. 25. Maidanik, Yu.F., Vershinin, S.V., Fershtater, Yu.G., Heat transfer enhancement in a loop heat pipe evaporator, Proceedings of 10th IHPC, September 1997, Stuttgart. 26. Smirnov, H.F., Transport Phenomena in Capillary-Porous Structures and Heat Pipes (CRC Press, 2009).
AN INVESTIGATION ON THERMAL CONDUCTIVITY AND VISCOSITY OF WATER BASED NANOFLUIDS I. TAVMAN AND A. TURGUT Mechanical Engineering Department, Dokuz Eylul University, 35100 Bornova, Izmir, Turkey,
[email protected]
Abstract. In this study we report a literature review on the research and development work concerning thermal conductivity of nanofluids as well as their viscosity. Different techniques used for the measurement of thermal conductivity of nanofluids are explained, especially the 3ω method which was used in our measurements. The models used to predict the thermal conductivity of nanofluids are presented. Our experimental results on the effective thermal conductivity by using 3ω method and effective viscosity by vibro-viscometer for SiO2–water, TiO2–water and Al2O3–water nanofluids at different particle concentrations and temperatures are presented. Measured results showed that the effective thermal conductivity of nanofluids increase as the concentration of the particles increase but not anomalously as indicated in the some publications and this enhancement is very close to Hamilton– Crosser model, also this increase is independent of the temperature. The effective viscosities of these nanofluids increased by the increasing particle concentration and decrease by the increase in temperature, and cannot be predicted by Einstein model.
1. Introduction Nanofluids are solid nanoparticles or nanofibers in suspension in a base fluid. To be qualified as nanofluid it is generally agreed that at least one size of the solid particle be less than 100 nm. Various industries such as transportation, electronics, food, medical industries require efficient heat transfer fluids to either evacuate or transfer heat by means of a flowing fluid. Especially with the miniaturization in electronic equipments, the need for heat evacuation has become more important in order to ensure proper working conditions for these elements. Thus, new strategies, such as the use of new, more conductive fluids are needed. Most of the fluids used for this purpose are generally poor heat conductors compared to solids (Fig. 1).
S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_8, © Springer Science + Business Media B.V. 2010
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It is well known that fluids may become more conductive by the addition of conductive solid particles. However such mixtures have a lot of practical limitations, primarily arising from the sedimentation of particles and the associated blockage issues. These limitations can be overcome by using suspensions of nanometer-sized particles (nanoparticles) in liquids, known as nanofluids. After the pioneering work by Choi of the Argonne National Laboratory, USA in 1995 [1] and his publication [2] reporting an anomalous increase in thermal conductivity of the base fluid with the addition of low volume fractions of conducting nanoparticles, there has been a great interest for nanofluids research both experimentally and theoretically. More than 970 nanofluid-related research publications have appeared in literature since then and the number per year appears to be increasing as it can seen from Fig. 2. In 2008 alone, 282 research papers were published in Science Citation Index journals. However, the transition to industrial practice requires that nanofluid technology become further developed, and that some key barriers, like the stability and sedimentation problems be overcome. 1000
Heat transfer fluids
Metal Oxide
Metal Cu
Thermal Conductivity (W/mK)
Al
100
Al2O3 CuO TiO2
10
1
Water Ethylene Glycol Oil
0.1
Figure 1. Thermal conductivity of typical materials (solids and liquids) at 300 K.
A review of the literature showed that the nanoparticles used in the production of nanofluids were: aluminum oxide (Al2O3), titanium dioxide (TiO2), nitride ceramics (AlN, SiN), carbide ceramics (SiC, TiC), copper (Cu), copper oxide (CuO), gold (Au), silver (Ag), silica (SiO2) nanoparticles and carbon nanotubes (CNT). The base fluids used were water, oil, acetone, decene and ethylene glycol. Modern technology allows the fabrication of materials at the nanometer scale, they are usually available in the market under different particle sizes and purity conditions. They exhibit
THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 141
unique physical and chemical properties compared to those of larger (micron scale and larger) particles of the same material. Nanoparticles can be produced from several processes such as gas condensation, mechanical attrition or chemical precipitation techniques [3]. Papers in the title containing either “nanofluid” or “nanofluids” searched by the ISI web of science-with conference proceedings on October 2009
Number of paper published per year
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150
121 91
100
40
50
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1 0
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6
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Figure 2. Publications on nanofluids since 1999.
Nanofluids are generally produced by two different techniques: a onestep technique and a two-step technique. The one-step technique makes and disperses the nanoparticles directly into a base fluid simultaneously. The two-step technique starts with nanoparticles which can usually be purchased and proceeds to disperse them into a base fluid. Most of the nanofluids containing oxide nanoparticles and carbon nanotubes reported in the open literature are produced by the two-step process. The major advantage of the two-step technique is the possibility to use commercially available nanoparticles, this method provides an economical way to produce nanofluids. But, the major drawback is the tendency of the particles to agglomerate due to attractive van der Waals forces between nanoparticles; then, the agglomerations of particles tend to quickly settle out of liquids. This problem is overcome by using ultrasonic vibration, to break down the agglomerations and homogenize the mixture. Figure 3 shows Al2O3–water nanofluids, (a) shows homogenization with ultrasonic vibration, (b) shows the same nanofluids without any homogenization process, we can easily see the settled nanoparticles.
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Figure 3. Al2O3–water nanofluids (a) treated with ultrasonic vibration, (b) untreated – settlement of nanoparticles.
The first publications on thermal conductivity of nanofluids were with base fluids water or ethylene-glycol (EG) and with nanoparticles such as aluminum-oxide (Al2O3) [4–7], copper-oxide (CuO) [4, 5, 7], titaniumdioxide (TiO2) [8], copper (Cu) [9, 10]. They all measured great enhancement in thermal conductivity for low particles addition, typical enhancement was in the 15–40% range over the base fluid for 0.5–4% nanoparticles volume concentrations in various liquids. The increase was from 5% to 60% for nanoparticles additions ranging from 0.1% to 5% by volume. These unusual results have attracted great interest both experimentally and theoretically from many research groups because of their potential benefits and applications for cooling in many industrials from electronics to transportation. Recent papers provide detailed reviews on al aspects of nanofluids, including preparation, measurement and modeling of thermal conductivity and viscosity [11–13, 24]. Very few studies [7, 14–19] have been performed to investigate the temperature effect on the effective thermal conductivity of nanofluids. In a recent study by Turgut et al. [16] on relative thermal conductivity of TiO2–water nanofluids, no temperature effect has been found like in the study by Masuda et al. [18] and Zhang et al. [19]. However, Wang et al. [17] measured an increase in relative thermal conductivity for the same nanofluid. Hence, to confirm the effects of temperature on the effective thermal conductivity of nanofluids, more experimental studies are essential. The experimental data reported in the literature is very scattered, for the same base fluid and the same particles there are many different results. Some researchers [16–19] measured only a moderate increase of effective thermal conductivity with the addition of nanoparticles. Their experimental results can be explained by classical Maxwell [20], Hamilton and Crosser [21] models for mixtures. A recent publication by Keblinski et al. [22] reveals this controversy about the scatter of experimental data and compares the experimental data from different
THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 143
authors for various water based nanofluids. He shows that this results fall within the upper and lower limits of classical two phase mixture theories. There are many publications on predictive models for effective thermal conductivity of nanofluids [5, 11, 23, 25–27], some of these publications make an overview of the existing models, and some drives their own model and compares with experimental data. None of the models is able to explain and predict an effective thermal conductivity value for the nanofluids. Although some review articles [28–30] emphasized the importance of investigating the viscosity of nanofluids, very few studies on effective viscosity were reported. Viscosity is as critical as thermal conductivity in engineering systems that employ fluid flow. Pumping power is proportional to the pressure drop, which in turn is related to fluid viscosity. More viscous fluids require more pumping power. In laminar flow, the pressure drop is directly proportional to the viscosity. Masuda et al. [18] measured the viscosity of TiO2–water nanofluids suspensions, they found that for 27 nm TiO2 particles at a volumetric concentration of 4.3% the viscosity increased by 60% with respect to pure water. In his work on the effective viscosity of Al2O3–water nanofluids, Wang et al. [5] measured an increase of about 86% for 5 vol% of 28 nm nanoparticles content. In their case, a mechanical blending technique was used for dispersion of Al2O3 nanoparticles in distilled water. They also measured an increase of about 40% in viscosity of ethylene glycol at a volumetric loading of 3.5% of Al2O3 nanoparticles. Das et al. [31] and Putra et al. [32] measured the viscosity of water-based nanofluids, for Al2O3 and CuO particles inclusions, as a function of shear rate they both showed Newtonian behavior for a range of volume percentage between 1% and 4%. Das et al. [50] also observed an increase in viscosity with an increase of particle volume fraction, for Al2O3/water-based nanofluids. In all cases the viscosity results were significantly larger than the predictions from the classical theory of suspension rheology such as Einstein’s model [33]. 2. Models for the Effective Thermal Conductivity of Nanofluids Many theoretical and empirical models have been proposed to predict the effective thermal conductivity of two phase mixtures. Comprehensive review articles have discussed the applicability of many of these models that appear to be more promising [34–36]. First, using potential theory, Maxwell [20] obtained a simple relationship for the conductivity of randomly distributed and non-interacting homogeneous spheres in a homogeneous medium. Maxwell model is good for low solid concentrations. Relative thermal conductivity enhancement (ratio of the effective thermal conductivity keff of nanofluid to base fluid kf) is,
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k eff / k f =
k p + 2k f + 2φ (k p − k f )
(1)
k p + 2k f − φ ( k p − k f )
where φ is the particle volume fraction of the suspension, kp is the thermal conductivity of the particle. According to Maxwell model the effective thermal conductivity of suspensions depending on the thermal conductivity of spherical particles, base liquid and the volume fraction of solid particles. Bruggeman [37] proposed a model to analyze the interactions among randomly distributed particles by using the mean field approach.
keff =
k 1 (3φ − 1)kp + (2 − 3φ )kf + f 4 4
[
]
Δ
(2)
where, (3) When Maxwell model fails to provide a good match with experimental results for higher concentration of inclusions, Bruggeman model can sufficiently be used. Hamilton and Crosser [21] modified Maxwell’s model to determine the effective thermal conductivity of non-spherical particles by applying a shape factor n. The formula yields, (4) where n = 3/ψ and ψ is the sphericity, defined by the ratio of the surface area of a sphere, having a volume equal to that of the particle, to the surface area of the particle. Yu and Choi [38] derived a model for the effective thermal conductivity of nanofluid by assuming that there is no agglomeration by nanoparticles in nanofluids. They assumed that the nanolayer surrounding each particle could combine with the particle to form an equivalent particle and obtained the equivalent thermal conductivity kpe of equivalent particles as fallows,
k pe =
[2(1 − γ ) + (1 + β ) (1 + 2γ )γ ] k 3
− (1 − γ ) + (1 + β )3 (1 + 2γ )
p
(5)
THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 145
where γ = klayer/kp, is the ratio of the nanolayer thermal conductivity to particle conductivity, and β = h/r is the ratio of nanolayer thickness to the original particle radius.
k eff / k f =
k pe + 2 k f + 2φ ( k pe − k f )(1 − β ) 3 k pe + 2 k f − φ ( k pe − k f )(1 + β )
3
(6)
Jang and Choi [39] devised a theoretical model that includes four modes of energy transport; the collision between basefluid molecules, the thermal diffusion of nanoparticles in the fluid, the collision between nanoparticles due to Brownian motion, and the thermal interactions of dynamic nanoparticles with base fluid molecules.
k eff / k f = (1 − φ ) +
kp kf
φ + 3C
df dp
φ Re 2d P Pr
(7)
where Redp is the Reynolds number defined by Redp=(CRMdp)/ν, C is a proportional constant, CRM is the random motion velocity of nanoparticles, ν is the dynamic viscosity of the base fluid, Pr is the Prandtl number, df and dp are the diameter of the base fluid molecule and particle. For typical nanofluids, the order of the Reynolds number and the Prandtl numbers are 1 and 10, respectively. Xie et al. [40] derived an expression for calculating enhanced thermal conductivity of nanofluid by considering The effects of nanolayer thickness, nanoparticle size, volume fraction, and thermal conductivity ratio of particle to fluid. The expression is: (8) with Θ=
β lf ⎡⎢(1 + γ )3 − β pl / β fl ⎤⎥ ⎣
(1 + γ )3 + 2β lf β pl
⎦
(9)
where
k −k β lf = l f
k l + 2k f
β pl =
k p − kl k p + 2k l
k −k β fl = f l
k f + 2k l
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and γ = δ/rp is the thickness ratio of nano-layer and nanoparticle. φT is the modified total volume fraction of the original nanoparticle and nano-layer, φT =φ (1+ γ)3. Besides these models there are many others models, but no single model explains the effective thermal conductivity in all cases. Besides the thermal conductivities of the base fluid and nanoparticles and the volume fraction of the particles, there are many other factors influencing the effective thermal conductivity of the nanofluids. Some of these factors are: the size and shape of nanoparticles, the agglomeration of particle, the mode of preparation of nanofluids, the degree of purity of the particles, surface resistance between the particles and the fluid. Some of these factors may not be predicted adequately and may be changing with time. This situation emphasizes the importance of having experimental results for each special nanofluid produced. 3. Experimental 3.1. MATERIALS
Properties of nanoparticles and base fluid used in this study are shown in Table 1. De-ionized water was used as a base fluid. In the nanofluid, nanoparticles tend to cluster and form agglomerates which reduce the effective thermal conductivity. It is known that ultrasonication break the nanoclusters into smaller clusters. Hong et al. [41] investigated the role of sonication time on thermal conductivity of iron (Fe) nanofluids. The thermal conductivity of each nanofluid showed saturation after a gradual increase as the sonication time was increased. The thermal conductivity of 0.2 vol% Fe nanofluid exhibited 18% enhancement with a 30 min sonication and was saturated after 30 min. So, in order to obtain good quality nanofluids, it is essential that the solid–liquid mixture be exposed to ultrasonication. TABLE 1. Properties of nanoparticles and base fluid used in nanofluids preparation.
3
Density (kg/m ) Thermal conductivity (W/mK) Average particle diameter (nm)
SiO 2
TiO 2
Al2O 3
water
2,220
3,800
3,700
1,000
1.38
10
46
0.613
12
21
30
–
A two-step method was used to produce water based nanofluids with, 0.45, 1.85 vol% concentrations of SiO2 nanoparticles; 0.2, 1.0 and 2.0 vol% concentrations of TiO2 nanoparticles and 0.5 and 1.5 vol% concentrations
THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 147
of Al2O3 nanoparticles. In the first stage of preparation of nanofluids, the proper amount of dry nanoparticles necessary to obtain the desired volume percentage was mechanically mixed in de-ionized water. The next step was to homogenize the mixture using ultrasonic vibration, to break down the agglomerations. In order to decide on a sonication time to be used in the preparation of nanofluids, we applied different sonication times for 1% by volume TiO2–water nanofluids and measured their thermal conductivity (Fig. 4). It may be seen that sonication time has practically no effect on thermal conductivity after 30 min, so we decided to use 30 min of sonication time. No surfactant was used in these experiments. Another possibility for preventing clustering of nanoparticles was to eventually use a surfactant. For this purpose sodium dodecylbenzenesulfonate (SDBS) was used as surfactant, it was mixed to pure de-ionized water at different ratio of SDBS/Al2O3, it was observed that the thermal conductivity of SDBS – water mixture decreased with the increasing SDBS ratios which means that the effect of this surfactant was to decrease the thermal conductivity of the base fluid (see Fig. 5). We further used this surfactant in 1% by volume Al2O3–water nanofluids at different ratio of SDBS/Al2O3, as it can be seen from Fig. 5, its effect on thermal conductivity was still negative. In other words, thermal conductivity of Al2O3–water nanofluids was better than with the same nanofluid with surfactant. So, we decided not to use a surfactant in the preparation of nanofluids. 1.035
Relative Thermal Conductivity
1.03 1.025 1.02 1.015 1.01 TiO2 -water 1% volume
1.005 1 0
5
10
15
20 25 30 35 40 45 Sonication Time (minute)
50
55
60
Figure 4. Relative thermal conductivity of (1% vol.) TiO2–water nanofluid as a function of the sonication time.
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Relative Thermal Conductivity
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1.05
(Al2O3+water)/(water)
1.04
(Al2O3-SDBS+water)/(water)
1.03
(SDBS+water)/(water)
1.02 1.01 1 0.99 0.98 0.97 0.96 0.95
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
(SDBS/Al2O3), mass ratio
Figure 5. Effect of SDBS surfactant on relative thermal conductivity of 1% by volume Al2O3–water nanofluids at different mass ratio of SDBS/Al2O3.
3.2. METHODS FOR MEASURING THERMAL CONDUCTIVITY OF NANOFLUIDS
Experimental studies on the thermophysical properties of liquids are especially very difficult. The main problem lies in the elimination of convectional heat transfer in the liquid and monitoring of the temperature fields and gradients during the measurement. Stationary as well as transient methods for measuring thermal conductivity or diffusivity of liquids are associated with a temperature gradient which in some cases may induce natural convection in the liquid. If there is a natural convection, the thermal conductivity of the liquid is then measured higher than the real thermal conductivity value. For this reason the temperature gradient must be kept as low as possible and the measurement time must be as short as possible. Although many methods are reported in the literature for the determination of thermal conductivity [42, 43] reliable data for these classes of materials are still lacking. With the growing interest for different commercial composite materials used in the casting industry and demands for more efficient coolants with greater heat transfer capabilities in the auto industry, more accurate measurement techniques are needed. The different techniques for measuring the thermal conductivity of liquids can be classified into two main categories: steady-state and transient methods. Both of these methods have some merits and disadvantages. The equipment for steady state method is simple and the governing equations for heat transfer are well known and simple. The main disadvantage is the very long experimental times required for the measurement and the necessity to keep
THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 149
all the conditions stable during this time. For nanofluids, the steady state methods are not very adequate, during the long measurement time particles may settle down or migrate; it is extremely difficult to keep everything stable during the experimental run. That is the reason why there are very few studies on thermal conductivity of nanofluids with steady state methods. Wang et al. [5] measured the effective thermal conductivity of metal oxide nanoparticle suspensions using a steady-state method. Somewhat later, Das and co-workers [7, 44] measured the effective thermal conductivity of metal and metal oxide nanoparticle suspensions using a temperature oscillation method. The transient hot wire (THW) method has been well developed and widely used for measurements of the thermal conductivities and, in some cases, the thermal diffusivities of fluids with a high degree of accuracy [6, 42]. More than 80% of the thermal conductivity measurements on nanofluids were performed by transient hot wire method [6, 8, 18, 19, 45–47]. Another method for measuring thermal diffusivity is the flash method developed by Parker et al. [48] and successfully used for the thermal diffusivity measurement of solid materials [49]. A high intensity short duration heat pulse is absorbed in the front surface of a thermally insulated sample of a few millimeters thick. The sample is coated with absorbing black paint if the sample is transparent to the heat pulse. The resulting temperature of the rear surface is measured by a thermocouple or infrared detector, as a function of time and is recorded either by an oscilloscope or a computer having a data acquisition system. The thermal diffusivity is calculated from this time–temperature curve and the thickness of the sample. This method is commercialized now, and there are ready made apparatus with sample holders for fluids. There is only one publication on nanofluids with this method, Shaikh et al. [50] measured thermal conductivity of carbon nanoparticle doped PAO oil. Finally, recent works on thermal conductivity measurements using the 3ω method have reported [16, 17]. This method is very accurate and fast will be explained fully in the next section. We used this method which has also the advantage of requiring small amounts of liquids for the measurement. 3.2.1. 3ω Method for Measuring Thermal Conductivity of Fluids This technique based on a hot wire thermal probe with AC excitation and 3ω lock-in detection. Since the principle and procedures of the technique have been described in details previously [51] only a brief description is given here. We consider a thermal probe (ThP) consisting of a metallic wire of length 2l and radius r immersed in a liquid sample, acting simultaneously as a heater and as a thermometer. The sample and probe thermophysical properties are the volume specific heat ρc and the thermal conductivity k, with the respective subscripts (s) and (p). The wire is excited by ac current
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at frequency f/2 and we assume that it is thermally thin in the radial direction so that the temperature θ ( f ) is uniform over its cross section. Since the electrical resistance of the wire is modulated by the temperature increase, the voltage across the wire contains a third harmonic V3ω proportional to θ ( f ). It is convenient to use a normalized (reduced) 3ω signal, F( f ) [52]. For r/μs 1, the temperature increase θ ( f ) generated by a modulated line heat source P in an infinite and homogeneous medium can be approximated by [53, 54]:
F( f ) ∝θ ( f ) = −
P/l 2π k s
σ r⎞ P/l ⎛ ⎜ γ + ln s ⎟ = − 2 ⎠ 2π k s ⎝
⎛ 1.26 r π ⎞ ⎜⎜ ln + i ⎟⎟ μs 4⎠ ⎝
(10)
where γ = 0.5772 is the Euler constant. The complex quantity σs is given by σs = (1 + i)/μs = (i2πf/αs)1/2 with μs the thermal diffusion length at frequency f and αs = ks/ρscs the thermal diffusivity. In this work we are concerned with the measurement of thermal properties of water-based nanofluids, relative to pure water (subscript w). From Eq. (10) one has:
k s Im( Fw ) = k w Im(Fs )
cot ϕ s − cot ϕ w =
and
sin(ϕ w − ϕ s ) 2 α = − ln s sin ϕ s sin ϕ w π αw
(11)
For small diffusivity difference the phase yields:
αs π (ϕ s − ϕ w ) = 1+ αw 2 sin 2 ϕ w
(12)
In principle, Eq. (11) give frequency-independent results of, but in practice there is an optimum frequency range such that r/μs < 1 in which ks and αs have stable and low noise values as a function of frequency. The first harmonic in the voltage signal is dominant and must be cancelled by a Wheatstone bridge arrangement. The selection of the third harmonic from the differential signal across the bridge is performed by a Stanford SR850 lock-in amplifier tuned to this frequency (Fig. 6 [55]). The thermal probe (ThP) is made of 40 μm in diameter and 2l = 19.0 mm long
THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 151
Ni wire (Fig. 7). The temperature amplitude θ in water was 1.25 K. The minimum sample volume for Eq. (10) to apply is that of a liquid cylinder centered on the wire and having a radius equal to about 3μs. At 2f = 1 Hz, this amounts to 25 μl. The method was validated with pure fluids (water, methanol, ethanol and ethylene glycol), yielding accurate k-ratios within ±2% (Eq. 11) and absolute α value for water within ±1.5% (Eq. 12).
Figure 6. Schematic diagram of 3ω experimental set-up.
Figure 7. Experimental set-up for 3ω method consisting of thermal probe (ThP), Wheatstone bridge and lock-in amplifier.
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3.3. VIBRATION VISCOMETER FOR MEASURING VISCOSITY OF NANOFLUIDS
The experimental setup for measuring the effective viscosity of nanofluids, consists of a Sine-wave Vibro Viscometer SV-10 and Haake temperaturecontrolled bath with 0.1°C. The SV-10 viscometer (A&D, Japan), has two thin sensor plates that are driven with electromagnetic force at the same frequency by vibrating at constant sine-wave vibration in reverse phase like a tuning-fork. The electromagnetic drive controls the vibration of the sensor plates to maintain constant amplitude. The driving electric current, which is an exciting force, will be detected as the magnitude of viscidity produced between the sensor plates and the sample fluid (Fig. 8 [56]). The coefficient of viscosity is obtained by the correlation between the driving electric current and the magnitude of viscidity. Since the viscosity is very much dependent upon the temperature of the fluid, it is very important to measure the temperature of the fluid correctly. By this viscometer we can detect accurate temperature immediately because the fluid and the detection unit (sensor plates) with small surface area/thermal capacity reach the thermal equilibrium in only a few seconds (Fig. 9). Its measurement range of viscosity is 0.3–10,000 mPas.
Figure 8. Schematic diagram of the vibro viscometer [56].
THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 153
Figure 9. Vibrator (sensor plates) and sample cup.
4. Results and Discussion 4.1. THERMAL CONDUCTIVITY OF NANOFLUIDS
Relative Thermal Conductivity
In Fig. 3 our experimental results for SiO2, Al2O3 and TiO2 samples at room temperature were compared with classical effective thermal conductivity model, known as Hamilton–Crosser model (Fig. 10) [21]. 1.08
water based nanofluids
1.07
TiO2 experimental
1.06
Al2O3 experimental SiO2 experimental
1.05
H-C model TiO2
1.04
H-C model Al2O3
1.03
H-C model SiO2
1.02 1.01 1 0
0.5
1
1.5
2
Particle Volume Fraction (%)
Figure 10. Relative thermal conductivity versus particle volume fraction of TiO2, Al2O3 and SiO2 nanofluids.
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Our experimental results for water based SiO2, Al2O3 and TiO2 nanofluids are lower than the H-C model. Moreover, comparison of the TiO2 nanofluids with the Al2O3 nanofluids showed that the highly thermal conductive material is not always the excellent application for enhancing the thermal transport property of nanofluids. Thermal conductivity of TiO2–water nanofluid has higher enhancement than the Al2O3–water nanofluid, even TiO2 bulk thermal conductivity value is lower than the Al2O3. Similar result was presented by Hong et al. [41] for Fe nanofluids compared with the Cu nanofluids. 4.2. VISCOSITY OF NANOFLUIDS
There are some theoretical formulas in the literature which predict the viscosity of particle suspension in a fluid. Most of the existing formulas were derived from the Einstein’s pioneering work [33]. His formula was based on the assumption of a linearly viscous fluid that contains dilute suspended spherical particles. Then by calculating the energy dissipated by the fluid flow around a single particle and by associating that energy with the work done for moving this particle relatively to the surrounding fluid, he obtained:
μ eff = μ l (1 + 2.5φ )
(13)
where φ is the volume fraction of particles, μl and μeff are the viscosity of the base fluid and effective viscosity of the mixture. This formula is valid for non-interacting particle suspension in a base fluid that is for the volume concentrations is less than 5%. Krieger and Dougherty [57] formulated a semi-empirical equation for relative viscosity expressed as ⎛ φ μ eff = μ l ⎜⎜ ⎜φ ⎝ m
⎞ ⎟ ⎟ ⎟ ⎠
− [η ]φ m
(14)
where φm is the maximum packing fraction and [η] is the intrinsic viscosity ([η] = 2.5 for hard spheres). For randomly mono-dispersed spheres, the maximum close packing fraction is approximately 0.64. Another model was proposed by Nielsen [58] for low concentration of particles. Nielsen’s equation is as follows:
φ / (1 − φm ) μ eff = μ l (1 + 1.5φ )e
(15)
THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 155
where φ and φm are the volume fraction of particles and the maximum packing fraction, respectively. The measurements of effective viscosity of SiO2–water, TiO2–water and Al2O3–water nanofluids at different particle volume concentrations were performed using Vibro Viscometer SV-10. To be use of the accuracy of the measurement the viscosity of water was measured before and after each experiment. The results of the measurements performed at room temperature are shown in Figs. 11–14. For SiO2–water nanofluids of 12 nm particle size, the experimental results are compared with the above cited 3 models in Fig. 11. It may be seen that measured viscosity values are well above the prediction of the models, the difference becoming larger as the volume concentration is increasing. In Fig. 12, these same results are compared with the existing literature values for the same nanofluids by Wang et al. [59] for 7 and 40 nm particle sizes and Kang et al. [60]. Our experimental results are of the same as those by Wang et al. [59] for the particle size of 7 nm, but larger than the other results. 5 SiO2-water
4.5 This study Einstein model [33])
Relative Viscosity
4
K-D model [57] 3.5
Nielsen model [58]
3 2.5 2 1.5 1 0
1
2 3 Particle Volume Fraction (%)
4
Figure 11. Relative viscosity of SiO2–water nanofluids as a function of nanoparticle volume fraction compared with the models.
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5
SiO2 - water
4.5
This study 12nm Wang et al. (7nm),[59]
Relative Viscosity
4
Wang et al. (40nm),[59] 3.5
Kang et al. (15 nm),[60]
3 2.5 2 1.5 1 0
1
2 3 Particle Volume Fraction (%)
4
Figure 12. Experimental results of relative viscosity of SiO2 nanofluids, compared to selected literature data.
In Fig. 13, we compared our experimental results on TiO2–water with the results of Masuda et al. [18], He et al. [46] and Murshed et al. [61] and also to Einstein model. All results are well above the prediction of the Einstein model. 1.7
TiO2-water
1.6 Turgut et al., [16] Masuda et al., [18] He et al., [46] Murshed et al., [61] Einstein model [33]
Relative Viscosity
1.5 1.4 1.3 1.2 1.1 1 0
0.5
1
1.5
2
Particle Volume Fraction (%)
Figure 13. Relative viscosity of TiO2–water nanofluids as a function of nanoparticle volume fraction.
THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 157 2
water based nanofluids
water 0.2% TiO2 1% TiO2 2% TiO2 0.45% SiO2 1.85% SiO2 0.50% Al2O3 1.50% Al2O3
.
1.6
Viscosity, mPa.s
1.8
1.4 1.2 1 0.8 0.6 0.4 20
25
30
35
40
45
50
Temperature, 8C
Figure 14. Comparison of effective viscosity of water based nanofluids with as a function of temperature.
Figure 14 shows the effective viscosity of all three nanofluids with different volume concentrations of particles, measured at temperatures between 20°C and 50°C. The viscosity of nanofluids increased dramatically with an increase in particle concentration and decreased with temperature, following the trend of the viscosity for pure water, for low particle concentrations. 5. Conclusions The thermal conductivities of SiO2–water, TiO2–water and Al2O3–water nanofluids were measured using a 3ω method for different particle concentrations and temperatures. The experimental results showed that the thermal conductivity enhancements were relatively in good agreement with the Hamilton–Crosser model, and they were moderated increases, not as high and sometimes qualified as anomalous increases as claimed by some researchers [4, 5, 7–10]. In fact the review of experimental studies clearly showed a lack of consistency in the reported results of various research groups. The effects of several important factors such as particle size and shapes, clustering of particles, temperature of the fluid, and dissociation of surfactant on the effective thermal conductivity of nanofluids were not investigated adequately. It is very important that more investigations should be performed, in order to confirm the effects of these factors on the thermal conductivity for wide range of nanofluids. From our results, we also noticed that, although thermal conductivity of TiO2 was much higher than Al2O3,
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the thermal conductivities of Al2O3–water nanofluids were significantly higher then TiO2–water nanofluids, which means that the thermal conductivity of the nanoparticles was not the only factor that determines the thermal conductivity of the nanofluids. We also found that the relative thermal conductivity of the nanofluid was not dependant on temperature. The effective viscosities of SiO2–water, TiO2–water and Al2O3–water nanofluids were measured. The results show that for low volume additions of nanoparticles the measured effective viscosity values follow quite well the viscosity values of pure water with a decrease in viscosity with increasing temperature and may be predicted by the Einstein law of viscosity. But, for higher additions of nanoparticles, the Einstein law of viscosity and other viscosity models failed to explain the large increase in viscosity values. Because of the large increase in effective viscosity, large pumping powers are required to circulate the nanofluid used in cooling systems. In order to have a good idea on the applicability of these nanofluids in real engineering systems, effective viscosity must be measured together with the thermal conductivity of the nanofluids. Acknowledgments This work has been supported by TUBITAK (Project no: 107M160), Research Foundation of Dokuz Eylul University (project no: 2009.KB.FEN.018) and Agence Universitaire de la Francophonie (Project no: AUF-PCSI 6316 PS821).
References 1. S.U.S. Choi, “Enhancing Thermal Conductivity of Fluids with Nanoparticles”, Developments and Applications of Non-Newtonian Flows, eds. D.A. Singer and H.P. Wang (1995) FED 231, 99–105, American Society of Mechanical Engineers, New York. 2. S.U.S. Choi, Z.G. Zhang, W. Yu, F.E. Lockwood and E.A. Grulke, Anomalous thermal conductivity enhancement in nano-tube suspensions, Applied Physics Letters, 79, 2252–2254 (2001). 3. V. Trisaksri and S. Wongwises, Critical review of heat transfer characteristics of nanofluids, Renewable and Sustainable Energy Reviews, 11, 512–523 (2007). 4. S. Lee, S.U.S. Choi, S. Li and J.A. Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles, Journal of Heat Transfer, 121, 280– 289 (1999). 5. X. Wang, X. Xu and S.U.S Choi, Thermal conductivity of nanoparticle-fluid mixture, Journal of Thermophysics and Heat Transfer, 13, 474–480 (1999).
THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 159 6. H. Xie, J. Wang, T. Xi, Y. Liu and F. Ai, Thermal conductivity enhancement of suspensions containing nanosized alumina particles, Journal of Applied Physics, 91, 4568–72 (2002). 7. S.K. Das, N. Putra, P. Thiesen and W. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids, Journal of Heat Transfer, 125, 567–574 (2003). 8. S.M.S. Murshed, K.C. Leong and C. Yang, Enhanced thermal conductivity of TiO2–water based nanofluids, International Journal of Thermal Science, 44, 367–373 (2005). 9. Y. Xuan and Q. Li, Heat transfer enhancement of nano-fluids, International Journal of Heat and Fluid Flow, 21, 58–64 (2000). 10. J.A. Eastman, S.U.S. Choi, S. Li, W. Yu and L.J. Thompson, Anomalously increased effective thermal conductivities of ethylene glycol based nanofluids containing copper nanoparticles, Applied Physics Letters, 78(6), 718–720 (2001). 11. S.M.S. Murshed, K.C. Leong and C. Yang, Thermophysical and electrokinetic properties of nanofluids – a critical review, Appl. Therm. Eng., 28, 2109–2125 (2008). 12. W.H. Yu, D.M. France, J.L. Routbort and S.U.S. Choi, Review and comparison of nanofluid thermal conductivity and heat transfer enhancements, Heat Transfer Engineering, 29, 432–460 (2008). 13. S.U.S. Choi, Nanofluids: From vision to reality through research, J. Heat Transfer, 131, 033106 (2009). 14. C.H. Li and G.P. Peterson, Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids), Journal of Applied Physics, 99(8), 084314 (2006). 15. C.H. Chon and K.D. Kihm, Thermal conductivity enhancement of nanofluids by Brownian motion, J. Heat Transfer, 127, 810 (2005). 16. A. Turgut, I. Tavman, M. Chirtoc, H. P. Schuchmann, C. Sauter and S. Tavman, Thermal conductivity and viscosity measurements of water-based TiO2 nanofluids, Int J Thermophys, 30, 1213–1226 (2009). 17. Z.L. Wang, D.W. Tang, S. Liu, X.H. Zheng and N. Araki, Thermal-conductivity and thermal-diffusivity measurements of nanofluids by 3ω method and mechanism analysis of heat transport, Int. J. Thermophys., 28, 1255–1268 (2007). 18. H. Masuda, A. Ebata, K. Teramae and N. Hishinuma, Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (dispersion of Al2O3, SiO2 and TiO2 ultra-fine particles), Netsu Bussei 4, 227–233 (1993). 19. X. Zhang, H. Gu, and M. Fujii, Experimental study on the effective thermal conductivity and thermal diffusivity of nanofluids, International Journal of Thermophysics, 27, 569–580 (2006). 20. J.C. Maxwell, A Treatise on Electricity and Magnetism (2nd Ed.), Clarendon Press, Oxford, U.K., 1881. 21. R.L. Hamilton and O.K. Crosser, Thermal conductivity of heterogeneous two component systems, Industrial and Engineering Chemistry Fundamentals, 1, 187–191 (1962).
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22. P. Keblinski, R. Prasher and J. Eapen, Thermal conductance of nanofluids: is the controversy over?, J. Nanopart Res., 10, 1089–1097 (2008). 23. X.Q. Wang and A.S. Mujumdar, A review on nanofluids - Part I Theoretical and numerical investigations, Brazilian Journal of Chemical Engineering, 25, 613–630 (2008). 24. X.Q. Wang and A.S. Mujumdar, A review on nanofluids – Part II Experiments and applications, Brazilian Journal of Chemical Engineering, 25, 631–628 (2008). 25. Q.Z. Xue, Model for effective thermal conductivity of nanofluids, Physics Letters A, 307, 313–317 (2003). 26. J. Avsec and M. Oblak, The calculation of thermal conductivity, viscosity and thermodynamic properties for nanofluids on the basis of statistical nanomechanics, International Journal of Heat and Mass Transfer, 50, 4331–4341 (2007). 27. P. Keblinski, S.R. Phillpot, S.U.S. Choi and J.A. Eastman, Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids). Int. J. of Heat and Mass Transfer, 45, 855–863 (2002). 28. J.A. Eastman, S.R. Phillpot, S.U.S. Choi and P. Keblinski, Thermal transport in nanofluids, Annual Review of Materials Research, 34, 219–246 (2004). 29. P. Keblinski, J.A. Eastman and D.G. Cahill, Nanofluids for thermal transport, Materials Today, 8, 36–44 (2005). 30. S.K. Das, S.U.S. Choi and H.E. Patel, Heat transfer in nanofluids – a review, Heat Transfer Engineering, 27, 3–19 (2006). 31. S.K. Das, N. Putra and W. Roetzel, Pool boiling characteristics of nanofluids, International Journal of Heat and Mass Transfer, 46, 851–862 (2003). 32. N. Putra, W. Roetzel and S.K. Das, Natural convection of nanofluids, Heat and Mass Transfer, 39, 775–784 (2003). 33. A. Einstein, Investigations on the Theory of the Brownian Movement, Dover Publications, Inc., New York, 1956. 34. I.H. Tavman, Effective thermal conductivity of granular porous materials, International Communications in Heat and Mass Transfer, 23(2), 169–179 (1996). 35. R.C. Progelhof, J.L. Throne and R.R. Ruetsch, Methods for predicting the thermal conductivity of composite systems: A review, Polym. Eng. Sci. 16, 615–625 (1976). 36. H.J. Ott, Thermal conductivity of composite materials, Plastic and Rubber Processing and Application, 1, 9–24 (1981). 37. D.A.G. Bruggeman, The calculation of various physical constants of heterogeneous substances I. The dielectric constants and conductivities of mixtures composed of isotropic substances, Ann. Phys. (Leipzig) 24, 636–664 (1935). 38. W. Yu and S.U.S. Choi, The role of interfacial layers in the enhanced thermal conductivity of nanofluids: A renovated Maxwell model, Journal of Nanoparticle Research, 5, 167–171 (2003). 39. S.P. Jang and S.U.S. Choi, Role of Brownian motion in the enhanced thermal conductivity of nanofluids, Applied Physics Letters, 84, 4316–4318 (2004). 40. H. Xie, M. Fujii and X. Zhang, Effect of interfacial nanolayer on the effective thermal conductivity of nanoparticle-fluid mixture, International Journal Heat Mass Transfer, 48, 2926–2932 (2005).
THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 161 41. K.S. Hong, T.K. Hong and H.S. Yang, Thermal conductivity of Fe nanofluids depending on cluster size of nanoparticles, Applied Physics Letters, 88, 031901 (2006). 42. K.S. Hong, T.K. Hong and H.S. Yang, Thermal Conductivity of Fe Nanofluids Depending on Cluster Size of Nanoparticles, Applied Physics Letters, 88, 031901 (2006). 43. Y. Nagasaka and A. Nagashima, Absolute measurement of the thermal conductivity of electrically conducting liquids by the transient hot wire method, J Phys E: Sci Instrum., 14, 1435–1440 (1981). 44. J.S. Powell, An instrument for the measurement of thermal conductivity of liquids at high temperatures, Meas. Sci. Technol., 2, 111–117 (1991). 45. H.E. Patel, S.K. Das and T. Sundararajan, Thermal conductivities of naked and monolayer protected metal nanoparticle based nanofluids: Manifestation of anomalous enhancement and chemical effects, Appl. Phys. Lett., 83, 2931– 2933 (2003). 46. D.H. Yoo, K.S. Hong and H.S. Yang, Study of thermal conductivity of nanofluids for the application of heat transfer fluids, Thermochim. Acta, 455, 66–69 (2007). 47. Y. He, Y. Jin, H. Chen, Y. Ding, D. Cang and H. Lu, Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe, Int. J. Heat Mass Transfer, 50, 2272–2281 (2007). 48. M.J. Assael, C.F. Chen, I. Metaxa and W.A. Wakeham, Thermal conductivity of suspensions of carbon nanotubes in water, Int. J. Thermophys., 25(4), 971– 985 (2004). 49. W.J. Parker, R.J. Jenkins, C.P. Butler and G.L. Abbott, Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity, J. Appl Phys, 32, 1679–1684 (1961). 50. I. Tavman, Flash method of measuring thermal diffusivity and conductivity, Nato Asi Series, Series E: Applied Sciences, 196, 923–936 (1990). 51. S. Shaikh, K. Lafdi and R. Ponnappan, Thermal conductivity improvement in carbon nanoparticle doped PAO oil: An experimental study, J. Appl. Phys., 101, 064302 (2007). 52. A. Turgut, C. Sauter, M. Chirtoc, J.F. Henry, S. Tavman, I. Tavman and J. Pelzl, AC hot wire measurement of thermophysical properties of nanofluids with 3 omega method, Europ. Phys. J. Special Topics, 153, 349–352 (2008). 53. M. Chirtoc. and J.F. Henry, 3ω hot wire method for micro-heat transfer measurements: From anemometry to scanning thermal microscopy (SThM), Europ. Phys. J., Special Topics, 153, 343–348 (2008). 54. H.W. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, Oxford University Press, London, UK (1959). 55. D.G. Cahill, Thermal conductivity measurement from 30 to 750 K: the 3 omega method, Rev. Sci. Instrum., 61, 802–808 (1990). 56. M. Chirtoc, X. Filip, J.F. Henry, J.S. Antoniow, I. Chirtoc, D. Dietzel, R. Meckenstock and J. Pelzl, Thermal probe self-calibration in ac scanning thermal microscopy, Superlattices and Microstructures, 35, 305–314 (2004).
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57. N. Izumo and A. Koiwai, Technological background and latest market requirements concerning “static viscosity” measurement with a tuning-fork vibration viscometer, in Proceedings of Asia-Pacific Symposium on Measurement of Mass, Force and Torque (APMF 2009), 1–4 June 2009, Tokyo, Japan, 51–57 (2009). 58. I.M. Krieger and T.J. Dougherty, A mechanism for non-Newtonian flow in suspensions of rigid spheres, Journal of Rheology, 3(1), 137–152 (1959). 59. L.E. Nielsen, Generalized equation for the elastic moduli of composite materials, J. Appl. Phys., 41(11), 4626–4627 (1970). 60. T. Wang, Z.Y. Luo, C.H. Shou, S.B. Zhang and K.F. Cen (2007). Experimental study on convection heat transfer of nanocolloidal dispersion in a turbulent flow, in Proceedings of the International Conference on Power Engineering 2007, 993–998 (2007). 61. H.U. Kang, S.H. Kim and J.M. Oh, Estimation of thermal Conductivity of nanofluid using experimental effective particle volume, Experimental Heat Transfer, 19, 181–191 (2006). 62. S.M.S. Murshed, K.C. Leong and C. Yang, Investigations of thermal conductivity and viscosity of nanofluids, International Journal of Thermal Sciences, 47(5), 560–568 (2008).
FORMATION OF DROPLETS AND BUBBLES IN MICROFLUIDIC SYSTEMS P. GARSTECKI
Department of Soft Condensed Matter, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland,
[email protected]
Abstract. The lecture will review the recent advances in the techniques for formation of bubbles of gas and droplets of liquid in two-phase microfluidic systems. Systems comprising ducts that have widths of the order of 100 μm produce suspensions of bubbles and droplets characterized by very narrow size distributions. These systems provide control over all the important parameters of the foams or emulsions, from the volumes of the individual bubbles and droplets, through the volume fraction that they occupy, the frequency of their formation, and the distribution of sizes, including monodisperse, multimodal and non-Gaussian distributions. The lecture will review the fundamental forces at play, and the mechanism of formation of bubbles and droplets that is responsible for the observed monodispersity.
1. Introduction 1.1. MICROFLUIDICS
Microfluidics is a concept that describes the science and technology of design, fabrication and operation of systems of microchannels that conduct liquids and gases. Typically, the channels have widths of tens to hundreds of micrometers and the speed of flow of the fluids is such that the viscous forces dominate over inertial ones. The resulting – linear – equations of flow and its laminar character provide for extensive control: the speed of flow obeys the simple Hagen–Poiseuille equation that relates the speed linearly to the pressure drop through the particular channel and to its inverse hydraulic resistance, which in term is a function of the dimensions of the channel and the viscosity of the fluid. This property, when combined with typically large values of the Peclet number [1] that reflect the fact that diffusional transport is typically slow in comparison to the flow, it is possible to control the profiles of concentration [2] of chemicals and S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_9, © Springer Science + Business Media B.V. 2010
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profiles of temperature [3] in the channels, all with minute consumption of the fluids and energy. These characteristics prompted for visions of use of the microfluidic chips in analytical chemistry and diagnostics. In the 1990s, the existing technologies of chemical analysis – chromatography and electrophoresis – which already took advantage of guiding fluids in channels of small crosssections inspired the vision of constructing more integrated devices (in the format of chips) for sensitive assays with high resolution and operating on small samples of fluids [4]. The vision of integration is one of the keys to the interest in microfluidics in general. Already first demonstrations of electrophoresis on chip [5] suggested that complicated protocols for chemical analyses will be feasible – as already demonstrated by a number of groups [6]. A crucial contribution to the explosion of research activity in the field of microfluidics was the development of approachable procedures for microfabrication [4]. Fast prototyping via lithography and replication of the masters in polydimethylosiloxane – a technique often related to as softlithography [7] – made it possible to go from the idea to the fabricated chip within a day, with facile reproduction of the existing masters for multiple experiments [7]. Now, about 20 years from the first demonstrations [5] the field has generated thousands of academic demonstrations of analytical techniques performed on-chip, including e.g. highly integrated systems [8] and commercial applications. 1.2. DROPLET MICROFLUIDICS
A new wave of interest and prospects for applications came in the beginning of this century with the demonstration from Thorsen et al. [9] of formation of monodisperse aqueous droplets in an organic carrier fluid performed on a microfluidic chip. Although the use of fluidic ducts of micron-scale crosssections for generation of monodisperse droplets [10] have been known, this demonstration was critical for establishing the new field. The observation that one can control the flow of immiscible fluids with similar fidelity as that practiced with simple fluids [11] was highly non-trivial: introduction of the interfacial forces results in complicated interactions with their magnitude depending on the curvature and surface area of the interface. In spite of this, and as will be described in this lecture, multiphase flows do subject themselves to extensive control. In particular, and of highest interest, are the processes of formation of droplets, bubbles, and more complicated objects, such as multiple droplets, particles and capsules. These phenomena and their understanding form the basis of a number of potential applications – both in the field of synthesis of new materials and formulations for the
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pharmaceutical, cosmetic and food industries, and in construction of systems for analytical and synthetic chemistry.
Figure 1. Number of scientific articles citing the word ‘microfluidics’ plotted as a function of the year of publication [ISI Web of Knowledge]. The dashed line gives an exponential growth of the number of publications in the years 1994 to ~2002.
The field of microfluidics has gone through the phase of rapid expansion and is now maturing (Fig. 1). The exponential explosion of interest in the field has slowly saturated and the field is transiting into the phase of more application oriented research. This is possible because the fundamental concepts and understanding – although still being areas of active investigation – have been already laid. Our lectures during the NATO Advanced Study Institute on Microsystems for Security in Cesme (2009) concentrated on the fundaments of understanding of (i) formation of droplets, and (ii) transport of droplets in complicated networks of channels. Here we discuss the first of these two subjects, describing the most important forces at play, the mechanism of formation of bubbles and droplets in common microfluidic geometries, and the show examples of the use of this technology. We note that this lecture does not strive to provide an in-depth review of the field, but rather an approachable introduction that contains the basic understanding of the most common techniques. 2. Interfacial Tension and Conventional Methods of Emulsification Immiscible fluids, when brought in contact, develop a well defined interface between them. The existence of this interface contributes a cost to the free energy of the system. This contribution Eγ, which is often related to as interfacial energy, is proportional to the surface area A of the interface. The
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coefficient of proportionality is the coefficient of interfacial tension γ with the units of force per length [N/m]. One can easily translate the equation Eγ′ = Aγ
(1)
that relates the energy with the surface area of the interface, into the language of forces.
Figure 2. The Laplace pressure – pressure exerted by curved interfaces – is proportional to the sum of the principal curvatures. This is why a deformed droplet restores its perfectly spherical shape. The red arrows signify the direction and magnitude of the restoring interfacial force.
If we consider a small a change of the shape of the interface, parameterized by a small displacement dr, the force will read: F = dEγ′/dr = γ dA/dr.
(2)
It is more convenient to express the force per unit area, which is the pressure exerted by an interface. For a sphere with A = 4πr2, we have: pγ = (1/A)(dEγ /dr) = γ(1/Α)(dA/dr) = 2γ(1/r).
(3)
The pressure inside a droplet being in equilibrium with its surrounding, immiscible fluid is larger than the pressure p outside exactly by the value of pγ. Importantly, for an arbitrary surface, the two principal radii of curvature may be pointing in opposite directions and then the Laplace pressure will be given by the difference of their magnitudes and oriented into the direction of the smaller radii of curvature – into the direction in which the interface is more concave (Fig. 2). This is why a cylindrical morphology of an immiscible fluid is unstable. Any infinitesimal undulation of the axial profile of the cylinder can be
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Figure 3. The Rayleigh–Plateau instability. A cylindrical morphology of an immiscible fluid is unstable: even the smallest undulation of the radius of the cylinder amplifies because the radial curvature at the point at which the radius is smaller than the average radius is larger than at the point in which the radius is larger than average. The resulting Laplace pressure drives the fluid out from the collapsing neck and the cylinder breaks up into droplets. The photograph on the right illustrates a jet of water breaking up into droplets in air.
decomposed – via a series expansion – into sinusoidal perturbations, and all of these perturbations characterized by a length larger than a certain critical value spontaneously amplify (Fig. 3) and the cylinder breaks into droplets. The speed of this spontaneous break-up can be estimated from dimensional analysis. When the viscous terms dominate the dynamics, the surface of the cylinder will be imploding with a speed that can be approximated as u = γ/μ, where μ is the viscosity of the fluid. The Rayleigh–Plateau instability underlies most of the common techniques of emulsification and atomization: it is enough to deform the immiscible fluid into elongated morphologies, and this deformation triggers the onset of the Rayleigh Plateau instability. There are several ways of deforming the immiscible fluids. For example, in a fountain the liquid (water) is ejected from a nozzle at a large speed. The inertia of water is much larger than the interfacial forces that act to minimize the interfacial area of the out-flowing water and an elongated jet can be readily formed. This jet subsequently undergoes the instability and breaks into small droplets. Similarly, a jet can be pulled from a reservoir of liquid by gravity (e.g. in a dripping faucet). In industry, the most common way of emulsification is shearing: a high magnitude shear stress is applied to a blend of two immiscible fluids, or a suspension of large droplets, and these droplets are elongated in the shear field into unstable, elongated shapes that subsequently break into smaller
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droplets. The interplay between the viscous shear forces and the interfacial forces is reflected by the value of the non-dimensional capillary number: Ca = μu/γ.
(4)
The mean size of the droplets formed by shearing can be approximated by equating an estimated shear stress τ in the system, given by the characteristic speed divided by the characteristic length L over which the liquid is sheared (e.g. the radius of the container): τ ~ μu/L, with an estimated interfacial restoring pressure pγ ~ γ/r. The radius r of the tightest curvature that can be created with shear τ can be then estimated from τ = pγ , which yields: r ≈ L(γ /μu) = LCa– 1.
(5)
Since the average diameter of the droplets formed via the Rayleigh–Plateau instability of a liquid cylinder is proportional (and similar) to the diameter of the unstable cylinder, r ∝ Ca– 1 also gives an estimate of the radii of the droplets formed by shearing. Importantly, in practically all common techniques of formation of drops and bubbles, the liquids are deformed geometrically with the use of a force of choice, and then they spontaneously break into smaller bits by the action of the interfacial tension. As we will discuss it below, emulsification in microfluidic devices constitutes a very different route to emulsification. 3. Microfluidic Emulsification One of the features that are particular to microfluidics – as opposed to other experiments on viscous flows or flows dominated by interfacial effects – is the physical confinement of the flow by the walls of the microchannels. As we describe below, this feature plays an important role in the processes of formation of bubbles and droplets. Although there are numerous variants and detailed technical solutions, the two most commonly used geometries for formation of bubbles and droplets on microfluidic chips are very simple: a T-junction and a flow-focusing geometry. The T-junction was introduced by Thorsen et al. [9] and comprises a main channel carrying the continuous fluid and a side channel that delivers the fluid-to-be-dispersed (Fig. 4). The flow-focusing geometry was first demonstrated in the work by A. GananCalvo on axisymmetric systems operating at higher Reynolds, capillary and Weber numbers. As shown early in 2003 by S. Anna and collaborators [12], this concept proved to be applicable also to the planar geometries of standard microfluidic chips.
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Figure 4. The T-junction [9] (Adapted from Ref. [13]). An axisymmetric flow-focusing geometry [10] (Adapted from Ref. [14]). A planar flow-focusing device [12] (Adapted from Ref. [15]).
3.1. FORMATION OF BUBBLES AND DROPLETS IN A PLANAR FLOW-FOCUSING GEOMETRY
Qualitatively, the operation of the microfluidic flow-focusing system can be described in the following way. Two immiscible phases (e.g. Nitrogen and water, or water and oil) are delivered via their inlet channels to the flowfocusing junction. In this junction, one central inlet channel, that delivers the fluid-to-be-dispersed (e.g. Nitrogen to be dispersed into bubbles) ends upstream of a small constriction (an orifice). From the sides of the central channel, two additional ones terminate upstream of the orifice. These side channels deliver the continuous fluid (e.g. aqueous solution of surfactant). It is important that these continuous phase wets the walls of the microfluidic device preferentially. Otherwise – if the fluid-to-be-dispersed – wets the walls, the resulting flows are erratic [16] and it becomes virtually impossible to form bubbles (droplets) in a reproducible and controllable process. The fluids are delivered to the chip with constant input conditions – either a fixed rate of flow or a fixed pressure applied to the inlet. Regardless of the choice of the boundary conditions [17] (fixed rate of flow or fixed pressure) a pressure gradient develops along the central axis of the flow focusing device and this pressure drop drives the two immiscible fluids through the constriction: the tip of the inner phase enters the orifice and starts to inflate a bubble (or fill a droplet) growing upstream of the orifice. At the same time, in the orifice, a neck develops on the inner stream and it begins to thin, breaks, releases a bubble (droplet) and retracts upstream to its original position. The range of pressures (rates of flow) applied to the inlets for which such a simple, periodic dynamics is observed depends on the particular system, and e.g. coupling between the dynamics of flow in the orifice and the flow in the outlet channel [18–20] yet it is typical for microfluidic system, that this simple mode of operation can be obtained and
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sustained in a stable operation. Also, typically the bubbles and droplets produced in this mode of operation are tightly monodisperse with the standard deviation of their diameter well below of 5% of the mean value.
Figure 5. The simple periodic mode of a flow-focusing device illustrated on five micrographs taken during the period of formation of a single bubble in this microfluidic flow-focusing device [15].
In our experiments [15] on using the microfluidic flow-focusing geometry for formation of monodisperse bubbles of Nitrogen in a continuous liquid of aqueous solutions of surfactant and glycerin we found that the volume of the bubbles (V ) depended on the pressure ( p) applied to the stream of gas, the rate of flow (Q) of the continuous liquid and its viscosity ( μ) (Fig. 5): V ∝ p/Qμ
(6)
In addition we noticed that the frequency ( f ) of formation of the bubbles was proportional to the product of Q and p: f ∝ pQ.
(7)
Interestingly, the volume of the bubbles depends on the ratio of p and Q, while the frequency of their formation on the product of the two values. This interdependence of V and f on p and Q is equivalent to a transformation of variables: (p, Q) → (V, f )
(8)
which allows for a simultaneous and independent tuning of the volume of individual bubbles and volume fraction of the gaseous phase in the resulting foam. As such, the microfluidic flow-focusing device is a perfect foammaker, as all the important parameters of a monodisperse foam can be controlled independently and in parallel.
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W liquid Wm
gas liquid
Zm
Z
500 µm 100 µm
t = 0 µs
230 µs
320 µs
400 µs
470 µs
Figure 6. Experiments on time-resolved tracking of the shape of the gas–liquid interface during the process of formation of a single bubble in a microfluidic flow-focusing device. From a video recording of the process of break-up, we extract the projection of the interface on the x–y plane (plane of the microfluidic device). We then extract the minimum width of the neck as a function of time (Adapted from Ref. [21]).
Quite surprisingly, alternation of the interfacial tension (γ) did not introduce significant changes in V. This observation is curious because (i) the proportionality between the volume of the bubble and a term (Qμ)−1 suggests a dependence on the capillary number, similar to that observed in classical shearing, (ii) the values of the capillary number for the experiment lay in the range of 10–3 to 10–1, suggesting that interfacial tension should dominate over the shear stresses or at least play an important role in the process of formation of bubbles. In order to understand the process of break-up with recorded high-speed videos (Fig. 6) of the profile of the gaseous tip during the process of formation of a bubble, for a wide range of values of p, Q, μ and γ. Analysis of these videos allowed us to determine the width (w) of the collapsing neck as a function of time and the speed of collapse ucollapse = dw/dt. We observed that this speed depends only on the value of the rate of flow of the continuous phase and is linearly proportional to Q. Second important observation is that the values of the speed of collapse that we recorded in our experiments were significantly smaller than the value of the capillary speed (γ/μ) which for our experiments should range between 10 and 100 m/s, while ucollapse lay in the range of 10–3 to 1 m/s.
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1 80
6
40
W
4
20
κ
2
0 −1
− 0.8 −0.6 − 0.4 − 0.2 t [ms]
0
0
dw/dt [m/s]
w [μm]
dw/dt
κ [1/mm]
60
8
0.92 mPas, 28.7 mN/m 6.1 mPas, 28.7 mN/m 10.84 mPas, 28.7 mN/m 0.92 mPas, 72 mN/m
0.1
0.01
0.001 0.01
0.1
q [ul/s]
1
10
Figure 7. Left chart shows the evolution of the width of the collapsing neck (w) as a function of time within the process of formation of a single bubble. The graph on the right shows the speeds of collapse (the slopes of the linear decay of w) as a function of the rate of flow of the continuous fluid for a range of parameters (p, μ, γ) (Adapted from Ref. [21]).
These observations suggest that the collapse of the gaseous thread – and the break-up of the stream of gas into bubbles – cannot be driven by interfacial stresses, as is the case in conventional emulsification techniques. The process of break-up can be qualitatively understood when one notices that the shape of the gaseous thread in the orifice is actually stable against the action of interfacial stresses (that is against a Rayleigh–Plateau type of an instability). This supposition was confirmed via numerical simulation of a catenoid-shaped membrane spun on two rectangular rims: one corresponding to the end of the inlet channel for gas, and the second to the terminus of the orifice. In addition, these simulations allowed for determination of the width of the neck of this membrane as a function of the volume (Vthread) enclosed inside the membrane, or – alternatively – of the remaining volume of the orifice and the inlet channels for the continuous fluid, outside of the membrane. The dependence of w on Vthread (Fig. 8) looks qualitatively similar to the dependencies of w on time recorded in our experiments (Fig. 7). The experimental traces of w(t) can be translated into w(V0 − Vthread) by multiplying time (t) by the rate of inflow of the continuous phase (Q). This construct allows for a quantitative comparison of the kinetics of break-up (collapse of the neck of the gaseous thread) recorded experimentally with the quasistatic evolution of the interface that traverses shapes that minimize their interfacial area for a given boundary condition (Vthread). This comparison yields an almost perfect agreement (Fig. 8) between experiment and the quasistatic evolution, for a wide range of the pressures, rates of flow, viscosities and interfacial tensions.
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Figure 8. Quasistatic break-up. The chart on the left shows the width of the neck of simulated catenoid-like interfaces as a function of the volume that is enclosed inside them. The plot on the right shows a quantitative comparison of the simulated – quasistatic – process with the experimental data for a range of parameters (Q, p, μ, γ) (Adapted from Ref. [21]).
The above observations can be explained as follows. Once the tip of the gaseous phase enters the orifice, it fills almost the entire cross-section of this microchannel. This is because the value of the capillary number is low: the interfacial forces dominate the shear stress, the tip assumes a compact, and area-minimizing shape, and restricts the flow of the continuous liquid to thin films between the interface and the walls of the orifice. As the flow in thin films is subject to an increased viscous dissipation (and resistance) the liquid inflowing from the inlet channels cannot pass through the orifice. Instead, the pressure upstream of the orifice rises and the liquid squeezes the neck of the stream of gas. As the rate of inflow of the continuous liquid is externally fixed to a constant value, this squeezing proceeds at a rate that is strictly proportional to Q and independent of all the other parameters (pressure, viscosity of the liquid, the value of interfacial tension). This model has been confirmed in detailed experiments by Marmottant et al. [22]. The quasistatic model of formation of bubbles explains the observed monodispersity of the bubbles: because the speed of collapse is much smaller than the capillary speeds and the speed of sound in the liquid, any perturbations in flow, pressure, or shape of the interface are equilibrated on timescales much shorter than the interval needed for formation of a single bubble.
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Figure 9. Formation of droplets in microfluidic flow-focusing devices. The micrographs on the left illustrate the process of formation of aqueous drops in an organic continuous fluid [S. Makulska, P. Garstecki, Institute of Physical Chemistry PAS]. The chart on the right shows the dependence of the volume of liquid droplets formed in a planar flow focusing device on the value of the capillary number (Adapted from Ref. [24]).
The quasistatic model of break-up can be extended also to the liquid– liquid systems. In the case of formation of droplets in microfluidic flowfocusing devices the situation is more complicated, because the viscosities of both of the liquids play a role in the process, and the shear stresses can be transferred between them (Fig. 9). Further, the quasistatic model will work only in the regimes in which the capillary speed is larger than the characteristic time for break up which is related to the time needed for filling the volume of the orifice with the continuous fluid. Nie et al. [23] and Lee et al. [24] reported detailed experiments on formation of droplets in planar microfluidic flow-focusing chips and identified distinct regimes of squeezing (the quasistatic mode), dripping, and jetting. Importantly, in the squeezing mode, the break-up obeys the quasistatic model with only a slight dependence of the diameter of the droplets on the value of the capillary number [24]. 3.2. FORMATION OF BUBBLES AND DROPLETS IN A T-JUNCTION
The T-junction, depicted in Fig. 4, is one of the most common geometries used in microfluidic chips to create discrete segments of immiscible fluids. The design of the apparatus is extremely simple – a main, straight channel, that carries the continuous fluid is joined from the side, usually at a right angle, by a channel that supplies the fluid-to-be-dispersed. The operation of the T-junction depends on the values of the speeds of flow of the two phases that can be parameterized by the value of the capillary number (Fig. 10). At low values of the capillary number (typically Ca < 10–2) formation of droplets obeys the squeezing model, that we will
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describe shortly below, at intermediate values of Ca the device operates in the dripping mode in which the viscous effects become noticeable, and finally, at highest rates of flow, the system develops a long jet from which droplets are sheared off.
Figure 10. Regimes of formation of droplets in microfluidic T-junction: squeezing at low values of the capillary numbers, dripping (with slight dependence of the volume of the droplets on the value of the Ca) for intermediate values of the capillary number, and jetting at high values of Ca (Adapted from Ref. [25]).
In the first demonstration of formation of monodisperse droplets in a microfluidic T-junction [9], on the basis of the experimental results on scaling of the droplet size with the rate of flow of the continuous fluid, it was hypothesized that the droplets are sheared off from the junction by the flow of the continuous fluid, similarly to the classical models of sheardriven emulsification. However, the fact that the break-up occurs in a confined geometry of the microchannels, and that the droplet growing off the inlet of the fluid-to-be-dispersed usually occupies a significant fraction of the cross-section of the main channel, suggest that the pressure drop along a growing droplet may be an important factor in the process. Garstecki et al. conducted careful experiments [13] in which they varied (i) the geometry of the device, (ii) the rates of flow of the two fluids, (iii) the viscosity of the continuous fluid and (iv) the value of the interfacial tension. These experimental results verified that at low values of the Capillary number – which are typical to those typical for flows in microsystems – indeed the mechanism of break-up is similar to that observed in the flowfocusing system. Namely, as the tip of the dispersed phase enters the main channel, and fills its cross-section, the hydraulic resistance to flow in the thin films between the interface and the walls of the obstructed microchannel creates an additional pressure drop along the growing droplet. This pressure drop has a primary influence on the dynamics of break-up: namely, once the main channel is obstructed by the growing droplet, the upstream interface of
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the droplet is pushed downstream by the continuous fluid at its – externally fixed – rate of flow. Once this interface is pushed against the downstream wall of the channel that delivers the fluid-to-be-dispersed to the junction, the neck connecting the stream of this fluid with the droplet breaks and the droplet is released. ~W
Vc
μc
μd
Vd
ε ~W/2 ~W W
Figure 11. Forces acting on the droplet growing in a T-junction. As the droplet fills the cross-section of the main channel, it is separated from the wall of the main channel by thin films of the continuous fluid, with the thickness of the film separating it from the wall that is opposite to the inlet for the dispersed phase marked as ε. The blue arrow symbolizes the interfacial forces that stabilize the droplet against breaking off from the junction. The green arrow indicates the shear stress that acts to break the droplet off, and scales as ε−n with n < 2. Finally, the black arrow denotes the pressure drop along the droplet, that scales as ε−m with m > 2 (The left panel adapted from DeMenech et al. [25]).
Within this simple model the volume of the droplet is determined only by the rates of flow of the two immiscible fluids and not by their material parameters (viscosities and interfacial tension between them). For the simplest geometry of the T-junction with the widths (w) of the main and side channels equal to their common height, the volume of the droplet is approximately equal to the initial volume of the droplet that blocks the channel (~w3) plus the volume of the to-be-dispersed fluid that flows into the droplet while it is squeezed. This last volume is equal to the rate of flow of the inner (droplet) phase (Qin) multiplied by the time that it takes to squeeze the collapsing neck of the inner phase by the outer fluid: tsqueeze ~ w3/Qout. Combining these two terms and normalizing by w3 yields an equation for normalized length of the droplet (Fig. 11): L/w = 1 + αQin/Qout.
(9)
The above equation correctly approximates the volumes of the droplets at low values of the Capillary numbers for a range of geometries of the Tjunctions, with the exact value of the constant α of order one depending on the aspect ratios of the widths and height of the microchannels forming the T-junction device.
FORMATION OF DROPLETS IN MICROFLUIDIC SYSTEMS 100
1
slope
= −1/5
slo pe =
10
10m Pas, 0.028 mL/s 10m Pas, 0.28 mL/s 100m Pas, 0.0028 mL/s 100m Pas, 0.028 mL/s 10 0m Pas, 0.028 mL/s
177
Vd
L/W
−1
1 1
1
λ=1 λ = 1/8
squeezing 0.1 0.01
0.1
1
Qwater /Qoil
squeezing 10
0.001
0.01 Ca
dripping 0.1
Figure 12. The graph on the left shows the dependence of the volume of the droplets (here length of the droplets) on the value of the ratio of the volumetric rates of flow of the inner and outer immiscible phases. The fact that series recorded for varied speed of flow, viscosity and interfacial tension overlay on each other confirm the validity of the squeezing model of break-up for low values of the capillary number (Adapted from Ref. [13]). The chart on the right shows the variation of the volume of the droplets with an increasing value of the capillary number, illustrating the transition from squeezing to dripping at Ca ~ 10–2 (Adapted from Ref. [25]).
As can be noticed in the right-hand side plot in Fig. 12, in both the squeezing and the dripping regimes, the shearing effects do play a role. In the squeezing regime these effects are secondary and the squeezing model approximates the volume of the droplets well. In the dripping regime, both the shear stress exerted by the continuous fluid on the growing droplet and the pressure drop along the growing droplet are important and both in simulations [25] and experiment [26] the scaling of the volume of the droplet exhibits a significant dependence on the value of the Capillary number. We refer the interested reader to the recent publications [25, 26] that detail the concepts, observations and understanding of formation of bubbles and droplets in microfluidic T-junctions. 3.3. SUMMARY
The mechanisms of formation of discrete segments of fluids in microfluidic flow-focusing and T-junction devices, that we outlined above point to (i) strong effects of confinement by the walls of the microchannels, (ii) importance of the evolution of the pressure field during the process of formation of a droplet (bubble), (iii) quasistatic character of the collapse of the streams of the fluid-tobe-dispersed, and (iv) separation of time scales between the slow evolution of the interface during break-up and fast equilibration of the shape of the interface via capillary waves and of the pressure field in the fluids via acoustic waves. These features form the basis of the observed – almost perfect – monodispersity of the droplets and bubbles formed in microfluidic systems at low values of the capillary number.
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3.4. EXTENSION OF THE TECHNIQUES OF FORMATION OF DROLETS
The control that can be exerted over the flow of immiscible fluids in microfluidic devices to formation of monodisperse droplets and bubbles can be extended to formation of more complicated objects and architectures of the droplets, such as multiple emulsions [27–32], Janus particles [33, 34] and other morphologies of liquid droplets, solidified particles and capsules [35– 39]. Figure 13 presents micrographs of the droplets, particles and capsules produced in exemplary techniques.
Figure 13. (a–c) Examples of multiple emulsions formed in microfluidic systems. (a) Adapted from Okushima et al. [29]. (b) Adapted from Seo et al. [30]. (c) Adapted from Utada et al. [31]. (d) ‘Composite emulsion’ formed by droplets of different composition and different volume formed in situ in a microfluidic device comprising three flow-focusing geometries integrated into one outlet channel (Adapted from Hashimoto et al. [40]). (e) Examples of anisotropic particles formed by either polymerization (spheres and disks, rods) of droplets of monomer or thermal setting of droplets of metal (ellipsoids) in situ in a microfluidic device (Adapted from Xu et al. [35]). (f) A micrograph of a nylon capsule polymerized in situ in a microfluidic device, with an aqueous core containing magnetic particles [39].
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4. Conclusions Microfluidic systems offer techniques for- and extensive control over-the processes of formation of bubbles, droplets, compound droplets, particles and capsules. Understanding of these processes form the basis for applications in on-chip systems for analytical an synthetic chemistry and in preparatory technologies.
References 1. H.A. Stone, A.D. Stroock, and A. Ajdari, Engineering flows in small devices: Microfluidics toward a lab-on-a-chip, Annual Review of Fluid Mechanics, 36, 381–411, (2004). 2. N.L. Jeon, S.K.W. Dertinger, D.T. Chiu, I.S. Choi, A.D. Stroock, and G.M. Whitesides, Generation of solution and surface gradients using microfluidic systems, Langmuir, 16, 8311–8316, (2000). 3. E.M. Lucchetta, J.H. Lee, L.A. Fu, N.H. Patel, and R.F. Ismagilov, Dynamics of Drosophila embryonic patterning network perturbed in space and time using microfluidics, Nature, 434, 1134–1138, (2005). 4. G.M. Whitesides, The origins and the future of microfluidics, Nature, 442, 368–373, (2006). 5. D.J. Harrison, F. K., K. Seiler, Z. Fan, C.S. Effenhauser, and A. Manz, Micromachining a Miniaturized Capillary Electrophoresis Based Chemical Analysis System on a Chip, Science, 261, 895–897, (1993). 6. D. Erickson and D.Q. Li, Integrated microfluidic devices, Analytica Chimica Acta, 507, 11–26, (2004). 7. D.C. Duffy, J.C. McDonald, O.J.A. Schueller, and G.M. Whitesides, Rapid prototyping of microfluidic systems in poly(dimethylsiloxane), Analytical Chemistry, 70, 4974–4984, (1998). 8. T. Thorsen, S.J. Maerkl, and S.R. Quake, Microfluidic large-scale integration, Science, 298, 580–584, (2002). 9. T. Thorsen, R.W. Roberts, F.H. Arnold, and S.R. Quake, Dynamic pattern formation in a vesicle-generating microfluidic device, Physical Review Letters, 86, 4163–4166, (2001). 10. A.M. Ganan-Calvo, Generation of steady liquid microthreads and micronsized monodisperse sprays in gas streams, Physical Review Letters, 80, 285– 288, (1998). 11. P.J.A. Kenis, R.F. Ismagilov, and G.M. Whitesides, Microfabrication inside capillaries using multiphase laminar flow patterning, Science, 285, 83–85, (1999). 12. S.L. Anna, N. Bontoux, and H.A. Stone, Formation of dispersions using “flow focusing” in microchannels, Applied Physics Letters, 82, 364–366, (2003). 13. P. Garstecki, M.J. Fuerstman, H.A. Stone, and G.M. Whitesides, Formation of droplets and bubbles in a microfluidic T-junction – scaling and mechanism of break-up, Lab on a Chip, 6, 437–446, (2006).
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14. P. Garstecki, A.M. Ganan-Calvo, and G.M. Whitesides, Formation of bubbles and droplets in microfluidic systems, Bulletin of the Polish Academy of Sciences, 53, 361–372, (2005). 15. P. Garstecki, I. Gitlin, W. DiLuzio, G.M. Whitesides, E. Kumacheva, and H.A. Stone, Formation of monodisperse bubbles in a microfluidic flowfocusing device, Applied Physics Letters, 85, 2649–2651, (2004). 16. R. Dreyfus, P. Tabeling, and H. Willaime, Ordered and disordered patterns in two-phase flows in microchannels, Physical Review Letters, 90, (2003). 17. T. Ward, M. Faivre, M. Abkarian, and H.A. Stone, Microfluidic flow focusing: Drop size and scaling in pressure versus flow-rate-driven pumping, Electrophoresis, 26, 3716–3724, (2005). 18. J.P. Raven and P. Marmottant, Periodic microfluidic bubbling oscillator: Insight into the stability of two-phase microflows, Physical Review Letters, 97, (2006). 19. J.P. Raven and P. Marmottant, Microfluidic Crystals: Dynamic Interplay between Rearrangement Waves and Flow, Physical Review Letters, 102, (2009). 20. M.T. Sullivan and H.A. Stone, The role of feedback in microfluidic flowfocusing devices, Philosophical Transactions of the Royal Society a-Mathematical Physical and Engineering Sciences, 366, 2131–2143, (2008). 21. P. Garstecki, H.A. Stone, and G.M. Whitesides, Mechanism for flow-rate controlled breakup in confined geometries: A route to monodisperse emulsions, Physical Review Letters, 94, (2005). 22. B. Dollet, W. van Hoeve, J.P. Raven, P. Marmottant, and M. Versluis, Role of the channel geometry on the bubble pinch-off in flow-focusing devices, Physical Review Letters, 100, (2008). 23. Z.H. Nie, M.S. Seo, S.Q. Xu, P.C. Lewis, M. Mok, E. Kumacheva, G.M. Whitesides, P. Garstecki, and H.A. Stone, Emulsification in a microfluidic flow-focusing device: effect of the viscosities of the liquids, Microfluidics and Nanofluidics, 5, 585–594, (2008). 24. W. Lee, L.M. Walker, and S.L. Anna, Role of geometry and fluid properties in droplet and thread formation processes in planar flow focusing, Physics of Fluids, 21, (2009). 25. M. De Menech, P. Garstecki, F. Jousse, and H.A. Stone, Transition from squeezing to dripping in a microfluidic T-shaped junction, Journal of Fluid Mechanics, 595, 141–161, (2008). 26. G.F. Christopher, N.N. Noharuddin, J.A. Taylor, and S.L. Anna, Experimental observations of the squeezing-to-dripping transition in T-shaped microfluidic junctions, Physical Review E, 78, (2008). 27. T. Nisisako, Microstructured devices for preparing controlled multiple emulsions, Chemical Engineering & Technology, 31, 1091–1098, (2008). 28. T. Nisisako, S. Okushima, and T. Torii, Controlled formulation of monodisperse double emulsions in a multiple-phase microfluidic system, Soft Matter, 1, 23–27, (2005). 29. S. Okushima, T. Nisisako, T. Torii, and T. Higuchi, Controlled production of monodisperse double emulsions by two-step droplet breakup in microfluidic devices, Langmuir, 20, 9905–9908, (2004). 30. M. Seo, C. Paquet, Z.H. Nie, S.Q. Xu, and E. Kumacheva, Microfluidic consecutive flow-focusing droplet generators, Soft Matter, 3, 986–992, (2007).
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31. R.K. Shah, H.C. Shum, A.C. Rowat, D. Lee, J.J. Agresti, A.S. Utada, L.Y. Chu, J.W. Kim, A. Fernandez-Nieves, C.J. Martinez, and D.A. Weitz, Designer emulsions using microfluidics, Materials Today, 11, 18–27, (2008). 32. A.S. Utada, E. Lorenceau, D.R. Link, P.D. Kaplan, H.A. Stone, and D.A. Weitz, Monodisperse double emulsions generated from a microcapillary device, Science, 308, 537–541, (2005). 33. T. Nisisako and T. Torii, Formation of biphasic Janus droplets in a microfabricated channel for the synthesis of shape-controlled polymer microparticles, Advanced Materials, 19, 1489–+, (2007). 34. T. Nisisako, T. Torii, T. Takahashi, and Y. Takizawa, Synthesis of monodisperse bicolored janus particles with electrical anisotropy using a microfluidic coflow system, Advanced Materials, 18, 1152–+, (2006). 35. S.Q. Xu, Z.H. Nie, M. Seo, P. Lewis, E. Kumacheva, H.A. Stone, P. Garstecki, D.B. Weibel, I. Gitlin, and G.M. Whitesides, Generation of monodisperse particles by using microfluidics: Control over size, shape, and composition, Angewandte Chemie-International Edition, 44, 724–728, (2005). 36. D. Dendukuri, S.S. Gu, D.C. Pregibon, T.A. Hatton, and P.S. Doyle, Stop-flow lithography in a microfluidic device, Lab on a Chip, 7, 818–828, (2007). 37. D.K. Hwang, D. Dendukuri, and P.S. Doyle, Microfluidic-based synthesis of non-spherical magnetic hydrogel microparticles, Lab on a Chip, 8, 1640–1647, (2008). 38. R.F. Shepherd, P. Panda, Z. Bao, K.H. Sandhage, T.A. Hatton, J.A. Lewis, and P.S. Doyle, Stop-Flow Lithography of Colloidal, Glass, and Silicon Microcomponents, Advanced Materials, 20, 4734–+, (2008). 39. S. Takeuchi, P. Garstecki, D.B. Weibel, and G.M. Whitesides, An axisymmetric flow-focusing microfluidic device, Advanced Materials, 17, 1067–+, (2005). 40. M. Hashimoto, P. Garstecki, and G.M. Whitesides, Synthesis of composite emulsions and complex foams with the use of microfluidic flow-focusing devices, Small, 3, 1792–1802, (2007).
TRANSPORT OF DROPLETS IN MICROFLUIDIC SYSTEMS P. GARSTECKI
Department of Soft Condensed Matter, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland,
[email protected]
Abstract. Microfluidics provides for a convenient playground for experiments on dynamic systems. Two phase microfluidic systems present a new class of behaviors that are both complex and stable. The dynamics of flow of droplets through micro-networks are one of such examples: they are complicated because there are long-range interactions between the droplets that modify the pressure distribution in the channels, at the same time the resulting complicated dynamics are robust against experimental disturbances. Flow of droplets through microfluidic networks provide a route to nontrivial and reversible operations on streams of bubbles, logic operations on droplets. This lecture will introduce the rudimentary physics of Stokes flow in a simple pipe, the recent experiments and simulations on the flow of droplets and bubbles through microfluidic networks, and the vision of complex and automated microfluidic chips that perform combinatorial operations on miniaturized chemical reaction beakers – droplets.
1. Introduction 1.1. DROPLET MICROFLUIDICS
Droplet microfluidics is a science and technology of controlled formation of droplets and bubbles in microfluidic channels. The first demonstration of formation of monodisperse aqueous droplets on chip – in a microfluidic T-junction [1] – was reported in 2001. Since then, a number of studies extended the range of techniques, from the T-junction [2–5], to flowfocusing [6–10] and other geometries [11], and the capabilities in the range of diameters of droplets and their architectures [12–16]. These techniques opened attractive vistas to applications in preparatory techniques [17–19], and – what is the focus of this lecture – analytical techniques based on performing reactions inside micro-droplets.
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1.2. FORMATION OF DROPS AT CONSTANT FORCING
The usual way of feeding the microfluidic systems with fluids is to apply either a constant rate of inflow into the chip, or a constant pressure at the inlet [20]. Formation of droplets or bubbles in systems with such, fixed, boundary conditions for flow is realtively well understood. Two microfluidic geometries are most commonly used: a microfluidic T-junction [1] or a microfluidic flow-focusing geometry [6]. After the introduction of the T-junction by Thorsen et al. [1] the details of the mechanism of operation of this system were studied experimentally by Garstecki et al. [3], Colin et al. [5], numerically by De Menech [21]. Recently, a thorough experimental study by Christopher et al. [4] characterized the relevant regimes of formation of droplets in detail and provided accurate analytical models for the scaling of the droplet volume. The flow focusing geometry was first introduced in an axi-symmetric system by Ganan-Calvo [22]. Later, the same concept was succesfully used in a – typical to current microfluidic techniques – planar chip by Anna et al. [6]. The mechanism of formation of bubbles in this planar system was characterized by Garstecki et al. [8] and Marmottant [9]. Later, Kumacheva et al. [23] and Anna et al. [10] extended this characterization to liquid– liquid systems and formation of droplets in continuous liquids at different viscosities of the two immiscible liquids, interfacial tension and geometries of the devices. 1.3. CHEMISTRY IN DROPLETS
The development of techniques and understanding of the processes of formation of monodisperse microdroplets constituted the fundaments for the vision of performing chemical and biochemical reactions inside these nanoand micro-liter liquid segments. Orignially, the interest in the use of microdroplets as reaction chambers stemmed from the opportunity to minimize the volume of liquid samples and – at the same time – obtain multiple measurements from identical, or continuously varied [24] compositions. The feature that the droplets can be practically formed at frequencies of hundreds or thousands droplets per second provides for reliable statistics. Within few years of the first demonstrations [25] it became realized, that performing reactions within droplets offer additional, highly attractive features [26]. These include, for example, the avoidance of dispersion of time of residence in the channels, that is inherent to pressure driven flow-through reaction chambers. This quality stems from the fact that the reaction mixture is enclosed, and constantly stirred [27], within the droplet. Second, the droplet systems provide for convenient and rapid mixing [27] that is otherwise one of the hallmark problems in single fluid microfluidcs. Further, the microfluidic
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droplet systems – via the simple correspondance between the time and position of the droplet flowing in a microchannel – offer for convenient temporal resolution and for control of the kinetic conditions of reactions [28]. 1.4. VISION OF INTEGRATED SYSTEMS
The numerous demonstrations of chemical and biochemical reactions performed in droplets on microfluidic chips [26] has inspired a more challenging vision of the development of automated microfluidic chips having the functionality of a macro-scale, conventional, chemical or biochemical laboratory. Within this vision, the systems should be able to perform reactions within the micro-droplets (i) fast, (ii) on small samples of reagents, and (iii) with reliable statistics of the results. At the same time, these systems need to be capable of performing complicated protocols (with varied temperature, exposition to light, titrations, controlled additions at desired times, separations, etc.) on droplets with on-demand formulated chemical compositions – reaction mixtures of arbitrary concentrations of a large number of reagents. To date, and for reasons that we explain below, the current capabilities fall short of this outstanding vision because they lack the versatility e.g. the commercial well-plate technology. 1.5. OPEN CHALLANGES
Extending the current capabilities of microfluidic droplet based systems for applications in chemistry certainly requires construction of the systems of complicated networks of microchannels, controlled introduction of droplets into these networks, controlled guiding of these droplets, sorting, merging, splitting etc. These requirements open questions and challenges in (i) understanding of the dynamics of transport of droplets through networks of microchannels, and (ii) construction of tools for computer controlled formation and guiding of droplets. As we discuss in more detail below, the flow of droplets through networks of microchannels provides for fascinating but also complex set of phenomena. These complicacies arise from the fact that a droplet (or bubble) traveling in a microchannel increases the hydraulic resistance to flow in that channel, and this – in turn – affects the distribution of pressure in the system, which has an effect on the trajectories of the subsequent droplets. Recent experiments [11, 29] have demonstrated that these properties of flow of droplets in networks can be used to demonstrate intricate processing of signals encoded in sequences of droplets (or intervals between droplets). For example, Fuerstman et al. [30] demonstrated ciphering and deciphering of signals in an all-fluidic microsystem. Prakash and Gershenfeld [31] showed logic operations performed by droplets traveling in appropriately designed microfluidic
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networks. These results, with the observation that the – even very intricate or complex – dynamics of multiphase flows in microchannels is robust to random disturbances or noise [30, 32] suggest that it should be possible to design and operate automated chips performing non trivial operations (e.g. merging, splitting, distributing in the network) on the micro reaction vessels (droplets). Performing thousands of different reactions on a single chip will certainly require computer controlled execution of the pre-encoded protocols. This execution necessitates the development of computer controlled modules for sorting (guiding) droplets and – above all – for introducing droplets of predesigned volumes at scheduled times of emission – a technique often called ‘droplet on demand’. In the last part of this lecture we will review also this subject. 1.6. THE PLAN OF THE LECTURE
We first introduce the basic concepts in physics of flow of simple and multiphase fluid in networks of microchannels. We then go on to demonstrate the phenomenology of the flow of droplets through the simplest network – a single loop of channels – and then provide examples of experiments on more complicated systems. The third part of the lecture introduces the subject of modeling of the dynamics of flow of units of resistance through networks of conductors, and show the results of these efforts and their correspondence to microfluidic flows. Finally, we provide an introduction to the subject of automation of flows of droplets in microchannels and demonstrate an example of the droplet-on-demand system constructed in our laboratory. 2. Flow of Simple and Multiphase Fluids Through Networks 2.1. SIMPLE FLUID IN A NETWORK OF MICROCHANNELS
One of the more beautiful techniques in fluid mechanics is the dimensional analysis, that provides – via simple calculations – a reliable judgment of the relative importance of the various forces that can drive or retard the flow of fluids. In short the procedure rests on construction of non-dimensional groups of parameters that constitute the so-called non-dimensional numbers. The most important non-dimensional number in fluid mechanics is the Reynolds number that judges the relative importance of the inertial and viscous effects. At low values of the Reynolds number – a situation that is common to microsystems – the Navier Stokes equation can be well approximated by the Stokes equation, that, in the absence of body forces, reads:
μΔ Δ u − ∇p = 0
(1)
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where μ is the viscosity of the fluid, u is the velocity field of the fluid, and p is the pressure field. The Stokes equation relates the speed of flow with the pressure gradient, and the relation between the two quantities is that of a simple proportionality. The resulting flow is highly regular (e.g. laminar, without turbulence), which is one of the fundaments of the control over flow of fluids at microscale. As will become important in one of the examples of droplet flow through networks of channels, the Stokes equation has also the interesting property that it is invariant with respect to the simultaneous change of the sign (orientation) of the velocity field and the gradient of pressure. A manifestation of this property is that if we allow a fluid to flow ‘forward’ for a given interval of time by application of a ‘positive’ difference of pressure between the inlet and outlet of the system, and then suddenly will change the sign of the pressure drop to the negative of the original value, the fluid will trace back its original trajectory, regardless of how complicated it were. Conveniently, when one considers the flow of simple fluids through channels, the Stokes equation – that describes the velocity field as a function of the pressure field – can be integrated to yield a very simple relation (Hagen–Poiseuille Law) between the difference (Δp) of pressures at inlet and outlet of the tube (channel) and the volumetric rate of flow (Q) of the simple fluid: Q = Δp/R,
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where L is the length of the capillary and r is its inner radius. For rectangular and other cross-sections the equation for R is more complicated, yet it can be analytically derived [33]. The Hagen–Poiseuille law is mathematically analogous to the Ohm’s Law. In addition, the conservation of mass (or flow for incompressible fluid) of fluid is analogous to the law of conservation of charge and current in electrical systems. This analogy allows for the use of Kirchoffs equations for calculation of the distribution of the volumetric flow of liquid between channels in a microfluidic network: once we know the resistances of all the channels in the network and the pressures at the inlet and outlet, we can calculate the speed of flow in any part of the network (Fig. 1).
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Figure 1. The analogy between the distribution of volumetric rate of flow of a simple fluid flowing through a network of microchannels and the Kirchoffs equations for the flow of current through a network of conductors.
2.2. FLOW OF DROPLETS AND BUBBLES THROUGH CHANNELS
In the absence of any obstacles in the channel, the simple fluid develops a parabolic profile of speed of flow: the fluid flows the fastest in the center of the channel, and rests at the walls of the capillary. When a droplet or bubble is introduced into this flow, the velocity field is modified. Because the droplet (bubble) separates the continuous liquid that is in front of it, from the liquid behind it, the parabolic profile can no longer be sustained, and close to the caps of the droplet addition recirculation of the continuous fluid is created. In addition, there is circulation of the liquid inside the droplet, and there is some flow along the droplet (or bubble) (see Fig. 2). All these effects increase the viscous dissipation in the carrier (continuous) fluid and the liquid inside a droplet. As a result, it demands a higher pressure drop along the capillary to maintain the same average speed of flow as without the bubble or droplet inside of it. Equivalently, for a constant pressure drop along the capillary the speed of flow decreases after the addition of the droplet (or bubble). This can be described by an increased resistance to flow in that capillary, or by an additional charge of resistance carried by the droplet (or bubble).
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Figure 2. The flow of a simple fluid through a microchannel develops a parabolic profile of speed of flow, that minimizes viscous dissipation for a given pressure drop Δp along the capillary. A droplet introduced into the flow modifies the flow field and increases dissipation. For a constant pressure drop this results in reduction of the volumetric rate of flow through that capillary.
The problem of characterization of the exact velocity field in the presence of a droplet in a capillary is difficult. It was first elaborated on by Taylor [34] and Bretherton [35] in 1960s. Taylor found a relation for the thickness (proportional to the capillary number Ca) of the film deposited on a capillary after passage of a semi-infinite bubble, while Bretherton proposed the scaling for the pressure drop along a finite bubble (proportional to the Ca2/3). Contemporary studies confirm the Bretherton scaling and provide numeric results for the exact resistance contributed by the droplets and bubbles [36–39]. Still, as the flow around a bubble (droplet) depends critically on a large number of parameters (volume of the immiscible segment, interfacial tension between the fluids, surface coverage with surfactant, viscosities of the two fluids, the speed of flow) a unified picture (or equations for the resistance introduced by bubbles and droplets in capillaries) is not yet available. 2.3. FLOW OF DROPLETS THROUGH A NETWORK OF CHANNELS
The fact that a droplet (or bubble) introduces additional resistance to flow in the given capillary has pronounced consequences on the dynamics of flow of discrete segments of immiscible fluids through microfluidic networks.
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Figure 3. The flow of simple fluid distributes between the two arms of the loop in inverse proportion to their hydraulic resistances. A droplet flowing in to the junction of the two arms of the loop flows into the arm that is characterized by the larger momentary rate of flow, or equivalently by the lower momentary resistance to flow. Once the droplet enters the channel it raises its hydraulic resistance and hence affects the choices (trajectories) of subsequent droplets.
As illustrated in Fig. 3, the flow of droplets through networks obeys dramatically different rules from the simple laws of distribution of flow of simple fluid between the nodes of the network. The trajectory of any given droplet depends on the positions of other droplets in the network. This coupling – or feedback – is transmitted via the pressure field and thus provides for long-range interactions. This in turn provides for the complexity of the flow. Figure 4 illustrates the experimental results on the flow of droplets through the simplest network – a single loop. At low frequencies of feeding of the droplets into the loop, only one droplet is present in the section of parallel channels at a time. This example clearly shows the nonlinearity (or binary character) of the flow of droplets. The experimental system was designed to be symmetric – i.e. the two arms of the loop have the same nominal length and cross-section. The finite resolution of the microfabrication technique [40] resulted in a small bias in resistances of the two arms. For a simple fluid, this small bias would result in an inversely proportional small bias in the rates of flow through the two arms. For droplets it results in a complete redirecting of all the droplets into one (here lower) arm of the loop. For higher frequencies of feeding a droplet arrives at the entrance to the loop while a previous one is still there. The presence of the previous droplets redirects the next one into the upper arm of the loop. At even higher frequencies more intricate temporal patterns of sequences of trajectories of the droplets can be observed.
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Figure 4. The flow of droplets through a section of two parallel microfluidic channels. (top row) a sequence of micrographs illustrating the trajectories of droplets flowing through the bottom arm of the loop. (bottom row) a sequence illustrating the effect of the presence of one droplet on the trajectory of the next one [29]. The numbers identify the droplets in order of their entry into the loop. The outlines of the channels were added in adobe illustrator.
3. Reversibility of Droplet Trains and Logic Operations on Droplets 3.1. REVERSIBILITY OF DROPLET TRAINS
The flow of droplet through the bifurcating channels can produce both periodic and irregular sequences of trajectories. This complex dynamics of flow roots in the (i) binary character of the choice of a that based on the momentary resistances of the two channels, (ii) a change of the resistance of one of the channels by a finite value of the added resistance of the droplet and (iii) long range character of the interactions between the droplets via the pressure field. All the above effects contribute to the observed complexity of the temporal patterns of the flow of droplets. On the other hand the flow of droplets proceeds at low values of the Reynolds number and is imbedded in a viscous flow that should – in principle – be described by the Stokes equation that is linear and reversible in the sense of symmetry with respect to the inversion of the orientations of the velocity of flow and of the gradient of pressure. The experiment illustrated in Fig. 5. demonstrated the highly unexpected feature of the microfluidic two-phase flow in that it combines the non-linear character of the interactions between the droplets, with the linearity of the underlying equations of flow of the carrier fluid. This combination provides for (i) the ability to construct complicated protocols of flow of droplets through microfluidic networks, and (ii) the feasibility of practical realization of such protocols thanks to their apparent robustness to random disturbances.
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Figure 5. The diagram on the left shows the trajectories of droplets first entering at uniform intervals and leaving the loop in a period 7 mode of seven different intervals, and then, after switching the direction of the pressure gradient, entering the loop at seven different intervals and leaving it at uniform intervals. The Poincare plots on the right show that the disturbances in the positions of the droplets in the channel in which they were stored did not amplify upon the reverse operation of the microfluidic loop (Adapted from Ref. [30]).
3.2. CIPHERING AND DICEPHERING SIGNALS ENCODED IN SEQUENCES OF DROPLETS
The fact that the processing of strings of bubbles can be reversed opens a possibility for a demonstration of a non-trivial operation on the information encoded into the intervals between the bubbles. Further, because the period 2
Figure 6. Left panel illustrates the symmetry of the period-2 sequence of intervals and shows corresponding Poincare maps constructed on the intervals between bubbles before, after the first loop and after the second loop. Right panel illustrates the ciphering/deciphering experiment (Adapted from Ref. [30]).
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sequences (short–long–short–long intervals) are symmetric with respect to forward/backward mirror symmetry, it is not necessary to reverse the flow: in spite it is sufficient to position a copy of the original loop downstream. Figure 6 illustrates the intervals between the bubbles entering the first loop (into these intervals a simple message is encoded), intervals after passing the first loop which amplifies small differences in intervals to an unreadable signal, and intervals after passing the second loop: a sequence that restores the original information. 3.3. LOGIC GATES
Prakash and Gershenfeld [31] demonstrated that appropriate design of the microfluidic network can provide for a range of logic operations on droplets. These operations included a demonstration of a AND–NOT, and AND–OR gate, in which the presence of a droplet coded for bit value 1, and absence of a droplet for a bit value 0. These authors constructed also a synchronizer of droplet flows, a flip-flop counter and a ring oscillator [31]. 4. Modeling of the Flow of Droplets Through Microfluidic Networks As it will be briefly described in this section, the phenomenology of droplet flows in microfluidic networks can be effectively recovered by simple numerical models [39, 41–43] that assume the generic features of the multiphase microfluidic flows. These very basic models offer an insight into the qualitative features of the dynamics. As the understanding and characterization of the flow of droplets and bubbles in capillaries, junctions, corners etc. progresses, it can be expected that the same simple models, with the appropriate numeric input will able to predict the trajectories of droplets flowing in real microfluidic networks. At the end of this section we provide an example of a quantitative match between experiment and numerical simulation. 4.1. CONSTRUCTION OF THE MODEL
Within the simplest numerical model the channels are represented as onedimensional wires and the droplets as non-dimensional points that traverse along the wires. Taking from the analogy between Hagen–Pouiseille Law and the Ohm, and Kirchoff Laws, it can be written, that if the pressure drop in a channel is Δp, the speed of flow (u) is: u =Q/A = Δp/ARtotal = Δp/A(R + nr)
(4)
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where A is a the cross-section of the channel, Rtotal is the total hydrodynamic resistance comprising the resistance of the channel (R) and the resistances introduced by the (n) droplets each carrying the same resistance r. In the simulation only the pressure drop (or flow rate) between inlet and outlet of the system is externally fixed and controlled. All the pressures and speeds of flow in the channels that comprise the network are calculated on the basis of the positions of the droplets, via the Kirchoffs laws. The flow of droplets, and in particular the acts of traversing of the droplets between the different channels in the network introduce step changes in these quantities. These occur when: (i) a new droplet enters the system, (ii) a droplet leaves the system, or (iii) a droplet traverses through an internal node. In the last case, when a droplet arrives at an internal junction, the droplet enters the channel with the largest momentary inflow (calculated before the act of the droplet entering the channel). The numerical scheme that executes the algorithm outlined above can be found in Refs. [41, 43]. 4.2. BIFURCATION DIAGRAMS AND COMBINATORIAL COMPOSITION OF PATTERNS
The numerical models provide a convenient tool for rapid scan of the dynamics of the flow of droplets over wide ranges of parameters of the system. For example, the top panels of Fig. 7 show a diagram of the intervals between droplets leaving the microfluidic loop for a large range of frequencies of feeding of the droplets into the system. One can clearly see bands of regular flows and bands of irregular (or highly complex) flow. Within the regular bands, the dynamics of the system is strictly periodic. From the numerical simulations we can extract the number of droplets in the loop for a particular regular band. A very interesting feature of this flow is that any given number (n) of droplets traversing the loop in a periodic fashion can generate a number (m) of distinct, periodic, sequence of the left/ right choices of subsequent droplets [43]. For example, eight droplets can generate ten distinct temporal patterns. Once the system settles in one of the patterns it repeats it ad infinitum. A small perturbation (an external stimulus) can switch the system to a different pattern [43].
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4.3. MODELLING AS A DESIGN TOOL
Even the simple numerical scripts that are currently used for simulation of droplet flows in microfluidic networks can provide for quantitative match with the experimental measurements (Fig. 8). The development of an ability for a quantitative prediction of the dynamics of physical systems will demand incorporation into the scripts the details characterizing the speed of flow of droplets, the resistance that they carry, the delays at junctions and corners.
Figure 8. A comparison of the positions of droplets in a loop in experiment (bottom micrographs) and in simulation (top renderings) at three different instants of time.
5. Automation The development of truly versatile chips for analytical, synthetic and biological chemistry will require not only the understanding of the flow in networks, but also the development of modules for active control over the flow, merging, splitting and above all, formation of droplets. Below we review the field of active control over formation of droplets and provide an example of a microfluidic droplet-on-demand system. 5.1. ACTIVE CONTROL OVER FLOW AT MICROSCALE
Techniques for formation of droplets on demand must provide – in contrast to the traditional techniques of formation of droplets at constant rate of flow or constant pressure – for the ability to issue the droplet at arbitrary times and with arbitrarily prescribed volume. This goal involves incorporation of a valve. It is necessary to control the flow of the fluid-to-be-dispersed: it needs to be stopped over arbitrarily long intervals and then opened with an external signal. In analogy to the classic division of hydraulic valves, there are two ways to construct a droplet on demand chip. First is to actively force the flow of fluid with external stimuli at predefined instants (that is, the fluid is ‘normally stopped’). The second way is to have the fluid
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normally flowing, and actively stopped. The valving of fluids at microscale can be done with the use of many different types of physical forces: electric (dielectrophoresis [44, 45] or a direct electrostatic force on a charged interface) [46], magnetic, capillary, electrowetting [47], Marangoni (e.g. thermocapillary flow) or mechanical (i.e. with the use of valves). For example, dielectrophoresis can be used in a system of two parallel electrodes [44]. In this system it is possible to control of generation of droplets with pulses of an alternating electric field [45]. Also electrowetting can be used to this end [47–49]. He et al. [46] demonstrated that short pulses of electrostatic potential applied along the axis of formation of water droplets in oil can generate a Taylor cone and formation of droplets via an electro-hydrodymic mechanism [50]. These droplets are typically polydisperse (3–25 μm) and it is difficult to produce individual droplets. Weitz et al. [51] demonstrated control over volumes and frequencies of formation of droplets with the use of electric field. Also thermocapillarity can be utilized to control the flow of the droplet (or bubble) phases: Baroud et al. demonstrated control over formation of droplets and guiding them with a laser beam [52]. The conceptually simplest approach to valving at small scales is to construct micromechanical valves. These approach, however, needs not be simple in terms of fabrication of the devices. Mechanical microvalves have two most popular varieties, both utilizing the deformation of elastic membranes in soft (PDMS) systems [53] proposed by Quake et al., and for rigid chips [54] by Grover et al. 5.2. DROPLET ON DEMAND SYSTEMS
To date, there is only a hand full of reports on microfluidic droplet on demand systems. Prakash and Gershenfeld [31] used such a system based on thermo-capillary effect in their experiments on droplet logic. In these experiments the fluid-to-be-dispersed flew into the droplet generating junction via a narrowing nozzle. This geometry blocked the flow by the action of the Laplace pressure. A micro-heater placed under the junction enabled lowering of the interfacial tension and generation of single bubbles for each 100 ms pulse of current. The Laplace blockade was used also by Attinger et al. [55], who utilized a piezoelectric actuator glued to a PDMS reservoir of the fluid-to-be-dispersed to force its flow through the narrowing junction. The actuation allowed for generation of monodisperse nL droplets at few Hz. Bransky et al. [56] integrated the piezoelectric actuator into the PDMS device and obtained slightly better results. The use of Laplace blockade strongly limits the range of pressures that can be applied to the droplet phase without overcoming the Laplace pressure of the order of ~10 mbar.
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Recently Lin and Su [57] and Wang et al. [58] utilized the pneumatically actuated PDMS valves [53] to control of the volumes of the droplets (~1 nL and above) and of the times of their emission with frequencies approaching 15 Hz. The drawback of these techniques lies in the use of PDMS, which is known [59] to be incompatible with many solvents. We have recently reported [60] a DOD system in a stiff polymeric device based on an integrated microvalve [54]. This system allows for formation of both droplets and bubbles on demand (Fig. 9), in both the flow-focusing and the T-junctions, and can be made compatible with any chemistry by the virtue of its compatibility with both polymeric and glass devices. 6. Conclusions The recent progress in understanding of the flow of droplets through networks of channels, and in automation of droplet flows suggest that construction of fully automated and truly versatile chips for chemical syntheses and analyzes to be performed on chip will be possible within the next few years of research. These techniques, with the advantages of performing chemistry inside droplets, that we reviewed in this lecture have a potential changing the laboratory standards. If this revolution is indeed to happen depends on a number of scientific, technical and marketing factors and remains to be seen.
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References 1. T. Thorsen, R.W. Roberts, F.H. Arnold, and S.R. Quake, Dynamic pattern formation in a vesicle-generating microfluidic device, Physical Review Letters, 86, 4163–4166, (2001). 2. J.D. Tice, H. Song, A.D. Lyon, and R.F. Ismagilov, Formation of droplets and mixing in multiphase microfluidics at low values of the Reynolds and the capillary numbers, Langmuir, 19, 9127–9133, (2003). 3. P. Garstecki, M.J. Fuerstman, H.A. Stone, and G.M. Whitesides, Formation of droplets and bubbles in a microfluidic T-junction – scaling and mechanism of break-up, Lab on a Chip, 6, 437–446, (2006). 4. G.F. Christopher, N.N. Noharuddin, J.A. Taylor, and S.L. Anna, Experimental observations of the squeezing-to-dripping transition in T-shaped microfluidic junctions, Physical Review E, 78, (2008). 5. P. Guillot and A. Colin, Stability of parallel flows in a microchannel after a T junction, Physical Review E, 72, (2005). 6. S.L. Anna, N. Bontoux, and H.A. Stone, Formation of dispersions using “flow focusing” in microchannels, Applied Physics Letters, 82, 364–366, (2003). 7. P. Garstecki, I. Gitlin, W. DiLuzio, G.M. Whitesides, E. Kumacheva, and H.A. Stone, Formation of monodisperse bubbles in a microfluidic flowfocusing device, Applied Physics Letters, 85, 2649–2651, (2004). 8. P. Garstecki, H.A. Stone, and G.M. Whitesides, Mechanism for flow-rate controlled breakup in confined geometries: A route to monodisperse emulsions, Physical Review Letters, 94, (2005). 9. B. Dollet, W. van Hoeve, J.P. Raven, P. Marmottant, and M. Versluis, Role of the channel geometry on the bubble pinch-off in flow-focusing devices, Physical Review Letters, 100, (2008). 10. W. Lee, L.M. Walker, and S.L. Anna, Role of geometry and fluid properties in droplet and thread formation processes in planar flow focusing, Physics of Fluids, 21, (2009). 11. D.R. Link, S.L. Anna, D.A. Weitz, and H.A. Stone, Geometrically mediated breakup of drops in microfluidic devices, Physical Review Letters, 92, (2004). 12. M. Seo, C. Paquet, Z.H. Nie, S.Q. Xu, and E. Kumacheva, Microfluidic consecutive flow-focusing droplet generators, Soft Matter, 3, 986–992, (2007). 13. T. Nisisako, T. Torii, T. Takahashi, and Y. Takizawa, Synthesis of monodisperse bicolored janus particles with electrical anisotropy using a microfluidic co-flow system, Advanced Materials, 18, 1152–+, (2006). 14. S. Okushima, T. Nisisako, T. Torii, and T. Higuchi, Controlled production of monodisperse double emulsions by two-step droplet breakup in microfluidic devices, Langmuir, 20, 9905–9908, (2004). 15. R.K. Shah, H.C. Shum, A.C. Rowat, D. Lee, J.J. Agresti, A.S. Utada, L.Y. Chu, J.W. Kim, A. Fernandez-Nieves, C.J. Martinez, and D.A. Weitz, Designer emulsions using microfluidics, Materials Today, 11, 18–27, (2008). 16. A.S. Utada, E. Lorenceau, D.R. Link, P.D. Kaplan, H.A. Stone, and D.A. Weitz, Monodisperse double emulsions generated from a microcapillary device, Science, 308, 537–541, (2005).
200
P. GARSTECKI
17. S.Q. Xu, Z.H. Nie, M. Seo, P. Lewis, E. Kumacheva, H.A. Stone, P. Garstecki, D.B. Weibel, I. Gitlin, and G.M. Whitesides, Generation of monodisperse particles by using microfluidics: Control over size, shape, and composition, Angewandte Chemie-International Edition, 44, 724–728, (2005). 18. D. Dendukuri, S.S. Gu, D.C. Pregibon, T.A. Hatton, and P.S. Doyle, Stop-flow lithography in a microfluidic device, Lab on a Chip, 7, 818–828, (2007). 19. D.K. Hwang, D. Dendukuri, and P.S. Doyle, Microfluidic-based synthesis of non-spherical magnetic hydrogel microparticles, Lab on a Chip, 8, 1640–1647, (2008). 20. M.T. Sullivan and H.A. Stone, The role of feedback in microfluidic flow-focusing devices, Philosophical Transactions of the Royal Society a-Mathematical Physical and Engineering Sciences, 366, 2131–2143, (2008). 21. M. De Menech, P. Garstecki, F. Jousse, and H.A. Stone, Transition from squeezing to dripping in a microfluidic T-shaped junction, Journal of Fluid Mechanics, 595, 141–161, (2008). 22. A.M. Ganan-Calvo, Generation of steady liquid microthreads and micronsized monodisperse sprays in gas streams, Physical Review Letters, 80, 285– 288, (1998). 23. Z.H. Nie, M.S. Seo, S.Q. Xu, P.C. Lewis, M. Mok, E. Kumacheva, G.M. Whitesides, P. Garstecki, and H.A. Stone, Emulsification in a microfluidic flow-focusing device: effect of the viscosities of the liquids, Microfluidics and Nanofluidics, 5, 585–594, (2008). 24. J.D. Tice, R.F. Ismagilov, and B. Zheng, Forming droplets in microfluidic channels with alternating composition and application to indexing concentrations in droplet-based assays, Abstracts of Papers of the American Chemical Society, 228, 106-CHED, (2004). 25. B. Zheng, L.S. Roach, and R.F. Ismagilov, Screening of protein crystallization conditions on a microfluidic chip using nanoliter-size droplets, Journal of the American Chemical Society, 125, 11170–11171, (2003). 26. H. Song, D.L. Chen, and R.F. Ismagilov, Reactions in droplets in microflulidic channels, Angewandte Chemie-International Edition, 45, 7336–7356, (2006). 27. H. Song, M.R. Bringer, J.D. Tice, C.J. Gerdts, and R.F. Ismagilov, Experimental test of scaling of mixing by chaotic advection in droplets moving through microfluidic channels, Applied Physics Letters, 83, 4664–4666, (2003). 28. H. Song and R.F. Ismagilov, Millisecond kinetics on a microfluidic chip using nanoliters of reagents, Journal of the American Chemical Society, 125, 14613– 14619, (2003). 29. F. Jousse, R. Farr, D.R. Link, M.J. Fuerstman, and P. Garstecki, Bifurcation of droplet flows within capillaries, Physical Review E, 74, (2006). 30. M.J. Fuerstman, P. Garstecki, and G.M. Whitesides, Coding/decoding and reversibility of droplet trains in microfluidic networks, Science, 315, 828–832, (2007). 31. M. Prakash and N. Gershenfeld, Microfluidic bubble logic, Science, 315, 832– 835, (2007). 32. P. Garstecki, M.J. Fuerstman, and G.M. Whitesides, Oscillations with uniquely long periods in a microfluidic bubble generator, Nature Physics, 1, 168–171, (2005).
TRANSPORT OF DROPLETS IN MICROFLUIDIC SYSTEMS
201
33. N.A. Mortensen, F. Okkels, and H. Bruus, Reexamination of Hagen–Poiseuille flow: Shape dependence of the hydraulic resistance in microchannels, Physical Review E, 71, (2005). 34. G.I. Taylor, Deposition of a viscous fluid on the wall of a tube, Journal of Fluid Mechanics, 10, 161–165, (1961). 35. F.P. Bretherton, The motion of long bubbles in tubes, Journal of Fluid Mechanics, 10, 166–188, (1961). 36. S.R. Hodges, O.E. Jensen, and J.M. Rallison, The motion of a viscous drop through a cylindrical tube, Journal of Fluid Mechanics, 501, 279–301, (2004). 37. D.A. Sessoms, M. Belloul, W. Engl, M. Roche, L. Courbin, and P. Panizza, Droplet motion in microfluidic networks: Hydrodynamic interactions and pressure-drop measurements, Physical Review E, 80, (2009). 38. M.J. Fuerstman, A. Lai, M.E. Thurlow, S.S. Shevkoplyas, H.A. Stone, and G.M. Whitesides, The pressure drop along rectangular microchannels containing bubbles, Lab on a Chip, 7, 1479–1489, (2007). 39. V. Labrot, M. Schindler, P. Guillot, A. Colin, and M. Joanicot, Extracting the hydrodynamic resistance of droplets from their behavior in microchannel networks, Biomicrofluidics, 3, (2009). 40. D.C. Duffy, J.C. McDonald, O.J.A. Schueller, and G.M. Whitesides, Rapid prototyping of microfluidic systems in poly(dimethylsiloxane), Analytical Chemistry, 70, 4974–4984, (1998). 41. M. Schindler and A. Ajdari, Droplet traffic in microfluidic networks: A simple model for understanding and designing, Physical Review Letters, 100, (2008). 42. O. Cybulski, SPICE’d Microfluidics, presentation at Coding and Computation in Microfluidics meeting at MIT, http://cba.mit.edu/events/07.05.fluid/. (2007). 43. O. Cybulski and P. Garstecki, Dynamic Memory in a Microfluidic System of Droplets Traveling Through a Simple Network of Microchannels, Lab on a Chip, (in press), (2009). 44. T.B. Jones, M. Gunji, M. Washizu, and M.J. Feldman, Dielectrophoretic liquid actuation and nanodroplet formation, Journal of Applied Physics, 89, 1441– 1448, (2001). 45. J. Zeng and T. Korsmeyer, Principles of droplet electrohydrodynamics for labon-a-chip, Lab on a Chip, 4, 265–277, (2004). 46. M.Y. He, J.S. Kuo, and D.T. Chiu, Electro-generation of single femtoliter- and picoliter-volume aqueous droplets in microfluidic systems, Applied Physics Letters, 87, (2005). 47. F. Malloggi, H. Gu, A.G. Banpurkar, S.A. Vanapalli, and F. Mugele, Electrowetting – A versatile tool for controlling microdrop generation, European Physical Journal E, 26, 91–96, (2008). 48. V. Srinivasan, V.K. Pamula, and R.B. Fair, An integrated digital microfluidic lab-on-a-chip for clinical diagnostics on human physiological fluids, Lab on a Chip, 4, 310–315, (2004). 49. R.B. Fair, Digital microfluidics: is a true lab-on-a-chip possible? Microfluidics and Nanofluidics, 3, 245–281, (2007). 50. A.M. Ganan-Calvo, Electro-flow focusing: The high-conductivity low-viscosity limit, Physical Review Letters, 98, (2007).
202
P. GARSTECKI
51. D.R. Link, E. Grasland-Mongrain, A. Duri, F. Sarrazin, Z.D. Cheng, G. Cristobal, M. Marquez, and D.A. Weitz, Electric control of droplets in microfluidic devices, Angewandte Chemie-International Edition, 45, 2556–2560, (2006). 52. M.L. Cordero, D.R. Burnham, C.N. Baroud, and D. McGloin, Thermocapillary manipulation of droplets using holographic beam shaping: Microfluidic pin ball, Applied Physics Letters, 93, (2008). 53. M.A. Unger, H.P. Chou, T. Thorsen, A. Scherer, and S.R. Quake, Monolithic microfabricated valves and pumps by multilayer soft lithography, Science, 288, 113–116, (2000). 54. W.H. Grover, A.M. Skelley, C.N. Liu, E.T. Lagally, and R.A. Mathies, Monolithic membrane valves and diaphragm pumps for practical large-scale integration into glass microfluidic devices, Sensors and Actuators B-Chemical, 89, 315–323, (2003). 55. J. Xu and D. Attinger, Drop on demand in a microfluidic chip, Journal of Micromechanics and Microengineering, 18, (2008). 56. A. Bransky, N. Korin, M. Khoury, and S. Levenberg, A microfluidic droplet generator based on a piezoelectric actuator, Lab on a Chip, 9, 516–520, (2009). 57. B.C. Lin and Y.C. Su, On-demand liquid-in-liquid droplet metering and fusion utilizing pneumatically actuated membrane valves, Journal of Micromechanics and Microengineering, 18, (2008). 58. W. Wang, C. Yang, and C.M. Li, On-demand microfluidic droplet trapping and fusion for on-chip static droplet assays, Lab on a Chip, 9, 1504–1506, (2009). 59. J.N. Lee, C. Park, and G.M. Whitesides, Solvent compatibility of poly (dimethylsiloxane)-based microfluidic devices, Analytical Chemistry, 75, 6544– 6554, (2003). 60. K. Churski, J. Michalski, and P. Garstecki, Droplet on demand system utilizing a computer controlled microvalve integrated into a stiff polymeric microfluidic device., Lab on a Chip, (in press), (2009).
THE FRONT-TRACKING METHOD FOR MULTIPHASE FLOWS IN MICROSYSTEMS: FUNDAMENTALS M. MURADOGLU
Department of Mechanical Engineering, Koc University, Istanbul, Turkey,
[email protected]
Abstract. The aim of this paper is to formulate and apply the front-tracking method to model multiphase/multifluid flows in confined geometries. The front-tracking method is based on a single-field formulation of the flow equations for the entire computational domain and so treats different phases as a single fluid with variable material properties. The effects of the surface tension are treated as body forces and added to the momentum equations as δ functions at the phase boundaries so that the flow equations can be solved using a conventional finite-difference or a finite-volume method on a fixed Eulerian grid. The interface, or front, is tracked explicitly by connected Lagrangian marker points. Interfacial source terms such as surface tension forces are computed at the interface using the marker points and are then transferred to the Eulerian grid in a conservative manner. Advection of fluid properties such as density and viscosity is achieved by following the motion of the interface. The method has been implemented for two (planar and axisymmetric) and fully three dimensional interfacial flows in simple and complex geometries confined by solid walls. The front-tracking method has many advantages including its conceptual simplicity, small numerical diffusion and flexibility to include multiphysics effects such as thermocapillary, electric field, soluble surfactants and moving contact lines. In this chapter, the fundamentals of the front-tracking method including the formulation and details of the numerical algorithm are presented.
1. Introduction Multiphase/multifluid flows are ubiquitous in microsystems since, as sizes continue to reduce in such devices, surface to volume ratio increases and thus surface forces become dominant over the volume forces. It is therefore of great importance to understand and manipulate multiphase/multifluid flows in micro channels [1, 2]. Direct simulation of multiphase flows is notoriously difficult mainly due to the presence of deforming phase boundaries. Strong interactions S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_11, © Springer Science + Business Media B.V. 2010
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between the phase boundaries and complex channel walls make the problem even more difficult in micro channels. Although efforts to compute the motion of multiphase flows are as old as computational fluid dynamics, progress was rather slow and simulations of finite Reynolds number multiphase flows were limited to very simple problems for a long time [3]. In the past two decades, however, major progress has been achieved and a variety of numerical methods have been developed and successfully applied to a wide range of interfacial flow problems [3–7]. The computational methods developed for interfacial flows can be classified into four major categories. The first class is the front-capturing method that explicitly captures the interface on a regular stationary grid. This is the oldest technique and is still widely used in applications. The marker-and-cell (MAC), the volume-offluid (VOF), the level-set, the constrained interpolation profile (CIP) and diffuse interface methods are the most popular examples of the front-capturing techniques [4–7]. The major problem that the front-capturing methods suffer is the excessive numerical diffusion that makes it difficult to maintain sharp boundary between the phases. The second class of methods employs separate grids in each phase and thus it potentially has the highest accuracy as discussed by Ryskin and Leal [8]. The major difficulty in using this class of methods is to generate grids in both phases and maintain them smooth throughout simulations. Due to this difficulty, the method is applicable only for simple geometries so it is not suitable for microfluidics as microchannels often involve complex geometries [9, 10]. The third class is the fronttracking method developed by Glimm et al. [11]. In this method, the interface is marked by Lagrangan grid but a separate fixed grid that is modified near the interface is also used in each phase. The fourth class is the boundary integral method that is applicable only in the Stokes flow regime [12]. Since the flow is very often in the Stokes flow regime in microchannels, this method can be used in microfluidic applications provided that a care is taken to make sure that flow remains in the creeping flow regime throughout the computational domain. Here, we describe a method that has been particularly successful for a wide range of multifluid and multiphase flow problems. The front-tracking method is based on a single-field formulation of the flow equations for the entire computational domain and so treats different phases as a single fluid with variable material properties [3, 13]. In fact, the front-tracking method discussed here is an application of the immersed boundary method of Peskin [14] to the interfacial flows. The front-tracking method can be properly described as a hybrid method between the front capturing and front-tracking technique [3]. In this method, the interface between the bubble and the ambient fluid is represented by connected Lagrangian marker points moving with the local flow velocity interpolated from the neighboring fixed Eulerian grid points. The front-tracking method has many advantages such
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as its conceptual simplicity, small numerical diffusion and flexibility to include multiphysics effects such as thermocapillary [15], electric field [16], soluble surfactants [17, 18] and moving contact lines [19]. However, its main disadvantage is probably the difficulty to maintain the communication between the Lagrangian marker points and Eulerian body-fitted curvilinear or unstructured grids. Tracking marker points is a trivial task in regular Cartesian grids but is considerably more difficult in curvilinear or unstructured grids. The auxiliary grid method has been recently developed to overcome this difficulty and been successfully applied to multiphase flow problems involving strong interactions between the phase boundaries and complex channel walls [9, 10]. The algorithm reduces particle tracking in curvilinear or unstructured grids to tracking on a uniform Cartesian grid with a look up table while retaining all the advantages of the front-tracking method. In this chapter, the fundamentals of the front-tracking method are described as a computational method that can be used as a design tool in microfluidic systems. 2. Mathematical Formulation The key to the front-tracking method, as well as to several other methods such as volume of fluid (VOF) [5], level-set [6] and diffuse interface methods, is the use of a single set of conservation equations for the entire flow field. To achieve this, differences in the material properties of the different phases should be accounted for and the interfacial phenomenon such as surface tension must be included by adding the appropriate interface terms to the governing equations [3]. Since these terms are concentrated at the boundary between the different fluids and the material properties and the flow field are, in general, discontinuous across the interface, the differential form of the governing equations must be interpreted either as a weak form, satisfied only in an integral sense, or all variables must be interpreted in terms of generalized functions. In the front-tracking method, the latter approach is taken. The fluid motion is assumed to be governed by the Navier–Stokes equations in all phases: r r rr r r r r r ∂ρv + ∇ ⋅ ( ρv v ) = −∇p + ρf + ∇ ⋅ μ(∇v + ∇T v ) + ∫ σκnδ( x − x f )ds. (1) ∂t This equation is valid in the entire flow field even if the material properties vary discontinuously across phase boundaries. In Eq. (1), ρ andr μ are r density and viscosity, v is the velocity field, p is pressure, and f is the body force. The effects of the interfacial tension are accounted for by the last term in Eq. (1). In this term, δ is two or three dimensional delta function, σ is surface tension coefficient, κ is the curvature of two-
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dimensional flow or twice of the mean curvature for three r v dimensional x to the interface, is the point at flow, n is a unit outward normal vector r which the equation is evaluated and x f is a point on the interface. Note that the surface tension coefficient is not necessarily constant and can depend on the temperature field and/or the surfactant concentration at the interface [15, 17]. The integral is taken over the entire interface. The flow is assumed to be incompressible:
r ∇ ⋅ v = 0.
(2)
We also assume that the material properties remain the same following a fluid particle, i.e.,
Dρ = 0; Dt r where D /Dt r = ∂ /∂t + v • ∇ is the function I( x,t) is defined such that
Dμ = 0, Dt
(3)
substantial derivative. An indicator it is zero in the continuous fluid and unity in the disperse phase. The material properties are then set in each phase by
r
r
ρ = ρi I ( x , t ) + ρo (1 − I ( x , t ));
r
r
μ = μi I ( x , t ) + μo (1 − I ( x , t )).
(4)
The indicator function is computed based on the location of the interface represented by marker points using the standard techniques [3]. On a regular grid, this process involves solution of a separable Poisson equation that can be solved very efficiently using a fast Poisson solver. In the case of complex geometries, the indicator function is still computed on a regular Cartesian grid using a fast Poisson solver and is then interpolated onto the curvilinear grid [9, 10]. Note that the computation of the indicator function is discussed in Section 3.5. 3.
Numerical Solution
Equations (1–4) are in the same form as the conventional flow equations so that they can be solved by standard numerical methods used for homogeneous flows. Once the interface has been advected and the surface tension computed, virtually any standard algorithm based on fixed grids can be used to integrate Eq. (1) in time. The grids used in the front-tracking method are shown in Fig. 1a for simple geometries and in Fig. 1b for the complex geometries. In simple geometries, the conservation equations are solved on a fixed Eulerian grid while the interface is tracked by a
FRONT-TRACKING METHOD: FUNDAMENTALS a
b
Stationary Eulerian Grid
Auxilary Uniform Cartesian Grid
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Curvilinear Grid
Lagrangian Grid Front
Front
Fluid I
Fluid I
Fluid II
Front Element
Marker Point
Fluid II
Figure 1. Computations of flow containing more than one phase. The governing equations are solved on a fixed grid but the phase boundary is represented by a moving “front,” consisting of connected marker points. (a) Grid system used in simple rectangular geometries and (b) the grid system used in complex geometries.
Lagrangian grid of lower dimension. The Lagrangian grid consists of linked marker points that move at the local flow velocity interpolated from the Eulerian grid. The interface element between two marker points are called a front element. Tracking the marker points is a trivial task in simple geometries but it is not easy in complex geometries and requires a special treatment. The auxiliary grid method developed by Muradoglu and Kayaap [10] overcomes this difficulty and reduces the tracking of Lagrangian points on curvilinear grids to tracking on a uniform Cartesian grid with a look up table as discussed below. The flow equations (Eqs. (1–4)) are solved using a finite-difference method or a finite-volume method. The finite-difference method is preferred when the flow geometry is simple whereas the finite-volume method is preferred for complex geometries. The finite-difference algorithm is based on the projection method of Chorin [20]. The version of the projection method employed here can be found in Tryggvason et al. [3]. The implementation of the fronttracking method combined with the finite-difference scheme is referred here as FD/FT method. The finite-volume method is based on the pseudo time stepping and is second order accurate both in time and space. The detailed discussion about the finite-volume method employed here can be found in Caughey [21] and Muradoglu and Gokaltun [9]. The implementation of the front-tracking method that uses the finite-volume method as flow solver is referred here as FV/FT method. 3.1. STRUCTURE OF LAGRANGIAN GRID
The Lagrangian grid consists of linked marker points. In two dimensions, the piece of the front element between the marker points is called a front
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element as shown in Fig. 1. There is a linked list that contains information about the neighbors of each marker points as well as the neighbors of each front element. This linked list gives a flexibility to remove or add a front element very easily in order to restructure the Lagrangian grid as will be discussed below. In three dimensions, the marker points form a surface as shown in Fig. 2. Three marker points make a triangular front element. Again a linked list is maintained such that each element knows the marker points that make its corners as well as its immediate neighboring elements. Note that a front element is allowed to share only one edge with its neighbor as sketched in Fig. 2.
Figure 2. Structure of the front in three dimensions. The interface is represented by a triangular grid. Each front element is allowed to share only one edge with its each neighbor (Adapted from Tryggvason et al. [3]).
3.2. RESTRUCTURING THE LAGRANGIAN GRID
Ideally the front elements must be uniform and remain so throughout the simulations. In addition, the size of the front elements must remain comparable to the Eulerian grid size in order to maintain good resolution. However, the interface moves and deforms. This dictates that the Lagrangian grid must be dynamically restructured during the simulations in order to avoid having too small or too large front elements. Restructuring of the Lagrangian grid is crucial in the front-tracking method since front elements that are too large compared to the Eulerian grid size result in lack of resolution while the front elements that are too small result in formation of “wiggles” much smaller than the grid size. In two dimensions, the restructuring is simply
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Figure 3. Restructuring the front in two dimensional case. The element that is larger than a prespecified threshold value is splitted (left) and the element that is smaller than a prespecified threshold value is deleted (right).
Figure 4. Restructuring the front in three dimensional case (Adapted from Tryggvason et al. [3]).
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done by splitting the elements that are larger than a prespecified value and removing the elements that are smaller than a prespecified value as shown in Fig. 3. In both splitting and deleting elements, a cubic Legendre polynomial is fitted to the marker points of the front element that is to be deleted and its immediate neighbors on each side as shown in the sketched (Fig. 3). This simple procedure conserves curvature but not necessarily the volume. Therefore a care must be taken not to do unnecessary restructuring operations. In the three dimensions, in addition to deletion and addition operations, the elements are also reshaped as shown in Fig. 4. Note that neither curvature nor the volume is conserved in any of the restructuring operations in threedimensional cases. Details of the restructuring can be found in the review paper by Tryggvason et al. [3]. 3.3. COMPUTING SURFACE TENSION FORCE
The surface tension force is computed at center of front elements. It is then converted into equivalent body force and distributed onto the neighboring Eulerian grid points in a conservative manner. The distribution procedure is discussed in the next section. The accurate treatment of the surface tension force is probably one of the most important ingredients of any computational method developed for computation of interfacial flows. In the present method, the interface is represented explicitly by the marker points and these discrete points are used to approximate the surface tension. Although there are several alternative ways, the procedure preferred here is based on fitting a cubic Legendre polynomial to the marker points of the front element for which the surface tension is to be computed and its immediate neighbors for two-dimensional computations. In the multiphase flow problems, we often need to find the surface tension force but not the curvature. The force acting on a small front element can be given by
r r r r r ∂σs δf s = ∫ σκnds = ∫ ds = (σs )2 − (σs )1 , (5) ∂ s Δs Δs r r r r where the identity κn = ∂s /∂s has been used. The vectors s1 and s2 in Eq.
(5) denote the unit tangent vectors computed at the end points of the front element as shown in Fig. 5a. In computing the unit tangent vectors, a cubic Lengedre polynomial is fit to the four marker points on each side of the corner. Since this can be done in two different ways, an average is taken to reduce the numerical error as shown in Fig. 5b. This procedure is highly accurate and robust as reviewed by Tryggvason et al. [3].
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Figure 5. Computation of unit tangent vectors in two-dimensional cases. Tangent vectors at the end points of mth element (sketch on the left). Approximation of unit tangent vectors (sketch on the right).
In three-dimensional case, surface tension computation is not as elegant as that in two-dimensional case but it has been still found satisfactory in a wide variety of multiphase flow computations [3]. In 3D, the mean curvature is given by
r
r
δf s = ∫ σκnds = ΔA
r
r r
(
r
ΔA
)
r r
r
∫ (n × ∇ ) × ndA = ∫ t × nds,
(6)
S
r
where the identity κn = n × t × n has been used. In the last step of Eq. (6), the Stokes theorem is employed to convert the surface integral into r a contour integral along the edges of the element (see Fig. 2). In Eq. (6), n is the unit outward normal vector to the surface of the front element and it is computed by fitting a quadratic surfacer to the marker points of the front element and its neighbors. The vector t is the unit tangent vector to the edge of the front element and is simply computed by taking difference between marker points sharing the same edge. The line integral in Eq. (6) is evaluated numerically by dividing each edge into four segments and using a midpoint rule in the same way as done by Tryggvason et al. [6]. The line integrals can be evaluated in two ways using the elements sharing the same edge. This fact is exploited by taking simple average of line integrals computed for each element sharing the same edge in order to reduce the numerical error as well as to ensure the conservation of the surface tension forces [3]. 3.4. COMMUNICATION BETWEEN EULERIAN AND LAGRANGIAN GRIDS
Information must be exchanged between the Eulerian and Lagrangian grids at every time step during a simulation. Therefore it is of crucial importance to maintain efficient and robust communication between these two grids. The surface tension force is computed at the interface and it needs to be
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transferred to the Eulerian grid in a conservative manner, which is called “smoothing operation” and is achieved using a distribution algorithm. The distribution algorithm approximates the δ functions appearing in Eq. (1). Let φf be an interface property expressed in units per unit area, then the corresponding grid value φg should be expressed in units per unit volume. The conservation of the total value of φf requires that
∫φ
Δs
f
r ( s )ds = ∫ φ g ( x )dv.
(7)
Δv
This is achieved at discrete level using a distribution function as
φ ijk = ∑ φ lϖ ijkl l
Δs l , Δx 3
(8)
where φl is the discrete approximation to the interface value of φf, φijk is the approximation to grid value φg, Δx is the Eulerian grid size and Δsl is the area of the front element l. In Eq. (8), ϖ lijk is the weight representing the discrete version of the distribution function. The weights can be selected in different ways but they must satisfy the conservation requirement:
∑ϖ ijk
l ijk
= 1,
(9)
where the summation is carried out over all the grid points used to distribute interface property φ l of the l th front element. In the front-tracking simulations, the distribution function suggested by Peskin [14] is usually used although other distribution functions can also be used. The marker points move at the local flow velocity interpolated from the Eulerian grid. The interpolation scheme is important since interpolation error may result in a violation of mass conservation. Ideally, the interpolation scheme must satisfy the mass conservation at the discrete level in the same way as done in the flow solver [19]. However, the Peskin distribution function or simple bi-linear interpolation is usually used in the fronttracking method [3]. Note that none of these interpolation schemes satisfies the mass conservation at discrete level. This is in fact an important factor for the change in drop volume especially for long simulations. 3.5. UPDATING THE MATERIAL PROPERTIES
The material properties such as density and viscosity vary discontinuously across the interface. However, it is desirable to have smooth transition of the properties between different phases for numerical stability and accuracy. One way to do this is to advent the material properties similar to the VOF or
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level-set methods [4, 5]. Alternatively, the boundary between phases can be moved first and then the material properties can be set based on the new location of the interface. The latter approach is usually preferred in the front-tracking computations. For this purpose, we define an indicator function I that is unity inside droplet and zero otherwise. Since the indicator function represents a unit jump across the interface, the gradient of the indicator function can be written as
r r r ∇I = ∫ n δ ( x − x f )ds,
(10)
and the discrete version of this equation is given by l r ∇ h I ijk = ∑ϖ ijk nl Δsl ,
(11)
l
l where Δsl is the area of the front element l and ϖ ijk is the same weight function as discussed in the previous section. Taking numerical divergence of Eq. (11) yields
∇ 2 I = ∇ h • (∇ h I ijk ),
(12)
which is a separable Poisson equation and can be solved very efficiently using a fast Poisson solver such as MUDPACK package [23]. Solution of Eq. (12) yields smooth transition of the indicator function at the interface. Once the indicator function is determined, then the material properties are simply set as a function of the indicator function:
ρ = ρ i I + (1 − I ) ρ o ;
μ = μ i I + (1 − I ) μ o
(13)
where subscripts “i” and “o” denotes the properties of the drop and ambient fluids, respectively. 3.6. TRACKING ALGORITHM
As mentioned above, the interface between different phases is represented by linked marker points moving at the local flow velocity. Since the flow equations are solved on the fixed Eulerian grid, it is of fundamental importance to maintain the communication between the Lagrangian and Eulerian grids. In simple geometries, this is a trivial task as the flow equations are solved on a regular Cartesian grid. However, the tracking of Lagrangian marker points is a formidable task in complex geometries where the flow equations must be solved on curvilinear or unstructured grids. To overcome this difficulty, Muradoglu and Kayaap [10] developed a very efficient and robust tracking algorithm. This algorithm is summarized as follows: At the beginning of a simulation, a uniform auxiliary Cartesian grid is generated such that it
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covers the entire computational domain as sketched in Fig. 1b. The uniform grid cell size is typically selected as half of the smallest grid size of the curvilinear grid. It is then found which uniform grid nodes reside in each curvilinear grid cell and this information is stored in an array. This operation can be easily done using vector algebra as sketched in Fig. 6. It is emphasized here that this is a preprocessing step and is done only once in each simulation. After this preprocessing step, in each time step, it is first determined where the marker points reside in the uniform grid by a simple division. Referring to Fig. 7, for instance, the marker point P is determined to reside in (I,J) node of the uniform grid and then the nodes of (I,J) cell reside in the curvilinear grid cells of (i,j), (i,j − 1) and (i − 1,j − 1). Therefore we conclude that the marker point P resides in the region consisting of the curvilinear grid cells of (i − 2:i + 1,j − 2:j + 1). Finally the cells (i − 2:i + 1,j − 2) and (i − 2,j − 2:j + 1) are eliminated based on the relative Figure 6. Preprocessing for determination distance of their outer nodes to the of which uniform Cartesian grid nodes point P. A the end of this process, it reside in each curvilinear grid cell. is determined that the marker point P resides in the domain composed by the curvilinear cells of (i − 1:i + 1,j − 1:j + 1). The further details of this j) (i, algorithm can be found in Muradoglu and Kayaap [10]. P The particle-tracking algorithm is (I,J) ) tested for the rigid body rotation of j-1 (ifluid in a circular channel as shown ) j-1 in Fig. 8. The radius of the outer 1(iboundary and the width of the channel are set to Rc = 1 and wc = 0.2, respectively. The velocity field is specified as u = yo – y and v = x – xo Figure 7. The tracking algorithm for curvilinear grids. where x and y are the two-dimensional Cartesian coordinates and xo and yo ate the centroid of the circular channel. A two-dimensional drop with diameter d = 0.15 is initialized at (x,y) = (0.1,1.0) and is set to motion by the fluid. Passive tracer particles are used for visualization. The particles are distributed inside the drop randomly and the particles occupying the first and third quadrant are identified as red and the other particles are blue. A coarse version of the curvilinear grid is shown in Fig. 8a. As can be seen in
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Fig. 8b, the drop makes rigid body motion as expected indicating the accuracy of the tracking algorithm. Accuracy of the tracking algorithm is quantified in Fig. 9. As can be seen in Fig. 9a, b, the tracking algorithm is second order accurate both in time and space.
Figure 8. (a) A coarse curvilinear grid and (b) rigid body motion of the drop. The drop is enlarged three times at the locations shown by the thick arrows.
(a)
100
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10−6
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Figure 9. Error in the position of the drop centroid (a) against the time step and (b) against the inverse of the total number of grid cells.
4. Validation The finite-difference/front-tracking method has been validated for a wide variety of test cases in simple geometries as reviewed by Trgyyvason et al. [3]. Therefore the emphasis is placed here on the accurate computations of interfacial flows in complex geometries as the complex geometries are ubiquitous in microfluidic applications. For this purpose, the FV/FT method that is designed to compute multiphase flows in complex geometries is first validated against the FD/FT method that can simulate flows only in simple
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geometries. Both FV/FT and FD/FT methods are first applied to compute the gravity-driven falling drop in a straight channel. The physical problem and the computational domain are shown in Fig. 10a. The computational domain is 5d in the radial direction and 15d in the axial direction, where d is the initial drop diameter. The drop centroid is initially placed at (rc,zc) = (0,12d) into otherwise quiescent ambient fluid. The details of the test case can be found in Muradoglu and Kayaalp [10]. Figure 10b shows the evolution of droplet for the Eotvos number Eo = 24. The results are obtained using two different implementations of the front-tracking method. This figure indicates that there is a good qualitative agreement between two different implementations. More quantitative comparison of these two different implementations are shown in Fig. 11a, b for the terminal velocity and percentage change in drop volume, respectively. These figures indicate again a good agreement between two implementations. Note that the change in drop volume is a good indicator for the accuracy of the numerical method and ideally the drop volume must remain constant. However, the drop volume changes due to accumulation of numerical errors. Figure 11b indicates that both implementations of the front-tracking method are quite accurate and total change in drop volume is less than a few percent for this challenging test case where drop undergoes large deformations.
Figure 10. (a) The schematic illustration of the physical problem and computational domain and (b) the evolution of drop for Eo = 24.
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Figure 11. (a) Terminal velocity of drop and (b) the percentage change in drop volume for Eo = 12 and Eo = 24.
The curvilinear implementation of the front-tracking method is then applied to study motion, deformation and breakup of viscous droplet passing through a constricted capillary tube. This buoyancydriven flow has been studied by Hemmat and Borhan [24] and computationally by Olgac et al. [25]. The computational domain and a portion of coarse version of the computational grid are shown in Fig. 12. The snapshots of the computed and experimental drop shapes are shown in Fig. 13. As can be seen in this figure, there is a remarkable agreement between the computed and experimental drop shapes indicating the performance of the Figure 12. The schematic illustration front-tracking method. The constant of the physical problem and a portion pressure contours and velocity vectors of coarse grid. are plotted in Fig. 14 in the vicinity of droplet while it passes though the throat and the expansion portions of the channel. This figure clearly shows the power of the front-tracking method to provide detailed information about the flow field inside and outside the droplet.
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Figure 13. Evolution of viscous droplet with breakup. The computed drop shapes (second and fourth rows) are in a good agreement with the experimental pictures taken by Hemmat and Borhan [24].
Figure 14. Velocity vectors (right portion) and pressure contours (left portion) in the vicinity of a buoyancy-driven viscous droplet while it passes through (a) the throat and (b) the expansion region of a constricted capillary tube.
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5. Conclusions The front-tracking method has been developed by Trgyyvason and coworkers and been successfully used for computational modeling of interfacial flows [3]. The method is essentially an implementation of the immersed boundary method of Peskin [14] to multiphase flow problems. The method has a number of advantages including its conceptual simplicity, small numerical diffusion and flexibility to include multiphysics effects such as thermocapillary, electric field, soluble surfactants and moving contact lines. These features of the front-tracking method make it a good candidate to be a viable design tool for microfluidic applications. It has been demonstrated that the explicit tracking of the interface facilitates increased accuracy especially for the cases where the interface undergoes extreme deformations. One of the most important disadvantages of the front-tracking method was the difficulty to maintain efficient communication between the Lagrangian marker points and curvilinear or unstructured Eulerian grid. This difficulty has been overcome by recent development of auxiliary grid method [9, 10]. Acknowledgement This work is supported by Turkish Academy of Sciences through GEBIP program.
References 1. H.A. Stone, A.D. Stroock and A. Ajdari. Engineering Flows in Small Devices: Microfluidics Toward a Lab-on-a-Chip, Annu. Rev. Fluid Mech., 36 (2004). 2. T.M. Squires and S.R. Quake, Microfluidics: Fluid Physics at the Nanoliter Scale, Rev. Modern Phys., 77(3), 977–1026 (2005). 3. G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, and Y.-J. Jan. A Front-Tracking Method for the Computations of Multiphase Flow, J. Comput. Phys., 169, 708–759 (2001). 4. S. Osher and R.P. Fedkiw, Level set methods: An overview, J. Comput. Phys., 169(2) (2001). 5. R. Scardovelli, S. Zaleski, Direct Numerical Simulation of Free-Surface and Interfacial Flow, Annu. Rev. Fluid Mech., 31 (1999). 6. J.A. Sethian, P. Smereka, Level Set Methods for Fluid Interfaces, Annu. Rev. Fluid Mech., 35 (2003). 7. T. Yabe, F. Xiao and T. Utsumi, The Constrained Interpolation Profile (CIP) Methods for Multiphase Analysis, J. Comput. Phys., 169(2), 708–759 (2001). 8. G. Ryskin and L.G. Leal, Numerical Solution of Free-Boundary Problems in Fluid Mechanics. Part 2. Bouyancy-Driven Motion of Gas Bubble Through a Quiescent Liquid, J. Fluid Mech., 148 (1984).
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9. M. Muradoglu, S. Gokaltun, Implicit Multigrid Momputations of Buoyant Light Drops Through Sinusoidal Constrictions, J. Appl. Mech., 71 (2004). 10. M. Muradoglu and A. D. Kayaalp. An Auxiliary Grid Method for Computations of Multiphase Flows in Complex Geometries, J. Comput. Phys., 214 (2006). 11 J. Glimm, J.W. Grove, X.L. Li, W. Oh and D.H. Sharp, A Critical Analysis of Rayleigh-Taylor Growth Rates, J. Comput. Phys., 169 (2001). 12. C. Pozrikidis, Interfacial Dynamics for Stokes Fow, J. Comput. Phys., 169 (2001). 13. S.O. Unverdi, G. Tryggvason, A Front-Tracking Method for Viscous Incompressible Multiphase Flows, J. Comput. Phys., 100 (1992). 14. C.S. Peskin, Numerical Analysis of Blood Flow in the Heart, J. Comput. Phys., 25 (1977). 15. S. Nas, M. Muradoglu, G. Tryggvason, Pattern Formation of Drops in Thermocapillary Migration, Int. J. Heat Mass Trans., 49(13–14), 2265–2276 (2006). 16 A. Fernandez, G. Tryggvason, J. Che and S.L. Ceccio, The Effects of Electrostatic Forces on the Distribution of Drops in a Channel Flow: Two-Dimensional Oblate Drops, Phys. Fluids, 17 (9), Art. No: 093302 (2005). 17. M. Muradoglu and G. Tryggvason, A Front-Tracking Method for Computation of Interfacial Flows with Soluble Surfactants, J. Comput. Phys., 227 (4), 2238– 2262 (2008). 18. S. Tasoglu, U. Demirci and M. Muradoglu, The Effect of Soluble Surfactant on the Transient Motion of a Buoyancy-Driven Bubble, Phys. Fluids, 20, 040805 (2008). 19. M. Muradoglu and S. Tasoglu, A Front-Tracking Method for Computational Modeling of Impact and Spreading of Viscous, Droplets on Solid Walls, Comput. Fluids (in press) (2009). 20. A.R. Chorin, Numerical solution of the Navier–Stokes equations, Math. Comput., 22 (1968). 21. D.A. Caughey, Implicit Multigrid Computation of Unsteady Flows Past Cylinders of Square Cross-Section, Comput. Fluids, 30, 939–960 (2001). 22. R. McDermott and S.B. Pope, The Parabolic Edge Reconstruction Method (PERM) for Lagrangian Particle Advection, J. Comput. Phys., 227, 5447–5491 (2008). 23. J. Adams, MUDPACK: Multigrid FORTRAN Software for the Efficient Solution of Linear Elliptic Partial Differential Equations, Appl. Math. Comput., 34 (1989). 24. M. Hemmat and A. Borhan, Buoyancy-Driven Motion of Drops and Bubbles in a Periodically Constricted Capillary, Chem. Eng. Commun., 150 (1996). 25. U. Olgac, A. Doruk Kayaalp and M. Muradoglu, Buoyancy-Driven Motion and Breakup of Viscous Drops in Constricted Capillaries, Int. J. Multiphase Flow, 32(9), 1055–1071 (2006).
THE FRONT-TRACKING METHOD FOR MULTIPHASE FLOWS IN MICROSYSTEMS: APPLICATIONS M. MURADOGLU
Department of Mechanical Engineering, Koc University, Istanbul, Turkey,
[email protected]
Abstract. The aim of this paper is to present computational modeling of multiphase/multifluid flows encountered or inspired by lab-on-a-chip applications. In particular, the motion and deformation of drops/bubbles moving through micro channels, the effects of channel curvature on the liquid film thickness between a large bubble and serpentine channel, chaotic mixing in a micodroplet moving through a serpentine channel, effects of channel curvature on the chaotic mixing and axial dispersion in a segmented gas–liquid flow, effects of soluble surfactants and modeling of a single cell epitaxi are discussed. Computational results are compared with the analytical results in limiting cases as well as with the available experimental data. Difficulties in mathematical and computational modeling of multiphase flow problems in Microsystems are emphasized and some remedies for these difficulties are offered.
1. Introduction The front-tracking method [1] has been successfully applied to multiphase flow problems encountered or inspired by lab-on-a-chip applications. Mutiphase/fluid problems are ubiquitous in microfluidic systems since the surface forces become dominant over the volume forces as the channel size gets smaller [2, 3]. Computational fluid dynamics (CFD) is ideally suited for simulation of microfluidic systems since flow is almost always laminar. In fact, flow is even in the Stokes flow regime in many microfluidic applications and lubrication type of approaches are relevant [2]. Therefore virtually any commercial CFD package can be used for the analysis of single phase flows in such systems. However the interaction of flow with deforming interface separating different phases as well as with the channel walls makes the multiphase flows highly complex and nonlinear. In addition, multiphysics effects such as thermocapillary, electric field, soluble surfactants and chemical reactions add further complexity to the problem. Thus the numerical simulation of multiphase flows is still a challenging task even S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_12, © Springer Science + Business Media B.V. 2010
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in the creeping flow regime and offers good research opportunity in this fast developing field. In addition, computational tools can provide detailed insight about the flow physics that is extremely difficult to obtain experimentally since the microsystems is not experimentally friendly environment due to limited optical access, seed particles smaller than wavelength of light, noise caused by Brownian motion of seed particles and large background reflections [2]. There are several computational methods developed for direct simulation of multiphase flows. Each numerical method has its own advantages and disadvantages. In particular, the front-tracking method has been successfully applied to a wide range of multiphase flow problems [1]. Here we discuss sample applications of the front-tracking method to multiphase/fluid problems encountered or inspired by microfluidic systems. The first application concerns with mixing in microsystems. It is well known that mixing is notoriously difficult in microsystems due to laminar nature of the flow and thus requires passive or active chaotic mixing protocols to homogenize the fluid streams over typical residence times in microchannels. It has been shown that viscous droplets moving through a serpentine channel can be used as a mixer and chemical reactor [4, 5]. This method has a number of advantages including elimination of axial dispersion completely. Similarly gas segmentation creates chaotic mixing in liquid slugs moving through curved channels and significantly reduces the axial dispersion [6]. The front-tracking method has been successfully used to simulate flows in these micromixers [6–10]. The simulations shed light on the ways to improve the mixing and to reduce axial dispersion [6]. Another important application of the front-tracking method is to simulate the drop/bubble formation in flow-focusing devices. Production of mono disperse drops/bubbles in microchannels is of fundamental importance for the success of the concept of lab-on-a-chip. It has been shown that flowfocusing can be effectively used for this purpose. Filiz and Muradoglu performed front-tracking simulations in order to understand the physics of the breakup mechanism and effects of the flow parameters on the droplet/ bubble size in the flow-focusing devices [11]. Surface active agents (surfactant) are either present as impurities that are difficult to remove from a system or they are deliberately added to fluid mixtures to manipulate interfacial flows. It has been well known that the presence of surfactant in a fluid mixture can critically alter the motion and deformation of bubbles moving through a continuous liquid phase. Probably, the best-known example is the retardation effect of surfactant on the buoyancy-driven motion of small bubbles. Numerous experimental studies have shown that the terminal velocity of a contaminated spherical bubble is significantly smaller than the classical Hadamard–Rybczynski prediction
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and approaches the terminal velocity of an equivalent solid sphere. The physical mechanism for this behavior was first consistently explained by Frumkin and Levich [12] by noting that the surfactant adsorbed from the bulk fluid is convected toward the back of the bubble and the resulting Marangoni stresses act to reduce the interface mobility. This reduction in surface mobility increases the drag force and, thus, reduces the terminal velocity. In microfluidic applications, surfactants are usually used to manipulate the multiphase flows in microchannels. Modeling of soluble surfactants is a challenging problem due to deforming interface and mass transfer between the bulk fluid and the interface. In addition, the Marangoni stresses caused by non-uniform distribution of the surfactant concentration at the interface further complicates the problem. The front-tracking method has been recently used successfully to accurately model the effects of soluble surfactants on the interfacial flows [13, 14]. A few sample results about effects of the soluble surfactant are presented here together with some numerical details. It is well known that the surface tension generally reduces with increasing temperature and thus Marangoni stresses are induced due to non-uniform surface tension at the interface caused by non-uniform temperature field. This is called thermocapillary effect and can be used to manipulate multiphase flows in microchannels. The front-tracking method can be used effectively to model the thermocapillary effects as shown by Nas and Tryggvason [15] and Nas et al. [16]. Here front-tracking modeling of thermocapillary effects is not discussed since it is very similar to and simpler than modeling the soluble surfactants. Finally impact and spreading of a viscous droplet on a partially wetting solid substrate will be discussed. It is known that no-slip boundary condition exhibits singular behavior at the moving contact line in the case of partially wetting solid surface. This singularity is removed when a slip model is used. However the slip mechanism is still not well understood. One popular approach employed to model the moving contact line is to dynamically set the contact angle using the experimental correlations between the apparent contact angle and the capillary number of the moving contact line. This approach is taken here and successfully applied to simulate impact and spreading of a viscous microdroplet on a partially wetting substrate with various static contact angles. The ultimate goal is to be able to develop a model for single cell epitaxi demonstrated experimentally by Demirci and Munteseno [17] and suggested as an alternative way of creating three dimensional tissues layer by layer using existing ink-jet printing technology. Some details of the numerical method, validation tests for the simple droplets and some preliminary results for the single cell epitaxi are presented.
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2. Mixing and Dispersion Mixing in microchannels is notoriously difficult since flow is usually laminar and molecular diffusion is not sufficient to mix fluid streams on the time scale of the typical residence time. The mixing is especially problematic when fluid stream containing macromolecules such as DNA are to be mixed. Diffusion coefficient of the macromolecules is typically one or two orders of magnitude smaller than that of small molecules [1]. Therefore it is necessary to develop mixing protocols that significantly enhance the mixing in laminar flow environment. Nearly all mixing protocols are based on the concept of chaotic advection [18, 19]. In addition to enhanced mixing, it is also desirable to have a uniform residence time distribution as much as possible. This requires significant reduction or complete elimination of axial dispersion [6]. Taylor demonstrated that nonuniform velocity profile causes axial dispersion that is inversely proportional to the molecular diffusion coefficient [20]. Ismagilov and coworkers have shown that a droplet can be used as micromixer [4, 5]. As droplet moves through a serpentine channel, streamlines periodically cross each other causing chaotic mixing within the droplet. Mixing inside droplet also completely eliminates the axial dispersion [4, 5]. Alternatively, Guenther et al. [6] demonstrated that chaotic mixing also occurs in the bulk fluid when a serpentine channel is segmented by injecting gas bubbles. This gas-segmented micromixer significantly reduces but cannot eliminate the axial dispersion completely due to leakage from the liquid film between the gas bubbles and channel wall. The front-tracking method has been successfully used to model the mixing in microdroplet moving through a serpentine channel, mixing and dispersion in gas-segmented micromixer and the effects of the channel curvature on the liquid film thickness between the gas bubble and channel wall. 2.1. MIXING IN MICRODROPLET
The front-tracking method is used to study the mixing in microdroplet that moves through a serpentine channel. Computations are performed in twodimensional setting in order to facilitate extensive simulations. Although the problem is studied in two-dimensional setting, the flow is time dependent and so time acts as a third dimension making it possible for streamline patterns at one time to cross the streamline patterns at a later time and so produce effective mixing via chaotic trajectories. The channel used in the computation consists of a straight entrance, a sinusoidal mixer and a straight exit section as sketched in Fig. 1. The droplet is placed in the entrance section and passive tracer particles are used to visualize and quantify the mixing. The tracer particles are initially distributed uniformly at random
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within the drop and the particles occupying the lower half of the drop are identified as “white” while the other particles are “black.” These particles are moved with the local flow velocity interpolated from the neighboring computational grid points using the same advection scheme as used for moving the interface marker points. The flow is assumed to be fully developed at the inlet and the pressure is fixed at the outlet. The detailed description of the problem can be found in Ref. [8]. Lm
Li
Le
L dc dd
Figure 1. The sketch of the channel used in the computations.
The evolution of mixing patterns as the droplet moves through the channel is shown in Fig. 2. The capillary number, Reynolds number, viscosity ratio and the bubble size relative to the channel width are set to Ca = 0.025, Re = 6.6, λ = 1 and Λ = 0.76, respectively. This figure clearly shows that chaotic mixing occurs within the droplet. The effects of capillary number are also studied. For this purpose, the computations are performed for the capillary numbers ranging between 0.00625 and 0.2. Figure 3 shows the mixing patterns at the exit of the channel. This figure indicates that the quality of mixing increases as the capillary number increases.
Figure 2. Evolution of mixing patterns as the droplet moves through the channel.
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Ca
0.2
Ca
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0.025
0.0125
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Figure 3. Effects of the capillary number on the mixing patterns at the exit of the channel.
The mixing entropy and intensity of segregation measures are used to quantify the mixing. For this purpose, the droplet area Sd is divided into small Nδ pixels with area of Sδ =δ2 such that Sd = NδSδ. Then a coarsegrained probability density function is defined as Dn = N(n)b/(N(n)b + N(n)w), where N(n)b and N(n)w are the number of black and white particles in nth pixel. The probability density function PDF is then defined as
D =
1 Nδ
Nδ
∑D n =1
=
n
Nδ , Nb + Nw
(1)
where Nb and Nw are total number of black and white particles, respectively. Based on the coarse grained density, the entropy of the mixtures is defined as
s = − D log D = −
1 N
Nδ
∑D n =1
n
log Dn
(2)
The entropy is always positive and has the maximum value of
s o = − D log D ,
(3)
when fluids get fully mixed. The intensity of segregation is defined as
I=
(D −
D
)
2
D (1 − D )
.
(4)
The intensity of segregation has an advantage of varying between zero (compete mixing) and unity (no mixing). Finally the mixing number measure developed by Stone and Stone [21] is also used. Note that the mixing number is independent of grid but it cannot provide any detailed information about the quality of mixing. Figure 4 shows the quantification of mixing for the same case as in Fig. 3. As can be seen in this figure, all the mixing measures are consistent and the quality if mixing increases as the capillary number decreases.
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Figure 4. Effect of the capillary number on mixing. (a) Mixing number, (b) intensity of segregation, (c) PDF, (d) entropy.
The effects of the other parameters can be found in Muradoglu and Stone [8]. 2.2. MIXING IN GAS-SEGMENTED CHANNEL
The front-tracking method is then applied to study mixing in liquid slugs moving through a gas-segmented serpentine channel. The problem is again studied in a two-dimensional setting as shown in Fig. 5. Again passive Li
Lm
Le
L
dc Ld
Figure 5. The sketch of the model serpentine channel used to study the mixing within the liquid slug moving through a gas-segmented serpentine channel.
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tracer particles are used to visualize and quantify the mixing. The molecular mixing is ignored. The particle initially occupying the lower portion of the channel are identified as black while those occupying the upper portion are white. The flow rate is specified at the inlet assuming a fully developed channel flow and the pressure is fixed at the exit. The particles crossing the bubble interfaces or the solid wall due to numerical error are reflected back into the computational domain. Here one sample result is shown as an example and the readers are referred to Dogan et al. [9] for a detailed discussion about this problem. Figure 6 shows the evolution of mixing patterns in the liquid slug. This figure clearly shows that a chaotic mixing occurs within the liquid slug as it moves through the channel. A careful examination also shows that there is some leakage through the liquid film between the gas bubbles and the solid wall even in the absence of molecular mixing and this issue will be discussed in Section 2.4.
Figure 6. Snapshots of mixing patterns for a two-bubble system. The top plots are the enlarged versions of the corresponding scatter plots shown in the channel (lower plots).
2.3. LIQUID FILM BETWEEN GAS BUBBLE AND CHANNEL WALL: EFFECTS OF CHANNEL CURVATURE
We next study the effects of the channel curvature on the liquid film thickness between a bubble that is much larger than the channel size and the channel wall. This problem was originally studied by Bretherton [22] for straight channel case and is generally called a Landau–Levich problem. In studying the mixing in gas-segmented serpentine channel, we observed computationally that the film thickness on the inner and outer walls of the curved channel is not the same and the film thickness on the inner channel is thinner than that on the outer wall. This observation motivated to study the effects of the channel curvature on the liquid film thickness. This problem is again studied in a simple two-dimensional setting and a lubrication analysis is also performed in the limit of vanishing capillary number. The computational setup and the lubrication model are sketched in Fig. 7. Here the results are briefly summarized and the interested readers are referred to
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Muradoglu and Stone [10] for complete information about the lubrication analysis and details of computational study. A simple lubrication analysis indicates that the inner film is thinner than that of the outer film, i.e., the film thickness gets thinner with increasing channel wall curvature. The inner and outer film thicknesses are given by Muradoglu and Stone [10]. wRi 2 1 = Ca ; Re effi = w, 2+β 2Ri + w 2 + β
hi∞ = 1.3375 Re effi Cai2 / 3 ;
Cai =
ho∞ = 1.3375 Re effo Ca
wRo 2 + 2β 1+ β Cao = Ca ; Re effo = w, = 2+β 2 Ro − w 2 + β
2/3 o
;
(5)
where Ca = μUb /σ is the capillary number.
Figure 7. (a) Sketch for motion of a large bubble in curved channel. (b) The lubrication model for the inner wall.
Figure 8a shows the film thickness distribution along the circular channel on the inner and outer walls for Ca = 0.1 and 0.01. This figure clearly shows that the inner layer is thinner than the outer layer as predicted by the lubrication theory. The inner and outer film thicknesses are plotted in Fig. 8b as a function of capillary number together with the Bertherton’s solution for the straight channel. This figure shows that the inner film is thinner while the outer film is thicker than the corresponding film thickness in a straight channel. When the film thicknesses are properly scaled, all the results collapse on the same curve as shown in Fig. 9a. This figure shows that there is a very good agreement between the computational results and the lubrication theory for small capillary numbers. In addition, the scaled film thickness collapses on the same curve as that obtained for the straight channel, i.e., the present theory maps the curved channel into an equivalent straight channel.
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Figure 8. (a) Computed film thickness on the inner and outer walls for Ca = 0.1 and 0.01. The inset shows a portion of computational grid. (b) The Film thicknesses as a function of capillary number.
Figure 9. The film thickness scaled by the effective radius versus the effective capillary number.
2.4. AXIAL DISPERSION IN GAS-SEGMENTED CHANNEL FLOW
Finally the front-tracking method is used to study the axial dispersion caused by the leakage through the liquid film between the gas bubble and the channel wall both in a straight and curved channels. Tracer particles are used for the visualization and quantification of the axial dispersion. The molecular diffusion is modeled by random walk of tracer particles. Figure 10 shows the schematic illustration of axial dispersion in two-bubble system and bubble train. The computational setup is similar to those used in the previous sections so it will not be given here. Interested readers are referred
FRONT-TRACKING METHOD: APPLICATIONS
231
to Muradoglu et al. [7]. Here only a two-bubble system is considered and computations are performed for various values of Peclet number. The results are plotted in Fig. 11.
Figure 10. Schematic illustration of a two-bubble system (top) and a bubble train (bottom).
Finally the effects of the channel curvature on the axial dispersion are examined. It is found that the channel curvature enhances the axial dispersion in gas-segmented serpentine channel and there is significant leakage from the liquid films between the bubble and the curved channel wall even in the absence of molecular diffusion [23]. A lubricating liquid layer forms and persists on the channel wall in the case of straight channel but this lubricating layer is periodically broken in the serpentine channel leading to enhanced axial dispersion. Here only one sample result is presented to show the effects of the channel curvature. Figure 12 shows the effects of the channel curvature on the axial dispersion. In Fig. 12a, the solute concentration within the liquid slug is plotted as a function of time both for straight and curved channels for a range of Peclet numbers at capillary number Ca = 0.01. As can be seen in this figure, the channel curvature generally enhances the leakage through the liquid films but the enhancement is more pronounced at high Peclet numbers. A simple theory is developed based the difference between film thicknesses on the inner and outer walls as discussed in Section 2.3 as well as in Muradoglu and Stone [10] in order to predict the amount of leakage caused solely by the channel curvature [23]. Figure 12b demonstrates that the theory predicts the axial dispersion successfully both for Ca = 0.01 and Ca = 0.005.
M. MURADOGLU
232
a
1 Pe → ∞
0.9 0.8
Pe = 105
0.7 Pe = 103
〈C〉 / 〈C〉 i
0.6
Pe = 104
0.5
Pe = 102
0.4 Pe = 10
0.3 0.2 0.1 0
b
Pe = 0 (Theory) 0
5
10 15 Non-dimensional time, t*
20
25
100 t* = 10 t* = 20
(〈C〉 i − 〈C〉) / 〈C〉 i
10−1 Slope = − 0.641
10−2 Slope = − 0.645
10−3
102
104 Peclet Number, Pe
106
Figure 11. (a) Evolution of tracer concentration in the liquid segment as a function of nondimensional time for various Peclet numbers. (b) Variation of the average tracer concentration as a function of the Peclet number at t* = 10.
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Figure 12. Effects of the channel curvature on the axial dispersion. (a) The variation of solute concentration within liquid slug as a function of time for various Peclet numbers in straight and serpentine channels. (b) Computational results and theoretical predictions in the absence of molecular diffusion for Ca = 0.01 and 0.005.
3. Soluble Surfactants Surfactants are either present as impurities that are difficult to remove from the system or are added deliberately to the bulk fluid to manipulate the interfacial flows [24]. Surfactants may also be created at the interface as a result of chemical reaction between the drop fluid and solutes in the bulk fluid [25, 26]. Surfactants usually reduce the surface tension by creating a buffer layer between the bulk fluid and droplet at the interface. Nonuniform distribution of surfactant concentration creates Marangoni stress at the interface and thus can critically alter the interfacial flows. Surfactants are widely used in numerous important scientific and engineering applications. In particular, surfactants can be used to manipulate drops and bubbles in microchannels [2, 25], and to synthesize micron or submicron size monodispersed drops and bubbles for microfluidic applications [27]. It is a challenging task to model the effects of interfacial flows with soluble surfactants since surfactants are advected and diffused both at the interface and in the bulk fluid by the motion of fluid and by molecular mechanism, respectively. Therefore the evolution equations of the surfactant concentrations at the interface and in the bulk fluid must be solved coupled with the flow equations. The surfactant concentration at the interface alters the interfacial tension and thus alters the flow field in a complicated way. This interaction between the surfactant and the flow field is highly nonlinear and poses a computational challenge.
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The front-tracking method has been recently developed and successfully applied to model the effects of soluble surfactants on the motion and deformation of viscous droplets [13, 14]. Here the method is not described in details but some sample results are presented in order to show the power of the front-tracking method to model this challenging flow problem. Complete information about the numerical method can be found in Ref. [14]. The method is tested for the effects of the soluble surfactants on the motion and deformation of buoyancy-driven gas bubbles. The physical problem is assumed to be axisymmetric and is schematically illustrated in Fig. 13. The bubble is initially clean and placed instantaneously at the centerline near the south boundary in otherwise quiescent ambient liquid. It is well known that contaminated spherical bubble moves much slower than that of a clean bubble and its terminal velocity approaches that of a solid sphere rather than the classical Hadamard–Rybczynski prediction [28]. This phenomena was first explained consistently by Levich [12]. The Marangoni stresses created by the non-uniform surfactant concentration Figure 13. Schematic at the interface act opposite to the viscous stresses illustration of the computand tries to immobilize the interface, which results ational setup. in no slip boundary conditions at the interface like a solid sphere. Figure 14a shows the terminal Reynolds number of clean and contaminated bubbles for various droplet sizes relative to the channel diameter. This figure clearly shows the retardation effect of the surfactants. The computed steady Reynolds number is plotted in Fig. 14b as a function of the channel confinement D/d and compared to the available experimental data collected by Clift et al. [28] both for the clean and contaminated cases. It is interesting to observe that the steady terminal Reynolds number of the contaminated bubble is significantly smaller than that of the clean bubble and approaches the steady Reynolds number of a solid sphere. The rigidifying effect of surfactant can also be seen in Fig. 15 where the velocity vectors and streamlines are plotted in the reference frame moving with the bubble centroid. Finally the effects of the elasticity number are demonstrated in Fig. 16 for an ellipsoidal bubble. Complete description of the numerical method and effects of the soluble surfactant on the buoyancy-driven bubble can be found in Refs. [13, 14].
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Figure 14. Reynolds number vs. nondimensional time for D/d = 1.6, 2.5, 5, 7.5, 10, and 15, and (b) steady Reynolds number vs. non-dimensional channel diameter for clean (solid lines) and contaminated (dashed lines) bubbles (Eo = 1 and Mo = 0.1).
Figure 15. Spherical bubble. The streamlines and the velocity vectors at steady-state in a coordinate system moving with the bubble centroid for (a) a clean bubble and (b) a contaminated bubble. Every third grid points are used in the velocity vector plots (Eo = 1 and Mo = 0.1).
Figure 16. Ellipsoidal bubble. (Top row) The contour plots of the constant surfactant concentration in the bulk fluid (left side) and the distribution of the surfactant concentration at the interface (right side).
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4. Modeling Contact Line Impact and spreading of a viscous droplet on solid wall is of fundamental importance in many engineering and natural processes including ink-jet printing, spray coating, DNA microarrays, spray cooling and fuel injection in engines [29]. It also finds applications in emerging technologies such as single cell epitaxi [17]. The three-phase moving contact line is a notoriously difficult problem involving highly complicated physical processes and offers a challenge for computational models. During the collision and till the equilibrium, droplet passes various phases in which inertial, viscous, capillary, and contact line forces are dominant. It is well known that the noslip boundary condition yields stress singularity at the contact line since the fluid velocity is finite at the free-surface but zero on the wall [29]. This singularity is usually removed by relaxing the no-slip boundary condition with a slip model. Although numerous models and solutions to this problem have been proposed, we are still far from reaching a consensus for a definitive answer [29]. Direct numerical simulation of interfacial flows is a formidable task mainly due to the presence of moving and deforming interface. The existence of the contact line makes the problem even more complicated. The front-tracking method has been recently extended to treat the moving contact line [19] and successfully applied to model single cell epitaxi [30]. The model is briefly described here and some sample results are presented. Figure 17 shows the computational setup and treatment of the contact line in the framework of front-tracking algorithm for an axisymmetric droplet collision. The droplet is assumed to connect the substrate when it crosses the threshold distance hth using either a linear or cubic extrapolation function as shown in the inset of Fig. 17b. The contact angle is determined dynamically and imposed explicitly. The experimental correlation collected by Kistler [31] is used to determine the dynamic contact angle in the same way as done by Sikalo et al. [32]. The method is first tested for droplet impact and relaxation to its final equilibrium shape. This is a simple test but provides significant information about the accuracy of the contact line treatment. For this test problem, computations are performed for a range of Eotvos number (Eo) that represents the importance of gravitational force relative to the surface tension force. The computational results are plotted in Fig. 18 where the analytical solutions are also shown for the limiting cases of Eo = 0 (no gravitational effects) and Eo →∞ (gravitational effects are dominant). It is seen that there is excellent agreement between the computational results and the analytical solutions in the limiting cases and there is smooth transition in between. This figure indicates that the front-tracking method predicts the final equilibrium shapes of the droplet for a wide range of Eotvos numbers.
FRONT-TRACKING METHOD: APPLICATIONS
(a)
237
(b)
Figure 17. (a) Schematic illustration of the computational setup. (b) Treatment of the contact line.
After the static test mentioned above, the method is now tested for the impact and spreading of a glycerin droplet on a wax substrate and the computational results are compared with the experimental data of Sikalo et al. [32]. The details of the experimental setup, material properties and computational model can be found in Refs. [33, 51]. The computed and experimental spread factor and contact line are plotted in Figs. 19a and b, respectively. These figures show that the present front-tracking method is a viable tool for simulation of interfacial flows involving moving contact lines. Finally the method is applied to study the impact and spreading of a compound droplet on a flat substrate as a model for the single cell epitaxi [17]. The single cell epitaxi is an emerging technology that utilizes the conventional inkjet printing technology to print biological cells precisely on a substrate in order to create 2D and 3D tissue. The purpose of the present model is to understand the complicated impact dynamics of droplet encapsulated biological cell and determine the optimal conditions for cell viability. In this model, the inner and outer droplets represent the biological cell and the encapsulating droplet, respectively. The biological cell is modeled as a highly viscous Newtonian droplet as a first step in developing a more realistic model in which the biological cell will be treated as a nonNewtonian fluid. Figure 20 shows an example simulation of the compound droplet model. This figure demonstrates the power of the numerical simulation that provides detailed information about the pressure contours and pressure distribution on the inner droplet (biological cell). The deformation and rate of deformation of the inner droplet are also plotted in Fig. 21 for various impact Reynolds numbers.
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Figure 18. The normalized static droplet height versus Eotvos number in the range Eo = 0:01 and Eo = 64. Solid and dashed lines denote the analytical solutions for the limiting cases of Eo ≪ 1 and Eo ≫ 1, respectively. The inset shows the initial conditions for the droplet relaxation test. 2.5
180
Exp. (Sikalo et al.) We = 802 Re = 106 We = 93 Re = 36 We = 51 Re = 27
160 2 Contanct Angle
140
R/R0
1.5 1 Exp. (Sikalo et al.) We = 802 Re = 106 We = 93 Re = 36 We = 51 Re = 27
0.5 0
0
2
6
4
8
120 100 80 60 40 20
10
0
0
2
4
6
t Vcol /D
t Vcol / D
(a)
(b)
8
10
Figure 19. Glycerin droplet spreading on the wax substrate. Time evolution of (a) the spread factor and (b) the dynamic contact angle.
FRONT-TRACKING METHOD: APPLICATIONS
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Figure 20. Evolution of compound droplet impacting on a flat surface (left half: pressure contours and right half: pressure distribution on the surface of the cell). Time evolves from left to right and from top to bottom.
Figure 21. Deformation and rate of deformation vs. nondimensional time for Re = 15, 20, 30, 40 and 45.
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5. Conclusions The front-tracking method developed by Unverdi and Tryggvason [34] has been successfully applied to interfacial flow problems encountered or inspired by microfluidic systems. It has been shown that the method can be used to study mixing in a micro-droplet moving through a serpentine channel, mixing within liquid slugs in gas-segmented serpentine channel, the effects of channel curvature on the Landau–Levich problem, axial dispersion, soluble surfactants and moving contact lines. The explicit tracking of the interface eliminates excessive numerical dissipation that frontcapturing methods such as VOF and level-set suffer and this feature makes the front-tracking method especially useful in microfluidic applications where it is often required to resolve thin fluid layers. Another important advantage of the front-tracking method is its ability to incorporate multiphysics effects such as thermocapillary, electric field, soluble surfactants, moving contact lines, chemical reactions etc. In this chapter, a few applications involving the multiphysics effects are presented as examples but more such applications can be found in the literature. The front-tracking method is only one example of computational tools that can be used in analysis and design of microfluidic systems. The computational methods for multiphase/fluid flows have been matured enough that they can be safely used as a design tool in microfluidics. In addition, they can be also very useful to discover or understand new flow physics emerging from the miniaturization of flow systems. Acknowledgement This work is supported by Turkish Academy of Sciences through GEBIP program.
References 1. G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, and Y.-J. Jan. A Front-Tracking Method for the Computations of Multiphase Flow, J. Comput. Phys., 169, 708–759 (2001). 2. H.A. Stone, A.D. Stroock, and A. Ajdari. Engineering Flows in Small Devices: Microfluidics Toward a Lab-on-a-Chip, Annu. Rev. Fluid Mech., 36 (2004). 3. T.M. Squires and S.R. Quake, Microfluidics: Fluid Physics at the Nanoliter Scale, Rev. Modern Phys., 77(3), 977–1026 (2005). 4. M.R. Bringer, C.J. Gerdts, H. Song, J.D. Tice, and R.F. Ismagilov, Microfluidic Systems for Chemical Kinetics That Rely on Chaotic Mixing in Droplets, Philos. Trans. R. Soc. London, Ser. A 362, 1087 (2004).
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5. H. Song, J.D. Tice, and R.F. Ismagilov, A Microfluidic System for Controlling Reaction Networks in Time, Angew. Chem., Int. Ed., 42 (2003). 6. A. Guenther, S.A. Khan, M. Thalmann, F. Trachsel, and K.F. Jensen, Transport and Reaction in Microscale Segmented Gas-Liquid Flow, Lab. Chip. 4 (2004). 7. M. Muradoglu, A. Guenther and Stone, A Computational Study of Axial Dispersion in Segmented Gas-Liquid Flow, Phys. Fluid, 19, 072109 (2007). 8. M. Muradoglu and Stone, Mixing in a Drop Moving Through a Serpentine Channel: A Computational Study, Phys. Fluid, 17, 073305 (2005). 9. H. Dogan, S. Nas, and M. Muradoglu, Mixing of Miscible Liquids in GasSegmented Serpentine Channels, Int. J. Multiphase Flow (in press) (2009). 10. M. Muradoglu and Stone, Motion of Large Bubbles in Curved Channels, J. Fluid Mech. 570 (2007). 11. I. Filiz and M. Muradoglu, A Computational Study of Drop Formation in an Axisymmetric Flow-Focusing Device, Proceedings of ASME, ICNMM2006, 4th International Conference on Nanochannels, Microchannels and Minichannels, June 19–21, Limerick, Ireland (2006). 12. A.A. Frumkin and V.G. Levich, On Surfactants and Interfacial Motion, Zh. Fiz. Khim. 21, 1183 (1947). 13. S. Tasoglu, U. Demirci, and M. Muradoglu, The Effect of Soluble Surfactant on the Transient Motion of a Buoyancy-Driven Bubble, Phys. Fluids, 20, 040805 (2008). 14. M. Muradoglu and G. Tryggvason, A Front-Tracking Method for Computation of Interfacial Flows with Soluble Surfactants, J. Comput. Phys., 227(4), 2238– 2262 (2008). 15. S. Nas and G. Tryggvason, Thermocapillary Interaction of Two Bubbles or Drops, Int. J. Multiphase Flow, 29 (2003). 16. S. Nas, M. Muradoglu, and G. Tryggvason, Pattern Formation of Drops in Thermocapillary Migration, Int. J. Heat Mass Trans., 49(13–14), 2265–2276 (2006). 17. U. Demirci and G. Montesano, Single Cell Epitaxy by Acoustic Picoliter Droplets, Lab on a Chip, 7 (2007). 18. S. Wiggins and J.M. Ottino, Foundations of Chaotic Mixing, Philos. Trans. R. Soc. London, Ser. A 362, 1087 (2004). 19. H. Aref, Stirring by Chaotic Advection, J. Fluid Mech., 143, 1 (1984). 20. G.I. Taylor, Deposition of Viscous Fluid on the Wall of a Tube, J. Fluid Mech., 10, 161 (1961). 21. Z.B. Stone and H.A. Stone, Imaging and Quantifying Mixing in a Model Droplet Micromixer, Phys. Fluids, 17, 063103 (2005). 22. F.P. Bretherton, The Motion of Long Bubbles in Tubes, J. Fluid Mech. 10, 166–188 (1961). 23. M. Muradoglu, Axial Dispersion in Segmented Gas-Liquid Flow: Effects of Channel Curvature, preprint to be submitted (2009). 24. H.A. Stone, Dynamics of Drop Deformation and Breakup in Viscous Fluids, Annu. Rev. Fluid Mech., 26 (1994). 25. M. Faivre, T. Ward, M. Abkarian, A. Viallat, and H.A. Stone, Production of Surfactant at the Interface of a Flowing Drop: Interfacial Kinetics in a
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26. 27. 28. 29. 30. 31. 32. 33. 34.
M. MURADOGLU Microfluidic Device, in: 57th APS Division of Fluid Dynamics Meeting, Seattle, WA, USA (2004). E.A. van Nierop, A. Ajdari, and H.A. Stone, Reactive Spreading and Recoil of Oil on Water, Phys. Fluids, 18(3), Art. No. 03810 (2006). S.L. Anna and H.C. Meyer, Microscale Tip Streaming in a Microfluidic Flow Focusing Device, Phys. Fluids, 18(12), Art. No. 12151 (2006). R. Clift, J.R. Grace, and M.E. Weber, Bubbles, Drops and Particles, Dover, Mineola (2005). A.L. Yarin, Drop Impact Dynamics: Splashing, Spreading, Receding, Bouncing ..., Annu. Rev. Fluid Mech. 38, 159–192 (2006). S. Tasoglu1, G. Kaynak, U. Demirci, A.J. Szeri, and M. Muradoglu, Impact of a Compound Droplet on a Flat Surface: A Model for Single Cell Epitaxi, preprint to be submitted (2009). S.F. Kistler, Hydrodynamics of Wetting, in: Wettability, edited by J.C. Berg, Marcel Dekker, New York (1993). S. Sikalo, H.D. Wilhelm, I.V. Roisman, S. Jakirlic, and C. Tropea, Dynamic Contact Angle of Spreading Droplets: Experiments and Simulations, Phys. Fluids, 17, 062103 (2005). M. Muradoglu and S. Tasoglu, A Front-Tracking Method for Computational Modeling of Impact and Spreading of Viscous, Droplets on Solid Walls, Comput. Fluids (in press) (2009). S.O. Unverdi, G. Tryggvason, A Front-Tracking Method for Viscous Incompressible Multiphase Flows, J. Comput. Phys., 100 (1992).
GAS FLOWS IN THE TRANSITION AND FREE MOLECULAR FLOW REGIMES A. BESKOK
Aerospace Engineering Department Old Dominion University, Norfolk, VA 23529,USA,
[email protected]
Abstract. We investigate pressure driven flow in the transition and freemolecular flow regimes with the objective of developing unified flow models for channels and ducts. These models are based on a velocity scaling law, which is valid for a wide range of Knudsen number. Simple slip-based descriptions of flowrate in channels and ducts are corrected for effects in the transition and free-molecular flow regimes with the introduction of a rarefaction coefficient. The resulting models can predict the velocity distribution, mass flowrate, pressure and shear stress distribution in rectangular ducts in the entire Knudsen flow regime.
1. Introduction In this chapter we develop a unified flow model that predicts the velocity profiles, and mass flowrate in two-dimensional channels and ducts in the entire Knudsen regime. Our approach is divided into two main steps: First, we will analyze the nondimensional velocity profile to identify the shape of the velocity distribution. Then, we will obtain the magnitude of the average velocity, and hence, obtain a prediction for the flowrate. 2. Velocity Scaling From the DSMC results and solutions of the linearized Boltzmann equation, it is evident that the velocity profiles in pipes, channels and ducts remain approximately parabolic for a large range of Knudsen number. This is also consistent with the analysis of the Navier–Stokes and Burnett equations in long channels, as documented in Ref. [1]. Based on this observation, we model the velocity profile as parabolic in the entire Knudsen regime, with a consistent slip condition. We write the dimensional form for velocity distribution in a channel of height h, S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_13, © Springer Science + Business Media B.V. 2010
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244
U ( x, y ) = F (
⎤ ⎡ ⎛ y ⎞2 ⎛ y ⎞ dP , μ o , h, λ ) ⎢ − ⎜ ⎟ + ⎜ ⎟ + U s ⎥ , dx ⎦⎥ ⎣⎢ ⎝ h ⎠ ⎝ h ⎠
where F (dP/dx, μ0, h, λ) shows the functional dependence of velocity on the pressure gradient, viscosity, channel height, and local mean free path. Temperature is assumed to be constant, and therefore the dynamic viscosity is also a constant. Here Us is the slip velocity, which satisfies the general slip boundary condition given by
Us −Uw =
1 − σ v ⎡ Kn ⎛ ∂U ⎞ ⎤ ⎜ ⎟ , σ v ⎢⎣1 − bKn ⎝ ∂n ⎠ s ⎥⎦
(1)
where b is the general slip coefficient [1]. Using this boundary condition yields
U ( x, y ) = F (
⎡ ⎛ y ⎞ 2 ⎛ y ⎞ ⎛ 2 − σ v ⎞ Kn ⎤ dP ⎟⎟ , μo , h, λ ) ⎢− ⎜ ⎟ + ⎜ ⎟ + ⎜⎜ ⎥. dx ⎢⎣ ⎝ h ⎠ ⎝ h ⎠ ⎝ σ v ⎠ 1 − bKn ⎥⎦
Assuming this form of velocity distribution, the average velocity in the channel ( U = Q& / h ) can be obtained as
U ( x) = F (
⎡ 1 ⎛ 2 − σ v ⎞ Kn ⎤ dP ⎟⎟ , μo , h, λ ) ⎢ + ⎜⎜ ⎥. 6 σ dx v ⎝ ⎠ 1 − bKn ⎦ ⎣
By nondimensionalizing the velocity distribution with the local average velocity, dependence on the local flow conditions F (dP/dx, μ0, h, λ) is eliminated. Therefore, the resulting relation is a function of Kn and y only. Assuming diffuse reflection (σv = 1) for simplicity, we obtain
⎡ ⎛ y ⎞2 ⎛ y ⎞ Kn ⎤ ⎥ ⎢− ⎜ ⎟ + ⎜ ⎟ + h h 1 − bKn ⎥ . U * ( y, Kn) = U ( x, y ) / U ( x) = ⎢ ⎝ ⎠ ⎝ ⎠ 1 Kn ⎥ ⎢ + ⎥ ⎢ 6 1 − bKn ⎦ ⎣
(2)
Equation (2) solely describes the shape of the velocity distribution, but it does not properly model the flowrate, which requires additional corrections, as will be shown in the next section.
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In Fig. 1 we plot the nondimensional velocity variation obtained in a series of DSMC simulations for Kn = 0.1, Kn = 1, Kn = 5, and Kn = 10. We also included the corresponding linearized Boltzmann solutions obtained in Ref. [2]. It is seen that the DSMC velocity distribution and the linearized Boltzmann solutions agree quite well. We can now use Eq. (2) and compare with the DSMC data by varying the parameter b, which for b = 0 corresponds to Maxwell’s first-order and for b = −1 to the second-order boundary condition in the slip regime only. Here we find that for b = −1, Eq. (2) results in an accurate model of the velocity distribution for a wide range of Knudsen number. From the figure, it is clear that the velocity slip is slightly overestimated with the proposed model for the Kn = 1 case. To obtain a better velocity slip, we varied the value of the parameter b by imposing, for example, b = −1.8 for the Kn = 1 case. Although a better agreement is achieved for the velocity slip, the accuracy of the model in the rest of the channel is destroyed.
− U(Y) /U
1.2
0.8
0.4
Kn = 0.1 0
0.2
b = −1 b=0 b = −1.8
Kn = 1.0 0.4
0.6
0.8
1
0
0.2
0.4
Y
0.6
0.8
1
Y
− U(Y) /U
1.2
0.8
DSMC Lin. Boltzmann
0.4 Kn = 5.0 0
0.2
Kn = 10.0 0.4
0.6 Y
0.8
1
0
0.2
0.4
0.6
0.8
1
Y
Figure 1. Velocity profile comparisons of the model (Eq. (2)) with DSMC and linearized Boltzmann solutions [2]. Maxwell’s first-order boundary condition is shown with dashed lines (b = 0), and the general slip boundary condition (b = −1) is shown with solid lines.
In Fig. 2 we show the nondimensionalized velocity distribution along the centerline and along the wall of the channels for the entire Knudsen number regime considered here, i.e., 0.01 ≤ Kn ≤ 30. We included in the
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plot data for the velocity slip and centerline velocity from 20 different DSMC runs, 15 for nitrogen (diatomic molecules) and 5 for helium (monatomic molecules). The differences between the nitrogen and helium simulations are negligible, and thus this velocity scaling model is independent of the gas type. The linearized Boltzmann solution of Aoki for a monatomic gas is also shown by triangles. This solution closely matches the DSMC predictions. Maxwell’s first-order boundary condition (b = 0) (shown by a solid line) erroneously predicts a uniform nondimensional velocity profile for large Knudsen number. The breakdown of slip flow theory based on the first-order slip boundary condition is realized around Kn = 0.1 and Kn = 0.4 for the wall and the centerline velocity, respectively. This finding is consistent with the commonly accepted limits of the slip flow regime. The prediction using b = −1 is shown by small dashed lines. The corresponding centerline velocity closely follows the DSMC results, while the slip velocity of the model with b = −1 deviates from DSMC in the intermediate range for 0.1 < Kn < 5. One possible reason for this is the effect of the Knudsen layer, a sublayer that is present between the viscous boundary layer and the wall, with a thickness of approximately one mean free path. For small Kn flows the Knudsen layer is thin and does not affect the velocity slip prediction too much. For very large Kn flows, the Knudsen layer covers the entire channel. However, for intermediate Kn values both the fully developed viscous flow (boundary layer) and the Knudsen layer exist in the channel. At this intermediate range, approximating the velocity profile to be parabolic neglects the Knudsen layers. For this reason, the model with b = −1 results in 10% error of the velocity slip at Kn = 1. However, the velocity distribution in the rest of the channel is described accurately for the entire flow regime. For a comparison we also included similar predictions by the secondorder slip boundary condition of Hsia and Domoto (large dashed line). The form of their boundary conditions is similar to Cercignani’s, Deissler’s, and Schamberg’s, and they all become invalid at around Kn = 0.1. This boundary condition performs worse than even the first-order Maxwell’s boundary condition for large Kn values. Only the general slip boundary condition predicts the scaling of the velocity profiles accurately. 3. Flowrate Scaling The volumetric flowrate in a channel is a function of the channel dimensions, fluid properties (μ0, λ), and pressure drop, and it can be written as
⎛ dP ⎞ Q& = G⎜ , μ o , h, λ ⎟ . ⎝ dx ⎠
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For a channel of height h, using the Navier–Stokes solution and the general slip boundary condition (1) we obtain
h 3 dP ⎡ 6 Kn ⎤ , Q& = − 1+ ⎢ 12 μ o dx ⎣ 1 − bKn ⎥⎦
(3)
where Kn = λ/h. 1.5
−
U/U
1
0.5
Lin. Botz. DSMC Data b=0 b = −1 b = −2 Hsia & Domoto
0 0.01
0.05
0.1
0.5
1
5
10
Kn
Figure 2. Velocity scaling at wall and centerline of the channels for slip and transition flows. The linearized Boltzmann solution of Aoki is shown by triangles, and the DSMC simulations are shown by points. Theoretical predictions of velocity scaling for different values of b, and Hsia and Domoto’s second-order slip boundary condition are also shown.
The flowrate for the continuum and free-molecular flows are both linearly dependent on dP/dx [3], and thus we choose to normalize the flowrate with the pressure gradient. This quantity is computed based on the DSMC simulations and is shown in Fig. 3 for nitrogen. For comparison we present the Q& / |dP/dx| predictions obtained using Maxwell’s first-order slip boundary condition (b = 0, dashed lines) and the general slip boundary condition (b = −1, dashed-dotted lines). In both cases the predictions are erroneous. The general slip boundary condition performs the worst for it is asymptotic to a constant value, while the DSMC data show a considerable
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increase with Kn. The first-order boundary condition follows the DSMC data, however with a significant error. The model in Eq. (1) gives good agreement with DSMC data and the linearized Boltzmann solutions for the nondimensional velocity profile, but it does not predict correctly the flowrate. This is expected, since the Navier– Stokes equations are invalid in this regime. In fact, the dynamic viscosity, which defines the diffusion of momentum due to the intermolecular collisions, must be modified to account for the increased rarefaction effects. The kinetic theory description for dynamic viscosity requires μ 0 ≈ λ v ρ where v is the mean thermal speed. Using mean free path λ in this relation is valid as long as intermolecular collisions are the dominant part of momentum transport in the fluid (i.e., Kn << 1). However, for increased rarefaction, the intermolecular collisions are reduced significantly, and in the free-molecular flow regime, only the collisions of the molecules with the walls should be considered. Therefore, in free-molecular channel flow the diffusion coefficient should be based on characteristic length scale h (channel height) and thus μ 0 ≈ hv ρ [4]. Since the diffusion coefficient is based on λ in slip or continuum flow regimes and h in the free-molecular flow regime, we propose to model the variation of diffusion coefficient with the following hybrid formula:
⎤ ⎡ ⎢ 1 ⎥ ⎡ 1 ⎤ = ρv λ ⎢ μ ≈ ρv ⎢ , ⎥ 1 1 ⎣1 + Kn ⎥⎦ ⎢ + ⎥ ⎣h λ ⎦ which can be simplified to
⎡ 1 ⎤ , ⎣1 + Kn ⎥⎦
μ ( Kn) = μo ⎢
(4)
where μ0 is the dynamic viscosity of the gas at a specified temperature and μ is the generalized diffusion coefficient. The variable diffusion coefficient model presented above is based on a simple analysis. In general, the increased rarefaction effects in our flowrate model can be taken into account by introducing a correction expressed as rarefaction coefficient Cr(Kn), which is a function of the Knudsen number. The flowrate is then obtained as
h 3 dP ⎡ 6 Kn ⎤ h 3 dP ⎡ 6 Kn ⎤ Q& = − 1 1 Cr ( Kn) , (5) + == − + 12 μ dx ⎢⎣ 1 − bKn ⎥⎦ 12 μ 0 dx ⎢⎣ 1 − bKn ⎥⎦
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where Cr(Kn) is a general function of Knudsen number. A possible model for Cr is suggested by Eq. (4) as
Cr ( Kn) = 1 + αKn ,
(6)
where α is a parameter. If we assume that α is constant in the entire Knudsen regime, the flowrate in the slip flow regime will be erroneously enhanced, resulting in
Figure 3. Volumetric flowrate (per channel width) per absolute value of the pressure gradient in (m3/(sPa)) as a function of Kn for nitrogen flow. The solid line represents the proposed model.
M& = 1 + (6 + α ) Kn + O( Kn 2 ) , & Mc where M& c corresponds to continuum mass flowrate. This model becomes inaccurate for a nonzero value of α in the slip flow regime. Moreover, in the free-molecular flow regime, for very long channels (L >> λ >> h) there are no physical values for α, since the flowrate increases logarithmically with
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Kn. For finite-length channels the flowrate is asymptotic to a constant value proportional to loge(L/h). Therefore, for finite-length two-dimensional channel flows, the coefficient α should smoothly vary from zero in the slip flow regime to an appropriate constant value in the free-molecular flow regime. The physical meaning of this behavior is that the dynamic viscosity remains the standard diffusion coefficient in the early slip flow regime. The value of α increases slowly with Kn in the slip flow regime, and therefore the effect of change of the diffusion coefficient is second-order in Kn. For this reason the experimental slip flow results are accurately predicted by the slip flow theory, which does not require change of the diffusion coefficient length scale from λ to channel height h. Variation of α as a function of Kn can be represented accurately with the following relation:
α = αo
2
π
(
)
tan −1 α1Kn β ,
(7)
where αo is determined to result in the desired free-molecular flowrate. Note that the values for α1 and β are the only two undetermined parameters of the model. 4. Model for Duct Flows The asymptotic values of the flowrate for duct flows at high Knudsen number are constants depending on the duct aspect ratio. This offers the possibility of obtaining a model for the rarefaction coefficient Cr(Kn) and in particular the coefficient α. The objective is to construct a unified expression for α (Kn) that represents the transition of α from zero in the slip flow regime to its asymptotic constant value in the free-molecular flow regime. We consider flows in ducts with aspect ratio (AR = w/h ≡ width/height) of 1, 2, and 4. The data are obtained by linearized Boltzmann solution in ducts with the corresponding aspect ratios. Our previous analysis was valid for the two-dimensional channels, where we reported flowrate per channel width. For duct flows, three-dimensionality of the flow field (due to the side walls of the duct) must be considered. In continuum duct flows, the flowrate formula developed for two-dimensional channel flows is corrected in order to include the blockage effects of the side walls. According to this, the volumetric flowrate in a duct with aspect ratio AR for no-slip flows is (see [5], p. 120)
wh ⎛ dP ⎞ Q& = C ( AR) ⎜− ⎟, 12 μ ⎝ dx ⎠ 3
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where C(AR) is the correction factor given as
⎡ 192( AR ) ∞ tanh(iπ 2( AR )) ⎤ C ( AR ) = ⎢1 − ∑ ⎥. π 5 i =1,3,5,... i5 ⎦ ⎣
(8)
With this correction, aspect ratios of 1, 2, and 4 ducts correspond to 42.17%, 68.60%, and 84.24% of the theoretical two-dimensional channel volumetric flowrate for no-slip flows, respectively. According to the new model, the volumetric flowrate for rarefied gas flows in ducts is
wh3 ⎛ dP ⎞ 6 Kn ⎞ ⎛ & Q = C ( AR) ⎜− ⎟(1 + αKn)⎜1 + ⎟, 12μ 0 ⎝ dx ⎠ ⎝ 1 − bKn ⎠ where the correction factor C(AR) is independent of the Knudsen number. The variation of α as a function of Kn is calculated by using the correction factors (C(AR)), the linearized Boltzmann solutions, and our model. This variation is given in Fig. 4. The rarefaction coefficient (Cr(Kn) = 1 + αKn) was introduced in order to model the reductions in the intermolecular collisions of the molecules as Kn is increased. In duct flows, both the height and the width of the duct are important length scales, and comparison of these length scales to the local mean free path is an important factor in the variation of α. It is seen in Fig. 4 that the transition in α occurs later for high aspect ratio ducts. An approximate formula can be derived to describe the mass flowrate in ducts of various aspect ratios as
⎛ 6 Kn ⎞ M& ⎟⎟ , ( AR)(1 + α Kn)⎜⎜1 + = C M& c ⎝ 1 − b Kn ⎠ where Kn is evaluated at average pressure. In Fig. 5 we present the variation of flowrate nondimensionalized with the corresponding no-slip value as a function of Kn in the slip and early transitional flow regimes. The linear increase of the flowrate with Kn and complete description of rarefied duct flows with the introduction of the correction factor C(AR) are observed. The slope of the nondimensionalized mass flowrate increases gradually with Kn. This is attributed to the gradual change in the rarefaction coefficient as presented in Fig. 4.
A. BESKOK
252 1.8 1.6 1.4 1.2
a
1 0.8 0.6 0.4 AR = 4 0.2
AR = 2 AR = 1
0 0.01
0.1
1
10
100
Kn
Figure 4. Variation of α as a function of Kn for various aspect ratio ducts.
˙C ˙ /M M
3
2
1 AR = ¥ AR = 4 AR = 2 AR = 1 0
0
0.1
0.2
0.3
0.4
Kn
Figure 5. Normalized flowrate variation in the slip and early transitional flow regimes for various aspect ratio (AR) duct flows. Symbols show the linearized Boltzmann solutions. Comparisons with the proposed model are also presented by lines.
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For the free-molecular scaling of the data we nondimensionalized the flowrate with
h 2 w ΔP , M& FM = 2 RT0 L which gives the correct order of magnitude for the flowrate. The exact value of the free-molecular flowrate in rectangular ducts is given by Thompson and Owens [7]
M& FM (h, w) = ΓM& FM ,
(9)
where 2 2 ⎛w ⎛h ⎛ w ⎞ ⎞⎟ ⎛ h ⎞ ⎞⎟ 2 ⎜ ⎜ + 1+ ⎜ ⎟ Γ = h w loge + 1 + ⎜ ⎟ + w h log e ⎜h ⎜w w⎠ ⎟ ⎝ h ⎠ ⎟⎠ ⎝ ⎝ ⎠ ⎝ , 2 2 3/ 2 3 3 (h + w ) h +w − + 3 3 2
where h and w are the height and width of the rectangular duct. For the aspect ratios (AR) of 1, 2, and 4 the above relation results in 0.8387, 1.1525, and 1.5008 times the free-molecular mass flowrate M& FM , respectively. Nondimensionalizing the model with the free-molecular mass flowrate & ( M FM ), we obtain
(1 + α Kn) ⎛ 6 Kn ⎞ M& ⎜⎜1 + ⎟, = C ( AR) & M FM 6 Kn ⎝ 1 − b Kn ⎟⎠ ___
where Kn is evaluated at channel average pressure. In Fig. 6 we present the variation of the nondimensionalized flowrate as a function of Kn. The duct flow data are due to Sone, and the two-dimensional channel data (shown by AR = ∞) are due to Sone (for Kn ≤ 0.17) and Cercignani (Kn > 0.17). Comparisons are made against the linearized Boltzmann solutions. For duct flows, good agreement of the model with the numerical data in the entire flow regime is obtained. The model is also able to capture Knudsen’s minimum accurately. The parameters used in the model are given in Table 1 for various aspect ratio channels. Note that α0 is
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determined from the asymptotic constant limit of flowrate (9) as Kn → ∞. Variation of α as a function of Kn, is modeled using Eq. (7) with α1 and β values given in Table 1. 5. Conclusions We developed a unified flow model that can accurately predict the volumetric flowrate, velocity profile, and pressure distribution in the entire Knudsen regime for rectangular ducts. The new model is based on the hypothesis that the velocity distribution remains parabolic in the transition flow regime, which is supported by the asymptotic analysis of the Burnett equations [1]. The general velocity slip boundary condition and the rarefaction correction factor are the two primary components of this unified model.
AR = ¥
10 9 8
AR = 4 AR = 2
7
AR = 1
6 5
˙ /M ˙ FM M
4
3
2
1 0.9 0.8 0.7 0.01
0.1
1
10
100
Kn
Figure 6. Free-molecular scaling of linearized Boltzmann solutions for duct flows of various aspect ratio. Comparisons with the proposed model are also presented by lines corresponding to different aspect ratios.
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The general slip boundary condition gives the correct nondimensional velocity profile, where the normalization is obtained using the local channel averaged velocity. This eliminates the flowrate dependence in modeling the velocity profile. For channel flows, we obtain b = −1 in the slip flow regime. Evidence based on comparisons of the model with the DSMC and Boltzmann solutions shows that b = −1 is valid in the entire Knudsen regime. In order to model the flowrate variations with respect to the Knudsen number Kn, we introduced the rarefaction correction factor as Cr =1+α Kn. This form of the correction factor was justified using two independent arguments: first, the apparent diffusion coefficient; and second, the ratio of intermolecular collisions to the total molecular collisions. We must note that α cannot be a constant. Physical considerations to match the slip flowrate require α → 0 for Kn ≤ 0.1, while α → αo in the free molecular flow regime. The variation of α between zero and a known αο value is approximated using Eq. (7) which introduced two empirical parameters α1 and β to the new model. Therefore, the unified model employs two empirical parameters (α1 and β) and two known parameters b = −1 and αo. Although this empiricism is not desired, the α value in Cr varies from zero in the slip flow regime to an order-one value of αo as Kn → ∞. Finally, the model is adapted to the finite aspect ratio rectangular ducts using a standard aspect ratio correction given in Eq. (7). TABLE 1. Parameters of the model for various aspect ratio duct flows. The only free parameters are α1 and β, as α0 is determined from the asymptotic constant limit of flowrate as Kn → ∞ .
(AR) = w/h 1 2 4
C(AR) 0.42173 0.68605 0.84244
α0 1.7042 1.4400 1.5272
α1 8.0 3.5 2.5
β 0.5 0.5 0.5
References 1. 2.
A. Beskok and G.E. Karniadakis. A model for flows in channels, pipes and ducts at micro and nano scales. Microscale Thermophys. Eng., 3(1):43–77 (1999). T. Ohwada, Y. Sone, and K. Aoki. Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard sphere molecules. Phys. Fluids A, 1(12):2042– 2049 (1989).
256 3. 4. 5. 6. 7.
A. BESKOK E.H. Kennard. Kinetic Theory of Gasses. McGraw-Hill Book Co. Inc., New York (1938). W.G. Polard and R.D. Present. On gaseous self-diffusion in long capillary tubes. Phys. Rev., 73 (7):762–774, April (1948). F.M. White. Viscous Fluid Flow. McGraw-Hill International Editions, Mechanical Engineering Series (1991). S. Loyalka and S. Hamoodi. Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation. Phys. Fluids A, 2 (11):2061– 2065 (1990). S.L. Thompson and W.R. Owens. A survey of flow at low pressures. Vacuum, 25:151–156 (1975).
MIXING IN MICROFLUIDIC SYSTEMS A. BESKOK Aerospace Engineering Department Old Dominion University, Norfolk, VA 23529, USA,
[email protected]
Abstract. Flow and species transport in micro-scales experience laminar, even Stokes flow conditions. In absence of turbulence, species mixing becomes diffusion dominated, and requires very long mixing length scales (lm). This creates significant challenges in the design of Lab-on-a-chip (LOC) devices, where mixing of macromolecules and biological species with very low mass diffusivities are often desired. The objectives of this chapter are to introduce concepts relevant to mixing enhancement in microfluidic systems, and guide readers in the design of new mixers via numerical simulations. A distinguishing feature is the identification of flow kinematics that enhance mixing, followed with systematic characterization of mixing as a function of the Schmidt number at fixed kinematic conditions. In this chapter, we briefly review the routes to achieve chaotic advection in Stokes flow, and then illustrate the characterization of a continuous flow chaotic stirrer via appropriate numerical tools, including the Poincaré section, finite time Lyapunov exponent, and mixing index. 1. Introduction Mixing is the process of homogenization of species distribution as a result of stirring and diffusion. While stirring brings the constituents to close proximity, and diffusion homogenizes through “blending of the constituents”. Using this simplified definition of mixing, stirring is indicative of flow kinematics that is often determined by the mixer geometry and flow conditions, which are primarily described by Reynolds number (Re), defined as the ratio of inertial and viscous forces (Other dimensionless groups can also exist based on the specific mixer design). The effects of diffusion are determined by the species that is being mixed, which can be characterized as a function of the Schmidt number (Sc) defined as the ratio of momentum and mass diffusivities. Although the characteristic lengths associated with LOC devices are very small − typically on the order of 100 μm − diffusion alone in the case of large molecules does not allow S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_14, © Springer Science + Business Media B.V. 2010
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for sufficiently fast mixing. For example, at room temperature, myosin’s diffusion coefficient in water is about 10−11 m2/s, and the time constant for the diffusion along a length of 100 μm is thus intolerably large, about 103 s. Therefore, mixing several fluids in reactors at the micron scale is not as easy as it might seem at first sight. Since the Reynolds numbers of flows in micro-devices are usually very small (i.e., Re ∼ O(1)), the flows are laminar and mixing enhancement cannot be reached by making use of turbulencelike flow patterns. In order to achieve reasonable speed and yield of chemical reactions and bioassays, micromixers must be necessarily integrated into the chips. The device integration step may bring several limitations regarding to the flow kinematics utilized in the mixer design, where simply increasing the flow rate (or Re) to mix different species may not be compatible with the upstream and downstream components of the LOC device. Given these limitations, one needs to determine the kinematically favorable conditions for mixing by choosing the mixer-geometry and flow conditions (Re, and other relevant dimensionless parameters), and then, ensure efficient mixing for various species by varying Sc under these predetermined kinematic conditions. Various types of micromixers have been designed, fabricated and experimentally characterized using fluorescent dyes to measure the fluorescence intensity at various sections of these mixers. In these studies, the mixing efficiency was quantified using standard deviation of the fluorescence intensity from a perfect mix [1–6]. A remarkable amount of the experiments utilized a single type of dye (i.e., fixed Schmidt number Sc), and the mixing length or mixing time was investigated as a function of the Peclet number (Pe ≡ Sc × Re), which gives the forced convection to diffusion ratio of a system, by varying the Reynolds number. An important overlooked aspect of this approach is that varying Re by keeping Sc fixed changes the flow kinematics. Especially, beyond the Stokes flow regime, significant changes in flow kinematics can be achieved by varying the flow rate, which may lead to different stirring conditions. Therefore, such studies should be interpreted as attempts to identify the flow kinematics that enhance mixing. A fundamentally important, yet mostly underappreciated aspect of mixing is characterization of the stirrer under fixed flow kinematics but for mixing of different species. This approach requires varying the Sc to vary the Peclet number at fixed Re. Only this latter approach should be used to assess the chaotic nature of species mixing based on the fluorescent dye experiments and numerical simulations of the species transport equations. Reasons of this claim will be substantiated in this chapter. The main objective of this chapter is to provide an introductory review on characterization of chaotic stirrers using appropriate numerical tools. The rest of this chapter is organized as follows: Section 2 reviews the
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general routes to achieve chaotic advection and gives examples of chaotic stirrers. Section 3 describes computational tools used for quantification of chaos and mixing efficiency. Finally, the chapter ends with concluding remarks. 2. Routes to Chaotic Advection Chaos was discovered and studied since almost a century ago, and has been mostly thought of in the context of turbulence. The concept of chaotic advection in laminar flows was introduced in the early 1980s by Aref [7]. Since then, a substantial number of investigators have demonstrated that chaotic advection occurs in a wide variety of laminar flows ranging from creeping flow to potential flow, and in different flow systems including unsteady two-dimensional flow, and both steady and time-dependent threedimensional flows [8–12]. The idea underlying chaotic advection is the observation that a certain regular velocity field, u(x, t ) can produce fluid pathlines, x(x o , t ) , which uniformly fill the volume in an ergodic way. The motion of passive tracers is governed by the advection equation:
x& = u(x, t), x(t = 0) = xo ,
(1)
Hereafter, bold letters represent vectors. In such velocity fields, fluid elements that are originally close to one another trace paths that diverge rapidly (exponentially fast in the ideal case), so that the material is dispersed throughout the volume very efficiently. This typically leads to significantly fast mixing. Therefore, chaotic advection in LOC devices can provide the best possibility of achieving efficient and thorough mixing of fluids. Due to the nature of the dynamical system, chaotic advection requires either time-dependent flow in simple 2-D geometries or complex 3-D geometries [9, 12]. Typically, active chaotic micro-mixers which are actuated externally by time-dependent energy sources (i.e., pressure, electric and/or magnetic fields) use time-dependent 2-D flow to achieve chaotic advection for mixing enhancement. On the other hand, passive chaotic micromixers typically use complex three-dimensional twisted conduits fabricated in various substrates such as silicon [13], polydimethylsiloxane (PDMS) [14], ceramic tape [15], or glass [13] to create 3-D steady flow velocity with a certain complexity to achieve chaotic advection. Typical examples of the aforementioned two routes to achieve chaotic advection and mixing in LOC devices are presented in the following.
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2.1. MIXING WITH CHAOTIC ADVECTION IN 2-D
Various active micromixers using 2-D time-dependent flow to achieve chaotic advection have been developed [16–19]. Since electroosmosis is very attractive for manipulating fluids in LOC devices, a chaotic electroosmotic stirrer developed by Qian and Bau [20] is described as an example to achieve chaotic advection and mixing by 2-D time-dependent electroosmotic flow. The electroosmotic chaotic stirrer developed by Qian and Bau [20] consists of a closed cavity (|x| ≤ L and |y| ≤ H) with two electrodes mounted along the walls x= ±L inducing an electric field, E, parallel to the x-axis. Four additional electrodes are embedded in the cavity’s upper and lower walls. These electrodes are not in contact with the liquid, and are used to control the ζ potential at the liquid-solid interface. The cavity contains an electrolytic solution. Various 2-D flow patterns are induced through the modulation of the zeta potentials along the top left, top right, bottom left, and bottom right walls. These flows are, however, highly regular. In the absence of diffusion, trace particles will follow the streamlines with no transport occurring transverse to the streamlines. To induce chaotic advection in the cavity, two different flow patterns, A and B, are alternated with a period of T. In other words, the flow field type A is maintained for a time interval 0< t
2.2. MIXING WITH CHAOTIC ADVECTION IN 3-D
In order to achieve chaotic advection in 3-D, steady flow in a geometry that has certain complexity created by 3-D microconduits can be used. When all the conduits lay in the same plane such as the zigzag and square-wave microconduit, the symmetry of the flow field is preserved, and chaotic
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advection occurs only at high Reynolds numbers (i.e., Re > 80). Previous results have shown that micromixers consisting of twisted pairs of bends with each pair forming a C-shape or L-shape only work well at moderate Reynolds numbers and are not efficient at low Reynolds numbers since the bend-induced vortices decay well before they may significantly stir the fluid [15]. Instead of using twisted complex 3-D geometry, ribs or grooves on the channel walls can lead to the formation of transverse velocity components at low Reynolds numbers [22–24], and thus create chaotic advection for mixing enhancement. The experimental results demonstrate that staggered herringbone mixer (SHM) works well in the range 0 < Re < 100 [23]. The SHM mixing is more efficient than that achieved with similar microfluidic channels devoid of internal structures like ribs and grooves. For example, The basic T-mixer (i.e., two co-flowing species under pressure driven-flow in a straight micro-channel) requires mixing lengths of about 1 and 10 m at Pe = 104 and 105, while the SHM mixer performs the same task within 1 and 1.5 cm, respectively. The mixing efficiency of the SHM mixer can be further greatly improved with ribs or grooves placed on both the top and bottom of the channel, which not only increases the driving force behind the lateral flow, but also allows for the formation of advection patterns that cannot be created with structures on the bottom alone [24]. We must reemphasize that the flow kinematics in these mixers are a function of the flow rate, and hence the Reynolds number. For example, in the case of mixers with bend-induced vortices, the Dean number is a function of Re, and experiments utilizing fluorescent dyes with constant Sc but different flow rates (Re) should be interpreted as a search for kinematically favorable stirring conditions. Such results should be characterized as a function of the Reynolds number, rather than the Peclet number, since these do not reveal the behavior of the device for mixing species with varying mass diffusivities. 3. Numerical Tools for Characterization of Chaotic Stirrers Mathematical modeling and numerical simulations of mixing in LOC devices provide a convenient and fast method for optimizing the design and operation parameters of a chaotic stirrer, which otherwise would require enormous effort. In the numerical studies, appropriate tools to qualitatively/ quantitatively characterize the stirrers are required. In the following we focus on the appropriate applications of some diagnostic tools such as the Poincaré section, finite time Lyapunov exponent (FTLE) and mixing index to characterize chaotic stirrers. Using a continuous-flow chaotic stirrer developed by Kim and Beskok [25] as an example, the applications and limitations of the aforementioned tools to characterize the stirrer are illustrated.
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Figure 1 shows the continuous-flow micro-mixer developed by Kim and Beskok [25], which consists of periodically repeating mixing blocks (the length and height of each block are L = 4h and H = 2h, respectively) with zeta potential patterned surfaces (Fig. 1a) that induce 2-D electroosmotic flow (Fig. 1b) under an axial electric field. A time-periodic flow can be generated by altering the axial electric field in the form of a cosine wave with a frequency of ω. In addition, a pressure-driven unidirectional flow in x-direction (see Fig. 1c) is superposed to the electroosmotic flow, with channel centerline velocity of U0. The flow field in the mixer is governed by the following dimensionless Navier-Stokes equations: ∇ ⋅u = 0 ,
∂u 1 2 + (u ⋅ ∇)u = −∇p + ∇ u. ∂t Re
(2)
(3)
The dimensionless species concentration distribution (C ) is described by the time-dependent convection-diffusion equation: ∂C 1 2 + (u ⋅ ∇)C = ∇ C. Pe ∂t
(4)
Using dimensional analysis, the mixer’s performance can be shown to depend on the following dimensionless parameters: Re =
ωh UHSh U ; St = ; A= 0 , ν UHS UHS
(5)
where Re and St are the Reynolds and Strouhal numbers, A is the ratio of the Poiseuille (U0) and electroosmotic flow velocities (UHS), which is kept constant (A = 0.8). Each repeated pattern of the mixer, a mixing block, has an aspect ratio of L/H = 2. It is also essential to assume quasi-steady flow, which further requires small Stokes numbers ( = Re × St ≤ 0.2 ). Figure 1d shows concentration contours obtained within eight mixing blocks for Re = 0.01, Pe = 1,000, and St = 1/2π, which shows rapid mixing between the red and blue streams, generating fully mixed (green contours) towards the mixer’s exit. Similar to the Qian and Bau’s mixer in Ref. [20], this mixer also utilizes electroosmotic flow, which operates in the Stokes flow regime. As a result, the streamlines are rather insensitive to the variations in Reynolds number.
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L=4h
(b)
H=2h (c)
(a)
(d)
Figure 1. Schematics of the continuous chaotic stirrer developed by Kim and Beskok [25]. The stirrer consists of periodically repeating mixing bocks with zeta potential patterned surfaces (a) and an electric field parallel to the x-axis is externally applied resulting in an electroosmotic flow (b). Combining a unidirectional (x-direction) pressure-driven flow (c) with electroosmotic flow under time-periodic external electric field (in the form of a Cosine wave with a frequency ω), a 2-D time-periodic flow is induced to achieve chaotic stirring in the mixer. Two fluid streams colored with red and blue are pumped into the mixer from the left and are almost well mixed after eight repeating mixing blocks for Re = 0.01, St = 1/2π, Pe = 1,000, and A = 0.8 (d).
Therefore, the flow kinematics in this system is determined mostly by the Strouhal number. 3.1. POINCARÉ SECTIONS
Poincaré maps are often used to qualitatively characterize the quality of stirring over a wide range of operating parameters because the Poincaré mapping visualizes invariant manifolds and Kolmogorov–Arnold–Moser (KAM) curves on a Poincaré section [10]. For a closed mixer, a Poincaré section consists of a finite number of points (where the number of points is the period of the advection cycles), which show the sequential positions of a specific fluid particle, and is obtained by integrating the advection equation (1) and recording the position at the end of each advection cycle. However, for an open flow system such as a channel flow, to obtain images to display the dynamic states in a physical channel domain (x,y) through time periodic projections is not straightforward, because motions of passive tracer particles are not bounded within a limited physical domain.
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Poincaré sections of a continuous-flow mixer can be obtained with the mapping method introduced by Niu and Lee [26]. We choose Poincaré section to be xn = n × L for the trajectory of any initial point, where L is the length of the mixing block and n = 1, 2, …, N. Particle trajectories will intersect boundaries of the mixing blocks successively at points P1, P2, …, PN. This mapping is defined as Pn+1 = Φp(Pn),
(6)
where Φp is the Poincaré mapping. At point Pn, the vertical positions of passive tracer particles are recorded in y axis of the Poincaré section, while time (t) increases to infinity with the repetition of mapping. In order to convert t into a periodic variable, we adopt a new variable α. Since the flow is periodic with a specified St, and 2π is a common factor in our definition of St, we defined α = modular (t, 2π). The values of α are recorded in the horizontal axis of the Poincaré section. Thus, mathematical expression of projection points on Poincaré section is Pn(αn, yn). Figure 2a depicts the Poincaré section of the continuous flow stirrer when St = 1/4π, and Re = 0.1. The Poincaré sections are obtained by numerically tracking four passive tracer particles initially located at (0.005, −0.5), (0.005, 0.0), (0.005, 0.5) and (0.005, 1.0) during 105 convective timescales (H/UHS). A quasi-periodic motion of the passive tracer particle that is initially located at (0.005, 0.0) results in a regular formation separating the upper and lower halves of the Poincaré section. A zoomed image showing this KAM boundary is presented in Fig. 2c. The passive tracer particles initially located at the upper and lower halves of the channel entry cannot pass this global barrier. In addition to this, there are two unstirred zones called void zones surrounded by well stirred zone (chaotic sea) at the bottom half of the Poincaré section. A zoomed image of these two void zones can be seen in Fig. 2b. Before we finish this subsection, we would like to discuss the practical limitations of the Poincaré sections, which require Lagrangian particle tracking for extended times. In reality, Fig. 2 presents stroboscopic images of the same four particles passing through thousands of mixing block boundaries. This has two basic implications. First, numerical calculation of the Poincaré sections requires either analytical solutions or high-order accurate discretizations of the velocity field. Otherwise, the results may suffer from numerical diffusion and dispersion errors, and the KAM boundaries may not be identified accurately. Second, it is experimentally difficult, if not impossible, to track particles (in three-dimensions) beyond a certain distance allowed by the field of view of the microscopy technique. Despite these
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limitations and challenges, the Poincaré sections can differentiate between the partially and totally chaotic flows. Overall, one would expect better mixing with decreased regular flow zones. The basic problem is that the Poincaré section method is qualitative, and it cannot determine the chaotic strength between the two fully chaotic systems, both resulting in featureless Poincaré sections. (b)
(a)
0.5
Zoom 2
0.0
y -0.5 Zoom 1
0
1
2
(c) 3 α
4
5
6
Figure 2. Poincaré section for four particles initially located at (0.005, −0.5) – black, (0.005, 0.0) – red, (0.005, 0.5) – green, and (0.005, 1.0) – blue, at stirring conditions of St = 1/4π, Re = 0.01, and A = 0.8 (a). The Poincaré sections in the zoomed area 1 with two void zones (b), and the global regular pattern in the zoomed area 2 (c).
3.2. FINITE TIME LYAPUNOV EXPONENT (FTLE)
In order to quantitatively characterize the chaotic strength in the case of featureless Poincaré sections, Lyapunov exponent (LE) needs to be calculated. Positive LE indicates the presence of chaos in the system and higher LE values are considered as higher chaotic strength. Calculation of the LE requires extremely long time integration, therefore, finite time Lyapunov exponent (FTLE), λFTLE, has been widely used in quantification of chaotic strength [21]. FTLE is calculated using the algorithm suggested by Sprott [27]. Briefly, arbitrary pairs of nearby points with an initial distance of |dx| are chosen, and the distance at the time of Δt, |dx(Δt)|, is evaluated to calculate ln(|dx(Δt)/dx| by integrating the particles’ paths. This process is repeated n times using the following mathematical expression:
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λFTLE =
⎛ dx( ( n +1) Δt ) ⎞ 1 1 ⎛ dx( Δt ) ⎞ 1 ln = ln ⎜ ⎟ ∑ ⎜ ∑ ⎜ dx( ( n) Δt ) ⎟⎟ . n Δt ⎝ dX ⎠ nΔt ⎝ ⎠
(7)
Figure 3 depicts the FTLE distribution obtained by tracking 4,000 passive tracer particle pairs at the end of ten time periods for the stirring case of St = 1/2π, Re = 0.01, and A = 0.8. The FTLE has a normal distribution with mean λFTLE = 0.1 and standard deviation σ = 0.03. The positive FTLE is consistent with the chaotic flow. 500
400
Frequency
300
200
100
0 0.000
0.025
0.050
0.075
0.100
0.125
0.150
λFTLE Figure 3. The FTLE distribution for mixing with St = 1/2π, Re = 0.01, and A = 0.8 obtained by tracking 4,000 passive particle pairs for ten time-periods.
3.3. MIXING INDEX
In order to quantify a mixer’s performance, the mixing index (M) is defined as [28]:
σ
1 = M= C∞ C∞
Ci2
− Ci
2
≈
⎞ 1 N ⎛ Ci ⎜⎜ − 1⎟⎟ N − 1 i =1 ⎝ C∞ ⎠
∑
2
(8)
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where Ci is the average concentration inside the ith section of a total of N interrogation areas and C∞ is the concentration value corresponding to the perfect mix. The < > symbol denotes averaging over the volume of a single mixing block. Based on the initial distribution of the species, a perfect mix would reach C∞ = 0.5. According to the definition in Eq. (8), a perfect mix results in M = 0. Hence, smaller values of M show better mixing. For the continuous flow mixer considered here, the mixing index varies as a function of the channel length, and it can be used as a metric to assess the mixing efficiency. Using the inverse of the mixing index (M−1) instead of itself is more preferable since M−1 → ∞, while M → 0. For example, M−1 = 20 corresponds to (1 − σ/C∞) × 100% = 95% mixing efficiency. Similarly, M−1 = 10 corresponds to 90% mixing. For a theoretical study, the dimensionless concentration is calculated from the species transport equation (4). For high Pe flows, solution of scalar transport equation is quite challenging and requires high accuracy both in time and space [19, 21]. Mixing-length (lm) and mixing-time (tm) is used to assess the mixing efficiency for continuous-flow and closed mixers, respectively. However, Pe dependence of mixing-length or -time must be investigated by varying the Schmidt number (i.e., different molecular dyes) while keeping the Reynolds number constant. The mixing process can be characterized globally by evaluating its lm – Pe behavior at fixed kinematic condition (i.e., constant Re and St). For laminar convective/diffusive transport, mixing length typically varies as lm ∝ Pe0.5. It is possible to reduce the mixing-length drastically by inducing chaotic stirring, which results in lm ∝ ln(Pe) for fully chaotic, and lm ∝ Peβ (with β < 1) for partially chaotic flows. Figure 4 depicts the dimensionless species concentration distribution in the continuous mixer when Pe=500 (a), 1,000 (b), and 2,000 (c), while the kinematic condition is fixed at St = 1/2π and Re = 0.01. Based on the spatial species concentration distribution, the mixing index, M, is then calculated using Eq. (8). Figure 5 depicts M−1 as a function of the dimensionless mixing length, lm/h, under the same kinematic condition (St = 1/2π and Re = 0.01) for Pe = 500 (rectangles), 1,000 (triangles), and 2,000 (circles). The corresponding 95%, 93% and 90% mixing efficiencies are also marked in Fig. 5. (a) (b) (c) Figure 4. Dimensionless species concentration distribution for Pe = 500 (a), 1,000 (b) and 2,000 (c) at St = 1/2π , Re = 0.01 and A = 0.8.
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−1
Figure 5. Mixing index inverse (M ) as a function of the normalized mixing length for Pe = 500, 1,000 and 2,000 at St = 1/2π, Re = 0.01, and A = 0.8.
As a succinct and clear evidence of global chaos, logarithmic relation between the mixing length (lm) and Pe should be investigated under the same kinematic condition. Figure 6 depicts the mixing length for 95%, 93%, and 90% mixing efficiency vs. ln(Pe) under the kinematic condition of St = 1/2π and Re = 0.01. The linear relationship between lm and ln(Pe) indicates fully chaotic flow in the mixer. Figure 6 can also be used to determine the length or number of mixing blocks of the mixer that is required to achieve a certain mixing efficiency. Before finishing this section, we would like to discuss the practical aspects of mixing index calculations. The method requires utilization of the species transport equation along with a flow solver, which presently exists
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Figure 6. Peclet vs. the normalized mixing length at 90%, 93%, and 95% mixing efficiencies for St = 1/2π, Re = 0.01 and A = 0.8 conditions.
in most commercial software packages. Therefore, the mixing index can be the preferred methodology to characterize the mixing efficiency. One must be careful about accuracy of the utilized numerical solver in case of long time integration errors, which have significant impacts on the results of the flow and species distribution. Although the color contour plots are often too forgiving, significant discrepancy in the M −1 values of high-order accurate solver from others is observed at high Pe values, because of the high numerical diffusion of the latter. Finally, the mixing index is relevant with the experimental observations based on mixing of fluorescent dyes. The decision for the desired M−1 value or the mixing efficiency can depend on the application. For example, certain applications may require perfect molecular diffusion for a reaction to take place. Numerical modeling of this situation could be challenging as it would require very large M −1 values, requiring very long numerical integration times and excessive number of mixing blocks for open mixers.
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4. Concluding Remarks We outlined the conditions and benefits of chaotic stirring in LOC devices. Based on Lagrangian particle tracking of passive tracers, the Poincaré sections provide qualitative detection of bad mixing zones, such as islands, and cannot differentiate the stirring performance after the Poincaré sections become featureless. When Poincaré section is featureless, FTLE should be used to quantify the chaotic strength. Strictly positive FTLE values indicate fully chaotic flow in the mixer, and the average value of the FTLE quantifies the chaotic strength. However, the computations of the Poincaré section and FTLE are very expensive since they both require accurate time integration and accurate resolution of the flow field. Alternatively, mixing index and scaling of lm as a function of Pe can be used to characterize the mixing behavior under fixed kinematic conditions by varying the Sc. Spatial distribution of species concentration can be determined either by numerically solving the species transport equation or from imaging analysis of fluorescence images obtained from experiments using confocal microscopy with dye additions. The relationship lm vs. Pe should be evaluated under fixed kinematic conditions (i.e., fixed Re, etc) to check whether the continuous-flow mixer is globally chaotic. Often lm ∝ Peβ with β < 1 is observed. Pure diffusion results in β = 1, while certain convective flows result in β = 0.5. For partially chaotic flows the value of β depends on the extent of the regular flow regions, and β → 0 as the regular flow zones diminish. For fully chaotic flows lm ∝ ln(Pe) is observed. Similarly, the logarithmic relation between the mixing time, tm and Pe should be investigated in a closed mixer at a fixed kinematic condition (i.e., fixed Re, etc.), where tm ∝ ln(Pe) indicates fully chaotic flow in closed mixers [21].
References 1. A.D. Stroock, S.K.W. Dertinger, A. Ajdari, I Mezic, H.A. Stone, G.M. Whitesides, Chaotic mixer for microchannels, Science, 295: 647–651 (2002). 2. N. Sasaki, T. Kitamori, H.B. Kim, AC electroosmotic micromixer for chemical processing in a microchannel, Lab Chip, 6: 550–554 (2004). 3. C. Simonnet, A. Groisman, Chaotic mixing in a steady flow in a microchannel, Physical Review Letters, 94(13): 134501 (2005). 4. S.H. Chang, Y.H. Cho, Static micromixers using alternating whirls and lamination, J. Micromech. Microeng., 15: 1397–1405 (2005). 5. A.P. Sudarsan and V.M. Ugaz, Fluid mixing in planar spiral microchannels, Lab Chip, 6: 74–82 (2006).
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6. H.M. Xia, C. Shu, S.Y.M. Wan, Y.T. Chew, Influence of the Reynolds number on chaotic mixing in a spatially periodic micromixer and its characterization using dynamical system techniques, J. Micromech. Microeng., 16(1): 53–61 (2006). 7. H. Aref, Stirring by chaotic advection, J. Fluid Mech., 143: 1–21 (1984). 8. H. Aref, Chaotic advection of fluid particles, Phil. Trans. R. Soc. Lond. A, 333: 273–288 (1990). 9. H. Aref, The development of chaotic advection, Phys. Fluids, 14: 1315–1325 (2002). 10. J.M. Ottino, The kinematics of mixing: stretching, chaos, and transport, Cambridge University Press, Cambridge, England (1989). 11. S. Wiggins and J.M. Ottino, Foundations of chaotic mixing, Phil Trans. Royal Soc. A, 362 (1818): 937–970 (2004). 12. M.A. Stremler, F.R. Haselton, H. Aref, Designing for chaos: applications of chaotic advection at the micro scale, Phil Trans. Royal Soc. A, 362(1818): 1019–1036 (2004). 13. R.H. Liu, M.A. Stremler, K.V. Sharp, M.G. Olsen, J.G. Santiago, R.J. Adrian, H. Aref, D.J. Beebe, A Passive three-dimensional ‘C-shape’ helical micromixer, J. Microelectromechanical Systems, 9(2): 190–198 (2000). 14. M.A. Stremler, M.G. Olsen, R.J. Adrian, H. Aref, D.J. Beebe, Chaotic mixing in microfluidic systems. Solid-state sensor and actuator workshop, Hilton Head, SC, June 4–8 (2000). 15. M. Yi, H.H. Bau, The kinematics of bend-induced mixing in microconduits. Int. J. Heat Fluid Flow, 24: 645–656 (2003). 16. N.T. Nguyen, Z.G. Wu, Micromixers – a Review, Journal of Micromechanics and Microengineering, J. Micromech. Microeng, 15(2): R1–R16 (2005). 17. S. Qian and J.F.L Duval, Mixers, In: Comprehensive Microsystems, edited by Y.B. Gianchandani, O. Tabata and H. Zappe, 2: 323–374, Elsevier (2007). 18. N.T. Nguyen, Micromixers: Fundamentals, Design and Fabrication, William Andrew Micro & Nano Technologies Series (2008). 19. D.A. Boy, F. Gibou, S. Pennathur, Simulation tools for lab on a chip research: advantages, challenges, and thoughts for the future, Lab Chip, 8: 1424–1431 (2008). 20. S. Qian, H.H. Bau, Theoretical Investigation of Electro-Osmotic Flows and Chaotic Stirring in Rectangular Cavities, App. Math. Modeling, 29: 726–753 (2005). 21. H.J. Kim, A. Beskok, Quantification of chaotic strength and mixing in a micro fluidic system, J. Micromech. Microeng., 17: 2197–2210 (2007). 22. T.J. Johnson, D. Ross, L.E. Locascio, Rapid Microfluidic Mixing, Analytical Chemistry, 74(1): 45–51 (2002). 23. A.D. Stroock, S.K.W. Dertinger, A. Ajdari, I. Mezic, H.A. Stone, G.M. Whitesides, Chaotic mixer for microchannels, Science, 295(5555): 647–651 (2002). 24. P.B. Howell, D.R. Mott, S. Fertig, C.R. Kaplan, J.P. Golden, E.S. Oran, F.S. Ligler, A microfluidic mixer with grooves placed on the top and bottom of the channel, Lab Chip, 5: 524–530 (2005).
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A. BESKOK
25. H.J. Kim and A. Beskok, Numerical Modeling of Chaotic Mixing in Electroosmotically Stirred Continuous Flow Mixers, ASME J. Heat Transfer 131(9): 092403 (2009). 26. X. Niu, Y.K. Lee, Efficient spatial-temporal chaotic mixing in microchannels, J. Micromech. Microeng., 13: 454–462 (2003). 27. J.C. Sprott, Chaos and Time-Series Analysis, Oxford University Press, Oxford, England (2003). 28. T.M. Antonsen, Z. Fan, E. Ott, E. Garcia-Lopez, The role of chaotic orbits in the determination of power spectra of passive scalars, Phys. Fluids, 8(11): 3094–3104 (1996).
AC ELECTROKINETIC FLOWS A. BESKOK
Aerospace Engineering Department Old Dominion University, Norfolk, VA 23529, USA,
[email protected]
Abstract. Alternating current (AC) electrokinetic motion of colloidal particles suspended in an aqueous medium and subjected to a spatially nonuniform AC electric field are examined using a simple theoretical model that considers the relative magnitudes of dielectrophoresis, electrophoresis, AC-electroosmosis, and Brownian motion. Dominant electrokinetic forces are explained as a function of the electric field frequency, amplitude, and conductivity of the suspending medium for given material properties and geometry. Parametric experimental validations of the model are conducted utilizing interdigitated microelectrodes with polystyrene and gold particles. The theoretical model provides quantitative descriptions of AC electrokinetic transport for the given target species in a wide spectrum of electric field amplitude and frequency, and medium conductivity. The presented model, previously published in Ref. [1], can be used as an effective framework for design and optimization of AC electrokinetic devices.
1. Introduction With the advancement of microfabrication methods, AC electrokinetic techniques such as electrophoresis (EP), dielectrophoresis (DEP) and AC electroosmosis (AC-EO) have been widely investigated and utilized for separating, sorting, mixing and detection of colloidal particles and biological species on microscale devices. AC electrokinetic techniques provide a great potential for development of micro total analysis systems (μ-TAS). Since colloidal motion is mainly induced by interaction with AC electric field, manipulation of sub-micrometer scale particles without mechanical moving parts is possible, and the direction and magnitude of the colloidal motion can be controlled by adjusting the frequency and amplitude of the applied electric field. Moreover, AC electrokinetic techniques are well suited for integration with other electronic components on a single chip with small foot print area. However, AC electrokinetic manipulation of colloidal particles is generally limited by the applicable electric field conditions and relative polarizability of the suspending medium compared to that of the particles and S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_15, © Springer Science + Business Media B.V. 2010
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electrodes. Accordingly, design and optimization process of AC electrokinetic devices require performance prediction and validation over specific operational ranges of electric field, which should be considered as a function of the electrode geometry, and electromechanical properties of the target species and suspending medium. For example, when the size and properties of the target species are fixed, DEP forces can be represented as a function of the ionic strength of media, electric field frequency and amplitude, and the electrode geometry. In order to utilize DEP for manipulating colloidal particles, magnitude of the DEP force should be large enough to dominate other forces. If this is induced using large electric fields, electrolysis of the suspending medium can occur. Relative polarizability of suspending medium can be controlled by adjusting molarity of the buffer solution to vary the direction and magnitude of DEP at certain frequency ranges. However, high conductivity media often causes undesirable electrothermal effects. It should be also noted that selection of the buffer conductivity is restrictive in the case of biological samples, since excessive osmotic stress can cause cell damage. Thus, design and development of devices for specific applications require characterization of each AC electrokinetic mechanism over the desired range of electric field strength and buffer concentration. In this chapter, we demonstrate an effective way of predicting the AC electrokinetic motion of colloidal particles in a microscale device. A modified scaling analysis is constructed by considering the relative magnitudes of AC electrokinetic motion (EP, DEP and AC-EO) and Brownian motion of colloidal particles on interdigitated microelectrodes, which have simple planar geometry and analytically obtained electric field. Dominant transport mechanisms at given electric field and material conditions are described using phase diagrams, and effects of particle’s relative polarizability and ionic concentration of buffer solution are explained. Then, the results are validated through parametric experiments for different kinds of colloidal particles (polymeric and metallic particles, and biological species) at various electric field conditions. Dominant transport mechanisms of each particle with different polarization characteristics are observed, and compared with the results of the scaling analysis. As a result, we have shown that the theoretical model can provide quantifiable information for AC electrokinetic motion of colloidal particles over broad ranges of electric field frequencies and amplitudes. 2. AC Electrokinetic Effects In the presence of non-uniform AC electric field, colloidal particles suspended in an aqueous medium experience electrokinetic forces including electrophoresis (EP), dielectrophoresis (DEP), and hydrodynamic drag force due
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to the bulk fluid motion induced by AC-electroosmosis (AC-EO) at a certain frequency range. In addition to electrical forces, the particles are also influenced by the Brownian motion. Lateral motions of colloidal particles are generally driven by interaction of these forces, and precise analysis for each transport mechanism is required for manipulation of particles in microfluidic devices. To reduce the effort involved in detailed numerical simulations and to gain understanding for the order of magnitude of each transport mechanism, we present a scaling analysis that predicts dominant forces in a microscale device based on the maximum displacement of colloidal particles on interdigitated microelectrodes. The scaling map results in prediction of the dominant transport mechanism at a given operational condition. It also enables production of phase diagrams that describe the particle motion as functions of the electric field frequency, amplitude and media conductivity. In the following, we present a simple particle displacement analysis for various AC electrokinetic effects. Assuming co-planar parallel interdigitated electrodes, the electric field between two electrodes can be assumed as halfcircular lines near the electrode surface. Various electrokinetic forces can be represented in simple analytical forms using this simplified electric field distribution. 2.1. AC ELECTROOSMOSIS
AC Electroosmosis is due to the interactions of the tangential electric field with the induced charges on each electrode, which results in electroosmotic force and fluid velocity in the horizontal direction. The AC-EO flow was previously explained in Refs. [2–4]. The tangential AC electric field produces electroosmotic fluid velocity due to the potential drop across double layer on the electrodes, which can be represented as [4] u EO =
(
)
εε 0 εε ∂ 2 Δφ D Et = − 0 Λ Δφ DL , η 4η ∂r
(1)
where ε0 and ε are the absolute permittivity and relative permittivity of the medium respectively, η is the viscosity, ΔφD and ΔφDL are the potential drop across diffuse layer and double layer respectively, and Et is the tangential electric field. The capacitance ratio Λ is given by, Λ = CS/(CS+CD), where CS is the capacitance of the Stern layer, and CD is the capacitance of the diffuse layer. CS = 0.007 F/m2 is used based on the experimental result of impedance measurements [4]. With expressions for resistance of the fluid and capacitance of the double layer, electric circuit analogy can be applied to model the double layer potential drop by [5, 6]
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Δφ DL =
V0 , 2(1 + jΩ)
(2)
where V0 is the applied voltage, j = − 1 , Ω=Λωεε0πr/2σλD, ω is the radian frequency, σ is the conductivity of the fluid, and λD is the Debye length. Then, the resultant displacement due to AC-EO motion can be expressed as [7] 1 εε V Ω2 X AC − EO = Λ 0 0 t. 8 ηr (1 + Ω 2 ) 2 2
(3)
AC-EO displacement becomes zero as the non-dimensional frequency Ω goes to zero or infinity, which represents a bell shaped function with both ends approaching zero. 2.2. DIELECTROPHORESIS
Dielectrophoresis is the motion of polarizable particles that are suspended in an ionic solution and subjected to a spatially non-uniform electric field. Polarizability of particle relative to the suspending medium determines the basic direction of DEP force (positive/negative DEP), which also strongly depends on the frequency of the applied electric field. In the case of electric field with constant phase, time-averaged DEP force can be represented as [8] 2
FDEP = 2πεε 0 a 3 Re{K }∇ E ,
(4)
where a is the particle radius, E is the electric field, and K is the ClausiusMossotti (CM) factor. For homogeneous particles suspended in a medium, the CM factor is given by
ε *p − ε * , K (ε , ε ) = * ε p + 2ε * * p
*
(5)
where ε* is the complex electric permittivity of the media, which can be represented as ε* = ε − jσ/ω. Subscript p refers to the particle. The CM factor represents effective polarizability of the particle with respect to the suspending medium, which is a strong function of the applied frequency. The value of Re{K} varies between +1 and −1/2. Depending on the sign of Re{K}, particle motion is induced towards the electrode surface (positive DEP), or away from the electrodes (negative DEP). Figure 1 shows the variation of Re{K} as a function of the electric field frequency and ionic strength of suspending medium for solid spherical dielectric particles with the parameters εp = 2.55, ε = 78.5, and σp = 0.01 S/m. The sign of Re{K} is
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1 1 µS/cm 10 µS/cm 100 µS/cm 1000 µS/cm
0.8 0.6
Re(K)
0.4
+DEP
0.2 0
−DEP
− 0.2 − 0.4 102
103
104
105 106 Frequency (Hz)
107
108
Figure 1. Real part of the Clausius-Mossotti factor for a solid spherical dielectric particle at various medium conductivities (for εp = 2.55, σp = 0.01 S/m, and ε = 78.5). Switch of the sign of Re{K} indicates switch between positive and negative dielectrophoresis.
switched from positive to negative around the crossover frequency (~2 MHz) for low conductivity buffer solution cases (10−5 S/m and 10−4 S/m). However, only negative Re{K} is observed in the whole frequency range for high conductivity buffer case (10−1 S/m), which shows limitation of positive DEP by the conductivity of buffer solution. Since DEP force is proportional to the gradient of electric field, small device scale and high operational voltage are required to amplify the DEP motion of suspended particles. Due to the potential loss induced by electrode polarization, actual potential supplied to the fluid can be expressed as [6] V fluid = V0 − 2Δφ DL = V0
jΩ . 1 + jΩ
(6)
Utilizing the half circular electric field approximation (E = Vfluid /πr) and assuming force balance with Stokes drag for small particles, characteristic DEP displacement can be represented as [7] X DEP =
1 3π 2
a 2 εε 0 β 2V0 t, η r3 2
Re{K }
(7)
where β2 = Ω2/(1+Ω2). It can be observed that β goes to unity as Ω approaches to infinity, and thus the effect of electrode polarization can be neglected for large Ω.
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(AC) Electrophoresis is the motion of electrically charged particles under the influence of an AC electric field. For thin electrical double layers (a/λD 1), dynamic mobility of spherical particles can be expressed as [9]
μd =
εε 0 ς p η
⎛ ωa 2 G⎜⎜ ⎝ ν
⎞ ⎟⎟ , ⎠
(8)
where ζp is the zeta potential of the particle, ν is the kinematic viscosity, and G is a function that represents inertial effects of particle motion as a function of the Womersley number α = a ω /ν , and is given as [9] G (α 2 ) =
1 + (1 + j )α / 2
1 + (1 + j )α / 2 + j (α / 9)(3 + ( ρ p − ρ ) / ρ ) 2
,
(9)
where ρp and ρ are the density of the particle and medium, respectively. Electrophoretic displacement can be derived from particle velocity (uEP = μdE) as X EP =
εε 0 ς p η
⎛ ωa 2 G⎜⎜ ⎝ ν
⎞⎛ βV0 ⎟⎟⎜ ⎠⎝ πr
⎞1 ⎟ sin(ωt ) , ⎠ω
(10)
where (βV0/πr) is an approximation for the half circular electric field with potential drop due to the electrode polarization. The maximum electrophoretic displacement can be determined based on the amplitude of the oscillatory motion as
X EP =
εε 0 ς p ⎛ βV0 ⎞ ⎛ ωa 2 ⎞ 2 ⎟ . ⎜ ⎟G ⎜ η ⎝ πr ⎠ ⎜⎝ ν ⎟⎠ ω
(11)
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2.4. BROWNIAN MOTION
Using Stokes–Einstein relation (D = kBT/6πaη), the expressions for characteristic displacements induced by random Brownian motion in one dimension is given by [7] X Brownian
⎛ k T ⎞ = ⎜⎜ B t ⎟⎟ ⎝ 3πaη ⎠
1/ 2
,
(12)
where kB is Boltzmann constant and T is the temperature. From the expression of each transport mechanism, comparisons of maximum displacements were obtained for scaling analysis. Figure 2 (left) hows the result of scaling analysis using 30 μm electrode spacing, 1 μm polystyrene particle properties, which are εp = 2.55, ρp = 1,050 kg/m3, and σp = 0.01 S/m.30 Homogeneous particle model was used with the parameters, ε = 78.5, D = 1 × 10−9 m2/s, ρ = 1,000 kg/m3, μ = 1 × 10−3 Ns/m2, V = 10 V. Relative magnitudes of characteristic particle displacement for each transport mechanism were compared, and the dominant transport mechanism with the largest displacement magnitude was predicted, as shown Fig. 2 (left). At conductivities less than 10−4 S/m (i.e. typical range of DI water), electrode polarization effects induce dominant AC-EO motion of the fluid at low frequencies (1–10 kHz). However, positive DEP starts to dominate as frequency increases, and negative DEP becomes significant after the crossover frequency (about 2 MHz). At conductivity values more than 10−2 S/m, positive DEP disappears since polarizability of the particle is less than that of medium, and the CM factor is negative over the whole frequency range. The AC-EO and negative DEP motions are relatively small at low frequencies where only Brownian motion is dominant. As frequency increases, AC-EO and negative DEP become dominant consecutively. It should be noted that the scaling map is generated to determine the dominant transport mechanisms based on the two dimensional electric field assumption. Thus, spatial variations for each transport mechanism, especially in three dimensional cases, can not be accounted precisely. However, these results are still applicable in design of more complex electrode systems since the complicated geometry of electrodes can be divided into several sub-regions with different characteristic lengths, allowing predictions of local colloidal motion. Electrokinetic manipulation of particles is not possible in some regions of the scaling maps due to electrolysis effects. We experimentally observed electrolysis at frequencies below 800 Hz and voltages above 1 V. To avoid electrode damage, experimental validations of the scaling maps described in the next section were conducted outside the electrolysis range. We also
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observed that electrothermal effects were insignificant in the ranges of experiments (~10 V). However, electrothermal effects can possibly dominate colloidal motion at higher voltage inputs, especially for cases with high conductivity buffers, since the power dissipation is directly proportional to the conductivity (W ~ σ E2). Although theoretical expressions are available, electrothermal effects are essentially related with three dimensional flow motions, and a different characteristic length scale is required to include electrothermal motions to the scaling analysis. Thus, explicit comparisons with other AC electrokinetic forces are not attempted in the presented study. 3. Experimental Validation of the Scaling Laws The theoretical results are validated through experimental observations of particle motion utilizing interdigitated microelectrodes with 30 μm spacing. Two different types of particles, 1 μm polystyrene particles (polymer), and 800 nm gold particles (metal), were tested for examining the effect of polarizability of each particle. Starting with randomly dispersed particles in initial state, steady state distribution of the particles was observed in each case after applying electric fields. The dominant transport mechanism was determined based on the particle distribution, and was compared with the scaling analysis. Properties of the particles and ionic solutions that were used in the scaling analysis are summarized in Ref. [1]. Figure 2 shows the results of scaling analysis for 1 μm polystyrene particles with experimental observations of particle motion suspended in distilled water, which has conductivity of 2.6 × 10−3 S/m. By feeding a fresh particle solution for each case, a random distribution of particles inside the fluid chamber was established in initial state. After applying 10 V peakto-peak AC electric field for 5 min at specified frequencies, steady state distribution of the particles was captured. Each test case is indicated on the phase diagram. Scaling maps are plotted in a frequency–conductivity plane to demonstrate transition of the dominant transport mechanism as a function of these two parameters. Effects of other parameters can be explained on scaling maps in different planes. We also observed voltage dependence of the dominant transport mechanism utilizing a voltage–frequency phase diagram for same buffer conductivity, and found that the transition is dependent only on the applied frequency, with the exception of low voltage regions (less than 1 V) where Brownian motion was mostly dominant. As predicted from the scaling analysis, transition of dominant transport mechanism can be seen on the experimental results, presented in Fig. 2 (right). AC-EO motion was observed at 1 kHz (case 1 ), where large amount of particles were concentrated on the center of the electrode surface, as predicted by the scaling analysis in Fig. 2. With increased frequency, the particles were forced to move towards the electrode gap and concentrated
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on edges of the electrodes by positive DEP motion. The strength of positive DEP was increased as the frequency was gradually increased up to 100 kHz (cases 2, 3 and 4). However, the DEP motion was decreased at 1 MHz (case 5 ). The increase in positive DEP till 100 kHz frequency can be explained with decrease of AC-EO motion, which competes with the positive DEP force. Since the positive DEP and AC-EO are effective in opposite directions, positive DEP increases as AC-EO decreases. In case 2, small amounts of particles were observed on the center of the electrode surface, while positive DEP motion was dominant on the electrode gap. This can be interpreted as a result of competition between the AC-EO motion of the bulk fluid and the positive DEP, where AC-EO motion is affecting the particle transport far from the electrode edges at 10 kHz frequency. Although the scaling map predicts AC-EO dominant transport of particles at 10 kHz frequency, positive DEP is effective near the electrode gap. In order to obtain more precise theoretical predictions near the region where AC-EO 8
Frequency, log(ω) (Hz)
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4 AC Electroosmosis 3 2 −5
Brownian −4 −3 −2 −1 Conductivity, log(σ) (S/m)
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Applying AC field after sedimenting for 3 hours
Figure 2. Frequency–conductivity phase diagram for 1 μm polystyrene particles (left). Steady state distribution of polystyrene particles suspended in distilled water (2.6 × 10−3 S/m) after applying 10 V peak-to-peak AC electric field for 5 min at specified frequencies (right). For image 1 , concentrated particles on the center of electrode surface driven by AC-EO mechanism are also shown. Due to the nature of negative DEP that repels particles away from the electrode surface, the particles for case 6 were sedimented for 3 h to capture their lateral motion at the image focal plane.
and DEP are balanced, further correlations with the experimental results for AC-EO motion by deriving an empirical value of capacitance ratio, Λ, in Eq. (1) would be required. Decrease of positive DEP near the crossover
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frequency (about 2 MHz) and negative DEP motion of particles at 10 MHz are well captured by cases 5 and 6. Due to the nature of negative DEP that repels particles away from the electrode surface, particles for case 6 were sedimented for 3 h prior to the experiments, which enabled observation of lateral motions at focal plane of the image. 3
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Figure 3. Voltage-frequency phase diagram for 800 nm gold particles (left). Steady state distribution of 800 nm gold particles suspended in 0.1 mM NaHCO3 buffer solution (1.8 × 10−3 S/m) after applying the specified AC electric field for 15 s (right).
Figure 3 shows theoretical and experimental results for 800 nm gold particles suspended in 0.1 mM NaHCO3 buffer solution. Images were captured after applying electric field at specified frequency and voltage for 15 s. Figure 3 (right) shows theoretically predicted dominant displacement map in the frequency–voltage phase plane at buffer conductivity of 1.8 × 10−3 S/m. As shown in the figure, only AC-EO and positive DEP appear as dominant transport mechanisms except in the low voltage region where Brownian motion is also dominant. Unlike the polymeric particles, polarizability variation of gold particles is negligible due to their higher conductivity (4.9 × 107 S/m) compared to that of the buffer solution. Therefore, only positive DEP force appears over 50 kHz. Figure 3 (right) shows experimental results consistent with the scaling map. At 1 kHz frequency (cases 1, 4 and 7 ), the particles were driven to the center of the electrode by AC-EO motion. The strength of the AC-EO motion was increased with increased voltage, and more particles were concentrated on the center of the electrode. For frequencies higher than 1 kHz, particles were concentrated on the edges of electrodes due to positive DEP motion. For cases 2 and 3, weak positive DEP motion was observed near the electrode gap, while Brownian
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motion was observed away from the electrodes as predicted in the phase diagram. With increased voltage, more particles were concentrated and pearl chains of particles were formed between the electrodes. 4. Conclusions A theoretical predictive tool for AC electrokinetic manipulation of micron size particles in a microfluidic device has been presented. Utilizing a scaling analysis that considers relative magnitudes of EP, DEP, AC-EO and Brownian motion, dominant transport mechanisms and their orders of magnitudes were explained over broad ranges of electric field frequency, amplitude and ionic strength of suspending medium. The resultant theoretical model was validated through parametric experimental examination of different types of colloidal particles including polymer (polystyrene), and metal (gold) particles. The AC electrokinetic motion of colloidal particles at various conditions of the electric field and suspending medium were well described in predictive manner. Quantitative information of AC electrokinetic mechanisms for target species and media over a broad range of electric field frequency and amplitude enables configuration of required electric field in early design stages, and provides an easy way to design frequency specific manipulations of various colloidal particles suspended in aqueous media without detailed numerical simulations. Therefore, the presented model can be applied in design and optimization of future AC electrokinetic devices in an effective way.
References 1. S. Park, A. Beskok, Alternating current electrokinetic motion of colloidal particles on interdigitated microelectrodes, Analytical Chemistry, 80(8): 2832– 2841 (2008). 2. N. G. Green, A. Ramos, A. Gonz´alez, H. Morgan, A. Castellanos, Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. I Experimental measurements, Phys. Rev. E, 61, 4011 (2000). 3. A. Gonz´alez, A. Ramos, N. G. Green, A. Castellanos, H. Morgan, Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. II A linear double layer analysis, Phys. Rev. E, 61, 4019 (2000). 4. N. G. Green, A. Ramos, A. Gonz´alez, H. Morgan, A. Castellanos, Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. III Observations of streamlines and numerical simulation, Phys. Rev. E, 66, 026305 (2002). 5. A. Ramos, H. Morgan, N. G. Green, A. Castellanos, AC electric field induced fluid flow in microelectrodes, J. Colloid Interface Sci. 217, 420 (1999).
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6. H. Morgan, N. G. Green, AC Electrokinetics: colloids and nanoparticles; Research Studies Press: Hertfordshire, (2003). 7. A. Castellanos, A. Ramos, A. Gonz´alez, N. G. Green, H. Morgan, Electrohydrodynamics and dielectrophoresis in Microsystems: Scaling laws, J. Phys. D: Appl. Phys. 36, 2584 (2003). 8. T. B. Jones, Electromechanics of Particles, Cambridge University Press: Cambridge (1995). 9. R. W. O’Brien, Electroacoustic equations for a colloidal suspension, J. Fluid Mech., 190, 71 (1988). 10. N. G. Green, H. Morgan, Dielectrophoresis of submicrometer latex spheres. 1. Experimental results, J. Phys. Chem. B, 103 (1), 41–50 (1999).
SCALING FUNDAMENTALS AND APPLICATIONS OF DIGITAL MICROFLUIDIC MICROSYSTEMS R.B. FAIR
Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA,
[email protected]
Abstract. With the first experimental demonstration of droplet flow on an electrowetting-on-dielectric (EWD) array platform in 2000, there has been significant interest in droplet actuation for lab-on-a-chip applications. A hydrodynamic scaling model of droplet actuation in a EWD actuator is presented that takes into account the effects of contact angle hysteresis, drag from the filler fluid, drag from the solid walls, and change in the actuation force while a droplet traverses a neighboring electrode. Based on this model, it is shown that scaling models of droplet splitting, actuation, and liquid dispensing all show a similar scaling dependence on [t/εr(d/L)]1/2, where t is insulator thickness and d/L is the aspect ratio of the device. It is also determined that reliable operation of a EWD actuator is possible as long as the device is operated within the limits of the Lippmann–Young equation. Also discussed are fluidic operations possible with digital microfluidics. Significant advances have been made in chip technology that allow for users to access digital microfluidic chips and to program these chips to perform numerous operations and applications on a common array of electrodes. Whereas in the past, microfluidic devices have been application specific, lacking reconfigurability and programmability, today’s digital microfluidic chips enable versatile, reconfigurable chip architectures that are capable of accommodating and adapting to multiple applications on the same platform.
1. Introduction Electrowetting-on-dielectric (EWD) microfluidics is based on the actuation of droplet volumes up to several microliters using the principle of modulating the interfacial tension between a liquid and an electrode coated with a dielectric layer [1]. An electric field established in the dielectric layer creates an imbalance of interfacial tension if the electric field is applied to only one portion of the droplet, which forces the droplet to move [2]. Droplets are usually sandwiched between two parallel plates – the bottom S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_16, © Springer Science + Business Media B.V. 2010
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being the chip surface, which houses an addressable electrode array, and the top surface being either a continuous ground plate or a passive top plate (the nature of the top plate is determined by the chip’s characteristics). Figure 1 diagrams this setup. The chip surface is coated with an insulating layer of Paralyene –C (~800 nm), and both the top and bottom surfaces are covered in a Teflon-AF thin film (~60 nm) to ensure a continuous hydrophobic platform necessary for smooth droplet actuation. A spacer separates the top and bottom plates, resulting in a fixed gap height. The gap is usually flooded with silicon oil which acts as a filler fluid, preventing droplet evaporation and reducing surface contamination [2]. Other insulators have also been used in EWD devices, such as silicon dioxide with Teflon [4, 5] and Teflon alone [6]. NOT TO SCALE
Top-plate (ground) Glass (0.7 mm) ITO (100 nm) Teflon AF (60 nm)
Fluid Layer Teflon AF (60 nm) Parylene C (800 nm) Cr (100 nm) Glass (1.1 mm)
Bottom-plate (control)
Figure 1. Side-view of digital microfluidic platform with a conductive glass top plate (left). A diagram of materials and construction of the actuator is shown (right). By adding a conductive top plate and adding individually addressed buried electrodes in the bottom plate, the droplet can be actuated from one electrode position to the next by the application of voltage.
The basic EWD device is based on charge-control manipulation at the solution/insulator interface of discrete droplets by applying voltage to control electrodes. The device exhibits bilateral transport, uses gate electrodes for charge-controlled transport, has a threshold voltage, and is a square-law device in the relation between droplet velocity and gate actuation voltage. Thus, the EWD device is analogous to the metal-oxide-semiconductor (MOS) field-effect transistor (FET), not only as a charge-controlled device, but also as a universal switching element [3]. Liquid volumes that can be actuated fall in the range of a few microliters and less. Whereas early demonstrations have been made with droplets between 100 nl and 2 µl, there is interest in scaling down to picoliters and below. The EWD parameters that must be considered in scaling actuator dimensions include: (1) threshold voltage for droplet actuation, (2) droplet splitting voltage, (3) droplet dispensing voltage from on-chip reservoirs, (4)
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voltage dependence of droplet velocity, and (5) droplet mixing times. To address the scaling issues of these device parameters requires an integrated analytical model for the fluidic functions of droplets placed between parallel plates in a EWD actuator. A hydrodynamic model of droplet actuation was constructed in a systematic manner that includes the effects of contact angle hysteresis, drag from the filler fluid, drag from the solid walls, and changes in the actuation force while a droplet traverses one electrode to the next. From this model, we have developed scaling rules for EWD parameters. This model is then applied to EWD actuator scaling. In addition, limits on applied actuator voltages are developed for reliable operation based on conditions for contact-angle saturation. 2. EWD Actuator Scaling Model The driving force of droplet transport is due to a change in surface tension when an electric potential is applied between a droplet and an electrode coated with an insulator of thickness t. When a voltage, V, is applied the charges on the surface of the insulator modify the surface tension between the droplet and the insulator. Then, the resulting change in contact angle of the droplet is described by the Lippmann–Young equation:
cos θ(V) = cos θ(0) +
εrεoV2 2tγ lg
(1)
where ε o (8.85 × 10−12 F/m) is the permittivity of vacuum, ε r is the dielectric constant of the insulator layer, V is the applied voltage, θ(0) is the non-actuated contact angle, θ(V) is the droplet contact angle when voltage V is applied, where γlg is the liquid-filler medium interfacial tension. Based on a model of the force balance on the contact line of a droplet and the Lippmann–Young equation, the velocity of a droplet undergoing EWD actuation has been derived, as shown in Eq. (1) [7].
εrεoV2 sin φ { cos α − γ lg sin α [sin θ(V)+ sin θ(0)]} 2t U= μ d 12μ o +2C v d L L d
(2)
where t is the dielectric thickness, α is the contact angle hysteresis, d is the gap of the actuator, L is the electrode pitch, φ is the advancement angle of the droplet, V is the applied voltage, θ(0) is the non-actuated contact angle,
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and θ(V) is the droplet contact angle when voltage V is applied, and VT is the threshold voltage for droplet actuation. The first term in the denominator is due to drag from the filler medium (oil or air), and the second term is due to drag on the droplet by the two opposing plates in the actuator. The velocity model of Eq. (2) is similar to the simplified model of Baird, which does not take into consideration drag from the filler medium or contact line resistance [8]. It is revealed in Eq. (2) that the velocity is proportional to the square of the applied voltage, which agrees with previous observations. Equation (2) also predicts that the droplet velocity will increase with the actuator aspect ratio, d/L, if the viscous drag term dominates over the filler medium drag. This follows since as the gap d increases, the drag on the droplet from the plate surfaces decreases. Such a dependence of droplet velocity on gap height in an air medium has been experimentally observed [9]. 2.1. THRESHOLD VOLTAGE SCALING
We have investigated the way in which VT scales with the physical dimensions of the EWD actuator and with the medium surrounding the droplet (oil or air). We have also explored the upper range of applied voltages and find that reliable actuator operation can only occur of the applied voltage remains below the contact-angle saturation voltage of the droplet. Other fluidic operations whose scaling behavior has been studied include droplet dispensing, splitting, and mixing. The threshold voltage for droplet actuation, VT, occurs when V = VT and U = 0 in Eq. (2). Thus, at the threshold of droplet actuation: VT = {2tγlg/εrεo [tanα(sinθ(VT) + sinθ(0)]}1/2
(3)
If the insulator is a combination of two dielectric layers of thickness t1 and t2 with relative dielectric constant ε1 and ε2 respectively, then t/εr = t1/ε1 + t2/ε2
(4)
Equation (2) can now be written as: U = sinφ εo cosα [V2 − VT2] 2t/εr [12µod/L + 2CvµdL/d]
(5)
With regard to scaling VT for a given filler medium, the dominant variables are insulator thickness and relative dielectric constant. Equation
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100 Oil Data: (parylene C/Teflon):
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80 (VT) (V)
70 60
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Oil Air Data: - Pollack - Cho - Moon - Cooney
40 30 20 10 0
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Figure 2. Threshold voltage scaling with insulator thickness (t/εr)1/2 for water droplets in silicone oil and air filler media.
(3) is plotted in Fig. 2 for water droplets in silicone oil. We have used γlg (oil) = 47 mN/m, θ(VT) = 104o, θ(0) = 125o, and α = 2–4o based on OCT measurements of moving droplets [10]. Threshold voltage data are included for actuators fabricated with parylene C insulators of different thicknesses (0.5, 0.8, 1, and 2 µm) with a thin Teflon overcoat. Reasonable agreement is achieved with experimental results. For droplet actuation in an air medium, we have included data in Fig. 2 from a number of sources [11–14]. Equation (3) is plotted in Fig. 2 for γlg (air) = 72.8 mN/m, θ(VT) = 95o, θ(0) = 110o, and α = 9o. Reasonable agreement is achieved with experimental results. 2.2. SCALING DROPLET SPLITTING
Perhaps the simplest fluidic operations in a EWD device are the splitting of a droplet and the merging of two droplets into one. The minimum splitting arrangement involves three serial electrodes [11]. Splitting occurs when the two outer electrodes are turned on and the contact angles θb2 are reduced, resulting in an increase in the radius of curvature, r2. With the inner electrode off, the droplet expands to wet the outer two electrodes. As a result the meniscus over the inner electrode contracts to maintain a constant volume (Fig. 3a). Thus, the splitting process is underway as the liquid forms a neck
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with radius R1. In general, the hydrophilic forces induced by the two outer electrodes stretch the droplet while the hydrophobic forces in the center pinch off the liquid into two daughter droplets [15]. Section B-B’ B R1 P2
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B’
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(a)
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Section A-A’ d
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(c) Figure 3. Droplet configuration for splitting (Cho et al. [11]).
A static criterion for breaking the neck in Fig. 3a is [16]: 1/R1 = 1/R2 – (cos θb2 – cos θb1)/d
(6)
The symbols are indicated in Fig. 3. According to Eq. (6), necking and splitting are facilitated when the gap height, d, is made smaller or the volume of the droplet is increased. If contact angle hysteresis is included, the condition for splitting in Eq. (6) becomes: 1/R1 = 1/R2 – cosα εrεo[V2 − VT2]/(2dtγlg)
(7)
Generalizing splitting to occur over N electrodes (necking occurs over N′ ≥ 1 electrodes, where N = N′ + 2), the minimum voltage required for splitting is approximated by using Ren’s relation for R1 [17]: V2 − VT2 ≈ 4γlg/εo[t/εr(d/L)] [1 − 1/(N′2+1)]
(8)
It is assumed that cos α = 1. It can be seen that the static splitting voltage depends on N′ and scales with [t/εr(d/L)]1/2.
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2.3. COMBINED SCALING EFFECTS
It has been shown that static models of droplet splitting, protrusion, and dispensing all show a similar dependence on [t/εr(d/L)]1/2 [7]. As a result, curves for splitting and dispensing with N = 3 electrodes are plotted on the same axes in Fig. 4a, b for actuation in silicone oil and in air respectively. Also plotted is EWD actuator threshold voltage versus [t/εr(d/L)]1/2 for d/L = 1 and the optimum mixing condition. It can be seen that all of the important fluidic operations can be scaled. Constant voltage scaling with fixed VT can occur by maintaining constant insulator thickness, t, and d/L. However, the question remains regarding the maximum actuation voltages that can be applied for reliable actuator operation. Instabilities in threshold voltage have been associated with contact angle saturation, insulator charging, and dielectric breakdown [14, 18, 19]. Thus scaling to assure reliable operation is now considered. Optimum Mixing
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Figure 4. Superimposed scaling of droplet splitting, dispensing, protrusion, threshold voltage and mixing in a EWD actuator in an oil filler medium (left) and air (right). (Adapted from [7]).
2.4. LIMITS ON ACTUATOR VOLTAGES
Experiments show that the Lippmann–Young equation (Eq. (1)) is valid for lower voltages, but beyond a critical voltage the contact angle reaches a lower limit, contrary to the prediction of Eq. (1). This phenomenon is known as contact angle saturation [20]. Thus for electrode voltages above the voltage at which contact angle saturation occurs, the scaling results presented here are no longer valid. While there have been numerous proposals regarding the origins of contact angle saturation, it still is not certain which effect prevails [18]. However, it is clear that the associated mechanism depends on the dielectric material used to insulate the buried electrodes of a EWD actuator and its thickness.
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The work of Berry et al. and others has suggested that increasing the applied voltage until contact angle saturation occurs was damaging to the insulator [21, 22]. Berry et al. later proposed that for a composite insulator consisting of an amorphous fluoropolymer coating of thickness t1 on an insulator of thickness t2, charge trapping occurs during contact angle saturation [23]. The onset of charge trapping was proposed to occur when the effective dielectric strength of the fluoropolymer layer, D1, is exceeded. The threshold voltage for this condition is given by the expression: Vtc = ε1D1t/εr = D1[ t1+ t2 (ε1/ε2)]
(9)
where ε1 is the dielectric constant of the amorphous fluoropolymer, and ε2 is the dielectric constant of the underlying insulator. For early actuators fabricated in our lab with composite dielectrics of 0.8 µm thick parylene C and 60 nm Teflon AF, it was observed that an actuator’s threshold voltage exhibited a time-dependent increase for applied electrode voltages of 60–100 V [14]. However, Eq. (9) predicts that insulator charging at V > 60 Vdc would occur in Pollack’s device at Vtc = 14.1 V. This value of charging voltage falls well below the observed threshold voltages reported by Pollack. From the standpoint of electrowetting contact angle saturation, the Lippmann–Young equation (Eq. (1) above) is valid up to V = Vsat at contact angle saturation. Assuming a composite insulator with a fluoropolymer layer over an underlying oxide layer, then at contact angle saturation Eq. (1) can be rewritten as Vsat = {2γlg/εoε1[t1 + t2(ε1/ε2)][cosθ(Vsat) − cosθ(0)]}1/2 200
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Figure 5. Calculated and measured contact angle saturation vs. insulator thickness (t/εr)1/2 for water droplets in air and silicone oil media.
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Calculated and measured contact angle saturation vs. insulator thickness (t/εr)1/2 for water droplets in air and silicone oil media are shown above in Fig. 5. It can be seen that the saturation voltage is essentially independent of the filler medium (silicone oil with γlg(oil) = 47 mN/m and air with γlg(air) = 72.8 mN/m), and essentially one curve represents Vsat vs [t/εr]1/2 for a variety of insulator systems. It can be seen above in Fig. 2 that an EWD actuator operating with a silicone oil filler medium has a lower VT for any given value of [t/εr]1/2. Since similar values of Vsat occur in both systems, an air filler medium will afford a smaller reliable operating voltage range than an oil system. 2.5. SECTION SUMMARY
In summary, it has been shown that static models of droplet splitting and liquid dispensing all show a similar dependence on [t/εr(d/L)]1/2. Scaling reduces the amount of linear displacement to dispense a droplet. Thus, the model shows that as long as t/εr(d/L) is held constant while L is decreased, the same number of dispensing electrodes required is fixed for constant (V2 − VT2)1/2. Therefore, scaling to smaller droplet volumes is favorable for droplet pinchoff with a correspondingly smaller linear displacement of liquid from the reservoir. Based on numerous studies reported in the literature, we conclude that reliable operation of a EWD actuator is possible as long as the device is operated within the limits of the Lippmann–Young equation. The upper limit on applied voltage, Vsat, corresponds to contact-angle saturation. For both silicone oil and air media, the values of Vsat vs. (t/εr)1/2 are essentially the same. The minimum 3-electrode splitting voltages as a function of aspect ratio d/L < 1 for an oil medium are less than Vsat. However, it is likely that conditions for uniform droplet splitting may require voltages that exceed Vsat. For an air medium the minimum voltage for 3-electrode droplet splitting exceeds Vsat for d/L ≥ 0.4. This observation implies that reliable splitting in air places tighter limits on the actuator aspect ratio. Similar conclusions also apply to droplet dispensing. 3. Applications Investigators have conducted extensive research on the basic principles and operations underlying the implementation of electrowetting-based digital microfluidic systems. The result is a substantial “microfluidic toolkit”. In biomedical applications it is required to transport biological liquids and beads. The transport of non-biological electrolytes using electrowetting has been demonstrated both in air [24] and in other immiscible media such as silicone oil [25]. And transport of polystyrene beads in solution [10] and
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magnetic beads [26] has been demonstrated. On the contrary, the transport of fluids containing proteins, such as enzyme-laden reagents and human physiological fluids is not as straightforward. This is because most proteins tend to adsorb irreversibly to hydrophobic surfaces, and contaminate them. In addition to contamination, protein adsorption can also render the surface permanently hydrophilic [27]. This is detrimental to transport, since electrowetting works on the principle of modifying the wettability of a hydrophobic surface, unless such contamination is intended for a particular application [28]. Examples of tools in the digital microfluidic toolkit will be reviewed. 3.1. DIGITAL MICROFLUIDIC TOOLKIT
Fluidic I/O: Loading samples and reagents on chip requires an interface between the microfluidic device and the outside world. Strategies for introducing samples and reagents onto a microfluidic chip are usually not discussed at length by workers in the field. Typically droplets are pipetted onto EWD chips and then the top plate is applied to close the system [14, 29]. The key is to provide a continuous-supply external source that keeps the on-chip reservoirs full. On-chip storage and dispensing: Reservoirs can be created on EWD devices in the form of large electrode areas that allow liquid droplet access and egress [10, 29]. Liquids from the I/O ports are stored in reservoirs. The basic lab-on-a-chip should have a minimum of three reservoirs – one for sample loading, one for the reagent, and one for collecting waste droplets, but this depends on the application. A fourth reservoir might be needed for a calibrating solution. Each reservoir should have independent control to allow either dispensing of droplets or their collection. Droplet dispensing refers to the process of aliquoting a larger volume of liquid into smaller unit droplets for manipulation on the electrowetting system. Droplet generation is the most critical component of an electrowetting-based lab-on-a-chip, because it represents the world-to-chip interface. Controlled droplet dispensing on chip can occur by extruding a liquid finger from the reservoir through activation of adjacent serial electrodes [17, 24, 33]. Mixing: Mixing of analytes and reagents in microfluidic devices is a critical step in building a lab-on-a-chip system [4, 41, 42]. Mixing in these systems can either be used for pre-processing, sample dilution, or for reactions between samples and reagents in particular ratios. The ability to mix liquids rapidly while utilizing minimum area greatly improves the throughput of such systems. However, as microfluidic devices are approaching the sub nano-liter regime, reduced volume flow rates and very low Reynolds numbers make mixing such liquids difficult to achieve in reasonable time scales. In an electrowetting-based digital microfluidic device, for example, typical
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times to perform elemental fluidic operations can be compared to passive mixing solely by diffusion of the contents of two coalesced droplets. Droplet splitting and merging: Perhaps the simplest fluidic operations in a EWD device are the splitting of a droplet and the merging of two droplets into one. For splitting a droplet three electrodes are used as described by Cho et al. [11]. During splitting the outer two electrodes are turned on and the contact angles are reduced, resulting in an increase in the radii of curvature. With the inner electrode off, the droplet expands to wet the outer two electrodes. Thus, the splitting process is underway as the liquid forms a neck. In general, the hydrophilic forces induced by the two outer electrodes stretch the droplet while the hydrophobic forces in the center pinch off the liquid into two daughter droplets [15]. Sample dilution and purification: In EWD devices, dilution has been investigated using a binary interpolating mixing algorithm and architecture [17, 43, 44]. Sample purification has been investigated on EWD devices for the specific application of Matrix-Assisted Laser Desorption/Ionization Mass Spectrometry (MALDI-MS) for protein analysis [5]. Sample preparation in EWD devices with a silicone oil medium requires an alternative method to sample drying. One method that has been investigated is the use of magnetic beads with attached analytes or antibodies localized onto the top plate or confined in solution by an external magnet. The beads then are washed with droplets transported to the bead site. This method has been successfully demonstrated in a DNA sequencing application and will be described. Sample washing methods are described. Molecular separation: When mass-limited samples are used in biochemical analysis, it is often required to isolate components that produce a signal of interest so that component can be further processed by amplification, modified, or extracted for identification. Such processes require initial separation followed by fractionation and collection. To date, there have been no reports of the full integration of electrophoresis and electrowetting. However, two papers have demonstrated droplet-based sample loading into a capillary electrophoresis tube [30, 31]. Itegration would require a digitalto-analog (D/A) interface from the EWD device, where a sample containing DNA, for example, would be presented to the input well of a capillary electrophoresis device for sample injection and plug focusing. lity to manipulate magnetic microspheres in solution on a EWD device will expand the variety of tasks that can be performed if the microspheres are used as analyte immobilization surfaces. Because the microspheres can be transported in solution and immobilized by a magnetic field, the use of microspheres on-chip will not alter the reconfigurability or reusability of the chip. The retention of 8 μm diameter magnetic microspheres during droplet splitting has been demonstrated on a digital microfluidic platform through 2,000 wash steps.
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3.2. ARCHITECTURE
The digital microfluidic architecture shown below in Fig. 6 [32] capitalizes on the flexibility of a unit flow grid array. At any given time, the array can be partitioned into “cells” that perform fluidic functions, such as storage, mixing, or transport. If the array is actuated by a clock that can change the voltage at each electrode on the array in one clock cycle, then the architecture has the potential for dynamically reconfiguring the functional cells at least once per clock cycle. Thus, once the fluidic function defined by a cell is completed, the cell electrode voltages can be reconfigured for the next function. Digital microfluidic architecture is under software-driven electronic control, eliminating the need for mechanical tubes, pumps, and valves that are required for continuous-flow systems. The compatibility of each chemical substance with the electro-wetting platform must be determined initially. Compatibility issues include the following: (1) Does the liquid’s viscosity and surface tension allow for droplet dispensing and transport by electrowetting? (2) Will the contents of the droplet foul the hydrophobic surfaces of the chip? (3) In systems with a silicone oil medium, will the chemicals in the droplet cross the droplet/oil interface, thus reducing the content in the droplet? (4) What type of detection method is suitable?
Figure 6. Two-dimensional electrowetting electrode array used in digital microfluidic architecture.
3.3. APPLICATIONS
Demonstrations of numerous applications of digital microfluidics have been made in the past five years. Some examples are presented below.
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3.3.1. Colorimetric Assays On-chip colorimetric assays for determining the concentrations of target analytes is a natural application for digital microfluidics [10, 33, 34]. The specific focus of work in this area has been on multiplexed assays, where multiple analytes can be measured in a single sample. The on-chip process steps include the following: (1) pre-diluted sample and reagent loading into on-chip reservoirs, (2) droplet dispensing of analyte solutions and reagents, (3) droplet transport, (4) mixing of analyte solutions.
Figure 7. Optical absorbance measurement instrumentation used to monitor color change due to colorimetric reactions on chip.
Srinivasan et al. have demonstrated a colorimetric enzyme-kinetic method based on the Trinder’s reaction used for the determination of glucose concentration [33]. At the end of the mixing phase, the absorbance is measured for at least 30 s, using a 545 nm LED-photodiode setup. The mixed droplet is held stationary by electrowetting forces during the absorbance measurement step, depicted in Fig. 7. 3.3.2. Chemiluminescent Assays Chemilumescent detection has been shown to be compatible with the digital microfluidic platform [35] and with diagnostic applications as well as sequencing DNA by synthesis [36]. In general, the on-chip chemistry must result in optical signal generation in the vicinity of a photodetector. Work in this area has been reported by Luan et al. with an integrated optical sensor based upon the heterogeneous integration of an InGaAs-based thin film photodetector with a digital microfluidic system [35].
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DNA sequencing-by-synthesis methods involve enzymatic extension by polymerase through the iterative addition of labeled nucleotides, often in an array format. The cascade begins with the addition of a known nucleotide to the DNA (or RNA) strand of interest. This reaction is carried out by DNA Polymerase. Upon nucleotide incorporation, pyrophosphate (PPi) is released. This pyrophosphate is converted to ATP by the enzyme ATP sulfurylase. The ATP then provides energy for the enzyme lucerifase to oxidize luciferin. One of the byproducts of this final oxidation reaction is light at approximately 560 nm. This sequence is shown in Fig. 8. The light can be easily detected by a photodiode, photomultiplier tube, or a charge-coupled device (CCD). Since the order in which the nucleotide addition occurs is known, one can determine the sequence of the unknown strand by formation of its complimentary strand. The entire pyrosequencing cascade takes about 3–4 s from start to finish per nucleotide added. Pyrosequencing of DNA has been performed on a digital microfluidic platform [36]. The chip was covered with a transparent top plate and filled with oil to create a microfluidic chamber in which droplets were programmably manipulated (dispensed, transported, merged, split) using electrical fields. Using a 211 bp DNA fragment derived from C. albicans genomic DNA, single stranded templates were prepared and attached to 2.8 µm magnetic beads. Results of a 20 bp read are shown in Fig. 9.
Figure 8. Illustration of solid-phase pyrosequencing. After incorporation of a nucleotide (in this case dATP), a washing step is used to remove the excess substrate.
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Figure 9. On-chip pyrosequencing results showing 17-bp sequencing of a 211-bp long C. albicans DNA template.
3.3.3. DNA Hybridization Testing There is significant interest in developing microfluidic systems that can function as portable, chip-scale DNA diagnostic sensors. The testing procedure involves isolating parasitic DNA from blood, cleaning the DNA, and detecting. This protocol is illustrated below in Fig. 10 [37]. The main fluidic functions required to achieve the detection of DNA are given in the flowchart. Using malaria detection as an example, the procedure starts having as input a 1 µl volume of blood. The first step is the sample preparation. This consists of detaching the infected cells, breaking their cellular membrane and extracting the DNA. As the amount of DNA is too scarce for successful detection to be considered, DNA must be replicated by using an amplification technique. Finally, a detection step is integrated in order to determine if an infection with one of the malaria parasites is present in the organism [37]. Magnetic bead separation implemented on a digital microfluidic platform is the first step in separating infected cells from other cells in whole blood [37, 38]. Magnetic beads can be made to selectively tag infected cells using antibody–antigen bonding. By locating the droplet containing beads and other cells over a magnet, separation can be achieved by washing a 2x droplet through the bead droplet. After 5–10 wash droplets pass, the bead droplet is relatively clean, only containing tagged cells on beads. This method does not result in bead loss [36]. Chemical cell lysis of infected cells is carried out to extract parasitic DNA. Droplets containing lysing agents are dispensed from their reservoirs, and are mixed with the bead droplets. After cell lysis, DNA strands need to be extracted from a mixture of the cell contents suspended in a droplet. To facilitate DNA extraction, the droplet is first heated to 95°C to convert the double stranded DNA to single stranded DNA. The droplet is then mixed
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with a droplet containing complementary DNA strands attached to magnetic beads. Magnetic bead separation is then repeated as described previously. After DNA extraction from the lysed cells, the droplet is heated to unbind the DNA from the magnetic beads. This droplet undergoes further magnetic bead separation, to separate the magnetic beads from the DNA strands. The resulting droplet, concentrated with DNA strands then undergoes PCR [39].
Figure 10. Malaria chip flowchart.
Dhar et al. [37] have pointed out that several detection schemes are possible for the malaria chip. A popular technique is flow cytometry, where sample processing is performed on-chip, and the chip is then used in conjunction with a commercial cytrometry device. An advantage of this technique is that it is well-established, but a major drawback is that the detector is rather large and not on-chip. An on-chip detection option is an integrated thin-film semiconductor light source, waveguide and detector capable of measuring changes in transmission. Or, instead of integrating a light source, such a scheme could measure changes in the chemiluminescence of the sample, as shown by L. Luan et al. [35]. Surface plasmon resonance (SPR) may also be a viable detection scheme. However, no one has shown that SPR can be integrated on a digital microfluidic chip [40]. 4. Conclusions Investigators working in the field of digital microfluidics have conducted extensive research on the basic principles and operations underlying the implementation of electrowetting-based microfluidic systems. The result is a substantial “microfluidic toolkit” of automated droplet operations, a sizable
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catalog of compatible reagents, and demonstrations of important chemical and biological assays. However, the lack of good integrated on-chip sensing methods and on-chip sample preparation currently are the biggest impediments to broad commercial acceptability of microfluidic technologies, including digital microfluidics. Other issues include system integration and interfacing to other laboratory formats and devices, packaging, reagent storage, and maintaining temperature control of the chip during field operation. The number and variety of analyses being performed on chip has increased along with the need to perform multiple-sample manipulations. It is often desirable to isolate components that produce a signal of interest, so that they can be detected. Currently, mass separation methods, such as capillary electrophoresis, are not an established part of the digital microfluidic toolkit, and integration of separation methods presents a significant challenge. Nevertheless, we will see the first introduction of commercial digital microfluidic chips into certain laboratory applications in the near future.
References 1. B. Berge, Electrocapillarite et mouillage de films isolants par l’eau, C. R. Acad. Sci. II 317, 157 (1993). 2. M.G. Pollack, R.B. Fair, and A.D. Shenderov, Electrowetting-based actuation of liquid droplets for microfluidic applications, Appl. Phys Lett 77, 1725–1727 (2000). 3. R.B. Fair, M.G. Pollack R. Woo, V.K. Pamula, H. Ren, T. Zhang, and J. Venkatraman, A microwatt metal-insulator-solution-transport (MIST) device for scalable digital bio-microfluidic systems, Technical Digest, Inter. Electron Device Meeting 367–370 (2001). 4. J. Fowler, H. Moon and C-J Kim, Enhancement of mixing by droplet-based microfluidics. Proc IEEE MEMS 97, 100 (2002). 5. H. Moon, A.R. Wheeler, R.L. Garrell, J.A. Loo, and C-J Kim, An integrated digital microfluidic chip for multiplexed proteomic sample preparation and analysis by MADDA-MS. Lab Chip 6, 1213–1219 (2006). 6. E. Seyrat and R.A. Hayes, Amorphous fluoropolymers as insulators for reversible low-voltage electrowetting, J Appl Phys 90, 1383–1386 (2001). 7. J.H. Song, R. Evans, Y.-Y. Lin, B.-N. Hsu, and R.B. Fair, A scaling model for electrowetting-on-dielectric microfluidic actuators, Microfluidics and Nanofluidics 7, 75–89 (2009). 8. E.S. Baird and K. Mohseni, A unified velocity model for digital microfluidics. Nanoscale and Microscale Thermophysical Engrg. 11, 109–120 (2007). 9. R.-F. Yue, J.-G. Wu, X.F. Zeng, M. Kang, and L.T. Liu, Demonstration of four fundamental operations of liquid droplets for digital microfluidic systems based on an electrowetting-on-dielectric actuator. Chin. Phys. Lett. 23, 2303– 2306 (2006).
302
R.B. FAIR
10. V. Srinivasan, V.K. Pamula, M.K. Pollack, and R.B. Fair, Clinical diagnostics on human whole blood, plasma, serum, urine, saliva, sweat, and tears on a digital microfluidic platform, Proceedings of MicroTAS 2003 1287–1290 (2003). 11. S.-K. Cho S.-K. Fan H. Moon H and C.-J. Kim, Towards digital microfluidic circuits: creating, transporting, cutting and merging liquid droplets by electrowetting-based actuation,” Tech. Dig. MEMS 2002 IEEE Inter Conf on Micro Electro Mechanical Systems, 11, 454–61 (2002). 12. H. Moon, S.-K. Cho, R.L. Garrell, and C.-J. Kim, Low voltage electrowettingon-dielectric. J Appl Phys 92, 4080–4087 (2002). 13. C.G. Cooney, C.-Y. Chen, M.R. Emerling, A. Nadim, and J.D. Sterling, Electrowetting droplet microfluidics on a single planar surface. Microfluidics and Nanofluidics 2, 435–446 (2006). 14. M.G. Pollack, Electrowetting-based Microactuation of Droplets for Digital Microfluidics. Ph.D. Thesis, Duke University (2001). 15. J. Berthier, P.H. Clementz, O. Raccurt , D. Jary, P. Claustre, C. Peponnet, and Y. Fouillet, Computer aided design of an EWOD microdevice, Sensors and Actuators A, 127, 283–294 (2006). 16. S.-K. Cho, H.Moon, J. Fowler, and C.-L. Kim, Splitting a liquid droplet for electrowetting-based microfluidics. Proceedings of 2001 ASME Inter Mech Eng Congress and Expo, November 11–16 New York, NY (2001). 17. H. Ren, Electrowetting-based sample preparation: an initial study for droplet transportation, creation and on-chip digital dilution. Ph.D. Thesis Duke University (2004). 18. A.G. Papathanasiou, A.T. Papaioannou, and A.G. Boudouvis, Illuminating the connection between contact angle saturation and dielectric breakdown in electrowetting through leakage current measurements. J. Appl. Phys. 103, 034901-1-4 (2008). 19. H.J. Verheijen and M.W.J. Prins, Reversible electrowetting and trapping of charge: model and experiments, Langmuir 15, 6616–6620 (1999). 20. M. Vallet, M. Vallade, and B. Berge, Limiting phenomena for the spreading of water on polymer films by electrowetting, Eur. Phys. J. B 11, 583–591 (1999). 21. S. Berry, J. Kedzierski, and B. Abedian, Low voltage electrowetting using thin fluoropolymer films. J. Colloid and Interface Sci. 303, 517–524 (2006). 22. J. Kedzierski and S. Berry, Engineering the electrocapillary behavior of electrolyte droplets on thin fluoropolymer films. Langmuir 22, 5690–5696 (2006). 23. S. Berry, J. Kedzierski, and B. Abedian, Irreversible electrowetting on thin fluoropolymer films. Langmuir 23, 12429–12435 (2007). 24. S.-K. Cho, H. Moon and C.-J. Kim, Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits, J. Microelectromech Sys 12 (1), 70–80 (2003). 25. M.G. Pollack, A. Shendorov and R.B. Fair, Electrowetting–based actuation of droplets for integrated microfluidics. Lab Chip 2, 96–101 (2002). 26. R.B. Fair, A. Khlystov, V. Srinivasan, V.K. Pamula, K.N. Weaver, Integrated chemical/biochemical sample collection, pre-concentration, and analysis on a digital microfluidic lab-on-a-chip platform. in Lab-on-a-Chip: Platforms, Devices, and Applications, L.A. Smith and D. Sobek, eds. Proc. of SPIE 5591 113–124 (2004).
SCALING FUNDAMENTALS AND APPLICATIONS
303
27. Y.-J. Yoon and R.L. Garrell, Preventing biomolecular adsorption in electrowetting-based biofluidic chips. Anal Chem 75, 5097–5102 (2003). 28. A.R. Wheeler, H. Moon, C.A. Bird, R.R. Orgazalek Loo, C-J Kim, J.A. Loo and R.L. Garrell, Digital microfluidics with in-line sample purification for proteomics analyses with MALDI-MS. Anal Chem 77, 534–540 (2005). 29. A.R. Wheeler, H. Moon, C-J Kim, J.A. Loo, and R.L. Garrell, Electrowettingbased microfluidics for analysis of peptides and proteins by matrix-assisted laser desorption/ionization mass spectrometry. Anal Chem 76, 4833–4838 (2004). 30. M. Abdelgawad, M.W.L. Watson and A.R. Wheeler, Hybrid microfluidics: a digital-to-channel interface for in-line sample processing and chemical separations, Lab Chip, 9, 1046–1051 (2009). 31. J. Gorbatsova, M. Jaanus and M. Kaljurand, Digital microfluidic sampler for a portable capillary electropherograph, Anal Chem 81, 8590–8595 (2009). 32. J. Ding, K. Chakrabarty and R.B. Fair, Scheduling of microfluidic operations for reconfigurable two-dimensional electrowetting arrays, IEEE Transactions on Computer-Aided Design of Integrated Circuits & Systems, 29, 1463–1468 (2001). 33. V. Srinivasan, V.K. Pamula and R.B. Fair, An integrated digital microfluidic lab-on-a-chip for clinical diagnostics on human physiological fluids, Lab Chip, 4, 310 (2004). 34. J. Aizenberg, T. Krupenkin and P. Kolodner, “Accelerated chemical reactions for lab-on-a-chip applications using electrowetting-induced droplet self oscillations.” Materials Research Society Symposium Proceedings 915, 103– 111 (2006). 35. L. Luan, R.D. Evans, D. Schwinn, R.B. Fair, and N.M. Jokerst, Chip scale integration of optical microresonator sensors with digital microfluidics systems, LEOS-2008, Newport Beach, CA, Nov. 9–13 (2008). 36. P. Thwar, J.L. Rouse, A.E. Eckhardt, P. Griffin, M.G. Pollack and R.B. Fair, “Digital microfluidic DNA sequencing,” Advances in Genome Bbiology and Technology (AGBT) Meeting, Marco Island, Florida, Feb., 2009. 37. S. Dhar, S. Drezdzon, E. Maftei (2008) unpublished. 38. Y. Wang, Y. Zhao, and K.C. Sung, “Efficient in-droplet separation of magnetic particles for digital microfluidics,” J. Micromechanics and Microengineering 17, 2148 (2007). 39. M.G. Pollack, P. Y. Paik, A. D. Shenderov, “Investigation of electrowettingbased microfluidics for real-time PCR applications.” In Proc. µTAS, 619–622 (2007). 40. L. Malic, T. Veres and M. Tabrizian, Two-dimensional droplet-based surface plasmon resonance imaging using electrowetting-on-dielectric microfluidics, Lab Chip, 9, 473–475 (2009). 41. V. Hessel, H. Lowe, and F. Schoenfeld, Micromixers-a review on passive and active mixing principles. Chem Engrg Sci. 60, 2479–2501 (2005). 42. T.M. Squires, and S.R. Quake, Microfluidics: fluid physics at the nanoliter scale. Rev Mod Phys. 77, 977–1026 (2005).
304
R.B. FAIR
43. R.B. Fair, V. Srinivasan, P. Paik, H. Ren, V.K. Pamula and M.G. Pollack, Electrowetting-based on-chip sample processing for integrated microfluidics. Tech Dig IEEE Inter Electron Dev Meeting, 779–782 (2003). 44. E.J. Griffith, A. Srinivas and M.K. Goldberg, Performance characterization of a reconfigurable planar-array digital microfluidic system. IEEE Trans Computer-Aided Des Integrated Cir and Sys. 25, 345–357 (2006).
MICROFLUIDIC LAB-ON-A-CHIP PLATFORMS: REQUIREMENTS, CHARACTERISTICS AND APPLICATIONS D. MARK1, S. HAEBERLE1,2, G. ROTH1,2, F. VON STETTEN1,2, AND R. ZENGERLE1,2 1
HSG-IMIT – Institut für Mikro- und Informationstechnik, WilhelmSchickard-Straße 10, 78052 Villingen-Schwenningen, Germany 2 Laboratory for MEMS Applications, Department of Microsystems Engineering (IMTEK), University of Freiburg, Georges-KoehlerAllee 106, 79110 Freiburg, Germany,
[email protected]
Abstract. This review summarizes recent developments in microfluidic platform approaches. In contrast to isolated application-specific solutions, a microfluidic platform provides a set of fluidic unit operations, which are designed for easy combination within a well-defined fabrication technology. This allows the implementation of different application-specific (bio-) chemical processes, automated by microfluidic process integration [1]. A brief introduction into technical advances, major market segments and promising applications is followed by a detailed characterization of different microfluidic platforms, comprising a short definition, the functional principle, microfluidic unit operations, application examples as well as strengths and limitations. The microfluidic platforms in focus are lateral flow tests, linear actuated devices, pressure driven laminar flow, microfluidic large scale integration, segmented flow microfluidics, centrifugal microfluidics, electrokinetics, electrowetting, surface acoustic waves, and systems for massively parallel analysis. The review concludes with the attempt to provide a selection scheme for microfluidic platforms which is based on their characteristics according to key requirements of different applications and market segments. Applied selection criteria comprise portability, costs of instrument and disposable, sample throughput, number of parameters per sample, reagent consumption, precision, diversity of microfluidic unit operations and the flexibility in programming different liquid handling protocols. 1. Introduction The increasing number of publications [2] and patents [3] related to microfluidics reveals how relevant the technology has become during the last years, also from a commercial perspective. Consequently, microfluidics has S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_17, © Springer Science + Business Media B.V. 2010
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established itself in academia and industry as a toolbox for the development of new methods and products in life sciences. However, the public visibility of microfluidic products is, with few exceptions, still very low. The question is: will microfluidics remain a toy for academic and industrial research or will it finally make the transition to an end-user product? Looking into the past, the first microfluidic technology was developed in the early 1950s when efforts to dispense small amounts of liquids in the nanoliter and sub-nanoliter range were made, providing the basics of today’s ink-jet technology [4]. In terms of fluid propulsion within microchannels with sub-millimeter cross sections, the year 1979 set a milestone when a miniaturized gas chromatograph (GC) was realized on a silicon (Si) wafer [5]. The first high-pressure liquid chromatography (HPLC) column microfluidic device, fabricated using Si-Pyrex technology, was published in 1990 by Manz et al. [6]. By the end of the 1980s and the beginning of the 1990s, several microfluidic structures, such as microvalves [7] and micropumps [8, 9] have been realized by silicon micromachining, providing the basis for automation of complex liquid handling protocols by microfluidic integration [10, 11]. This was the advent of the newly emerging field of “micro total analysis systems” (µTAS [12]), also called “lab-on-a-chip” [13]. At the same time, much simpler yet very successful microfluidic analysis systems based on wettable fleeces emerged: First very simple “dipsticks” for e.g. pH measurement based on a single fleece paved the way for more complex “test strips” that have been sold as “lateral-flow tests” in the late 1980s [14]. Examples that are still on the market today are test strips for pregnancy [15], drug abuse [16–18], cardiac markers [19] and also upcoming bio-warfare protection [20]. Among the devices that completely automated a biochemical analysis by microfluidic integration into one miniature piece of hardware, the test strips became the first devices that obtained a remarkable market share and still remain one of the few microfluidic systems which is sold in high numbers. Until today, most of the revenue in the field of lab-on-a-chip is created on a business-to-business, but not on a business-to-consumer basis [21], as the vast majority of research in the field only approaches the stage of demonstrators and is not followed by the development of products for endusers. Among the hurdles for market entry are high initial investments and running fabrication costs [22]. Furthermore, the multitude of individual labon-a-chip solutions developed so far cannot compete with the flexibility of state of the art liquid handling approaches, e.g. with pipetting robots. Instead of the time-consuming and expensive developments of applicationspecific microfluidic solutions, we propose to base microfluidic developments on a microfluidic platform approach, where a combinable set of liquid handling steps together with a suitable fabrication technology enable the flexible and affordable implementation of biochemical protocols in a market-relevant
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framework. Hence, the intention of this review is to provide an overview on lab-on-a-chip applications that are based on a microfluidic platform approach. According to their actuation scheme, we subdivide microfluidic platforms into five groups, namely: capillary, pressure driven, centrifugal, electrokinetic and acoustic systems, as depicted in Fig. 1. After providing a short general introduction to unique properties, requirements, and applications for microfludic platforms, the review focusses on a detailed discussion of the microfluidic platforms listed in Fig. 1. First, the defintion and the general principle of the microfluidic plaform is presented. Afterwards, already implemented unit operations as well as application examples are briefly discussed for each platform. This is summed up by highlighting the strengths and limitations of each platform, mainly with respect to the selection criteria. The review is concluded by an attemp to provide a selection scheme for microfluidic platforms which is based on platform characteristics and application requirements. This review contains examples of microfluidic platforms for lab-on-a-chip applications which were selected as fitting to our platform definition and no comprehensiveness is claimed. The review should, however, provide the reader with some orientation in the field and the ability to select platforms with appropriate characteristics on the basis of application-specific requirements.
Figure 1. Microfluidic platforms classified according to actuation method.
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2. The Framework for Microfluidic Platforms: Unique Properties, Requirements and Applications 2.1. MICROFLUIDICS AS AN ENABLING TECHNOLOGY: FROM CLASSICAL LIQUID HANDLING TO SINGLE-CELL HANDLING
A number of classical, macroscopic liquid handling systems for perfoming analytical and diagnostic assays have been in use for many decades. Examples are petri dishes, culture bottles and microtitre plates (also called microplates). Petri dishes have been first described in 1887 [23] and culture bottles [24] are in use since around 1850. Since roughly 60 years ago, they are manufactured as plastic disposables. In comparison, microtiter plates are quite “modern,” having first been described in 1951 [25]. Based on these standards, highly automated high throughput solutions have been developed within the last decades (“pipetting robots”) and are the current “gold standard” in the market. They offer a huge potential for many applications since they are very flexible as well as freely programmable. Microfluidic platforms have to test themselves against these established systems and offer new opportunities. Expectations quoted in this context are [26]: • Higher sensitivity • Lower cost per test • Shorter time-to-result • Less laboratory space consumption Additionally, scaling effects lead to new phenomena and permit entirely new applications that are not accessible to classical liquid handling platforms, such as: 6 • High grade of parallelization (up to around 10 ) • Laminar flow with liquid gradients down to single-cell length scales • High-speed serial processing (at single cell level) Structures of the size of a cell or smaller In the following, the effects and phenomena leading to the abovementioned expectations and the potential for new applications will be outlined briefly. It is obvious that the amount of reagent consumption can be decreased significantly by scaling down the assay volume. Additionally, by reducing the footprint of each individual test, a higher degree of parallelization can be achieved in a limited laboratory space. A prime example for microfluidic tests with minimal reagent consumption are parallel reactions in hundreds of thousands individual wells with picoliter-volumes [27], which took genome sequencing to a new level [28] hardly achievable by classical liquid handling platforms. With decreasing length scales, capillary forces become increasingly dominant over volume forces. This permits purely passive liquid actuation
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used in the popular capillary test strips. Another effect is the onset of laminar flow at low Reynolds numbers in small channels. This enables the creation of well-defined and stable liquid–liquid interfaces down to cellular dimensions. Therefore, large concentration gradients can be applied and the effects monitored at the single cell level [29] (Fig. 2). In summary, laminar flow conditions and controlled diffusion enable temporally and spatially highly resolved reactions with little reagent consumption. A different paradigm using the possibility of controlling interfaces in microfluidic applications is the concept of droplet-based microfluidics, also called “digital microfluidics” [30]. The on-demand generation of liquid micro-cavities either in air or a second immiscible liquid enables the manipulation of small quantities of reagents down to single cells at high throughput [31]. Control and manipulation of such droplets can be achieved by another favorable aspect of the high surface-to-volume ratio in microfluidics: the possibility to control the liquid flow by electrically induced forces or electrowetting [32]. Having the huge background of theoretical and practical knowledge in electronics, this is obviously a desirable property. Additional helpful properties of small assay volumes are fast thermal relaxation and low power consumption for liquid manipulation and thermal control. This can speed up assays that require thermocycling, such as PCR, which was realized in numerous microfluidic applications [33].
Figure 2. Concept of differential manipulation in a single bovine capillary endothelial cell using multiple laminar flows. (a, b), Chip layout: 300 × 50 µm channels are used to create laminar interfaces between liquids from different inlets. (c) Fluorescence image of a cell locally exposed to red and green fluorophores in a laminar flow. (d) Migration of fluorophores over time (scale bars, 25 µm). This shows the high potential for accurate spatial control and separation of liquids achievable in microfluidic laminar flows. (Adapted by permission from Macmillan Publishers, Ltd: Nature [29], copyright 2001.)
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This short summary shows that there is the potential for many novel applications and improvements over the state-of-the-art within the abovementioned criteria of sensitivity, cost, time, and size. However, despite a myriad of publications about microfluidic components, principles and applications, very few successful products with a relevant market share have emerged from this field so far. In the next chapter, we will outline probable reasons and present emerging paradigm changes for the future research in microfluidics. 2.2. THE NEED FOR THE MICROFLUIDIC PLATFORM APPROACH
Definition of a Microfluidic Platform: A microfluidic platform provides a set of fluidic unit operations, which are designed for easy combination within a well-defined fabrication technology. A microfluidic platform allows the implementation of different application-specific (bio-)chemical processes, automated by microfluidic process integration. In the last two decades, thousands of researchers spent a huge amount of time to develop micropumps [34–37], microvalves [38], micromixers [39, 40], and microfluidic liquid handling devices in general. However, a consistent fabrication and interfacing technology as one prerequisite for the efficient development of lab-on-a-chip systems is very often still missing. This missing link can only be closed by establishing a microfluidic platform approach which allows the fast and easy implementation of analytical assays based on common building blocks. The idea follows the tremendous impact of platforms in the ASIC industry in microelectronics, where validated elements and processes enabled faster design and cheaper fabrication of electronic circuitries. Conveying this to the microfluidic platform approach, a set of validated microfluidic elements is required, each able to perform a certain basic liquid handling step or unit operation. Such basic unit operations are building blocks of laboratory protocols and comprise fluid transport, fluid metering, fluid mixing, valving, separation or concentration of molecules or particles (see Table 1) and others. Every microfluidic platform should offer an adequate number of microfluidic unit operations that can be easily combined to build application-specific microfluidic systems.
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TABLE 1. Common features of microfluidic platforms.
Microfluidic unit operations • Fluid transport • Fluid metering • Fluid valving • Fluid mixing • Separation • Accumulation • Reagent storage • Incubation, etc.
Fabrication technology • Validated manufacturing technology for the whole set of fluidic unit operations (prototyping and mass fabrication) • Seamless integration of different elements … preferable in a monolithic way … or by a well defined easy packaging technique
This concept, however, does not imply that every microfluidic platform needs to provide a complete set of all the unit operations listed in Table 1. It is much more important that the different elements are connectable, ideally in a monolithically integrated way or at least by a well defined, ready-to-use interconnection and packaging process. Therefore at least one validated fabrication technology is required to realize complete systems from the individual elements within a microfluidic platform. 2.3. MARKET REQUIREMENTS AND PLATFORM SELECTION CRITERIA
The requirements on microfluidic platforms differ largely between different market segments. Following a roadmap on microfluidics for life sciences [41], the four key market segments for microfluidic lab-on-a-chip applications are, according to their market size: in vitro diagnostics, drug discovery, biotechnology and ecology. The largest market segment, in vitro diagnostics, can be subdivided into point-of-care testing (e.g. for self-testing in diabetes monitoring or cardiac marker testing in emergency medicine) and central laboratory based testing (e.g. core laboratory in a hospital). Especially the self- and point-of-care testing segments offer huge potential for microfluidics, since portability is an important requirement. Drug discovery in the pharmaceutical industry is the second largest segment. Here, enormous effort is undertaken to identify new promising drug candidates in so called high-throughput screening (HTS) or massively parallel analysis [42]. After screening promising candidates, so-called hits have to be validated and characterized (hit characterization). Also cell-
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based assays received increasing interest over the last years [43, 44]. These assays often require the handling of single cells, which becomes possible using microfluidic approaches. This market segment requires high sample throughput and low costs per test. The third segment is the biotech market with the fermentation-based production (e.g. for biopharmaceuticals or food). This industry shows a great demand for on-line process monitoring and analyses in the field of process development. Here, low sample volumes and programmability are important factors. Ecology is another market segment, comprising the field of agriculturaland water-analysis, either as spot tests or as continuous monitoring. Included are also applications related to homeland security, e.g. the detection of agents that pose biological threats. This market benefits from portable systems with preferably multi-parameter capabilities. These diverse fields of applications are associated with a number of analytical and diagnostic tasks. This outlines the field for the microfluidic technology, which has to measure itself against the state-of-the-art in performance and costs. Table 2 gives an exemplary overview on some important requirements of the different market segments and application examples, with respect to the following selection criteria: • Portability: miniaturized, handheld device with low energy consumption • Sample throughput: number of samples/assays per day • Cost of instrument: investment costs of the instrument (“reader”) • Cost of disposables: defining the costs per assay (together with reagent consumption) • Number of parameters per sample: number of different parameters to be analyzed per sample • Low reagent consumption: amount of sample and / or reagents required per assay • Diversity of unit operations: the variety of laboratory operations that can be realized • Precision: the volume and time resolution that is possible • Programmability: the flexibility to assay adaptations • These criteria will be discussed for each of the platforms described in this review.
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TABLE 2. Market segments for microfluidic lab-on-a-chip applications and their requirements*.
2.4. REQUIREMENTS FROM APPLICATIONS AND ASSAYS ON LIQUID HANDLING PLATFORMS
Here, a short overview of the fields of applications that are typically addressed by microfluidic platforms is presented. A first field of application is biotransformation, the breakdown and generation of molecules and products by the help of enzymes, bacteria, or eucariotic cells cultures. This comprises fermentation, the break down and re-assembly of molecules (e.g fermentation of sugar to alcohol), and (bio)synthesis the build-up of complex molecules (e.g. antibiotics, insulin, interferon, steroids). Especially in the field of process development challenges are to handle a large number of different liquids under controlled conditions such as temperature or pH, in combination with precise liquid control down to nL or even pL volumes. Some examples of microfluidic liquid handling platforms are given for fermentation in micro bioreactors [45–52], the biosynthesis of radiopharmaceuticals [53], and antibody screening, phage- and ribosome-display technologies [54, 55].
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Another major field of application is analytics. The analysed molecule (analyte) can be from a variety of biomolecules, including proteins and nucleic acids. Here, the main requirements are effective mixing strategies and highly precise liquid handling for quantitative results. Also, automation and portability combined with a large set of unit operations for the implementation of complex analytical protocols are required. As an emerging field, cellular assays are the most challenging format, since the cells have to be constantly kept in an adequate surrounding to maintain their viability and activity (control of pH, O2, CO2, nutrition, etc.). Cellular tests useful to assess the effect of new pharmaceutical entities at different dosing concentrations on toxicity, mutagenity, bioavailability and unwanted side effects. The most exciting prospect is the establishment of assays with single-cell analyses [56, 57]. Requirements on cellular assays include high-througput solutions as well as a low reagent consumption per test. After this short overview, the next chapter will summarize the liquid handling challenges that arise from the different liquids associated with these fields of applications. 2.5. REQUIREMENTS FROM (BIO)CHEMISTRY ON LIQUID HANDLING PLATFORMS
A great challenge of biochemical applications for microfluidics is the handling of a large variation of liquids and their respective properties such as surface tension, contact angle on the substrate material (non-Newtonian) viscosity and so on. Also, an inter-sample variation e.g. due to physiological differences between patients has to be managed by a robust microfluidic system. In the following, a short summary of typical sample materials and their interactions with the microfludic substrate is given. Also, strategies to prevent unfavorable interactions are outlined. In general, the microfluidic substrates should be inert against the expected sample and assay reagents which might comprise organic or inorganic solvents or extreme pH values [58]. Likewise, the sample must not be affected by the microfluidic substrate in any way that could influence the analytical result. For example, nucleic acids are critical molecules because of their negative charge and tendency to adhere to charged surfaces such as metal oxides. Similar problems occur with proteins or peptides which exist in a variety of electrical charges, molecular sizes, and physical properties. In addition to possible adsorbtion onto the surfaces, their catalytic (enzymatic) activities can be influenced by the substrate [59–62]. A general countermeasure against the interaction of biomolecules and microfluidic substrates is the blocking of substrates with another suitable biomolecule which is added in excess. For instance bovine serum albumine (BSA) adsorbs to nearly any surface thus passivating it [63, 64]. Another significant challenge
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in microfluidic production technology is to retain the activity of pre-stored proteins. Thermal bonding [65, 66] or UV curing steps might destroy the proteins and render the assay useless. Experience shows that this set of challenges needs to be considered at the very beginning of a fluidic design, since the listed problems can jeopardize the functionality of the whole system if addressed too late. 3. Lateral Flow Tests Definition of lateral flow tests: In lateral flow tests, also known as test strips (e.g. pregnancy test strip), the liquids are driven by capillary forces. Liquid movement is controlled by the wettability and feature size of the porous or microstructured substrate. All required chemicals are pre-stored within the strip. The presence of an analyte is typically visualized by a colored line. 3.1. GENERAL PRINCIPLE
The first immunoassay performed in a capillary driven system was reported in 1978 [67]. Based on this technique, the commonly known “over-thecounter pregnancy test” was introduced into the market in the middle of the 80’s. Today, this microfluidic platform is commonly designated as a “lateral flow test (LAT)” [14]. Other terms are “test strip”, “immunochromatographic strip”, “immunocapillary tests” or “sol particle immunoassay (SPIA)” [68]. Astonishingly, hardly any publications from a microfluidic point of view or in terns of material classification exist, and apparently many “company secrets” are kept unpublished [69]. The “standard LAT” consists of an inlet port and a detection window (Fig. 3a). The core comprises several wettable materials providing all biochemicals for the test and enough capillary capacity to wick the sample through the whole strip. The sample is introduced into the device through the inlet into a sample pad (Fig. 3b), which holds back contaminations and dust. Through capillary action, the sample is transported into the conjugate pad, where antibodies conjugated onto a signal-generating particle are rehydrated and bind to the antigens in the sample (Fig. 3c). This binding reaction continues as the sample flows in the incubation and detection pad. On the test line a second type of antibody catches the particles coated with antigens, while a third type of antibodies catch particles which did not bind to an analyte on the control line. The control line shows a successfully processed test while the detection line shows the presence or absence of a specific analyte (Fig. 3d). Typically the result becomes visible after 2–15 min.
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Over the last decades, LAT transformed from a simply constructed device into a more and more sophisticated high-tech platform with internal calibrations and quantitative readout by a hand-held reader (Fig. 4) [70].
Figure 3. Schematic design of a lateral flow test (According to [69]): (a) sample pad (sample inlet and filtering), conjugate pad (reactive agents and detection molecules), incubation and detection zone with test and control lines (analyte detection and functionality test) and final absorbent pad (liquid actuation). (b) Start of assay by adding liquid sample. (c) Antibodies conjugated to colored nanoparticles bind the antigen. (d) Particles with antigens bind to test line (positive result), particles w/o antigens bind to the control line (proof of validity).
3.2. UNIT OPERATIONS
The different pads in the test strip represent different functions such as loading, reagent prestorage, reaction, detection, absorbtion and liquid actuation. The characteristic unit operation of LATs is the passive liquid transport via capillary forces, acting in the capillaries of a fleece, a microstructured surface, or a single capillary. The absorption volume of an absorption pad defines how much sample is wicked through the strip and provides metering of the sample [69]. The sample pad usually consists of cellulose or cross-linked silica and is used for filtering of particles and cells as well as separating the analyte from undesired or interfering molecules, which is absorbed in the pad [71]. The conjugation pad is made of cross-linked silica and is used as dry-reagent storage for antibodies specific to the antigen conjugated to the signal generating particle. The conjugates are typically colored or fluorescent nanoparticles with sizes up to 800 nm, which unobstructedly flow through the fleeces together with the sample. Most often colloidal gold [20] or latex
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[72] and more rarely carbon, selenium, quantum dots, or liposomes [73] are the choice of nanoparticles. The length, material (mainly nitro-cellulose) and pore-size (50 nm to 12 µm, depending on the applied nanoparticles) of the detection and incubation pad define the incubation time [69]. The detection and enrichment of the conjugates is achieved on the antibody-bearing lines. Analyte detection is performed on the test line and proof of assay validity on the control line. The readout is typically done by naked eye for absence (1 colored line) or presence (2 colored lines) of a minimum analyte amount. A readout with a reader enables quantitative analyte detection [70, 74]. For multi-analyte detection [69] or semi-quantitative setups [75] several test lines are applied. Within the last years, new LAT designs have been developed in combination with the device-based readout in handheld systems. Here a complex capillary channel network provides the liquid actuation (Fig. 4). Antibodies conjugated to nanoparticles or special enzymes are prestored at the inlet. The incubation time is defined by the filling time of the capillary network. Typically, readout is done quantitatively by fluorescence or electrochemical detection. The time-to-result is usually several seconds. Blood glucose or coagulation monitoring are the most common applications for such quantitative readouts [70]. To accommodate aging, batch-to-batch variations and sample differences and also to achieve higher precision and yield of the assay, several internal controls and calibrations are automatically performed during analysis by the readout device.
Figure 4. LAT for blood coagulation with handheld read-out according to Cosmi et al. [70, 74]. (Image (a) courtesy of Roche Diagnostics.) (a) Loading of blood, (b) the blood flows from the inlet into the fluidic network rehydrating the coagulation chemistry. The “drop detect” electrodes detect whether blood is applied and measure the incubation times. Several capillaries are filled and the filling is monitored with according electrodes. A Ag/AgCl electrode is used as standard electrode for calibration and analysis. Finally the analyte gets quantified by optical or electrochemical detection.
3.3. APPLICATION EXAMPLES
Lateral flow tests were among the first successfully commercialized microfluidic products. A huge amount of assays has been developed on the capillary test strip platform during the past 30 years [76]. Today, they serve a wide
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field of applications, including health biomarkes (pregnancy [14, 77], heart attack [71], blood glucose [78], metabolic disorders [79]), small molecules (drug abuse [80], toxins [81], antibiotics [82]), infectious agents (anthrax [83], salmonella [84], viruses [85]), pre-amplified DNA [86] and RNA applications [83], and even whole bacteria [87]. Some of the more recent designs and publications show even the detection of DNA [85] without the need of amplification by PCR, which would open yet another vast field of new applications. First trials for massively parallel screening in combination with microarrays were made in lateral flow tests [71, 83]. 3.4. STRENGTHS AND LIMITATIONS
The fact that 6 billion glucose test strips were sold in 2007 [88] already indicates that the LAT may be seen as a gold-standard microfluidic platform in terms of cost, handling simplicity, robustness, market presence and the number of implemented lab-on-a-chip applications [69]. The amount of sample and reagent consumption are quite low, and the concept is mainly used for qualitative or semi-quantitative assays. Especially the complete disposable test carriers with direct visual readout, easy handling, and a time-to-result between seconds and several minutes are predestined for untrained users. The simplicity of the test strip is also its major drawback. Assay protocols within capillary driven systems follow a fixed process scheme with a limited number of unit operations, imprinted in the microfluidic channel design itself. Highly precise liquid handling and metering is also extremely challenging [69]. The depenency of the purely capillary liquid actuation on the sample properties can also be a major problem, leading to false positive or negative results [15] or decreased precision. New designs allow applications with quantitative analysis, but require a readout device (mainly handheld) [70, 74]. High-throughput or screening applications are possible, but quite difficult to implement. In total, the lateral flow test is a well established platform with a large but limited field of applications and consequently a benchmark for the home-care and IVD sector in terms of cost per assay and simplicity. 4. Linear Actuated Devices Definition of linear actuated devices: Linear actuated devices control liquid movement by mechanical displacement (e.g. a plunger). Liquid control is mostly limited to a one-dimensional liquid flow (no branches or alternative paths) with the corresponding possibilities and limitations to assay implementation. The degree of integration is very high, with liquid calibrants and reaction buffers pre-stored in pouches.
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4.1. GENERAL PRINCIPLE
One of the first examples of a linear actuated device was the i-STAT® for quantitative bedside testing, introduced in the early 1990s by Abbott Point of Care Inc., NJ, USA. It relied on active liquid actuation by displacement [89]. Compared to lateral flow tests, this principle was one step ahead in result quantification and possible applications, but also in complexity of the processing device and disposable. The characteristic actuation principle of the linear actuated platform is the mechanical linear propulsion of liquids with no branching. Normally, the liquid actuation is performed by a plunger which presses on a flexible pouch, displacing its content. Another common attribute is the prestorage of all required reagents (liquid and dry) on the disposable test carrier (cartridge). Systems based on this platform thus offer fully integrated sample-to-result processing in relatively short time. 4.2. UNIT OPERATIONS
Basically, the linear actuated platform relies on only two unit operations: Liquid transport and reagent storage. Liquid transport is achieved by mechanical displacement (e.g. with a plunger). By pressing on flexible compartments of the disposable, the liquid can be transported between reservoirs [89]. Alternatively, a weakly bonded connection to an adjacent reservoir can be disrupted, or the connection to a neighbouring cavity selectively blocked [90]. Liquid reagent storage can easily be implemented by integrating pouches into the cartridge. Mixing can also be realized on the linear actuated platform by moving liquids between neighbouring reservoirs [90]. 4.3. APPLICATION EXAMPLES
One example of a linear actuated device is of course the previously mentioned i-STAT® analyzer from Abbott Point-of-Care [91]. Using different disposable cartridges, several blood parameters (blood gases, electrolytes, coagulation, cardiac markers, and hematology) can be determined with the same portable handheld analyzer for automated sample processing and read-out (Fig. 5a). Since only the disposable polymer cartridge is contaminated with the blood sample and thus has to be disposed after performing the diagnostic assay, the analyzer device itself is reusable. Typical response times of the system are in the order of a few minutes. The system features an integrated calibration solution that is prestored in the disposable. The analysis process takes only a few steps: As depicted in Fig. 5, the blood sample (a few drops) is filled into the cartridge by capillary
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forces (b) and placed into the analyzer (c). First, the calibrant solution is released and provides the baseline for an array of thin-film electrodes integrated in the disposable. Then the sample is pushed into the measuring chamber and displaces the calibrant. Thereby, the blood parameters which can be determined by the sensor array of the specific disposable are measured and presented at the integrated display of the handheld analyzer. Several studies showed good agreement between laboratory results and this POCsystem [89, 92, 93]. A second example is the Lab-in-a-tube (Liat™) analyzer from IQuum [94]. This bench-top device with disposable test tubes contains all necessary reagents for amplification-based nucleic acid tests. It integrates sample preparation, amplification and detection and is a fully integrated sample-toresult platform with response times between 30 and 60 min. Handling of the platform requires only a few steps: The sample (e.g. 10 µL of whole blood) is collected in the collection tube that is integrated into the disposable, the barcode on the disposable is scanned, and the tube is then inserted into the analyzer. The disposable features compartmentalized chambers in a tube which contain different reagents and can be connected via peelable seals (Fig. 6). Liquid control is performed by actuators that compress the compartments, displacing the liquid into adjacent chambers [90]. Sample preparation includes a nucleic acid purification step: Magnetic beads serve as solid nucleic acid binding phase and are controlled by a built-in magnet. For nucleic acid amplification, compartments can be heated and the liquid is transferred between two different temperature zones thus cycling the sample. The system is capable of real-time fluorescence readout.
Figure 5. Images and handling procedure of the i-STAT® analyzer. (a) Photograph depicting the portable i-STAT® analyzer for clinical blood tests [91]. (b) Depending on the blood parameters to be measured, a certain disposable cartridge is filled with blood by capillary forces from the finger tip. (c) Afterwards loaded into the analyzer for assay processing and readout. (Images courtesy of Abbott Point of Care.)
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Figure 6. Functional principle and exemplary processing steps in a nucleic acid test in the Lab-in-a-tube analyzer according to Chen et al. [90]. The disposable contains pouches with reagents (light blue) which are actuated by plungers while clamps open and close fluidic connections to adjacent pouches. (a) Sample is inserted (red). (b) Sample is mixed with prestored chemicals containing magnetic capture-beads. (c) Unwanted sample components are moved to a waste reservoir while the capture-beads are held in place by a magnet. (d–e) Further processing steps allow sequential release of additional (washing)-buffers and heating steps (red block) for lysis and thermocycling demands. The system allows optical readout by a photometer (PM).
4.4. STRENGTHS AND LIMITATIONS
The presented commercially available examples show that automation and time-reduction by microfluidic systems with active processing devices can indeed be achieved in a market-relevant context. The potential of the linear actuated device platform certainly lies in its simplicity and the ability for long-term liquid reagent storage. The presented application examples are portable and show a high degree of assay integration, requiring no external sample pre- or post processing steps. Typical liquid (sample) volumes handled on the platform are in the range of 10–100 µL, which is adequate for pointof-care diagnostic applications (capillary blood from finger tip). While disposables can generally be mass-produced, these can become somewhat expensive due to the integration of sensors (i-STAT®) and liquid reagents (iSTAT® and Liat™). Time-to-result varies between minutes and approximately 1 h, depending on the assay. The advantage of full integration with pre-stored reagents comes at the price of an imprinted protocol that cannot be changed for a specific test carrier. The number of unit operations is somewhat limited, in particular separation, switching, and aliquoting as well as precise metering are difficult to realize. This hinders the implementation of more complex assays and laboratory protocols in linear actuated systems, such as integrated genotyping with a plurality of genetic markers or multiparameter assays.
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5. Pressure Driven Laminar Flow Definition of pressure driven laminar flow: The laminar flow platform comprises liquid handling and (bio-) chemical assay principles, based on the stable hydrodynamic conditions in pressure driven laminar flows through microchannels. The samples are processed by injecting them into the chip inlets using external pumps or pressure sources, either batch-wise or in a continuous mode. 5.1. GENERAL PRINCIPLE
As mentioned earlier, liquid flow in microchannels is typically strictly laminar over a wide range of flow rates and channel dimensions. Pressure driven laminar flow offers several opportunities for assay implementation: − − −
Predictable velocity profiles Controllable diffusion mixing Stable phase arrangements, e.g. in co-flowing streams
These advantages have been utilized for several lab-on-a-chip applications in the past. Probably the oldest example is the so-called “hydrodynamic focusing” technology [95], used to align cells in continuous flow for analysis and sorting in flow cytometry [96, 97]. Today, many technologies still use laminar flow effects for particle counting [98] or separation [99–103]. However, pressure driven laminar flow can also be utilized to implement other (bio-)chemical assays for lab-on-a-chip applications as described within this section. Especially nucleic acid based diagnostic systems received a great deal of interest in the last decade, since the first introduction of a combined microfluidic PCR and capillary electrophoresis in 1996 by Woolley et al. [104]. 5.2. UNIT OPERATIONS
The basic unit operation on the pressure driven laminar flow platform is the contacting of at least two liquid streams at a microfluidic channel junction (see Fig. 7). This leads to controlled diffusional mixing at the phase interface, e.g. for initiation of a (bio-) chemical reaction [105]. It can also be applied for the lateral focusing of micro-objects like particles or cells in the channel [95]. The required “flow focusing” channel network consists of one central and two symmetric side channels, connected at a junction to form a common outlet channel. By varying the ratio of the flow rates, the lateral width of the central streamline within the common outlet channel can be adjusted very accurately. Consequently, micro-objects suspended in the liquid flowing
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through the central channel are focused and aligned to this well-defined streamline position. If the available duration for a (bio-) chemical reaction needs to be limited, the contacted liquid streams can again be separated further downstream as shown in [105]. For the separation of micro-objects like living cell or micro-beads from a liquid stream, several technologies have been presented relying either on geometrical barriers [105], or magnetic forces [106, 107]. Sorting of microobjects, i.e. the selective separation based on size or any other feature, was implemented using magnetic forces [108, 109], acoustic principles [110], dielectrophoresis [111], or hydrodynamic principles [99–101, 112] on the pressure driven laminar flow platform. The common principle of all these technologies is a force acting selectively on the suspended micro-objects (particles or cells), while the liquid stream stays more or less unaffected.
Figure 7. Contacting on the laminar flow platform. Three different liquid streams are symmetrically contacted at an intersection point. This microfluidic structure is also referred to as “flow focusing structure” [95].
A great number of valving principles exists on the pressure driven laminar flow platform, summarized in a review by Oh and Ahn [38]. Active as well as passive solutions have been presented. However, no standards have emerged so far, so the choice and implementation of valves remains a difficulty on this platform. A possible approach is to transfer the valving functionality off-chip [113], thus decreasing the complexity and cost of the disposable. 5.3. APPLICATION EXAMPLES
One recently established technology on the pressure driven laminar flow platform is the so called “phase transfer magnetophoresis (PTM)” [106]. Magnetic microparticles flowing through a microfluidic channel network are attracted by a rotating off-chip permanent magnet, and can consequently be transferred between different co-flowing liquid streams. As a first application, DNA purification with magnetic beads was successfully
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demonstrated with a yield of approximately 25% [106] (first prototype). Thus, this system provides continuous DNA-extraction capability which could serve as an automated sample preparation step for flow-through PCR, in e.g. bioprocess monitoring (of fermentation) applications. Other microfluidic applications based on the manipulation of magnetic microparticles with external permanent magnets have been shown. One example is the free-flow magnetophoresis [108, 109], which can be utilized to sort magnetic microparticles by size. A large number of microfluidically automated components for batchwise nucleic acid diagnostics based on pressure driven laminar flow chips have been published and summed up in several reviews [33, 114, 115]. However, a totally integrated system remains a challenge, since the integration of sample preparation proved difficult [115], although it seems to be in reach, as the next two examples show. Easley et al. showed integrated DNA purification, PCR, electrophoretic separation and detection of pathogens in less than 30 min [116]. The assay was performed on a pressure driven four layer glass/PDMS chip with elastomeric valves. Temperature cycling for PCR was achieved by IR radiation. Only the sample lysis step was not integrated in the microfluidic chip. Detection of Bacillus anthracis from infected mice and Bordetella pertussis from a clinical sample was successfully demonstrated. An integrated µTAS system for the detection of bacteria including lysis, DNA purification, PCR and fluorescence readout has also been published recently [113]. A microfluidic plastic chip with integrated porous polymer monoliths and silica particles for lysis and nucleic acid isolation was used for detection (Fig. 8). A custom-made base device provided liquid actuation and off-chip valving by stopping liquid flow from the exits of the chip, utilizing the incompressibility of liquids. Detection of 1.25 × 106 cells of B. subtilis was demonstrated with all assay steps performed on-chip. 5.4. STRENGTHS AND LIMITATIONS
One strength of the platform lies in its potential for continuous processing of samples. Continuous sample processing is of utmost importance for online monitoring of clinical parameters, process control in fermentation, water quality control or cell sorting. Typically one or a few parameters are monitored. The application examples showed one system capable of continuous DNA extraction as well as other implementations that integrated complex batchwise protocols such as nucleic acid analysis. The platform is in principle compatible to polymer mass-production technologies such as injection molding, enabling inexpensive disposable microfluidic chips. A difficulty of the platform is the necessity to connect the pressure source to the (disposable) chip, which decreases the portability and requires additional
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manual steps. Another challenge is Taylor dispersion [117] of streamwise dispersed samples which can make it hard to accurately track analyte concentrations. Unit operations on the platform are optimized for mixing and separation processes and somewhat limited in other aspects such as aliquoting.
Eluate Propulsion Buffer
SPE Column
PCR Mix Mixer 2 Reservoir 2 PCR Channel Air In
Waste 1 Mixer 1 Exhaust GuSCN Sample In Sample Reservoir Reservoir 1 Mixer 1 Detection Well
Mixer 2 Exhaust Elution Buffer
Waste 2 70% EtOH
Figure 8. Chip for integrated detection of bacteria including lysis, DNA isolation and PCR published by Sauer-Budge et al. [113].
6. Microfluidic Large Scale Integration Definition of microfluidic large scale integration: Microfluidic large scale integration describes a microfluidic channel circuitry with chip-integrated valves based on a flexible membrane between a liquid-guiding and a pneumatic control-channel layer. The valves are closed (opened) by applying an overpressure (underpressure) on the controlchannel, leading to deflection (withdrawal) of the membrane into the liquid-guiding channel.
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6.1. GENERAL PRINCIPLE
The microfluidic large scale integration platform (LSI) arose in the year 1993 [118]. At the same time, a novel fabrication technology for microfluidic channels, called soft lithography made its appearance. Soft lithography is based on the use of elastomeric stamps, molds and conformable photomasks to fabricate and replicate microstructures [119]. Using this technology, the monolithic fabrication of all necessary fluidic components within one single elastomer material (Polydimethylsiloxane, PDMS) became possible, similar to the silicon-based technology in microelectronics. PDMS, also known as silicone elastomer, is an inexpensive material offering several advantages compared to silicon or glass. It is a cheap, rubber-like elastomer with good optical transparency and biocompatibility. A detailed review on the use of PDMS for different fields of applications can be found in [120]. The strength of the technology became obvious, when Stephen Quake’s group expanded the technology towards the multilayer soft-lithography process, MSL [121]. With this technology, several layers of PDMS can be hermetically bonded on top of each other resulting in a monolithic, multilayer PDMS structure. This enables the fabrication of microfluidic chips with densely integrated microvalves, pumps and other functional elements. Today, this technology is pushed forward by the company Fluidigm Corp., CA, USA. 6.2. UNIT OPERATIONS
Based on the high elasticity of PDMS, the elementary microfluidic unit operation is a valve which is typically made of a planar glass substrate and two layers of PDMS on top of each other. One of the two elastomer layer contains the fluidic ducts while the other elastomer layer features pneumatic control channels. To realize a microfluidic valve, a pneumatic control channel crosses a fluidic duct as depicted in Fig. 9a. A pressure p applied to the control channel squeezes the elastomer into the lower layer, where it blocks the liquid flow. Because of the small size of this valve in the order of 100 × 100 µm2, a single integrated fluidic circuit can accommodate thousands of valves. Comparable to developments in microelectronics, this approach is called “microfluidic large scale integration” (LSI) [122]. The valve technology called NanoFlex™ (Fluidigm) is the core technology of the complete platform. For example, by placing two such valves at the two arms of a T-shaped channel a fluidic switch for the routing of liquid flows between several adjacent channels can be realized. Liquid transport within the fluid channels can be accomplished by external pumps while the PDMS multilayer device merely works passively as integrated valves, or an integrated pumping mechanism can be achieved by combining several microvalves and actuating them in a peristaltic sequence (Fig. 9d).
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Metering of liquid volumes can be achieved by crossed fluid channels and a set of microvalves. Therefore, the liquid is initially loaded into a certain fluid channel and afterwards segmented into separated liquid compartments by pressurizing the control channel.
Figure 9. Realization of the main unit operations on the multilayer PDMS based LSI platform [123]. The NanoFlex™ valve (a) can be closed (b) by applying a pressure p to the control channel. Therewith, microfluidic valves (c), peristaltic pumps (d) and mixing structures (e) can be designed.
Also mixing can be realized using the above described pumping mechanism by the subsequent injection of the liquids into a fluidic loop (Fig. 9e) through the left inlet (right outlet valve is closed). Afterwards, the inlet and outlet valves are closed and the three control channels on the orbit of the mixing loop are displaced with a peristaltic actuation scheme leading to a circulation of the mixture within the loop [124]. Thereby the liquids are mixed and can be flushed out of the mixer by a washing liquid afterwards. Using this mixing scheme, the increase of reaction kinetics by nearly two orders of magnitude has been demonstrated in surface binding assays [125]. However, the key feature to tap the full potential of the large scale integration approach is the multiplexing technology allowing for the control of N fluid channels with only 2 log2 N control channels. Based on this principle, a microfluidic storage device with 1,000 independent compartments of approximately 250 pL volume and 3,574 microvalves has been demonstrated [122]. 6.3. APPLICATION EXAMPLES
One application example on the microfluidic LSI platform is the extraction of nucleic acids (NA) from a small amount of cells [126, 127] for cell-based assays. For the extraction of NA from a cell suspension, the cell membrane has to be destroyed first (chemical lysis of the cell). Afterwards, the NA are specifically separated from the residual cell components using a solid phase extraction method based on an NA affinity column (paramagnetic beads). This extraction protocol is completely implemented on the microfluidic
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platform using the basic unit operations for valving, metering, mixing and switching of liquids. Measurable amounts of mRNA were extracted in an automated fashion from as little as a single mammalian cell and recovered from the chip [126]. Based on this technology, the development of a nucleic acid processor for complete single cell analysis is under way [128–130]. Also many other applications have been implemented on the LSI platform over the last years: protein crystallization [131], immunoassays [132], automated culturing of cells [133] or multicellular organisms [134] and DNA synthesizing [135]. From a commercial perspective, Fluidigm Corp. has launched three different products based on the large scale integration platform within the last years: the BioMarkTM technology for molecular biology (e.g. TaqMan® assay), the TOPAZ® system for protein crystallography, and the Fluidigm® EP1 system for genetic analysis. Especially the EP1 system bears a large potential for high-throughput screening applications such as sequencing [136], multiparallel PCR [137], single-cell analysis [138], siRNA- [139] or antibody-screening [140], kinase- [141] or expression-profiling [142]. 6.4. STRENGTHS AND LIMITATIONS
The microfluidic LSI platform certainly has the potential to become one of the most versatile microfluidic platforms especially for high-throughput applications. It is a flexible and configurable technology which stands out by its suitability for large scale integration. The PDMS fabrication technology is comparably cheap and robust, and thus suitable to fabricate disposables. Reconfigured layouts can be assembled from a small set of validated unit operations and design iteration periods for new chips are in the order of days. Some of the system functions are hardware defined by the fluidic circuitry but others like process sequences can easily be programed externally. Limitations of the platform are related to the material properties of PDMS: for example, chemicals which the elastomer is not inert to cannot be processed, and elevated temperatures such as in micro-reaction technology are not feasible. Also for the implementation of applications in the field of point-of-care diagnostics, where a handheld device is often required, the LSI platform seems not to be beneficial at the moment. Thereto external pressure sources and valves would have to be downsized to a smaller footprint, which is of course technically feasible, but the costs would be higher in comparison to other platform concepts. However, as a first step towards downsizing the liquid control equipment, the use of a Braille system was successfully demonstrated [143].
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7. Segmented Flow Microfluidics Definition of segmented flow microfluidics: Segmented flow microfluidics describes the principle of performing an assay within small liquid droplets immersed in a second immiscible continuous phase (gas or liquid). For process automation, the droplets are handled within microchannels, where they form alternating segments of droplets and the ambient continuous phase. 7.1. GENERAL PRINCIPLE
The segmented flow microfluidic platform relies on a multiphase fluid flow through microchannels. Generally, the applied technologies can be divided into the following categories: • Two-phase gas–liquid • Two-phase liquid–liquid • Three-phase liquid–liquid In principal, droplets of a dispersed liquid phase are immersed in a second continuous gas (two-phase gas–liquid) or liquid (two-phase liquid– liquid) phase within a microchannel. Thereby, the inner liquid droplets are separated by the continuous carrier liquid along the channel. If the size of the inner phase exceeds the cross sectional dimensions of the channel, the droplets are squeezed to form non-spherical segments, also called “plugs”. Following this flow scheme, the platform is called segmented flow microfluidics. In some applications, the stability of the phase-arrangement is increased by additional surfactants as the third phase, stabilizing the plug interface (three-phase liquid–liquid) [144]. An external pressure is applied for the transport of the plugs. A comprehensive general discussion of the platform can also be found in recent review papers [30, 145, 146]. 7.2. UNIT OPERATIONS
The most elementary unit operation on the segmented flow platform is the initial generation of the droplets (see Table 3). This step can also be considered a metering, since the liquid volumes involved in the subsequent reaction within the droplet are defined during the droplet formation process. Generally, two different microfluidic structures have been reported for a controlled and continuous generation of droplets: the flow focusing structure as depicted in Fig. 7 [147, 148] and the T-shaped junction [149, 150], respectively. The size of the droplet is influenced by the strength of the shear forces at the channel junction (higher shear forces lead to smaller droplets) for both droplet formation mechanisms.
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To use droplets inside channels as reaction confinements, the different reactants have to be loaded into the droplet. Therefore, a method to combine three different sample liquid streams by a sheath flow arrangement with subsequent injection as a common droplet into the carrier fluid has been shown by the group of Rustem F. Ismagilov at the University of Chicago, IL, USA [151] (see Fig. 10). Different concentrations and ratios of two reagent sub-streams plus a dilution buffer merge into one droplet and perform a so called on-chip dilution [152]. The mixing ratios can be adjusted by the volume flow ratio of the three streams. Using a combination of two opposing T-junctions connected to the same channel, the formation of droplets of alternating composition has been demonstrated [153]. Using a similar technique, the injection of an additional reactant into a liquid plug moving through the channel at an additional downstream T-junction has been demonstrated [154]. Not only liquid chemical reagents but also other components like cells have been loaded into droplets [155]. The merging of different sized droplets showing different velocities to single droplets has been demonstrated successfully [151]. In the same work, the controlled splitting of droplets at a channel branching point has been shown. Using a similar method, the formation of droplet emulsions with controlled volume fractions and drop sizes has been realized [156]. Mixing inside the droplets can be accelerated by a recirculating flow due to shear forces induced by the motion along the stationary channel wall [157]. This effect is even more pronounced if two liquids of differing viscosities are mixed within the droplet [158]. Based on the recirculating flow, a mixing scheme for the segmented flow platform has been proposed using serpentine microchannels [159]. Within each channel curvature the orientation between the phase pattern in the droplet and the direction of motion is changed so that the inner recirculation leads to stretching and folding of the phases. Under favorable conditions, sub-millisecond mixing can be achieved and has been employed for multi-step synthesis of nanoparticles [154]. A detailed and theoretical description of this mixing effect is given in [160]. Besides the mixing within liquid droplets dispersed into another liquid carrier phase, also mixing within the carrier phase can be accelerated by a segmented flow. The injection of gas-bubbles into a continuous liquid stream forming a segmented gas–liquid flow has been described by Klavs Jensen and his group at MIT [161, 162]. The gas bubbles are introduced into the liquid flow and initiate recirculation flows within the liquid segments in between due to the motion along the channel wall. The gas bubbles can be completely separated from the liquid stream using a planar capillary separator after the reaction is finished. Using that technology, the synthesis of colloidal silica particles has been demonstrated [163]. Another microfluidic mixing
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scheme based on a gas–liquid segmented flow uses an additional repeated separation and re-combining of the channel [164]. TABLE 3. Overview and examples of unit operations and applications on the segmented flow microfluidic platform.
Microfluidic unit operations Droplet generation Droplet merging Droplet splitting Droplet sorting Droplet internal mixing Droplet sorting
Reference [30, 144, 146–149, 168, 169] [30] [151] [30] [30, 161, 162] [170]
Applications (Single) cell analysis Single organism analysis DNA assays Drug screening Protein crystallization Chemical synthesis
Reference [31, 145, 168, 171] [170, 172] [173–175] [169] [176–181] [146, 154, 157]
The incubation time of the reagents combined inside a droplet at the injection position can easily be calculated at a certain point of observation from the traveling distance of the droplet divided by the droplet velocity. Thus, the incubation time can be temporally monitored by simply scanning along the channel from the injection point to farther downstream positions. This is a unique feature of the platform and enables the investigation of chemical reaction kinetics on the order of only a few milliseconds [152]. On the other hand, also stable incubation times on the order of a week have been demonstrated [165]. This is enabled by separating the droplet compartments with a carrier fluid that prevents evaporation and diffusion. Using this approach, several 60 nL liquid droplets containing one or a few cells were generated within a microfluidic chip and afterwards flushed into a Teflon capillary tube for cultivation. The cell densities were still as high as in conventional systems after 144 h of growth within the droplets. Additional unit operations based on charged droplets and electric fields have been added to the segmented flow platform by David A. Weitz and coworkers [166]. Using dielectrophoresis, the sorting of single droplets out of a droplet train (switching) at rates up to 4 kHz has been shown [167]. The segmented flow technology augmented with electric field based unit operations is currently commercialized by the company Raindance Technologies, MA, USA.
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7.3. APPLICATION EXAMPLES
Table 3 gives an overview of the microfluidic unit operations and applications that have been already implemented on the segmented flow platform. They all take advantage of the enclosed reaction confinement within the droplets, either for analytical applications (cell analysis, single organism analysis, DNA assays, drug screening, protein crystallization) or chemical synthesis. Protein crystallization, for example, is realized on the segmented flow platform by forming droplets out of three liquids, namely the protein solution, a buffer and the precipitant within oil as the carrier phase [176, 182]. The precipitant concentration inside the droplet is adjusted via the buffer and precipitant flow rates respectively. Therewith, different concentrations are generated and transferred into a glass capillary for later X-ray analysis [177]. The effect of mixing on the nucleation of protein crystallization has been investigated by combining the described crystallization structure with a serpentine mixing channel [181]. Fast mixing has been found to be favorable for the formation of well-crystallized proteins within the droplets [180]. Recently, also a chip for rapid detection and drug susceptibility screening of bacteria has been presented [169] as one example of a high-throughput screening application. The channel design is depicted in Fig. 10. Plugs of the bacterial solution, a fluorescent viability indicator, and the drugs to be screened are injected into the carrier fluid. The different drug solutions (antibiotics: vancomycin (VCM), levofloxixin (LVF), ampicillin (AMP), cefoxitin (CFX), oxicillin (OXA), and erythromycin (ERT)) are separated by an air spacer plug within the drug trial channel. Plugs containing VCM were used as baseline, because VCM inhibited this S. aureus strain in macroscale experiments. No plugs containing VCM or LVF had a fluorescence increase greater than three times the baseline, indicating that MRSA was sensitive to these antibiotics.
Figure 10. Droplet based drug screening. The plugs containing the drugs (D1–D4) get mixed with a bacterial solution and a viability dye. In case of potent drugs the bacteria die and the droplet shows no staining. (Image adapted from Boedicker et al. [169].)
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7.4. STRENGTHS AND LIMITATIONS
The main advantages of the segmented flow microfluidic platform are the small volume liquid segments (controllable with high precision in the nanoliter range), acting as reaction confinements. This leads to little reagent consumption as well as a high number of different experiments that can be performed within a short period of time, which makes the platform a promising candidate for high throughput screening applications, e.g. in the pharmaceutical industry. Therefore, also the quasi-batch-mode operation scheme within nanoliter to microliter sized droplets is beneficial since it represents a consistent further development of classic assay protocols in e.g. well plates. The large number of existing unit operations enables the effective manipulation of the liquid segments. Furthermore, the completely enclosed liquid droplets allow the incubation and storage of liquid assay results over a long period of time without evaporation. However, a limitation of the platform is that handling of small overall sample volumes is not possible due to the volume consumption during the runin phase of the flow within the microchannels. This and the manual connection to external pumps renders the platform less suitable for point-of-care applications. Another drawback is the need for surfactants that are required for high stability of the plugs. They sometimes interfere with the (bio-) chemical reaction within the plugs and thus can limit the number of possible applications on the platform. 8. Centrifugal Microfluidics Definition of centrifugal microfluidics: The centrifugal microfluidic platform uses inertial and capillary forces on a rotating microstructured substrate for liquid actuation. Relevant inertial (pseudo-) forces include the centrifugal force, Euler force and Coriolis force. The substrate is often disk-shaped. Liquid flow is possible in two dimensions but with the limitation that active liquid transport is always directed radially outwards. Active components can be limited to one rotational axis. 8.1. GENERAL PRINCIPLE
The approach of using centrifugal forces to automate sample processing dates back to the end of the 1960s [183]. At that time, centrifugal analyzers were first used to transfer and mix a series of samples and reagents in the volume range from 1 to 110 µL into several cuvettes, followed by spectrometric monitoring of reactions and real-time data processing. Controlling microfluidic networks by just one rotary axis has an obvious charm to it, since no connections to the macro-world, such as pumps, are required. Moreover, the
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required centrifugal base devices can be simple and therefore robust. Rotational frequencies can be controlled very well and a radially constant centrifugal pseudo-force guarantees pulse-free liquid flow. Scientific work and applications based on centrifugal microfluidics have continuously been published since these early beginnings, although the most attention to the topic arose again in the last two decades, as summarized in several reviews [1, 184, 185]. However, the concept is still somewhat exotic compared to the large number of pressure driven systems existing today, possibly attributed to the difficulty of monitoring liquid flow under rotation and the dependency of liquid flow on microchannel surface quality [186]. This results in high initial investment in monitoring equipments and prototyping lines. Nevertheless, considerable advances towards integrated systems have been made in the last decades. In the beginning of the 1990s, the company Abaxis [187] developed the portable clinical chemistry analyzer [188, 189]. This system consists of a plastic disposable rotating cartridge for processing of the specimen, preloading of dried reagents on the cartridge, and an analyzer instrument for actuation and readout. A next generation of centrifugal devices emerged from the technical capabilities offered by microfabrication and microfluidic technologies [190– 193]. Length scales of the fluidic structures in the range of a few hundred micrometers allow parallel processing of up to hundred units assembled on a single disk. This enables high throughput by highly parallel and automated liquid handling. In addition, assay volumes can be reduced to less than 1 µL. Particular fields such as drug screening [191], where precious samples are analyzed, benefit from these low assay volumes. Today, many basic unit operations for liquid control on the centrifugal microfluidic platform are known and new ones are continuously being developed, enabling a number of applications in the fields of point-of-care testing, research, and security. 8.2. UNIT OPERATIONS
Liquid transport is initiated by the centrifugal force fω directed outwards in the radial direction. The centrifugal force can be scaled over a wide range by the frequency of rotation ω. Together with a tunable flow resistance of the fluidic channels, small flow rates in the order of nL/s as well as high throughput continuous flows up to 1 mL/s [194] can be generated. Therefore, scaling of flow rates over six orders of magnitude independent from the chemical composition, ionic strength, conductivity or pH value of the liquid can be accomplished, opening a wide field of possible applications. Also, liquid transport at rest can be achieved by capillary forces, depending on the channel geometry and the wetting properties of the liquid.
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Liquid valves can be realized by several different microfluidic structures on the centrifugal platform. In general, they can be purely passive, as depicted in Fig. 11, or require an active component outside the microfluidic substrate. First, the passive valves will be summarized: A very simple valve arises at the sudden expansion of a microfluidic channel e.g. into a bigger reservoir: the geometric capillary valve (Fig. 11a). The valving mechanism of this capillary valve is based on the energy barrier for the proceeding of the meniscus, which is pinned at the sharp corner. This barrier can be overcome under rotation due to the centrifugal pressure load of the overlying liquid plug [191, 195, 196]. For a given liquid plug position and length, i.e. for a given set of geometric parameters, the valve is influenced by only the frequency of rotation, and a critical burst frequency ωc can be attributed to every valve structure. Another possibility to stop the liquid flow within a channel is the local hydrophobic coating of the channel walls [197–200] (hydrophobic valve) (Fig. 11b). This valve is opened as soon as the rotational frequency exceeds the critical burst frequency ωc for this geometry and surface properties. A third method (Fig. 11c) utilizes the stopping effect of compressed air in an unvented receiving chamber. This centrifugo-pneumatic valve stops liquid up to much higher pressures than capillary valves for small receiving chamber volumes (≤40 µL). The air counter-pressure in the unvented receiving chamber can be overcome at high centrifugal frequencies, at which the liquid–air interface becomes unstable and enables a phase exchange, permitting liquid flow [201, 202]. Another method is based on a hydrophilic S-shaped siphon channel (hydrophilic siphon valve), wherein the two liquid–gas interfaces are leveraged at high frequencies of rotation [188] (Fig. 11d). Below a critical frequency ωc however, the right-hand meniscus proceeds beyond the bend, thus allowing the centrifugal force to drain the complete liquid from the siphon.
Figure 11. Passive centrifugal microfluidic valves. (a) Positioning of valves relative to center of rotation and centrifugal force, (b) geometric capillary valve [191], (c) hydrophobic valve [197], (d) centrifugo-pneumatic valve [201]and (e) hydrophilic siphon valve [188].
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One example of an active valve is an irradiation-triggered “sacrificial” valve published by Samsung Advanced Institute of Technology (Laser Irradiated Ferrowax Microvalve, LIFM) [203]. A ferrowax plug is used to close channels off during the fabrication of the microfluidic network. A laser source in the processing device can be utilized to melt the ferrowax plug and thus allow liquid passage (normally-closed valve). A modification of this technique also allows closing channels off by illuminating a ferrowax reservoir that expands into a channel and seals it (normally-open valve). An advantage of this valve is that it allows liquid control depending solely on the moment of the laser actuation, so it does not depend on the rotational speed or liquid properties. This comes at the cost of a more complex production process and base device. An alternative approach for the active control of liquid flows on the centrifugal platform is followed by the company Spin-X technologies, Switzerland. A laser beam individually opens fluidic interconnects between different channel layers on a plastic substrate (Virtual Laser Valve, VLV). This enables online control of the liquid handling process on the rotating module for adjusting metered volumes and incubation times within a wide range. Due to this, the Spin-X platform works with a standardized fluidic cartridge that is not custom made for each specific application, but can be programed online during a running process. Combining one of the above-mentioned valve principles at the radially outward end of a chamber with an overflow channel at the radially inward end results in a metering structure [204]. The metered liquid portion is directly set by the volume capacity of the chamber. With highly precise micro-fabrication technologies, small coefficients of variations (CV, standard deviation divided by mean value), e.g. a CV < 5% for a volume of 300 nL [205] and also metered volumes of as little as 5 nL have been achieved [198]. By arranging several metering structures interconnected via an appropriate distribution channel, simple aliquoting structures can be realized [201, 206]. These structures split a sample into several defined volumes, enabling the conduction of several assays from the same sample in parallel. Different mixing schemes have been proposed on the centrifugal platform. Considering mixing of continuous liquid flows within a radially directed rotating channel, the perpendicular Coriolis force automatically generates a transverse liquid flow [194]. A continuous centrifugal micromixer, utilizing the Coriolis stirring effect, showed an increasing mixing quality towards very high volume throughputs of up to 1 mL/s per channel [194] (Coriolis mixer). Besides the mixing of continuous liquid flows, also the homogenization of discrete and small liquid volumes located in chambers is of importance especially when analyzing small sample volumes (batch-mode mixing), since homogenous mixing obviously speeds up diffusion-limited chemical and biological reactions due to the close proximity between analytes. One possibility to enhance the mixing is the active agitation of the liquid within
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a mixing chamber by inertia related shear forces (Euler force), induced by a fast change of the sense of rotation (shake-mode-mixing) [204] or change of rotational frequency (unidirectional shake-mode-mixing) [207]. Shakemode mixing leads to reduced mixing times in the order of several seconds compared to several minutes for pure diffusion based mixing. A further downscaling of mixing times below 1 s using magnetic microparticles, located in the mixing chamber, has also been demonstrated [208]. Accelerated mixing can also be achieved by an interplay of capillary and intermittent centrifugal forces [209]. For routing (switching) of liquids, a switch utilizing the transversal Coriolis force to guide liquid flows between two outlets at the bifurcation of an inverse Y-shaped channel [210] or at nozzle leading into a chamber [211] has been presented. Depending on the sense of rotation, the Coriolis force is either directed to the left or to the right, guiding the liquid stream into one of two downstream reservoirs at the bifurcation. Another method for liquid routing based on different wetting properties of the connected channels has been reported by Gyros AB, Sweden [212]. The liquid stream is initially guided towards a radial channel, exhibiting a hydrophobic patch at the beginning. Therefore, the liquid is deflected into a branching non-hydrophobic channel next to the radial one. For high frequencies of rotation, the approaching liquid possesses enough energy to overcome the hydrophobic patch and is therefore routed into the radial channel [213]. A further possibility to switch liquid flows is to utilize an “air cushion” between an initial first liquid entering a downstream chamber and a subsequent liquid. The centrifugally generated pressure of the first liquid is transmitted via the air cushion to the subsequent liquid and forces it via an alternative route into a chamber placed sideways to the main channel [214]. The separation of plasma from a whole blood sample is the prevalent first step within a complete analytical protocol for the analysis of whole blood. Since blood plasma has lower density compared to the white and red blood cells it can be found in the upper phase after sedimentation in the artificial gravity field under rotation. The spatial separation of the obtained plasma from the cellular pellet can be achieved via a capillary channel that branches from the sedimentation chamber at a radial position where only plasma is expected [189]. Another method uses preseparation of the cellular and plasma phase during the sample flow through an azimuthally aligned channel of 300-µm radial width [199]. The obtained plasma fraction is thereafter split from the cellular components by a decanting process. Another concept enables plasma separation of varying blood sample volumes in a continuous process. The sedimentation occurs in an azimuthally curved channel due to centrifugal- and Coriolis forces, enabling up to 99% separation efficiency between two outlets for a diluted sample with 6% hematocrit
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[215]. An overview over centrifugal microfluidic unit operations and related applications can be found in Table 4. 8.3. APPLICATION EXAMPLES
Table 4 shows some applications that have been realized on the centrifugal microfluidic platform. At the top of the applications section, sample preparation modules (plasma separation, DNA extraction) are shown. This is followed by assays based on the detection of proteins, nucleic acids and small molecules (clinical chemistry). Two additional applications are presented at the end of the table, demonstrating chromatography and protein crystallization. Some instructive examples are discussed in more detail below. TABLE 4. Overview and examples of unit operations and applications for the centrifugal microfluidic platform.
Microfluidic unit operations Capillary valving Hydrophobic valving Siphon valving Laser-triggered valve Centrifugo-pneumatic valving Metering Aliquoting Mixing Coriolis switching Reagent storage Applications Integrated plasma separation Cell lysis and/or DNA Extraction Protein based assays Nucleic acid based assays Clinical chemistry assays Chromatography Protein crystallization
Reference [185, 191, 193, 195, 196, 216–223] [185, 197–199] [185, 188, 189, 207, 224, 225] [203, 226–228] [201, 214] [185, 189, 193, 197–199, 203–205, 224, 225, 227] [183, 185, 188, 189, 197, 201, 229] [183, 185, 188, 189, 193, 194, 203–205, 207, 208, 220, 224, 225, 227, 229–232] [185, 204, 210, 214, 215, 233] [220, 234] Reference [185, 199, 204, 215, 224–227, 235] [227, 233, 236] [183, 191, 197, 204, 216, 220, 222, 224–226, 229, 237] [216, 221, 238] [188, 189, 204, 205, 217–219, 225, 232, 239] [240] [198]
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Madou et al. from the University of California, Irvine showed a series of capillary valves to perform enzyme-linked immunosorbent assays (ELISAs) on the centrifugal platform [222]. The different assay liquids are held back in reservoirs connected to the reaction chamber via valves of different burst frequency. The capillary valves are opened subsequently by increasing the frequency of rotation. It was shown that in terms of detection range the centrifugally conducted assay has the same performance as the conventional method on a 96-well plate, but with less reagent consumption and shorter assay time. Gyros AB, Sweden [212] uses a flow-through sandwich immunoassay at the nanoliter scale to quantify proteins within their Gyrolab™ Workstation. Therefore, a column of pre-packed and streptavidin-coated microparticles is integrated in each one of 112 identical assay units on the microfluidic disk. Each unit has an individual sample inlet and a volume definition chamber that leads to an overflow channel. Defined volumes (200 nL) of samples and reagents can be applied to the pre-packed particle column. The laser induced fluorescent (LIF) detector is incorporated into the Gyrolab™ Workstation. Using this technology, multiple immunoassays have been carried out to determine the imprecision of the assay result. The day-to-day (total) imprecisions (CV) of the immunoassays on the microfluidic disk are below 20% [197]. The assays are carried out within 50 min with sample volumes of 200 nL. In comparison, the traditional ELISA performed in a 96-well plate typically takes several hours and requires sample volumes of several hundred microliters. A fully integrated colorimetric assay for determination of alcohol concentrations in human whole blood has been shown on the centrifugal Bio-Disk platform [205]. After loading the reagents into the reagents reservoir, a droplet of untreated human blood taken from a finger tip is loaded into the inlet port of the microstructure. By mixing the blood sample with the reagents, an enzymatic reaction is initiated, changing the color of the mixture depending on the alcohol concentration. After sedimentation of the residual blood cells, the absorbance is monitored in a real-time manner via a laser beam that is reflected into the disk plane on integrated V-grooves [232]. Using this automated assay and readout protocol the concentration of alcohol in human whole blood was determined within only 150 s. The results were comparable to common point-of-care tests and required a minute blood volume of just 500 nL. Also a protein crystallization assay has been demonstrated on the centrifugal microfluidic platform [198]. First, a defined volume of the protein solution is dispensed into the protein inlet and transported into the crystallization chamber. Afterwards, the preloaded precipitant is metered under rotation and transferred into the crystallization chamber as soon as a hydrophobic valve breaks. In the last step, the preloaded oil is released at
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yet a higher frequency and placed on top of the liquid stack within the crystallization chamber, to prevent evaporation. The successful crystallization of proteinase K and catalase could be demonstrated. Samsung Advanced Institute of Technology showed a fully integrated immunoassay for Hepatitis B- and other antibodies, starting from 150 µL whole blood on a centrifugal base device including a laser for controlling ferrowax valves and a read-out-unit [226]. A limit of detection comparable to a conventional ELISA and an assay time of 30 min were reported. On the same platform, enrichment of pathogens and subsequent DNA extraction was also shown (Fig. 12) [227]. The microfluidic structure features an integrated magnet that controls the position of coated magnetic particles which are used to capture target pathogens and lyse them by laser irradiation. With a total extraction time of 12 min, down to 10 copies/µL DNA concentration in a spiked blood sample of 100 µL could be specifically extracted and detected in a subsequent external PCR. Reagents are loaded by the operator prior to the process.
Figure 12. centrifugal microfluidic structure for pathogen-specific cell capture, lysis and DNA purification [227]. The microfluidic network comprises structures for plasma separation, mixing, and laser-triggered valves. For manipulation of the magnetic capture-beads, a movable magnet is integrated into the cartridge.
8.4. STRENGTHS AND LIMITATIONS
Two major advantages of the centrifugal microfluidic platform are the modular setup of the system with disposable and easily exchangeable plastic cartridges and the many existing unit operations, which allow highly precise liquid handling. The fabrication costs of the disposables are governed by the specific
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implementation of unit operations. Necessary global or local surface modification or the integration of active (ferrowax) valves, post-replication treatment, assembly and reagent pre-storage steps can increase the cost of the disposables. Mostly, they are made out of plastic and thus suitable for mass-production. The presented unit operations allow the automation of complex assay protocols. The cost for the base instrument depends heavily on read-out and temperature control modules. The motor required for liquid control is generally required to be able to achieve very stable and defined rotational speed and acceleration, also adding to the costs. However, compared to (several) high-precision syringe pumps, this solution is generally cheaper and allows a higher degree of integration. Due to the rotational symmetry of the disks, optionally some degree of parallelization can be achieved. Also, the rotational symmetry is beneficial for fast readout and temperature uniformity between cavities at the same radial position. However, as soon as any additional actuation or sensing function is required on the module during rotation and if a contact free interfacing is not applicable, things become challenging from a technical point of view. Especially interfacing to electric readout modules on the disk is difficult, since the rotating setup does not allow for wire connections between the disposable and the base instrument. The platform also lacks flexibility compared to others that allow online programming of fluidic networks within one piece of hardware that fits all, since most of the logic functions as well as their critical frequencies are permanently imprinted into the channel network. However, the Virtual Laser Valve technology is an exception in this respect and allows online programming in a centrifugal system. Space restrictions are also an issue, since the required footprint (disk surface) increases quadratically with the number of connected unit operations (radial length). The low centrifugal forces near the center of rotation and the difficulty of transporting liquids radially inward are other challenges in the fluidic design process. Also, completely portable solutions are currently still only a vision. 9. Electrokinetics Definition of electrokinetics: The electrokinetic platform uses electric charges, fields, field gradients or temporally fluctuating electrical fields for liquid actuation. The actuation is provided between different electrodes, and several effects (eletrophoresis, dieletrophoresis, osmotic flow, polarization) superimpose each other, depending on the sample liquid. Besides liquid actuation, the effects can also be used for separation of molecules and particles, detection, and catalysis.
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9.1. GENERAL PRINCIPLE
One of the first applications for electrokinetics was the analysis of chemical compounds via electrophoretic separation within capillaries in 1967 [241], long before the term “microfluidics” emerged. In the beginning, glass capillaries made from drawn glass tubes were used, whereas today well defined microchannels are established and commonly used. The actuation principle of the electrokinetic platform relies on the movement of liquid in an induced electric double layer and charged particles (ions) in an electric field applied along a microfluidic channel. The simple setup of electrokinetic systems consisting of microfluidic channels and electrodes without moving parts explains the early advent of electrokinetic platforms for microfluidic lab-on-a-chip applications. 9.2. UNIT OPERATIONS
In a microfluidic channel, a charged solid surface induces an opposite net charge in the adjacent liquid layer (electric double layer). As soon as an electric potential is applied along the channel, the positively charged liquid molecules are attracted by electrostatic forces and thus move towards a corresponding electrode (Fig. 13a). Due to viscous coupling, the bulk liquid is dragged along by the moving layer and liquid actuation with a planar velocity profile is generated (electroosmotic flow (EOF) [242]). The velocity profile is constant and dispersion only occurs by molecular diffusion. This motion is superimposed by the movement of ions and charged molecules, which are attracted or repelled by the electrodes depending on their charge (Fig. 13b). The velocity of the molecule depends on its charge and hydrodynamic radius and enables the distinction between different molecular entities. This effect is used for separation of charged molecules and is called electrophoresis.
Figure 13. Basic electrokinetic effects. (According to Atkins et al. [242].) (a) Electroosmotic flow (EOF), (b) electrophoresis (EP), (c) dielectrophoresis (DEP).
Based on the electroosmotic flow, metering of volumes down to the picoliter range can be achieved. While the sample liquid is injected and crosses an intersection point of two perpendicular channels, the electrodes
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and therefore the flow along the main channel is switched off. Then, the electrodes in the side channel are activated. This displaces a small plug at the intersection into the side channel, resulting in metering of a sample volume depending on the geometry of the intersection area. The mixing of two co-flowing streams was shown on the electrokinetic platform by applying an AC voltage [241]. A 20-fold reduction in mixing time compared to molecular diffusion has been reported. Also complete biological assays comprising cell lysis, mixing, and DNA amplification have been presented [243]. A modification to electrophoresis is free-flow electrophoresis, which enables the continuous separation of a mixture according to charge with subsequent collection of the sample band of interest [244]. For this, an transverse electric field is applied in pressure driven flow within a broad and flat microchamber. While passing this extraction chamber, the species contained in the sample flow are deflected depending on their charge and thus exit the chamber through one of several outlets. Another electrokinetic effect is based on polarization of particles within an oscillating electrical field or field gradient (dielectrophoresis), as depicted in Fig. 13c. Dielectrophoresis is applied in many fields, e.g. for the controlled separation and trapping of submicron bioparticles [245], for the fusion and transport of cells [246], or the separation of metallic from semiconducting carbon nanotubes [13, 247–249]. Other applications are cell sorting [250, 251] and apoptosis of cells [252, 253]. 9.3. APPLICATION EXAMPLES
Capillary electrophoresis systems were the first micro total analysis systems and emerged as single chip solutions from the analytical chemistry field in the 1990s [254]. Several companies utilize microfluidic capillary electrophoretic chips for chemical analysis, with capillaries of typically 10–100 µm diameter [255]. Today, Caliper Life Sciences, MA, USA [255] and Agilent Technologies, CA, USA [256] offer microfluidic chips for DNA and Protein analysis. Liquid propulsion is provided via electroosmosis and combined with capillary electrophoretic separation. The sample is electroosmotically transported and metered inside the chip, then separated via capillary electrophoresis and analysed by fluorescence detection. (Fig. 14). The whole assay is performed within minutes, instead of hours or days. First combinations of microfluidic integrated electrophoresis with microarrays were published in 1998 by Nanogen Inc., CA, USA [257]. This approach resulted in a 20-fold faster hybridization and more specific binding of DNA onto the microarray. This was the first step into the direction of a platform for massively parallel analysis.
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Figure 14. Microfluidic realization of capillary electrophoresis analysis on the electrokinetic platform. (Adapted from [123]. (© Agilent Technologies, Inc. 2007. Reproduced with permission, courtesy of Agilent Technologies, Inc.) After the sample has been transported to the junction area (a) it is metered by the activated horizontal flow and injected into the separation channel (b). Therein, the sample components are electrophoretically separated (c) and readout by their fluorescence signal (d). The complete microfluidic CE-chip is depicted in the center.
9.4. STRENGTHS AND LIMITATIONS
Electroosmotic actuation of liquids enables pulse-free pumping without any moving parts. Liquid manipulation at high precision can be achieved by the existing unit operations. In addition, electroosmotic flow does not lead to Taylor dispersion [117] as in pressure driven systems and thus enables high yield chromatographic separations. The seamless integration with electrophoresis, an established technology in use since 100 years [258], is another obvious strength. In microfluidic systems, applications can benefit from faster heat dissipation, better resolution, and faster separation. Miniaturization of electrophoretic analysis enables the automation and parallelization of tests with small dead volumes, thus reducing the required amount of sample. A technical problem in capillary electrophoresis systems is the changing pH-gradient due to electrolysis or electrophoresis itself. Also streaming currents which counteract the external electric field or gas bubbles as a result of electrolysis at the electrodes are problematic. Also a massively parallel setup cannot be constructed due to the heat generated by the electrophoresis itself. In addition, handheld devices are almost impossible due to the necessity of high voltages in combination with high energy consumption. Overall, miniaturized electrophoresis is established as a fast and efficient method for the separation and analysis of bio-molecules.
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10. Electrowetting Definition of electrowetting: The electrowetting platform relies on the movement of liquid droplets due to electrically induced local changes in wettability. This is normally achieved by applying a voltage to individual electrodes of an electrode-array. Increasing the voltage at an electrode decreases the local contact angle, and a droplet placed at the edge of the activated electrode will move towards it. 10.1. GENERAL PRINCIPLE
The electrowetting effect was first described by Lippmann in 1875 [259]. Interest in this effect was spurred again in the 1990s, when researchers started placing thin insulating layers on the metallic electrodes to separate it from the often conductive liquids in order to eliminate electrolysis [260]. The basic electrowetting effect is depicted in Fig. 15a. The wettability of a solid surface increases due to polarization and electric fields as soon as a voltage is applied between the electrode and the liquid droplet above (separated by the dielectric insulating layer) [260]. This so-called “electrowetting-ondielectric” (EWOD) [261] effect is therefore a tool to control the contact angle of liquids on surfaces.
Figure 15. The electrowetting effect. (According to Mugele et al. [260].) (a) If a voltage V is applied between a liquid and an electrode separated by an insulating layer, the contact angle of the liquid–solid interface is decreased and the droplet “flattens”. (b) Hydrophobic surfaces enhance the effect of electrowetting. For “electrowetting on dielectrics” (EWOD) several individual addressable control electrodes (here on the bottom) and a large counter-electrode are used. The droplet is pulled to the charged electrodes.
This invention paved the way for the application of the electrowetting effect as a liquid propulsion principle for lab-on-a-chip systems [262, 263]. To utilize the EWOD technology for programable liquid actuation, a liquid droplet is placed between two electrodes covered with insulating, preferably hydrophobic, dielectric layers (Fig. 15b). The liquid droplet is steered by the electrode array on one side and by a large planar ground electrode on the opposite side. Activating selected electrodes allows programing of a path which the droplet follows. The droplet needs to be large enough to cover
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parts of at least four addressable electrodes at all times, allowing twodimensional movement. If a voltage is applied to one of the control electrodes covered by the droplet, it moves onto the activated electrode pad. Successive activation of one electrode after the other will drag the droplet along a defined path. This freedom to program the liquid movement enables the implementation of different assays on the same chip. The universal applicability of moving droplets by EWOD was shown with several media such as ionic liquids, aqueous surfactant solutions [264], and also biological fluids like whole blood, serum, plasma, urine, saliva, sweat, and tear fluid [265]. 10.2. UNIT OPERATIONS
The droplet formation, i.e. initial metering, is the elementary unit operation of the platform. Metered droplets can be produced from an on-chip reservoir in three steps [265]. First, a liquid column is extruded from the reservoir by activating a series of adjacent electrodes. Second, once the column overlaps the electrode on which the droplet is to be formed, all the remaining electrodes are turned off, forming a neck in the column. The reservoir electrode is then activated during the third and last step, pulling back the liquid and breaking the neck, leaving a droplet behind on the metering electrode. Using this droplet metering structure, droplets down to 20 nL volume can be generated with a standard deviation of less than 2% [265]. A similar technology can be used for the splitting of a droplet into several smaller droplets [32]. Since the droplet volume is of great importance for the accuracy of all assays, additional volume control mechanisms such as on-chip capacitance volume control [266] or the use of numerical methods for the design of EWOD metering structures [267] have been proposed. Once the droplets are formed, their actuation is accomplished by the EWOD effect as described above. Also the merging of droplets can be achieved easily with the use of three electrodes. Two droplets are individually guided to electrodes separated from each other by a third one. Deactivating these two electrodes and activating the third separation electrode pulls the droplets together [268]. The most basic type of mixing within droplets on the EWOD platform is an oscillation, forwards and backwards, between at least two electrodes. Another mixing scheme is the repetitive movement of the droplet on a rectangular path. The shortest mixing time for two 1.3 µL droplets in linear oscillation on 4 electrodes was about 4.6 s [269]. In another work, the mixing times of 1.4 µL droplets could be further reduced to less than 3 s using two-dimensional arrays [270].
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10.3. APPLICATION EXAMPLES
Applications based on EWOD are in the development phase and quite close to market products. For example, an enzymatic colorimetric assay for (pointof-care) diagnostic applications has been successfully implemented, and glucose concentration in several biological liquids (serum, plasma, urine, and saliva) was determined with comparable results to standard methods [265]. The microfluidic chip layout for the colorimetric glucose assay is depicted in Fig. 16. It features reservoirs, injection structures (metering) and a network of electrodes for droplet transport, splitting and detection.
Figure 16. Electrowetting platform (EWOD). Implementation of a colorimetric glucose assay in a single chip. Four reservoirs with injection elements are connected to an electrode circuitry, where the droplets are mixed, split and transported to detection sites for readout. (Adapted from Srinivasan et al. [265].)
Also the use of an EWOD system for the automated sample preparation of peptides and proteins for matrix-assisted laser desorption–ionization mass spectrometry (MALDI-MS) was reported. In that work, standard MALDIMS reagents, analytes, concentrations, and recipes have been demonstrated to be compatible with the EWOD technology, and mass spectra comparable to those collected by conventional methods were obtained [271]. Also a PCR assay has been realized on the platform by temperature cycling of a droplet at rest [272]. Additional informations about the EWOD platform can be found in a comprehensive review [273]. 10.4. STRENGTHS AND LIMITATIONS
The strengths of the platform are the very small liquid volumes in the nanoliter range that can be handled with high precision, and the freedom to program the droplet movement. This cuts down sample and reagent consumption and allows a maximum of flexibility for the implementation of different assay
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protocols. The simple setup without any moving parts can be fabricated using standard lithographic processes. The programmable control of small droplets has its particular potential in assay optimization, since it allows varying the protocal over a certain range on the same chip. However, although the sample and reagent consumption is low, portable systems for e.g. point-of-care applications have not yet been demonstrated due to the bulky electronic instrumentation required to operate the platform. Another drawback is the influence of the liquid properties on the droplet transport behaviour, i.e. different patient materials will show different wetting abilities and thus lead to differences in volume or movement speed. Also the long-term stability of the hydrophobic surface coatings and the contamination risk is problematic, since every droplet can potentially contaminate the surface and thus lead to false results and also change the contact angle for the successor droplets. Another issue is the possible electrolysis caused by the electric fields themselves. Strategies for high throughput applications have not been demonstrated to date. In summary, the EWOD technique bears great potential to manipulate many single droplets in parallel. While first applications have been shown, the EWOD concept is still at a stage of development, shortly before entering the IVD markets [273]. 11. Surface Acoustic Waves Definition of surface acoustic waves: Surface acoustic waves (SAW) are acoustic shock waves on the surface of a solid support. An emitted SAW induces an acoustic pressure inside a droplet placed on the surface. If this pressure exceeds a critical value, the droplet is moved away from the SAW source. The surface is hydrophobically coated to facilitate droplet movement. By placing several SAW sources around an area, the droplet can be freely maneouvered. 11.1. GENERAL PRINCIPLE
An alternative to the electrowetting based transportation of droplets on a plane surface has been proposed by the group of Achim Wixforth at the University of Augsburg, Germany [274]. The approach is based on surface acoustic waves (SAW), which are mechanical waves with amplitudes of typically only a few nanometers. The surface acoustic waves are generated by a piezoelectric transducer chip (e.g. quartz) fabricated by placing interdigital electrodes (interdigital transducer, IDT) on top of a piezoelectric layer. Liquid droplets situated on the hydrophobic surface of the chip can be moved by the SAWs if the acoustic pressure exerted on the liquid droplet is
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high enough (Fig. 17) [275]. The actuation of small amounts of liquids with viscosities extending over a large range (from 1 to 1,000 mPa·s) has been shown [276]. This approach is also sometimes referred to as “flat fluidics”, because no cover or slit is required as in the EWOD approach.
Figure 17. Surface acoustic wave (SAW). (According to Tan et al. [277].) The shock waves induce a stream on the solid–liquid interface and lead finally to a movement of the droplet (amplitude of acoustic wave not to scale).
11.2. UNIT OPERATIONS
Metering is accomplished by moving a liquid droplet over a small hydrophilic “metering spot” via surface acoustic waves, leaving behind a small metered liquid portion due to the interplay between the surface tension force (keeping the droplet on the spot) and the acoustic force (pushing the droplet forward). Since those two forces scale differently over the droplet size, the splitting of the initial droplet into two droplets (one sitting on the metering spot and the other propagating forward) occurs. The smaller droplet is not transported since it stays unaffected by the acoustic wave. Also aliquoting has been shown by moving the initial droplet over a hydrophobic/hydrophilic checkerboard pattern [274]. Mixing is an intrinsic unit operation of the SAW platform. A droplet which is placed on the substrate and is influenced by a SAW shows internal liquid circulation due to the vibrating forces of the wave. This internal circulation leads to mixing [274]. 11.3. APPLICATION EXAMPLES
A PCR protocol has been implemented on the SAW plaform, based on 200 nL droplets and an additional heating element placed underneath the substrate surface for temperature cycling while the droplet is at rest [278]. However, since the nanoliter-sized droplet possesses a high surface-to-volume ratio,
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the liquid volume would decrease rapidly due to evaporation at the elevated temperatures required for the PCR reaction. Therefore, the aqueous liquid droplet is covered with a droplet of immiscible mineral oil with a smaller contact angle. This droplet-in-droplet configuration can still be moved via surface acoustic waves on the substrate surface. The concentration of DNA could be monitored by online fluorescent measurement providing a sensitivity of 0.1 ng [278]. 11.4. STRENGTHS AND LIMITATIONS
As in the EWOD platform, the SAW platform also allows the handling of small nanoliter sized liquid volumes in droplets on planar surfaces. The transport mechanism using surface acoustic waves though is more flexible since it depends only on the viscosity and surface tension of the liquid. However, the programmability is in turn limited since the position of the interdigital electrodes and especially the hydrophobic/hydrophilic areas determine the possible liquid handling processes. Another disadvantage is the long-term stability and the complexity of these hydrophobic and hydrophilic surface coatings, and thus costs of the disposable chip as well as the instrument. 12. Systems for Massively Parallel Analysis Definition of massively parallel analysis: Massively parallel analysis or “high throughput screening” allows the parallel handling of several hundred to up to billions of assays or samples within one run, and performs an according readout for each assay in parallel. Main application examples are microarrays, bead based assays and picowellplates. 12.1. GENERAL PRINCIPLE
In this chapter, solutions for highly parallel assay processing are presented. These are not per se microfluidic platforms by our definition, since they do not offer a set of easily combined unit operations and are quite inflexible in terms of assay layout. They are nevertheless presented here, since the small reaction volumes per assay and partly the liquid control systems are based on microfluidic platforms. The significant market for repetitive analyses, which allows high development costs for proprietary, optimized systems, does not necessarily require a platform approach, but can benefit from microfluidic production technologies and liquid handling systems.
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The massively parallel assay systems are a result of the increasing demand of the pharmaceutical industry for repetitive assays [279, 280] to cover the following objectives: − − − −
Screening of chemical libraries with millions of compounds [281] Screening of known drugs against new targets, different cell lines or patient material [282, 283] Multiparameter analysis of cell signaling and single cell analysis [284] All omic analyses such as genomics, transcriptomics, proteomics, glucomics, metabolomics [285]
With every newly discovered receptor or protein, all known drugs, predrugs, and chemical compounds should be tested for interaction in means of binding, activity change, or enzymatic activity. Also the analysis of gene activity or gene sequencing requires new and massively parallel testing in numbers of hundred thousands to billions. These tests consume a lot of time, material, effort, and money, but could lead to precious results (e.g. in case of a new blockbuster-drug) [286]. The challenging task to monitor millions of different binding reactions is partially solved by microarrays [287] (mainly in the case of DNA and RNA) or bead based assays in combination with picowell plates. Microarrays [287] are matrices with spots of different chemical compounds on a surface (Fig. 18a). The number of spots ranges from a few dozen to up to several millions. The microarray is incubated with the sample and each spot interacts with the sample in parallel, leading to as many parallel assays as there are spots on the microarray. Typically a microarray is read out by fluorescence and used for nucleic acid or protein analysis. Picowell plates [288, 289] consist of millions of small wells (<50 µm in diameter) (Fig. 18c). In each well, either one chemical compound or one single cell is deposited. After the deposition, the picowell plate acts as a “microarray” with each position bearing a unique chemical compound or cell. Afterwards, all assays are performed similar to a microarray. In bead based assays [281, 290] small solid phase spheres (Fig. 18b) or particles are used. Each bead is bearing one unique chemical compound. Such a bead library can consist of billions of different beads. For screening, the beads are mixed and incubated with the sample and consecutively with the assay buffers, performing one assay at each bead in parallel. The readout is commonly fluorescence based and the positive beads are sorted out and analysed one by one in series. Typically this technique is used for binding assays or DNA-analysis. The pioneers of each field who introduced this system to the market are: Microarrays by Affymetrix, CA, USA [291], bead based arrays by Luminex Corp., TX, USA [292, 293] and Illumina, Inc., CA, USA [294, 295], and picowell plates by 454 Life Sciences, CT, USA [289].
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Figure 18. Images of the different systems for massively parallel screening. (a) Microarray [287] after binding, providing two different fluorophores in red and green. Unchanged genes remain yellow. Up- or down regulated genes appear in red or green. (b) 3 µm silica spheres, as example for bead-based assays [281, 290], deposited on the front end of glass fibers. (c) Empty wells of a picowellplate [288, 289]. In each well a single cells or beads is deposited, incubated and analyzed.
12.2. MICROFLUIDIC COMPONENTS AND APPLICATIONS
Here, the microfluidic actuation principles that are utiziled in massively parallel analysis are outlined briefly. This is followed by some commercial application examples. Due to the similar principle, microarrays and picowell plates are presented together, followed by bead based assays. 12.2.1. Micorarrays/Picowell Plates For micorarrays/picowell plates liquid actuation and metering can be achieved by different actuation principles. Mainly capillary filling of a cardridge [291], or pressure driven systems are used [286, 287]. In other cases, the liquid actuation was achieved by centrifugal systems, electrophoresis, surface accoustic waves, electrowetting, and several other principles. Incubation and mixing is realized by diffusion and in some cases enhanced by sonication, surface acoustic waves, or electric fields. Washing is achieved by displacing the sample with the consecutive liquid. The classical (parallel) readout of binding or interaction between the molecules is performed by fluorescence (Fig. 18a, c) [291]. An interesting feature is that some of the picowell plates are made from glass fiber bundles and thus present a perfect interface between the light generating bead and the detector, often a CCD-camera [289, 294, 295]. Today, the company Affymetrix offers microarrays with >2,000,000 unique compounds. The fluidic system is quite simple. The sample is manually loaded with a pipette into the chip, and capillary forces transfer the sample to the incubation chamber. Incubation and mixing is enhanced by a moving air bubble actuated by slow rotation. The company 454 Life Sciences offers picowell plate systems for the performance of massively parallel gene sequencing [289]. Beads containing
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roughly 10 million identical DNA copies are loaded into the picowell plate with a pressure driven system, where each beads sediments into one cavity. Different biomolecules are washed over the wells, interacting with the beads inside. In the case of a positive reaction, a quantitative enzymatic reaction, the pyro-sequencing [296], results in the emission of light. This system allows for parallel sequencing of 106 beads in a single run. 12.2.2. Bead Based Assays For bead based assays, liquid actuation and metering is most often pressure driven or performed with a pipetting robot in a microtiter plate. Mixing can be performed by any kind of mixing process according to the different actuation principles (diffusion, sonication, SAW, shaking, electrokinetic, electrophoretic, pressure driven pumping through microchannels etc.). The beads are separated from the liquid by centrifugation or with the help of magnetic fields and can then be transferred into another liquid. Typically, detection and readout are enabled with a fluorescent marker. The beads are then analyzed either sequentially or in parallel. For sequential analysis the beads are transferred into a capillary and cross several laser beams and detectors one after the other. In that case, the beads bear a coding to identify them [292, 293]. For the massively parallel analysis the beads are transferred onto a planar surface or into a picowell plate (Fig. 18b, c). Bead based assays are commercialized by Luminex since 1997 [292]. A microtiterplate is used for incubation and a capillary for bead transfer into the reader. Illumina [294, 295] expanded this concept radically by the use of 3 µm silica spheres, each bearing a unique DNA strand. The spheres are deposited on one end of a glass fiber connected to a detector. The spheres are incubated with a DNA sample, and in case of a binding event, the according sphere emits a light signal into the glass fiber. The current system allows handling of millions of unique compounds [297]. 12.3. STRENGTHS AND LIMITATIONS
Today, many manual steps and skilled personnel are required for the described systems and a “real” microfluidic platform is still not reached. However, microarrays, picowell plates and bead based assays are a very useful combination of solid phase and liquid handling for massively parallel assays in the number of millions. The material consumption per assay is quite low and the reaction time quite fast. The time-to-result is longer compared to a single assay, but several magnitudes faster compared to serially performing the same number of assays. A strong limitation of this systems is the reliability, reproducibility, and identification of artefacts. Therefore a positive binding event in these systems is always counterchecked in a microtiter plate experiment to verify
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the binding event. The whole system itself cannot be designed as handheld and is quite expensive (several 10,000€ per run for sequencing), but is inexpensive in terms of cost per assay and material consumption (less than a cent per sequenced base) [298]. 13. Criteria for the Selection of a Microfluidic Platform After the previous discussion of the platform approach and the presentation of some prominent examples for microfluidic platforms, this section will attempt to summarize the strengths and limitations of each platform presented in Fig. 1. This should provide the reader with some guidance to select platforms based on the selection criteria presented in Table 2. The given platform characteristics are based on the reviewed literature and the experience of the authors, taking into consideration properties such as material of the TABLE 5. Characteristics of microfluidic platforms with respect to certain selection criteria.
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disposable, necessary processing equipment, production technologies, published variety of unit operations, published data concerning precision, throughput, or multiparameter-testing. Beneficial platforms can be selected by identifying imperative requirements of a certain application, e.g. portability, low reagent consumption and high precision for point-of-care diagnostics, which are then compared to the characterisitcs of the available platforms. The platform characteristics are compiled in Table 5, also showing the potential of classical liquid handling technologies using pipetting robots. It is obvious that some of the microfluidic platform approaches are dedicated to certain fields of application. For example, the classical liquid handling technology enables high sample throughput and has a high programmability, but the main drawback is the lack of portability and the high equipment costs for complex automated workstations. These properties limit its use to large laboratories. The lateral flow test platform fulfills the requirements for point-of-care diagnostic applications quite well (low reagent consumption, good portability, and additionally low costs). However, as soon as the diagnostic assay requires higher precision or exceeds a certain level of complexity (e.g. if an exact metering of the sample volume or sample aliquoting is required), also new approaches like linear actuated devices and centrifugal microfluidics become advantageous for point-ofcare applications. They enable more sophisticated liquid handling functions, which is for instance required for nucleic acid based tests. The pressure driven laminar flow platform is especially interesting for online monitoring applications, since it enables continuous flows compared to the merely “batch-wise” operation of most of the other microfluidic platforms (i.e. handling discrete liquid volumes). Some of the platforms can also be considered as “multi-application” platforms, which is of special interest in the field of research instrumentation. Here, portability is of less importance, and the number of multiple parameters per sample as well as programmability (potentially also during an assay run) gains impact. The microfluidic large scale integration and the droplet based electrowetting and surface acoustic waves platforms are such versatile examples. For high-throughput screening applications, on the contrary, a high number of assays need to be performed within an acceptable period of time. Consequently flexibility is less important, and throughput and costs are the main issues. Thus, approaches like segmented flow and systems for massively parallel analysis are interesting candidates for these applications. An increasing number of application examples is based on the transfer of unit operations and fabrication technologies between research groups by literature or collaboration. This shows the advance of the platform approach in the research community. We strongly believe that this trend of platform-
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based development will continue in the field of microfluidics. If research time and development costs of microfluidic applications can be reduced significantly by this approach, and the spectrum of applications increases correspondingly, this could finally lead to the commercial breakthrough of microfluidic products. Acknowledgements We would like to thank our colleagues Junichi Miwa and Sven Kerzenmacher for their helpful suggestions and assistance during the preparation of this manuscript.
References 1. S. Haeberle and R. Zengerle, Microfluidic platforms for lab-on-a-chip applications, Lab on A Chip, vol. 7, no. 9, pp. 1094–1110, 2007. 2. A. E. Kamholz, Proliferation of microfluidics in literature and intellectual property, Lab on A Chip, vol. 4, no. 2, pp. 16N–20N, 2004. 3. C. Haber, Microfluidics in commercial applications; an industry perspective, Lab on A Chip, vol. 6, no. 9, pp. 1118–1121, 2006. 4. H. P. Le, Progress and trends in ink-jet printing technology, Journal of Imaging Science and Technology, vol. 42, no. 1, pp. 49–62, Jan. 1998. 5. S. C. Terry, J. H. Jerman, and J. B. Angell, Gas-Chromatographic Air Analyzer Fabricated on A Silicon-Wafer, Ieee Transactions on Electron Devices, vol. 26, no. 12, pp. 1880–1886, 1979. 6. A. Manz, Y. Miyahara, J. Miura, Y. Watanabe, H. Miyagi, and K. Sato, Design of An Open-Tubular Column Liquid Chromatograph Using Silicon Chip Technology, Sensors and Actuators B-Chemical, vol. 1, no. 1–6, pp. 249–255, Jan. 1990. 7. S. Shoji, M. Esashi, and T. Matsuo, Prototype Miniature Blood-Gas Analyzer Fabricated on A Silicon-Wafer, Sensors and Actuators, vol. 14, no. 2, pp. 101–107, June 1988. 8. H. T. G. Van Lintel, F. C. M. Vandepol, and S. Bouwstra, A Piezoelectric Micropump Based on Micromachining of Silicon, Sensors and Actuators, vol. 15, no. 2, pp. 153–167, Oct. 1988. 9. V. Gass, B. H. Vanderschoot, S. Jeanneret, and N. F. Derooij, Integrated Flow-Regulated Silicon Micropump, Sensors and Actuators A-Physical, vol. 43, no. 1–3, pp. 335–338, May 1994. 10. E. Verpoorte, A. Manz, H. Ludi, A. E. Bruno, F. Maystre, B. Krattiger, H. M. Widmer, B. H. Vanderschoot, and N. F. Derooij, A Silicon Flow Cell for Optical-Detection in Miniaturized Total Chemical-Analysis Systems, Sensors and Actuators B-Chemical, vol. 6, no. 1–3, pp. 66–70, Jan. 1992.
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11. P. Arquint, M. Koudelkahep, B. H. Vanderschoot, P. Vanderwal, and N. F. Derooij, Micromachined Analyzers on A Silicon Chip, Clinical Chemistry, vol. 40, no. 9, pp. 1805–1809, Sept. 1994. 12. A. Manz, N. Graber, and H. M. Widmer, Miniaturized Total ChemicalAnalysis Systems – A Novel Concept for Chemical Sensing, Sensors and Actuators B-Chemical, vol. 1, no. 1–6, pp. 244–248, Jan. 1990. 13. D. J. Harrison, A. Manz, Z. H. Fan, H. Ludi, and H. M. Widmer, Capillary Electrophoresis and Sample Injection Systems Integrated on A Planar Glass Chip, Analytical Chemistry, vol. 64, no. 17, pp. 1926–1932, Sept. 1992. 14. T. Chard, Pregnancy Tests – A Review, Human Reproduction, vol. 7, no. 5, pp. 701–710, May 1992. 15. J. M. Hicks and M. Iosefsohn, Reliability of Home Pregnancy-Test Kits in the Hands of Laypersons, New England Journal of Medicine, vol. 320, no. 5, pp. 320–321, 1989. 16. D. J. Litman, R. H. Lee, H. J. Jeong, H. K. Tom, S. N. Stiso, N. C. Sizto, and E. F. Ullman, An Internally Referenced Test Strip Immunoassay for Morphine, Clinical Chemistry, vol. 29, no. 9, pp. 1598–1603, 1983. 17. L. Wilhelm, S. Jenckel, and R. Junker, Test strip handling in screening for drugs of abuse in the clinical toxicological setting, LaboratoriumsmedizinJournal of Laboratory Medicine, vol. 32, no. 3, pp. 168–174, May 2008. 18. R. Pacifici, M. Farre, S. Pichini, J. Ortuno, P. N. Roset, P. Zuccaro, J. Segura, and R. de la Torre, Sweat testing of MDMA with the Drugwipe (R) analytical device: A controlled study with two volunteers, Journal of Analytical Toxicology, vol. 25, no. 2, pp. 144–146, Mar. 2001. 19. A. H. B. Wu, Laboratory and near patient testing for cardiac markers, Journal of Clinical Ligand Assay, vol. 22, no. 1, pp. 32–37, 1999. 20. Rong-Hwa S., Huey-Fen S., and Shiao-Shek T, Colloidal gold based immunochromatogaphic assay for detection of ricin, Toxicon, vol. 40, pp. 255–258, 2002. 21. H. Becker, Chips, money, industry, education and the “killer application” Lab on A Chip, vol. 9, no. 12, pp. 1659–1660, 2009. 22. H. Becker, It’s the economy.., Lab on A Chip, vol. 9, pp. 2759–2762, 2009. 23. R.J. Petri, Eine kleine Modification des Koch’schen Plattenverfahrens, Centralblatt für Bacteriologie und Parasitenkunde, vol. 1, pp. 279–280, 1887. 24. J. O. Corliss, Two most remarkable Amoeba men: Joseph Leidy (1823– 1891) of Philadelphia and Eugene Penard (1855–1954) of Geneva, Protist, vol. 152, no. 1, pp. 69–85, May 2001. 25. J. Hüser, R. Mannhold, H. Kubinyi, and G. Folkers, High-Throughput Screening in Drug Discovery (Methods and Principles in Medicinal Chemistry), 1 ed Wiley-VCH, 2006. 26. G. M. Whitesides, The origins and the future of microfluidics, Nature, vol. 442, no. 7101, pp. 368–373, July 2006. 27. J. H. Leamon, W. L. Lee, K. R. Tartaro, J. R. Lanza, G. J. Sarkis, A. D. deWinter, J. Berka, and K. L. Lohman, A massively parallel PicoTiterPlate (TM) based platform for discrete picoliter-scale polymerase chain reactions, Electrophoresis, vol. 24, no. 21, pp. 3769–3777, 2003.
358
D. MARK ET AL.
28. M. Margulies, M. Egholm, W. E. Altman, S. Attiya, J. S. Bader, L. A. Bemben, J. Berka, M. S. Braverman, Y. J. Chen, Z. T. Chen, S. B. Dewell, L. Du, J. M. Fierro, X. V. Gomes, B. C. Godwin, W. He, S. Helgesen, C. H. Ho, G. P. Irzyk, S. C. Jando, M. L. I. Alenquer, T. P. Jarvie, K. B. Jirage, J. B. Kim, J. R. Knight, J. R. Lanza, J. H. Leamon, S. M. Lefkowitz, M. Lei, J. Li, K. L. Lohman, H. Lu, V. B. Makhijani, K. E. Mcdade, M. P. McKenna, E. W. Myers, E. Nickerson, J. R. Nobile, R. Plant, B. P. Puc, M. T. Ronan, G. T. Roth, G. J. Sarkis, J. F. Simons, J. W. Simpson, M. Srinivasan, K. R. Tartaro, A. Tomasz, K. A. Vogt, G. A. Volkmer, S. H. Wang, Y. Wang, M. P. Weiner, P. G. Yu, R. F. Begley, and J. M. Rothberg, Genome sequencing in microfabricated highdensity picolitre reactors, Nature, vol. 437, no. 7057, pp. 376–380, 2005. 29. S. Takayama, E. Ostuni, P. Leduc, K. Naruse, D. E. Ingber, and G. M. Whitesides, Laminar flows – Subcellular positioning of small molecules, Nature, vol. 411, no. 6841, p. 1016, 2001. 30. S. Y. Teh, R. Lin, L. H. Hung, and A. P. Lee, Droplet microfluidics, Lab on A Chip, vol. 8, no. 2, pp. 198–220, 2008. 31. A. Huebner, M. Srisa-Art, D. Holt, C. Abell, F. Hollfelder, A. J. deMello, and J. B. Edel, Quantitative detection of protein expression in single cells using droplet microfluidics, Chemical Communications, no. 12, pp. 1218–1220, 2007. 32. S. K. Cho, H. J. Moon, and C. J. Kim, Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits, Journal of Microelectromechanical Systems, vol. 12, no. 1, pp. 70–80, Feb. 2003. 33. C. S. Zhang and D. Xing, Miniaturized PCR chips for nucleic acid amplification and analysis: latest advances and future trends, Nucleic Acids Research, vol. 35, no. 13, pp. 4223–4237, 2007. 34. S. Shoji and M. Esashi, Microflow devices and systems, Journal of Micromechanics and Microengineering, vol. 4, no. 4, pp. 157–171, Dec. 1994. 35. D. J. Laser and J. G. Santiago, A review of micropumps, Journal of Micromechanics and Microengineering, vol. 14, no. 6, p. R35–R64, June 2004. 36. P. Woias, Micropumps – past, progress and future prospects, Sensors and Actuators B-Chemical, vol. 105, no. 1, pp. 28–38, Feb. 2005. 37. P. Gravesen, J. Braneberg, and O. S. Jensen, Microfluidics-a review, Journal of Micromechanics and Microengineering, vol. 3, no. 4, pp. 168–182, Dec. 1993. 38. K. W. Oh and C. H. Ahn, A review of microvalves, Journal of Micromechanics and Microengineering, vol. 16, no. 5, p. R13–R39, May 2006. 39. N. T. Nguyen and Z. G. Wu, Micromixers – a review, Journal of Micromechanics and Microengineering, vol. 15, no. 2, p. R1–R16, Feb. 2005. 40. V. Hessel, H. Lowe, and F. Schonfeld, Micromixers – a review on passive and active mixing principles, Chemical Engineering Science, vol. 60, no. 8–9, pp. 2479–2501, Apr. 2005. 41. J. Ducrée and R. Zengerle, FlowMap – Microfluidics Roadmap for the Life Sciences. Norderstedt, Germany: Books on Demand GmbH, 2004.
MICROFLUIDIC LAB-ON-A-CHIP PLATFORMS
359
42. M. Banks, A. Cacace, J. O’Connel, and J. Houston, “High-Troughput Screening: Evolution of Technology and Methods,” in Drug Discovery Handbook, 1 ed. S. C. Gad, Ed. Cary, North Carolina: John Wiley & Sons, Inc., 2005, pp. 559– 602. 43. G. E. Croston, Functional cell-based uHTS in chemical genomic drug discovery, Trends in Biotechnology, vol. 20, no. 3, pp. 110–115, 2002. 44. S. A. Sundberg, High-throughput and ultra-high-throughput screening: solution- and cell-based approaches, Current Opinion in Biotechnology, vol. 11, no. 1, pp. 47–53, 2000. 45. H. L. T. Lee, P. Boccazzi, R. J. Ram, and A. J. Sinskey, Microbioreactor arrays with integrated mixers and fluid injectors for high-throughput experimentation with pH and dissolved oxygen control, Lab on A Chip, vol. 6, no. 9, pp. 1229–1235, 2006. 46. S. T. Yang, X. D. Zhang, and Y. Wen, Microbioreactors for high-throughput cytotoxicity assays, Current Opinion in Drug Discovery & Development, vol. 11, no. 1, pp. 111–127, Jan. 2008. 47. Y. Wen and S. T. Yang, The future of microfluidic assays in drug development, Expert Opinion on Drug Discovery, vol. 3, no. 10, pp. 1237– 1253, Oct. 2008. 48. V. Hessel and H. Lowe, Microchemical engineering: Components, plant concepts user acceptance – Part I, Chemical Engineering & Technology, vol. 26, no. 1, pp. 13–24, Jan. 2003. 49. H. Lowe and W. Ehrfeld, State-of-the-art in microreaction technology: concepts, manufacturing and applications, Electrochimica Acta, vol. 44, no. 21–22, pp. 3679–3689, 1999. 50. W. Ehrfeld, H. Lowe, V. Hessel, and T. Richter, Potential applications of chemical and biological microreactors, Chemie Ingenieur Technik, vol. 69, no. 7, pp. 931–934, July 1997. 51. D. M. Roberge, L. Ducry, N. Bieler, P. Cretton, and B. Zimmermann, Microreactor technology: A revolution for the fine chemical and pharmaceutical industries? Chemical Engineering & Technology, vol. 28, no. 3, pp. 318– 323, Mar. 2005. 52. H. Pennemann, V. Hessel, and H. Lowe, Chemical microprocess technology – from laboratory-scale to production, Chemical Engineering Science, vol. 59, no. 22–23, pp. 4789–4794, Nov. 2004. 53. A. M. Elizarov, Microreactors for radiopharmaceutical synthesis, Lab on A Chip, vol. 9, no. 10, pp. 1326–1333, 2009. 54. Y. L. Liu, J. D. Adams, K. Turner, F. V. Cochran, S. S. Gambhir, and H. T. Soh, Controlling the selection stringency of phage display using a microfluidic device, Lab on A Chip, vol. 9, no. 8, pp. 1033–1036, 2009. 55. P. H. Bessette, X. Y. Hu, H. T. Soh, and P. S. Daugherty, Microfluidic library screening for mapping antibody epitopes, Analytical Chemistry, vol. 79, no. 5, pp. 2174–2178, Mar. 2007. 56. L. M. Borland, S. Kottegoda, K. S. Phillips, and N. L. Allbritton, Chemical Analysis of Single Cells, Annual Review of Analytical Chemistry, vol. 1, pp. 191–227, 2008.
360
D. MARK ET AL.
57. T. C. Chao and A. Ros, Microfluidic single-cell analysis of intracellular compounds, Journal of the Royal Society Interface, vol. 5, p. S139–S150, Oct. 2008. 58. H. Becker and L. E. Locascio, Polymer microfluidic devices, Talanta, vol. 56, no. 2, pp. 267–287, 2002. 59. T. B. Christensen, C. M. Pedersen, K. G. Grondhal, T. G. Jensen, A. Sekulovic, D. D. Bang, and A. Wolff, PCR biocompatibility of lab-on-a-chip and MEMS materials, Journal of Micromechanics and Microengineering, vol. 17, no. 8, pp. 1527–1532, Aug. 2007. 60. F. Reynolds, J. Pitha, P. M. Pitha, and D. Grundberg, Inhibition of CellFree Protein-Synthesis by Poly(9-Vinyladenine), Poly (1-Vinyluracil), and Corresponding Vinyl Copolymer, Biochemistry, vol. 11, no. 17, pp. 3261– 3266, 1972. 61. S. Landi, H. R. Held, and M. C. Tseng, Comparative Study of C-14 Labeled Purified Proteins and Their Adsorption to Glass, Applied Microbiology, vol. 20, no. 5, pp. 696–703, 1970. 62. L. Gunasekara, W. M. Schoel, S. Schurch, and M. W. Amrein, A comparative study of mechanisms of surfactant inhibition, Biochimica et Biophysica ActaBiomembranes, vol. 1778, no. 2, pp. 433–444, Feb. 2008. 63. H. Schonheyder and P. Andersen, Effects of Bovine Serum-Albumin on Antibody Determination by the Enzyme-Linked Immunosorbent-Assay, Journal of Immunological Methods, vol. 72, no. 1, pp. 251–259, 1984. 64. A. G. Papavassiliou and D. Bohmann, Optimization of the Signal-To-Noise Ratio in South-Western Assays by Using Lipid-Free Bsa As Blocking Reagent, Nucleic Acids Research, vol. 20, no. 16, pp. 4365–4366, Aug. 1992. 65. J. Steigert, S. Haeberle, T. Brenner, C. Muller, C. P. Steinert, P. Koltay, N. Gottschlich, H. Reinecke, J. Ruhe, R. Zengerle, and J. Ducrée, Rapid prototyping of microfluidic chips in COC, Journal of Micromechanics and Microengineering, vol. 17, no. 2, pp. 333–341, Feb. 2007. 66. C. W. Tsao and D. L. Devoe, Bonding of thermoplastic polymer microfluidics, Microfluidics and Nanofluidics, vol. 6, no. 1, pp. 1–16, Jan. 2009. 67. C. Glad and A. O. Grubb, Immunocapillary-Migration – New Method for Immunochemical Quantitation, Analytical Biochemistry, vol. 85, no. 1, pp. 180–187, 1978. 68. J. H. W. Leuvering, P. J. H. M. Thal, M. V. D. Waart, and A. H. W. M. Schuurs, Sol Particle Agglutination Immunoassay for Human Chorionic-Gonadotropin, Fresenius Zeitschrift fur Analytische Chemie, vol. 301, no. 2, p. 132, 1980. 69. G. A. Posthuma-Trumpie, J. Korf, and A. van Amerongen, Lateral flow (immuno) assay: its strengths, weaknesses, opportunities and threats. A literature survey, Analytical and Bioanalytical Chemistry, vol. 393, no. 2, pp. 569–582, Jan. 2009. 70. B. Cosmi, G. Palareti, M. Moia, M. Carpenedo, V. Pengo, A. Biasiolo, P. Rampazzo, G. Morstabilini, and S. Testa, Accuracy of a portable prothrombin time monitor (Coagucheck) in patients on chronic oral anticoagulant therapy: A prospective multicenter study, Thrombosis Research, vol. 100, no. 4, pp. 279– 286, Nov. 2000.
MICROFLUIDIC LAB-ON-A-CHIP PLATFORMS
361
71. T. J. Clark, P. H. McPherson, and K. F. Buechler, The Triage Cardiac Panel, Point of Care, vol. 1, no. 1, pp. 42–46, 2002. 72. S. Birnbaum, C. Uden, C. G. M. Magnusson, and S. Nilsson, Latex-Based Thin-Layer Immunoaffinity Chromatography for Quantitation of Protein Analytes, Analytical Biochemistry, vol. 206, no. 1, pp. 168–171, Oct. 1992. 73. H. W. Wen, W. Borejsza-Wysocki, T. DeCory, and R. Durst, Development of a competitive liposome-based lateral flow assay for the rapid detection of the allergenic peanut protein Ara h1, Analytical and Bioanalytical Chemistry, vol. 382, no. 5, pp. 1217–1226, July 2005. 74. “Evaluation of the CoaguChek XS System,” International Evaluation Workshop, Heidelberg, Germany, 2009. 75. W. Leung, C. P. Chan, T. H. Rainer, M. Ip, G. W. H. Cautherley, and R. Renneberg, InfectCheck CRP barcode-style lateral flow assay for semiquantitative detection of C-reactive protein in distinguishing between bacterial and viral infections, Journal of Immunological Methods, vol. 336, no. 1, pp. 30–36, July 2008. 76. A. Heller and B. Feldman, Electrochemical glucose sensors and their applications in diabetes management, Chemical Reviews, vol. 108, no. 7, pp. 2482–2505, July 2008. 77. Joelle Daviaud, Dominique Fournet, Chantal Ballongue, Guy-Pierre Guillem, Alain Leblanc, ClaudeCasellas, and Bernard Pan, Reliability of Home Pregnancy-Test Kits in the Hands of Laypersons, New England Journal of Medicine, vol. 320, no. 5, pp. 320–321, Feb. 1989. 78. P. Bohme, M. Floriot, M. A. Sirveaux, D. Durain, O. Ziegler, P. Drouin, and B. Guerci, Evolution of analytical performance in portable glucose meters in the last decade, Diabetes Care, vol. 26, no. 4, pp. 1170–1175, Apr. 2003. 79. S. C. Lou, C. Patel, S. F. Ching, and J. Gordon, One-Step Competitive Immunochromatographic Assay for Semiquantitative Determination of Lipoprotein(A) in Plasma, Clinical Chemistry, vol. 39, no. 4, pp. 619–624, Apr. 1993. 80. L. Wilhelm, S. Jenckel, and R. Junker, Test strip handling in screening for drugs of abuse in the clinical toxicological setting, LaboratoriumsmedizinJournal of Laboratory Medicine, vol. 32, no. 3, pp. 168–174, May 2008. 81. R. Krska and A. Molinelli, Rapid test strips for analysis of mycotoxins in food and feed, Analytical and Bioanalytical Chemistry, vol. 393, no. 1, pp. 67–71, Jan. 2009. 82. H. L. Xie, W. Ma, L. Q. Liu, W. Chen, C. F. Peng, C. L. Xu, and L. B. Wang, Development and validation of an immunochromatographic assay for rapid multi-residues detection of cephems in milk, Analytica Chimica Acta, vol. 634, no. 1, pp. 129–133, Feb. 2009. 83. D. J. Carter and R. B. Cary, Lateral flow microarrays: a novel platform for rapid nucleic acid detection based on miniaturized lateral flow chromatography, Nucleic Acids Research, vol. 35, no. 10 May 2007. 84. J. A. A. Ho, S. C. Zeng, W. H. Tseng, Y. J. Lin, and C. H. Chen, Liposomebased immunostrip for the rapid detection of Salmonella, Analytical and Bioanalytical Chemistry, vol. 391, no. 2, pp. 479–485, May 2008.
362
D. MARK ET AL.
85. K. A. Edwards and A. J. Baeumner, Liposome-Enhanced Lateral-Flow Assays for the Sandwich-Hybridization Detection of RNA, Methods in Molecular Biology, pp. 185–215, 2009. 86. P. L. A. M. Corstjens, M. Zuiderwijk, M. Nilsson, H. Feindt, R. S. Niedbala, and H. J. Tanke, Lateral-flow and up-converting phosphor reporters to detect single-stranded nucleic acids in a sandwich-hybridization assay, Analytical Biochemistry, vol. 312, no. 2, pp. 191–200, Jan. 2003. 87. P. Yager, T. Edwards, E. Fu, K. Helton, K. Nelson, M. R. Tam, and B. H. Weigl, Microfluidic diagnostic technologies for global public health, Nature, vol. 442, no. 7101, pp. 412–418, July 2006. 88. J. Hu, The evolution of commercialized glucose sensors in China, Biosensors & Bioelectronics, vol. 24, no. 5, pp. 1083–1089, 2009. 89. K. A. Erickson and P. Wilding, Evaluation of A Novel Point-Of-Care System, the I-Stat Portable Clinical Analyzer, Clinical Chemistry, vol. 39, no. 2, pp. 283–287, Feb. 1993. 90. S. Chen, G. Selecman, and B. Lemieux, Expanding rapid nucleic acid testing, IVD Technology, vol. 7, p. 51, 2004. 91. U. Abbott Point-of-Care, “Abbott Point-of-Care, USA,” 2006. 92. B. S. Karon, R. D. Mcbane, R. Chaudhry, L. K. Beyer, and P. J. Santrach, Accuracy of capillary whole blood international normalized ratio on the CoaguChek S, CoaguChek XS, and i-STAT 1 point-of-care analyzers, American Journal of Clinical Pathology, vol. 130, no. 1, pp. 88–92, 2008. 93. E. Jacobs, E. Vadasdi, L. Sarkozi, and N. Colman, Analytical evaluation of iSTAT Portable Clinical Analyzer and use by nonlaboratory health-care professionals, Clinical Chemistry, vol. 39, no. 6, pp. 1069–1074, June 1993. 94. www.iquum.com, “IQuum, Inc.,” 2009. 95. L. Spielman and S. L. Goren, Improving Resolution in Coulter Counting by Hydrodynamic Focusing, Journal of Colloid and Interface Science, vol. 26, no. 2, pp. 175–182, 1968. 96. G. Valet, Past and present concepts in flow cytometry: A European perspective, Journal of Biological Regulators and Homeostatic Agents, vol. 17, no. 3, pp. 213–222, 2003. 97. D. Huh, W. Gu, Y. Kamotani, J. B. Grotberg, and S. Takayama, Microfluidics for flow cytometric analysis of cells and particles, Physiological Measurement, vol. 26, no. 3, p. R73–R98, 2005. 98. X. D. Wu, C. H. Chon, Y. N. Wang, Y. J. Kang, and D. Q. Li, Simultaneous particle counting and detecting on a chip, Lab on A Chip, vol. 8, no. 11, pp. 1943–1949, 2008. 99. M. Yamada and M. Seki, Microfluidic particle sorter employing flow splitting and recombining, Analytical Chemistry, vol. 78, no. 4, pp. 1357– 1362, Feb. 2006. 100. M. Yamada and M. Seki, Hydrodynamic filtration for on-chip particle concentration and classification utilizing microfluidics, Lab on A Chip, vol. 5, no. 11, pp. 1233–1239, 2005. 101. M. Yamada, M. Nakashima, and M. Seki, Pinched flow fractionation: Continuous size separation of particles utilizing a laminar flow profile in a
MICROFLUIDIC LAB-ON-A-CHIP PLATFORMS
102. 103. 104.
105. 106. 107. 108. 109. 110. 111.
112. 113. 114. 115. 116.
363
pinched microchannel, Analytical Chemistry, vol. 76, no. 18, pp. 5465–5471, Sept. 2004. S. Chang and Y. H. Cho, A continuous size-dependent particle separator using a negative dielectrophoretic virtual pillar array, Lab on A Chip, vol. 8, pp. 1930–1936, 2008. A. A. S. Bhagat, S. S. Kuntaegowdanahalli, and I. Papautsky, Continuous particle separation in spiral microchannels using dean flows and differential migration, Lab on A Chip, vol. 8, pp. 1906–1914, 2008. A. T. Woolley, D. Hadley, P. Landre, A. J. de Mello, R. A. Mathies, and M. A. Northrup, Functional Integration of PCR Amplification and Capillary Electrophoresis in a Microfabricated DNA Analysis Device, Analytical Chemistry, vol. 68, no. 23, pp. 4081–4086, 1996. K. Sato, A. Hibara, M. Tokeshi, H. Hisamoto, and T. Kitamori, Integration of chemical and biochemical analysis systems into a glass microchip, Analytical Sciences, vol. 19, no. 1, pp. 15–22, Jan. 2003. M. Karle, J. Miwa, G. Roth, R. Zengerle, and F. von Stetten, “A Novel Microfluidic Platform for Continuous DNA Extraction and Purification Using Laminar Flow Magnetophoresis,” 2009, pp. 276–279. J. H. Kang and J. K. Park, Magnetophoretic continuous purification of single-walled carbon nanotubes from catalytic impurities in a microfluidic device, Small, vol. 3, no. 10, pp. 1784–1791, Oct. 2007. N. Pamme and A. Manz, On-chip free-flow magnetophoresis: Continuous flow separation of magnetic particles and agglomerates, Analytical Chemistry, vol. 76, no. 24, pp. 7250–7256, Dec. 2004. N. Pamme and C. Wilhelm, Continuous sorting of magnetic cells via on-chip free-flow magnetophoresis, Lab on A Chip, vol. 6, no. 8, pp. 974–980, 2006. T. Laurell, F. Petersson, and A. Nilsson, Chip integrated strategies for acoustic separation and manipulation of cells and particles, Chemical Society Reviews, vol. 36, no. 3, pp. 492–506, 2007. U. Kim, C. W. Shu, K. Y. Dane, P. S. Daugherty, J. Y. J. Wang, and H. T. Soh, Selection of mammalian cells based on their cell-cycle phase using dielectrophoresis, Proceedings of the National Academy of Sciences of the United States of America, vol. 104, no. 52, pp. 20708–20712, 2007. J. Takagi, M. Yamada, M. Yasuda, and M. Seki, Continuous particle separation in a microchannel having asymmetrically arranged multiple branches, Lab on A Chip, vol. 5, no. 7, pp. 778–784, 2005. A. F. Sauer-Budge, P. Mirer, A. Chatterjee, C. M. Klapperich, D. Chargin, and A. Sharon, Low cost and manufacturable complete microTAS for detecting bacteria, Lab on A Chip, 2009. P. A. Auroux, Y. Koc, A. deMello, A. Manz, and P. J. R. Day, Miniaturised nucleic acid analysis, Lab on A Chip, vol. 4, no. 6, pp. 534–546, 2004. L. Chen, A. Manz, and P. J. R. Day, Total nucleic acid analysis integrated on microfluidic devices, Lab on A Chip, vol. 7, pp. 1413–1423, Aug. 2007. C. J. Easley, J. M. Karlinsey, J. M. Bienvenue, L. A. Legendre, M. G. Roper, S. H. Feldman, M. A. Hughes, E. L. Hewlett, T. J. Merkel, J. P. Ferrance, and J. P. Landers, A fully integrated microfluidic genetic analysis system
364
117. 118.
119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131.
D. MARK ET AL. with sample-in-answer-out capability, Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 51, pp. 19272– 19277, Dec. 2006. G. Taylor, Dispersion of Soluble Matter in Solvent Flowing Slowly Through A Tube, Proceedings of the Royal Society of London Series A – Mathematical and Physical Sciences, vol. 219, no. 1137, pp. 186–203, 1953. A. Kumar and G. M. Whitesides, Features of Gold Having Micrometer to Centimeter Dimensions Can be Formed Through A Combination of Stamping with An Elastomeric Stamp and An Alkanethiol Ink Followed by Chemical Etching, Applied Physics Letters, vol. 63, no. 14, pp. 2002–2004, Oct. 1993. J. A. Rogers and R. G. Nuzzo, Recent progress in soft lithography, Materials Today, vol. 8, no. 2, pp. 50–56, Feb. 2005. S. K. Sia and G. M. Whitesides, Microfluidic devices fabricated in poly(dimethylsiloxane) for biological studies, Electrophoresis, vol. 24, no. 21, pp. 3563–3576, Nov. 2003. M. A. Unger, H. P. Chou, T. Thorsen, A. Scherer, and S. R. Quake, Monolithic microfabricated valves and pumps by multilayer soft lithography, Science, vol. 288, no. 5463, pp. 113–116, Apr. 2000. T. Thorsen, S. J. Maerkl, and S. R. Quake, Microfluidic large-scale integration, Science, vol. 298, no. 5593, pp. 580–584, Oct. 2002. S. Haeberle and R. Zengerle, Microfluidic Platforms for Lab-on-a-Chip Applications, Lab on A Chip, vol. 7, no. 9, pp. 1094–1110, 2007. S. R. Quake and A. Scherer, From micro- to nanofabrication with soft materials, Science, vol. 290, no. 5496, pp. 1536–1540, Nov. 2000. H. P. Chou, M. A. Unger, and S. R. Quake, A Microfabricated Rotary Pump, Biomedical Microdevices, vol. 3, no. 4, pp. 323–330, 2001. J. W. Hong, V. Studer, G. Hang, W. F. Anderson, and S. R. Quake, A nanoliter-scale nucleic acid processor with parallel architecture, Nature Biotechnology, vol. 22, no. 4, pp. 435–439, Apr. 2004. J. W. Hong and S. R. Quake, Integrated nanoliter systems, Nature Biotechnology, vol. 21, no. 10, pp. 1179–1183, Oct. 2003. J. S. Marcus, W. F. Anderson, and S. R. Quake, Microfluidic single-cell mRNA isolation and analysis, Analytical Chemistry, vol. 78, no. 9, pp. 3084–3089, May 2006. J. S. Marcus, W. F. Anderson, and S. R. Quake, Parallel picoliter RT-PCR assays using microfluidics, Analytical Chemistry, vol. 78, no. 3, pp. 956– 958, Feb. 2006. J. Liu, C. Hansen, and S. R. Quake, Solving the “world-to-chip” interface problem with a microfluidic matrix, Analytical Chemistry, vol. 75, no. 18, pp. 4718–4723, Sept. 2003. M. J. Anderson, C. L. Hansen, and S. R. Quake, Phase knowledge enables rational screens for protein crystallization, Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 45, pp. 16746–16751, 2006.
MICROFLUIDIC LAB-ON-A-CHIP PLATFORMS
365
132. E. P. Kartalov, J. F. Zhong, A. Scherer, S. R. Quake, C. R. Taylor, and W. F. Anderson, High-throughput multi-antigen microfluidic fluorescence immunoassays, Biotechniques, vol. 40, no. 1, pp. 85–90, 2006. 133. R. Gomez-Sjoberg, A. A. Leyrat, D. M. Pirone, C. S. Chen, and S. R. Quake, Versatile, fully automated, microfluidic cell culture system, Analytical Chemistry, vol. 79, pp. 8557–8563, 2007. 134. J. Melin, A. Lee, K. Foygel, D. E. Leong, S. R. Quake, and M. W. M. Yao, In Vitro Embryo Culture in Defined, Sub-microliter Volumes, Developmental Dynamics, vol. 238, no. 4, pp. 950–955, 2009. 135. Y. Y. Huang, P. Castrataro, C. C. Lee, and S. R. Quake, Solvent resistant microfluidic DNA synthesizer, Lab on A Chip, vol. 7, no. 1, pp. 24–26, 2007. 136. R. A. White, P. C. Blainey, H. C. Fan, and S. R. Quake, Digital PCR provides sensitive and absolute calibration for high throughput sequencing, Bmc Genomics, vol. 10 Mar. 2009. 137. S. Bhat, J. Herrmann, P. Armishaw, P. Corbisier, and K. R. Emslie, Single molecule detection in nanofluidic digital array enables accurate measurement of DNA copy number, Analytical and Bioanalytical Chemistry, vol. 394, no. 2, pp. 457–467, May 2009. 138. A. R. Wheeler, W. R. Throndset, R. J. Whelan, A. M. Leach, R. N. Zare, Y. H. Liao, K. Farrell, I. D. Manger, and A. Daridon, Microfluidic device for single-cell analysis, Analytical Chemistry, vol. 75, no. 14, pp. 3581–3586, July 2003. 139. J. D. Berndt, T. L. Biechele, R. T. Moon, and M. B. Major, Integrative analysis of genome-wide RNA interference screens, Sci Signal, vol. 2, no. 70, p. t4, 2009. 140. J. A. Weinstein, N. Jiang, R. A. White, D. S. Fisher, and S. R. Quake, HighThroughput Sequencing of the Zebrafish Antibody Repertoire, Science, vol. 324, no. 5928, pp. 807–810, May 2009. 141. V. G. Oehler, J. Qin, R. Ramakrishnan, G. Facer, S. Ananthnarayan, C. Cummings, M. Deininger, N. Shah, F. McCormick, S. Willis, A. Daridon, M. Unger, and J. P. Radich, Absolute quantitative detection of ABL tyrosine kinase domain point mutations in chronic myeloid leukemia using a novel nanofluidic platform and mutation-specific PCR, Leukemia, vol. 23, no. 2, pp. 396–399, Feb. 2009. 142. J. E. Lee, M. L. Fusco, and E. O. Saphire, An efficient platform for screening expression and crystallization of glycoproteins produced in human cells, Nature Protocols, vol. 4, no. 4, pp. 592–604, 2009. 143. W. Gu, X. Y. Zhu, N. Futai, B. S. Cho, and S. Takayama, Computerized microfluidic cell culture using elastomeric channels and Braille displays, Proceedings of the National Academy of Sciences of the United States of America, vol. 101, no. 45, pp. 15861–15866, Nov. 2004. 144. C. Holtze, A. C. Rowat, J. J. Agresti, J. B. Hutchison, F. E. Angile, C. H. J. Schmitz, S. Koster, H. Duan, K. J. Humphry, R. A. Scanga, J. S. Johnson, D. Pisignano, and D. A. Weitz, Biocompatible surfactants for water-influorocarbon emulsions, Lab on A Chip, vol. 8, no. 10, pp. 1632–1639, Oct. 2008.
366
D. MARK ET AL.
145. C. E. Sims and N. L. Allbritton, Analysis of single mammalian cells on-chip, Lab on A Chip, vol. 7, no. 4, pp. 423–440, 2007. 146. A. Huebner, S. Sharma, M. Srisa-Art, F. Hollfelder, J. B. Edel, and A. J. deMello, Microdroplets: A sea of applications?, Lab on A Chip, vol. 8, pp. 1244–1254, 2008. 147. S. L. Anna, N. Bontoux, and H. A. Stone, Formation of dispersions using “flow focusing” in microchannels, Applied Physics Letters, vol. 82, no. 3, pp. 364–366, Jan. 2003. 148. M. Joanicot and A. Ajdari, Applied physics – Droplet control for microfluidics, Science, vol. 309, no. 5736, pp. 887–888, Aug. 2005. 149. T. Nisisako, T. Torii, and T. Higuchi, Droplet formation in a microchannel network, Lab on A Chip, vol. 2, no. 1, pp. 24–26, 2002. 150. D. Malsch, N. Gleichmann, M. Kielpinski, G. +. Mayer, T. Henkel, D. Mueller, V. van Steijn, C. Kleijn, and M. Kreutzer, Dynamics of droplet formation at T-shaped nozzles with elastic feed lines, Microfluidics and Nanofluidics, Mar. 2009. 151. H. Song, J. D. Tice, and R. F. Ismagilov, A microfluidic system for controlling reaction networks in time, Angewandte Chemie-International Edition, vol. 42, no. 7, pp. 768–772, 2003. 152. H. Song and R. F. Ismagilov, Millisecond kinetics on a microfluidic chip using nanoliters of reagents, Journal of the American Chemical Society, vol. 125, no. 47, pp. 14613–14619, Nov. 2003. 153. B. Zheng, J. D. Tice, and R. F. Ismagilov, Formation of droplets of alternating composition in microfluidic channels and applications to indexing of concentrations in droplet-based assays, Analytical Chemistry, vol. 76, no. 17, pp. 4977–4982, Sept. 2004. 154. I. Shestopalov, J. D. Tice, and R. F. Ismagilov, Multi-step synthesis of nanoparticles performed on millisecond time scale in a microfluidic dropletbased system, Lab on A Chip, vol. 4, no. 4, pp. 316–321, 2004. 155. M. Y. He, J. S. Edgar, G. D. M. Jeffries, R. M. Lorenz, J. P. Shelby, and D. T. Chiu, Selective encapsulation of single cells and subcellular organelles into picoliter- and femtoliter-volume droplets, Analytical Chemistry, vol. 77, no. 6, pp. 1539–1544, Mar. 2005. 156. D. R. Link, S. L. Anna, D. A. Weitz, and H. A. Stone, Geometrically mediated breakup of drops in microfluidic devices, Physical Review Letters, vol. 92, no. 5, p. 054503, Feb. 2004. 157. J. D. Tice, H. Song, A. D. Lyon, and R. F. Ismagilov, Formation of droplets and mixing in multiphase microfluidics at low values of the Reynolds and the capillary numbers, Langmuir, vol. 19, no. 22, pp. 9127–9133, Oct. 2003. 158. J. D. Tice, A. D. Lyon, and R. F. Ismagilov, Effects of viscosity on droplet formation and mixing in microfluidic channels, Analytica Chimica Acta, vol. 507, no. 1, pp. 73–77, Apr. 2004. 159. H. Song, M. R. Bringer, J. D. Tice, C. J. Gerdts, and R. F. Ismagilov, Experimental test of scaling of mixing by chaotic advection in droplets moving through microfluidic channels, Applied Physics Letters, vol. 83, no. 22, pp. 4664–4666, Dec. 2003.
MICROFLUIDIC LAB-ON-A-CHIP PLATFORMS
367
160. M. R. Bringer, C. J. Gerdts, H. Song, J. D. Tice, and R. F. Ismagilov, Microfluidic systems for chemical kinetics that rely on chaotic mixing in droplets, Philosophical Transactions of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, vol. 362, no. 1818, pp. 1087–1104, May 2004. 161. A. Gunther, S. A. Khan, M. Thalmann, F. Trachsel, and K. F. Jensen, Transport and reaction in microscale segmented gas–liquid flow, Lab on A Chip, vol. 4, no. 4, pp. 278–286, 2004. 162. A. Gunther, M. Jhunjhunwala, M. Thalmann, M. A. Schmidt, and K. F. Jensen, Micromixing of miscible liquids in segmented gas–liquid flow, Langmuir, vol. 21, no. 4, pp. 1547–1555, Feb. 2005. 163. S. A. Khan, A. Gunther, M. A. Schmidt, and K. F. Jensen, Microfluidic synthesis of colloidal silica, Langmuir, vol. 20, no. 20, pp. 8604–8611, Sept. 2004. 164. P. Garstecki, M. A. Fischbach, and G. M. Whitesides, Design for mixing using bubbles in branched microfluidic channels, Applied Physics Letters, vol. 86, no. 24, p. 244108, June 2005. 165. K. Martin, T. Henkel, V. Baier, A. Grodrian, T. Schon, M. Roth, J. M. Kohler, and J. Metze, Generation of larger numbers of separated microbial populations by cultivation in segmented-flow microdevices, Lab on A Chip, vol. 3, no. 3, pp. 202–207, 2003. 166. D. R. Link, E. Grasland-Mongrain, A. Duri, F. Sarrazin, Z. D. Cheng, G. Cristobal, M. Marquez, and D. A. Weitz, Electric control of droplets in microfluidic devices, Angewandte Chemie-International Edition, vol. 45, no. 16, pp. 2556–2560, 2006. 167. K. Ahn, C. Kerbage, T. P. Hunt, R. M. Westervelt, D. R. Link, and D. A. Weitz, Dielectrophoretic manipulation of drops for high-speed microfluidic sorting devices, Applied Physics Letters, vol. 88, no. 2, p. 024104, Jan. 2006. 168. J. F. Edd, D. Di Carlo, K. J. Humphry, S. Koster, D. Irimia, D. A. Weitz, and M. Toner, Controlled encapsulation of single-cells into monodisperse picolitre drops, Lab on A Chip, vol. 8, no. 8, pp. 1262–1264, Aug. 2008. 169. J. Q. Boedicker, L. Li, T. R. Kline, and R. F. Ismagilov, Detecting bacteria and determining their susceptibility to antibiotics by stochastic confinement in nanoliter droplets using plug-based microfluidics, Lab on A Chip, vol. 8, no. 8, pp. 1265–1272, 2008. 170. W. W. Shi, J. H. Qin, N. N. Ye, and B. C. Lin, Droplet-based microfluidic system for individual Caenorhabditis elegans assay, Lab on A Chip, vol. 8, no. 9, pp. 1432–1435, 2008. 171. A. Huebner, L. F. Olguin, D. Bratton, G. Whyte, W. T. S. Huck, A. J. de Mello, J. B. Edel, C. Abell, and F. Hollfelder, Development of quantitative cell-based enzyme assays in microdroplets, Analytical Chemistry, vol. 80, no. 10, pp. 3890–3896, May 2008. 172. A. Funfak, A. Brosing, M. Brand, and J. M. Kohler, Micro fluid segment technique for screening and development studies on Danio rerio embryos, Lab on A Chip, vol. 7, no. 9, pp. 1132–1138, 2007.
368
D. MARK ET AL.
173. A. Reichert, J. Felbel, M. Kielpinski, M. Urban, B. Steinbrecht, and T. Henkel, Micro Flow-Through Thermocycler with Simple Meandering Channel with Symmetric Temperature Zones for Disposable PCR-Devices in Microscope Slide Format, J. Bionic. Eng., vol. 5, pp. 291–298, 2008. 174. Y. Schaerli, R. C. Wootton, T. Robinson, V. Stein, C. Dunsby, M. A. A. Neil, P. M. W. French, A. J. deMello, C. Abell, and F. Hollfelder, ContinuousFlow Polymerase Chain Reaction of Single-Copy DNA in Microfluidic Microdroplets, Analytical Chemistry, vol. 81, no. 1, pp. 302–306, 2009. 175. M. Srisa-Art, A. J. deMello, and J. B. Edel, High-throughput DNA droplet assays using picoliter reactor volumes, Analytical Chemistry, vol. 79, no. 17, pp. 6682–6689, 2007. 176. B. Zheng, J. D. Tice, L. S. Roach, and R. F. Ismagilov, A droplet-based, composite PDMS/glass capillary microfluidic system for evaluating protein crystallization conditions by microbatch and vapor-diffusion methods with on-chip X-ray diffraction, Angewandte Chemie-International Edition, vol. 43, no. 19, pp. 2508–2511, 2004. 177. M. K. Yadav, C. J. Gerdts, R. Sanishvili, W. W. Smith, L. S. Roach, R. F. Ismagilov, P. Kuhn, and R. C. Stevens, In situ data collection and structure refinement from microcapillary protein crystallization, Journal of Applied Crystallography, vol. 38, pp. 900–905, Dec. 2005. 178. L. S. Roach, H. Song, and R. F. Ismagilov, Controlling nonspecific protein adsorption in a plug-based microfluidic system by controlling interfacial chemistry using fluorous-phase surfactants, Analytical Chemistry, vol. 77, no. 3, pp. 785–796, Feb. 2005. 179. B. Zheng, J. D. Tice, and R. F. Ismagilov, Formation of arrayed droplets of soft lithography and two-phase fluid flow, and application in protein crystallization, Advanced Materials, vol. 16, no. 15, pp. 1365–1368, Aug. 2004. 180. B. Zheng, C. J. Gerdts, and R. F. Ismagilov, Using nanoliter plugs in microfluidics to facilitate and understand protein crystallization, Current Opinion in Structural Biology, vol. 15, no. 5, pp. 548–555, Oct. 2005. 181. D. L. Chen, C. J. Gerdts, and R. F. Ismagilov, Using microfluidics to observe the effect of mixing on nucleation of protein crystals, Journal of the American Chemical Society, vol. 127, no. 27, pp. 9672–9673, July 2005. 182. B. Zheng, L. S. Roach, and R. F. Ismagilov, Screening of protein crystallization conditions on a microfluidic chip using nanoliter-size droplets, Journal of the American Chemical Society, vol. 125, no. 37, pp. 11170–11171, Sept. 2003. 183. N. G. Anderson, Computer Interfaced Fast Analyzers, Science, vol. 166, no. 3903, pp. 317–324, 1969. 184. M. Madou, J. Zoval, G. Y. Jia, H. Kido, J. Kim, and N. Kim, Lab on a CD, Annual Review of Biomedical Engineering, vol. 8, pp. 601–628, 2006. 185. J. Ducrée, S. Haeberle, S. Lutz, S. Pausch, F. v. Stetten, and R. Zengerle, The centrifugal microfluidic Bio-Disk platform, Journal of Micromechanics and Microengineering, vol. 17, no. 7, p. S103–S115, 2007. 186. J. M. Koo and C. Kleinstreuer, Liquid flow in microchannels: experimental observations and computational analyses of microfluidics effects, Journal of Micromechanics and Microengineering, vol. 13, no. 5, pp. 568–579, Sept. 2003.
MICROFLUIDIC LAB-ON-A-CHIP PLATFORMS
369
187. U. Abaxis Inc., “Abaxis Inc., USA, ” 2006. 188. C. T. Schembri, V. Ostoich, P. J. Lingane, T. L. Burd, and S. N. Buhl, Portable simultaneous multiple analyte whole-blood analyzer for point-of-care testing, Clin. Chem., vol. 38, no. 9, pp. 1665–1670, Sept. 1992. 189. C. T. Schembri, T. L. Burd, A. R. Kopfsill, L. R. Shea, and B. Braynin, Centrifugation and Capillarity Integrated Into A Multiple Analyte WholeBlood Analyzer, Journal of Automatic Chemistry, vol. 17, no. 3, pp. 99–104, May 1995. 190. M. Madou and G. J. Kellogg, The LabCD: A Centrifuge-Based Microfluidic Platform for Diagnostics, Proc. SPIE Systems and Technologies for Clinical Diagnostics and Drug Discovery, vol. 3259, pp. 80–93, 1998. 191. D. C. Duffy, H. L. Gillis, J. Lin, N. F. Sheppard, Jr., and G. J. Kellogg, Microfabricated Centrifugal Microfluidic Systems: Characterization and Multiple Enzymatic Assays, Analytical Chemistry, vol. 71, no. 20, pp. 4669– 4678, 1999. 192. G. Ekstrand, C. Holmquist, A. E. Örlefors, B. Hellman, A. Larsson, and P. Andersson, “Microfluidics in a Rotating CD,” 2000, pp. 311–314. 193. M. Madou, J. Lee, S. Daunert, S. Lai, and C.-H. Shih, Design and fabrication of cd-like microfluidic platforms for diagnostics: microfluidic functions, Biomedical Microdevices, vol. 3, no. 3, pp. 245–254, 2001. 194. S. Haeberle, T. Brenner, H. P. Schlosser, R. Zengerle, and J. Ducrée, Centrifugal micromixer, Chemical Engineering & Technology, vol. 28, no. 5, pp. 613–616, May 2005. 195. H. Cho, H. Y. Kim, J. Y. Kang, and T. S. Kim, How the capillary burst microvalve works, Journal of Colloid and Interface Science, vol. 306, no. 2, pp. 379–385, Feb. 2007. 196. J. M. Chen, P. C. Huang, and M. G. Lin, Analysis and experiment of capillary valves for microfluidics on a rotating disk, Microfluidics and Nanofluidics, vol. 4, no. 5, pp. 427–437, May 2008. 197. N. Honda, U. Lindberg, P. Andersson, S. Hoffman, and H. Takei, Simultaneous multiple immunoassays in a compact disc-shaped microfluidic device based on centrifugal force, Clinical Chemistry, vol. 51, no. 10, pp. 1955–1961, Oct. 2005. 198. C. P. Steinert, J. Mueller-Dieckmann, M. Weiss, M. Roessle, R. Zengerle, and P. Koltay, “Miniaturized and Highly Parallel Protein Crystallization on a Microfluidic Disc,” Kobe, Japan: 2007, pp. 561–564. 199. S. Haeberle, T. Brenner, R. Zengerle, and J. Ducrée, Centrifugal extraction of plasma from whole blood on a rotating disk, Lab on A Chip, vol. 6, no. 6, pp. 776–781, June 2006. 200. J. Ducree, S. Haeberle, S. Lutz, S. Pausch, F. von Stetten, and R. Zengerle, The centrifugal microfluidic bio-disk platform, Journal of Micromechanics and Microengineering, vol. 17, no. 7, pp. 103–115, July 2007. 201. D. Mark, T. Metz, S. Haeberle, S. Lutz, J. Ducrée, R. Zengerle, and F. von Stetten, Centrifugo-Pneumatic Valve for Metering of Highly Wetting Liquids on Centrifugal Microfluidic Platforms, Lab on A Chip, 2009. 202. D. H. Sharp, An Overview of Rayleigh-Taylor Instability, Physica D, vol. 12, no. 1–3, pp. 3–18, 1984.
370
D. MARK ET AL.
203. J. M. Park, Y. K. Cho, B. S. Lee, J. G. Lee, and C. Ko, Multifunctional microvalves control by optical illumination on nanoheaters and its application in centrifugal microfluidic devices, Lab on A Chip, vol. 7, no. 5, pp. 557–564, 2007. 204. J. Steigert, M. Grumann, T. Brenner, K. Mittenbühler, T. Nann, J. Rühe, I. Moser, S. Haeberle, L. Riegger, J. Riegler, W. Bessler, R. Zengerle, and J. Ducrée, Integrated Sample Preparation, Reaction, and Detection on a Highfrequency Centrifugal Microfluidic Platform, Journal of the Association for Laboratory Automation (JALA), vol. 10, no. 5, pp. 331–341, 2005. 205. J. Steigert, M. Grumann, T. Brenner, L. Riegger, J. Harter, R. Zengerle, and J. Ducrée, Fully Integrated Whole Blood Testing by Real-Time Absorption Measurement on a Centrifugal Platform, Lab on A Chip, vol. 6, no. 8, pp. 1040–1044, 2006. 206. J. V. Zoval and M. J. Madou, Centrifuge-based fluidic platforms, Proceedings of the IEEE, vol. 92, no. 1, pp. 140–153, Jan. 2004. 207. S. Lutz, V. Reitenbach, D. Mark, J. Ducrée, R. Zengerle, and F. von Stetten, “Unidirectional Shake-Mode for mixing highly wetting fluids on Centrifugal Platforms,” 2008. 208. M. Grumann, A. Geipel, L. Riegger, R. Zengerle, and J. Ducrée, Batch-mode mixing on centrifugal microfluidic platforms, Lab on A Chip, vol. 5, no. 5, pp. 560–565, 2005. 209. C. T. Schembri and M. P. Caren, “Method of mixing by intermittent centrifugal force,” US7147362, Dec. 12, 2006. 210. T. Brenner, T. Glatzel, R. Zengerle, and J. Ducrée, Frequency-dependent transversal flow control in centrifugal microfluidics, Lab on A Chip, vol. 5, no. 2, pp. 146–150, 2005. 211. S. Haeberle, L. Naegele, R. Zengerle, and J. Ducrée, “A Digital Centrifugal Droplet Switch For Routing of Liquids,” Tokyo, Japan: 2006, pp. 570–572. 212. S. Gyros AB, “Gyros AB, Sweden, ” 2006. 213. G. Ekstrand and T. Thorsen, “Liquid Router,” WO Patent WO2005032999, 2005. 214. J. Kim, H. Kido, R. H. Rangel, and M. J. Madou, Passive flow switching valves on a centrifugal microfluidic platform, Sensors and Actuators BChemical, vol. 128, no. 2, pp. 613–621, Jan. 2008. 215. J. L. Zhang, Q. Q. Guo, M. Liu, and J. Yang, A lab-on-CD prototype for high-speed blood separation, Journal of Micromechanics and Microengineering, vol. 18, no. 12, p. 125025, 2008. 216. G. J. Kellogg, T. E. Arnold, B. L. Carvalho, D. C. Duffy, and N. F. Sheppard, Jr., “Centrifugal Microfluidics: Applications,” 2000, pp. 239–242. 217. I. H. A. Badr, R. D. Johnson, M. J. Madou, and L. G. Bachas, Fluorescent ion-selective optode membranes incorporated onto a centrifugal microfluidics platform, Analytical Chemistry, vol. 74, no. 21, pp. 5569–5575, Nov. 2002. 218. R. D. Johnson, I. H. Badr, G. Barrett, S. Lai, Y. Lu, M. J. Madou, and L. G. Bachas, Development of a fully integrated analysis system for ions based on ion-selective optodes and centrifugal microfluidics, Analytical Chemistry, vol. 73, no. 16, pp. 3940–3946, Aug. 2001.
MICROFLUIDIC LAB-ON-A-CHIP PLATFORMS
371
219. A. S. Watts, A. A. Urbas, E. Moschou, V. G. Gavalas, J. V. Zoval, M. Madou, and L. G. Bachas, Centrifugal Microfluidics with Integrated Sensing Microdome Optodes for Multiion Detection, Analytical Chemistry, vol. 79, no. 21, pp. 8046–8054, Nov. 2007. 220. L. G. Puckett, E. Dikici, S. Lai, M. Madou, L. G. Bachas, and S. Daunert, Investigation into the applicability of the centrifugal microfluidics development of protein-platform for the ligand binding assays incorporating enhanced green fluorescent protein as a fluorescent reporter, Analytical Chemistry, vol. 76, no. 24, pp. 7263–7268, Dec. 2004. 221. G. Jia, K. S. Ma, J. Kim, J. V. Zoval, R. Peytavi, M. G. Bergeron, and M. J. Madou, Dynamic automated DNA hybridization on a CD (compact disc) fluidic platform, Sensors and Actuators B: Chemical, vol. 114, no. 1, pp. 173–181, Mar. 2006. 222. S. Lai, S. Wang, J. Luo, L. J. Lee, S. T. Yang, and M. J. Madou, Design of a compact disk-like microfluidic platform for enzyme-linked immunosorbent assay, Analytical Chemistry, vol. 76, no. 7, pp. 1832–1837, Apr. 2004. 223. C. Lu, Y. Xie, Y. Yang, M. M. Cheng, C. G. Koh, Y. Bai, L. J. Lee, and Y. J. Juang, New valve and bonding designs for microfluidic biochips containing proteins, Analytical Chemistry, vol. 79, no. 3, pp. 994–1001, Feb. 2007. 224. L. Riegger, J. Steigert, M. Grumann, S. Lutz, G. Olofsson, M. Khayyami, W. Bessler, K. Mittenbühler, R. Zengerle, and J. Ducrée, “Disk-based Parallel Chemiluminescent Detection of Diagnostic Markers for Acute Myocardial Infarction,” Istanbul, Turkey: IEEE-MEMS 2006 conference, 2006. 225. S. Lutz, P. Lang, I. Malki, D. Mark, J. Ducrée, R. Zengerle, and F. von Stetten, “Lab-on-a-Chip Cartridge for Processing of Immunoassays with Integrated Sample Preparation,” 2008. 226. B. S. Lee, J. N. Lee, J. M. Park, J. G. Lee, S. Kim, Y. K. Cho, and C. Ko, A fully automated immunoassay from whole blood on a disc, Lab on A Chip, vol. 9, pp. 1548–1555, 2009. 227. Y. K. Cho, J. G. Lee, J. M. Park, B. S. Lee, Y. Lee, and C. Ko, One-step pathogen specific DNA extraction from whole blood on a centrifugal microfluidic device, Lab on A Chip, vol. 7, no. 5, pp. 565–573, Feb. 2007. 228. S. SpinX Technologies, “SpinX Technologies, Switzerland,” 2006. 229. C. A. Burtis, N. G. Anderson, J. C. Mailen, C. D. Scott, T. O. Tiffany, and W. F. Johnson, Development of A Miniature Fast Analyzer, Clinical Chemistry, vol. 18, no. 8, pp. 753–761, 1972. 230. J. Ducrée, S. Haeberle, T. Brenner, T. Glatzel, and R. Zengerle, Patterning of flow and mixing in rotating radial microchannels, Microfluidics and Nanofluidics, vol. 2, no. 2, pp. 97–105, 2006. 231. J. Ducrée, T. Brenner, S. Haeberle, T. Glatzel, and R. Zengerle, Multilamination of flows in planar networks of rotating microchannels, Microfluidics and Nanofluidics, vol. 2, no. 1, pp. 78–84, 2006. 232. M. Grumann, J. Steigert, L. Riegger, I. Moser, B. Enderle, K. Riebeseel, G. Urban, R. Zengerle, and J. Ducrée, Sensitivity enhancement for colorimetric glucose assays on whole blood by on-chip beam-guidance, Biomedical Microdevices, vol. 8, no. 3, pp. 209–214, Sept. 2006.
372
D. MARK ET AL.
233. S. Haeberle, S. Pausch, R. Burger, S. Lutz, F. von Stetten, R. Zengerle, and J. Ducrée, “Automation of nucleid acid extraction by a coriolis-force actuated droplet router,” Paris, France: 2007, pp. 1231–1233. 234. J. Hoffmann, D. Mark, R. Zengerle, and F. von Stetten, “Liquid Reagent Storage and Release for Centrifugally Operated Lab-on-a-Chip Systems Based on a Burstable Seal,” 15 ed 2009. 235. A. P. Wong, M. Gupta, S. S. Shevkoplyas, and G. M. Whitesides, Egg beater as centrifuge: isolating human blood plasma from whole blood in resourcepoor settings, Lab on A Chip, vol. 8, no. 12, pp. 2032–2037, 2008. 236. H. Kido, M. Micic, D. Smith, J. Zoval, J. Norton, and M. Madou, A novel, compact disk-like centrifugal microfluidics system for cell lysis and sample homogenization, Colloids and Surfaces B-Biointerfaces, vol. 58, no. 1, pp. 44–51, 2007. 237. S. A. Lange, G. Roth, S. Wittemann, T. Lacoste, A. Vetter, J. Grassle, S. Kopta, M. Kolleck, B. Breitinger, M. Wick, J. K. H. Horber, S. Dubel, and A. Bernard, Measuring biomolecular binding events with a compact disc player device, Angewandte Chemie-International Edition, vol. 45, no. 2, pp. 270–273, 2006. 238. M. Focke, B. Faltin, T. Hoesel, C. Mueller, J. Ducrée, R. Zengerle, and F. von Stetten, “Blow molding of polymer foils for rapid prototyping of microfluidic cartridges,” 2008, pp. 988–990. 239. R. A. Potyrailo, W. G. Morris, A. M. Leach, T. M. Sivavec, M. B. Wisnudel, and S. Boyette, Analog Signal Acquisition from Computer Optical Disk Drives for Quantitative Chemical Sensing, Analytical Chemistry, vol. 78, no. 16, pp. 5893–5899, Aug. 2006. 240. A. Penrose, P. Myers, K. Bartle, and S. McCrossen, Development and assessment of a miniaturised centrifugal chromatograph for reversed-phase separations in micro-channels, The Analyst, vol. 129, no. 8, pp. 704–709, 2004. 241. N. Sasaki, T. Kitamori, and H. B. Kim, AC electroosmotic micromixer for chemical processing in a microchannel, Lab on A Chip, vol. 6, no. 4, pp. 550–554, 2006. 242. P. W. Atkins, Physikalische Chemie 1987, pp. 781–802. 243. C. Y. Lee, G. B. Lee, J. L. Lin, F. C. Huang, and C. S. Liao, Integrated microfluidic systems for cell lysis, mixing/pumping and DNA amplification, Journal of Micromechanics and Microengineering, vol. 15, no. 6, pp. 1215– 1223, June 2005. 244. D. E. Raymond, A. Manz, and H. M. Widmer, Continuous Sample Pretreatment Using A Free-Flow Electrophoresis Device Integrated Onto A Silicon Chip, Analytical Chemistry, vol. 66, no. 18, pp. 2858–2865, Sept. 1994. 245. H. Morgan, M. P. Hughes, and N. G. Green, Separation of submicron bioparticles by dielectrophoresis, Biophysical Journal, vol. 77, no. 1, pp. 516–525, July 1999. 246. U. Zimmermann and J. Vienken, Electric Field-Induced Cell-To-Cell Fusion, Journal of Membrane Biology, vol. 67, no. 3, pp. 165–182, 1982.
MICROFLUIDIC LAB-ON-A-CHIP PLATFORMS
373
247. R. Krupke, F. Hennrich, H. von Lohneysen, and M. M. Kappes, Separation of metallic from semiconducting single-walled carbon nanotubes, Science, vol. 301, no. 5631, pp. 344–347, July 2003. 248. A. Manz, D. J. Harrison, E. M. J. Verpoorte, J. C. Fettinger, A. Paulus, H. Ludi, and H. M. Widmer, Planar Chips Technology for Miniaturization and Integration of Separation Techniques Into Monitoring Systems – Capillary Electrophoresis on A Chip, Journal of Chromatography, vol. 593, no. 1–2, pp. 253–258, Feb. 1992. 249. D. J. Harrison, K. Fluri, K. Seiler, Z. H. Fan, C. S. Effenhauser, and A. Manz, Micromachining A Miniaturized Capillary Electrophoresis-Based Chemical-Analysis System on A Chip, Science, vol. 261, no. 5123, pp. 895– 897, Aug. 1993. 250. C. S. Effenhauser, A. Manz, and H. M. Widmer, Glass Chips for High-Speed Capillary Electrophoresis Separations with Submicrometer Plate Heights, Analytical Chemistry, vol. 65, no. 19, pp. 2637–2642, Oct. 1993. 251. L. Wang, J. Lu, S. A. Marukenko, E. S. Monuki, L. A. Flanagan, and A. P. Lee, Dual frequency dielectrophoresis with interdigitated sidewall electrodes for microfluidic flow-through separation of beads and cells, Electrophoresis, vol. 30, no. 5, pp. 782–791, Mar. 2009. 252. P. Patel and G. H. Markx, Dielectric measurement of cell death, Enzyme and Microbial Technology, vol. 43, no. 7, pp. 463–470, Dec. 2008. 253. C. J. Huang, A. L. Chen, L. Wang, M. Guo, and J. Yu, Electrokinetic measurements of dielectric properties of membrane for apoptotic HL-60 cells on chip-based device, Biomedical Microdevices, vol. 9, no. 3, pp. 335–343, June 2007. 254. J. M. Ramsey, S. C. Jacobson, and M. R. Knapp, Microfabricated Chemical Measurement Systems, Nature Medicine, vol. 1, no. 10, pp. 1093–1096, Oct. 1995. 255. U. Caliper Life Sciences, “Caliper Life Sciences, USA,” 2007. 256. U. Agilent Technologies Inc., “Agilent Technologies Inc., USA,” 2007. 257. J. Cheng, E. L. Sheldon, L. Wu, A. Uribe, L. O. Gerrue, J. Carrino, M. J. Heller, and J. P. O’Connell, Preparation and hybridization analysis of DNA/ RNA from E-coli on microfabricated bioelectronic chips, Nature Biotechnology, vol. 16, no. 6, pp. 541–546, 1998. 258. W. Kohlrausch, Leitfaden der Praktischen Physik, 31 ed BiblioBazaar, 1875. 259. G. Lippmann, Relations entre les phénomènes électrique et capillaries, Ann. Chim. Phys., vol. 5, pp. 494–549, 1875. 260. F. Mugele and J. C. Baret, Electrowetting: From basics to applications, Journal of Physics-Condensed Matter, vol. 17, no. 28, p. R705–R774, July 2005. 261. J. Lee, H. Moon, J. Fowler, T. Schoellhammer, and C. J. Kim, Electrowetting and electrowetting-on-dielectric for microscale liquid handling, Sensors and Actuators A-Physical, vol. 95, no. 2–3, pp. 259–268, Jan. 2002. 262. M. G. Pollack, R. B. Fair, and A. D. Shenderov, Electrowetting-based actuation of liquid droplets for microfluidic applications, Applied Physics Letters, vol. 77, no. 11, pp. 1725–1726, Sept. 2000.
374
D. MARK ET AL.
263. J. Lee and C. J. Kim, Surface-tension-driven microactuation based on continuous electrowetting, Journal of Microelectromechanical Systems, vol. 9, no. 2, pp. 171–180, June 2000. 264. D. Chatterjee, B. Hetayothin, A. R. Wheeler, D. J. King, and R. L. Garrell, Droplet-based microfluidics with nonaqueous solvents and solutions, Lab on A Chip, vol. 6, no. 2, pp. 199–206, Feb. 2006. 265. V. Srinivasan, V. K. Pamula, and R. B. Fair, An integrated digital microfluidic lab-on-a-chip for clinical diagnostics on human physiological fluids, Lab on A Chip, vol. 4, no. 4, pp. 310–315, 2004. 266. H. Ren, R. B. Fair, and M. G. Pollack, Automated on-chip droplet dispensing with volume control by electro-wetting actuation and capacitance metering, Sensors and Actuators B-Chemical, vol. 98, no. 2–3, pp. 319–327, Mar. 2004. 267. J. Berthier, P. Clementz, O. Raccurt, D. Jary, P. Claustre, C. Peponnet, and Y. Fouillet, Computer aided design of an EWOD microdevice, Sensors and Actuators A-Physical, vol. 127, no. 2, pp. 283–294, Mar. 2006. 268. M. G. Pollack, A. D. Shenderov, and R. B. Fair, Electrowetting-based actuation of droplets for integrated microfluidics, Lab on A Chip, vol. 2, no. 2, pp. 96–101, 2002. 269. P. Paik, V. K. Pamula, M. G. Pollack, and R. B. Fair, Electrowetting-based droplet mixers for microfluidic systems, Lab on A Chip, vol. 3, no. 1, pp. 28–33, 2003. 270. P. Paik, V. K. Pamula, and R. B. Fair, Rapid droplet mixers for digital microfluidic systems, Lab on A Chip, vol. 3, no. 4, pp. 253–259, 2003. 271. A. R. Wheeler, H. Moon, C. J. Kim, J. A. Loo, and R. L. Garrell, Electrowetting-based microfluidics for analysis of peptides and proteins by matrix-assisted laser desorption/ionization mass spectrometry, Analytical Chemistry, vol. 76, no. 16, pp. 4833–4838, Aug. 2004. 272. Y. H. Chang, G. B. Lee, F. C. Huang, Y. Y. Chen, and J. L. Lin, Integrated polymerase chain reaction chips utilizing digital microfluidics, Biomedical Microdevices, vol. 8, no. 3, pp. 215–225, 2006. 273. R. B. Fair, Digital microfluidics: is a true lab-on-a-chip possible?, Microfluidics and Nanofluidics, vol. 3, no. 3, pp. 245–281, 2007. 274. A. Wixforth, Acoustically driven planar microfluidics, Superlattices and Microstructures, vol. 33, no. 5–6, pp. 389–396, May 2003. 275. A. Wixforth, C. Strobl, C. Gauer, A. Toegl, J. Scriba, and Z. von Guttenberg, Acoustic manipulation of small droplets, Analytical and Bioanalytical Chemistry, vol. 379, no. 7–8, pp. 982–991, Aug. 2004. 276. D. Beyssen, L. Le Brizoual, O. Elmazria, and P. Alnot, Microfluidic device based on surface acoustic wave, Sensors and Actuators B-Chemical, vol. 118, no. 1–2, pp. 380–385, Oct. 2006. 277. M. K. Tan, J. R. Friend, and L. Y. Yeo, Microparticle collection and concentration via a miniature surface acoustic wave device, Lab on A Chip, vol. 7, no. 5, pp. 618–625, 2007. 278. Z. Guttenberg, H. Muller, H. Habermuller, A. Geisbauer, J. Pipper, J. Felbel, M. Kielpinski, J. Scriba, and A. Wixforth, Planar chip device for PCR and hybridization with surface acoustic wave pump, Lab on A Chip, vol. 5, no. 3, pp. 308–317, 2005.
MICROFLUIDIC LAB-ON-A-CHIP PLATFORMS
375
279. S. Fox, S. Farr-Jones, L. Sopchak, A. Boggs, and J. Comley, High-Throughput Screening: Searching for Higher Productivity, Journal of Biomolecular Screening, vol. 9, no. 4, pp. 354–358, Aug. 2004. 280. R. P. Hertzberg and A. J. Pope, High-throughput screening: new technology for the 21st century, Current Opinion in Chemical Biology, vol. 4, no. 4, pp. 445–451, Aug. 2000. 281. O. Ramstrom, T. Bunyapaiboonsri, S. Lohmann, and J. M. Lehn, Chemical biology of dynamic combinatorial libraries, Biochimica et Biophysica ActaGeneral Subjects, vol. 1572, no. 2–3, pp. 178–186, Sept. 2002. 282. D. M. Brown, M. Pellecchia, and E. Ruoslahti, Drug identification through in vivo screening of chemical libraries, Chembiochem, vol. 5, no. 6, pp. 871– 875, June 2004. 283. U. F. Vogel and B. D. Bueltmann, Simple, inexpensive, and precise paraffin tissue microarrays constructed with a conventional microcompound table and a drill grinder, American Journal of Clinical Pathology, vol. 126, no. 3, pp. 342–348, Sept. 2006. 284. J. F. Desnottes, New targets and strategies for the development of antibacterial agents, Trends in Biotechnology, vol. 14, no. 4, pp. 134–140, Apr. 1996. 285. S. B. Rawool and K. V. Venkatesh, Steady state approach to model gene regulatory networks – Simulation of microarray experiments, Biosystems, vol. 90, no. 3, pp. 636–655, Nov. 2007. 286. G. H. W. Sanders and A. Manz, Chip-based microsystems for genomic and proteomic analysis, Trac-Trends in Analytical Chemistry, vol. 19, no. 6, pp. 364–378, June 2000. 287. A. Brazma, Minimum Information About a Microarray Experiment (MIAME) – Successes, Failures, Challenges, Thescientificworldjournal, vol. 9, pp. 420–423, 2009. 288. P. Pantano and D. R. Walt, Ordered nanowell arrays, Chemistry of Materials, vol. 8, no. 12, pp. 2832–2835, 1996. 289. M. Margulies, M. Egholm, W. E. Altman, S. Attiya, J. S. Bader, L. A. Bemben, J. Berka, M. S. Braverman, Y. J. Chen, Z. T. Chen, S. B. Dewell, L. Du, J. M. Fierro, X. V. Gomes, B. C. Godwin, W. He, S. Helgesen, C. H. Ho, G. P. Irzyk, S. C. Jando, M. L. I. Alenquer, T. P. Jarvie, K. B. Jirage, J. B. Kim, J. R. Knight, J. R. Lanza, J. H. Leamon, S. M. Lefkowitz, M. Lei, J. Li, K. L. Lohman, H. Lu, V. B. Makhijani, K. E. Mcdade, M. P. McKenna, E. W. Myers, E. Nickerson, J. R. Nobile, R. Plant, B. P. Puc, M. T. Ronan, G. T. Roth, G. J. Sarkis, J. F. Simons, J. W. Simpson, M. Srinivasan, K. R. Tartaro, A. Tomasz, K. A. Vogt, G. A. Volkmer, S. H. Wang, Y. Wang, M. P. Weiner, P. G. Yu, R. F. Begley, and J. M. Rothberg, Genome sequencing in microfabricated highdensity picolitre reactors, Nature, vol. 437, no. 7057, pp. 376–380, Sept. 2005. 290. D. R. Walt, Molecular biology - Bead-based fiber-optic arrays, Science, vol. 287, no. 5452, pp. 451–452, Jan. 2000. 291. A. C. Pease, D. Solas, E. J. Sullivan, M. T. Cronin, C. P. Holmes, and S. P. A. Fodor, Light-Generated Oligonucleotide Arrays for Rapid DNA-Sequence Analysis, Proceedings of the National Academy of Sciences of the United States of America, vol. 91, no. 11, pp. 5022–5026, May 1994.
376
D. MARK ET AL.
292. S. A. Dunbar, C. A. Vander Zee, K. G. Oliver, K. L. Karem, and J. W. Jacobson, Quantitative, multiplexed detection of bacterial pathogens: DNA and protein applications of the Luminex LabMAP system, J. Microbiol. Methods, vol. 53, no. 2, pp. 245–252, May 2003. 293. “Handbook Luminex Beadarray,” 2009. 294. K. L. Gunderson, S. Kruglyak, M. S. Graige, F. Garcia, B. G. Kermani, C. F. Zhao, D. P. Che, T. Dickinson, E. Wickham, J. Bierle, D. Doucet, M. Milewski, R. Yang, C. Siegmund, J. Haas, L. X. Zhou, A. Oliphant, J. B. Fan, S. Barnard, and M. S. Chee, Decoding randomly ordered DNA arrays, Genome Research, vol. 14, no. 5, pp. 870–877, May 2004. 295. J. B. Fan, K. L. Gunderson, M. Bibikova, J. M. Yeakley, J. Chen, E. W. Garcia, L. L. Lebruska, M. Laurent, R. Shen, and D. Barker, Illumina universal bead arrays, Dna Microarrays Part A: Array Platforms and WetBench Protocols, vol. 410, p. 57–+, 2006. 296. M. Ronaghi, S. Karamohamed, B. Pettersson, M. Uhlen, and P. Nyren, Realtime DNA sequencing using detection of pyrophosphate release, Analytical Biochemistry, vol. 242, no. 1, pp. 84–89, Nov. 1996. 297. “VeraCode Research Guide,” 2007. 298. D. Ryan, M. Rahimi, J. Lund, R. Mehta, and B. A. Parviz, Toward nanoscale genome sequencing, Trends in Biotechnology, vol. 25, no. 9, pp. 385–389, 2007.
MICROFLUIDIC LAB-ON-A-CHIP DEVICES FOR BIOMEDICAL APPLICATIONS DONGQING LI Department of Mechanical & Mechatronics Engineering University of Waterloo, Waterloo, Ontario, Canada N2L 3G1,
[email protected]
Abstract. Microfluidics is key to miniaturize bio-chemical and biomedical methods and processes into chip based technology. Basics of electrokinetic microfluidics will be reviewed first. Three types of lab-on-a-chip devices, PCR lab-on-a-chip, flow cytometer lab-on-a-chip and immunoassay lab-ona-chip are discussed here. The working principle, key microfluidic processes and the current status of these lab-on-a-chip devices are reviewed.
1. Introduction Lab-on-a-chip devices are miniature laboratories built on a thin glass or plastic chip of several centimeters in dimension, with a network of microchannels (e.g., 100 μm in width). These small chips can duplicate the specialized functions as their room-sized counterparts in clinical diagnoses. The advantages of these lab-on-a-chip devices include markedly reduced reagent consumption, short analysis time, automation and portability. Generally, a lab-on-a-chip device must perform many microfluidic functions such as pumping, flow switching, incubating, sequentially loading solutions and washing. A very large pressure gradient is required to generate liquid flow in microchannels since the flow resistance is reversely proportional to the fourth power of transverse channel dimension. It would be unpractical and difficult to use pressure-driven flow to control the sequential loading and washing processes in a portable microfluidic system. Alternatively, electrokinetic forces can be used to drive liquid flow in microchannels. All solid surfaces acquire electrostatic charges when they are in contact with an aqueous solution. The surface charge in turn attracts the counterions in the liquid to the region close to the surface, forming the electric double layer. Under a tangentially applied electrical field, the excess counter-ions in the double layer region will move, resulting in a bulk liquid
S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_18, © Springer Science + Business Media B.V. 2010
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motion via viscous effect. This is known as the electroosmotic flow [1]. Generally, the electroosmotic flow velocity is given by:
ε ε ζ veof = − r o E μ
(1)
where ε and ε0 are the dielectric constants in the medium and in the vacuum, respectively; μ is the viscosity of the liquid; ζ is the zeta potential of the channel wall surface; and E is the applied electric field. In a microfluidic chip, there are a number of wells at the ends of the microchannel branches. These wells provide not only reservoirs for samples and reagents, but also the connection of electrodes to liquid in the microchannels. The liquid flow control is realized by applying different voltages to different wells simultaneously. In this way one can control the flow rate, and let one solution flowing through a microchannel in the desired direction while keeping all other solutions stationary in their wells and channels. A charged particle will move relatively to the surrounding stationary liquid under the influence of applied electric field; this is generally referred to as electrophoresis. The particle’s electrophoretic velocity:
vep =
ε rε oζ p E μ
(2)
where ζp is the zeta potential of the particle. In a microchannel, the motion of the particles/cells is determined by the combined effect of electroosmosis (the liquid motion) and electrophoresis. Understanding of the net motion of the particles or cellsin a microchannel is important for transporting and separating particles/cells in a lab-on-a-chip device [1, my book]. In a non-uniform electrical field, a dielectric particle in a dielectric liquid will be polarized and subject to non-symmetric electrical force. Consequently, the particle is induced to move under the net electric force. Such a motion of the particle is known as dielectrophoresis. Dielectrophoresis has been used to concentrate and separate particles/cells in microchannels. In the development of lab-on-a-chip technology, a key is to develop the ability to pump the liquids and transport sample/reagent molecules as well as biological cells in a microchannel network. This can be achieved by using the electroosmotic flow and electrophoresis. Mixing of different solutions and dispensing a specified amount of one solution from one microchannel into another microchannel are important to many microfluidic chips. There are extensive research works done in these areas [1]. Furthermore, precise control of temperature is often critical to on-chip biochemical reactions. In the following the PCR lab-on-a-chip, flow cytometer lab-on-a-chip and immunoassay lab-on-a-chip will be reviewed.
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2. Real-Time PCR Lab-on-a-Chip Many biological identification processes and biomedical diagnosis processes utilize deoxyribonucleic acid (DNA) analysis based methods, such as DNA sequencing to identify a specific DNA for forensic applications. However, all these analyses have to start with a sufficient amount of DNA molecules. To do so, a molecular biology method, the polymerase chain reaction (PCR) is used. Generally speaking, the polymerase chain reaction (PCR) is a technique to amplify a single or few copies of a piece of a DNA molecule to generate millions or more copies of the same DNA molecule. In addition to the chemistry involved, the PCR method relies on thermal cycling, i.e., repeated heating and cooling of the reaction for DNA melting and enzymatic replication of the DNA. Typically, PCR thermal cycling involves the following: Denaturation step: This step is the first regular cycling event and consists of heating the reaction to about 95°C for 20–30 s. It generates single strands of DNA by melting of DNA template and primers, disrupting the hydrogen bonds between complementary bases of the DNA strands. Annealing step: The reaction temperature is lowered to 50–65°C for about 30 s allowing annealing of the primers to the single-stranded DNA template. Stable DNADNA hydrogen bonds are only formed when the primer sequence very closely matches the template sequence. The polymerase binds to the primertemplate hybrid and begins DNA synthesis. Extension/elongation step: The temperature at this step depends on the DNA polymerase used; in the case of Taq polymerase, a temperature of 72°C is used with this enzyme. At this step the DNA polymerase synthesizes a new DNA strand complementary to the DNA template strand by adding dNTPs (Deoxynucleoside triphosphates) that are complementary to the template in 5′ to 3′ direction, condensing the 5′-phosphate group of the dNTPs with the 3′-hydroxyl group at the end of the nascent (extending) DNA strand. Theoretically, after each PCR thermal cycle, the amount of DNA target is doubled, leading to exponential amplification of the specific DNA fragment in the solution. The above described PCR can only amplify the number of copies of a DNA molecules in the sample. In order to know what DNA or specific DNA sequence it is, however, one has to perform additional analyses, such as using gel electrophoresis or DNA sequencing method to find the answer. A direct DNA identification method, called the real-time PCR, combining both the PCR with fluorescent detection, is most useful in this regard. Real-time PCR uses a fluorescently labeled oligonucleotide probe, which eliminates the need for laborious and time-consuming post-PCR processing (e.g., gel electrophoresis). In real-time PCR, a reporter fluorescence dye and a quencher dye are attached to an oligonucleotide probe. Negligible fluorescence from the reporter dye’s emission is observed when both dyes
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are attached to the probe. Once PCR amplification begins, DNA polymerase cleaves the probe, and the reporter dye is released from the probe, separated from the quencher dye during every amplification cycle, and generates a sequence-specific fluorescent signal. Real-time PCR detection is based on monitoring the fluorescent signal intensity produced proportionally during the amplification of a specific PCR product (e.g., an influenza DNA); therefore, it is a direct and quantitative method with high sensitivity. However, there are limitations to the applications of the real-time PCR technique. Currently, the instruments for conducting real-time PCR are bulky and expensive, are available only in large hospitals and major medical centers, and are not available for field or point-of-testing applications. In addition to the initial capital cost, the cost of reagents in real-time PCR is significantly high, partially because of the relatively large reagent consumption. The average thermal cycling speed of some PCR machines is as low as about 1°C/s. In order to apply the real-time PCR technology as a rapid, accurate, and direct detection tool for field or point-of-testing applications, it is highly desirable to miniaturize the real-time PCR instrument. To miniaturize the real-time PCR and make it a lab-on-a-chip method, one must realize the following two key functions: (1) Control the on-chip thermal cycling, i.e., control the temperature of the PCR reaction wells on the chip. (2) Detect the fluorescent signals during the PCR. There are many reported works on conducting PCR on small chips. Both static chamber PCR chips and dynamic flow-through PCR chips were reported. PCR chips have been made by various materials such as silicon, glass, polycarbonate, polyamide and PMMA. Contact and non-contact heating as well as Joule heating were used to power the thermal cycling [2]. However, in these efforts, although PCR reactions were conducted on chips in micro wells or microchannels, to analyze the amplified PCR products, it still requires using the conventional gel electrophoresis or desk-top fluorescence microscopes. For example, among the static chamber PCR chip devices, Yang et al., reported a micro PCR system in which the temperature of the micro reactor was controlled by two Peliter thermolelectric devices sandwiching the reactor [3]. The PCR chip is made of polycarbonate, and fabricated by a direct laser writing method. A commercial fluorescence analyzer was used to detect the amplified products after the thermal cycling. Lin and Lee et al developed a PCR system with a reaction well fabricated in a silicon wafer sealed with a glass substrate and placed a heater at the bottom of the silicon wafer [4]. In their design, a small reaction volume was used to increase the temperature uniformity. Gel electrophoresis was employed to analyze the amplifications. Nagai’s group and Matsubara’s group presented micro array PCR chips patterned on silicon wafer. A commercial thermal cycler was used to conduct the PCR and a fluorescence microscope or micro scanner was employed to measure the fluorescence intensity of the
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PCR products [5, 6]. In dynamic flow-through PCR devices, PCR reactants were heated and cooled by transporting the reactants through different temperature zones. A typical flow-through thermal cycler was presented in literature with thin film platinum heaters and sensors patterned onto a silicon wafer to generate three different temperature zones [7–10]. PCR reactions were also achieved in a continuous flow mode in a ring chamber with controlled temperature regions [11, 12]. Comparing with the static chamber PCR systems, the flow-through PCR can reduce the heating and cooling time and thus shorten the total time of PCR reaction. However, it is difficult to insulate the different temperature zones, to exam the PCR results and to collect the PCR product for further analysis. Another hindrance for flow-through systems is the unalterable number of cycles dependent upon chip design. Recently a portable real-time PCR device was demonstrated [13, 14]. This device has a miniature thermal cyclyer performing the PCR thermal cycling operation. The disposable PCR reaction chip is made of polydimethylsiloxane (PDMS) and glass chips, and has four reaction wells. The well size can be as small as 0.5 μL. A miniature laser-fiber optic system is developed for detecting the fluorescent signals from the four wells during the PCR process. Precise control of the temperature at the three levels and the holding time at each temperature level is critical for a successful PCR. In this device, the heating is achieved by using an external heater under the PCR chip, and the cooling is realized by using a cooling fan. Figure 1 shows the typical temperature profile in a PCR thermal cycling process. The temperature in this figure was measured by using thermal couples embedded in the wells. 110 100
Temperature
90 80 70 60 50 Well Temperature Denaturing (94C) Extension (72C) Annealing (55C)
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Figure 1. The actual temperature of the reactants in the wells of the PCR chip. This temperature was measured by thermocouple embedded in the well.
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Figure 2. An example result of on-chip real-time PCR detection of E. coli O157 H7.
Figure 2 shows a typical fluorescent detection result. The optic fiber sensors delivered excitation laser and received the emission fluorescent light signals from each well, and pass the fluorescent signals through an optic filter and to a photo-detector. The signals are then processed by a PDA. In this particular example, The DNA concentration is 12.5 ng/μl in well 1, 1.25 ng/μl in well 2 and 3, and 0.0 ng/μl in well 4 (negative control). For the cases with the same initial concentration of a template DNA of 1.25 ng/μl (well 2 and well 3), the measured fluorescent intensity started to increase at essentially the same cycle number, the 20th cycle. The fluorescence intensity started to increase earlier (17th cycle) for well 1 than well 2 and 3 due to its higher DNA concentration (12.5 ng/μl). In addition, the curve for the negative control is flat, which is expected. The plateau phase intensity of well 1 is different from that of well 2 (well 3). This may be due to the optic loss difference of fiber optical switch from channel to channel. In real-time PCR, it is the slope of the intensity–cycle number curve that is important. The loss difference does not affect the slop of the curve, and affect only the final intensity value. Real-time PCR Lab-on-a-Chip technology has wide spectrum of applications in biomedical diagnosis of pathogen infections, food safety and bio-defense. The major advantages include significantly smaller amount of sample and reagent consumption, high speed and portability. For example, Fig. 3 shows an example of detecting Flu virus H5 (birds flu) on a chip. It took only about 8–10 min to generate positive detection results. In comparison with the 3 h required for the same tests done in a conventional real-time PCR instrument, this is a significant saving in the testing time.
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0.18 0.16 0.14
Intensity (a. u.)
0.12 0.10
Conc=0.1ng/uL
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Figure 3. Examples of the detected fluorescent signals from a real-time PCR chip for detecting Flu virus H5.
3. Flow Cytometer Lab-on-a-Chip Flow cytometer is a device that measures certain physical and chemical characteristics of cells as the cells travel in suspension one by one passing a sensing point. By labeling the cells with fluorescent molecules that bind with high specificity to one particular cellular constituent, it is possible to measure the contents of the constituent. The flow cytometer is capable of rapid, quantitative, multi-parameter analysis of heterogeneous cell populations on a cell-by-cell basis.
Sample solution Fluidic system
Optic detector
Laser Optic filters
Figure 4. Illustration of the working principle of flow cytometer.
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In the operation of a flow cytometer, a fluidic handling system will first pump the sample solution containing biological cells into the instrument. The key function of the fluidic system is to focus the flow, that is, using laminar flow streams from the side to squeeze the central sample solution stream. The objective of the flow focusing is to make the central stream so thin that its diameter is close to the size of a single cell. In this way, cells in the sample solution will move in a single line, one following another. Another key component in the flow cytometer is the optic detection system, as illustrated in Fig. 4. The cells will move through a sensing point where a laser beam shines. The cells pass through the laser beam will be detected by using, for example, light scattering method so that the number of cells in the sample will be counted. Some cells may be labeled with a specific fluorescent dye. When they pass through the sensing point, the laser will excite the dye, the emitted fluorescent light will pass through the optic filter and be detected by the photo-detector. The signal will be sent to a computer to be analyzed. In this way, the number of a specific type of cells labeled with that dye can be determined. Some flow cytometers have another function – cell sorting. After the fluorescent detection point, a vibrating mechanism is used to cause the stream of cells to break into individual droplets. An electrical charging ring is placed just at the point where the stream breaks into droplets. A charge is placed on the ring based on the immediately-prior fluorescence measurement result, and the opposite charge is trapped on the droplet as it breaks from the stream. The charged droplets then fall through an electrostatic deflection system that diverts droplets into containers based upon their charge. However, the flow cytometers are bulky and expansive, and are available only in large reference laboratories. In addition, the required sample volumes are quite large, usually in the 100 µL range. Many clinical applications require frequent blood tests to monitor patients’ status and the therapy effectiveness. It is highly desirable to use only small amount of blood samples from patients for each test. Furthermore, it is highly desirable to have affordable and portable flow cytometry instruments for field applications, point-of-care applications and applications in resource-limited locations. To overcome these drawbacks and to meet the increasing needs for versatile cellular analyses, efforts have been made recently to apply microfluidics and lab-ona-chip technologies to flow cytometric analysis of cells. From the working principle of the conventional flow cytometers as described above, we see that a flow cytomete on a chip must have the following functions: (1) Flow focusing. (2) Counting and detecting cells/ particles. (3) Sort the cells/particles. The general idea of flow focusing is to use one or more laminar flow streams to “compress” the stream of the sample solution. By controlling the flow rates of the side streams, the size of the sample stream can be controlled to a size close to that of the to-be-
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measured cells. As shown in Fig. 5, the flow focusing can be realized in a cross-shaped microchannel. The sample solution is colored with a dye (green) and carries particles. The sample solution is transported from left to right by using electroosmotic flow. A buffer solution is also driven by electroosmotic flow and enters the intersection from the two perpendicular channels and then flow to the downstream (the left). The two side streams squeeze the sample solution stream so thin that the particles in the sample stream have to move in a single line, one following another.
Figure 5. Electrokinetic flow focusing of particles through a crossing microchannel in a microfluidic chip.
Development of microchannel-based flow cytometers has been reported recently. Tung et al. produced a flow cytometer chip using PDMS (polydimethylsiloxane) for fluorescence-labeled particle detection using a two-color, multi-angle detection system via embedded fibers [15]. While a remarkable accomplishment, their chip unfortunately lacks portability as it requires a manually operated external liquid handling system (e.g., two syringe pumps, tubing and valves) to focus the cell-carrying stream in the detection channel. A flow cytometer chip using electrokinetic flow focusing was reported by Fu et al. [16]. This chip consists of a glass plate with a pair of embedded optical fibers for counting particles moving through a microchannel. All these reports demonstrate only one function, i.e. counting the number of the single-sized particles. However, a practical flow cytometer must be able to handle mixtures of diverse cells that must be differentiated
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and counted by size and by their fluorescent dye tags. Significant research is needed to develop these functions for microfluidic flow cytometer chips. For this purpose, Li’s group reported a simple multi-functional particle detection PDMS chip [17]. This chip generates liquid flow and particle motion electrokinetically, and uses two pairs of parallel optical fibers embedded in the chip to measure particle speed and size, and to count particles. More recently, a new microfluidic method was developed to counting the particles flowing through microchannels, not by the optic method as described previously, but by an electric method. This method is called the microfluidic differential resistive pulse sensor method [18]. Figure 6 below illustrates the principle of this method. C A
VD1 B
D
Vin+ +
V+
R1
R3 R2
VD2
V−
Vout
−
Vin− Differential Amplifier
Figure 6. Chip design and system setup for one-stage differential amplification. A DC voltage (V1 – V–) is applied to drive the particles from A to B. Trans-aperture voltage (VD1 and VD2) modulation are sensed by the two gate branches to C and D, which are the positive and negative inputs of the differential amplifier, respectively. The resistances of the three sections in the main channel are denoted by R1, R2, R3, respectively.
The PDMS microfluidic chip was fabricated on a glass substrate following the standard soft lithography protocol. The chip consists of a pair of mirrorsymmetric channels (with sensing apertures) that are separated by a wall of 100 mm in thickness and share the same sample input (A) and waste reservoirs (B), as shown in Fig. 6. The fluidic conduit is connected to the electronic circuits by platinum-wire electrodes submerged in four reservoirs. A DC bias (V1 –V–) was applied across the channel to induce the electroosmotic flow, which drove the particles through the sensing apertures from reservoir A to reservoir B. There are two gate branches connected to the differential amplifier at the upstream ends of both sensing apertures to detect the transaperture voltage modulation when particles are translocated.
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For microchip-detection system developed in this study, there are two major types of noise sources. One is the from the electrical power system, such as the system power supply and the ambient illumination, which has a characteristic frequency of 60 Hz. The other is from the intrinsic noise of the electronic components, such as the thermal fluctuation in a resistor, which can generate various interferences from several hundred hertz to over several megahertz. The major advantage of the symmetric dual channel design is that it renders identical noise level for the output signals (VD1 and VD2) from both gate branches. The voltage component common to the amplifier inputs (Vin1 and Vin2) are called “common-mode voltage” (CMV). Obviously, the various noises coupled in VD1 and VD2 constitute the CMV of the amplifier. When the two branches are connected to a differential amplifier of high “common-mode rejection ratio” (CMRR), the noise comprised in the CMV can be rejected significantly at the final output (Vout). Ideally, when there is no particle passing through either of the two sensing apertures, ideally Vin1 is equal to Vin2 in amplitude for a perfectly symmetric fluid circuit. Thus, the two inputs will cancel each other and the amplified output is zero. When a particle passes through either one (but only one at a time) of the two sensing apertures, on top of the DEV, the resulting voltage modulation causes an additional input difference DV between Vin1 and Vin2, which is amplified by the differential gain. That is why this method can largely increase the signal to noise ratio. The lowest volume ratio of the particles detected to the sensing aperture is 0.0004% using twostage amplification, which is about ten times lower than that of current commercial Coulter counters and similar devices reported in literature so far. 1
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signal strength [v]
0
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Figure 7. Example result of detecting 520 nm and 1 μm particles by the microfluidic resistive pulse sensor.
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Figure 7 is an example of detecting 520 nm and 1 μm particles by the microfluidic resistive pulse sensor. Combining the above described microfluidic differential resistive pulse sensor method with a miniature laser-fiber optic fluorescent detector, the simultaneous detection of fluorescent and non-fluorescent particles has been demonstrated [19]. This method is simple, inexpensive, and easy to operate, and can achieve highly sensitive and accurate detection without relying on any conventional bulky instruments. Excellent agreement was achieved by comparing the results obtained by this chip system with the results from a commercial flow cytometer for a variety of samples of mixed fluorescent and non-fluorescent particles. In a recent work, Li’s group reported a fluorescence-activated particle counting and sorting system based on the electrokinetic flow switching [20]. Figure 8 below illustrates the experimental system. The chip has a crossmicrochannel. When a particle labeled with a specific fluorescent dye passes the intersection, it will be detected by a fiber optic system. A DC electric pulse is triggered by pre-set fluorescent threshold to automatically dispense the particles into the side collection reservoir. Otherwise, if the particle does not carry the correct fluorescent dye, it will be continuously transported to the downstream waste collection well with the electrokinetic flow. It has been proved that this system responses fast and accurately and 15 μm fluorescent particles can be sorted from a mixture with non-fluorescent particles. Figure 9 shows the automatic sorting of 15 μm fluorescent particles from 4.85 and 25 μm non-fluorescent particles in this chip.
Figure 8. Schematics of the flow cytometer chip system.
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Figure 9. Trajectories of a 15 μm fluorescent particle and 4.85 and 25 μm non-fluorescent particles. They are obtained by superposing a series of consecutive images of the moving particles. The 15 μm particle shows longer streak because of its increased velocity in the dispensing branch D. Under the same exposure time, faster motion causes longer streaks.
It has been widely recognized that AIDS is becoming one of the leading epidemic causes of adult deaths globally, especially in developing countries where the prohibitive expenses of the conventional assay technology limits the access for the vast majority of the HIV-infected individuals. Among the most important clinical parameters, enumeration of the peripheral blood CD4+ T lymphocytes is a key factor for determining disease progression and monitoring efficacy of the treatment. A decrease in the total count of CD4+ T lymphocytes, the critical immune cells infected by HIV, is one of the hallmarks of HIV disease. In addition to absolute CD4+ T cell number, the CD4+ percentage (ratio of the CD4+ T cells to the total lymphocytes) is also an important clinical parameter, especially in pediatric HIV infection. Therefore the CD4 percentage provides more accurate prediction for the risk of opportunistic infection than does the absolute CD4 cell number. Recently, the above-described microfluidic differential resistive pulse senor method was combined with a miniaturized fluorescent fiber optic detection method to detect CD4+ cells from blood samples [21]. Figure 10 shows an example of such a detection. The results were compared with the commercial flow cytometer, and the agreement was excellent.
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Figure 10. Detection of 50% stained CD4 cells by the Resistive Pulse Sensing (RPS) current signal and by the fluorescence signal. The upper plot and left axis indicate the RPS signal; the lower plot and right axis indicate the fluorescent signal.
4. Immunoassay Lab-on-a-Chip Immunoassay (IA) is a biochemical method to measure the presence and the concentration of a substance in a biological liquid, typically serum or urine, using the reaction of an antibody to its antigen. The assay takes advantage of the specific binding of an antibody to its antigen. Generally antigens are proteins carried by bacteria and viruses. They prompt the generation of antibodies and can cause an immune response. Antibodies are gamma globulin proteins that are found in blood or other bodily fluids of vertebrates, and are used by the immune system to identify and neutralize foreign objects, such as bacteria and viruses. The binding of an antibody to an antigen is type specific, i.e., they are like a key and lock; they must match each other exactly or will not bind. Immunoassay (IA) is the predominant analytical technique for the determination of a variety of pathogens. However, conventional plate-based heterogeneous IA is a multistage, labor-intensive process that requires sequential loading different reagents, washing and incubation. It takes 4–5 h, and requires skilled technicians. In order to reduce the human error during the bench-top immunoassay processes, automation of immunoassay has focused on the development of robotic systems for solution handling in microarray-based immunoassay. However, the microarray immunoassays depend on a complex robotic system for solution manipulation, and hence are limited to be used in large hospitals only. Miniaturization of the immunoassay has been researched and different assay formats have been tested in microfluidic systems since late 1990s.
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Stokes et al. [22] used sandwiched immunoassay with mixed cellulose membrane for solid support. The antigens were immobilized into an array pattern, resembling the dot-ELISA strategy, to detect multiple bacteria. However, their method involves using mechanical pumps that are prone to breakdown and leakage, and has no portability. Dodge et al. [23] utilized electroosmotically-pumped flow for a microchannel immunoassay. In their experiments the entire channel was first coated with an antibody layer, which subsequently reacted with each component of the immunoassay. The final product was detected by laser excitation of a Cy5 conjugate. This strategy lacks the multiplex capability of the dot-ELISA array design because the microchannel was coated with only one concentration of antibody. It should be pointed out that, in Dodge’s work, the assay was done manually for all the steps. Similarly, in the works of Sia et al. [24] and Kartalov et al. [25], other than the reaction occurred in a microchannel, the fluid manipulation was done manually for all the steps, and complex external steel tubes, valve arrays, and plumbing were required to supply reagents to the channels. They used a fluorescence microscope for detection. Therefore, the whole IA system depends on a conventional lab, and is not a portable device. The critical issues to develop a practical immunoassay lab-on-a-chip technology are integration, automation, multiplexity and portability. An immunoassay lab-on-a-chip device must perform the following microfluidic functions: pumping, flow switching, incubating, sequentially loading solutions and washing. A very large pressure gradient is required to generate liquid flow in microfluidic devices since the flow resistance is reversely proportional to the fourth power of transverse channel dimension. It will be impractical and difficult to use pressure-driven flow to control the sequential loading and washing processes in a portable microfluidic system. Alternatively, electrokinetic forces can be used to drive liquid flow in microchannels. In a microfluidic chip, there are a number of wells at the ends of the microchannel branches. These wells provide not only reservoirs for samples and reagents, but also the connection of electrodes to liquid in the microchannels. The liquid flow control is realized by applying different voltages to different wells simultaneously. In this way we can control the flow rate, and let one solution flowing through a microchannel in the desired direction while keeping all other solutions stationary in their wells and channels. In a recent work, Li’s group has developed a simple electrokineticallycontrolled IA chip, as shown in Fig. 11, for detecting H. pylori and E. coli [26–28]. In this chip, an H-shaped microchannel network was fabricated using PDMS. The operation parameters (i.e., the applied voltage at each electrode and the duration) obtained from numerical simulation were applied to a desktop DC voltage sequencer to control the IA chip operation. Multiantigen immobilization was accomplished by adsorbing the antigen molecules onto a PDMS-coated glass slide with the aid of a microfluidic network.
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Immobilized lysate antigen of E. coli O157: H7 at different concentrations was assayed and the low detection limit was 3 μg/mL. The assay also demonstrated very good specificity: different microbial lysate antigens were immobilized, including E. coli and H. pylori, and the primary and secondary antibodies were mixtures of different species. The assay time is only 25 min (the conventional lab based assay requires over 3 h); the sample consumed was less than 12 μL. While still an un-optimized chip, this IA chip shows a great potential in detecting multiple pathogen efficiently. More recently, the development of an electrokinetically-controlled, highthroughput immunoassay for testing multiple clinical samples against PDMS layer
Glass slide
Figure 11. Picture of an immunoassay chip with a H-shaped microchannel, and the sequential steps of an automatic IA processes. The surface of the reaction channel wall is coated with probing antigens. The solution delivery occurs in the dark colored channels whereas in the light colored channels, the solution remains stationary. The arrows indicate the flow direction. (a) Dispensing and incubation of the primary antibody; (b) washing off the primary antibody by a buffer solution; (c) dispensing and incubation of the secondary antibody; (d) washing off the secondary antibody by a buffer solution.
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multiple pathogen targets was reported [29]. The microfluidic design of this immunoassay chip can be seen from Fig. 12. The automatically controlled sequential microfluidic processes are shown in Fig. 13. With effective control of the microfluidic transport process in a compact microfluidic network, this microfluidic immunoassay lab-on-a-chip is capable of detecting ten samples simultaneously in 22 min. E. coli O157:H7 antibody and H. pylori antibody in buffer solutions were detected down to 0.02 μg/mL (130 pM) and 0.1 μg/mL (670 pM), respectively. The microfluidic immunoassay was also applied to screen for E. coli O157:H7 antibody or H. pylori antibody from human serum. In the 18 samples of human serum tested, E. coli O157:H7-positive or H. pylori-positive sera were accurately distinguished from the corresponding negative sera. Simultaneous screening of both antibodies from human serum was also proved feasible. With non-specific binding effectively suppressed by 10% (w/v) BSA, the assay results showed no evidence of adsorption of serum proteins to channel walls and consequent disturbance to electrokinetic transport. These results, thus, prove the applicability of electrokineticallydriven heterogeneous immunoassay chip to clinical environments (Fig. 14).
Immobilized probing
Figure 12. Illustration of the microchannel network in the multiplex immunoassay chip.
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Figure 13. Steps in the electrokinetically-controlled immunoassay. Arrows indicate flow direction. Solid arrows stand for major flows, and dashed arrows, minor flows. (a) Loading and incubation of samples. Sample solutions were dispensed from the sample wells to the reaction region and discharged into the waste well. (b) Washing of samples. Buffer solution flushed sample solutions from the reaction region back into the sample wells. (c) Second washing of samples. Sample solutions having entered the antibody channel during the previous three steps were flushed into the waste well. (d) Loading and incubation of detection antibody. (e) Washing of detection antibody.
Figure 14. Simultaneous detection of both antibodies from human serum. Antigens of H. pylori and E. coli O157:H7 were coated alternately, as indicated at the bottom of the image. Samples are labeled from S1 to S10 and the contents of the each sample are indicated on the right side of the image. Capital “P” or “N” denotes a positive or negative sample, respectively. For S1 to S7, the dilution of serum was 1:100. S8 and S9 were mixed samples of H. pylori-positive and E. coli O157:H7-positive serum. The overall serum dilution was 1:50 for S8 and S9, in order to match the concentration of each antibody to that in the corresponding unmixed serum. For example, the concentration of H. pylori antibody in S1 and S8 were equivalent.
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5. Summary Electrokinetic microfluidics provides important tools for transforming many processes of conventional labs into on-chip processes, making it possible to miniaturize many biochemical and biomedical methods and control the operation of the lab-on-a-chip devices. This article does not intend to provide a comprehensive review on the three lab-on-a-chip devices discussed here. By reviewing the real-time PCR lab-on-a-chip device (or bio-chemical reactor chip), flow cytometer lab-on-a-chip device and immunoassay labon-a-chip device, this article attempts to illustrate how biochemistry, microfluidics, optic detection and electronic control can be integrated to develop lab-on-a-chip technology for practical applications such as in medical diagnosis, and food safety. It is clear that significant advances are needed before we cam reach this goal, particularly in integration, automation, multiplexity and portability.
References 1. Dongqing Li, “Electrokinetics in Microfluidics”, Academic, London, 2004. 2. G. Hu, Q. Xiang, R. Fu, B. Xu, R. Venditti, and D. Li, Electrokinetically controlled real-time PCR in microchannel using Joule heating effect. Analytica Chimica Acta, 557, 146–151 (2006). 3. Y. Liu, C. B. Rauch, R. L. Stevens, R. Lenigk, J. Yang, D. B. Rhine, and P. Grodzinski, DNA amplification and hybridization assays in integrated plastic monolithic devices, Analytical Chemistry, 74, 3063 (2002). 4. Y. C. Lin, C. Yang, and M. Y. Huang, Simulation and experimental validation of micro polymerase chain reaction chips, Sensors and Actuators B: Chemical, 71, 127 (2000). 5. H. Nagai, Y. Murakami, K. Yokoyama, E. Tamiya, and Y. Morita, Development of microchamber array for picoliter PCR. Analytical Chemistry, 73, 1043 (2001). 6. Y. Matsubara, K. Kerman, M. Kobayashi, S. Yamamura, Y. Morita, Y. Takamura, and E. Tamiya, On-chip nanoliter-volume multiplex TaqMan polymerase chain reaction from a single copy based on counting fluorescence released microchambers. Analytical Chemistry, 76, 6434 (2004). 7. M. U. Kopp, A. Mello, and A. Manz, Chemical amplification: continuous-flow PCR on a chip, Science 280, 1046 (1998). 8. I. Schneegass, R. Brautigam, and J. M. Kohler, Miniaturized flow through PCR with different temperature types in a silicon chip thermocycler. Lab on a Chip, 1, 42–9 (2001). 9. P. J. Obeid, T. K. Christopoulos, H. J. Crabtree, and C. J. Backhouse, Microfabricated device for DNA and RNA amplification by continuous-flow polymerase chain reaction and reverse transcription polymerase chain reaction with cycle number selection, Analytical Chemistry, 75, 288 (2003).
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10. M. Hashimoto, P. C. Chen, M. W. Mitchell, D. E. Nikitopoulos, S. A. Soper, and M. C. Murphy, Rapid PCR in a continuous flow device, Lab on a Chip 4, 638 (2004). 11. J. Liu, M. Enzelberger, and S. Quake, A nanoliter rotary device for polymerase chain reaction, Electrophoresis, 23, 1531 (2002). 12. K. Sun, A. Yamaguchi, Y. Ishida, S. Matsuo, and H. Misawa, A heaterintegrated transparent microchannel chip for continuous flow PCR, Sensors and Actuators B: Chemical, 84, 283 (2002). 13. Q. Xiang, B. Xu, and D. Li, Miniature real time PCR on chip with multichannel fiber optical fluorescence detection module, Biomedical Microdevices, 9, 443–449 (2007). 14. Q. Xiang, B. Xu, R. Fu, and D. Li, Real Time PCR on Disposable PDMS chip with a miniaturized thermal cycler, Biomedical Microdevices, 7, 273–279 (2005). 15. Y. C. Tung, M. Zhang, C. T. Lin, K. Kurabayashi, and S. J. Skerlos. PDMSbased opto-fluidic micro flow cytometer with two-color, multi-angle fluorescence detection capability using PIN photodiodes. Sensors and Actuators B: Chemical, 98, 356–367 (2004). 16. L. M. Fu, R. J. Yang, C. H. Lin, Y. J. Pan, and G. B. Lee, Electrokinetically driven micro flow cytometers with integrated fiber optics for on-line cell/particle detection. Analytica Chimica Acta, 507, 163–169 (2004). 17. Q. Xiang, X. Xuan, B. Xu, and D. Li, Multi-functional particle detection with embedded optical fibers in a poly(dimethylsiloxane) chip, Instrumentation Science & Technology, 33, 597–607 (2005). 18. X. Wu, Y. Kang, Y. N. Wang, D. Xu, Deyu Li, and Dongqing Li, Microfluidic differential resistive pulse sensor, Electrophoresis, 29, 2754–2759 (2008). 19. X. Wu, C. Chon, Y. Kang, Y. Wang, and D. Li, Simultaneous particle counting and detecting on a chip, Lab-on-Chip, 8, 1943–1949 (2008). 20. Y. Kang, X. Wu, Y. Wang, and D. Li, On-chip fluorescence-activated particle counting and sorting system, Analytica Chimica Acta, 626, 97–103 (2008). 21. Y. N. Wang, Y. Kang, D. Xu, L. Barnett, S. A. Kalams, Deyu Li, and Dongqing Li, On-chip total counting and percentage determination of CD4+ T lymphocytes, Lab-Chip, 8, 309–315 (2008). 22. D. L. Stokes, G. D. Griffin, and T. Vo-Dinh, Detection of E. coli using a microfluidics-based antibody biochip detection system, Fresenius Journal of Analytical Chemistry, 369, 295–301 (2001). 23. A. Dodge, K. Fluri, , E. Verpoorte, and N. F. de Rooij, Electrokinetically driven microfluidic chips with surface-modified chambers for heterogeneous immunoassays, Analytical Chemistry, 73, 3400–3409. 24. S. K. Sia, V. Linder, B. A. Parviz, A. Siegel, and G. M. Whitesides, An integrated approach to a portable and low-cost immunoassay for resource-poor settings, Angewandte Chemie-International Edition, 43, 498–502 (2004). 25. E. P. Kartalov, J. F. Zhong, A. Scherer, S. R. Quake, C. R. Taylor, and W. F. Anderson, High-throughput multi-antigen microfluidics fluorescence immunoassays, BioTechniques, 40, 85–90 (2006). 26. Y. Gao, F. Lin, G. Hu, P. Sherman, and D. Li, Development of a novel electrokinetically-driven microfluidic immunoassay for detection of Helicobacter pylori, Analytica Chimica Acta, 543, 109–116 (2005).
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27. G. Hu, Y. Gao, P. Sherman, and D. Li, A Microfluidic chip for heterogeneous immunoassay using automatic electrokinetical control, Microfluidics and Nanofluidics, 1, 346–355 (2005). 28. Y. Gao, G. Hu, P. Sherman, and D. Li, An automatic electrokineticallycontrolled immunoassay lab-on-a-chip for simultaneous detection of multiple microbial antigens, Biomed Microdevices, 7, 301–312 (2005). 29. Y. Gao, P. Sherman, Y. Sun, and D. Li, A multiplexed high-throughput electrokinetically-controlled immunoassay for the detection of bacterial antibodies in human serum, Analytica Chimica Acta, 606, 98–107 (2008).
CHIP BASED ELECTROANALYTICAL SYSTEMS FOR MONITORING CELLULAR DYNAMICS A. HEISKANEN, M. DUFVA, AND J. EMNÉUS
Department of Micro- and Nanotechnology, Technical University of Denmark, Ørsteds Plads 345 East, DK-2800 Kgs. Lyngby, Denmark,
[email protected]
Abstract. Electroanalytical methods are highly compatible with micro- and nano-machining technology and have the potential of invasive but “nondestructive” cell analysis. In combination with optical probes and imaging techniques, electroanalytical methods show great potential for the development of multi-analyte detection systems to monitor in real-time cellular dynamics.
1. Introduction In cell biology and pharmacology, the determination of cellular functions and responses to exogenous effectors is a general part of the scientific quest. However, assays that, for instance, determine the activity of an enzyme upon induction of gene expression are customarily conducted after the cells have been lysed, and the resulting cell extract or a further purified enzyme fraction is used for the assay [1]. Furthermore, high-throughput screening (HTS) of compound libraries in drug discovery has strongly relied on assays conducted using purified or isolated targets, i.e. enzymes, ion channels, signaling proteins as well as cell surface- and nuclear receptors [2]. The fundamental question is: How reliable and true are the obtained results that are based on an isolated fraction of the whole system, i.e. a cell, organ or organism? In a living cell, the different cellular functions and subcellular compartments, although to a certain degree autonomous, they are at the same time strongly dependent on feedback from each other. As examples can be mentioned the activity of enzymes that transfers electrons to or from different cellular metabolites, such as glucose, which is the main energy source of mammalian cells, and the activation of G protein coupled receptors (GPCRs) that mediate external signals upon binding of a ligand to the receptor, giving rise to an intracellular cascade of biochemical events, leading to the execution of a certain function. The significance of cell-based assays as a source of information that yields a more holistic view of the cellular dynamics, i.e. the interaction of S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_19, © Springer Science + Business Media B.V. 2010
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biological functions in general and the intercompartmental biological effect of different compounds has been recognized in HTS of compound libraries in drug discovery. The advantages are associated with the involvement of the entire cellular environment as the modulator of the monitored responses whether these are primarily connected to the activation of GPCRs, ion channels or enzyme activity. If an assay involves binding of a ligand to a receptor (target), this takes place in the real biological environment of the target. Additionally, when the target is located in the intracellular environment, a cell-based assay also gives possibility to screen for secondary cellular events (multi-parameter monitoring) as well as bioavailability of the used test compounds [3]. Work featuring methods and techniques for assaying biological parameters in the context of intact cells comprise e.g. intracellular [4] and extracellular [5] monitoring of oxygen consumption, monitoring of enzyme activity and cofactor availability [6–9], cellular adhesion [10] as well as cellularly released secondary metabolites [11, 12] and G-protein coupled receptor (GPCR) activation [13]. Although cell-based assays have been strongly implemented in drug discovery, they are primarily in microtiter plate format, including applications for even 1,536 well-plates [14] and screening of compound libraries of 100,000 compounds [15]. Implementation of cell-based assays in HTS suffers, however, from problems caused by the microtiter plate format. These concern reliability of temperature and CO2 control in the incubator as well as increased evaporation and difficulties involved in liquid handling due to the large number of wells comprising an extremely small volume [15]. The emergence of perfusion based microfluidic cell culture chips (see Chapter “Perfusion Based Cell Culture Chips” of this book) with the inherent technological capability to undergo sufficient miniaturization and parallelization represents a new trend that can both alleviate the drawbacks of microtiter plate based assays and facilitate real-time monitoring of cellular dynamics instead of only end-point detection. 2. Detection of Cellular Dynamics 2.1. DETECTION TECHNIQUES
2.1.1. Fluorescence Detection As consequence of implementation of parallelization in microfluidic cell culture chips, detection of biologically relevant cellular parameters imposes further requirements on the development of the applied detection techniques. Using available motorized microscope stages, time-lapse fluorescence microscopy is a widely applied technique in monitoring cellular responses. Alternatively, fluorescent plate readers facilitate real-time monitoring in highly parallelized systems (readouts for 1,536 well microtiter plate format).
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Implementation of fluidic functions inside a plate reader is however not a straightforward task. For short-term detection, the chip depicted in Fig. 10f [16] in the Chapter “Perfusion Based Cell Culture Chips” of this book could be amenable for use with a plate reader since its function does not require any external pump. However, for long- term real-time monitoring, this system is not suitable due to the need for a CO2 incubator. An alternative approach could be based on a multichannel pump, suitable for integration with a polymeric microfluidic cell culture chip independent of a CO2 incubator. The pump shown in Fig. 10b [17] in the Chapter “Perfusion Based Cell Culture Chips” of this book could function as the basis for such an approach. Fluorescence based monitoring of dynamic cellular processes is not, however, a complete solution to the need of detection in cell culture systems. Long-term monitoring causes photobleaching of fluorophores and photodamage to the cells in the case of autofluorescence detection [18]. To alleviate the problem with photobleaching [19] and photodamage [20], twophoton excitation microscopy has emerged as a microscopic technique. However, the required instrumentation is expensive and the technique itself does not facilitate easy automation and high-throughput monitoring. Furthermore, fluorescence detection, in general, is not suitable for monitoring of all relevant parameters of cellular dynamics. For instance, monitoring of calcium triggered vesicular release (exocytosis) of cellular secondary metabolites, such as the neurotransmitter dopamine or hormone insulin, is not possible directly using fluorescence detection. Only indirect detection of the process has been demonstrated using, for instance, internal reflection fluorescence microscopy of co-exocytosed fluorescent dye upon loading of cellular vesicles [21]. 2.1.2. Electrochemical Detection In many cases, monitoring of cellular dynamics involves detection of molecules that are either released or taken up by the cells. Monitoring of such parameters comprises (i) nutrients and primary metabolites (e.g. glucose [22], lactate [23] and oxygen [5]), (ii) secondary metabolites, such as neurotransmitters (e.g. dopamine [12] and glutamate [11]) and hormones (e.g. insulin [24]), and (iii) compounds resulting from xenobiotic1 metabolism and physical stress (e.g. hydrogen peroxide and superoxide radical [25], glutathione conjugates [26] quinones [27] and quinols [28]). All the listed compounds are examples of species that can be detected electrochemically either directly as electroactive species or by using enzymes as the biorecognition element.
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In xenobiotic metabolism, foreign compounds, such as drugs and toxicants, are enzymatically detoxified.
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Figure 1 illustrates the detection scheme of such cellular factors: Extracellularly placed electrodes are used to detect compounds that are produced in cellular metabolism and released by the cells either based on active transport or diffusion through the plasma membrane. Analogously, compounds used by the cells in their metabolism are taken up from the extracellular environment and consequently the decrease in concentration is detected.
Figure 1. A schematic illustration of electrochemical monitoring of cellular dynamics. An extracellularly placed electrode is used to detect cellular release and uptake of molecules.
Traditionally, extracellular microelectrodes that have been used to detect, for instance, release of compounds have been placed adjacent to the cell body using a micromanipulator [29] or scanning electrochemical microscope (SECM) [27]. Such measurements are normally conducted using cells that form a part of a population in a culture vessel, such as a Petri dish. Although the published results, have contributed to a highly accurate and mechanistic description of the studied biological phenomena based on single-cell measurements, the approach to use micromanipulated microelectrodes has some severe drawbacks. Detection cannot be automated and throughput is limited. Furthermore, the required instrumentation and operational skills are beyond what normally are needed for electrochemical detection. A new approach has emerged that applies microchips having planar microelectrodes on a substrate, most commonly an oxidized surface of a silicon wafer (for fabricational aspects, see [30]), simultaneously functioning as the substrate, on which cells either sediment or grow. The approach to use chip based electroanalytical systems to monitor the dynamics of processes in living cells facilitate the possibility to integrate the detection systems to microfluidic cell culture chips. In virtue of the functional principle of such systems, cells can be cultured on the platform where detection takes place. Hence, the measurements can be conducted in an environment that has been tailor-made for proper adaptation to the requirements of the cultured cells. Furthermore, such miniaturized systems possess the capability to achieve operational automation and facilitate measurements
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on a small population of cells or even single cells. Aside from single-cell measurements, the miniaturization of systems, comprising a microfluidic cell culture chip with an integrated microchip for electrochemical detection, also enables utilization of small amounts of chemicals that are needed as cellular effectors to, for instance, trigger certain metabolic responses. This feature facilitates cell-based assays with a high degree of parallelization without extensive increase in the incurred expenses. Electrochemical measurements on cells are primarily conducted using impedimetric [10], potentiometric [31] and amperometric measurements [12]. In this chapter, amperometric measurements are described based on examples comprising monitoring of cellular redox environment and detection of exocytosis, i.e. Ca2+-triggered release of cellular secondary metabolites, e.g. the neurotransmitter dopamine [12]. In amperometric measurements, most commonly, a three-electrode configuration controlled by a potentiostat is applied: A microelectrode functioning as the working electrode (WE) is in direct contact with the cells the measurements are to be conducted on and has a certain poised potential, at which the detected chemical species is either oxidized2 or reduced. A reference electrode (RE) is used under potentiostatic control to adjust the applied potential of the WE with respect to the third electrode, the counter electrode (CE),3 which is the site of the electrochemical process complementary to the one taking place at the WE. If oxidation of a chemical species involving the donation of n electrons is detected at the WE, a corresponding number of electrons are accepted arbitrarily at the CE by any chemical species in the electrolyte that is used as the medium of measurements. Hence, the electrochemical processes taking place at the electrode–electrolyte interface of the WE and CE together with the potentiostat form a closed electrical circuit that facilitates movement of electrons that can be registered as a faradaic current. The faradaic current (I), according to Faraday’s law of electrolysis, is directly proportional to the number of moles of molecules oxidized or reduced (Eq. (1)):
I=
Q nFn x = t t
(1)
where Q is the total charge carried by the electrons that are accepted or donated, t is the time during which the current is recorded, n is the number
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2 In amperometry, oxidation refers to donation of a number of electrons from a chemical species to an electrode and reduction refers to acceptance of a number of electrons by a chemical species from an electrode. 3 In electrochemical literature, counter electrode is oftentimes also called auxiliary electrode.
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of accepted or donated electrons, F is the Faraday constant (96,485 C mol–1) and nx is the number of moles of the chemical species oxidized or reduced. In amperometry, the applied potential at the WE is chosen to provide a sufficient driving force, overpotential, for the desired electrochemical process, i.e. oxidation or reduction. Each electroactive chemical species is characterized by a certain reduction potential (E°), at which the oxidized and reduced form of the species are in equilibrium.4 Since oxidation or reduction of different chemical species that are detected in biological systems is also pH dependent due to involvement of proton transfer, the formal potential (E°′) is used instead of reduction potential. The tabulated values of formal potential for different chemical species are usually valid at pH 7. The formal potential also implicitly comprises the contribution of activity coefficients. A sufficient overpotential for oxidation or reduction is obtained by poising the WE at a potential that is more positive or negative, respectively, than the formal potential of the detected species. This means that at the chosen potential, predominantly either oxidation or reduction takes place independent of whether both the oxidized and reduced component of the redox couple are present. For example, in a system containing the redox couple, ferrocyanide ([Fe(CN)6]4–)/ferricyanide ([Fe(CN)6]3–), which has the reduction potential 274 mV with respect to a Ag/AgCl5 RE [32], at an applied potential of 400 mV with respect to a Ag/AgCl RE, [Fe(CN)6]4– is oxidized whereas [Fe(CN)6]3– is not affected by the electrode process. Generally, the effect of an applied overpotential at a WE can be presented using an energy level diagram schematically depicting the energy levels of the electrons in the electrode material as well as the lowest unoccupied (LU) and highest occupied (HO) molecular orbital (MO). When the overpotential is sufficiently positive, to make the energy of electrons in the electrode material lower than that of the energy of the HOMO of the species to be oxidized, electrons can be donated to the electrode, resulting in oxidation (Fig. 2A). In the opposite case, a negative potential rendering the
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At equilibrium, the oxidized and reduced form of an electroactive species, collectively termed as redox couple, are reduced and oxidized, respectively, at an equal rate. 5 Most often, the tabulated values of formal potential are given with respect to the normal hydrogen electrode (NHE), which has the defined potential 0 V. However, in practise, a silver/silver chloride (Ag/AgCl) electrode or a plain metal surface (e.g. Au or Pt) is commonly used as a RE. An Ag/AgCl RE, having an internal electrolyte of saturated KCl, has a characteristic potential of 197 mV with respect to the NHE. A plain metal surface, on the other hand, does not have a characteristic potential that can be expressed in terms of NHE. Instead, its potential depends on the prevailing conditions, affected by the deposited species and the electrolyte. E.g., if a Au surface is used as an RE to adjust the potential of, for instance, another Au surface (WE), both the RE and WE are affected by the same conditions. The equilibrium potential between such electrodes is ideally 0 V and a poised potential is directly an overpotential with respect to the equilibrium potential.
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electrons in the electrode material with an energy higher than that of the energy of the LUMO of the species to be reduced, electrons can be donated by the electrode, resulting in reduction (Fig. 2B).
Figure 2. Energy diagrams schematically illustrating oxidation-reduction (redox) reactions. (A) An electrode material with a sufficiently positive potential can accept an electron from the highest occupied molecular orbital (HOMO) of species A, which is oxidized (A → A+ + e−). (B) An electrode material with a sufficiently negative potential can donate an electron to the lowest unoccupied molecular orbital (LUMO) of species B, which is reduced (B + e− → B−).
3. Monitoring of Cellular Redox Environment 3.1. CELLULAR REDOX ENVIRONMENT
3.1.1. Cellular Redox Couples Organisms obtain the necessary energy and building blocks for cellular functions, such as locomotion, contraction and biosynthesis, from digested food. The main constituents of food, carbohydrates, fats and proteins, are digested to the monomers making up the biopolymeric structures. Carbohydrates consist of different hexoses, such as glucose, fructose and galactose. Fats are esters of glycerol and fatty acids with different length of carbon skeleton. Proteins are formed of amino acids through amide
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linkages. The resulting hexoses, glycerol, fatty acids and amino acids are taken up by cells, where they undergo further degradation, i.e. catabolic processes. Partly, products of the catabolic processes are utilized for synthesis of new biomolecules needed for building new cellular material to maintain the cellular structures and sustain the needs of growth, i.e. anabolic processes. However, these processes require energy, which also comes from the catabolic processes. In order not to release the entire energy contents in one single process, which would be too exothermic for the cells to bear, the cells may store the energy in the form of catabolic intermediates, e.g. reduced cofactors nicotinamide adenine dinucleotide (NADH) and nicotinamide adenine dinucleotide phosphate (NADPH) as well as acetyl coenzyme A (Acetyl-CoA), the energy of which can be released in subsequent processes to synthesize, for instance, adenosine-5′-triphosphate (ATP) for energy requiring cellular processes. Collectively, NADH and NADPH as well as the corresponding oxidized forms, NAD+ and NADP+, respectively, are referred to as cellular redox couples. Examples of other redox couples are flavin adenine dinucleotide (FAD-FADH2) involved in metabolic processes, and glutathione (GSSG-GSH) involved in cellular detoxification processes to alleviate, for instance, oxidative stress. The general functional principle of cellular redox couples is to participate in enzymatic processes catalyzing oxidation or reduction of nutrients and other biomolecules. The oxidized form of a redox couple functions as an electron acceptor, whereas the reduced form functions as an electron donor. 3.1.2. Definition of Cellular Redox Environment Each of the cellular redox couples has a characteristic formal potential, the value of which is valid under equimolar composition of the oxidized and reduced form. However, the functions of living cells require a nonequimolar composition. For instance, in the case of the redox couple NADP+-NADPH, the ratio [NADP+]/[NADPH] << 1, and for NAD+NADH, the ratio [NAD+]/[NADH] can approach 1,000. The small value of [NADP+]/[NADPH] and consequently an excess of NADPH is necessary to maintain the biosynthetic processes that utilize NADPH. The large value of [NAD+]/[NADH] indicates the presence of an excess of NAD+, which is needed to support, for instance, mitochondrial respiration that involves continuous reduction of NAD+. The actual potential (E) a redox couple has is dependent on the ratio of the oxidized form to the reduced form according to the Nernst equation (Eq. (2)):
E = E°' +
RT [Ox ] ln nF [Red ]
(2)
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where [Ox] and [Red] are the concentration of the oxidized and reduced form, respectively, and all the other symbols are as previously described. Although the prevailing potential of the redox couples, e.g. NADP+/ NADPH and NAD+/NADH, determined by the concentration ratio of the individual components, indicates the instantaneous direction of cellular processes, reductive or oxidative, also the actual concentration of the reduced components are significant in determining the cellular reducing capacity. The cellular redox environment (CRE) is a combination of the influence of the potential of different cellular redox couples and their reducing capacity. Schafer and Buettner have defined CRE as the sum of products of potential and reducing capacity of each cellular redox couple according to Eq. (3) [33]. n (redox couple)
CRE =
Σ
i =1
E i × [Red ]i
(3)
3.1.3. The Biological Significance of CRE CRE has a significant role in controlling different cellular functions, e.g. signaling and enzyme activation [34], ultimately being responsible for controlling cellular growth and differentiation. Upon too drastic or uncontrollable perturbations of CRE, cells may undergo either programmed cell death (apoptosis) or necrosis. Considering the diversity of cellular functions involved in the response to and defense against oxidative stress as well as genetic engineering, a modification of the definition of CRE presented by Schafer and Buettner [33] is necessary. Aside from only including the reducing capacity and potential of different cellular redox couples, also the cellular activity of different redox enzymes, such as cytochrome P450 (cyt P450), NAD(P)H: Quinone oxidoreductase1 (NQO1)6 and the complexes of the mitochondrial electron transport chain (ETC), should be taken into consideration. This would give a more functional definition, which goes beyond merely observing the redox state of the different redox couples. Such an approach emphasizes the significance of determining both the cellular availability of relevant redox couples, such as NAD(P)+/NAD(P)H, and the activity of certain key enzymes directly in living cells. Perturbations in CRE may arise as a consequence of cellular functions as well as environmental factors and pathological disorders. However, no clear categorization is possible since the causative factors and consequences may be interrelated. Pathological disorders, such as cancer, may be caused by perturbations in CRE and when the full pathogenic state has been
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NQO1 is also known as DT-diaphorase.
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reached, the disorder itself may cause further perturbations in CRE. On the other hand, a perturbation in CRE caused by one pathological disorder may serve as the causative factor for the onset of another disorder. This is, for instance, valid in the relationship between mitochondrial disorders and neurodegenerative diseases. An additional cause for perturbations in CRE has arisen with the emergence of microbial strain engineering. In this case, the perturbations are desired and capable of improving the strain properties for a certain application. Although the normal function of the mitochondrial ETC yields water upon reduction of O2 by Complex IV through four consecutive one-electron transfers, according to estimations 1–2% of the O2 taken up by cells results in formation of H2O2 [35], which originates from superoxide radical (O2–) generated by the ETC complexes. Through the generation of O2–, mitochondria are a major contributor to cellular oxidative stress, which has been implicated as a causal factor for neurodegenerative diseases, such as Parkinson’s disease [36], and cancer [37]. The effect of oxidative stress in the development of different pathological disorders is mediated through mechanisms involving lipid peroxidation, DNA fragmentation and protein modification [38]. Cells have different defense mechanisms to counteract the deleterious effects of oxidative stress. These include, for instance, enzymatic conversion of O2− into H2O2 and further into water in reactions involving oxidation of GSH to GSSG. GSSG-GSH is a cellular redox couple that strongly contributes to the overall CRE. In order to maintain the reducing capacity of GSH, and hence effective protection against oxidative stress, cells utilize NADPH-dependent enzymatic reactions for reducing GSSG. Despite varying functions, the pools of different cellular redox couples are interconnected. Although the rigorous cellular defense against oxidative stress is capable of normalizing the perturbations of CRE caused by normal activity of the ETC, the effect of mitochondrially caused oxidative stress may be more prominent in pathological disorders that cause abnormal function of the ETC and deficiency in enzyme activity involved in elimination of O2−, reduction of GSSG or formation of NADPH. Organisms are exposed to a myriad of harmful chemicals, such as quinones, that may induce oxidative stress by increasing the intracellular concentration of reactive oxygen species (ROS) including O2−. Especially, the liver cells have enzymes that function as a defense against such external attack. Two examples of such enzymes are cyt P450 and NQO1. The redox reactions catalyzed by cyt P450 utilize NADPH as cofactor, whereas those catalyzed by NQO1 utilize either NADH or NADPH as cofactor. An additional defense mechanism functioning against the effect of harmful chemicals is based on the action of GSH, which may either contribute to scavenging the formed ROS or directly conjugate with the chemicals, after which they may be expelled from the cells [39]. These examples show a
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direct connection between the effect of harmful chemicals and CRE, involving the pools of different redox couples and ultimately cellular catabolism. Cyt P450 and NQO1 have a fundamental difference in their function as defense against harmful chemicals. Cyt P450 catalyzes one-electron reduction reactions, which, for instance, upon reduction of quinones yield semiquinone free radicals. These, like free radicals in general, are short lived and tend to react with biomolecules oxidizing them or with O2 forming of O2−. NQO1, on the other hand, catalyzes two-electron reductions, which in the case of quinones yield the fully reduced form, hydroquinone. Study of the properties of cancer cells has revealed that in certain types of cancer the expression of the gene encoding for NQO1 is up-regulated in comparison to normal cells. This has opened the possibility to employ quinoid substances for chemotherapy, which selectively can affect cancer cells at the same time minimizing the harmful effects on normal cells [40]. When the enzymatically reduced quinones are auto-oxidized, the resulting oxidative stress selectively causes apoptosis in cancer cells. In research, the determination of NQO1 activity in general or screening for NQO1 substrates, to be used as chemotherapeutic drugs, as well as screening for the inductive effect of certain compounds on the expression of the gene encoding for NQO1 in different cell lines [1] has become significant. An additional aspect concerning cancer cells is that, due to depressed vascularization, and hence lack of oxygen, they have an up-regulated function of the NADH forming glycolytic pathway (GP) [41]. This results in increased ATP production through the Cytosolic substrate level phosphorylation instead of ATP synthesis in the mitochondria. The other significant consequence is that NADH from the GP is more abundantly available, indicating that NADH availability is also significant for the activity of the NQO1. Especially in microbial strain engineering, metabolic pathways are altered either by deleting a gene, cloning a gene from another organism, or overexpressing a naturally existing gene. Applications relying on these approaches range from fundamental research of cellular functions to industrial exploitation of microbes. In research towards the elucidation of mechanisms that control the function of catabolic pathways in Saccharomyces cerevisiae (baker’s yeast), the gene PGI1 encoding for phosphoglucose isomerase (PGI), the enzyme that functions as the branching point between the NADH forming GP and the NADPH forming cytosolic pathway, the pentosephosphate pathway (PPP), has been deleted. Studies have revealed that as the consequence of the deletion of PGI1, glucose catabolism is diverted into the PPP, which very rapidly depletes the NADP+ pool [42]. In an analogous way, fructose is only catabolized in the GP producing NADH. Hence, the deletion of one gene strongly influences the reducing capacity of the NADP+-NADPH and NAD+-NADH redox couple as well as their potential.
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During ethanol production from lignocellulosic hydrolysates in S. cereviciae another problem has been observed; upon acidic pretreatment, the raw material yields toxic compounds, such as 5-hydroxymethyl furfural (HMF), which inhibit fermentation [43]. Gene expression analysis of a S. cerevisiae mutant with increased tolerance to HMF showed that the gene ADH6, encoding for the NADPH-dependent alcohol dehydrogenase6 (ADH6), was up-regulated. ADH6 exerts aldehyde reducing activity [44], and is hence capable of reducing HMF. Over-expression of this gene in a nontolerant S. cerevisiae strain made the cells overcome inhibition with the concomitantly increased consumption of NADPH. Despite the resulting shift in CRE with respect to the NADP+-NADPH redox couple, the cells are able to grow in the presence of HMF. 3.2. MEDIATED AMPEROMETRIC REAL-TIME MONITORING OF CELLULAR REDOX ENVIRONMENT
Coupling between a biologically catalyzed reaction and an electrochemical reaction, referred to as bioelectrocatalysis, is the constructional principle for enzyme-based electrochemical biosensors. This means that the flow of electrons from a donor through the enzyme to an acceptor must reach the electrode in order for the corresponding current to be detected. In case a direct electron transfer between the active site of an enzyme and an electrode is not possible, a small molecular redox active species, e.g. hydrophobic ferrocene, meldola blue and menadione as well as hydrophilic ferricyanide, can be used as an electron transfer mediator. This means that the electrons from the active site of the enzyme reduce the mediator molecule, which, in turn, can diffuse to the electrode, where it donates the electrons upon oxidation. When these mediator molecules are employed for coupling of an enzymatic redox reaction to an electrode at a constant potential, the resulting application can be referred to as mediated amperometry or mediated bioelectrocatalysis. Monitoring of the intracellular redox activity in eukaryotic cells imposes the requirement that the utilized mediator is capable of readily crossing the plasma membrane into the intracellular environment to communicate with the enzyme(s), the activity of which is to be monitored. This strictly requires the utilization of a lipophilic mediator that can diffuse through the plasma membrane. Using chip based amperometric detection on S. cerevisiae, menadione was shown to possess the desired properties [28]. Figure 3 depicts the functional principle of the chip based detection technique to monitor CRE in eukaryotic cells, which aside from the lipophilic menadione,
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also utilizes the hydrophilic mediator, [Fe(CN)6]3−. The lipophilic menadione (M) diffuses through the plasma membrane into the intracellular environment, where it is distributed between different subcellular compartments, undergoing reduction to menadiol (MH2) (Scheme 1) by NAD(P)H-dependent menadione reducing enzymes (MREs). A short review of MREs and the different metabolic processes that provide the reduced cofactors for menadione reduction in S. cerevisiae can be found in the Supplementary Material of Heiskanen et al. [7]. NAD(P)H originates from the oxidative catabolic pathways in the cytosol, the PPP and the GP, as well as the mitochondrial tricarboxylic acid (TCA) cycle that produces NADH. The equally hydrophobic MH2 diffuses through the plasma membrane into the extracellular environment, where it can surrender its electrons to [Fe(CN)6]3− upon the concomitant reduction of [Fe(CN)6]3− to [Fe(CN)6]4− and regeneration of M, which can continue redox cycling by diffusing back into the intracellular environment. The bioelectrocatalytic process is completed by oxidation of [Fe(CN)6]4− at the microelectrode that has been poised at the potential of 400 mV vs. a Ag/AgCl electrode. For each intracellularly reduced M two electrons are shuttled to the electrode. Figure 4A shows the obtained current upon introduction of menadione based on the basal level of NAD(P)H in cells as well as in response to glucose, which increases the level of NAD(P)H through the activity of the GP and the PPP. The current-time trace also illustrates the fact that due to the hydrophilicity of [Fe(CN)6]3−, which remains in the extracellular environment, no considerable response is obtained. [Fe(CN)6]3− is used for enhancing the amplitude of the amperometric signal as well as the kinetics of the response. During real-time measurements, only 2 mM of [Fe(CN)6]3− are needed due to continuous reoxidation of the formed [Fe(CN)6]4− at the electrode. Figure 4B shows an electrode microchip for mediated amperometry with S. cerevisiae cells.
Scheme 1. Menadione reduction by MREs to menadiol.
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Figure 3. The functional mechanism of the ferricyanide-menadione double mediator system. The driving force for electron flow from the highly reduced substrates to the mediators and finally to the utilized electrodes is the increasing reduction potential of the components involved in the processes along the shown potential gradient.
Figure 4. (A) Current-time trace recorded upon introduction of [Fe(CN)6]3–, menadione and glucose to S. cerevisiae cells on an electrode microchip. (B) A silicon microchip for mediated amperometry (upper panel) and a microscope image of S. cerevisiae cells on a microband electrode (width/length: 25/1,000 µm). (Reprinted with permission from Ref. [8], © 2009 Elsevier BV.) (Lower panel).
The biological function of the double mediator system is based on the controlled metabolic perturbation caused by menadione, which serves as an analytical tool. Menadione reduction competes for the available NAD(P)H in the entire cellular environment. Hence, depending on what endogenous processes there are that supply and consume NAD(P)H, the obtained amperometric signal either increases or decreases with respect to a utilized control. Menadione is also known for its ability to increase oxidative stress but the utilized concentration, 100 µM, can be regarded as non-destructive [26], when short-lived measurements are conducted. The technique can answer to different biological questions depending on how an experiment is designed.
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The technique is found useful in screening of changes in NADPH and NADH availability as the consequence of (i) genetic modifications (genotype), such as deletion [6, 8] or over expression [9] of a gene, (ii) changes in phenotype as exemplified by respiratory and fermentative cells [8], (iii) the simultaneous influence of different subcellular compartments (cytosol vs. mitochondria) on the cellular response to different chemicals [8]. Upon parallelization by using multiple electrode arrays, the technique facilitates simultaneous monitoring of different geno- and phenotypes [8]. Figure 5 depicts the obtained relative responses to glucose and fructose using a S. cerevisiae deletion mutant strain lacking the gene PGI1 (EBY44 strain) in comparison with a non-modified laboratory strain (CEN.PK) [6].
Figure 5. Relative responses to glucose and fructose (left panels in A and B) obtained for S. cerevisiae cells (A) with and (B) without phosphoglucose isomerase (PGI). (Right panels in A and B: a schematic presentation of the pentose phosphate pathway (PPP) and glycolytic pathway (GP); the deletion of PGI1 gene is indicated in B.)
The responses are relative with respect to the baseline current recorded prior to introducing either glucose or fructose. In the presence of PGI1, introduction of either glucose or fructose results in an equal availability of NAD(P)H and hence an equal current response (Fig. 5A). Upon deletion of PGI1, glucose is predominantly shuttled into the PPP increasing the availability of NADPH, whereas fructose is catabolized through the GP with a concomitant increase in the availability of NADH. A considerable difference can be seen in the obtained current response (Fig. 5B). The result also demonstrates that NADPH is the preferred cofactor for MREs.
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Additionally, the technique is capable of delivering in vivo enzyme kinetics data as dose response curves, which can be fitted to the four-parameter logistic equation (Eq. (4)):
Δi = Bottom +
Top - Bottom log (XC50 )
⎛ 10 ⎜ log[S] ⎝ 10
1+ ⎜
(Hill slope )
⎞ ⎟⎟ ⎠
(4)
The response is expressed in either nA or % (relative response), XC50 is either IC50 or EC50, the Hill slope is the midpoint slope, and the bottom and top indicate the response for the minimal and maximal curve asymptote, respectively. Data for enzyme kinetics is obtained through titration with the utilized substrate or another effector, such as an inhibitor or a competing substrate. The titration curves in Fig. 6A were obtained by titration with HMF in studies involving a S. cerevisiae strain overexpressing the ADH6 gene encoding for the NADPH dependent alcohol dehydrogenase6 (ADH6 strain) and the corresponding parental strain with an empty plasmid (control strain) [9]. The titration curves show the response of MREs, which is decreasing due to the decreasing NADPH pool as the consequence of consecutive additions of HMF. The data for the dose response curve is obtained as the difference between consecutive steady-states; now, however, the differences are negative and an absolute value is taken. Figure 6B shows the corresponding dose response curves. As can be seen, the dose response curves do not show the sigmoidal shape characteristic of the four-parameter logistic equation. This is due to the fact that the Hill slope is 1 and the bottom is zero, i.e. initially at 0 µM addition the response (decrease in current) is 0 nA. Mathematically, the obtained curves have the same hyperbolic form as the well known Michaelis–Menten equation. However, the curves are expressed in the form of current vs. concentration, yielding IMAX instead of VMAX (Eq. (5)):
× [S] MAX Δi = Iapp K M, cell + [S]
(5)
where [S] is the concentration of any substrate and K app M, cell is the apparent cellular Michaelis–Menten constant. In order to convert these into a more informative or conventional VMAX with, for instance, unit nmol substrate/min, Faraday’s law of electrolysis (Eq. (6)) can be used to obtain the number of moles of substrate corresponding to a given value of current:
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Figure 6. (A) Current-time traces for S. cerevisiae cells recorded upon titration with 5hydroxymethyl furfural (HMF). (Reprinted with permission from Ref. [9], © 2009 American Chemical Society.) (B) Dose response curves based on Δi values in (A). (Lower panel: a schematic presentation of the ADH6 catalyzed NADPH dependent reduction of HMF.)
60 × I MAX n V MAX = S = τ nF
(6)
where nS generally refers to the number of moles of a substrate oxidized or reduced, τ is the time-base of VMAX (e.g. min) and 60 is the conversion factor between the time-base of VMAX (min) and IMAX (s). The other symbols are as previously described. Other enzyme kinetic parameters can be derived from the obtained VMAX and KM by using knowledge regarding the number of cells involved in the assay [8, 9]. Ultimately, the determined kinetic parameters should purely reflect the intracellular electron transfer but they cannot be separated from other contributions, such as mass transport across the plasma membrane into the cells and out of the cells, extracellular reaction between menadiol and ferricyanide, mass transfer of
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ferrocyanide to the electrode and oxidation of ferrocyanide at the electrode. Due to the influence of these factors, the determined enzyme kinetic parameters are referred to as apparent. The extracellular mass transfer steps are also affected by convection in the utilized fluidic system where electrode chip is placed. Additionally, the intracellular electron transfer is dependent on the concentration of the participating species, i.e. the concentration of the entering menadione and competing substrate etc. as well as NAD(P)H, the latter of which also determines the potential of the redox couple. When determining the enzyme kinetic parameters for a competing substrate, such as HMF, the most significant criterion is that the mass transfer and electron transfer of menadione reduction is not slower than the corresponding processes of the studied substrate in order not to become the limiting factor. 4. Monitoring of Exocytosis 4.1. THE BIOLOGICAL SIGNIFICANCE OF EXOCYTOSIS
Signal propagation by neurons takes place through both electrical and chemical means. Along the axon of a neuron, opening and closing of Na+ and K+ ion channels, increasing the Na+ and K+ conductance, generates and propagates action potentials. When a propagating action potential in the form of ionic current reaches the gap between two neurons, the electrical mode of signal propagation is converted into its chemical counterpart. This change in the mode of signal propagation takes place in a finite gap between two neurons (~100 nm wide [45]), the synaptic cleft. The arrival of a propagating action potential to the synapse results in the opening of a Ca2+ ion channel, increasing the intracellular Ca2+ concentration of the pre-synaptic neuron from a normally low level (~100 nM) to concentrations 1,000-fold higher in the microenvironment near the Ca2+ ion channels [45]. Through a cascade of biochemical processes, the inflow of Ca2+ serves as a trigger of fast and regulated excretion, exocytosis, of a signaling molecule, neurotransmitter, which propagates the neuronal signal across the synaptic cleft. Secretion of different regulatory substances through a Ca2+ dependent machinery is not only limited to neurons, but also includes, for instance, insulin-secreting pancreatic β-cells and catecholamine-secreting chromaffin pheochromocytoma (PC12) cells of the adrenal gland. The significance lies, however, in the nature of the secreted compound and the receptors to which this compound functions as a ligand. Much of the information illustrating the overall process of exocytotic release of neurotransmitters from their storage vesicles originates from studies using chromaffin and PC12 cells. Although these are not neurons and hence the catecholamines in their vesicles do not function as neurotransmitters, the functional principle of the release is the same as the release of catecholamines and other neurotransmitters from
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pre-synaptic neurons. This process contains four distinct stages: (i) docking, (ii) priming, (iii) triggering and (iv) fusion/exocytosis. During docking, vesicles loaded with the neurotransmitter molecules are brought to the vicinity of the plasma membrane at the site of the synapse (active zone). During priming, vesicles are bound to the plasma membrane through complex formation between certain plasma membrane and vesicle membrane proteins. An exocytotic event is triggered as the consequence of Ca2+ ion influx through ion channels that are opened upon arrival of a propagating action potential. In exocytosis, the vesicle membrane fuses with the plasma membrane in the active zone resulting in opening of a fusion pore. Upon electrical, mechanical and chemical stimulation (e.g. using an elevated K+ ion concentration) of cells capable of undergoing exocytosis, the neurotransmitters or other signaling substances are released as packages of one vesicle at a time. This mode is referred to as quantal release. Hence, in neuronal synapses, the overall postsynaptic response is a sum of discrete responses corresponding to single vesicles. In large vesicles, the number of released neurotransmitter molecules per exocytotic event (quantum) can be several millions, whereas in small neuronal vesicles the number of neurotransmitter molecules can be as low as 3,000–30,000 [46]. 4.2. DETECTION PRINCIPLE
Amperometry is the most widely utilized electrochemical technique for monitoring of exocytosis. Its fundamental application was presented by Wightman and his co-workers [29]. The technique was originally presented using carbon-fiber microelectrodes (CFME) as WEs and most of the described applications are based on this approach [47]. The position of CFMEs can be adjusted under microscopic observation using a micromanipulator. The electrode surface is placed into a close contact with the plasma membrane of the monitored cell, the separation being of the order of magnitude of the diffusion layer [48]. The close proximity of the electrode surface to the plasma membrane provides a sufficient temporal resolution to monitor single-vesicle exocytotic events. Aside from good temporal resolution, amperometry also provides a superior quantitative sensitivity down to 31 zmol7 (~18,700 molecules) of catecholamines [49] and 7.8 zmol (~4,700 molecules) of serotonin [50], as well as a spatial resolution at best ranging from the level of 1 µm [51] down to the size of a single vesicle (~100 nm) [52] in catecholamine detection. Hence, amperometry can yield accurate quantitative and high-resolution spatio-temporal information regarding single-vesicle exocytotic events.
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1 zmol ≡ 1·10−21 mol.
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15.0
B.
10.0
5.0
0
C. A
B
5.0
10.0
0
15.0
D E
C
F G
D
Figure 7. (A) A SEM image of an array of well-electrodes capable of accommodating sigle cells (left panel) and a magnification of a single well-electrode (right panel). (Reprinted with permission from Ref. [53], © 2003 American Chemical Society.) (B) An AFM image of an array of microelectrodes in the size regime of a single cell. (Reprinted with permission from [54], © 2002 IOP Publishing Ltd.) (C) A schematic view of a microfluidic system (left panel) able to capture single cells in the middle of a ring-electrode and a microscope image of a PC12 cell on a ring-electrode (right panel). (Reprinted with permission from Ref. [55], © 2008 The Royal Society of Chemistry.)
Emergence of lithographic techniques in electrode fabrication has opened new possibilities for monitoring of exocytosis using chip based electroanalytical systems [30]. Primarily, these systems utilize planar electrodes, facilitating detection of exocytosis from vesicles at the active zones near the basal membrane in contact with the electrode surface. However, Chen et al. have reported on monitoring of exocytosis from single cells utilizing well-electrodes [53] (Fig. 7A) In this case, detection covers active zones in a large fraction of a cell. Planar electrodes cannot be positioned to a certain part of a monitored cell, somewhat decreasing the spatial resolution. However, with an additional system for guiding and positioning cells, a single cell can be placed on measuring electrodes to monitor single-vesicle exocytotic events with good spatial resolution. Figure 7B shows an electrode microchip having an array of four platinum microelectrodes around a central area [54, 56]. Simultaneous detection of dopamine exocytosis from single chromaffin cells accommodated on top of the electrode array could be used to localize the opening of a fusion pore with a high spatial resolution. Left and right panel of Fig. 7C show a schematic view of a microfluidic cell handling system and a ring-shaped microelectrode with a single rat pheochromocytoma (PC12) cell in the middle of the electrode, respectively [55]. In virtue of an aperture in the middle of the ring-electrode,
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single cells could be captured and held in position to facilitate exocytosis measurements that provided a high spatial resolution of the position of the active zone having the dopamine-releasing vesicle. Neurotransmitter Vesicle synaps
Dopamin
HO
HO
Elektrod
CH2CH2NH3+
O
CH2CH2NH3+ + 2H+ + 2e
O
Oxidation av Dopamin
Figure 8. (A) A schematic view of the proximity of a cell to the surface of a planar electrode and the reaction of dopamine oxidation.
Figure 9. (A) A train of exocytotic spikes representing single-vesicle exocytotic events, (B) an enlargement of the spike encircled in (A) showing the different parameters of eocytotic spikes, and (C) a microscope image of PC12 cells on ring-electrodes. (Reprinted with permission from Ref. [12], © 2007 Wiley-VCH Verlag GmbH & Co. KGaA.)
The application of chip based electroanalytical systems having planar electrodes provides good temporal resolution and sensitivity for monitoring of exocytosis. The distance between a cell and the underlying electrode is of the same order of magnitude as the distance between a presynaptic and postsynaptic neuron in vivo. Hence, no specific arrangements are needed to achieve a certain separation between an electrode and a cell, as is the case when using CFMEs. Figure 8 shows schematically the placement of a cell on a planar electrode and the release of dopamine molecules, which are immediately oxidized at the potential (e.g. 700 mV vs. a Ag/AgCl RE) poised at the WE and the dopamine oxidation reaction. The proximity of a cell to the electrode surface ensures that sufficient detection kinetics is achieved to monitor exocytosis from a single vesicle of a single cell. Since the duration of an exocytotic event can be below 10 ms, the primary constraint is to have
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a potentiostat capable of sampling at the rate of 5,000–10,000 Hz. Figure 9A shows a train of spikes, each of which represents a single-vesicle exocytotic event monitored using circular electrodes (Fig. 9C) [12]. Figure 9B shows a magnification of one of the spikes in Fig. 9A, featuring the different details and hence the parameters that can be obtained to characterize exocytotic events, e.g. the peak width at half height (t½), the spike amplitude (imax). Additionally, the kinetics of an event can be characterized by the rise time (RT), i.e. the time required for recording 25–75% of the imax. By integrating the current of each spike, it is possible to determine the total charge (Q) associated with the oxidation of the released molecules from one vesicle. Application of Faraday’s law of electrolysis (Eq. (1)) can then yield the total number of released molecules. The proximity also facilitates high sensitivity since the released molecules can be detected before they are able to diffuse into the surrounding space. Figure 9B illustrates the ultimate capability of chip based electroanalytical systems showing a foot signal that is the consequence of initial leakage of molecules through an opening fusion pore. The number of molecules contributing to a foot signal can be below 30,000 [12] and the duration of such a signal only a fraction of the total duration of an exocytotic event. Aside from single-cell exocytosis measurements, chip based electrochemical systems also facilitate applications where exocytosis is monitored from a population of growing [57–61] or differentiating adherent cells [61]. This approach provides the possibility to conduct exocytosis measurements in systems where cells are cultured, making cells fully adapted to the environment and eliminating the necessity of trypsinization as a part of the preparation of cells for measurements. When utilizing systems with cultured cells, parallelization in terms of multiple electrodes can be also effectively applied to conduct simultaneous measurements providing a sufficient statistical control. Furthermore, automation of measurements can be implemented to achieve capability for high-throughput screening, for instance, to study drug effects on neurotransmitter release. Figure 10 shows a microfluidic system with an integrated electrode ship having a microelectrode array for monitoring exocytosis [60]. Detection from a cell population increases the duration of an exocytotic event to seconds since each recorded event is an averaged sum of many single-vesicle events from several cells. Figure 11A shows current-time traces for recorded exocytotic events from populations of growing PC12 cells (traces 1–3) [61]. The cell population corresponding to the measurements are shown in Fig. 11B (panels 1–3). The inset of Fig. 11A shows a current-time trace for an exocytotic event from a population of differentiated PC12 cells and the corresponding population is shown in Fig. 11B (panel 4). This current-time trace shows a distinct characteristic compared to traces 1–3, i.e. the rising and descending portions have a clearly steeper slope, which indicates a faster process. This
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Figure 10. (A) A microfluidic system with integrated microelectrode arrays to monitor exocytosis from cultured cells. (Reprinted with permission from Ref. [60], © 2008 American Chemical Society.)
Figure 11. (A) Current-time traces for exocytotic events recorded from populations of growing (traces 1–3) and differentiating (trace 4) PC12 cells. (B) PC12 cell populations used for recording traces 1–4. (Reprinted with permission from [61], © 2008 The Chemical and Biological Microsystems Society.)
was attributed to mainly two factors: (i) a closer proximity of the adherent differentiated cells compared to the more roundish albeit spread nondifferentiated cells and (ii) the presence of only distinctly distributed active zones in differentiated cells in comparison with non-differentiated cells where vesicles are located throughout the cell body. The first characteristic of the differentiated cells gives rise to faster diffusion of the released dopamine to the electrode surface and the second characteristic makes the overall duration of the monitored exocytosis shorter than those monitored from non-differentiated cells. The longer duration of exocytotic events that are recorded from a population of cells also offers the possibility to widen the spectrum of detectable compounds from electroactive catecholamines, serotonin and histamine to, for instance, glutamate [11], the detection of which requires enzyme-based biosensors having a response time at best in the regime of seconds.
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5. Conclusions Despite the fact that amperometry on planar electrodes decreases the spatial resolution in comparison with systems, where microelectrodes are positioned adjacent to a cell using a micromanipulator or SECM instrument, it at the same time possess the greatest possibilities for developing monitoring systems with a sufficient degree of fabricational freedom in order to realize goals that also require handling, culturing and differentiation of cells in applications, e.g. characterization of differentiating neuronal stem cells and their integration into brain tissue. Moreover, further miniaturization to nanosized electrode structures could provide the possibility to address only a very small section of a differentiated cell, e.g. ideally the junction between a pre- and postsynaptic neuron. Furthermore, no matter whether the goal is analysis of single cells or cell populations, only chip based systems are capable of providing a sufficient throughput and the automation necessary for screening in drug discovery, decreasing the need of continuous intervention by an operator. Acknowledgments The EU FP7 NMP project EXCELL is kindly acknowledged for financial support.
References 1. A. Begleiter and J. Fourie, Induction of nqo1 in cancer cells, Methods in Enzymology, 382, 320–351 (2004). 2. J.R. Broach and J. Thorner, High-throughput screening for drug discovery, Nature, 384(6604 Suppl), 14–16 (1996). 3. G.S. Sittampalam, S.D. Kahl and W.P. Janzen, High-throughput screening: Advances in assay technologies, Current Opinion in Chemical Biology, 1(3), 384–391 (1997). 4. A.V. Zhdanov, M.W. Ward, J.H.M. Prehn and D.B. Papkovsky, Dynamics of intracellular oxygen in pc12 cells upon stimulation of neurotransmission, Journal of Biological Chemistry, 283(9), 5650–5661 (2008). 5. M. Brischwein, E.R. Motrescu, E. Cabala, A.M. Otto, H. Grothe and B. Wolf, Functional cellular assays with multiparametric silicon sensor chips, Lab on a Chip, 3, 234–240 (2003). 6. C.F. Spegel, A.R. Heiskanen, N. Kostesha, T.H. Johanson, M.F. GorwaGrauslund, M. Koudelka-Hep, J. Emneus and T. Ruzgas, Amperometric response from the glycolytic versus the pentose phosphate pathway in saccharomyces cerevisiae cells, Analytical Chemistry, 79(23), 8919–8926 (2007).
CHIP BASED ELECTROANALYTICAL SYSTEMS
423
7. A. Heiskanen, C. Spegel, N. Kostesha, S. Lindahl, T. Ruzgas and J. Emneus, Mediator-assisted simultaneous probing of cytosolic and mitochondrial redox activity in living cells, Analytical Biochemistry, 384(1), 11–19 (2009). 8. N. Kostesha, A. Heiskanen, C. Spégel, B. Hahn-Hägerdal, M.-F. GorwaGrauslund and J. Emnéus, Real-time detection of cofactor availability in genetically modified living saccharomyces cerevisiae cells – simultaneous probing of different geno- and phenotypes, Bioelectrochemistry, 76(1–2), 180–188 (2009). 9. N. Kostesha, J.R.M. Almeida, A. Heiskanen, B. Hahn-Hägerda, M.-F. GorwaGrauslund and J. Emnéus, Electrochemical probing of in vivo 5-hydroxymethyl furfural reduction in saccharomyces cerevisiae, Analytical Chemistry, In Press. 10. C. Tiruppathi, A.B. Malik, P.J. Delvecchio, C.R. Keese and I. Giaever, Electrical method for detection of endothelial-cell shape change in real-time – assessment of endothelial barrier function, Proceedings of the National Academy of Sciences of the United States of America, 89(17), 7919–7923 (1992). 11. J. Castillo, A. Blochl, S. Dennison, W. Schuhmann and E. Csoregi, Glutamate detection from nerve cells using a planar electrodes array integrated in a microtiter plate, Biosensors and Bioelectronics, 20, 2116–2119 (2005). 12. C. Spégel, A. Heiskanen, J. Acklid, A. Wolff, R. Taboryski, J. Emnéus and T. Ruzgas, On-chip determination of dopamine exocytosis using mercaptopropionic acid modified microelectrodes, Electroanalysis, 19(2–3), 263–271 (2007). 13. N.C. Yu, J.M. Atienza, J. Bernard, S. Blanc, J. Zhu, X.B. Wang, X. Xu and Y.A. Abassi, Real-time monitoring of morphological changes in living cells by electronic cell sensor arrays: An approach to study g protein-coupled receptors, Analytical Chemistry, 78(1), 35–43 (2006). 14. S.A. Titus, L. Xiao, N. Southall, J.M. Lu, J. Inglese, M. Brasch, C.P. Austin and W. Zheng, Cell-based pde4 assay in 1536-well plate format for high-throughput screening, Journal of Biomolecular Screening, 13(7), 609–618 (2008). 15. C.B. Maddox, L. Rasmussen and E.L. White, Adapting cell-based assays to the high-throughput screening platform: Problems encountered and lessons learned, Journal of the Association for Laboratory Automation, 13(3), 168–173 (2008). 16. I. Meyvantsson, J.W. Warrick, S. Hayes, A. Skoien and D.J. Beebe, Automated cell culture in high density tubeless microfluidic device arrays, Lab on a Chip, 8(5), 717–724 (2008). 17. P. Skafte-Pedersen, D. Sabourin, M. Dufva and D. Snakenborg, Multi-channel peristaltic pump for microfluidic applications featuring monolithic pdms inlay, Lab on a Chip, 9(20), 3003–3006 (2009). 18. D.W. Piston and S.M. Knobel, Real-time analysis of glucose metabolism by microscopy, Trends in Endocrinology and Metabolism, 10(10), 413–417 (1999). 19. G.H. Patterson and D.W. Piston, Photobleaching in two-photon excitation microscopy, Biophysical Journal, 78(4), 2159–2162 (2000). 20. B. Rajwa, T. Bernas, H. Acker, J. Dobrucki and J.P. Robinson, Single- and two-photon spectral imaging of intrinsic fluorescence of transformed human hepatocytes, Microscopy Research and Technique, 70(10), 869–879 (2007). 21. A.M. Aravanis, J.L. Pyle, N.C. Harata and R.W. Tsien, Imaging single synaptic vesicles undergoing repeated fusion events: Kissing, running, and kissing again, Neuropharmacology, 45(6), 797–813 (2003).
424
A. HEISKANEN, M. DUFVA, AND J. EMNÉUS
22. N. Pereira Rodrigues, Y. Sakai and T. Fujii, Cell-based microfluidic biochip for the electrochemical real-time monitoring of glucose and oxygen, Sensors and Actuators B: Chemical, 132(2), 608–613 (2008). 23. S.A.M. Marzouk, V.V. Cosofret, R.P. Buck, Y. Hua, W.E. Cascio and S.S.M. Hassan, Amperometric monitoring of lactate accumulation in rabbit ischemic myocardium, Talanta, 44(9), 1527–1541 (1997). 24. M.G. Roper, W.-j. Qian, B.B. Zhang, R.N. Kulkarni, C.R. Kahn and R.T. Kennedy, Effect of the insulin mimetic l-783,281 on intracellular [ca2+] and insulin secretion from pancreatic î²-cells, Diabetes, 51(suppl 1), S43–S49 (2002). 25. S.p. Arbault, N. Sojic, D. Bruce, C. Amatore, A. Sarasin and M. Vuillaume, Oxidative stress in cancer prone xeroderma pigmentosum fibroblasts. Realtime and single cell monitoring of superoxide and nitric oxide production with microelectrodes, Carcinogenesis: an information retrieval publication, 25(4), 509–515 (2004). 26. J. Mauzeroll and A.J. Bard, Scanning electrochemical microscopy of menadioneglutathione conjugate export from yeast cells, Proceedings of the National Academy of Sciences of the United States of America, 101(21), 7862–7867 (2004). 27. S.A. Rotenberg and M.V. Mirkin, Scanning electrochemical microscopy: Detection of human breast cancer cells by redox environment, Journal of Mammary Gland Biology and Neoplasia, 9(4), 375–382 (2004). 28. A. Heiskanen, J. Yakovleva, C. Spégel, R. Taboryski, M. Koudelka-Hep and T. Ruzgas, Amperometric monitoring of redox activity in living yeast cells: Comparison of menadione and menadione sodium bisulfite as electron transfer mediators, Electrochemical Communications, 6(2), 219–224 (2004). 29. R.M. Wightman, J.A. Jankowski, R.T. Kennedy, K.T. Kawagoe, T.J. Schroeder, D.J. Leszczyszyn, J.A. Near, E.J. Diliberto and O.H. Viveros, Temporally resolved catecholamine spikes correspond to single vesicle release from individual chromaffin cells, Proceedings of the National Academy of Sciences of the United States of America, 88(23), 10754–10758 (1991). 30. C. Spegel, A. Heiskanen, Lars Henrik D. Skjolding and J. Emnéus, Chip based electroanalytical systems for cell analysis, Electroanalysis, 20(6), 680–702 (2008). 31. J.D. Rabinowitz, J.F. Vacchino, C. Beeson and H.M. McConnell, Potentiometric measurement of intracellular redox activity, Journal of the American Chemical Society, 120(10), 2464–2473 (1998). 32. I.M. Kolthoff and J.J. Lingane, Polarography, 2nd ed., Vol. 2, 1952, New York: Interscience. p. 480. 33. F.Q. Schafer and G.R. Buettner, Redox environment of the cell as viewed through the redox state of the glutathione disulfide/glutathione couple, Free Radical Biology and Medicine, 30(11), 1191–1212 (2001). 34. Y.J. Suzuki, H.J. Forman and A. Sevanian, Oxidants as stimulators of signal transduction, Free Radical Biology and Medicine, 22(1–2), 269–285 (1997). 35. B. Chance and G.R. Williams, The respiratory chain and oxidative phosphorylation, Advances in Enzymology and Related Subjects of Biochemistry, 17, 65–134 (1956).
CHIP BASED ELECTROANALYTICAL SYSTEMS
425
36. J.L. Cadet and C. Brannock, Free radicals and the pathobiology of brain dopamine systems, Neurochemistry International, 32(2), 117–131 (1998). 37. A.P. Arrigo, Gene expression and the thiol redox state, Free Radical Biology and Medicine, 27(9–10), 936–944 (1999). 38. T.G. Hastings and M.J. Zigmond, Neurodegenerative disease and oxidative stress: Insights from an animal model of parkinsonism, Neurodegenerative diseases: Molecular and cellular mechanisms and therapeutic advances, G. Fiskum, Editor, 1996, Plenum Press: New York, p. 37–46. 39. H. Sies, Intracellular effects of glutathione conjugates and their transport from the cell, Glutathione conjugation, H. Sies and B. Ketterer, Editors, 1988, Academic Perss Limited: London, p. 175–197. 40. S.Y. Sharp, L.R. Kelland, M.R. Valenti, L.A. Brunton, S. Hobbs and P. Workman, Establishment of an isogenic human colon tumor model for nqo1 gene expression: Application to investigate the role of dt-diaphorase in bioreductive drug activation in vitro and in vivo, Molecular Pharmacology, 58(5), 1146–1155 (2000). 41. H. Pelicano, D.S. Martin, R.H. Xu and P. Huang, Glycolysis inhibition for anticancer treatment, Oncogene, 25(34), 4633–4646 (2006). 42. E. Boles, W. Lehnert and F.K. Zimmermann, The role of the nad-dependent glutamate-dehydrogenase in restoring growth on glucose of a saccharomycescerevisiae phosphoglucose isomerase mutant, European Journal of Biochemistry, 217(1), 469–477 (1993). 43. A. Petersson, J.R.M. Almeida, T. Modig, K. Karhumaa, B. Hahn-Hagerdal, M.F. Gorwa-Grauslund and G. Liden, A 5-hydroxymethyl furfural reducing enzyme encoded by the saccharomyces cerevisiae adh6 gene conveys hmf tolerance, Yeast, 23(6), 455–464 (2006). 44. C. Larroy, M.R. Fernandez, E. Gonzalez, X. Pares and J.A. Biosca, Characterization of the saccharomyces cerevisiae ymr318c (adh6) gene product as a broad specificity nadph-dependent alcohol dehydrogenase: Relevance in aldehyde reduction, Biochemical Journal, 361, 163–172 (2002). 45. T.L. Schwarz, Release of neurotransmitters, Fundamental neuroscience, 3rd ed., L. Squire, D. Berg, F. Bloom, S. Du Lac, A. Ghosh and N. Spitzer, Editors, 2008, Academic Press: San Diego, p. 157–180. 46. R.M. Wightman and C.L. Haynes, Synaptic vesicles really do kiss and run, Nature Neuroscience, 7(4), 321–322 (2004). 47. C. Amatore, S. Arbault, M. Guille and F. Lemaitre, Electrochemical monitoring of single cell secretion: Vesicular exocytosis and oxidative stress, Chemical Reviews, 108(7), 2585–2621 (2008). 48. E.R. Travis and R.M. Wightman, Spatio-temporal resolution of exocytosis from individual cells, Annual Review of Biophysics and Biomolecular Structure, 27, 77–103 (1998). 49. T.K. Chen, G.O. Luo and A.G. Ewing, Amperometric monitoring of stimulated catecholamine release from rat pheochromocytoma (pc12) cells at the zeptomole level, Analytical Chemistry, 66(19), 3031–3035 (1994). 50. D. Bruns and R. Jahn, Real-time measurement of transmitter release from single synaptic vesicles, Nature, 377(6544), 62–65 (1995).
426
A. HEISKANEN, M. DUFVA, AND J. EMNÉUS
51. K.T. Kawagoe, J.A. Jankowski and R.M. Wightman, Etched carbon-fiber electrodes as amperometric detectors of catecholamine secretion from isolated biological cells, Analytical Chemistry, 63(15), 1589–1594 (1991). 52. W.Z. Wu, W.H. Huang, W. Wang, Z.L. Wang, J.K. Cheng, T. Xu, R.Y. Zhang, Y. Chen and J. Liut, Monitoring dopamine release from single living vesicles with nanoelectrodes, Journal of the American Chemical Society, 127(25), 8914–8915 (2005). 53. P. Chen, B. Xu, N. Tokranova, X.J. Feng, J. Castracane and K.D. Gillis, Amperometric detection of quantal catecholamine secretion from individual cells on micromachined silicon chips, Analytical Chemistry, 75(3), 518–524 (2003). 54. A.F. Dias, G. Dernick, V. Valero, M.G. Yong, C.D. James, H.G. Craighead and M. Lindau, An electrochemical detector array to study cell biology on the nanoscale, Nanotechnology, 13(3), 285–289 (2002). 55. C. Spegel, A. Heiskanen, S. Pedersen, J. Emneus, T. Ruzgas and R. Taboryski, Fully automated microchip system for the detection of quantal exocytosis from single and small ensembles of cells, Lab on a Chip, 8(2), 323–329 (2008). 56. H. Ismail, K. Kassandra, B. Khajak, D. Gregor, V. Vicente, G.Y. Ming, G.C. Harold, L. Manfred and L. Ramon, Electrochemical imaging of fusion pore openings by electrochemical detector arrays, Proceedings of the National Academy of Sciences of the United States of America, 102(39), 13879–13884 (2005). 57. M.e.W. Li, D.e.M. Spence and R.e.S. Martin, A microchip-based system for immobilizing pc 12 cells and amperometrically detecting catecholamines released after stimulation with calcium, Electroanalysis, 17(13), 1171–1180 (2005). 58. H.F. Cui, J.S. Ye, Y. Chen, S.C. Chong, X. Liu, T.M. Lim and F.S. Sheu, In situ temporal detection of dopamine exocytosis from l-dopa-incubated mn9d cells using microelectrode array-integrated biochip, Sensors and Actuators B-Chemical, 115(2), 634–641 (2006). 59. H.F. Cui, J.S. Ye, Y. Chen, S.C. Chong and F.S. Sheu, Microelectrode array biochip: Tool for in vitro drug screening based on the detection of a drug effect on dopamine release from pc12 cells, Analytical Chemistry, 78(18), 6347– 6355 (2006). 60. Y. Chen, C. Guo, L. Lim, S. Cheong, Q. Zhang, K. Tang and J. Reboud, Compact microelectrode array system: Tool for in situ monitoring of drug effects on neurotransmitter release from neural cells, Analytical Chemistry, 80(4), 1133– 1140 (2008). 61. A. Heiskanen, C. Spégel, J. Tønnesen, Z. Fohlerova, L. Goulart, J. Hansen, M. Kokaia, T. Ruzgas, M. Dufva and J. Emnéus, Development of a microfluidic on-line culture system for combined electrochemical and optical real-time detection of cellular processes, Proceeding of the Twelfth International Conference on Miniaturized Systems for Chemistry and Life Sciences, October 12–16, 2008, San Diego, CA.
PERFUSION BASED CELL CULTURE CHIPS A. HEISKANEN, J. EMNÉUS, AND M. DUFVA
Department of Micro- and Nanotechnology, Technical University of Denmark, Ørsteds Plads 345 East, DK-2800 Kgs. Lyngby, Denmark,
[email protected]
Abstract. Performing cell culture in miniaturized perfusion chambers gives possibilities to experiment with cells under near in vivo like conditions. In contrast to traditional batch cultures, miniaturized perfusion systems provide precise control of medium composition, long term unattended cultures and tissue like structuring of the cultures. However, as this chapter illustrates, many issues remain to be identified regarding perfusion cell culture such as design, material choice and how to use these systems before they will be widespread amongst biomedical researchers.
1. Introduction Since Ross Granville Harrison conducted the first successful in vitro cell culture experiment in 1907 by cultivating frog embryonic nerve tissue in a drop of frog lymphatic fluid [1], in vitro cell cultures have become widely accepted as a means to study cellular functions in general and responses to different chemical species in drug discovery and toxicological testing. Ever since, this first published experiment has paved the way for the development of cell culture techniques and culture vessels and still serves as the fundament for biomedical research. This is valid despite the fact that cells are grown under rather non-realistic conditions, i.e., most often batch cultures are used where cells are grown on plastic surfaces in a medium that has been selected to support cell growth, containing, for instance, fetal bovine serum even though the studied cells are not necessarily of bovine origin. The studied cells have also often undergone genetic modifications and moreover lack the tissue like environment that provides the relevant network of cell-to-cell communication that resembles what one normally finds in multi-cellular organisms and even in microbiological communities. In spite of the mentioned drawbacks of traditional in vitro batch cell culture techniques, these are still the main tools used to study cellular functions, basically, because corresponding experiments in animals are time consuming, expensive and nowadays considered unethical. It would be, S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_20, © Springer Science + Business Media B.V. 2010
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however, desirable for biologists to have access to in vitro cell culture tools capable of providing a more in vivo like cellular microenvironment. Usually a cell experiment is based on endpoint detection, i.e., the cells are perturbed at a certain time point and killed at a later one to record changes in particular biomarkers. A number of different analytical tools, e.g. DNA and protein microarrays, 2D gel electrophoresis and mass spectrometry, are used to conduct extensive mapping of these changes in the transcriptome, proteome, metabolome, etc. Despite the wealth of information gained, only a snapshot of the physiological state of the cells is revealed. Transient changes in expression/chemical modifications are missed and, furthermore, single-cell variation is difficult to catch. To overcome these limitations, detection of events with single-cell resolution is needed in order to understand tissue function. Miniaturization of biological experiments will provide biologists with a completely novel toolset to understand how multicellular organisms function [2, 3]. With microfluidic cell culture networks, having integrated arrays of miniaturized sensors (e.g. optical, electrochemical), biologists will have access to experimental methods that provide a more in vivo like environment for cells, at the same time allowing studies of both dynamic (e.g. interrelation between gene, protein and metabolite), transient (e.g. exocytosis) and more permanent changes (e.g. stem cells developing into a specific phenotype) in cell physiology on single cell level. 2. Perfusion Culture Chips Versus Traditional Culture Vessels On the laboratory-scale, batch cell culturing is mainly conducted in flasks, dishes or microtiter plates (Fig. 1), however industrial-scale bioreactors with perfusion (continuous culture) are also available for production of, e.g. antibodies and other proteins. In both laboratory- and industrial-scale systems, a large volume of cell medium is available in comparison with the cell volume to provide the cultured cells with sufficient amount of nutrients. 2.1. MODE OF MASS TRANSFER
On laboratory-scale, in culture vessels that are kept in a CO2 incubator for pH control, at short distances and long time scales nutrients reach the cells, and metabolic waste products are transported away from the cells, via diffusion.1 However, consumption of nutrients and production of metabolic
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Diffusion refers to random Brownian motion of solutes from a region with a higher concentration to one with a lower concentration.
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waste during prolonged culturing causes formation of concentration gradients, which can result in significant natural convection2 (mixing).
Figure 1. Traditional laboratory-scale cell culture vessels, flasks (left panel), Petri dishes (mid panel) and microtiter plates (right panel). (From the web site: www.nuncbrand.com)
As the consequence of this, the metabolic waste products are initially distributed evenly in the bulk medium but accumulated with time in batch culture systems. Furthermore, as a part of normal culture operations, the vessels are taken out from the incubator for microscopic observations, which can cause movement of the bulk medium and formation of temperature gradients, consequently contributing to forced and natural convection, respectively. In industrial-scale bioreactors, the applied perfusion creates forced convection, which is the primary mode of mass transfer. The common feature of all the conventional systems, laboratory- or industrial scale, is that due to the long distances and the large medium volume in comparison with the cell volume, the significance of convection is pronounced. Consequently, mass transfer in such systems takes place in all directions (x-, y- and z-direction) with a comparable magnitude, as is schematically shown in Fig. 2a. In virtue of the characteristic small dimensions and the applied low flow rates, the flow is laminar in perfusion based microfluidic cell culture chips. Consequently, convection only exists in the direction of the applied flow (x-direction), whereas in the directions perpendicular to the flow (y- and z-direction) only diffusion contributes to mass transfer. This is schematically illustrated in Fig. 2b, depicting a pronounced flow in x-direction. Due to short distances, mass transfer by diffusion is sufficiently effective in providing nutrients and removing metabolic waste during continuous perfusion, eliminating formation of concentration gradients, and hence accumulation of metabolic waste. Furthermore, the small dimensions of microfluidic cell
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2 Convection refers to mass transfer of solutes along with currents in the fluid. It arises as consequence of concentration and temperature gradients (natural convection) or shaking/ swirling of the fluid (forced convection).
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culture chips facilitate effective heat transfer. Hence, even in chips that are operated in a CO2 incubator and occasionally taken out for microscopic observations, no considerable temperature gradients are formed. This ensures that aside from convection due to the applied flow, no other source of convection affects the function of microfluidic cell culture chips [4].
Figure 2. A schematic view of the relative magnitude of mass transfer in x, y and z-direction in a (A) traditional cell culture vessel and (B) microfluidic cell culture chip.
2.2. IN VIVO LIKE PROPERTIES
The primary goal in using perfusion based microfluidic cell culture chips is to achieve a high degree of control over the microenvironment that the cultured cells are exposed to, i.e. to create a microenvironment that resembles the one cells are exposed to in vivo. In order to illustrate the difference between traditional culture vessels and perfusion based microfluidic cell culture chips, an “effective culture volume” (ECV) has been proposed as a descriptive concept [4]. ECV is a combined function of the characteristic mode of mass transfer (convection or diffusion), the magnitude of the mass transfer in all directions (x, y, z) in space (Fig. 2) as well as the extent of protein adsorption to the surfaces in a system. In vivo systems, e.g. tissue as part of an organ, are characterized by a fluid volume that is comparable to the volume of the cells in the tissues as well as by diffusive mass transfer. Based on these features the ECV of in vivo systems is small. To facilitate a semi-quantitative comparison of mass transfer in traditional in vitro culture vessels and perfusion based microfluidic cell culture chips, the Péclet number (Eq. 1) has been used [4]:
Pe =
vL D
(1)
where v is the velocity by which mass transfer takes place, L is the length in a certain direction (x, y, or z) in space and D is the diffusion coefficient. The smaller the calculated Péclet number is the more diffusion dominates in a system. Due to the large distances as well as a comparable velocity of mass transfer in all directions in traditional culture vessels, the characteristic Péclet numbers are large. The opposite is valid in microfluidic culture chips, where all the distances are short and a significant convective mass transfer at a low velocity only takes place in x-direction.
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Another way of describing mass transfer in culture systems is surface area to volume (SAV) ratio [4]. Especially, in systems with gas permeable walls, such as microfluidic cell culture chips made of a gas permeable polymer, e.g. polydimethylsiloxane (PDMS), large SAV characterizes the efficiency of gas equilibration in the system. The calculated values of SAV can show a large variation between traditional cell culture vessels and microfluidic cell culture chips with different dimensions, ranging from the value of 6.3 cm–1 for a Petri dish with a 60-mm diameter and 5 ml of culture medium to the value of 780 cm–1 for a microfluidic channel with the dimensions 53 µm (width) × 50 µm (height) × 7 mm (length) [5]. Aside from the efficiency of mass transfer, SAV also influences adsorption of proteins and other biomolecules on the walls of a culture system that generally are hydrophobic. The larger the value of SAV is the greater is the observed adsorption. The disadvantage of increased adsorption is the potential removal of necessary biomolecules that are either available in the utilized cell culture medium or secreted by the cells. However, for many in vitro cell culture applications, the utilized cell culture surfaces have to be coated with an adhesion promoting factor, such as a polyelectrolyte (poly-D-lysine or polyethyleneimine) or an extracellular matrix (ECM) component (laminin or collagen). Such a coating can also alleviate the problem caused by increased adsorption of biomolecules. Based on the above described properties of different in vitro cell culture systems, traditional culture vessels are associated with a large Péclet number and a small SAV as well as a very small cell volume to medium volume ratio. As a consequence of the these properties, the ECV of any traditional culture vessel is very large, meaning that in the experimental design, there is no possibility to create a microenvironment to resemble that of in vivo systems. On the other hand, in the design of microfluidic cell culture chips, the characteristic dimensions can be chosen to give a small Péclet number, large SAV and a cell volume to medium volume ratio that approaches unity. This ability to tailor make the properties of a cell culture system to resemble the ones that cells are exposed to in vivo is one of the fundamental driving forces behind research targeting the development of perfusion based microfluidic cell culture systems. 3. Design of Perfusion Based Cell Culture Chips When designing perfusion based microfluidic cell culture chips, the primary areas of concern are the type of flow profile a system generates and an appropriate approach for fluid delivery into the system that facilitates the planned cell based experiments. Upon making a structural design that meets the set requirements, the subsequent step comprises the choice of material and method of fabrication suitable for the chosen material.
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3.1. FLOW PROFILES
Although numerous cell culture chip designs and corresponding applications have been published until the present, they all primarily represent a variation of two basic structures: a microfluidic channel (type 1) or a chamber with various inlets (type 2). The existing flow profiles in a microfluidic system can be divided into those of vertical (see Section 3.1.1) and lateral (see Section 3.1.2) flow. The significance of the vertical flow profile is determined by whether the stream lines of the applied flow reach the bottom of a system, hence directly exerting an effect on the growing cells. The lateral flow is significant in determining whether the applied flow is uniform throughout the lateral space of a channel or chamber. Finite element simulations using, e.g. COMSOL Multiphysics, provide an easy way of testing whether a preliminary design possesses the desired flow profile. 3.1.1. Vertical Flow Profile Figure. 3a, b show microscope images of culture systems having microfluidic channels (type 1) [5] and chambers (type 2) [6], respectively. Figure 3c, d shows schematic drawings of the systems of type 1 and 2, respectively, and Fig. 3e, f shows finite element simulations of the vertical flow profile in terms of a velocity field for the systems. Especially, in the case of the simple microfluidic channel of type 1, the velocity field of the applied flow uniformly covers the entire height of the channel. Even in the case of the chamber of type 2, the bottom of which is slightly below the inlet and outlet (in the presented case the height difference is 50 µm), the velocity field of the applied flow reaches the bottom at such a distance that the cells can directly be affected. Hence, in spite of how low a flow rate is being chosen (1.3 µl/h in type 1 and 0.94 µl/h in type 2), the cultured cells can be exposed to shear stress if the applied flow reaches the bottom of the system where the cells reside. Shear stress (τ) can be described by Eq. (2):
τ=
6 μQ 2
h w
(2)
where µ is the viscosity, Q is the volumetric flow rate, h is height and w is the width of the system. In the presented cases, successful cell culture
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Figure 3. A microscope image of microfluidic cell culture chips having (A) channels (type 1) (Reprinted with permission from Ref. [5], copyright 2005 The Royal Society of Chemistry) and (B) chambers (type 2) (Reprinted with permission from Ref. [6], copyright 2006 American Chemical Society). A schematic view and finite element simulation of the vertical flow profile (velocity field) of type 1 (C and E) and type 2 (D and F).
experiments could be performed using myoblasts (type 1) and primary hepatocytes (type 2). However, the chosen design features and operational parameters have to be adapted to the cell type to be cultured. In the case of certain cell types, such as endothelial cells lining the blood vessels, shear stress represents the normal in vivo environment, and is hence a desired feature in a culture system, only achievable in a microfluidic cell culture chip in contrast to laboratory-scale cell culture vessels. Since usually no information is available regarding the specific requirements of a cell type,
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different designs may need to be tested in order to find one that provides relevant conditions for the planned experiments. If the goal is to minimize the shear stress influencing the cells, three parameters in Eq. (2) can be altered, i.e. the volumetric flow rate can be decreased and the height or width of the system can be increased. The simplest alternative is to increase the height of the system since the effect of changing the flow rate, albeit easily tested through simulations, may severely affect the mass transfer in the system and an increase in the width cannot necessarily be implemented without also increasing the footprint of the entire system. Figure 4a shows a cell culture system where the height difference between the channels and the bottom of the chamber has been increased to 1 mm [7, 8] (type 3). The velocity field (Fig. 4b) clearly indicates that the stream lines of the applied flow pass the bottom at a distance where the cultured cells are not directly affected by the flow; instead the nutrients are transported to the cells and the metabolic waste away from the cells solely by diffusion. Although the system of type 3 is functional in cell culturing [7] effectively eliminating shear stress, it possesses a limitation if the intended usage is to study transient biological responses to administered cellular effectors. This is caused by the increased height, which increases the diffusion distance of the effectors to the cells. In this specific case, even a considerable increase in the volumetric flow rate from the applied flow rate of 1.7 µl/min cannot remove the limitation in mass transfer. Hence, if the system of type 3 is to be used for studying cellular responses, further optimization of the height is needed. A.
B. x10− 3
Max: 1.526e-5 −5 x10 1.4 1.2 1 0.8
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2 1.5 1 0.5
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0 −0.5 −0.015 −0.01 − 0.005
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Figure 4. (A) An image of a microfluidic cell culture chip having 1 mm height difference between the bottom of the chamber and the channels (type 3) (inset: An enlargement of a flow equalizer that generates an even lateral distribution of streamlines). (B) A finite element simulation of the vertical flow profile (velocity field) of the system in (A). (Reprinted with permission from Ref. [8], copyright 2008 The Chemical and Biological Microsystems Society.)
3.1.2. Lateral Flow Profile The simulations of the vertical flow profile only show a cross-sectional view of a channel or chamber. However, whether such a cross-sectional view is valid throughout the lateral area of a channel or chamber is dependent on the uniformity of the lateral flow profile of the studied system.
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In the narrow channels representing type 1 in Section 3.1.1, the applied flow is uniform throughout the lateral area of each channel. However, the same system also has wider channels (width 1.2 mm) with three inlets and outlets. Figure 5a shows the velocity field of such a channel, indicating that the stream lines are clearly focused toward the midsection of the channel. Figure 5c, e show velocity fields for the same channel under the hypothetical premise that the channel only has a single inlet and outlet. The simulations show that for straight channels, a decreasing width of the inlet increases the focusing of the stream lines toward the midsection of the channel. In the case of the chamber of type 2 in Section 3.1.1, Fig. 5b shows the velocity field of the system, indicating strong limitations in the uniformity of the lateral flow profile. Even an increase in the number of inlets and outlets cannot improve the situation in this type of a system (Fig. 5d). Only by making the chamber elongated with a gradually widening inlet and outlet (Fig. 5f), the uniformity of the lateral flow profile can be improved. Type 3 of Section 3.1.1 represents an alternative approach to achieve a genuinely uniform lateral flow profile, which is very little dependent on the applied flow rate. Figure 6 shows the velocity field of the system and the inset of Fig. 4a shows a flow equalizer that facilitates the generation of uniform lateral flow.
Figure 5. Finite element simulations of lateral flow profile (velocity field) of (A) type 1 and (B) type 2 system. Modified versions of type 1 (C and E) and type 2 system (D and F).
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Figure 6. Finite element simulation of lateral flow profile (velocity field) of type 3 system with flow equalizers. (Reprinted with permission from Ref. [8], copyright 2008 The Chemical and Biological Microsystems Society.)
3.2. FLUID DELIVERY
Fluid delivery into a microfluidic cell culture chip has three primary purposes: (i) cell seeding, (ii) perfusion with culture medium, and (iii) introduction of cellular effectors during an assay. In the simplest format, a system has one inlet, which is used for all three purposes (Fig. 4a). If the fluidic path that is used for cell seeding is long and has multiple branches such as the flow equalizer in Fig. 4a, premature sedimentation of cells along the fluidic path is easily the consequence. In order to alleviate such a problem, a dedicated inlet for cell seeding is recommended; such a system is shown in Fig. 7a [7]. The system has, however, a common inlet for perfusion with culture medium and introduction of cellular effectors.
Figure 7. Microfluidic cell culture chip with (A) a dedicated inlet for cell seeding and (B) an inlet for perfusion with culture medium and an orthogonal inlet for concentration gradient generation. (Reprinted with permission from Ref. [9], copyright 2004 Wiley Periodicals Inc.)
As already was pointed out in Section 3.1.1, the system depicted in Fig. 4a does not provide a sufficiently fast mass transfer to facilitate an assay to study transient responses to cellular effectors. Above, a suggested
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improvement was a further optimization of the height difference between the channels and the bottom of the chamber. An alternative approach would be to retain the inlet with the present height difference but construct an additional inlet with a decreased height difference to obtain fast mass transfer for introduction of cellular effectors. Another reason why perfusion of culture medium and introduction of a cellular effector should preferably be designed using separate inlets is the necessity to introduce different concentrations of the effector in order to acquire a complete concentration response profile. Figure 7b depicts a system with an inlet for perfusion with culture medium and an orthogonal inlet for concentration gradient generation. 3.3. CHOICE OF MATERIAL
Materials that are chosen for fabrication of microfluidic cell culture chips have to possess properties that provide a biocompatible environment for the cultured cells. However, biocompatibility is not a concept with a straight forward definition. A material that facilitates good cell adhesion and growth, resulting in formation of normal cell morphology may for certain experiments be considered as biocompatible.3 Such a material may, however, still cause changes in the cellular gene expression profile [10], making it unsuitable for experiments that are strictly dependent on an unaltered expression of certain genes. Most of the published microfluidic cell culture chips are predominantly fabricated of materials that facilitate fast prototyping; however, no profound characterization of their biocompatibility has been performed. Hence, in order to recognize microfluidic cell culture chips, not just as an alternative for traditional laboratory-scale culture vessels, but as a concept that can facilitate cell culture experiments with an added value unavailable in traditional culture systems, such as automated high-throughput cell based assays, more research has to be devoted to systematic elucidation of the biocompatibility of materials that are presently being used or could be used for fabrication. The most widely used material for fabrication of microfluidic systems, and hence also microfluidic cell culture chips, is PDMS, which in many systems is utilized in combination with glass. PDMS is fabrication wise well suited for prototyping, whereas it is not in the same degree amenable to mass reproduction. A new emerging trend is, however, fabrication using thermoplastic polymers, such as polymethylmethacrylate (PMMA), cyclic olefin copolymer (COC) and polycarbonate (PC), which can be used for
______
3 Since many fabrication materials are primarily tested by observing their ability to facilitate formation of normal cell morphology and growth kinetics in comparison with commercial cell culture vessels, a better term instead of biocompatibility would be biocomparability.
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both mass reproduction and prototyping. Inherently, PDMS and thermoplastic polymers have different properties, which make them suitable materials for a different set of applications. Together, these materials and the necessary fabrication techniques form a complementary toolbox to realize different types of microfluidic cell culture chips depending on the experimental requirements for specific applications. 3.3.1. PDMS PDMS is an inexpensive transparent silicon based elastomer that in virtue of its general optical properties and insignificant autofluorescence is highly suitable for applications relying on microscopic monitoring. Based on cell culture tests involving monitoring of growth kinetics and morphological characterization of several cell types on PDMS surfaces that have undergone different treatments, the material is considered to be non-cytotoxic [11, 12]. However, concern has been raised regarding adsorption/absorption of proteins and smaller biomolecules on its hydrophobic surface or in its pores and crevices [13–16], as well as leakage of uncured oligomers from the polymer matrix [13]. Adsorption/absorption of biomolecules primarily results in depletion of necessary factors provided by the medium or secreted by the cells. It is an equilibrium-based phenomenon resulting in partitioning of the biomolecules between the PDMS material and the aqueous phase. Consequently, in a fluidic environment, new biomolecules (in the case of those provided by the medium) continuously arrive and are adsorbed/absorbed while a portion of the previously adsorbed/absorbed ones are detached from the PDMS material. As long as there is a sufficient supply of biomolecules in the medium, cell growth is not hampered. However, small molecules and proteins that are secreted by the cells and necessary for control of cellular functions (autocrine and paracrine factors) can potentially be removed to an extent strongly competing with the cellular capacity to excrete them. Secondly, adsorption of proteins, even if they were supplied by the medium and only transiently adsorbed on the hydrophobic surface of PDMS, causes an even more severe problem. The hydrophobic interaction of proteins with PDMS results in their denaturation due to the exposure of the hydrophobic core of the protein. The efficient gas permeability of PDMS imposes some restrictions to the usage of the fabricated microfluidic cell culture chips. PDMS allows equilibration of the culture medium with oxygen directly from the ambient, and upon need of additional oxygenation, thin PDMS membranes (ca. 100 µm thick) can be used for controlled oxygenation of the culture medium [6]. However, in an analogous way, due to this efficient gas permeability, the chips release CO2 unless kept in a CO2 incubator, thus changing the pH inside the cell culture chamber. Consequently, PDMS-based chips cannot
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be operated on a microscope stage to facilitate continuous monitoring by time-lapse microscopy unless an incubator is adapted to the stage. Gas permeability also causes permeation to water vapor [13], which even inside a humidified CO2 incubator results in evaporation, and consequently increased osmolality. Since its description by Duffy et al. [17], soft lithographic prototyping of microfluidic systems using PDMS has been touched in many publications. Briefly, a mixture of curing agent and PDMS base (usually 1:10 ratio) is casted on a master that is a negative structure of the microfluidic system to be fabricated. Masters can be fabricated using a variety of machining techniques on different polymeric materials or UV lithography to machine silicon wafers or pattern a positive or negative photoresist, e.g. SU-8, on silicon or borosilicate wafers. Curing of PDMS can be done at either ambient temperature or at an elevated temperature. PDMS can be used to fabricate a complete system comprising the bottom, microfluidic channels and chamber together with the lid. A widely adopted approach is, however, to fabricate the microfluidic channels and chamber of PDMS and sandwich them between solid substrates, such as glass slides. Oxidation of PDMS by, for instance, oxygen plasma [17] or corona [18] treatment renders the surface with hydroxylic functionalities as part of the silicon network, capable of irreversible bonding with a clean and dry glass surface or another PDMS surface. (A schematic illustration of soft lithographic prototyping and bonding of PDMS can be found in Ref. [19].) 3.3.2. Thermoplastic Materials Limitations of PDMS-based microfluidic cell culture chips, i.e. gas permeability and pronounced absorption of biomolecules, have led to development of systems based on alternative polymeric materials. Thermoplastics, such as PMMA, COC and PC, are examples of inexpensive transparent polymers possessing optical properties that facilitate development of systems suitable for microscopic monitoring. Thermoplastics have, however, significant autofluorescence at certain characteristic excitation wavelengths, the influence of which has to be determined when developing chips for specific applications. Based on preliminary tests performed by different workers, thermoplastic materials are considered to be non-cytotoxic. However, such tests have primarily involved monitoring of cell morphology and growth kinetics. In a more detailed study published by Stangegaard et al. the function of PMMA as cell culture substrate for HeLa cells was characterized using gene expression profiling. COC has also been approved by the U.S. Food and Drug Administration (FDA) as biocompatible [14]. The obtained results indicated that material wise PMMA is comparable to commercial polystyrenebased cell culture substrates. Despite the fact that thermoplastic polymers possess surface functionalities, such as acrylate groups, that render the
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surfaces with a certain degree of hydrophilicity, contact angle measurements have indicated that the surfaces are, however, so strongly hydrophobic [20] that absorption of biomolecules can be pronounced. Thermoplastic polymers are not, however, as porous as PDMS [14], which means that absorption primarily takes place on the polymer surface. Since thermoplastic polymers are not gas permeable, the usage of the fabricated microfluidic cell culture chips is not dependent on a humidified CO2 incubator. This means that experiments can be performed on, for instance, a microscope stage to facilitate time-lapse microscopic monitoring. In such systems, constant osmolality is maintained since no evaporation takes place. Hence, the only basic requirements are a supply of culture medium that has been equilibrated with O2 and CO2 and a temperature control system independent of an incubator, such as an integrated resistive indium-tin oxide (ITO) film based heater [7] or a Peltier-type semiconductor element [8]. The possibility to use a microfluidic cell culture chip independent of an incubator, significantly increases the number of degrees of freedom in experimental design, paving the way to implementation of systems that facilitate high-throughput real-time monitoring of cellular responses throughout growth and differentiation instead of only performing endpoint detection. Fabrication of microfluidic cell culture chips of thermoplastic polymers is possible based on both replication and micromachining techniques [21, 22]. Replication techniques comprise, for instance, casting, injection molding and hot embossing, while laser ablation and micromilling are examples of micromachining techniques. In the context of system development, micromachining techniques that facilitate fast prototyping are the most significant ones, and hence briefly described here. (More detailed description of the techniques can be found elsewhere [23, 24].) Both techniques are based on controlled removal of the polymer to form the fluidic channels and chambers. The used polymer materials are obtained from commercial sources as extruded sheets. In laser ablation, a computer-controlled system directs laser pulses to the polymer surface. Commercial laser ablation instruments utilize, for instance, eximer lasers (UV range) or CO2 lasers (IR range). In the case of eximer lasers, the UV light directly disrupts bonds in the polymer molecules forming short fragments that become volatile as result of the elevated temperature generated by the laser pulses. IR generated by CO2 lasers heats the polymeric material causing heat induced scission the polymer molecules and, in an analogous way as eximer lasers, volatilization of the small molecular fragments. The chosen type of laser, as consequence of the wavelength range, influences the resolution of an instrument. Generally, the depth and width of fluidic channels is determined indirectly by adjusting the power, frequency and sweep rate of the laser pulse. This means that a certain channel depth
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results from optimization of process parameters. Furthermore, the profile of the created channels is dependent on whether a single beam pass or multiple beam pass has been applied. In the first case, V-shaped channels (Fig. 8a) are formed, whereas in the second case, the channels become more Gaussianshaped (Fig. 8b). A consequence of the laser effect on the polymer, a considerable bubble formation, and hence increased porosity has been observed in laser ablated zones (Fig. 8b). Although the formed porosity only influences the created channels, not the regions that directly form the cell culture substrate, it may contribute to increased absorption of biomolecules supplied in the culture medium. For a deeper understanding of the behavior of thermoplastic systems, this aspect should be studied more systematically. In micromilling, a computer-controlled system is used to operate small cutting tools that in multiple passages remove the polymer from regions where channels are to be defined. This means that the channel depth and width can be precisely determined and these are only dependent on the accuracy of the servo-control of the utilized instrument and cutting tool, respectively. The walls of the created channels become fully vertical (Fig. 8c). Although the channels have a certain surface roughness as consequence of the milling process, no porosity has been observed.
Figure 8. Microscopic images of channel geometry as the result of laser ablation based on (A) single and (B) multiple beam pass as well as (C) micromilling.
All the parts of microfluidic cell culture chips, i.e. the machined part comprising the microfluidic channels as well as the lid and bottom, are fabricated of the chosen thermoplastic polymer. This means that all these components have to be bonded to each other to complete the fabrication of a chip. Prior to bonding, all the components have to be thoroughly cleaned with ethanol to remove the lubricant that remains from the industrial fabrication of the used polymer sheets as well as the polymer fragments that are formed during machining of the components to be bonded. Bonding of thermoplastic components can generally be done under increased pressure and elevated temperature. During the procedure, the applied heat induces diffusion of the polymer molecules to form an irreversible sealing between two adjacent polymer components. Two alternative approaches of heatassisted bonding can be used: (i) Purely heat assisted and (ii) UV-heat – assisted bonding. In the former case, the applied temperature needs to reach the glass transition temperature (Tg) of the polymer, whereas in the latter
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one a lower temperature (80–100°C) can be applied. The reason why a different applied temperature is needed for bonding can be explained based on the effect of the UV-treatment which can disrupt bonds in the polymer molecules, resulting in formation of smaller fragments that more easily undergo inter-diffusion between the polymer components to complete the bonding. Commercially available polymer sheets that are used for fabrication have a considerable batch-to-batch variation, which affects, for instance, the size distribution of the polymer molecules, ultimately affecting the Tg and ethanol solubility (considerable in the case of PMMA). Due to these reasons, optimization of the bonding procedure may be required for a new batch of polymer. This primarily concerns the choice of temperature and degree of compression. However, changes in ethanol solubility due to batch-to-batch variation can also influence cleaning of the machined polymer components. Especially in the case of laser ablation, ethanol can enter the pores created in the laser ablated regions and swell the polymer, causing disruption of fluidic channels. In the case of some polymer batches, it has been necessary, for instance, to preheat the machined polymer components for 20–30 s at a temperature close to the Tg. This closes the pores to such an extent that the tendency for swelling is eliminated. 4. Operation of Perfusion Culture and Cell Based Assays Up to the present, an increasing number of applications using perfusion based microfluidic cell culture chips have been published using a variety of cell types. However, due to the different type of fabricated chips and applications, no general protocols are available in a way corresponding as in traditional in vitro cell culture. It is, though, possible to outline the general steps of the necessary procedures with guidelines regarding significant factors to be taken into consideration. Common to all cell culture experiments in microfluidic cell culture chips is the chip preparation comprising sterilization as well as surface coating with an adhesion factor if required by the utilized cell type. Following chip preparation, the fluidic operations include cell seeding, perfusion culture (including cell differentiation if applicable for the conducted experiment) and cell based assay. A variety of techniques have been applied for sterilizing microfluidic cell culture chips and covered by reviews [12, 25] and references therein, such as autoclaving, UV light, oxygen plasma, gamma irradiation, ethylene oxide exposure and perfusion with ethanol, hypochlorite or sodium hydroxide. The applicability of the different techniques primarily depends, aside from what is available in a laboratory, on the type of system and the fabrication material. Autoclaving is an effective method but not suitable for chips fabricated of thermoplastic polymers. The applied temperature and pressure
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can cause deformation of the polymeric materials. On the other hand, temperature tolerance of PDMS-based chips is good and these can be effectively sterilized by autoclaving. For thermoplastic chips, the simplest techniques to apply are those involving perfusion with ethanol or an aqueous solution. Due to ethanol solubility of, for instance, PMMA, ethanol perfusion may break the chips, and hence hypochlorite or sodium hydroxide perfusion the most suitable ones, especially the latter of which has proven to be, aside from efficiency, also a fast technique. Even a 5-min treatment with 500 mM NaOH has been sufficient to completely sterilizing a system with a complex network of channels. When using perfusion with a chemical, thorough rinsing is crucial in order to remove the chemical. If NaOH is used perfusion with cell culture tested phosphate buffer is significant to adjust the pH in all the microenvironments of a chip. Direct perfusion with culture medium, prior to using phosphate buffer, is not advisable since coagulation of serum proteins in the microenvironments is possible as consequence of the high pH. In the case of UV light, despite its general suitability to different materials, it is necessary to carefully determine the permeability of the chosen fabrication material in order to ensure that the internal compartments of a chip can be penetrated by the applied UV exposure. Especially, in the case of thermoplastic chips, machined regions may become opaque decreasing permeability to UV. If the utilized cells require coating with an adhesion factor, such as a polyelectrolyte, e.g. poly-D-lysine or polyethyleneimine, or an ECM component, e.g. collagen or laminin, this is done most easily by filling the chip with a solution having a sufficient concentration of the factor and letting it stand for an appropriate time, usually for at least 1.5–2 h. For thermoplastic chips, which are bonded at elevated temperature, this is the only option in order not to destroy the coating. On the other hand, in the case of PDMSbased chips using, for instance, a glass bottom, it is possible to initially coat the entire glass surface or pattern it with the necessary adhesion factor prior to bonding the chip. This is made possible by the fact that all the components can be sterilized separately prior to coating or patterning, followed by oxygen plasma treatment of the PDMS part of the chip after which the chip can be bonded. After completed preparation of a chip, cell seeding is the first task in conducting the planned cell culture experiment. Seeding can be done either using a syringe pump or by manual injection. The most crucial factor to be considered is the rate of injection in order not to harm the cells and, on the other hand, not to allow premature sedimentation of cells along the fluidic path. The latter may easily be the consequence if a system does not have a dedicated short channel for cell seeding. Furthermore, the longer the utilized channel the more difficult it is to determine the cell density during seeding since a considerable number of cells may remain in the channels.
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Subsequent to cell seeding, a lag period is required prior to starting perfusion with medium. This is necessary to ensure a sufficient cell adhesion. During perfusion with medium, to facilitate either growth or differentiation, the chosen volumetric flow rate is very crucial. It influences, in terms of the geometry of the fabricated chip, whether shear stress is induced affecting the cells. It has to be noted, however, that shear stress is not automatically a factor that should be eliminated. In the case of, for instance, endothelial cells from blood veins shear stress may be needed as a factor influencing the cells. In such a case, a perfusion based microfluidic cell culture chip clearly provides conditions that are not available in traditional cell culture vessels. Aside from shear stress, the applied flow rate also influences how fast chemicals are removed from the microenvironment the cells encounter. In the case of metabolic waste a sufficiently fast removal can be optimal. However, the biomolecular factors secreted by cells should have a sufficient residence time to ensure that they can exert the necessary biological effect. Hence, to find a suitable flow rate it is necessary to balance between all the different factors, induced shear stress, removal of metabolic waste and removal of cell secreted factors. Considering the complexity of the situation, pilot experiments are required to adjust the flow rate to both the geometry of the chip and the utilized cell type. In connection with cell based assays that are to be conducted after completed cell growth or differentiation, oftentimes a certain cellular effector needs to be introduced to determine the cellular response. Depending on how fast the studied response is the applied flow rate has to be adjusted in order to provide a sufficient mass transfer so that the utilized cellular effector promptly reaches the cells. A suitable flow rate during a cell based assay can be several times higher than that applied during perfusion culture. For determining dopamine exocytosis, i.e. release of dopamine, from rat pheochromocytoma cells, Cui et al. applied a volumetric flow rate of 300 µl/min to apply 20-µl pulses of the secretagogue K+ to induce exocytosis [26]. However, it has to be emphasized that even an increased flow rate cannot provide a sufficient mass transfer for an optimal cell based assay unless the geometry of the fabricated chip facilitates this (see discussion in Section 3). In contrast to fast cellular responses, certain processes may require stimulation over several hours, which mean that the flow rate does not need to be increased, at least not significantly, from the one applied during perfusion culture. 5. Applications of Perfusion Based Cell Culture Chips Due to the over 100 years of development, in vitro cell culture techniques and systems have reached such a state of development and acceptance that, despite some general advantages of perfusion based cell culture chips, such
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as small ECV, the fabrication and usage of these systems is not justifiable unless the experiments that can be performed provide a technological added value and answer biological questions, which is not possible in traditional in vitro systems. In this section, the present developments in perfusion based microfluidic cell culture chips are outlined, highlighting systems that (i) utilize gradient formation, (ii) facilitate high-throughput experiments, and (iii) enable organ mimicking. 5.1. GRADIENT SYSTEMS
The flow rate and thus the convection rate in a microfluidic cell culture chip can be set precisely with a high degree of spatial and temporal control simply by adjusting pump speed. The diffusion rate is determined by the diffusion constant of the compounds in the medium where diffusion takes place. It is therefore a straight forward task in a fluidic system to create gradients of compounds or sharp boundaries between media with different composition over biological specimens to, for instance, deduce mechanism of chemotaxis [27] and understand how polarity is created in Drosophila embryos by exposing one side of a 400 µm embryo to hot medium and the other side to cold medium [28] (Fig. 9a). Furthermore, since convection can be controlled with micrometer precision in microfluidic systems, it is possible to generate complex gradient patterns (Fig. 9b), facilitating applications with a large number of different concentrations on either a linear [9] (Fig. 7b) or logarithmic [29] scale. Such systems are capable of automated generation of concentration-dependent responses, which can be utilized in highly parallelized systems to achieve high-throughput screening of, for instance, drug candidates in drug discovery as well as toxic compounds originating
Figure 9. (A) A schematic illustration of a microfluidic cell culture chip with a Drosophila melanogaster embryo exposed to cold and warm medium in a gradient forming intersection of two merging fluidic paths (left panel) and microscopic image of an embryo in the system. (Reprinted with permission from Ref. [28], copyright 2005 Nature Publishing Group.) (B) A finite element simulation to visualize generation of a stable gradient in perfusion systems.
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from industrial production or uncontrolled development of chemical and biological warfare agents. However, a great deal of research has to be devoted to study the stability of these gradients. Furthermore, the function of gradient generators is susceptible to bubbles in microfluidic channels to the extent of complete destruction of the conducted experiments without any possibility to trace back what caused the encountered problem. 5.2. HIGH-THROUGHPUT SYSTEMS
However, not all the examples given above are mainstream biological experiments in which a number of factors are tested against another set of factors to determine a mechanism. Such tests have successfully been performed in batch cultures and can be scaled up to large combinatory experiments using microtiter plates and robotics [30]. Several attempts have been made to implement high-throughput cell analysis in terms of perfusion based microfluidic cell culture chips. All the different systems represent ways of parallelization; however, the different approaches facilitate different type of high-throughput experiments. The published applications represent the following categories [25]: Systems with (i) microarrays, (ii) gradient generators, (iii) valved arrays, and (iv) individually addressable channels. Microarrays have a high density of positions to accommodate a large number of different cell types [31] (Fig. 10a). Limitation in implementation of fluidic connections and pumping system is limiting the scale of the experiments that are possible to perform, primarily facilitating experiments with only one soluble factor at a time. Recent advances in interconnection (>144 experiments/cm2) to be performed [32] (Fig. 10b, c). Gradient generating systems, discussed above, facilitate experiments using only one cell type at a time to be tested with different concentrations of one soluble factor. Systems incorporating valved arrays provide the capability to control seeding of different cell types and their subsequent testing using several soluble factors [33] (Fig. 10d). Another variant of valved arrays is presented in Fig. 10e, showing a system that utilizes integrated peristaltic pumps and multiplexing to address any individual chamber or a group of chambers [34]. An alternative approach to high-throughput perfusion systems is based on individually addressable channels, utilizing the fact that fluids can enter into microfluidic networks by capillary forces. This phenomenon is the fundament of an interconnection and pump free high-throughput perfusion system where robotics control the addition of medium to an array of fluidic channels that follows the footprint and layout of a microtiter plate [35, 36] (Fig. 10f).
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Figure 10. Microfluidic cell culture chips for high-throughput cell culture experiments featuring: (A) microarray. (Reprinted with permission from Ref. [31], copyright 2004 Nature Publishing Group.) (D) 8 × 8 valved array. (Reprinted with permission from Ref. [32], copyright The Royal Society of Chemistry 2007.) (E) 96-chamber valved array with integrated peristaltic pump. (Reprinted with permission from Ref. [33], copyright 2007 American Chemical Society.) (F) 192-channel array with individually addressable microchannels in microtiter plate format. (Reprinted with permission from Ref. [34], copyright The Royal Society of Chemistry 2008.) (B) An image of a 12-channel peristaltic pump for submicroliter fluid delivery to microarray systems to be used in recombinatorial cell-based assays. (Reprinted with permission from Ref. [35], copyright The Royal Society of Chemistry 2009.) (C) A schematic view of recombinatorial experiments featuring the orthogonality between cell seeding and introduction of soluble factors.
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5.3. 3D CULTURE SYSTEMS
Both traditional in vitro cultures and perfusion based microfluidic cell culture chips are based on monolayers of adherent cells. Although such cultures have generally been accepted as model systems representing cellular functions, increased interest has been directed toward 3D cultures in vivo like cell–cell and cell–ECM contacts are formed, resembling the organization of tissues. This approach has been proposed for cell based assays using traditional systems [37]. The biological relevancy in using 3D culture systems has also increased interest in constructing perfusion based microfluidic 3D cell culture chips. The general approach is based on incorporating cells in a suitable matrix that supports formation of cell–cell contacts in 3 dimensions. The matrix with cells is then confined in a microfabricated scaffold allowing perfusion to provide culture medium. The three basic variants of scaffold and perfusion are (i) well with perfusion from above [38] (Fig. 11a), (ii) micropillar array rows with perfusion on the sides [39] (Fig. 11b), and (iii) micropillar array filled channels with flow through the matrix [40] (Fig. 11c). In the case of scaffolds in well and micropillar array row format, the flow passes the matrix with the cells and only diffusion from the side of the matrix takes nutrients to the cells and metabolic waste away from the cells. On other hand, in the case of scaffold where micropillar arrays fill the whole channel, the property of ECM matrix to shrink upon solidification at 37°C has been utilized to create a channel through the matrix to facilitate effective mass transfer in the system. The concept of micropillar arrays filling channels has been further developed to obtain parallelized arrays of arrays with gradient generation as an approach to achieve high-throughput 3D culture in chip format [41] (Fig. 11d). 6. Conclusions Powerful biological experimental setups can be realized with miniaturized perfusion chambers. Spatial and temporal control over growth factors can mimic in vivo conditions and enable testing of the importance of these factors for various cellular functions. Even if strongly promising examples of the usability of cell perfusion systems exist, widely spread use of these systems is limited. One of the reasons is that perfusion chips can take many forms in terms of geometry and materials and, at present, little is known about the impact of these parameters on cell culture or, indeed, if these parameters can bias experiments. To couple usage of different designs to particular types of experiments is a major challenge for the future. Furthermore, reliable and standardized operating procedures for these chips need to be developed.
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Figure 11. Microfluidic cell culture chips for 3D cell culture experiments featuring perfusion (A) over a well. (Reprinted with permission from Ref. [38], copyright 2007 Elsevier BV.) (B) On the sides of micropillar row. (Reprinted with permission from Ref. [39], copyright The Royal Society of Chemistry 2007.) (C) Through a micropillar array. (Reprinted with permission from Ref. [40], copyright 2005 Wiley-VCH Verlag GmbH & Co. KGaA.) Accommodating the matrix containing the cells. (D) A parallelized system based on the concept in (C). (Reprinted with permission from Ref. [41], copyright 2007 Wiley-VCH Verlag GmbH & Co. KGaA.)
Acknowledgments The EU FP7 NMP project EXCELL is kindly acknowledged for financial support.
References 1. R.G. Harrison, Observations on the living developing nerve fiber, The Anatomical Record, 1, 116–118 (1907). 2. P.S. Dittrich and A. Manz, Lab-on-a-chip: Microfluidics in drug discovery, Nature Reviews Drug Discovery, 5(3), 210–218 (2006).
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3. J. El-Ali, P.K. Sorger and K.F. Jensen, Cells on chips, Nature, 442(7101), 403–412 (2006). 4. G.M. Walker, H.C. Zeringue and D.J. Beebe, Microenvironment design considerations for cellular scale studies, Lab on a Chip, 4(2), 91–97 (2004). 5. A. Tourovskaia, X. Figueroa-Masot and A. Folch, Differentiation-on-a-chip: A microfluidic platform for long-term cell culture studies, Lab on a Chip, 5(1), 14–19 (2005). 6. B.J. Kane, M.J. Zinner, M.L. Yarmush and M. Toner, Liver-specific functional studies in a microfluidic array of primary mammalian hepatocytes, Analytical Chemistry, 78(13), 4291–4298 (2006). 7. S. Petronis, M. Stangegaard, C.B.V. Christensen and M. Dufva, Transparent polymeric cell culture chip with integrated temperature control and uniform media perfusion, Biotechniques, 40(3), 368–376 (2006). 8. A. Heiskanen, C. Spégel, J. Tønnesen, Z. Fohlerova, L. Goulart, J. Hansen, M. Kokaia, T. Ruzgas, M. Dufva and J. Emnéus, Development of a microfluidic on-line culture system for combined electrochemical and optical real-time detection of cellular processes, Proceeding of the Twelfth International Conference on Miniaturized Systems for Chemistry and Life Sciences, October 12–16, 2008, San Diego, CA. 9. P.J. Hung, P.J. Lee, P. Sabounchi, R. Lin and L.P. Lee, Continuous perfusion microfluidic cell culture array for high-throughput cell-based assays, Biotechnology and Bioengineering, 89(1), 1–8 (2005). 10. M. Stangegaard, Z. Wang, J.P. Kutter, M. Dufva and A. Wolff, Whole genome expression profiling using DNA microarray for determining biocompatibility of polymeric surfaces, Molecular Biosystems, 2(9), 421–428 (2006). 11. J.N. Lee, X. Jiang, D. Ryan and G.M. Whitesides, Compatibility of mammalian cells on surfaces of poly(dimethylsiloxane), Langmuir: the ACS journal of surfaces and colloids, 20(26), 11684–11691 (2004). 12. L. Kim, Y.C. Toh, J. Voldman and H. Yu, A practical guide to microfluidic perfusion culture of adherent mammalian cells, Lab on a Chip, 7(6), 681–694 (2007). 13. M.W. Toepke and D.J. Beebe, Pdms absorption of small molecules and consequences in microfluidic applications, Lab on a Chip, 6(12), 1484–1486 (2006). 14. R. Mukhopadhyay, When pdms isn’t the best, Analytical Chemistry, 79(9), 3248–3253 (2007). 15. K.J. Regehr, M. Domenech, J.T. Koepsel, K.C. Carver, S.J. Ellison-Zelski, W.L. Murphy, L.A. Schuler, E.T. Alarid and D.J. Beebe, Biological implications of polydimethylsiloxane-based microfluidic cell culture, Lab on a Chip, 9(15), 2132–2139 (2009). 16. R. Mukhopadhyay, Hard-soft microfluidic device bypasses drawbacks of pdms, Analytical Chemistry, 81(13), 5108–5108 (2009). 17. D.C. Duffy, J.C. McDonald, O.J.A. Schueller and G.M. Whitesides, Rapid prototyping of microfluidic systems in poly(dimethylsiloxane), Analytical Chemistry, 70(23), 4974–4984 (1998). 18. K. Haubert, T. Drier and D. Beebe, Pdms bonding by means of a portable, low-cost corona system, Lab on a Chip, 6(12), 1548–1549 (2006).
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19. Folch Lab, 3d microfluidic devices, Research/Technology Development, (2007), Available from: http://faculty.washington.edu/afolch/FolchLabResearchProjects. htm#. 20. H. Shadpour, H. Musyimi, J.F. Chen and S.A. Soper, Physiochemical properties of various polymer substrates and their effects on microchip electrophoresis performance, 18th International Symposium on MicroScale Bioseparation (MSB 2005), Feb 12–17, 2005, New Orleans, LA. 21. H. Becker and C. Gartner, Polymer microfabrication methods for microfluidic analytical applications, Electrophoresis, 21(1), 12–26 (2000). 22. H. Becker and L.E. Locascio, Polymer microfluidic devices, Talanta, 56(2), 267–287 (2002). 23. D. Snakenborg, H. Klank and J.P. Kutter, Microstructure fabrication with a co2 laser system, Journal of Micromechanics and Microengineering, 14(2), 182–189 (2004). 24. P. McKeown, From micro- to nano-machining - towards the nanometre era, Sensor Review, 16(2), 4–10 (1996). 25. I. Meyvantsson and D.J. Beebe, Cell culture models in microfluidic systems, Annual Review of Analytical Chemistry, 1, 423–449 (2008). 26. H.F. Cui, J.S. Ye, Y. Chen, S.C. Chong and F.S. Sheu, Microelectrode array biochip: Tool for in vitro drug screening based on the detection of a drug effect on dopamine release from pc12 cells, Analytical Chemistry, 78(18), 6347–6355 (2006). 27. N.L. Jeon, H. Baskaran, S.K.W. Dertinger, G.M. Whitesides, L. Van de Water and M. Toner, Neutrophil chemotaxis in linear and complex gradients of interleukin-8 formed in a microfabricated device, Nature Biotechnology, 20(8), 826–830 (2002). 28. E.M. Lucchetta, J.H. Lee, L.A. Fu, N.H. Patel and R.F. Ismagilov, Dynamics of drosophila embryonic patterning network perturbed in space and time using microfluidics, Nature, 434(7037), 1134–1138 (2005). 29. L. Kim, M.D. Vahey, H.Y. Lee and J. Voldman, Microfluidic arrays for logarithmically perfused embryonic stem cell culture, Lab on a Chip, 6(3), 394–406 (2006). 30. C.B. Maddox, L. Rasmussen and E.L. White, Adapting cell-based assays to the high-throughput screening platform: Problems encountered and lessons learned, Journal of the Association for Laboratory Automation, 13(3), 168– 173 (2008). 31. D.G. Anderson, S. Levenberg and R. Langer, Nanoliter-scale synthesis of arrayed biomaterials and application to human embryonic stem cells, Nature Biotechnology, 22(7), 863–866 (2004). 32. P. Skafte-Pedersen, D. Sabourin, M. Dufva and D. Snakenborg, Multi-channel peristaltic pump for microfluidic applications featuring monolithic pdms inlay, Lab on a Chip, 9(20), 3003–3006 (2009). 33. K.R. King, S.H. Wang, D. Irimia, A. Jayaraman, M. Toner and M.L. Yarmush, A high-throughput microfluidic real-time gene expression living cell array, Lab on a Chip, 7(1), 77–85 (2007). 34. R. Gomez-Sjoberg, A.A. Leyrat, D.M. Pirone, C.S. Chen and S.R. Quake, Versatile, fully automated, microfluidic cell culture system, Analytical Chemistry, 79(22), 8557–8563 (2007).
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35. I. Meyvantsson, J.W. Warrick, S. Hayes, A. Skoien and D.J. Beebe, Automated cell culture in high density tubeless microfluidic device arrays, Lab on a Chip, 8(5), 717–724 (2008). 36. H.M. Yu, C.M. Alexander and D.J. Beebe, A plate reader-compatible microchannel array for cell biology assays, Lab on a Chip, 7(3), 388–391 (2007). 37. B.A. Justice, N.A. Badr and R.A. Felder, 3d cell culture opens new dimensions in cell-based assays, Drug Discovery Today, 14(1–2), 102–107 (2009). 38. M.H. Wu, S.B. Huang, Z.F. Cui, Z. Cui and G.B. Lee, Development of perfusion-based micro 3-d cell culture platform and its application for high throughput drug testing, Sensors and Actuators B-Chemical, 129(1), 231–240 (2008). 39. Y.C. Toh, C. Zhang, J. Zhang, Y.M. Khong, S. Chang, V.D. Samper, D. van Noort, D.W. Hutmacher and H.R. Yu, A novel 3d mammalian cell perfusionculture system in microfluidic channels, Lab on a Chip, 7(3), 302–309 (2007). 40. T. Frisk, S. Rydholm, H. Andersson, G. Stemme and H. Brismar, A concept for miniaturized 3-d cell culture using an extracellular matrix gel, Electrophoresis, 26(24), 4751–4758 (2005). 41. T. Frisk, S. Rydholm, T. Liebmann, H.A. Svahn, G. Stemme and H. Brismar, A microfluidic device for parallel 3-d cell cultures in asymmetric environments, Electrophoresis, 28(24), 4705–4712 (2007).
APPLICATIONS OF MAGNETIC LABS-ON-A-CHIP MARTIN A.M. GIJS
Laboratory of Microsystems, Ecole Polytechnique Fédérale de Lausanne, CH 1015 Lausanne EPFL, Switzerland,
[email protected]
Abstract. Using magnetic micro- and nanoparticles (beads) in microfluidic chips opens new perspectives for miniaturized applications in analytical sciences. Four important application areas of magnetic particles in microfluidic systems are discussed. The first one is that of manipulation of living cells. The latter can be labeled using magnetic beads that are specifically recognizing certain biomarkers on the cell surface. In this way, a well determined type of cells can be separated out of a complex matrix. Magnetic particles can also be used as substrates in a nucleic acid assay allowing specific detection and application in diagnosis. Immuno-assays represent another vast area of application for magnetic particles. The latter can either be used as mobile substrate in the assay, or the particle can play the role of magnetic detection label. Finally, a last field of application we discuss is the use of magnetic particles held in a microfluidic flow for catalytic applications.
1. Introduction Magnetic nanoparticles have been synthesized with a number of different compositions [1] that include iron oxides, such as magnetite (Fe3O4) and maghemite (γ-Fe2O3), pure metals, such as Fe and Co, or alloys, such as CoPt3 and FePt. Magnetic nanoparticles prepared from co-precipitation and thermal decomposition are the most widely studied. Synthesis in microfluidic chips is an alternative technique for very controlled realization of magnetic particles. Maintaining the stability of magnetic particles for a long time without agglomeration or precipitation problems is a prerequisite for applications. Particle protection results in magnetic beads having a core-shell structure, where the role of the shell is to protect the magnetic core against environmental influence. Besides protecting individual magnetic nanoparticles, it is also possible to embed a number of magnetic nanoparticles or magnetic material in a polymer or silica matrix to form composites. In this way, one can synthesize micro-beads that, due to a higher magnetic content, are more easy and rapid to manipulate magnetically than the primary magnetic S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_21, © Springer Science + Business Media B.V. 2010
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nanoparticles. Such types of beads (size around 1 μm) are therefore often used in microfluidic systems [2, 3]. A protective shell around a magnetic particle or a protective matrix not only protects the particle against degradation, but can also be used to functionalize the bead surface with specific molecules, like used in catalytic applications, or for use in experiments with proteins, cells, etc. Proteins may bind/adsorb to hydrophobic surfaces, such as found in polymer-coated beads, forming a monolayer that is resistant to washing. It may also be desirable to have a strong covalent binding between the particle surface and the protein. This is achievable through specific groups at the particle surface (–COOH –NH2, –CONH2, –OH groups) which via an activating reagent bind to –NH2 or –SH groups on the proteins. Also streptavidin, biotin, histidine, protein A, protein G, … can be grafted on the bead surface for specific biorecognition reactions. As-prepared silica-coated beads can be used to recover and purify the total DNA content of a lysed cell solution. For example, sample DNA can be bound to a silica surface after chemical cell lysis in a guanidine thiocyanate binding buffer. 2. Magnetic Cell Manipulation Most cell types are essentially non-magnetic and can be magnetically activated’ with magnetic nano- or microparticles using digestion of the particles by the cell or using a (specific) ligand–receptor interaction at the cell surface. The majority of literature data on magnetic bead-based cell separation deals with the separation of white blood cells, cancer cells or bacteria from serum or blood. Blood has two main components, plasma and cells, each representing about half of the blood volume. There are three main types of cells with different functions: erythrocytes or red blood cells, leukocytes or white blood cells and platelets. The specificity of antibodies to match a desired antigen on the cell surface has become a cornerstone in cell separation. Currently, the majority of commercial cell separation systems are based on fluorescent flow cytometers or other complicated instrumentation. The most commonly used methods for cell sorting are fluorescenceactivated cell sorting (FACS) [4] and magnetic cell sorting (MACS) [5]. Microfluidic systems have been used in combination with magnetic beads to separate unlabeled red blood cells from a raw blood sample [6] or to select specific types of white blood cells [7]. Rare cells, like stem cells [8] or circulating cancer cells, have been separated from a complex sample matrix. Also magnetically labeled bacteria have been separated from blood samples, as illustrated in Fig. 1.
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Figure 1. Separation of E. coli cells bound to magnetic nanoparticles in a flow (from left to right) of PBS in a 200 μm wide channel. The composite bright images were generated by overlaying sequential frames of corresponding movies taken at the beginning, middle and end (left to right) of the microfluidic channel, in the presence or absence of a neodymium disk magnet placed below the channel (bottom and top image, respectively) [9].
3. Magnetic Nucleic Acid Assays An application area where magnetic beads play a standard role is that of nucleic acid assays. In macroscopic lab-bench protocols, magnetic beads are generally used as mobile substrates for the capture and extraction of nucleic acids [10, 11]. With the increasing interest in the combination of microfluidics and magnetic beads, the step towards on-chip processing of nucleic acids is logical [12]. Publications demonstrated the feasibility of miniaturizing magnetic nucleic acid assays, while maintaining the procedures and protocols known from batch-type applications. Figure 2 summarizes the steps followed in an assay, where magnetic beads can be applied with differing purposes and at different phases of the assay. The first phase of the protocol involves the specific capture of the molecules of interest, and is followed by a washing or purification step to remove the matrix of unbound molecules. Some systems use the magnetic character of the beads in the detection step, where their stray field is measured, for example using a magnetoresistive sensor. The processing step, in between purification and detection, requires the miniaturization of the labeling or polymerase chain reaction amplification steps and is important for performing a complete on-chip nucleic acid assay.
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Figure 2. Schematic of the basic steps of chip-based magnetic nucleic acid assay using magnetic beads as a substrate for the assay [12].
4. Magnetic Immunoassays Magnetic bead-based immunoassays performed in the microfluidic format have attracted particular interest, because of the multiple advantages and promising potential applications. Basically, an immunoassay consists in using antibodies (Abs) as chemical reagents to analyze target molecules, called antigens (Ags). The technique is based on the specific recognition of a target antigen (t-Ag) by its Ab. When brought into contact, Ag and Ab form, due to specific and strong molecular interactions, a stable immunocomplex structure (see Fig. 3a). Immunoassays are amongst the most important techniques used for biological molecule analysis. They are widely used both in research and analytical sciences, and have been explored for many applications, ranging from environmental analysis to clinical diagnosis. Depending on the experimental design, the number of Abs involved in the immunocomplex formation reaction is varying. A t-Ag, like a bacteria toxin, can be directly immobilized on a reaction substrate and can be quantified with a labeled detection antibody (d-Ab) in a direct immunoassay, involving a single type of Ab. This technique is however limited, since t-Ags for direct surface immobilization have to be available. A more flexible technique, called sandwich immunoassay, consists to flank the t-Ag to be detected between a capture antibody (c-Ab) linked to a reaction substrate and a labeled d-Ab (see Fig. 3b). In this technique, the t-Ag is specific for both c-Ab and d-Ab. Also an enzyme can be used to label the d-Ab, and, in
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this case, flowing the enzyme substrate through the magnetic bead reaction chamber leads to the formation of a detectable product (see Fig. 3c). As an enzyme is a biomolecule able to convert its specific substrate to a product by catalyzing a biochemical reaction, the advantage of this technique is the possibility to generate many detectable molecules with only a few immunocomplexes, increasing thereby the detection sensitivity.
Figure 3. (a) Schematic representation of the reaction between an antibody (Ab) and its specific antigen (Ag) to form an AbAg immunocomplex. (b) Schematic representation of sandwich immunocomplex formation. A surface-linked capture antibody (c-Ab) is reacting with its target antigen (t-Ag). Then, a labeled detection antibody (d-Ab) is reacting with the t-Ag. (c) Schematic representation of an immunocomplex formed with a d-Ab labeled with an enzyme [12].
We now present a first example of an on-chip immuno-assay involving magnetic particles: an original concept was proposed to perform a complete on-chip sandwich immunoassay on magnetic nanoparticles that are selfassembled in chains in a uniform magnetic field [13–15]. The magnetic chains were retained over periodically enlarged cross-sections of a microfluidic channel. Thereby they strongly interact with the flow and capture rapidly the total of a low number of target molecules from nanoliter sample volumes. As example, the detection of murine monoclonal antibodies was
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demonstrated in a non-competitive sandwich immunoassay with a detection limit of 1 ng/mL in nanoliters of hybridoma cell culture medium. When brought into a homogeneous magnetic field, a solution of magnetic nanoparticles that is led in the microchannel spontaneously self-assembled in periodic magnetic chains [16] located at the larger cross-sections of the microchannel. These geometrically trapped nanoparticle chains were at the basis of a maximum fluid perfusion through the magnetic chain structure and the capture efficiency of this system.
Figure 4. (a) Optical image of five self-assembled magnetic chains. (b) Fluorescence microscopic image of 30 consecutive self-assembled magnetic microbead chains after the realization of the direct control immunoassay. (c) Fluorescence intensity along the microchannel axis due to the formation of the two-Ab fluorescent immunocomplexes on the magnetic microbeads, as derived from images like shown in (b) [15].
Figure 4a shows an optical image of five self-assembled magnetic chains before c-Ab coating. During experiments, the magnetic beads first assemble in primary linear chains in the narrow and wide sections of the microchannel before constituting 40 µm-long magnetic chains that stay trapped in the 40 µm-large section of the microchannel. The chains are clearly more complex than a simple pearl-like chain. We observe in Fig. 4a linear chains of ~1.5 µm diameter with local small imperfections. To estimate the number of magnetic microbeads constituting a chain, we calculated the number of magnetic microbeads initially present in one trapping unit of the microchannel (a volume of 3.2 × 10–9 mL consisting of one large and one narrow section of the microchannel). With an initial magnetic microbead concentration of 10 mg/mL, we concluded that a single magnetic chain is constituted of approximately 240 magnetic microbeads. Figure 4b shows a fluorescence microscopy image of ~30 chains in the microchannel obtained after completion of a full on-chip immunoassay. The two-Ab fluorescent immunocomplexes are clearly located at the surface of the chains, indicating the high capture efficiency of the magnetic microbeads. Figure 4c shows the fluorescence intensity along the microchannel axis due to the binding of the two-Ab fluorescent immunocomplexes on magnetic microbeads, as derived from
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images like shown in Fig. 4b. Each peak corresponds to a single fluorescent magnetic chain. In this immunoassay, all chains that were periodically trapped over the 2 mm long microchannel (representing a total number of 120 chains) show a strong fluorescence intensity. The large number of c-Ab linked to the surface of the magnetic microbeads are equivalently distributed over the 240 microbeads per chain × 120 (chains) = 28,800 magnetic microbeads in the microchannel. During flowing of the c-Ab solution, 1.22 × 108 c-Ab molecules are introduced in the microchannel. On average, 4,167 c-Ab are linked at the surface of each microbead in the microchannel, and this by only consuming 6.12 nL of c-Ab solution. We also reported a concept for a sandwich immunoassay that is completely performed on-chip using streptavidin-coated beads as substrate [17]. The latter were electrostatically self-assembled on aminosilane micropatterns at the bottom of a microfluidic channel. We used mouse IgG diluted in phosphate buffered saline (PBS) with 1% bovine serum albumin (BSA) solution as target antigen. The fluorescent sandwich immunocomplex was formed on the beads during the operation of the chip both in stop-flow and continuous flow modes. Target mouse IgG antigen could be detected down to a concentration of 15 ng/mL in stop-flow mode and 250 pg/mL in continuous flow mode, using only 1,300 nL of sample volume. For the stop-flow immunoassay, the beads were patterned in the form of double lines using a (3-aminopropyl) triethoxysilane (APTES) solution. The width of one APTES double line pattern was 5 μm and the distance between two adjacent double line patterns was 20 μm. For the continuous flow immunoassay, the beads were patterned in the form of dots using APTES dot templates of 2.5 μm diameter. The pitch between the dot patterns in the vertical direction was 15 μm and the thus formed vertical columns had a pitch of 7.5 μm. Atomic Force Microscopy (AFM) was used to study the topography of an individual APTES pattern in more detail. The AFM image of Fig. 5a presents the “ridge effect”: the average APTES thickness on the ridges is ~250 nm, while in between it is only ~30 nm. The origin of the ridge effect is the capillary force acting between the APTES solution and the vertical side walls of the photoresist patterns needed for defining the line patterns. This capillary effect caused the formation of an APTES meniscus and thus, during curing, results in an accumulation of APTES molecules at the photoresist side walls. Figure 5b is an optical micrograph showing streptavidin-coated beads patterned in the form of lines on the APTES ridges. The streptavidin-coated beads are negatively charged at ~pH > 5 and the APTES layer is, due to the partial protonation of its amine groups, positively charged at pH ≤ 8 [18]. As our bead solution has a pH ~ 7.4, the beads that are moving close to the APTES ridges are attracted due to the electrostatic interactions. However, we observed that, when the bead solution has filled the channel and is incubated under no-flow conditions, the beads
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stick everywhere on the APTES pattern, and not only on the ridges. The patterned beads are able to withstand the washing steps that are subsequently performed during the immunoassay, resisting flowing velocities as high as 8 mm/s. In the case of line patterns, we can estimate, using optical microscopy, about 70 beads per APTES ridge and thus ~140 beads per APTES double line pattern. In the case of a dot pattern (see Fig. 5c), ~4 beads are present on average per APTES dot.
Figure 5. (a) AFM image showing APTES patterns with the ridges formed at the line boundaries originating from a lift-off micropatterning process. Optical micrographs of bead micropatterns (b) in the form of double lines and (c) in the form of dots. The insert in (c) is a SEM photograph of beads attached to a single dot [17].
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After the bead micropatterning process, the microchannel walls were blocked using PBS-BSA 1% solution for ~2 min. This step is essential to avoid the unspecific adsorption of Abs/Ags on the microchannel walls. Following this, we graft the biotin-labeled capture Abs on the bead surface by flowing 10 μg/mL of capture Ab solution inside the microchannel and let it incubate for 2 min. After washing with PBS solution, the t-Ag solution is introduced. For the stop-flow mode immunoassay, the microchannel volume (130 nL) is filled and incubated with the Ag solution in a step-wise/ incremental fashion and the total number of filling steps is determining the Ag solution volume used in the assay. For example, incubation of 1,300 nL is based on 10 consecutive filling/incubation steps, each one taking 2 min. For the continuous flow mode immunoassay, in total 1,300 nL of t-Ag solution, in the concentration range of 0–1 ng/mL, was flown inside the channel at a constant flow rate of 0.25 nL/s. Hereafter, we washed the channel using PBS solution and then the channel was filled and incubated with mouse-detection Ab solution (10 μg/mL) for 2 min. Final washing was performed by flowing PBST 0.05% solution for 2 min. After the final washing step, all the beads present in the incubation volume showed comparable fluorescence. Figure 6a shows the fluorescence intensity averaged along the direction of the bead chains for three consecutive bead line-patterns. These fluorescent profiles correspond to the incubation of 1,300 nL of target m-Ag solution at different concentrations (0–75 ng/mL). The 0 ng/mL intensity profile, taken after an immunoassay protocol without applying t-Ag solution, corresponds to the autofluorescence of the beads. Indeed, using bare beads in the microfluidic channel, without having applied the sandwich immunoassay protocol, results in an intensity profile that is nearly identical to the 0 ng/mL fluorescent signal, confirming that the unspecific adsorption of fluorescent detection Abs is negligible. The total fluorescence intensity, corresponding to the immunoresponse of a given t-Ag concentration, can be obtained by integrating the fluorescence intensity profiles, like the ones shown in Fig. 6a and by subtracting the bare bead fluorescence intensity. Figure 6b shows the calibration curves for the quantification of the t-Ag for three different sample incubation volumes. Each point and error bar correspond to the statistical average and variance over three nominally identical immunoassay experiments, respectively. Incubating 1,300, 520 and 130 nL of t-Ag solution allows to detect t-Ag concentrations down to 15, 35 and 75 ng/mL, respectively. This clearly indicates that, by incubating more t-Ag volume, the detectable concentration is lower.
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Figure 6. (a) Fluorescence signal measured from three consecutive bead patterns after performing an immunoassay in stop-flow mode using a sample volume of 1,300 nL at different m-Ag antigen concentrations. (b) Integrated fluorescence obtained from fluorescent intensity profiles like shown in Fig. 6a for three different volumes of t-Ag solution exposing the bead patterns [17].
Given that there are 800 APTES line patterns in the chip’s incubation volume, we can estimate a total number of ~112,000 beads exposed during the stop-flow immunoassay. For the three incubation volumes used, one finds that the physical detection limit, imposed by our fluorescence excitation and detection set-up, corresponded to the presence of about 700 fluorescent immunocomplexes per bead. For example, using a target Ag concentration of 15 ng/mL and 1,300 nL incubation volume involves in total ~8 × 107 t-Ag molecules, meaning, on average 700 molecules per bead. These results indicate that higher assay sensitivity is promoted, either by increasing the incubated sample volume, by decreasing the number of beads in the incubation volume, or by operating the immunoassay in a continuous flow mode. In the latter case, for the flow rates used, the t-Ag will be captured and concentrated
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on the bead patterns that are situated most upstream in the flow, rather than getting equally distributed over all the beads. 5. Catalytic Applications A field where magnetic particles have potential to play an important future role is catalysis. Introduced in small quantity compared to other reagents in the system, the catalyst is a substance which enhances the reactivity between reagents, but is not consumed during the chemical reaction. Catalysis is generally separated into two subclasses: homogeneous catalysis, where the catalysts are totally spread (dissolved) in the reaction media, and heterogeneous catalysis, where they are attached to a supporting matrix or surface. Homogenous catalysis is the most efficient, as all catalytic sites are easily accessible to reagents. However, homogeneous catalysis suffers from an important drawback: it is difficult to separate the catalyst from reaction products at the end of the reaction process [19]. Heterogeneous catalysis partially overcomes this drawback. Here, the catalysts are immobilized at the surface of a supporting (and when possible soluble) matrix and are recovered after reaction by separation (for example precipitation and/or filtration) from the reaction products. However, a subsequent decrease of catalytic activity and selectivity is generally observed during reactions. It is due to steric effects from the support, which limits reagent diffusion to the surface-anchored catalysts. Also the bonds between the catalyst and the ligand are often broken and reformed during catalytic reactions. If this happens, the catalyst may break away from the support and become dissolved. This ‘leaching’ problem leads to loss of activity of the catalyst, when it is used with a continuous liquid flow. Magnetic nanoparticles can be used as the support for catalysts and can facilitate catalyst separation from the reaction media [20–24]. However, the low surface energy and easy aggregation of magnetic nanoparticles can hinder their practical applications. To overcome these drawbacks, magnetic nanoparticles have been introduced in mesoporous silica structures [25, 26]. This type of magnetic nanoparticle-based materials, which combine the advantages of both mesoporous silicas and magnetic particles, are potentially very interesting supports for the immobilization of catalysts. 6. Conclusions We have identified four important biological application areas for magnetic particle handling in microfluidic systems: cell handling and separation, nucleic acid processing and detection, immunoassays, and catalysis. We showed that specific magnetic labeling permits to select or deplete certain
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cell types from a complex matrix, thanks to the combination of magnetic labeling with magnetic separation principles. When introducing a raw cell sample on a microfluidic chip or cartridge, it is possible to capture the DNA, purify and process it, and detect a specific DNA sequence on-chip. One can also detect, with high sensitivity, various types of proteins and disease markers, by developing immunoassays that combine magnetic particles, microfluidics, antigen–antibody interactions, and this by using a number of different detection principles. Finally, keeping a magnetically suspended plug of magnetic particles as catalyst support in a microfluidic flow is also of interest for catalytic processes. While the domain of catalytic applications of magnetic particles in microfluidic systems is of more emerging nature than the other mentioned applications, we expect it to be a domain of strong activity in the near future.
References 1. A.H. Lu, E.L. Salabas, and F. Schuth: Magnetic nanoparticles: Synthesis, protection, functionalization, and application. Angewandte Chemie-International Edition 46, 1222–1244 (2007) 2. M.A.M. Gijs: Magnetic bead handling on-chip: new opportunities for analytical applications. Microfluidics and Nanofluidics 1, 22–40 (2004) 3. N. Pamme: Magnetism and microfluidics. Lab on a Chip 6, 24–38 (2006) 4. W.A. Bonner, R.G. Sweet, H.R. Hulett, and Herzenbe.La: Fluorescence Activated Cell Sorting. Review of Scientific Instruments 43, 404 (1972) 5. R. Manz, M. Assenmacher, E. Pfluger, S. Miltenyi, and A. Radbruch: Analysis and Sorting of Live Cells According to Secreted Molecules, Relocated to a Cell-Surface Affinity Matrix. Proceedings of the National Academy of Sciences of the United States of America 92, 1921–1925 (1995) 6. K.H. Han and A.B. Frazier: Paramagnetic capture mode magnetophoretic microseparator for high efficiency blood cell separations. Lab on a Chip 6, 265–273 (2006) 7. D.W. Inglis, R. Riehn, J.C. Sturm, and R.H. Austin: Microfluidic high gradient magnetic cell separation. Journal of Applied Physics 99 (2006) 8. L.R. Moore, A.R. Rodriguez, P.S. Williams, K. McCloskey, B.J. Bolwell, M. Nakamura, J.J. Chalmers, and M. Zborowski: Progenitor cell isolation with a high-capacity quadrupole magnetic flow sorter. Journal of Magnetism and Magnetic Materials 225, 277–284 (2001) 9. N. Xia, T.P. Hunt, B.T. Mayers, E. Alsberg, G.M. Whitesides, R.M. Westervelt, and D.E. Ingber: Combined microfluidic-micromagnetic separation of living cells in continuous flow. Biomedical Microdevices 8, 299–308 (2006) 10. V. Leb, M. Stocher, E. Valentine-Thon, G. Holzl, H. Kessler, H. Stekal, and J. Berg: Fully automated, internally controlled quantification of hepatitis B virus DNA by real-time PCR by use of the MagNA pure LC and LightCycler instruments. Journal of Clinical Microbiology 42, 585–590 (2004)
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11. T. Schlaurman, R. de Boer, R. Patty, M. Kooistra-Smid, and A. van Zwet: Comparative evaluation of in-house manual, and commercial semi-automated and automated DNA extraction platforms in the sample preparation of human stool specimens for a Salmonella enterica 5'-nuclease assay. Journal of Microbiological Methods 71, 238–245 (2007) 12. M.A.M. Gijs, F. Lacharme, and U. Lehmann: Microfluidic applications of magnetic particles for biological analysis and catalysis. Chemical Reviews (2010) 13. F. Lacharme, C. Vandevyver, and M.A.M. Gijs: Magnetic bead retention device for full on-chip sandwich immuno-assay. in: 21st IEEE International Conference on Micro Electro Mechanical Systems MEMS 2008, 184–187 (2008) Tucson, AZ, USA. 14. F. Lacharme, C. Vandevyver, and M.A.M. Gijs: Full on-chip nanoliter immunoassay by geometrical magnetic trapping of nanoparticle chains. Analytical Chemistry 80, 2905–2910 (2008) 15. F. Lacharme, C. Vandevyver, and M.A.M. Gijs: Magnetic beads retention device for sandwich immunoassay: comparison of off-chip and on-chip antibody incubation. Microfluidics and Nanofluidics 479–487 (2009) 16. J. Liu, M. Lawrence, A. Wu, M.L. Ivey, G.A. Flores, K. Javier, J. Bibette, and J. Richard: Field-Induced Structures in Ferrofluid Emulsions. Physical Review Letters 74, 2828–2831 (1995) 17. V. Sivagnanam, B. Song, C. Vandevyver, and M.A.M. Gijs: On-chip immunoassay using electrostatic assembly of streptavidin-coated bead micropatterns. Analytical Chemistry 81, 6509–6515 (2009) 18. K. Sarweswaran, W. Hu, P.W. Huber, G.H. Bernstein, and M. Lieberman: Deposition of DNA rafts on cationic SAMs on silicon [100]. Langmuir 22, 11279–11283 (2006) 19. D.J. Cole-Hamilton: Homogeneous catalysis – new approaches to catalyst separation, recovery, and recycling. Science 299, 1702–1706 (2003) 20. R. Abu-Reziq, H. Alper, D.S. Wang, and M.L. Post: Metal supported on dendronized magnetic nanoparticles: Highly selective hydroformylation catalysts. Journal of the American Chemical Society 128, 5279–5282 (2006) 21. A.G. Hu, G.T. Yee, and W.B. Lin: Magnetically recoverable chiral catalysts immobilized on magnetite nanoparticles for asymmetric hydrogenation of aromatic ketones. Journal of the American Chemical Society 127, 12486– 12487 (2005) 22. S.Z. Luo, X.X. Zheng, H. Xu, X.L. Mi, L. Zhang, and J.P. Cheng: Magnetic nanoparticle-supported Morita-Baylis-Hillan catalysts. Advanced Synthesis & Catalysis 349, 2431–2434 (2007) 23. P.D. Stevens, G.F. Li, J.D. Fan, M. Yen, and Y. Gao: Recycling of homogeneous Pd catalysts using superparamagnetic nanoparticles as novel soluble supports for Suzuki, Heck, and Sonogashira cross-coupling reactions. Chemical Communications 4435–4437 (2005) 24. Y. Zheng, P.D. Stevens, and Y. Gao: Magnetic nanoparticles as an orthogonal support of polymer resins: Applications to solid-phase Suzuki cross-coupling reactions. Journal of Organic Chemistry 71, 537–542 (2006)
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25. J. Li, Y.M. Zhang, D.F. Han, Q. Gao, and C. Li: Asymmetric transfer hydrogenation using recoverable ruthenium catalyst immobilized into magnetic mesoporous silica. Journal of Molecular Catalysis a-Chemical 298, 31–35 (2009) 26. J. Lee, D. Lee, E. Oh, J. Kim, Y.P. Kim, S. Jin, H.S. Kim, Y. Hwang, J.H. Kwak, J.G. Park, C.H. Shin, and T. Hyeon: Preparation of a magnetically switchable bioelectrocatalytic system employing cross-linked enzyme aggregates in magnetic mesocellular carbon foam. Angewandte Chemie-International Edition 44, 7427–7432 (2005)
MAGNETIC PARTICLE HANDLING IN MICROFLUIDIC SYSTEMS MARTIN A.M. GIJS
Laboratory of Microsystems, Ecole Polytechnique Fédérale de Lausanne, CH 1015 Lausanne EPFL, Switzerland,
[email protected]
Abstract. We present techniques and methodologies for the manipulation of magnetic micro- and nanoparticles (‘beads’) in microfluidic systems. We first introduce the most important forces that act on magnetic particles in a microfluidic system. Starting with the magnetic force that is responsible for the primary actuation of the magnetic particles, we discuss the viscous drag force induced when the particles are moving with a speed different from the liquid in the microfluidic channel. These forces can be combined in time and space to realize the basic manipulation steps of magnetic beads in a microfluidic system: retention, separation, mixing and transport. We also discuss the use of beads as magnetic detection labels or as magnetic force mediators inside droplets.
1. Introduction Since the introduction of the concept of micro Total Analysis System or µTAS in 1990 [1], this field, also called that of lab-on-a-chip or miniaturized analysis systems, has grown explosively. Microfluidics has shown to provide attractive solutions for many problems in chemical and biological analysis and has especially high potential for point-of-care testing or security applications. Three of the most important advantages of using fluidic systems of reduced dimension for analytical applications are the possibility of using minute quantities of sample and reagents, as problems of fluidic connectors with large dead volumes can be avoided in an integrated lab-on-a-chip, relatively fast reaction times, when molecular diffusion lengths are of the order of the microchannel dimension, and a large surface-to-volume ratio offering an intrinsic compatibility between the use of microfluidic systems and surface-based assays.
S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_22, © Springer Science + Business Media B.V. 2010
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Parallel to the boom of microfluidic systems, nanomaterials and nanoparticles have become a popular topic in research. When brought into a microfluidic channel, nano- and microparticles offer a relatively large specific surface for chemical binding. Also such small particles can be advantageously used as a ‘mobile substrate’ in catalysis, for bio-assays or even for in vivo applications. Magnetic nano- and microparticles have additional advantages beyond those mentioned for non-magnetic particles: having embedded magnetic entities, they can be magnetically manipulated using permanent magnets or electromagnets, independent of normal microfluidic or biological processes [2, 3]. This extra degree of freedom is at the basis of the improved exposure of the functionalized bead surface to the surrounding liquid, due to the increased relative motion of the bead with respect to the fluid. 2. Magnetic Particles The synthesis, protection and functionalization of magnetic particles were reviewed by Lu et al. [4] and Horák et al. [5]. Suspensions of magnetic particles or magnetic fluids are stable dispersions using an organic or aqueous carrier medium. Specific requirements of the bead matrix such as biocompatibility, biodegradability and stability in the different media, must be combined with a preferable uniform size distribution and a correct shape. The magnetic material content determines the magnetic behavior of the beads and must be associated with suitable measures of protection against corrosion. For use in specific target applications, the bead surface needs also to be functionalized in order to allow covalent bonding or simple unspecific adsorption of biomolecules (proteins, antibodies, nucleic acids) or cells. Many types of magnetic beads are commercially available and most of them are usually tailor-made for a specific application. Maintaining the stability of magnetic beads for a long time without unwanted agglomeration or precipitation problems can be an issue that has to be avoided for applications. Particle protection strategies result in magnetic beads having a core-shell structure, where the role of the shell is to protect the magnetic core against environmental influence. Several coating strategies exist, ranging from coating the magnetic nanoparticles with organic surfactants and polymers, with inorganic compounds like silica, with carbon, to coating with precious metals. Besides simply coating individual magnetic nanoparticles, it is also possible to embed a number of magnetic nanoparticles or magnetic material in a polymer or silica matrix to form composites. This way, one can synthesize micro-beads that, due to a higher magnetic content, are more easy and rapid to manipulate magnetically than the primary magnetic nanoparticles. Such type of ‘composite’ beads (size around 1 μm) is therefore often used in microfluidic systems.
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To stabilize magnetic nanoparticles after synthesis, electrostatic or steric repulsion can also be used to keep the nanoparticles dispersed in a nonagglomerated colloidal state. For the so-called ferrofluids [6], the stability results from a control of surface charges and the use of specific surfactants. Surfactants or polymers can be chemically linked to or physically adsorbed to the magnetic particles, creating repulsive forces (due to steric hindrance) that balance the attractive magnetic, electrostatic and van der Waals force. Polymers containing functional groups, such as carboxylic acids, phosphates and sulfates, can bind to the surface of iron oxide [7], while surface-modified magnetic nanoparticles with certain biocompatible polymers are intensively studied beyond the field of microfluidics for magnetic-field-directed drug targeting [8] and as contrast agents for magnetic resonance imaging [9, 10]. 3. Forces on Magnetic Particles It is important to note that a magnetic induction gradient is required to exert a translation force, a uniform field giving only rise to a torque. The magnetic force acting on a point-like magnetic dipole or ‘magnetic moment’ m in a magnetic induction field B can be written as function of the derivative of the magnetic induction [11, 12] Fm =
1
μ0
(m ⋅ ∇ )B
(1)
Superparamagnetic nanoparticles have zero magnetization in the absence of a magnetic field, as their magnetic anisotropy energy (proportional to their magnetic volume) is typically much smaller than the thermal energy. They therefore essentially behave as non-magnetic particles in the absence of a magnetic field. The slope of their magnetization curve at low fields is characterized by the magnetic susceptibility χ. In case of superparamagnetic nanoparticles in a biological medium, one can write for the moment at small fields the linear relation m = Vμ0 M = Vμ 0 Δχ H , with M the magnetization of the particle and Δχ the difference in magnetic susceptibility between the magnetic bead and the surrounding liquid medium. Using the relation B = μ0H , equation (1) for a superparamagnetic particle in the linear susceptibility regime becomes Fm =
V Δχ
μ0
(B ⋅ ∇ )B
(2)
The magnetic moment of a superparamagnetic particle generally is smaller than that of a larger ferromagnetic microparticle. Hence, the magnetic force on a superparamagnetic particle will be smaller, which eventually will result in slower magnetic separation processes. However, the advantage of
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superparamagnetic particles is the possibility to simply ‘switch off’ the magnetic effects by removing the external magnetic induction. The magnetic force of equation (1) or (2) is responsible for the unique possibilities offered by magnetic beads. In many applications, a magnetically labeled material is separated from a liquid solution by passing the fluid mixture through a region where there is a magnetic field gradient that can immobilize the tagged material via magnetic forces. Often there is a magnetic translational driving force and the liquid solution is static. In the equilibrium state, the magnetic force Fm is opposed to the hydrodynamic drag force Fd acting on the magnetic particle. The hydrodynamic drag is a consequence of the velocity difference between the magnetic particle and the liquid Δv and, for a spherical particle with radius r, is given by [13] Fd = 6πη r Δv
(3)
where η is the viscosity of the medium surrounding the particle (for water, η = 8.9 × 10 –4 N s/m2). When immersed in an ionic aqueous solution, the substrate and particles also acquire a surface charge through the adsorption of ions present in the solution and/or the presence of charged surface groups. This surface charge is neutralized by mobile ions of opposite charge in the solution, forming the so-called double layer. When the double layers of two surfaces overlap, an electrostatic interaction occurs, resulting in either a repulsive or an attractive force, which eventually can lead to sticking of the beads to surfaces or to unwanted agglutination effects. Besides the magnetic, viscous and electrical forces on magnetic beads, several other forces exist, like gravitational and Brownian forces. 4. Manipulation of Magnetic Particles The spatial and temporal combination of the forces introduced in previous section allows designing procedures or manipulation protocols, which are at the basis of the applications of magnetic beads. Figure 1 contains schematic diagrams representing basic manipulations of magnetic beads in microfluidic systems. In separation (Fig. 1a), magnetic beads are retained from a flow by focusing a magnetic field over the channel using electromagnets [14], coils or permanent magnets. Also systems with miniaturized soft magnetic microstructures exist [15], which can be coupled to a macroscopic electromagnet or placed in the magnetic induction field of a macroscopic permanent magnet. Magnetic transport [16–18] (Fig. 1b) is -magneticallymore challenging than separation, as it requires stronger and long-range
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magnetic forces to move the magnetic beads within the liquid, without needing a microfluidic flow. The use of magnetic beads as labels for detection [19] is shown in Fig. 1c: a magnetic bead is bound to the surface of the microchannel and a magnetic field sensor monitors its stray field, when the particle is placed in an external magnetic induction. A particularly interesting property of magnetic beads is that they can be magnetically suspended in a microfluidic channel using magnetic forces, without the requirement of having a supporting substrate [20, 21]. Such trapping of beads or magnetic particle superstructures can be advantageous, if one wants to have a high exposure of the beads to a liquid flow. Also, when locally alternating magnetic fields are applied, for example via soft magnetic field focusing structures, a dynamic agitation of the magnetic beads is possible that can be used to mix the essentially laminar flow patterns within a microfluidic channel (Fig. 1d) [22].
Figure 1. Schematic basic manipulation steps of magnetic beads in a microfluidic chip. (a) Separation of magnetic beads from a flow by actuation of electromagnets or positioning of magnets. (b) Transport of magnetic beads using long-range magnetic forces provided by an electromagnet or magnet. (c) Detection of the stray field of a bead by a magnetic field sensor, after specific binding of the labeled bead on the sensor surface. (d) Mixing of two laminar streams by dynamic agitation of a bead superstructure using a locally applied alternating magnetic field between two soft magnetic tips [23].
4.1. MAGNETIC SEPARATION AND TRANSPORT
Magnetic separator design can be as simple as the application and removal of a permanent magnet to the wall of a test tube to cause particle aggregation, followed by removal of the supernatant. However, in a microfluidic system, it is preferable to increase the separator efficiency by producing regions with a high magnetic field gradient to capture the magnetic beads as they flow by in the carrier medium. Continuous flow magnetic particle and
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cell separation systems can have a macroscopic dimension from the magnet point of view, but, from a liquid transport point of view, they may be called ‘microfluidic’, as their functioning is based on the presence of laminar flow patterns [24].
Figure 2. (a) Schematic diagram of a magnetic quadrupole separator. (b) Schematic diagram of a magnetic dipole separator. Different types of magnetic particles will be deflected into different outlet ports [23].
For example, Fig. 2a is a schematic diagram of a so-called quadrupole magnet configuration, where four magnets are arranged in order to induce a maximum magnetic field gradient towards the outer side of an annular liquid carrying tube, inserted in the free space between the magnets [25]. The separation takes place within a laminar flow of the carrier fluid along the thin annular channel. A magnetic field gradient is imposed across the thin dimension of the channel, perpendicular to the direction of the flow. The sample mixture is arranged to enter the system close to one of the channel walls and, as the sample is carried along the channel by the flow of the fluid, those components that interact more strongly with the field gradient are carried transverse across the channel thickness. A division of the flow at the channel outlet using a stream splitter completes the separation into two fractions. The technique was given the name split-flow thin fractionation, a derivative of field flow fractionation, as separation is obtained within a mobile phase without the use of a stationary phase [26, 27]. Figure 2b is a schematic diagram of a magnetic dipole separator. In this device, magnetic beads migrate perpendicular to the direction of the flow at a rate proportional to their magnetic content. This permits separation of the injected sample into multiple outlet streams based on the magnetic properties of each bead species [28]. Magnetic separation is different from magnetic transport in the sense that, in separation, the beads are retained or separated by action of a magnetic field, but transported using a liquid flow. In magnetic transport, magnetic
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forces effectively transport the particle, which requires magnetic fields and magnetic forces that act on a longer range than necessary for separation, where magnetic beads approach very closely the magnetic actuation region by the fluid motion. Transport is a difficult task using current-actuated coils, as the magnetic susceptibility Δχ of the magnetic beads is rather weak (typically ≤ 1), due to small magnetic core volumes and demagnetization effects of the particles Figure 3 shows video sequences of moving clusters of magnetic beads observed in a cylindrical capillary, as induced by using an array of millimetersize coils. The coils are placed in a uniform static magnetic field, the role of which is to impose a permanent magnetic moment to the beads. The very small magnetic field gradient of a planar coil is then sufficient to displace the beads. The long-range displacement is assured by arranging adjacent coils in the array with spatial overlap in a three-phase actuation scheme. The figure shows how one can combine the magnetic fields from adjacent coils properly in time and create a magnetic field maximum, which is effectively propulsing the microbeads in the capillary.
Figure 3. Magnetic microbead transport in a cylindrical capillary over long-range distances using an array of simple planar coils (coil diameter = 3.5 mm). Transport of magnetic beads (1 μm diameter, Promega) is enabled by sequential actuation of the coils in a three-phase scheme (1, 2, 3) (I = ±1 A) [16].
4.2. MAGNETIC PARTICLES AS LABELS FOR DETECTION
A common approach to detecting biological molecules is to attach a label that produces an externally observable signal. The label may be a radioisotope, enzyme, fluorescent molecule or charged molecule, but also magnetic beads can be used as labels for biosensing. Magnetic labels have several advantages over other labels. The magnetic properties of the beads are stable over time, especially since the magnetism is not affected by reagent chemistry or subject to photo-bleaching (a problem with fluorescent
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labeling). There is also no significant magnetic background present in a biological sample and magnetic fields are not screened by aqueous reagents or biomaterials. In addition, magnetism can be used to remotely manipulate the magnetic particles. Finally, a number of very sensitive magnetic field detection devices have been developed during recent years, like giant magnetoresistance (GMR) [29] and spin-valve [30, 31] magnetic sensors that enable the measurement of extremely weak magnetic fields, such as the magnetic stray field generated by the magnetization of a single magnetic microbead.
Figure 4. Detection of magnetic beads on 16 magnetoresistive sensor elements of the BARC chip. The noise level is determined by measuring the signal before beads are injected and after they are washed off [32].
Researchers have developed a microsystem for the capture and detection of micron-sized, paramagnetic beads on a chip containing an array of GMR sensors, the so-called Bead ARray Counter (BARC) [19, 32–34]. The BARC is based on a sandwich assay, where the target molecule is bound to an immobilized probe on the GMR sensor, after which the magnetic label is bound to the target using specific ligand-receptor interactions. Figure 4 shows that single 2.8 μm diameter magnetic beads can be detected using 80×5 μm2 GMR sensor strips. The graphs show the voltage signals, corresponding to the resistance change, from 16 of the 64-sensor elements on the chip with and without adsorbed beads. The signal due to a single bead varies from strip to strip depending on whether the bead is directly on top of the sensor (elements 2 and 15), not present (11 and 14), or near the edge of the sensor (all others).
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4.3. MIXING WITH MAGNETIC PARTICLES
Most of the magnetic bead-related phenomena discussed so far were based on the interaction of individual beads with the magnetic field. An interesting property of magnetic beads is that they can form linear-like chain structures or more complex Supra Particle Structure (SPS), when placed in a magnetic field due to the magnetic dipole interaction between beads. When the magnetic induction can be very locally applied, it is possible to have a small-size magnetic SPS or bead ‘plug’ spanning the cross-section of a microchannel, which will be characterized by a strong perfusion by a liquid flow. Microfluidic mixing was demonstrated based on the dynamic motion of a SPS of ferromagnetic beads that are retained within a microfluidic flow using a local alternating magnetic field [35]. The latter induces a rotational motion of the magnetic particles, thereby strongly enhancing the fluid perfusion through the magnetic structure that behaves as a dynamic random porous medium. The result is a very strong particle-liquid interaction that can be controlled by adjusting the magnetic field frequency and amplitude, as well as the liquid flow rate, and is at the basis of very efficient liquid mixing. The principle was demonstrated using a microfluidic chip made of poly(methyl methacrylate) with integrated soft ferromagnetic plate structures. The latter were part of an electromagnetic circuit and served to locally apply a magnetic field over the section of the microchannel. Starting from a laminar flow pattern of parallel fluorescein dye and nonfluorescent liquid streams, a 95% mixing efficiency using a mixing length of only 400 μm and at liquid flows of the order of 0.5 cm/s was demonstrated (see Fig. 5).
Figure 5. (a) Schematic diagram of a microfluidic Y-channel structure flanked by two soft magnetic iron parts. The photographs (b–e) are taken at different locations and represent the fluorescent intensity over the channel; (b) is taken before the mixing region and shows the laminar flow pattern of parallel fluorescent and non-fluorescent streams; (c) is taken directly in the mixing region; (d) is after the mixing using a sinusoidal external field with f = 20 Hz; (e) is after mixing using a square-shaped external field at f = 5 Hz [35].
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4.4. MAGNETIC DROPLETS
In contrast to continuous flow microfluidics, droplet microfluidics, also called ‘digital microfluidics’, handles only small self-enclosed liquid entities [36, 37]. The advantage of droplet handling is the strong reduction of the transported volumes and the possibility of working simultaneously with a multitude of different samples in the same system. In order to perform reactions between the different droplets, the system however needs to be able to execute various droplet manipulation steps, such as transport, merging, mixing and splitting. Among the solutions presented in recent years, which range from electrowetting to acoustic actuation, magnetic droplet manipulation offers the advantage of long-range magnetic forces, which do not rely on the intrinsic properties of the manipulated medium and do not interact with most biological materials [38]. This non-interaction on the other hand requires the introduction of magnetic material into the droplets, where the latter translates an applied magnetic field gradient into a force pulling the droplet into the direction of the gradient [39]. A challenge in magnetic droplet manipulation is the application of a sufficiently strong magnetic induction gradient. In some cases, an external magnet is used, which can be moved according to the requirements of the droplet manipulation [40]. In combination with a suitable three-dimensional structuring of the surface to create barrier or gating structures, all droplet manipulation steps, like separation, transport and fusion, can be implemented, but at the cost of increasing system complexity and decreasing flexibility [41]. In other work, magnetic particle concentration and separation was demonstrated in droplets moving in a channel [42, 43] or near the bottom of an oil-filled reservoir [44], by using both permanent magnet-induced forces and electrowetting-on-dielectric droplet manipulation. A different approach is the use of a matrix of coils to generate local magnetic field gradients. In this case, the magnetic particles no longer follow a moving magnet, but are controlled by the changing topology of the applied magnetic field [45–47]. Since the actuating field gradient only acts on the particles enclosed inside the droplet, the magnetic force is transferred onto the droplet via the droplet wall. The moving particles accumulate at the droplet boundary and push the droplet into the desired direction. As a consequence, the droplet moves as long as the magnetic actuation is larger than the friction exerted by the surrounding liquid and surfaces. In cases a droplet should stay in place, the local friction needs to be increased, either by introducing three-dimensional obstacles [48] or by varying the wetting properties of the surface in contact with the droplet [49] (see Fig. 6).
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Figure 6. Merge, mix, split, and transport were the main manipulation steps used for on-chip droplet-based DNA purification. The system was able to extract genomic material from dilute raw cell samples by using the actuation of magnetic microparticles within the droplet using a matrix of coils [50].
5. Conclusions We have discussed the main forces acting on magnetic particles and the physics of magnetic actuation. Probably the most prominent advantage of magnetic beads over other solid supports is that these particles can be magnetically probed and manipulated using permanent magnets or electromagnets, independent of normal chemical or biological processes. Introducing these particles in miniaturized fluidic or lab-on-a-chip systems provides further advantages, as miniaturized systems that completely integrate various processes, from raw sample pretreatment until specific biological detection, are achievable. This qualifies these systems for point-of-care or in-field testing. In a subsequent chapter, we will identify and discuss the most important biological application areas for microfluidic systems that involve magnetic particle handling.
References 1. A. Manz, N. Graber, and H.M. Widmer: Miniaturized Total Chemical-Analysis Systems - a Novel Concept for Chemical Sensing. Sensors and Actuators B-Chemical 1, 244–248 (1990). 2. M.A.M. Gijs: Magnetic bead handling on-chip: new opportunities for analytical applications. Microfluidics and Nanofluidics 1, 22–40 (2004). 3. N. Pamme: Magnetism and microfluidics. Lab on a Chip 6, 24–38 (2006).
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4. A.H. Lu, E.L. Salabas, and F. Schüth: Magnetic nanoparticles: Synthesis, protection, functionalization, and application. Angewandte Chemie-International Edition 46, 1222–1244 (2007). 5. D. Horák, M. Babic, H. Mackova, and M.J. Benes: Preparation and properties of magnetic nano- and microsized particles for biological and environmental separations. Journal of Separation Science 30, 1751–1772 (2007). 6. S.S. Papell: US patent 3215572 (1965). 7. R.M. Cornell and U. Schertmann: The Iron Oxides: Structure, Properties, Reactions, Occurrence and Uses. (1996), Weinheim: VCH. 8. A. Petri-Fink, M. Chastellain, L. Juillerat-Jeanneret, A. Ferrari, and H. Hofmann: Development of functionalized superparamagnetic iron oxide nanoparticles for interaction with human cancer cells. Biomaterials 26, 2685–2694 (2005). 9. R. Lawaczeck, H. Bauer, T. Frenzel, M. Hasegawa, Y. Ito, K. Kito, N. Miwa, H. Tsutsui, H. Volger, and H.J. Weinmann: Magnetic iron oxide particles coated with carboxydextran for parenteral administration and liver contrasting Pre-clinical profile of SH U555A. Acta Radiologica 38, 584–597 (1997). 10. D.K. Kim, Y. Zhang, J. Kehr, T. Klason, B. Bjelke, and M. Muhammed: Characterization and MRI study of surfactant-coated superparamagnetic nanoparticles administered into the rat brain. Journal of Magnetism and Magnetic Materials 225, 256–261 (2001). 11. S. Chikazumi: Physics of Magnetism. (1964), Malabar, Florida, USA: Robert E. Krieger Publishing Company. 12. Y. Moser, T. Lehnert, and M.A.M. Gijs: Quadrupolar magnetic actuation of superparamagnetic particles for enhanced microfluidic perfusion. Applied Physics Letters 022505 (2009). 13. F.M. White: Fluid Mechanics. (1999): McGraw-Hill. 14. J.W. Choi, T.M. Liakopoulos, and C.H. Ahn: An on-chip magnetic bead separator using spiral electromagnets with semi-encapsulated permalloy. Biosensors & Bioelectronics 16, 409–416 (2001). 15. T. Deng, M. Prentiss, and G.M. Whitesides: Fabrication of magnetic microfiltration systems using soft lithography. Applied Physics Letters 80, 461–463 (2002). 16. A. Rida, V. Fernandez, and M.A.M. Gijs: Long-range transport of magnetic microbeads using simple planar coils placed in a uniform magnetostatic field. Applied Physics Letters 83, 2396–2398 (2003). 17. C.S. Lee, H. Lee, and R.M. Westervelt: Microelectromagnets for the control of magnetic nanoparticles. Applied Physics Letters 79, 3308–3310 (2001). 18. H. Lee, Y. Liu, R.M. Westervelt, and D. Ham: IC/Microfluidic hybrid system for magnetic manipulation of biological cells. Ieee Journal of Solid-State Circuits 41, 1471–1480 (2006). 19. D.R. Baselt, G.U. Lee, M. Natesan, S.W. Metzger, P.E. Sheehan, and R.J. Colton: A biosensor based on magnetoresistance technology. Biosensors & Bioelectronics 13, 731–739 (1998). 20. F. Lacharme, C. Vandevyver, and M.A.M. Gijs: Full on-chip nanoliter immunoassay by geometrical magnetic trapping of nanoparticle chains. Analytical Chemistry 80, 2905–2910 (2008). 21. A. Rida and M.A.M. Gijs: Dynamics of magnetically retained supraparticle structures in a liquid flow. Applied Physics Letters 85, 4986–4988 (2004).
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22. A. Rida, L. T., and M.A.M. Gijs: Microfluidic mixer using magnetic beads. in: 7th International Conference on Miniaturized Chemical and Biochemical Analysis Systems, October 5–9, 2003, Squaw Valley, California USA., 579– 582 (2003). 23. M.A.M. Gijs, F. Lacharme, and U. Lehmann: Microfluidic applications of magnetic particles for biological analysis and catalysis. Chemical Reviews (2010). 24. J.J. Chalmers, M. Zborowski, L.P. Sun, and L. Moore: Flow through, immunomagnetic cell separation. Biotechnology Progress 14, 141–148 (1998). 25. G.P. Hatch and R.E. Stelter: Magnetic design considerations for devices and particles used for biological high-gradient magnetic separation (HGMS) systems. Journal of Magnetism and Magnetic Materials 225, 262–276 (2001). 26. F. Carpino, L.R. Moore, M. Zborowski, J.J. Chalmers, and P.S. Williams: Analysis of magnetic nanoparticles using quadrupole magnetic field-flow fractionation. Journal of Magnetism and Magnetic Materials 293, 546–552 (2005). 27. M. Hoyos, L.R. Moore, K.E. McCloskey, S. Margel, M. Zuberi, J.J. Chalmers, and M. Zborowski: Study of magnetic particles pulse-injected into an annular SPLITT-like channel inside a quadrupole magnetic field. Journal of Chromatography A 903, 99–116 (2000). 28. N. Pamme and A. Manz: On-chip free-flow magnetophoresis: Continuous flow separation of magnetic particles and agglomerates. Analytical Chemistry 76, 7250–7256 (2004). 29. M.N. Baibich, J.M. Broto, A. Fert, F.N. Vandau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas: Giant Magnetoresistance of (001)Fe/ (001) Cr Magnetic Superlattices. Physical Review Letters 61, 2472–2475 (1988). 30. B. Dieny, V.S. Speriosu, S. Metin, S.S.P. Parkin, B.A. Gurney, P. Baumgart, and D.R. Wilhoit: Magnetotransport Properties of Magnetically Soft SpinValve Structures. Journal of Applied Physics 69, 4774–4779 (1991). 31. P.P. Freitas, F. Silva, N.J. Oliveira, L.V. Melo, L. Costa, and N. Almeida: Spin valve sensors. Sensors and Actuators a-Physical 81, 2–8 (2000). 32. R.L. Edelstein, C.R. Tamanaha, P.E. Sheehan, M.M. Miller, D.R. Baselt, L.J. Whitman, and R.J. Colton: The BARC biosensor applied to the detection of biological warfare agents. Biosensors & Bioelectronics 14, 805–813 (2000). 33. M.M. Miller, P.E. Sheehan, R.L. Edelstein, C.R. Tamanaha, L. Zhong, S. Bounnak, L.J. Whitman, and R.J. Colton: A DNA array sensor utilizing magnetic microbeads and magnetoelectronic detection. Journal of Magnetism and Magnetic Materials 225, 138–144 (2001). 34. J.C. Rife, M.M. Miller, P.E. Sheehan, C.R. Tamanaha, M. Tondra, and L.J. Whitman: Design and performance of GMR sensors for the detection of magnetic microbeads in biosensors. Sensors and Actuators a-Physical 107, 209–218 (2003). 35. A. Rida and M.A.M. Gijs: Manipulation of self-assembled structures of magnetic beads for microfluidic mixing and assaying. Analytical Chemistry 76, 6239–6246 (2004). 36. R. Mukhopadhyay: Diving into droplets. Analytical Chemistry 78, 1401–1404 (2006).
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37. K. Jensen and A. Lee: The science & applications of droplets in microfluidic devices - Foreword. Lab on a Chip 4, 31N–32N (2004). 38. A.A. Garcia, A. Egatz-Gomez, S.A. Lindsay, P. Dominguez-Garcia, S. Melle, M. Marquez, M.A. Rubio, S.T. Picraux, D.Q. Yang, P. Aella, M.A. Hayes, D. Gust, S. Loyprasert, T. Vazquez-Alvarez, and J. Wang: Magnetic movement of biological fluid droplets. Journal of Magnetism and Magnetic Materials 311, 238–243 (2007). 39. R. Mukhopadhyay: Magnetic dust mobilizes droplets. Analytical Chemistry 77, 55A–55A (2005). 40. A. Egatz-Gomez, S. Melle, A.A. Garcia, S.A. Lindsay, M. Marquez, P. Dominguez-Garcia, M.A. Rubio, S.T. Picraux, J.L. Taraci, T. Clement, D. Yang, M.A. Hayes, and D. Gust: Discrete magnetic microfluidics. Applied Physics Letters 89, (2006). 41. M. Shikida, M. Koyama, N. Nagao, R. Imai, H. Honda, M. Okochi, H. Tsuchiya, and K. Sato: Agitation of magnetic beads by multi-layered flat coils. Sensors and Actuators B-Chemical 137, 774–780 (2009). 42. Y. Wang, Y. Zhao, and S.K. Cho: Efficient in-droplet separation of magnetic particles for digital microfluidics. Journal of Micromechanics and Microengineering 17, 2148–2156 (2007). 43. G.J. Shah and C.J. Kim: Meniscus-Assisted High-Efficiency Magnetic Collection and Separation for EWOD Droplet Microfluidics. Journal of Microelectromechanical Systems 18, 363–375 (2009). 44. T. Ohashi, H. Kuyama, K. Suzuki, and S. Nakamura: Control of aqueous droplets using magnetic and electrostatic forces. Analytica Chimica Acta 612, 218–225 (2008). 45. U. Lehmann, S. Hadjidj, V.K. Parashar, C. Vandevyver, A. Rida, and M.A.M. Gijs: Two-dimensional magnetic manipulation of microdroplets on a chip as a platform for bioanalytical applications. Sensors and Actuators BChemical 117, 457–463 (2006). 46. A. Beyzavi and N.T. Nguyen: One-dimensional actuation of a ferrofluid droplet by planar microcoils. Journal of Physics D-Applied Physics 42, (2009) 47. N.T. Nguyen, A. Beyzavi, K.M. Ng, and X.Y. Huang: Kinematics and deformation of ferrofluid droplets under magnetic actuation. Microfluidics and Nanofluidics 3, 571–579 (2007). 48. M. Shikida, K. Inouchi, H. Honda, and K. Sato: Magnetic handling of droplet in micro chemical analysis system utilizing surface tension and wettability. in: 17th IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2004), 359–362 (2004) Maastricht, The Netherlands. 49. U. Lehmann, V. Parashar, S. Hadjidj, A. Rida, and M.A.M. Gijs: Two dimensional magnetic manipulation of microdroplets on a chip. in: Digest of Technical Papers of Transducers 2005, 77–80 (2005) Seoul, Korea. 50. U. Lehmann, C. Vandevyver, V.K. Parashar, and M.A.M. Gijs: Droplet-based DNA purification in a magnetic lab-on-a-chip. Angewandte Chemie-International Edition 45, 3062–3067 (2006).
AC ELECTROKINETIC PARTICLE MANIPULATION IN MICROSYSTEMS HYWEL MORGAN AND TAO SUN Nano Research Group, School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK,
[email protected]
Abstract. Lab-on-Chip systems integrate multiple functionalities on a single platform. Automated or remote manipulation and analysis of particles and fluids is a key element in microfluidic devices. Microelectrodes can be integrated into these devices to generate large electric fields and field gradients using low voltages. Electrokinetics is an attractive method for integrating particle manipulation and separation within such systems. The electrokinetic forces are easy to control by designing optimum electrode structures and choice of field and frequency. In this chapter, the theory of AC electrokinetics is reviewed and example applications for manipulation of particles are provided. The use of dielectrophoresis (DEP) for manipulating micro particles is then described, together with a discussion on scaling issues.
1. Introduction Microfluidic systems offer integration of multiple functions on a single platform. Automated or remote manipulation and analysis of particles and fluids is a key element in micro-technologies and Lab-on-a-Chip. In most Lab-on-a-Chip systems, samples are suspended in an aqueous electrolyte: a conducting fluid medium. The reduction in size of these systems leads to a number of changes in system behavior, for example the behavior of fluid is dominated by viscosity. Also it is reasonable easy to generate very large electric fields and field gradients in micro-systems using quite low voltages. External pumps are often used to move fluid, but there is a growing interest in using electrokinetics to move liquids and solid particles within microchips using integrated electrodes. Electrokinetics is particularly attractive on the scale of micro-fluidics systems. The forces are easy to control by designing optimum electrode structures and choice of field and frequency. AC electrokinetics [1–3] describes the translational motion of particles in S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_23, © Springer Science + Business Media B.V. 2010
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AC electric fields and includes: dielectrophoresis (DEP), travelling wave dielectrophoresis (twDEP) and electrorotation (ROT). Generally, nonuniform electric fields are used in AC electrokinetics. The assumption that the uniform field solution for the dipole moment is valid, is referred to as the dipole moment approximation, and is sufficient if the size of the particle is small compared to the scale of the electric field non-uniformity, which is true for most cases. In this chapter, we describe the forces on particles due to the action of AC fields, and discuss applications for manipulation of particles. We finish with a discussion of scaling effects. 2. AC Electrokinetic Theory 2.1. CLAUSIUS–MOSSOTTI FACTOR
For a homogeneous solid dielectric sphere (a particle with a radius of R) in a homogeneous dielectric medium, charges will accumulate at the interface between the particle and the medium. This results in an effective or induced dipole moment across the particle. The potential of the effective dipole moment Peff can be considered as an increment to the potential distribution of the applied field, which is given by: ⎛ ε% p − ε%m Peff = 4πε m ⎜ ⎜ ε% + 2ε% m ⎝ p
⎞ 3 ⎟⎟ R E ⎠
(1)
where ε% = ε − jσ / ω is the complex permittivity, j2 = −1, ω the angular frequency. The subscripts p and m refer to particle and medium respectively. E is the electric field. The effective dipole moment is frequency-dependent with the dependence characterized by the Clausius–Mossotti factor f%CM :
ε% p − ε%m f%CM = ε% p + 2ε%m
(2)
Separating the real and imaginary part of the Clausius–Mossotti factor give a Debye relaxation of the form: ⎛ σ p −σ m ⎞ ⎛ ε p − εm ⎜ ⎟−⎜ ⎛ ε p − ε m ⎞ ⎜⎝ σ p + 2σ m ⎟⎠ ⎜⎝ ε p + 2ε m + Re ⎡⎣ f%CM ⎤⎦ = ⎜ 2 ⎜ ε p + 2ε m ⎟⎟ 1 + ω 2τ MW ⎝ ⎠
⎞ ⎟⎟ ⎠
(3)
AC ELECTROKINETIC PARTICLE MANIPULATION
Im ⎡⎣ f%CM ⎤⎦ =
⎡⎛ ε p − ε m ⎢⎜⎜ ⎣⎢⎝ ε p + 2ε m
⎞ ⎛ σ p − σ m ⎞⎤ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥ ωτ MW ⎠ ⎝ σ p + 2σ m ⎠ ⎦⎥ 2 1 + ω 2τ MW
483
(4)
with
τ MW =
ε p + 2ε m σ p + 2σ m
(5)
where Re[ ] and Im[ ] represent the real and imaginary part of, respectively.
τMW is referred to as the Maxwell-Wagner relaxation time constant.
Figure 1. Plot of the variation of the real and imaginary parts of the Clausius–Mossotti factor as a function of frequency.
Equation (3) shows that the real part of the Clausius–Mossotti factor goes to a low frequency (ω = 0) limiting value of (σp−σm)/(σp+2σm), i.e. it depends on the conductivity of the particle and the medium. At high frequency ( ω → ∞ ) the limiting value is (εp−εm)/(εp+2εm) and the polarization is dominated by the permittivity of the particle and the medium. From Eq. (4), the imaginary part of the Clausius–Mossotti factor is zero at both low and high frequencies; at the Maxwell-Wagner relaxation frequency fMW = 1/(2πτMW) it has a value of [(εp−εm)/(εp+2εm) − (σp−σm)/ (σp+2σm)]/2. Both the real and imaginary parts of the Clausius–Mossotti factor govern the movement of particles in AC electric field, but in different
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ways. Figure 1 shows the real and imaginary parts of the Clausius–Mossotti factor and also the regions of different electrokinetic behavior, as detailed in the following sections. 2.2. DIELECTROPHORESIS
In practical DEP systems, a small particle (e.g. a bead) is suspended in an electrolyte (such as sodium chloride). When an electric field is applied, charge moves and accumulates at the interface between the particle and the electrolyte. Following application of the field, charges do not move instantaneously; typically they take a few microseconds to reach equilibrium. At low frequencies, the movement of free charge can keep pace with the changing direction of the field. However, as the field frequency increases there comes a point where the charges no longer have sufficient time to respond. At high frequencies, free charge movement is no longer the dominant mechanism responsible for charging the interface. Instead the polarization of the bound charges (permittivity) dominates. The difference between these two states is termed a dielectric dispersion. The amount of charge at the interface depends on the field strength and the dielectric properties (conductivity and permittivity) of the particle and the electrolyte. However, there is a slight asymmetry in the charge density on the particle which gives rise to an effective or induced dipole across the particle. Note that if the field is removed the dipole disappears, it is “induced”. The magnitude of the dipole moment depends on the amount of charge and the size of the particle. For a spherical particle in an electrolyte subject to a uniform applied electric field, three cases can be considered: (i) When the polarisability of the particle is much greater than the electrolyte, more charge accumulates inside the interface than outside. Figure 2a shows the distributions of the charges and the resulting effective dipole moment aligns with the direction of the applied electric field. (ii) When the particle polarisability is much less than the electrolyte, as shown in Fig. 2b, there are less charges inside the particle than outside. The effective dipole moment is in the opposite direction to the applied field. (iii) The third case is where the polarisability of the particle and electrolyte are the same and there is no net dipole (not shown). When a particle is subjected to a non-uniform electric field the situation is as shown in Fig. 3. When the particle polarisability is greater than the suspending medium, the electric field vectors bend towards the particle, meeting the surface at right angles and the field inside the particle is nearly zero, as shown in Fig. 3a. The converse is shown in Fig. 3b, where the
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Figure 2. (a) and (b) Diagram showing the charge distribution for a suspending system containing a single particle. In (a) the particle is more polarizable than the medium. In (b) the particle is less polarizable than the medium. (c) and (d) Numerical simulations showing the electric field distribution in the system. (c) Particle more polarizable than the medium. (d) Particle less polarizable than the medium.
particle polarisability is less than the electrolyte. The field vectors now bend around the particle as if it were an insulator. When the polarisability of the particle and electrolyte are the same it is as if the particle does not exist and the field lines are parallel and continuous everywhere. The imbalance of forces on the induced dipole gives rise to particle movement, called dielectrophoresis (DEP) [1]. When the polarisability of the particle is greater than its surrounding medium, the direction of the dipole is with the field and the particle experiences a force called positive DEP: the particle moves towards the high field region (Fig. 3a). The opposite situation gives rise to negative DEP (Fig. 3b); and the particle moves away from regions of high electric fields.
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Figure 3. Diagram showing the principle of dielectrophoresis (DEP), which only occurs in a non-homogeneous electric field. (a) Particle more polarizable than the medium; positive dielectrophoresis (pDEP); (b) particle less polarizable than the medium; negative dielectrophoresis (nDEP).
Importantly, the induced dipole is also a function of frequency. Therefore, we see that the direction in which the particle moves is not only a function of the properties of the particle and the suspending medium but also the frequency of the applied field. The time-averaged dielectrophoretic force on the dipole is given by: 1 1 % ⋅∇ E %*⎤ FDEP = Re ⎡⎣( p% ⋅ ∇ ) E% * ⎤⎦ = v Re ⎡⎣α% E ⎦ 2 2
(
)
(6)
where p% is the induced dipole moment phasor, v the volume of the particle, α% the effective polarisability and * indicates complex conjugate. If the nonuniform electric field has no spatially dependent phase, the dielectrophoretic force simplifies to:
1 %2 FDEP = v Re [α% ] ∇ E 4
(7)
For a spherical particle, Eq. (7) becomes: %2 FDEP = πε m R3 Re ⎡⎣ f%CM ⎤⎦ ∇ E
(8)
According to Eq. (8), if the electric field is uniform, the gradient of the 2
magnitude of the field is zero ( ∇ E% = 0 ), which means that there is no
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DEP force. The frequency dependence and the direction of the DEP force are governed by the real part of the Clausius–Mossotti factor. If the particle is more polarisable than the medium, ( Re ⎡⎣ f%CM ⎤⎦ > 0), the particle is attracted to high intensity electric field regions. This is termed as positive dielectrophoresis (pDEP). Conversely, if the particle is less polarisable than the medium, ( Re ⎡⎣ f%CM ⎤⎦ < 0), the particle is repelled from high intensity field regions and negative dielectrophoresis (nDEP) occurs. Therefore the real part of the Clausius–Mossotti factor characterizes the frequency dependence of the DEP force, as demonstrated in Fig. 1. In practice, it is difficult to measure the DEP force due to the effects of Brownian motion and electrical field-induced fluid flow [3]. Instead, the DEP crossover frequency can be measured as a function of medium conductivity and provides sufficient information to determine the dielectric properties of the suspended particles. The DEP crossover frequency, fcross, is the transition frequency point where the DEP force switches from pDEP to nDEP or vice versa. According to Eq. (6), the crossover frequency is defined to be the frequency point where the real part of the Clausius– Mossotti factor equals zero: f cross =
1 2π
(σ m − σ p )(σ p + 2σ m ) (ε p − ε m )(ε p + 2ε m )
=
1
σm −σ p
2π
ε p − εm
f MW
(9)
where fMW is again the Maxwell-Wagner relaxation frequency, labeled in Fig. 1. In addition to measurements of crossover frequency, the DEP-induced particle velocity can be measured to characterize particles. The DEP induced particle velocity, uDEP, is directly proportional to the DEP force [4] according to:
u DEP =
⎞ FDEP ⎛ F + ⎜ u0 − DEP ⎟ e − t / tm 6π Rη ⎝ 6π Rη ⎠
(10)
where η is the viscosity of the medium and u0 is the initial velocity. The time constant tm is referred to as the momentum relaxation time and is: tm =
m 6π Rη
(11)
where m is the mass of the particle. For a typical cell the momentum relaxation time is of the order of tens of microseconds and can be ignored.
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Therefore in practice, a measurement of particle velocity is a direct measure of the force on that particle 2.3. TRAVELLING WAVE DIELECTROPHORESIS
Masuda et al. [5, 6] were the first to demonstrate that travelling electric fields, generated by sequentially phase-shifted AC voltages, can be used to induce translational motion of particles. Practically, for travelling wave dielectrophoresis (twDEP) to occur, the particle should experience nDEP and be levitated above the electrodes. In a travelling field it experiences a linear force propelling it along the electrode array. Fuhr et al. [7] presented a theoretical model to explain the behavior of microparticles in a travelling electric field generated with a linear array of electrodes. Huang et al. [8] used interdigitated electrodes of comb geometry (Fig. 4) to generate travelling electric fields, established by sequentially addressing the electrodes with a four-phase sinusoidal voltages (90° phase shift) and keeping directly opposing electrodes on either side of the channel phase-shifted from each other by 180°.
Figure 4. Diagram showing an interdigitated electrode array used to induce travelling wave dielectrophoresis. The cells move over the electrodes along the channel in the direction opposite to that of the travelling field. Cells on the left-hand (right-hand) side of the channel rotate in a clockwise (anti-clockwise) sense while moving.
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In electric fields with spatially varying phases, Eq. (6) can be expanded as:
( (
1 % 2 − 1 v Im [α% ] ∇ × Re ⎡E % % FDEP = v Re [α% ] ∇ E ⎣ ⎤⎦ × Im ⎡⎣E ⎤⎦ 4 2
))
(12)
For a spherical particle, Eq. (12) becomes:
( (
% 2 − 2πε R3 Im ⎡ f% ⎤ ∇× Re ⎡E % % FDEP = πε mR3 Re ⎣⎡ f%CM ⎦⎤ ∇ E m ⎣ ⎤⎦ × Im ⎡⎣E⎤⎦ ⎣ CM ⎦
)) (13)
The first term on the right is the DEP force. The second term on the right is the additional travelling wave dielectrophoretic force, which propels the particle moving along the electrode arrays. If there is no spatially varying phase, the imaginary part of the electric field is zero ( Im ⎡⎣E% ⎤⎦ = 0 ), which means there is no twDEP. Generally, in order to generate a twDEP force, the frequency of the excitation voltage and the conductivity of the medium should be chosen to satisfy two conditions: (i) the particle experiences nDEP so that it is levitated above the electrodes. (ii) the imaginary part of the Clausius–Mossotti factor is non-zero. As shown in Fig. 1, at low frequencies, the real part of the Clausius–Mossotti factor is positive, the imaginary part of the Clausius–Mossotti factor is zero except for the mid frequency range where twDEP is possible. 2.4. ELECTROROTATION
The action of an external electric field on a polarisable particle creates an induced dipole moment. The two ends of the dipole experience an equal and opposite force tending to align the dipole parallel to the field generating a torque and causing it to rotate. This phenomenon is called electrorotation (ROT). The direction and rate of rotation depends on the frequency and spatial configuration of the field and also the dielectric properties of the suspending medium and the particles. The phenomenon of ROT was explored in detail by Arnold and Zimmerman [9, 10]. ROT has been widely used in biotechnology, to measure the viability of cells and bacteria [11–14], biocide testing [15] and cell characterization [16–21]. The time-averaged torque on a particle is given by Jones [22]:
(
1 % * ⎤ = −v Im [α% ] Re ⎡E % % Γ ROT = Re ⎡p% × E ⎣ ⎤⎦ × Im ⎡⎣E ⎤⎦ ⎦ 2 ⎣
)
(14)
For a spherical particle, this becomes: 2 Γ ROT = −4πε m R3 Im ⎡⎣ f%CM ⎤⎦ E%
(15)
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Equation (15) shows that the frequency-dependent property of the ROT torque depends on the imaginary part of the Clausius–Mossotti factor. The particle rotates with or against the electric field, depending on whether the imaginary part of the Clausius–Mossotti factor is negative or positive. If the charge relaxation time constant of the particle is smaller than that of the medium (τp = εp/σp < τm = εm/σm), the particle rotates with the field. If τm < τp, the particle rotates against the field. The torque is measured indirectly by analyzing the rotation rate (angular velocity) of the particle, given by Arnold and Zimmerman [10]: RROT (ω ) = −
ε m Im ⎡⎣ f%CM ⎤⎦ E% 2η
2
ξ
(16)
where RROT(ω) is the rotation rate and ξ is a scaling factor that accounts for the fact that neither the viscosity nor the electric field strength are precisely known. Again owing to the viscous nature of the system the momentum relaxation time is small resulting in a constant angular velocity that is proportional to the torque. Therefore the frequency spectra of both the DEP force and ROT torque provide information on the dielectric properties of biological particles in suspension. The relationship between DEP and ROT can be further examined using Argand diagrams [23, 24], where the real and imaginary parts of the Clausius–Mossotti factor are mapped onto the complex plane as a function of frequency. 2.5. MULTIPOLES
All the theories presented above are based on the dipole approximation. However, the dipole approximation can lead to significant inaccuracies for the case where the scale of the electric field non-uniformity is large compared to the size of the particle. For example, a particle at a field null will have no net induced dipole moment. Therefore the force on the particle will arise from induced higher-order moments, which are not considered in the dipole approximation. Multipolar theory has been developed by Jones [22, 25–27] and Washizu [28, 29] and Wang et al. [30]. Multipoles can be classified into the linear and general multipoles. For linear multipoles, as shown in Fig. 5a, the formation of a dipole can be considered as a monopole (a point charge) a certain distance away from another monopole of opposite sign. The quadrupole is formed by the superposition of an oppositely polarized dipole at a distance from the original dipole. The higher order multipole is formed in a similar method. The linear multipoles are applicable only when the electric field is axisymmetric, otherwise general multipoles
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should be used. For general multipoles, every order of multipole is composed of several dipoles. The moment of order n + 1 is formed by two closely spaced nth order moment of opposite polarity as shown in Fig. 5b.
Figure 5. Diagram showing the generation of multipoles (a) linear multipoles (b) general multipoles.
Calculations of the multipolar force and torque can be performed using the effective moment method [22]. Using the dyadic tensors, the nth order time-averaged multipolar DEP force F ( n ) DEP , and ROT torque Γ ( n ) ROT are given by Jones and Washizu [27]: F
Γ
( n)
(n)
ROT
⎡ ⎤⎤ 1 ⎢ 1 ⎡⎢ &&& ( n ) n n * ⎥ % = Re p% [⋅] ( ∇ ) E ⎥ 2 ⎢ n! ⎢ ⎥⎥ ⎦⎦ ⎣ ⎣
(17)
⎡ ⎤ ⎤ 1 ⎢ 1 ⎡⎢ &&& ( n ) n −1 n −1 *⎥ % ⎥ % = Re ×E p [⋅] ( ∇ ) ⎥ 2 ⎢ (n − 1)! ⎢ ⎥ ⎣ ⎦ ⎣ ⎦
(18)
DEP
&&&
For a spherical particle, the nth order of moment p% ( n ) and Clausius– Mossotti factor f% ( n ) are: CM
&&& 4πε m R 2 n +1n % ( n ) n −1 % p% ( n ) = f CM ( ∇ ) E (2n − 1)!!
(19)
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ε% p − ε%m nε% p + (n + 1)ε%m
(20)
According to Eq. (20), the multipolar DEP force and ROT torque on a particle can be determined as long as the electric field distribution in the system is known. 3. Particle Manipulation in Microsystems AC electrokinetic techniques, particularly DEP, have been used for the manipulation, separation, focusing, trapping and handling of latex spheres [31–34], viruses [35–39], bacteria [40–45] and cells [46–50]. Many different electrode geometries have been used to perform DEP. 3.1. CASTELLATED ELECTRODE ARRAY
The castellated electrode array was first used by Pethig’s group [40, 41] to dielectrophoretically collect particles. Similar configurations (e.g. sawtooth electrode array [36] and interleaved electrodes [47]) were used for separating biological particles [51–55]. Figure 6a, b shows a diagram of this type of electrode together with an electric field plot. Typical electrode dimensions are 10–100 μm width and gap. Note that the field is maximum at the electrode tips and minimum in the gaps between electrodes. Such an electrode array has been widely used to characterize the behavior of particles. Those experiencing pDEP collect on the tips, and those experiencing nDEP in the gaps. Figure 6c shows a diagram of this.
Figure 6. (a) Diagram showing the structure of castellated electrode array. (b) Numerical simulation showing the high and low electric field region within the electrode array. (c) Diagram showing the separation mechanism of colloidal particles using DEP in castellated electrode array.
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3.2. INTERDIGITATED ELECTRODE ARRAY
The interdigitated electrode array also generates field non-uniformities and is widely used for DEP and also twDEP. Figure 7 shows such an electrode showing the voltage sequence used for DEP. This design of electrode is often used in DEP separation systems, since it generates a DEP force that decays exponentially from the surface. Also twDEP can be generated in the same system using four signals with phase shifts of 90°, sequentially applied to the electrodes. This generates a travelling electric field with a spatially dependent phase.
Figure 7. Diagram showing an experimental system used for DEP or twDEP. The interdigitated electrode array is fabricated on a glass substrate and energized with different AC signals. For DEP, the electrodes are connected to voltages with 180° phase shifts. For twDEP, the electrodes are connected to a frequency generator with 90° phase shift. w is the electrode width, g is the electrode gap and h is the height of the channel.
A number of papers have derived analytical expressions for the electric field generated by this interdigitated electrode arrays. The methods include Green’s theorem [56], Green’s function [57, 58], half-plane Green’s function [59] and Fourier series [60, 61]. However, these analytical solutions all involve approximations. In both the Green’s theorem and Fourier series methods, it is assumed that the potential varies linearly with distance in the electrode gaps. In the method of Green’s function, the gradient of the electric field magnitude squared is influenced by the choice of a characteristic length scale. In the method of half-plane Green’s function, a linear approximation for the surface potential in the gaps between the electrodes is adopted. Moreover, the presence of the upper surface of the fluidic channels (the insulating lid in real devices), which imposes a Neumann condition on the solution of the potential, was not considered in Refs. [56–60]. In Ref. [61], this condition was analyzed using a closed form of Fourier series, but the solution approximates the potential distribution in the electrode gaps to a linear function. Other approaches, such as the charge density method [52]
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and finite element method [62] are accurate but computationally expensive. Recently, Sun et al. [63] used a Schwarz–Christoffel Mapping method to derive analytical solutions for the electric fields and the dielectrophoretic and travelling-wave dielectrophoretic forces for the interdigitated electrode arrays. The analytical solutions for the DEP and twDEP forces are related to the geometrical constant of the device: electrode length, gap distance and the channel height. Figure 8a shows that the DEP force (direction and magnitude) for the DEP interdigitated electrode array, demonstrating that while the DEP force vectors point towards the electrode edge. The maximum in the DEP force is at the electrode edge with four minima in each corner.
Figure 8. DEP force vectors and magnitude for an interdigitated electrode array. The electrodes are drawn in the figure. (a) The DEP force (direction and magnitude) for DEP. (b) The DEP force (direction and magnitude) in a twDEP array. (c) The twDEP force (direction and magnitude) in a twDEP array. (d) ROT component (magnitude) for twDEP (Sun et al. [63]).
Figure 8b shows the direction and the magnitude of the DEP force component for the twDEP array. The behaviour is similar to the DEP force in a DEP array. Above a certain height, the direction of the DEP force at every position points straight towards the electrode plane, with an exponentially decreasing magnitude. The DEP force magnitude plot clearly shows the maxima at the edges of the electrode. The minima in the centre of the
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electrodes and the gap can also be seen. Figure 8c shows the direction and the magnitude of the twDEP force component. Approaching the bottom, the vectors point in the opposite direction. In the region directly above the edges of the electrode, the vectors show a circular pattern. There are three twDEP force minima in the near field region. Along the surface of the electrode, the magnitude of twDEP force increases towards the edge of the electrode. However, it does not go to a maximum above the edge of the electrodes. Instead, it rapidly drops to a minimum over the electrode edge because the vectors are re-circulating in this region. Figures 8d shows the magnitude of the ROT torque in the twDEP array. The direction of the torque is in the third dimension (i.e. out of the page). The magnitude of the torque goes to a maximum at the edge of the electrode. 3.3. POLYNOMIAL ELECTRODES
The polynomial electrodes design has four electrodes with edges defined by a hyperbolic function in the centre and parallel edges out to an arbitrary distance. The theoretical principle of this electrode design has been described by Huang and Pethig [46]. The polynomial electrode can be used for trapping and characterization of biological particles [33, 37, 39] using either pDEP and nDEP, as shown in Fig. 9.
Figure 9. (a) Image showing pDEP of 557 nm diameter latex spheres on polynomial electrodes. (b) Image showing nDEP of 557 nm diameter latex spheres on polynomial electrodes (Green et al. [33]).
3.4. CONTINUOUS SEPARATION
A continuous DEP separation system was developed by Markx and Pethig [64]. Steric drag force produced by a gentle fluid flow in the chamber was used to separate cells by selectively lifting cells out of potential energy wells generated by the electric field. Holmes and Morgan [65] designed a continuous flowing DEP fractionation system, consisting of two separate arrays of interdigitated electrodes, as shown in Fig. 10a. The particles are
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first focused in the flow stream to a central plane of the flow channel by nDEP, and then attracted by pDEP to the separation electrodes (Fig. 10b).
Figure 10. (a) Schematic showing the continuous DEP separator. (b) Image showing separation of THP-1 cells (green) and PBMCs (red) (Holmes and Morgan [65]).
3.5. DEP FIELD-FLOW FRACTION SYSTEM
Field flow fraction (FFF) describes a method for separating particles based on combining a deterministic force with hydrodynamic separation. A typical configuration is shown in Fig. 11. The system consists of a channel with interdigitated microelectrodes patterned on the bottom substrate. Particles are introduced into the system and when the field is switched on they experience nDEP, moving to equilibrium positions which are defined according to the balance of dielectrophoresis (DEP) and gravity (buoyancy). Different types of particles move to different equilibrium positions in the
Figure 11. Diagram showing the principle of dielectrophoretic field-flow fractionation (DEP-FFF).
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system. Application of a laminar flow carries particles out of the device at a rate that depends on their original equilibrium position. Since different types of the particles are transported at different rates [66–69], a sample can be separated and fractionated along the channel. 3.6. INSULATOR-BASED DEP
Dielectrophoresis does not always have to be performed with conducting metal electrodes. For example, 3D insulating-post arrays [34, 44, 45] have been developed to trap and separate live and dead bacteria using DC voltages applied across the length of a microchannel. The insulating posts in the channel create obstructions in the pathways of the electric field producing non-uniformities in the electric field distribution in the channel, causing particle DEP, as shown in Fig. 12a. Here two different species of bacteria are dielectrophoretically trapped in two distinct regions (Fig. 12b).
Manifold
Reservoir opening Electric field lines being squeezed between the insulating posts
Vacuum line Reservoir
Region of lower field strength Negative dielectrophoresis
Microchannels containing insulating posts Electrode
post
Glass chip Outlet reservoir Inlet reservoir 10 µm height Electrode
Region of higher field strength Positive dielectrophoresis Flow direction
Flow direction
Figure 12. (a) Schematic showing the setup of the insulating-posts geometry and the principle of generating non-uniform electric field in the microchannel. (b) Image showing the separation of live (green) and dead (red) E. coli by creating 60 V/mm electric field (Lapizco-Encinas et al. [45]).
A continuous-flow dielectrophoretic spectrometer system has been developed based on insulating DEP techniques with three-dimensional geometries on an insulating substrate [70]. Different field gradients were generated by fabricating devices in polymers with constrictions in the channel depth to create a device that continuously separates particles with controls of transverse channel position. 3.7. SINGLE CELL TRAPPING
Single cell trapping is important in many applications of biotechnology, such as the study of cell-cell interaction, drug screening and diagnostics. Electric field cages that generate nDEP forces to trap single cells were
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introduced by Fuhr et al. [71] in the early of 1990s. Since then single cell trapping systems have been widely studied [72–81]. Müller et al. [72] used planar quadrupole electrode configuration to trap and concentrate micrometer and sub-micrometer particles. A 3-D microelectrode system [73] consisting of two layers of electrode structures was designed to focus, trap and separate cells and latex beads using nDEP. Schnelle et al. [75] fabricated an AC cage with octode electrode to trap cells against a fluid stream. Manaresi et al. [76] used 0.35 µm CMOS technology to fabricate a complex microelectrode array for manipulating a large number of individual cells.
Figure 13. Image showing the dynamic array cytometer consisting of single cell traps (Voldman et al. [78]).
Voldman and colleagues [77–82] developed multiple single cell DEP traps. Figure 13 is an example of an array of traps, made with sets of four electroplated gold electrodes arranged trapezoidally [78, 79]. The device is was used to obtain luminescence information of the trapped cells and also to sort them. An review of cell manipulation techniques using electrical forces has been published by Voldman [83]. Various electrode geometries such as the quadrupole and octopole electrode, nDEP microwells, point-and-lid geometry and ring-dot geometry are described and evaluated. Recently, a novel design of particle trap that uses nDEP in high conductivity physiological media was reported [84]. The single cell trap consists of a metal ring electrode and a surrounding ground plane, as shown in Fig. 14a. The ring electrodes creates a closed electric field cage in the centre (Fig. 14b). Figure 14c shows 15 μm diameter beads trapped against a fluid flow.
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Figure 14. (a) Diagram showing the structure of ring electrodes. The ring traps are fabricated from two Ti/Pt layers (yellow) with a benzocyclobutene dielectric layer (blue). (b) Numerical simulation showing DEP force vectors and electric field distribution in the ring trap. (c) Four 40 µm diameter ring traps from an array of 48 traps. Single beads are captured by nDEP (Thomas et al. [84]).
4. Scaling in AC Electrokinetic Microsystems Neglecting electrohydrodynamic forces, the two main forces that act on particles in addition to DEP are gravity and Brownian motion. As the size of the particle is reduced, so the effects of Brownian motion become greater. Therefore, to enable the dielectrophoretic manipulation of sub-micron particles using realistic voltages, the characteristic dimensions of the system must be reduced, to increase the electric field. However, a high strength electric field also produces a force on the suspending electrolyte, causing fluid flow [85]. Indeed, this motion may be a far greater limiting factor than Brownian motion. The force and velocity associated with Brownian motion have zero average. However the random displacement of the particle follows a Gaussian profile. To move an isolated particle in a deterministic manner during this period, the displacement due to the deterministic force should be greater than that due to the random (Brownian) motion. This consideration is meaningful only for single isolated particles. For a collection of particles, diffusion of the ensemble must be considered. Calculations of the typical displacements for particles can be made provided the electric field (and gradient) is known [86, 87]. The simplest
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geometry is a semi-infinite parallel plate structure, consisting of two coplanar rectangular electrodes with an infinitely small gap, as shown in Fig. 15a [85].
Figure 15. (a) Simple electrode geometry consisting of two parallel plate electrodes with a small gap used to calculate the typical particle displacements. (b) Particle displacement in one second versus particle radius for a particle of mass density 1,050 kg m−3. The characteristic length for used in this figure is r = 25 μm.
In this geometry, the field as a function of radial distance (r) is E = V/πr, where V is the amplitude of the applied voltage and r is the distance to the centre of the gap. The influence of Brownian motion, gravity and DEP on a single particle can be calculated for this electrode structure, and are summarized in Fig. 15b [85]. The plot shows the displacement of a particle during a time interval of one second as a function of particle radius, a. For a radius of 25 μm, at 5 V, it can be seen that the displacement due to Brownian motion is greater than that due to DEP if the particle is less than 0.4 μm diameter. Also, gravity is less important than DEP for any particle sizes, since both scales as a2. The deterministic manipulation of particles smaller than 0.4 μm can be achieved if the magnitude of the applied voltage is increased, or the characteristic length of the system r is reduced. The figure shows the effect of increasing the voltage by a factor of three, which increases the displacement due to DEP by one order of magnitude. Although Fig. 15b shows that it should be relatively easy to move small particles simply by increasing the electric field, this naïve assumption presumes that no other forces appear in the system. This is generally not the case, and the action of the electric field on the fluid must be considered. To summarize, the DEP force depends on the electric field gradient, which changes with the length scale of the electrodes; DEP is a short range effect. From the perspective of the design of microsystems for particle manipulation, different electrode shapes and sizes can be fabricated relatively easily. The forces scale in a complex manner with system dimensions, frequency, field, etc.
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5. Conclusions The behavior of particles and fluids on the microscale is determined by a number of forces. In AC field, the electrokinetic forces act on the induced dipole. Electrohydrodynamic forces are predominantly due to double layer charge or body forces due to gradients in conductivity and/or permittivity created by thermal gradients. In separation systems, buoyancy force can be significant (as in FFF) but often the magnitude of this force is much lower than the other forces for micron sized particles. The DEP force depends on the gradient of the energy density, which changes on the length scale of the electrodes and is a short range effect. The DEP force can be modulated by changing the frequency and electrical properties of the suspending medium. The electrokinetics forces scale in a complex manner with system dimensions, frequency, field etc. AC electrokinetic manipulation of particles and fluids is a powerful and flexible enabling technology which has many applications in microfluidic systems.
References 1. H. A. Pohl, Dielectrophoresis, Cambridge University Press, Cambridge (1978). 2. R. Pethig, Dielectric and electronic properties of biological materials, Wiley, UK (1979). 3. H. Morgan and N. G. Green, AC Electrokinetics: colloids and nanoparticles, Research Studies Press, Ltd. Baldock, Hertfordshire, England (2003). 4. Y. Huang, R. Hölzel, R. Pethig and X-B. Wang, Differences in the AC electrodynamics of viable and non-viable yeast cells determined through combined dielectrophoresis and electrorotation studies, Phys. Med. Biol., 37, 1499–1517 (1992). 5. S. Masuda, M. Washizu and I. Wadare, Separation of small particles suspended in liquid by non-uniform travelling field, IEEE Trans. Ind. Appl., 23, 474–480 (1987). 6. S. Masuda, M. Washizu and I. Kawabata, Movement of blood cells in liquid by nonuniform travelling field, IEEE Trans. Ind. Applicat., 24, 214–222 (1988). 7. G. Fuhr, R. Hagedorn, T. Müller and J. Gimsa, Asynchronous travelling-wave induced linear motion of living cells, Studia Biophys, 140, 79–102 (1991). 8. Y. Huang, X-B. Wang, J. A. Tame and R. Pethig, Electrokinetic behaviour of colloidal particles in travelling electric field: studies using yeast cells, J. Phys. D: Appl. Phys., 26, 1528–1535 (1993). 9. W. M. Arnold and U. Zimmerman, Rotating-field-induced rotation and measurement of the membrane capacitance of single mesophyll cells of Avena sativa, Z. Naturforsch., 37c, 908–915 (1982).
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10. W. M. Arnold and U. Zimmerman, Electrorotation: development of a technique for dielectric measurements on individual cells and particles, J. Electrostat., 21, 151–191 (1988). 11. X-F. Zhou, G. H. Markx, R. Pethig and I. M. Eastwood, Differentiation of viable and non-viable bacteria biofilms using electrorotation, Biochim. Biophys. Acta, 1245, 85–93 (1995). 12. C. E. Hodgson and R. Pethig, Determination of the viability of Escherichia coli at the single organism level by electrorotation, Clin. Chem., 44, 2049–2051 (1998). 13. C. Dalton, A. D. Goater, J. Drysdale and R. Pethig, Parasite viability by electrorotation, Colloid. Surface. A: Physicochem. Eng. Aspects, 195, 263–268 (2001). 14. C. Dalton, A. D. Goater, R. Pethig and H. V. Smith, Viability of Giardia intestinalis cysts and viability and sporulation state of Cyclospora cayetanensis oocysts determined by electrorotation, Appl. Environ. Microbiol., 67, 586–590 (2001). 15. X-F. Zhou, G. H. Markx and R. Pethig, Effect of biocide concentration on electrorotation spectra of yeast cells, Biochim. Biophys. Acta, 1281, 60–64 (1996). 16. K. L. Chan, P. R. C. Gascoyne, F. F. Becker and R. Pethig, Electrorotation of liposomes: verification of dielectric multi-shell model for cells, Biochim. Biophys. Acta, 1349, 182–196 (1997). 17. R. Hölzel, Electrorotation of single yeast cells at frequencies between 100 Hz and 1.6 GHz, Biophys. J., 73, 1103–1109 (1997). 18. X-F. Zhou, J. P. H. Burt and R. Pethig, Automatic cell electrorotation measurements: studies of the biological effects of low-frequency magnetic fields and of heat shock, Phys. Med. Biol., 43, 1075–1090 (1998). 19. J. Yang, Y. Huang, X-J. Wang, X-B. Wang, F. F. Becker and P. R. C. Gascoyne, Dielectric properties of human leukocytes subpopulations determined by electrorotation as a cell separation criterion, Biophys. J., 76, 3307– 3314 (1999). 20. M. Cristofanilli, G. D. Gasperis, L. S. Zhang, M. C. Huang, P. R. C. Gasconye and G. N. Horotobagyi, Automated electrorotation to reveal dielectric variations related to HER-2/neu Overexpression in MCF-7 sublines, Clin. Cancer Res., 8, 615–619 (2002). 21. C. Dalton, A. D. Goater, J. P. H. Burt and H. V. Smith, Analysis of parasites by electrorotation, J. Appl. Microbio.,96, 24–32 (2004). 22. T. B. Jones, Electromechanics of particles, Cambridge University Press, Cambridge (1995). 23. X-B. Wang, R. Pethig and T. B. Jones, Relationship of Dielectrophoretic and electrorotational behaviour exhibited by polarized particles, J. Phys. D: Appl. Phys. 25, 905–912 (1992). 24. X-B. Wang, Y. Huang, R. Holzel, J. P. H. Burt and R. Pethig, Theoretical and experimental investigations of the interdependence of the dielectric, Dielectrophoretic and electrorotational behaviour of colloidal particles, J. Phys. D: Appl. Phys.,26, 312–322 (1993). 25. T. B. Jones, Multipole corrections to dielectrophoretic force, IEEE Trans. Ind. Appls., IA-21, 930–934 (1985).
AC ELECTROKINETIC PARTICLE MANIPULATION
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26. T. B. Jones and M. Washizu, Equilibria and dynamics of DEP-levitated particle: multipolar theory, J. of Electrostat., 33, 199–212 (1994). 27. T. B. Jones and M. Washizu, Multipolar dielectrophoretic and electrorotation theory, J. of Electrostat., 37, 121–134 (1996). 28. M. Washizu, Precise calculation of dielectrophoretic force in arbitrary field, J. of Electrostat., 29, 177–188 (1992). 29. M. Washizu and T. B. Jones, Multipolar dielectrophoretic force calculation, J. of Electrostat., 33, 187–198 (1994). 30. X. Wang, X-B Wang and P. R. C. Gascoyne, General expressions for dielectrophoretic force and electrorotational torque derived using the Maxwell stress tensor method, J. of Electrostat., 39, 277–295 (1997). 31. H. Morgan, M. P. Hughes and N. G. Green, Separation of submicron bioparticles by dielectrophoresis, J. Biophys., 77, 516–525 (1999). 32. M. P. Hughes and H. Morgan, Dielectrophoretic characterization and separation of antibody-coated submicrometer latex spheres, Anal. Chem., 71, 3441–3445 (1999). 33. N. G. Green, A. Ramos and H. Morgan, Ac electrokinetics: a survey of submicrometer particle dynamics, J. Phys. D: Appl. Phys., 33, 632–641 (2000). 34. E. B. Cummings and A. K. Singh, Dielectrophoresis in microchips containing arrays of insulating posts: theoretical and experimental results, Anal. Chem., 75, 4724–4731 (2003). 35. H. Morgan and N. G. Green, Dielectrophoretic manipulation of rod-shaped viral particles, J. Electrostat., 42, 279–293 (1997). 36. N. G. Green and H. Morgan, Manipulation and trapping of sub-micron bioparticles using dielectrophoresis, J. Biochem. Biophys. Methods, 35, 89–102 (1997). 37. M. P. Hughes, H. Morgan, F. J. Rixon, J. P. H. Burt and R. Pethig, Manipulation of herpes simplex virus I by dielectrophoresis, Biochem. Biophys. Acta, 1425, 119–126 (1998). 38. M. P. Hughes, H. Morgan and F. J. Rixon, Dielectrophoretic manipulation and characterization of herpes simplex virus type I capsids, European Biophys. J., 30, 268–272 (2001). 39. M. P. Hughes, H. Morgan and F. J. Rixon, Measuring the dielectric properties of herpes simplex virus type I virions with dielectrophoresis, Biochem. Biophys. Acta, 1571, 1–8 (2002). 40. J. A. R. Price, J. P. H. Burt and R. Pethig, Applications of a new optical technique for measuring the dielectrophoretic behaviour of micro-organisms, Biochim. Biophys. Acta, 964, 221–230 (1988). 41. J. P. H. Burt, T. A. K. A-Ameen and R. Pethig, An optical dielectrophoresis spectrometer for low-frequency measurements on colloidal suspensions, J. Phys. E: Sci. Instrum., 22, 952–957 (1989). 42. G. H. Markx, P. A. Dyda and R. Pethig, Dielectrophoretic separation of bacteria using a conductivity gradient, J. Biotechnol., 51, 175–180 (1996). 43. M. P. Hughes and H. Morgan, Measurement of bacterial flagellar thrust by negative dielectrophoresis, Biotechnol. Prog., 15, 245–249 (1999). 44. B. H. Lapizco-Encinas, B. A. Simmons, E. B. Cummings and Y. Fintschenko, Insulator-based dielectrophoresis for the selective concentration and separation of live bacteria in water, Electrophoresis, 25, 1695–1704 (2004).
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45. B. H. Lapizco-Encinas, B. A. Simmons, E. B. Cummings and Y. Fintschenko, Dielectrophoretic concentration and separation of live and dead bacteria in an Array of insulators, Anal. Chem., 76, 1571–1579 (2004). 46. Y. Huang and R. Pethig, Electrode design for negative dielectrophoresis, Meas. Sci. Technol., 2, 1142–1146 (1991). 47. P. R. C. Gascoyne, Y. Huang, R. Pethig, J. Vykoukal and F. F. Becker, Dielectrophoretic separation of mammalian cells studied by computerized image analysis, Meas. Sci. Technol., 3, 439–445 (1992). 48. Y. Huang, R. Hölzel, R. Pethig and X-B. Wang, Differences in the AC electrodynamics of viable and non-viable yeast cells determined through combined dielectrophoresis and electrorotation studies, Phys. Med. Biol., 37, 1499–1517 (1992). 49. S. Archer, T. T. Li, A. T. Evans, S. T. Britland and H. Morgan, Cell reactions to dielectrophoretic manipulation, Biochem. Biophys. Res. Comm., 257, 687– 698 (1999). 50. R. Pethig, V. Bressler, C. Carswell-Crumption, Y. Chen, L. Foster-Haje, M. E. García-Ojeda, R. S. Lee, G. M. Lock, M. S. Talary and K. M. Tate, Dielectrophoretic studies of the activation of human T lymphocytes using a newly developed cell profiling system, Electrophoresis, 23, 2057–2063 (2002). 51. R. Pethig, Y. Huang, X. B. Wang and J. P. H. Burt, Positive and negative dielectrophoretic collection of colloidal particles using interdigitated castellated microelectrodes, J. Phys. D: Appl. Phys. 24, 881–888 (1992). 52. X-B Wang, Y. Huang, J. P. H. Burt, G. H. Markx and R. Pethig, Selective dielectrophoretic confinement of bioparticles in potential energy wells, J. Phys. D: Appl. Phys. 26, 1278–1285 (1993). 53. P. R. C. Gascoyne, J. Noshari, F. F. Becker and R. Pethig, Use of dielectrophoretic collection spectra for characterizing differences between normal and cancerous cells, IEEE Trans. Indus. Appl., 30, 829–834 (1994). 54. F. F. Becker, X-B. Wang, Y. Huang, R. Pethig, J. Vykoukal and P. R. C. Gascoyne, The removal of human leukaemia cells from blood using interdigitated microelectrodes, J. Phys. D: Appl. Phys. 27, 2659–2662 (1994). 55. F. F. Becker, X-B. Wang, Y. Huang, R. Pethig, J. Vykoukal and P. R. C. Gascoyne, Separation of human breast cancer cells from blood by differential dielectric affinity, PNAS. 92, 860–864 (1995). 56. X. Wang, X-B. Wang, F. F. Becker and P. R. C. Gascoyne, A theoretical method of electric field analysis for dielectrophoretic electrode arrays using Green’s theorem, J. Phys. D: Appl. Phys., 29, 1649–1660 (1996). 57. M. Garcia and D. S. Clague, The 2D electric field above planar sequence of independent strip electrodes, J. Phys. D: Appl. Phys., 33, 1747–1755 (2000). 58. E. Liang, R. L. Smith and D. S. Clague, Dielectrophoretic manipulation of finite sized species and the importance of the quadrupolar contribution, Phys. Rev. E, 70, 066617 ( 2004). 59. D. S. Clague and E. K. Wheeler, Dielectrophoretic manipulation of macromolecules: The electric field, Phys. Rev. E, 64, 026605 (2001). 60. H. Morgan, A. G. Izquierdo, D. Bakewell, N. G. Green and A. Ramos, The dielectrophoretic and travelling wave forces generated by interdigitated electrode arrays: analytical solution using Fourier series, J. Phys. D: Appl. Phys., 34, 1553–1561 (2001).
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61. D. E. Chuang, S. Loire and I. Mezić, Closed-form solutions in the electric field analysis for dielectrophoretic and travelling wave interdigitated electrode arrays, J. Phys. D: Appl. Phys., 36, 3073–3078 (2003). 62. N. G. Green, A. Ramos and H. Morgan, Numerical solution of the dielectrophoretic and travelling wave forces for interdigitated electrode arrays using the finite element method, J. Electrostat., 56, 235–254 (2002). 63. T. Sun, H. Morgan and N. G. Green, Analytical solutions of ac electrokinetics in interdigitated electrode arrays: electric field, dielectrophoretic and travellingwave dielectrophoretic forces, Phys. Rev. E., 76, 046610 (2007). 64. G. H. Markx and R. Pethig, Dielectric separation of cells: continuous separation, Biotech. Bioeng., 45, 337–343 (1995). 65. D. Holmes and H. Morgan, Cell positioning and sorting using dielectrophoresis, Eur. Cell. Mater., 4, 120–122 (2002). 66. G. H. Markx, J. Rousselet and R. Pethig, DEP-FFF: field-flow fractionation using non-uniform electric fields, J. Liquid Chromatography Relat. Technol., 20, 2857–2872 (1997). 67. G. H. Markx, R. Pethig and J. Rousselet, The dielectrophoretic levitation of latex beads, with reference to field-flow fractionation, J. Phys. D: Appl. Phys., 30, 2470–2477 (1997). 68. J. Rousselet, G. H. Markx and R. Pethig, Separation of erythrocytes and latex beads by dielectrophoretic levitation and hyperlayer field-flow-fraction, Colloid. Surface. A: Physicochem. Eng. Aspects, 140, 209–216 (1998). 69. P. R. C. Gascoyne and J. Vykoukal, Dielectrophoresis-based sample handling in general-purpose programmable diagnostic instruments, IEEE Proc. 92, 22– 42 (2004). 70. B. G. Hawkins, A. E. Smith, Y. A. Syed and B. J. Kirby. Continuous-Flow particle separation by 3D insulative dielectrophoresis using coherently shaped, dc-biased, ac electric fields, Anal. Chem. 79, 7291–7300 (2007). 71. G. Fuhr, W. M. Arnold, R. Hagedorn, T. Müller, W. Benecke, B. Wagner and U. Zimmermann, Levitation, holding and rotation of cells within traps made by high-frequency fields, Biochim. Biophys. Acta, 1108, 215–223 (1992). 72. T. Müller, A. Gerardino, T. Schnelle, S. G. Shirley, F. Bordoni, G. D. Gasperis, R. Leoni and G. Fuhr, Trapping of micrometre and sub-micrometre particles by high-frequency electric fields and hydrodynamic forces, J. Phys. D: Appl. Phys., 29, 340–349 (1996). 73. T. Müller, G. Gradl, S. Howitz, S. Shirley, T. Schnelle and G. Fuhr, A 3-D microelectrode system for handling and caging single cells and particles, Biosens. Bioelectron., 14, 247–256 (1999). 74. T. Schnelle, T. Müller and G. Fuhr, The influence of higher moments on particle behaviour in dielectrophoretic field cages, J. Electrostat., 46, 13–28 (1999). 75. T. Schnelle, T. Müller and G. Fuhr, Trapping in AC octode field cages, J. Electrostat., 50, 17–29 (2000). 76. N. Manaresi, A. Romani, G. Medoro, L. Altomare, A. Leonardi and M. Tartagni, A CMOS chip for individual cell manipulation and detection, IEEE J. Solid-State Circ., 38, 2297–2305 (2003).
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77. J. Voldman, R. A. Braff, M. Toner, M. L. Gray and M. A. Schmidt, Holding forces of single-particle dielectrophoretic traps, Biophys. J., 80, 531–541 (2001). 78. J. Voldman, M. L. Gray, M. Toner and M. A. Schmidt, A microfabricatedbased dynamic array cytometer, Anal. Chem.74, 3984–3990 (2002). 79. J. Voldman, M. Toner, M. L. Gray and M. A. Schmidt, Design and analysis of extruded quadrupolar dielectrophoretic traps, J. Electrostat., 57, 69–90 (2003). 80. A. Rosenthal and J. Voldman, Dielectrophoretic traps for single-particle patterning, Biophys. J., 88, 2193–2205 (2005). 81. B. M. Taff and J. Voldman, A scalable addressable positive-dielectrophoretic cell-sorting array, Anal. Chem., 77, 7976–7983 (2005). 82. A. Rosenthal, B. M. Taff and J. Voldman, Quantitative modeling of dielectrophoretic traps, Lab Chip, 6, 508–515 (2006). 83. J. Voldman, Electrical forces for microscale cell manipulation, Annu. Rev. Biomed. Eng., 8, 425–454 (2006). 84. R. S. Thomas, H. Morgan and N. G. Green, Negative DEP traps for single cell immobilisation, Lab Chip, 9, 1534–1540 (2009). 85. A. Ramos, H. Morgan, N. G. Green and A. Castellanos, Ac electrokinetics: a review of forces in microelectrode structures, J. Phys. D: Appl. Phys., 31, 2338–2353 (1998). 86. D. J. Tritton, Physical fluid dynamics, Oxford University Press, New York (1988). 87. D. J. Acheson, Elementary fluid dynamics, Oxford University Press, New York (1990).
MICROFLUIDIC IMPEDANCE CYTOMETRY: MEASURING SINGLE CELLS AT HIGH SPEED TAO SUN AND HYWEL MORGAN
Nano Research Group, School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK,
[email protected]
Abstract. High throughput single cell microfluidic analysis platforms offer the ability to characterize large numbers of individual cells (or more generally particles) at high speed. Miniature flow cytometers offer new methods for the rapid analysis of single cells. Impedance analysis of single cells provides information on cell size (volume), membrane and cytoplasmic characteristics. The technology has developed rapidly and offers the prospects of new approaches for counting and differentiating cells with applications from basic research to point of care diagnostics.
1. Introduction Flow cytometry is a well established technique for counting, identifying and sorting cells [1, 2]. Modern commercial fluorescence-activated-cell-sorting (FACS) machines can analyze thousands of cells per second, but are generally expensive complex machines that are unsuited to handling small sample volumes. Lab-On-Chip (LOC) technologies [3–9], offer new approaches to cell assays, and new technologies are being developed for high speed cell manipulation. Individual cells can be identified on the basis of differences in size and dielectric properties using electrical techniques that are non-invasive and label-free. Characterization of the dielectric properties of biological cells is generally performed in two ways, with AC electrokinetics or impedance analysis. AC electrokinetic techniques are used to study of the behavior of particles (movement and/or rotation) and fluids subjected to an AC electric field. The electrical forces act on both the particles and the suspending fluid and have their origin in the charge and electric field distribution in the system. They are the basis of phenomena such as dielectrophoresis [10–14], travelling wave dielectrophoresis [15, 16], electrorotation [17, 18] and electroorientation [19].
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Electrical impedance spectroscopy (EIS), measures the AC electrical properties of particles in suspension from which the dielectric parameters of the particles can be obtained. The earliest work on bio-impedance measurements can be traced back to the 1910s [20–22] that compared the low and high frequency conductivity of erythrocytes. The frequencydependence of the conductivity was measured (due to the cell membrane) and this paper was the first to estimate the conductivity of the interior of an erythrocyte. In 1924 and 1925, Fricke published a series of papers [23–25] that described the electrical conductivity and capacity of disperse systems using principles laid down by Maxwell [26]. Measurements of the capacitance of the suspending system [27–29] were used to estimate the capacitance and thickness of the cell membrane. Cole [30, 31] used Maxwell’s mixture equation to derive the complex impedance of a single shell cell in suspension. Schwan pioneered the field of cell impedance analysis [32, 33], and identified three major dielectric dispersions (α, β and γ) in biological cells. The dispersion occurring at the lowest frequency is the α-dispersion which is attributed to polarisation of the double layer around a colloidal particle. The β-dispersion occurs in the MHz regime and originates from charging of the capacitive cell membrane. It is the most widely measured and used to determine cell membrane capacitance. Schwan’s contributions to the dielectric measurements of biological material have been summarized by Foster [34]. 2. Theory Impedance is the ratio of the voltage across a system to the current passing through the system. It measures the dielectric properties (permittivity and conductivity) of the system. The dielectric behavior of colloidal particles in suspension is generally described by Maxwell’s mixture theory [26]. This relates the complex permittivity of the suspension to the complex permittivity of the particle, the suspending medium and the volume fraction. Based-on Maxwell’s mixture theory, shelled-models have been widely used to model the dielectric properties of particles in suspension [35–40]. A single shelled spherical model is shown in Fig. 1a. The complex permittivity of the mixture is ε%mix :
ε%mix = ε%m
1 + 2Φf%CM 1 − Φf%CM
with
ε% p − ε%m f%CM = ε% p + 2ε%m
(1)
where ε% = ε − jσ / ω is the complex permittivity, j2 = −1, ω the angular frequency, f%CM is the Clausius–Mossotti and Ф is the volume fraction. The subscripts p and m refer to particle and medium respectively.
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Figure 1. (a) Diagram of a single shelled spherical particle, representing a cell in suspension. (b) Plot showing the real and imaginary parts of the Clausius–Mossotti factor of the mixture, calculated for different conductivities of the medium. The following parameters for the medium and a cell were used: εo = 8.854 × 10−12 Fm−1, R = 3 × 10−6 m, d = 5 × 10−9 m, εm = 80 × εo, εmem = 5 × εo, σmem = 10−8 Sm−1, εi = 60 × εo, σi = 0.4 Sm−1.
The complex permittivity of the cell, ε% p is a function of the dielectric properties of membrane and cytoplasm, cell membrane ε%mem and internal properties ε%i , and cell (inner radius R and membrane thickness d) given by:
ε% p = ε%mem
⎛ ε%i − ε%mem ⎞ ⎟ ⎝ ε%i + 2ε%mem ⎠ with γ = R + d R ⎛ ε% − ε% ⎞ γ 3 − ⎜ i mem ⎟ ⎝ ε%i + 2ε%mem ⎠
γ 3 + 2⎜
(2)
The Clausius–Mossotti factor f%CM , characterizes the frequency-dependent effective dipole moment. Separating the real and imaginary part of the Clausius–Mossotti factor give a Debye relaxation of the form: ⎛ σ p −σ m ⎞ ⎛ ε p − εm ⎜ ⎟−⎜ ⎛ ε p − ε m ⎞ ⎜⎝ σ p + 2σ m ⎟⎠ ⎜⎝ ε p + 2ε m Re ⎡⎣ f%CM ⎤⎦ = ⎜ + 2 ⎜ ε + 2ε ⎟⎟ 1 + ω 2τ MW m ⎠ ⎝ p
⎞ ⎟⎟ ⎠
(3)
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Im ⎡⎣ f%CM ⎤⎦ =
⎡⎛ ε p − ε m ⎢⎜⎜ ⎣⎢⎝ ε p + 2ε m
⎞ ⎛ σ p −σm ⎟⎟ − ⎜⎜ ⎠ ⎝ σ p + 2σ m 2 1 + ω 2τ MW
⎞⎤ ⎟⎟ ⎥ ωτ MW ⎠ ⎦⎥
(4)
with
τ MW =
ε p + 2ε m σ p + 2σ m
(5)
where Re[ ] and Im[ ] are the real and imaginary part of, respectively. In AC electrokinetics [12], the frequency dependence and the direction of the dielectrophoretic force are governed by the real part of the Clausius– Mossotti factor, whilst the electrorotation spectrum depends on the imaginary part of the Clausius–Mossotti factor. Figure 1b shows spectra of the real and imaginary parts of the Clausius–Mossotti factor of a cell for different suspending medium conductivities (see legends for details). In Eq. (5), τMW is referred to as the Maxwell-Wagner relaxation time constant. For single cells in suspension, the suspending system has two intrinsic relaxation frequencies. The first relaxation (time constant τ1), occurs at low frequencies and is due to Maxwell-Wagner polarisation of cell membrane-suspending medium interface. The second relaxation (time constant τ2) occurs at higher frequencies, and is due to polarisation between the suspending medium and the cell cytoplasm, when the cell membrane capacitance is effectively short-circuited. Figure 1b shows these two relaxations as the real and imaginary parts of the Clausius–Mossotti factor. For a cell the DEP component (real part) is always negative at low frequencies but at intermediate frequencies this varies with the conductivity of the suspending medium. Note that there are two ROT peaks (imaginary part of Clausius–Mossotti factor), each of which corresponds to the two relaxations. Characterization of the dielectric properties of single cells is often performed by analyzing the rotation spectra, in conjunction with measurements of the low frequency DEP cross-over point [11, 12]. Pauly and Schwan [41] described two characteristic relaxation time constants in terms of cell properties: ⎛ 1− Φ ⎞ 1 +⎜ σ i ⎝ 2 + Φ ⎟⎠ σ m τ 1 = RCmem ⎡ 1 ⎛ 1− Φ ⎞ 1 ⎤ 1 + RGmem ⎢ + ⎜ ⎟ ⎥ ⎣σ i ⎝ 2 + Φ ⎠ σ m ⎦ 1
(6a)
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τ2 =
ε i + 2ε m σ i + 2σ m
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(6b)
Their results are based on three approximations: (i) The conductivity of the cell membrane was considered to be very small compared with the cytoplasm and the suspending medium conductivity (σmem << σm and σi). (ii) The membrane thickness is small when compared with the cell inner radius (d << R). (iii) The displacement current in the suspending medium and the cytoplasm is negligible compared with the conduction current (εm = εi = 0). Taken together, these three approximations make τ1 independent of the permittivity of the suspending medium and the cytoplasm, and τ2 independent of the permittivity and conductivity of the membrane. Recently we used Laplace transforms of Maxwell’s mixture equation (Eqs. (1) and (2)) to derive complete analytical expressions for the two characteristic relaxation time constants [39]. The impedance of a system, e.g. cells in suspension, is related to the complex permittivity through Z% mix =
1 jωε%mix G f
(7)
where Gf is a geometric constant, which for an ideal parallel plate electrode system is simply the ratio of electrode area to gap. This equation, together with Eq. (1) allows the complex permittivity of a suspension of cells to be determined from the frequency-dependent impedance measurements. For single cell impedance analysis, the cell is located in an electric field generated by two micro-electrodes, where the field in this case is not uniform and the effect of the divergent field (fringing field) must be considered to correctly model the impedance. This requires detailed analysis of the field geometry and a modification to Gf. For simplified analysis of the system an electrical circuit analogue is often used and such an approach was developed by Foster and Schwan [42]. The cell is approximated to a resistor that describes the cytoplasm in series with a capacitor for the membrane as shown in Fig. 2. The cell membrane resistance is generally much greater than the reactance of the membrane and is ignored. Likewise the capacitance of the cell cytoplasm can be ignored when its reactance is compared to the cell cytoplasm resistance. The values of the electrical components in the circuit are as follows:
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Suspending medium: Rm =
1 σ m (1 − 3Φ / 2)G f
(8a)
Cm = ε ∞ G f
(8b)
Simplified cell components: Cmem =
9ΦRCmem,0 4
Gf
⎛ 1 1 ⎞ 4⎜ + ⎟ 2σ σi ⎠ Ri = ⎝ m 9Φ G f
(8c)
(8d)
with membrane capacitance (per unit area) Cmem,0 = ε mem / d . The limiting high frequency permittivity of the suspension is related to the suspending medium permittivity according to
ε∞
⎡
ε m ⎢1 − 3Φ ⎣
ε m − εi ⎤ ⎥ 2ε m + ε i ⎦
(8e)
Foster and Schwan’s simplified circuit model has been used to interpret single cell impedance measurements [43–45] providing good agreement with experiments. However, in certain cases, both the cell membrane and cytoplasm properties cannot be ignored, for example during electroporation [46] or cell lysis [47], where the resistance of the cell membrane and the capacitance of the cytoplasm vary widely. In this case, the complete equivalent circuit model should be used. For a single-shelled spherical particle this includes the resistance of the membrane and the capacitance of the cytoplasm [48]. Using the circuit schematic in Fig. 2, simulations can be performed using PSpice (Orcad Capture, Cadence Inc. USA). The advantage of circuit simulation compared to mixture theory is that the impedance spectrum of the system not only includes the properties of the cell and the medium but also the passive (resistor and capacitor) and active (op-amps) components in the detection circuit. It is important to determine the effect of these parameters on the spectrum. The simulations can also indicate optimal parameters (i.e. frequency, medium conductivity, etc.) and also provide guidance in optimizing the circuit.
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Figure 2. Diagram showing the equivalent circuit model for a cell in suspension. The electrical double layer (EDL) on the surface of the electrodes is model as a capacitor CDL.
Figure 3 shows the magnitude and phase of the differential impedance signal for a 3 μm (radius) cell. Below 1 MHz, the EDL limits the sensitivity, since most of the excitation voltage is dropped across the EDL. The magnitude of the signal increases, as the frequency goes up. The maximum magnitude of the impedance depends on the size of the cell. With increasing frequency, the impedance spectrum is dominated by the dielectric properties of the cell membrane and the cytoplasm.
Figure 3. Plot of the magnitude and phase of the impedance signal of a single cell in suspension from the PSpice circuit simulation.
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3. Single Cell Impedance Microfluidic Cytometry Impedance flow cytometry uses microelectrodes integrated into the walls or top and bottom of the microchannel. Ayliffe et al. [49] were the first to demonstrate single cell impedance measurements in a micro-device. They fabricated a microchannel (10 µm wide and 4.3 µm high) from epoxy-based photoresist on glass substrate with integrated gold electrodes (8 µm wide and 4 µm thick). This device showed the ability to differentiate impedance differences in cells, demonstrating the potential of single cell impedance analysis. Sohn et al. [50] developed “capacitance cytometry” and claimed to measure the DNA content of eukaryotic cells at 1 kHz. A significant advance in the technology was reported by Gawad et al. [43], who demonstrated differentiation of beads and also erythrocytes and ghost cells. The principle of single cell impedance analysis is shown in Fig. 4a. Two pairs of microelectrodes are fabricated on the top and bottom of a microchannel. The electrodes are energized with a voltage at one or more discrete frequencies, generating non-uniform electric field within the channel. One pair is for sensing the electric current fluctuation, induced by the cell and the other measures the electric current passing through the pure medium and acts as a reference. When a cell flows through the sensing region, the electric field distribution within the channel is altered. To detect the impedance signal from a single cell, microelectrodes are fabricated with sizes similar to the cells, in the range 10–30 µm. The electric currents from two sensing volumes are converted into voltage signals using trans-impedance amplifiers. Then, a differential amplifier subtracts the difference between the two current signals. Lock-in amplifiers are used to demodulate the in-phase and out-phase impedance signals at the stimulating frequency, whilst rejecting noise at other frequencies (Fig. 4b). The differential variation in impedance is measured as a pair of peaks. The output signals from the lock-in amplifiers are sampled with a 16 bit data acquisition card. Data analysis is performed using software written to extract the impedance information, such as the magnitude and phase. For the microfluidics (Fig. 4b): a valve selects different liquid inputs, for example washing or priming liquids. A motorized syringe pump is used for fast purging of the whole line at high pressure to prevent channel clogging and a sample valve selects either cleaning liquid or sample. Pressure control of the sample tube is provided by a high-precision pressure regulator, allowing precise control of fluid flow. The level of the liquid in the collection vials is set so as to produce a small back-flow when atmospheric pressure is applied to the sample.
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Figure 4. (a) Diagram showing a microfluidic chip used for high throughput single particle impedance spectroscopy. Individual particles flow along the microfluidic channel (channel height, h). The microelectrodes (width w and length l) measure the electrical impedance of the cell. (b) The experimental set up for single cell impedance analysis, including microfluidic control.
Electrical and fluidic interconnections to the chip are made using a custom built connection block, machined from PEEK polymer. Fluidic and electrical connections are made by clamping the chip within the block. Spring loaded connectors are used to make contact with the chip electrodes and miniature O-rings used to seal the fluidic connection between the block and chip. Microfluidic tubing and connectors are used to connect the PEEK block to the sample, waste and wash reservoirs. The connector block is mounted on a PCB which has the impedance detection circuitry and the
Figure 5. Photographs showing the experimental setup: assembled microchip and mechanical holder mounted on the printed circuit board (for differential impedance sensing) above a microscope.
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DEP driving electronics. The entire assembly is mounted on an x-y-z stage above a microscope objective, allowing alignment of the chip and accurate positioning of the optical detection region within the microfluidic channel. Figure 5 shows the photographs of the assembled chip and hold mounted above microscope lens. In impedance microfluidic cytometers, two types of microelectrodes are used to measure the impedance signal: parallel facing electrodes and coplanar electrodes, as shown in Fig. 6.
Figure 6. Schematic diagram showing a microfluidic impedance cytometer with two different electrode arrangements. (a) Parallel facing electrodes, with two pairs of electrodes arranged opposite each other; (b) coplanar electrodes with electrodes fabricated only on the bottom of the channel.
The non-homogeneous electric field distribution causes variation in the impedance signal amplitude, since particles flowing at different positions in the channel, experience different electric field strength. Accurate mapping of the electric field distribution within the microchannel is required to model the impedance spectrum of a single cell. Gawad et al. [51] performed 3D finite element modelling of a pair of parallel facing electrodes to calculate the electric field and compared numerical solutions with Maxwell’s mixture equation. Linderholm et al. [52, 53] and Sun et al. [40] used Schwarz–Christoffel mapping method to analytically solve the electric field distribution for coplanar and parallel facing electrodes designs. Figure 7 shows the plots of the electric field lines and the magnitude of the electric field in the coplanar and parallel facing electrodes, respectively. It can be
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observed that control of particle position is more significant for the coplanar design than for the parallel electrode configuration because the electric field distribution in latter design is least divergent [40].
Figure 7. (a) Plots of the electric field lines and magnitude (V/m) for the coplanar electrodes (log10 scale). (b) Plots showing of the electric field lines and magnitude (V/m) for the parallel facing electrodes (log10 scale). Note that the channel extends to infinity on both sides.
The geometric constant in Eq. (7) relates the measured impedance to the system complex permittivity. To account for the non-homogeneity of the electric field distribution in the cytometer a value for Gf needs to be derived [51]. The geometric factor depends on the length of the electrode, width and height of the channel and full derivations of this geometric factor for both coplanar and parallel facing electrodes designs have been derived in Sun et al. [40]. 4. Developments and Applications In recent years, several technologies such as white noise stimulation, hydrodynamic focusing and trapping arrays have been implemented within single cell impedance microfluidic cytometry to achieve broadband spectroscopy, improvement in sensitivity and continuous time course measurements.
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Single cell impedance analysis in micro-cytometry is conventionally performed at high speed, usually with two excitation signals. Measurement of the frequency spectrum for a single cell population can be performed by sweeping a stimulation signal over a range of frequencies while cells flow through the device [43, 51, 54–56]. The disadvantage of this approach is that although single cells are measured the data represents the average for the population and is not a true measurement of an individual cell. A high speed multi-frequency analysis system to characterise single particles was developed by Fuller et al. [57], using multiple fixed frequencies demodulated with lock-in systems. However, the system is complicated and requires a large amount of mixed-signal hardware. Sun and Gawad et al. [44, 58, 59] developed a broadband impedance spectroscopy technique for single cell analysis in a time window as short as 1 ms. The technique uses a pseudorandom white noise (maximum length sequence, MLS) as a stimulating signal instead of single frequency sinusoidal signals, as shown in Fig. 8a. The MLS single cell impedance measurement system is shown in Fig. 8b, where the signal generators and lock-in amplifiers of a conventional system (Fig. 4b) are replaced with the MLS signal. Software is used to transform the sampled output response into the impulse response of the system using the Fast M-sequence Transform (FMT). The transfer-function of the system is obtained from the FFT, finally giving the impedance spectrum. Figure 8c shows variations of the real part of the transfer-function of the system due to the passage of two sizes of beads, plotted for four discrete frequencies (out of 512 separate frequencies measured). The figure demonstrates how MLS measures the impedance of every bead at many different frequencies at the same time. Figure 8d shows the MLS data, the single frequency data and the PSpice simulation results for 5.49 μm diameter beads. MLS measurement provides 512 discrete frequencies in approximately 1 ms. The AC single frequency measurement data for ten different frequencies was measured over several minutes and is the average signal for 200 beads at every frequency. The figure shows good agreement for all three methods, indicating that the MLS system correctly measures the impedance spectrum for a single particle. However a limitation of MLS technology is degradation of the signal-to-noise ratio of the system, since MLS is extremely vulnerable to slight time variances, for example changes in the flow of cells in the microchannel. Sun et al. [60] applied adaptive filtering technique in an adaptive line enhancer mode to reduce the noise. In laminar flow, the viscous force of the fluid dominates over the inertial force so that in microfluidics, hydrodynamic focusing techniques can be used to increase the sensitivity of the system. Rodriguez-Trujillo et al. [61, 62] used a sheath flow with a lower conductivity than the central sample flow to concentrate the electric field lines into the impedance sensing region. A 3D hydrodynamic focusing scheme was proposed by Scott et al.
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[63], in which a stepped outlet channel was fabricated to create a narrow sample stream on the floor of the channel for close interaction with the impedance sensing electrodes. Very recently, a similar focusing strategy to Rodriguez-Trujillo et al. [62] was adopted by Watkins et al. [64] to ensure that cells flow in single-file consistently close to the sensing electrodes. The sensitivity of impedance analysis can be increased further using an insulating sheath flow consisting of an oil phase, focusing a sample into the central stream as shown in Fig. 9a by Bernabini et al. [65]. This figure shows a wide microfluidic channel (250 μm) with pairs of opposing electrodes. The oil sheath ensures that the current density is concentrated only in the conducting liquid. Using this technique it is possible to detect differences between micron-sized particles in a very wide channel. For example, Fig. 9b, c shows impedance scatter plots for mixtures of beads and E. coli. The impedance data is plotted as phase against the magnitude of the low frequency signal (503 kHz). The data is triggered on the low frequency inphase impedance signal and, in both cases, clear discrimination between the two different populations is observed.
Figure 8. (a) Diagram showing the principle of MLS single cell impedance analysis. (b) Diagram showing the structure and data flow path of the MLS impedance measurement system. (c) Variations of the real part of the transfer-function signal as a function of time, for two different beads, at four selected frequencies. (d) Real and imaginary part of the impedance spectrum for the 5.49 μm bead obtained from PSpice simulation, MLS measurements and AC single frequency measurements, showing good agreement.
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Figure 9. (a) Diagram showing the hydrodynamic focusing scheme using oil in the sheath flows. (b) Scatter plot of phase against low frequency impedance magnitude for a mixture of 1 µm and 2 µm diameter polystyrene beads. The plots are color coded based on the fluorescence measured from each bead. (c) Scatter plot of phase against low frequency impedance magnitude for a mixture of E. coli and 2 µm diameter polystyrene beads. The plots are color coded based on the fluorescence measured from each particle.
In contrast to continuous flow systems, there is often need to monitor single cells in culture for long periods of time. Microfluidic devices are ideally suited to this, and one example of a multiplexed single cell assay technology is the hydrodynamic cell trapping arrays, which are used to capture large numbers of individual cells for kinetic analysis within a microfluidic device [66, 67]. These arrays can be integrated with impedance sensing electrodes, for example, Jang and Wang [68] fabricated a threepillar microstructure to capture single HeLa cells in a microchannel and perform electrical impedance analysis of single cells. Hua and Pennell [69] fabricated a chevron like structure of electrodes in a microfluidic channel to capture single cells and measure volume changes using impedance. Malleo et al. [70] demonstrated continuous differential impedance analysis of single cells held by hydrodynamic cell traps. Figure 10a shows the way in which individually addressable electrodes together with micron-sized traps are integrated in a microfluidic platform. Measurements are performed on cells that are hydrodynamically trapped by normalizing the spectrum of a trap containing a single cell to a neighboring counterpart empty trap. Longterm studies are therefore not influenced by local changes in temperature, pH, or conductivity. The system was tested by assaying the transient response of HeLa cells to the lysing effects of the surfactant Tween (Fig. 10b) and the kinetics of the pore-forming toxin streptolysin-O (Fig. 10c) were
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measured. Perfusion of the toxin elicited exponential decays in the differential impedance response with time constants inversely proportional to toxin concentration. The combination of single hydrodynamic cell trapping with single cell impedance analysis provides a scalable label-free cell analysis system. The throughput of cell capturing-type devices is limited unless a large numbers of traps can be fabricated in the channel [66, 67, 71]. The integration of electrodes together with multiplexed impedance measurements increases the complexity of the system compared with flow-through systems and for large arrays of traps complex active matrix methods will be needed to measure the signals from multiple electrodes.
Figure 10. (a) Images of single cell trapping device with microelectrodes for impedance measurements. (b) Traces of three individual cells showing the typical change in impedance when a single HeLa Cells is perfused with Tween 20. (c) Data showing the effect of SLO on the impedance spectrum from single cells. The data represented here was sampled at the frequency of 300 kHz.
Single cell impedance analysis methods have recently been developed for biomedical, clinical and point-of-care (PoC) diagnostic applications. Mishra et al. [72] used protein coated microelectrodes to capture the CD4+ cells and showed a linear relationship between the measured impedance and the number of the captured CD4+ cells, although single cell sensitivity was not demonstrated. The device is aimed at a low cost method for counting CD4+ cells and therefore diagnosing and managing patients with HIV/ AIDS. Cheng et al. [73] used various designs of electrode patterns to count cells by measuring impedance changes in the suspending systems. The
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detection sensitivity is 20 cells μL−1. Single cell sensitivity was demonstrated by Wang et al. [74] who integrated a metal oxide semiconductor field effect transistor (MOSFET) into a microfluidic chip, and together with optical detection was able to count purified lymphocytes. The device has the potential to reduce the cost of HIV diagnosis and treatment. A significant development in the application of single cell impedance systems was recently demonstrated by Holmes et al. [56], who showed how a complete white blood cell differential (or complete) count be performed on a few microlitres of human blood. Lymphocytes, monocytes and neutrophils could be identified and counted. Figure 11a shows the measured frequency-dependent properties of these three main leukocyte sub-populations, together with PSpice circuit simulations. The data shows that the impedance varies with cell size and membrane capacitance across the frequency spectrum. Figure 11b shows a scatter plot for whole human blood (depleted of RBCs) where the three common leukocytes can be clearly identified. The microfluidic cytometer was tested using blood taken from volunteers and benchmarked against a commercial blood analysis system. The lymphocyte, monocyte and granulocyte counts were determined from a two-dimensional Gaussian probability profiles. Figure 11c shows the correlation (95%) between the impedance cytometer and standard haematology analysis. This technology should find applications in a number of diagnostic and research areas, for example cell cycle analysis, apoptosis and toxicity/viability assays.
Figure 11. (a) Single cell impedance spectra for populations of T-lymphocytes, monocytes, neutrophils. Each point is the average for about 1,500 events and shows the mean and standard deviation of the measurement data. The dashed lines show the best fit PSPICE circuit simulation. (b) Scatter plot of opacity vs the low frequency impedance magnitude for saponin/formic acid treated whole blood and 7.18 μm beads. (c) The WBC distributions from a micro-impedance cytometer referenced against a commercial full blood analyser. (Adapted with permission from Holmes et al. (2009) [56], copyright © 2009, RSC.)
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5. Conclusions Electrical impedance analysis offers a simple and non-invasive method of characterising cells and cellular events at the single cell level. It can be used to determine cells on the basis of size and allows label free discrimination of different types of cells on the basis of different membrane properties. As an analytical technique, it does not offer the sensitivity and specificity offered by conventional (fluorescent) antibody based methods. However, it is a technique that can complement other sensing methods and in certain cases offers high sensitivity and throughput. Impedance-based analytical can measure changes in membrane conductivity, for example during cell lysis or poration, and provides information in real time at the single cell level. The method can measure small changes in cell membrane capacitance and cell size, and this provides a simple means to characterise cells. Combining impedance analysis methods with other analytical techniques on a microfluidic format will provide a comprehensive analysis platform. This enables thousands of individual single cells to be assayed with high temporal resolution. To compete with traditional fluorescent-based analytical methods that use antibodies, an analogous electrical labelling method must be developed. Impedance based cannot compete with the specificity and complexity of molecular detection techniques, but it will continue to find a place within the range of analytical techniques used within microfluidic systems.
References 1. H. M. Davey. and D. B. Kell, Flow cytometry and cell sorting of heterogeneous microbial populations: the importance of single-cell analyses, Microbiological Reviews, 60, 641–696 (1996). 2. H. M. Shapiro, The evolution of cytometers, Cytometry A, 58A, 13–20 (2004). 3. A. Manz, D. J. Harrison. E. M. J. Verpoorte, J. C. Fettinger, A. Paulus, H. Lüdi and H. M. Widmer, Planar chips technology for miniaturization and integration of separation techniques into monitoring systems-capillary electrophoresis on a chip, J. Chromatog., 593, 253–258 (1992). 4. G. M. Whitesides and A. D. Stroock, Flexible Methods for Microfluidics, Phys. Today, 54, 42–48 (2001). 5. T. Thorsen, S. J. Maerkl and S. R. Quake, Microfluidic large-scale integration, Science, 298, 580–584 (2002). 6. D. J. Beebe, G. A. Mensing and G. M. Walker, Physics and applications of microfluidics in biology, Annu. Rev. Biomed. Eng., 4, 261–286 (2002). 7. H. A. Stone, A. D. Stroock and A. Ajdari, Engineering flows in small devices: microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid. Mech., 36, 381–411 (2004).
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8. T. M. Squires and S. R. Quake, Microfluidics: fluidic physics at the nanoliter scale, Rev. Mod. Phys., 77, 977–1026 (2005). 9. G. M. Whitesides, The origins and the future of microfluidics, Nature, 442, 368–373(2006). 10. H. A. Pohl, Dielectrophoresis, Cambridge University Press, Cambridge (1978). 11. R. Pethig, Dielectric and electronic properties of biological materials, Wiley, UK (1979). 12. H. Morgan and N. G. Green, AC Electrokinetics: colloids and nanoparticles, Research Studies Press, Ltd. Baldock, Hertfordshire, England (2003). 13. J. Voldman, Electrical Forces for microscale cell manipulation, Annu. Rev. Biomed. Eng., 8, 425–454 (2006). 14. T. Sun, H. Morgan and N. G. Green, Analytical solutions of ac electrokinetics in interdigitated electrode arrays: Electric field, dielectrophoretic and travelling-wave dielectrophoretic forces, Phys. Rev. E, 76, 046610 (2007). 15. Y. Huang, X. B. Wang, J. A. Tame and R. Pethig, Electrokinetic behaviour of colloidal particles in travelling electric-fields: studies using yeast cells, J. Phys. D. Appl. Phys., 26, 1528–1535 (1993). 16. H. Morgan, N. G. Green, M. P. Hughes, W. Monaghan and T. C. Tan, Large area travelling-wave dielectrophoresis particle separator, J. Micromech. Microeng., 7, 65–70 (1997). 17. W. M. Arnold and U. Zimmermann, Electro-rotation: development of a technique for dielectric measurements on individual cells and particles, J. Electrostat., 21, 151–191 (1988). 18. J. Yang, Y. Huang, X. J. Wang, F. F. Becker and P. R. C. Gascoyne, Dielectric properties of human leukocyte subpopulations determined by electrorotation as a cell separation criterion, J. Biophys., 76, 3307–3314 (1999). 19. T. B. Jones, Electromechanics of particles, Cambridge University Press, Cambridge (1995). 20. R. Höber, Eine Methode die elektrische Leitfaehigkeit im Innern von Zellenzu messen, Arch. Ges. Physiol., 133, 237–259 (1910). 21. R. Höber, Ein zweites Verfahren die Leitfaehigkeit im Innern von Zellen ze messem, Arch. Ges. Physiol., 148, 189–221(1912). 22. R. Höber, Messungen der inneren Leitfaehigkeit von Zelen III, Arch. Ges. Physiol., 150, 15–45 (1913). 23. H. Fricke, A mathematical treatment of the electrical conductivity of colloids and cell suspensions, J. Gen. Physiol., 6, 375–384 (1924). 24. H. Fricke, A mathematical treatment of the electric conductivity and capacity of disperse systems, I. The electric conductivity of a suspension of homogeneous spheroids, Phys., Rev., 24, 575–587 (1924). 25. H. Fricke, A mathematical treatment of the electric conductivity and capacity of disperse systems, II. The capacity of a suspension of conducting membrane for a current of low frequency, Phys., Rev., 26, 678–681 (1925). 26. J. C. Maxwell, A treatise on Electricity and Magnetism, Oxford, Clarendon Press (1873). 27. H. Fricke, The electric capacity of suspensions of a red corpuscles of a dog, Phys., Rev., 26, 682–687 (1925).
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525
28. H. Fricke,The electric capacity of suspensions with special reference to blood, J. Gen. Physiol., 9, 137–152 (1925). 29. H. Fricke, The electric resistance and capacity of blood for frequencies between 800 and 4.5 million cycles, J. Gen. Physiol., 9, 153–167 (1925). 30. K. S. Cole, Electric impedance of suspensions of spheres, J. Gen. Physiol., 12, 29–36 (1928). 31. K. S. Cole, Electric impedance of suspensions of Arbacia eggs, J. Gen. Physiol., 12, 37–54 (1928). 32. H. P. Schwan, Electrical properties of tissue and cell suspensions, Adv. Biol. Med. Phys., 5, 147–209 (1957). 33. H. P. Schwan, Determination of biological impedances, Phys. Tech. Bio. Res., WL Nastuk New York: Academic, 6, 323–406 (1963). 34. K. R. Foster and H. P Schwan, Dielectric properties of tissues and biological materials: a critical review, Crit. Rev. Biomed. Eng., 17, 25–104 (1989). 35. T. Hanai, Theory of the dielectric dispersion due to the interfacial polarization and its application to emulsion, Kolloid-Z, 171, 23–31 (1960). 36. D. Wachner, M. Simeonova and J. Gimsa, Estimating the subcelluar absorption of electric field energy: equations for an ellipsoidal single shell model, Bioelectroch., 56, 211–213 (2002). 37. D. A. Stewart, T. R. Gowrishankar., K. C. Smith and J. C. Weaver, Cylindrical cell membranes in uniform applied electric field: validation of a transport lattice method, IEEE Trans. Biomed. Eng., 52, 1643–1653 (2005). 38. K. Asami, Dielectric dispersion in biological cells of complex geometry simulated by the three-dimensional finite difference method. J. Phys. D: Appl. Phys., 39, 492–499 (2006). 39. T. Sun, S. Gawad, N. G. Green and H. Morgan, Dielectric spectroscopy of single cells: time domain analysis using Maxwell’s mixture equation, J. Phys. D. Appl. Phys., 40, 1–8 (2007). 40. T. Sun, N. G. Green, S. Gawad and H. Morgan, Analytical electric field and sensitivity analysis for two microfluidic impedance cytometer designs, IET Nanobiotechnol., 1, 69–79 (2007). 41. H. Pauly and H. P. Schwan, Uber die Impedanz einer Suspension von kugelformigen Teilchen mit einer Schale, Z. Naturf. B, 14, 125–131(1959). 42. K. R. Foster, Herman P. Schwan: a scientist and pioneer in biomedical engineering, Annu. Rev. Biomed. Eng., 4, 1–27 (2002). 43. S. Gawad, L. Schild and Ph. Renaud, Micromachined impedance spectroscopy flow cytometer for cell analysis and particle sizing, Lab Chip, 1, 76–82 (2001). 44. T. Sun, S. Gawad, C. Bernabini, N. G. Green, and H. Morgan, Broadband single cell impedance spectroscopy using maximum length sequences: theoretical analysis and practical considerations, Meas. Sci. Technol. 18, 2859–2868 (2007d). 45. H. Morgan, T. Sun, D. Holmes, S. Gawad and N. G. Green, Single cell dielectric spectroscopy, J. Phys. D: Appl. Phys., 40, 61–70 (2007). 46. T. Y. Tsong, Electroporation of cell membranes, Biophys. J. 60, 297–306 (1991). 47. H. Lu, M. A. Schmidt and K. F. Jensen, A microfluidic electroporation device for cell lysis, Lab Chip, 5, 23–29 (2005). 48. T. Sun, C. Bernabini and H. Morgan, Single-colloidal particle impedance spectroscopy: complete equivalent circuit analysis of polyelectrolyte microcapsules, Langmuir, DOI: 10.1021/1a903609u (2009).
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49. H. E. Ayliffe, A. B. Frazier and R. D. Rabbit, Electric impedance spectroscopy using microchannels with integrated metal electrodes, J. Microelectromech. Syst. 8, 50–57 (1999). 50. L. L. Sohn, O. A. Saleh, G. R. Facer, A. J. Beavis, R. S. Allan and D. A. Notterman, Capacitance cytometry: measuring biological cells one by one, PNAS, 97, 10687–10690 (2000). 51. S. Gawad, K. Cheung, U. Seger, A. Bertsch and Ph. Renaud, Dielectric spectroscopy in a micromachined flow cytometer: theoretical and practical considerations, Lab Chip, 4, 241–251 (2004). 52. P. Linderholm and Ph. Renaud, Comment on ‘AC frequency characteristics of coplanar impedance sensors as design parameters’, Lab Chip, 5, 270–279 (2005). 53. P. Linderholm, U. Seger and Ph. Renaud, Analytical expression for electric field between two facing strip electrodes in microchannel, Electron. Lett. IEE, 42, 145–147 (2006). 54. K. Cheung, S. Gawad and Ph. Renaud, Impedance spectroscopy flow cytometry: on-chip label-free cell differentiation, Cytometry Part A, 65A, 124–132 (2005). 55. H. Morgan, D. Holmes and N. G. Green, High speed simultaneous single particle impedance and fluorescence analysis on a chip, Curr. Appl. Phys., 6, 367–370 (2006). 56. D. Holmes, D. Pettigrew, C. H. Reccius, J. D. Gwyer, C. V. Berkel, J. Holloway, D. E. Davie and H. Morgan, Leukocyte analysis and differentiation using high speed microfluidic single cell impedance cytometry, Lab Chip, 9, 2881–2889 (2009). 57. C. K. Fuller, J. Hamilton, H. Ackler, P. Krulevitch, B. Boser, A. Eldredge, F. Becker, J. Yang and P. Gascoyne, Microfabricated multi-frequency particle impedance characterization system Proc. µTAS Symp., Enschede, The Netherlands May 2000, 265–268. 58. T. Sun, D. Holmes, S. Gawad, N. G. Green and H. Morgan, High speed multifrequency impedance analysis of single particles in a microfluidic cytometer using maximum length sequences, Lab Chip, 7, 1034–1040 (2007). 59. S. Gawad, T. Sun, N. G. Green and H. Morgan, Impedance spectroscopy using maximum length sequences: Application to single cell analysis, Rev. Sci. Instr., 78, 054301 (2007). 60. T. Sun, C. V. Berkel, N. G. Green and H. Morgan, Digital signal proceesingmethods for impedance microfluidic cytometry, Microfluid Nanofluid, 6, 179–187 (2009). 61. R. Rodriguez-Trujillo, C. A. Mills, J. Samitier and G. Gomila, Low cost micro-Coulter counter with hydrodynamic focusing, Microfluid Nanofluid, 3, 171–176 (2007). 62. R. Rodriguez-Trujillo, O. Castillo-Fernandez, M. Garrido, M. Arundell, A. Valencia and G. Gomila, High-speed particle detection in a micro-Coulter counter with two-dimensional adjustable aperture, Biosens. Bioelectron., 24, 290–296 (2008). 63. R. Scott, P. Sethu and C. K. Harnett, Three-dimensional hydrodynamic focusing in a microfluidic Coulter counter, Rev. Sci. Instr., 79, 046104 (2008).
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64. N. Watkins, B. M. Venkatesan, M. Toner, W. Rodriguez, R. Bashir, A robust electrical microcytometer with 3-dimensional hydrofocusing, Lab Chip, DOI: 10.1039/b912214a (2009). 65. C. Bernabini, D. Homes and H. Morgan, Detection and discrimination of bacteria and micro-particles by micro-impedance spectroscopy, Lab Chip (submitted) (2009). 66. D. D. Carlo, L. Y. Wu and L. P. Lee, Dynamic single cell culture array, Lab Chip, 6, 1445–1449 (2006). 67. D. D. Carlo, L. Y. Wu and L. P. Lee, Single-cell enzyme concentrations, kinetics, and inhibition analysis using high-density hydrodynamic cell isolation arrays, Anal. Chem., 78, 4925–4930 (2006). 68. L. S. Jang and M. H. Wang, Microfluidic device for cell capture and impedance measurement, Biomed. Microdevices, 9, 737–743 (2007). 69. S. Z. Hua and T. Pennell A microfluidic chip for real-time studies of the volume of single cells, Lab Chip, 9, 251–256 (2009). 70. D. Malleo, J. T. Nevill, L. P. Lee and Morgan H, Continuous differential impedance spectroscopy of single cells, Microfluid Nanofluid (accepted) (2009). 71. A. M. Skelley, O. Kirak, H. Suh, R. Jaenisch and J. Voldman, Microfluidic control of cell pairing and fusion, Nat. Methods, 6, 147–152 (2009). 72. N. N. Mishra, S. Retterer, T. J. Zieziulewicz, M. Isaacson, D. Szarowski, D. E. Mousseau, D. A. Lawrence and J. N. Turner,On-chip micro-biosensor for the detection of human CD4(+) cells based on AC impedance and optical analysis. Biosens Bioelectron., 21, 696–704. (2005). 73. X. Cheng, Y. Liu, D. Irimia, U. Demirci, L. Yang, L. Zamir, W. R. Rodríguez, M. Toner and R. Bashir, Cell detection and counting through cell lysate impedance spectroscopy in microfluidic devices, Lab Chip, 7, 746–755 (2007). 74. Y. N.Wang, Y. Kang, D. Xu, C. H. Chon, L. Barnett, S. A. Kalams, D. Li and D. Li, On-chip counting the number and the percentage of CD4+ T lymphocyte, Lab Chip, 8, 309–315 (2008).
OPTOFLUIDICS DAVID ERICKSON
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, 14850, USA,
[email protected]
Abstract. Optical devices which incorporate liquids as a fundamental part of the structure can be traced at least as far back as the eighteenth century where rotating pools of mercury were proposed as a simple technique to create smooth mirrors for use in reflecting telescopes. The development of modern microfluidic and nanofluidic devices has enabled a present day equivalent of such devices centered on the marriage of fluidics and optics which we refer to as “Optofluidics.” We review here two optofluidic technologies of relevance to microsystems for security. For the first of these, I will focus on our efforts to novel biomolecular optical sensing architectures for pathogen detection and genetic screening. Two approaches will be discussed; the first exploiting optical resonance in silicon photonic devices and the second using Surface Enhanced Raman Spectroscopy (SERS) based detection. Preliminary data for serotype specific Dengue virus detection and Interleukin immunoassay will be presented. In the second area we will demonstrate how photonic devices can be used to drive micro- and nanoscale transport processes when traditional mechanisms (e.g. pressure and electrokinetics) fail. Here it will be demonstrated how the concentration and amplification of the optical field inside slot waveguides and ring resonators results in extremely large scattering and polarization forces. These forces can be used to trap organic and inorganic targets ranging in size from tens of microns to handfuls of nanometers. Some of the advanced analytical, numerical and experimental techniques used to investigate and design these systems will be discussed as well as issues relating to integration and their fabrication.
1. Nanoscale Optofluidic Sensor Arrays Photonic crystal resonator based biosensors [1] have generated a lot of recent interest due to their ability to confine light within sub-wavelength modal volumes thus allowing for ultra-small detection sites. In addition, photonic crystal based architectures allow for a much larger degree of lightS. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_25, © Springer Science + Business Media B.V. 2010
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matter interaction making them significantly more sensitive as compared to evanescent field based sensing techniques. The NOSA platform consists of multiple evanescently coupled 1-D photonic crystal resonators situated along a single bus waveguide. A central cavity in the 1-D photonic crystal structure of each resonator gives rise to a defect state [1] in the photonic bandgap. This results in a resonant dip in the output spectrum of the bus waveguide. By tailoring the cavity length, each of the evanescently coupled 1-D resonators is designed to possess a unique resonant wavelength. Figure 1d illustrates the steady-state electric field intensity distribution within the 1-D resonator at the resonant wavelength. The binding of target biomolecules to the surface of the resonator induces a slight increase in the local refractive index around it. The interaction of the resonant optical field with the bound target biomolecules at the sensor surface and within the photonic crystal holes results in a red-shift in the corresponding resonant wavelength of the resonator. Put simply, the increase in the refractive index of the optical cavity caused by the presence of bound mass increases the effective optical length of the cavity and thereby the wavelength of light that will
Figure 1. Current Nanoscale Optofluidic Sensor Arrays. (a) 3D rendering of the NOSA device. (b) 3D rendering after association of the corresponding antibody to the antigen immobilized resonator. (c) Experimental data illustrating the successful detection of 45 µg/ml of antistreptavidin antibody. The blue trace shows the initial baseline spectrum corresponding to Fig. 1a where the first resonator is immobilized with streptavidin. The red trace shows the test spectra after the association of anti-streptavidin. (d) Finite difference time domain (FDTD) simulation of the steady state electric field distribution within the 1-D photonic crystal resonator at the resonant wavelength. (e) SEM image demonstrating the two-dimensional multiplexing capability of the NOSA architecture.
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resonate within it (Fig. 1c). The output optical spectrum from the bus waveguide can be constantly monitored and binding of target biomolecules to the resonator is inferred when a red-shift is observed. Since each evanescently coupled 1-D resonator possesses a unique resonance in the output spectrum, multiplexed detection along a single waveguide is facilitated (Fig. 1e). In the case shown here, each of the 1-D resonators is initially functionalized with a unique capture molecule. The sample containing target bio-molecules is made to flow over the 1-D resonators while the output spectrum is monitored. By observing the combination of resonances that red-shift it is possible to determine which target molecules were present in the detection sample. Analysis of the degree of red-shift provides quantitative information regarding the amount of bound mass which can be correlated to concentration of target molecule present in a sample. Figure 1e is an SEM image of a NOSA array, illustrating the two-dimensional multiplexing capabilities of the platform. Fabrication of the devices is done using standard e-beam and photolithography and microfluidic integration techniques described in detail in our recent works [2, 3]. We refer reviewers to these published works rather than detail the process here in order to focus more on the biological results. 1.1. MASS SENSITIVITY
The first of our preliminary results we demonstrate here is mass sensitivity. To do this we use a polyelectrolyte multilayer “layer-by-layer” deposition technique. Briefly, multilayers of polyethyleneimine and polyacrylic acid were deposited on the glutaraldehyde functionalized NOSA device, and on similarly functionalized silicon wafers in parallel. After deposition of each layer, output spectra were recorded to quantify shift in resonant wavelengths and polyelectrolyte multilayer film thickness was determined on silicon wafers using ellipsometry. Output spectra were compared to the initial baseline spectra to determine resonance shift (Δλ, in nm), and were plotted against film thickness as shown in Fig. 2. Baseline spectra were taken on 5 NOSA resonators and parallel silicon wafers after surface functionalization. A film thickness of 3.11 nm corresponds to the molecular thickness of native oxide, amine-terminated silane monolayer, and glutaraldehyde functionalization, each of which contributes ~1 nm to total film thickness. Since the field at the sensor surface exhibits an exponential decay, the growth of the polyelectrolyte multilayer and the resulting effect on resonance shift were fit to an exponential model as shown in Fig. 2.
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Figure 2. Optical response to polyelectrolyte layer growth. (a) Effect of polyelectrolyte multilayer thickness on resonance shift. Data have been fit to an exponential model; (b) error bars represent standard deviation.
To estimate the total mass sensitivity of the device we use this multilayer technique along with the measurements reported by Ganesan et al. [4] who determined the bound mass on a scanning probe cantilever due to the self-assembly of PEI and PAA monolayers. They reported measuring 24 pg of bound mass for a five layer polyelectrolyte stack over a surface area of 0.9 × 10−4 cm2 which corresponded to a bound surface mass density of 2.67 × 10−7 g/cm2. The functionalized surface area of a single 1-D photonic crystal resonant sensor including the internal surface area of the holes is 8.36 μm2. Assuming the same surface mass density as above, we calculate the total bound mass on a NOSA sensor for a five layer stack of polyelectrolyte monolayers to be 22.3 fg. The corresponding red-shift in the resonant wavelength was observed to be 3.53 nm. The smallest resolvable red-shift can be approximated as the linewidth/50 [5] which is approximately
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0.01 nm in our system. Thus we estimate the smallest amount of bound mass that can be detected by our current sensor system to be 63 ag corresponding to a surface mass coverage of 7.5 pg/mm2.
Figure 3. Increase in absolute sensitivity as a function of number of functionalized holes. FDTD simulation showing the mass sensitivity of the device plotted as a function of the number of functionalized holes. The blue circles indicate the sensitivity values calculated from the simulations.
As we expand on below there are two methods by which we can increase this detection sensitivity. Figure 3 shows how by reducing the number of functionalized holes in the resonator the total amount of mass will increase. As can be seen a device sensitivity of 3.5 nm/fg is possible with the first two holes being functionalized. Assuming the same detectable linewidth as the above, an absolute LOD on the order of 3 ag can be achieved. One method by which this could be done is by exploiting some of the recent work done on improving the Q-factor of such 1-D resonators [6, 7]. The combination of these techniques will help pave the way towards the detection of sub-attogram amounts of bound mass. 1.2. LABEL-FREE MULTIPLEXED INTERLEUKIN IMMUNOASSAY
Another advantage of our approach over other optical resonator designs is its suitability for performing multiplexed detections. Due to the fabrication process and the planar nature of the device, it is easy to fabricate a single
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bus waveguide coupled to many 1-D photonic crystal resonators for performing multiplexed detections. In contrast, multiplexed detections in microtoroid, microsphere and some microdisk sensors requires complicated alignment of tapered optical fibers in free space [8] thus making these sensors prohibitive for performing highly parallel detections in a robust, integrated sensor platform. Given our observed linewidth and the 100 nm operational range of a standard 1,550 nm tunable laser, we expect that 50 1D resonators could be incorporated along a single waveguide. Another important advantage of the NOSA design is that the small cavity size results in each resonator possessing a large free spectral range (FSR) of over 200 nm. In comparison, most WGM sensors have cavity lengths over 100 μm resulting in a maximum FSR of 3–5 nm. The large FSR for our NOSA architecture enables each resonator to have a single resonant peak in the output spectrum, thus facilitating interpretation of the multiplexed output signal. The larger FSR of our sensor design also allows for a higher number of resonant sensors to be multiplexed along a waveguide as compared to WGM sensors. Figure 4a shows the resulting spectra after introducing 1 μg/ml of interleukin 8 along with 10 μg/ml of interleukin 6, followed by sequential association of secondary antibodies corresponding to each of these interleukins. In the figure, the resonant wavelengths numbered 1–5 correspond to control (glutaraldehyde functionalized), streptavidin-functionalized control, anti-interleukin 6, anti-interleukin 4, and anti-interleukin 8, respectively (Fig. 4b). The test spectrum (red) is superimposed over the baseline spectrum (blue) to illustrate the lack of significant non-specific binding. We observe shifts in the resonance corresponding to immobilized monoclonal anti-interleukin 8 (0.58 nm) and 6 (0.68 nm), but no significant shift in the resonance corresponding to immobilized monoclonal anti-interleukin 4. This further supports the ability of the NOSA device to function as a multiplexed biosensor with little cross-reactivity or non-specific binding. We note here that, as alluded to above, physiologically relevant concentrations of serum interleukins for in-vivo monitoring are on the order of 1–10 pg/ml, which is within the detection limits of available ELISA techniques [9, 10] but not existing label-free techniques. In its current design, our device can detect antibodies in a concentration range of 1 µg/ml to 1 mg/ml, which is of clinical significance in medical diagnostics (i.e. HIV detection), and drug screening but below that desired above.
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Figure 4. Multipexed detection of interleukins. (a) Spectra for resonators labeled 1–5 that correspond to control, streptavidin-functionalized control, anti-interleukin 6, anti-interleukin 4, and anti-interleukin 8, respectively. The trace in blue shows the initial baseline spectrum. The red trace corresponds to the test spectrum after introducing 10 µg/ml of interleukin 6 along with 1 µg/ml of interleukin 8, followed by the sequential association of secondary antibodies corresponding to each of these interleukins. We clearly see shifts corresponding to the resonators functionalized with anti-interleukin 6 and 8 (Resonance 3 and 5, respectively) while the other resonances do not shift appreciably thus indicating the lack of non-specific binding. Fabry-Perot resonances were filtered out in both spectra by performing a fast Fourier transform. (b) Reaction stages at each of five resonators.
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Figure 5. Measurement of binding kinetics. Trace of recorded power at a fixed wavelength λm as a function of time during the association of 45 µg/ml of anti-streptavidin antibody to a streptavidin functionalized resonator which clearly shows the reaction proceeding to saturation. The inset shows the correspondence of points at the start and end of the trace to the initial baseline and final red-shifted resonant spectrum.
1.3. KINETIC MONITORING
Instead of continuously tuning the laser across its operational range to record the output spectrum, it is also possible to monitor the output power at a fixed wavelength along the sloping profile of a resonant dip in the spectrum. As the resonant dip red-shifts due to the binding of target biomolecules, the power recorded at this fixed wavelength is observed to correspondingly increase as a function of time. Much like SPR sensors, it is possible to monitor biomolecular interactions in real-time and perform binding kinetic studies using this platform. Figure 5 shows the output power at a fixed wavelength for the association of 45 μg/ml anti-streptavidin antibody to a resonator on which streptavidin was immobilized. As expected, we clearly observe the association of anti-streptavidin to the sensor surface proceeding to saturation.
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2. Optofluidic Surface Enhanced Raman Spectroscopy
Figure 6. (a) Schematic diagram of an optofluidic SERS device for the detection of DENV-2 using the electro-active microwell (diameter of 10 µm and height of 8 µm). (b) The upper gold electrode patterned PDMS layer. (c) The optical arrangement for laser focusing on the microwell of an optofluidic chip. (d)–(e) 10 μm electroactive microwells are used to attract and concentrate SERS enhancers from the solution so they can be optically probed. Applying the polarity shown in (d) attracts particles and (e) rejects them.
Broadly speaking there are two ways in which a SERS detection reaction can be carried out on chips: homogeneously, where the target becomes bound or absorbs onto the solution phase metallic nanoparticles which act as Raman enhancers or heterogeneously, where the solution phase targets interact with the surface phase SERS active clusters such as roughened electrodes, or precipitated silver and gold nanoparticles (NPs) (Fig. 6). The former of these has the same advantages as all homogeneous reactions (i.e. faster reaction rate and relative ease of implementation) as well as enhanced
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uniformity and repeatability of the SERS enhancement since the nanoparticles can be synthesized with high uniformity.
Figure 7. (a) SERS spectra of gold NPs after immobilization of capture probes and application of MCH to protect against non-specific absorption. (b) SERS spectra after hybridization with DENV-4a (negative control) and (c) with DENV-2a (target DNA) using the functionalized gold NPs. The concentration of each target DNA in hybridization reaction is 3 nM.
To address this we have recently developed unique “optofluidic” based on chip SERS devices. The chip exploits our previously developed electroactive microwells [11] which are used here to enhance mixing for DNA hybridization and concentration for sample enrichment (Fig. 7). The chip comprises of a glass substrate with lithographically patterned electrodes. The substrate and electrodes are covered with an electrically insulating polyimide layer into which 10 μm diameter wells and microfluidic system are etched. After completion we align and bond the PDMS cover to the bottom substrate such that the wells align with the spaces in the upper electrodes. Details of our work are available in recent publications [12, 13], however briefly to here we show, SERS detection experiments conducted using nanoparticles functionalized with probes specific to DENV-2 and introducing (in separate experiments) DENV-2a and DENV-4a targets. Figure 8 shows the SERS spectra collected on-chip for (a) no target DNA
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(b) DENV-4a (negative control) and DENV-2a (positive control). In the latter two cases the concentration of targets in solution was 3 nM. As can be seen in Fig. 3, our results show that almost no detectable Raman signal was observed from the control gold NPs, nor the gold NPs hybridized with DENV-4a. As expected, Fig. 7c shows the correct spectroscopic fingerprints corresponding to TAMRA-labelled DENV-2a. 3. Nanoscale Optofluidic Transport Free-space optical manipulation techniques in microfluidic systems have recently generated a significant amount of interest. Such techniques range from traditional optical tweezing (see a recent review by Grier [14]), rotational manipulation of components based on form birefringence [15] to more recent electro-optic approaches such as that by Chiou et al. [16]. As an example of a direct device integration, Wang et al. [17] developed an optical force based cell sorting technique whereby radiation pressure was used to direct rare cells into separate streams following a green florescent protein (GFP) detection event. Though very subtle and complex manipulations have been demonstrated (e.g. Curtis et al. [18]), the majority of these implementations tend to be “binary”, meaning they rely on either the ability to trap or not trap a particle based on whether the conditions for trapping stability are met [19–21]. Recently a number of studies have extended these ideas to exploit the dependence of this trapping potential on the particle properties, enabling much more advanced and subtle operations. As an example, MacDonald et al. [22] demonstrated an optical lattice technique where particles of different sizes were sorted into different streams depending on their strength of repulsion to regions of high optical intensity. Imasaka and coworkers [23–26] provided the initial foundations for optically driven separation techniques, which they termed optical chromatography [27–31]. 3.1. BRIEF OVERVIEW OF OPTICALLY TRAPPING AND TRANSPORT PHYSICS
Before continuing we briefly introduce the analytical equations which describe optically driven transport and trapping of a Rayleigh particle as they will help describe the advantages of the approach to be developed here. Below we will discuss the limitations of these equations and introduce our more comprehensive model. As mentioned above the scattering and adsorption forces exerted on a particle results from the momentum transfer of incident photons and act in the direct of optical propagation. For a Rayleigh (i.e. sub wavelength) particle (see Svoboda and Block [19], and others [20, 32, 33]) these propulsive forces take the form,
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Fscat =
8π 3 Ioα 2ε m 3cλ4
(1a)
Fabs =
2πεm I o Im(α ) cλ
(1b)
where α = 3V(ε – εm)/(ε + 2εm), V is the particle volume, c and λ are the speed and wavelength of light, εp and εm are the dielectric constants of the particle and material and Io is the incident intensity. In the direction perpendicular to the optical propagation there exists a polarization induced force, given by
Fgrad =
2π∇I oα , c
(2)
which acts to attract particles to the region of highest intensity (e.g. to the center of a focused beam). 3.2. LIMITATION OF EXISTING OPTICAL MANIPULATION TECHNIQUES
The precision with which particles can be trapped and transported with optical techniques is what makes them useful for biological analysis. For nanoscopic analysis however these systems are fundamentally limited by the use of free space optics. It is well known [34] that the diffraction limit places a lower bound on size to which light can be focused is given by dmin = 1.2 λ/NA, where NA is the numerical aperture and λ is the wavelength. In an aqueous environment and for an 850 nm wavelength and with a high numerical aperture the minimum spot size is 550 nm. Since light intensity is given by the input power divided by the illuminated area, this places a fundamental limitation on the trapping (through ∇Io in Eq. (2)) and propulsive forces that can be applied to a nanoparticle. From the above equation the simple solutions are to either reduce the wavelength of the laser (e.g. into the blue) or increase the effective numerical aperture (e.g. Solid Immersion Lenses, SIL). Decreasing the wavelength to 488 nm would reduce the spot size by slightly less than half but this also serves to increase Fscat and Fabs which can push the particle out of the trap. The SIL technique has been developed in a number of different flavors [35–37] with the general principal being that increasing the refractive index of the optical head gives one a nominal improvement in ultimate resolution (1/ni). We will place these limitations in the context of our proposed approach below.
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3.3. OPTICAL/ELECTRICAL MANIPULATION OF SMALL MOLECULES – WHY IS IT HARD?
As mentioned, the fundamental limitation of existing optical confinement devices that operate in free space is diffraction, which places a lower bound on the size of a laser spot and equivalently an upper bound on the gradient forces which can be used to confine objects. As such optical tweezers are typically operable on dielectric targets with sizes down to approximately 100 nm [38]. Below this size motion can be biased [39] but stable trapping cannot be obtained. Referring back to Eq. (2) the primary reason for this is that the trapping potential contains a third power dependence on target radius (through volume in the α parameter). As such trapping a target approximately ten times smaller than what can be done at present (~100 nm) requires a 1,000-fold increase in the trapping force. This has to be done in such a way that absorptive heating does not cause localized boiling of the fluid and that the increased scattering and absorptive forces do not push the target out of the trap. A number of authors have demonstrated optical manipulation of metallic nanoparticles [19, 40] and single dimensional nanowires [41]. In these cases the trap stability is dependent on exploiting the high adsorption properties metallic structures to create multiple beam radiation pressure traps or having at least one micrometer length scale (as in the nanowires). As such none of these methods are directly applicable to small “round” dielectric target like those of interest here. Recently, Cohen and Moerner [42] developed an electrokinetically based trapping system which, with the aid of an extensive optical-electrical feedback mechanism, was able to trap single semiconductor quantum dots (diameter ~ 10 nm) for over 10 s in a glycerol-water solution. This system relies on an active feedback mechanism in which manipulation of a series of high strength electrical fields are used to “beat” Brownian motion and the use of glycerol to increase the solution viscosity. In buffer solutions, trapping of targets below a few 10 s of nanometers was not possible. This technique has recently been improved upon [43] to the point where single proteins can be trapped in buffers, however the technique remains complicated and requires extensive feedback control to maintain stability. 3.4. NANOPHOTONIC DEVICES FOR OPTICAL TRAPPING
Nanophotonics can be defined as interaction of light with matter at nanometer scales [44]. Nanophotonic devices (e.g. waveguides, ring resonators, photonic crystals, and a host of others too numerous to list here, see Saleh and Teich [45] or Pollock and Lipson [46]) have found numerous applications in fields ranging from telecommunications and computing to biochemical sensing and detection. As illustrated in Fig. 8, nanophotonic devices confine light
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by total internal reflection over very long distances with very little lengthwise dilution of the optical energy.
Figure 8. Comparison between traditional and nanophotonic optical trapping. Nanophotonics allows concentration of the optical energy to smaller cross sectional areas and sharper trapping forces due to the sharp gradients in the evanescent field.
Though the light is confined to propagate in a single direction, a nonpropagating, exponentially decaying, component of this optical mode (referred to as the evanescent field) extends outside the waveguide. The
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degree of this extension depends on the refractive index contrast between the waveguide and the surrounding media [45], however is generally on the order of 100 nm. This optical gradient partially polarizes the particle near the waveguide, resulting in an extremely strong Lorenz force analogous to the trapping force in traditional optical tweezers. When this particle is trapped within the evanescent field, a certain percentage of the photons which flow through the waveguide are either scattered (radiated in a random direction) or absorbed when they contact the particle. These scattering and adsorption events result in momentum transfer to the particle and a net forward velocity. 3.5. CRITICALLY ENABLING ADVANTAGES
In the context of optical trapping nanophotonic devices have two important advantages over the state of the art. 1. Extremely high optical trapping stability. From Eq. (2) the trapping force is proportional to the gradient in the intensity. The extremely high decay rate of the optical energy outside the waveguide leads to a very high trapping force. This will allow us to overcome the limitation of traditional optical traps. Because the trapping occurs near a large surface, the ability to reject heat is also greater enabling higher power densities than would normally be possible in free space. The focus of the proposed work here is to demonstrate how this can be enhanced through the use of optically resonant devices. 2. Insensitivity to surface/solution conditions. Electrokinetic trapping and transport techniques are compatible only with a limited class of fluids, exhibit extreme sensitivity to surface conditions and are difficult to use with semiconductor substrates such as silicon (as it relies on an insulating substrate). Our technique is much less dependent on these conditions and can be used in a broader class of systems. 3.6. DEMONSTRATION OF TRAPPING AND TRANSPORT ON SOLID CORE WAVEGUIDES
In a recent work we have been able demonstrate an optical trapping platform based on planar waveguides that are integrated with microfluidic channels [47, 48]. Other works have shown propulsion of dielectric particles along waveguides [49] including waveguides made of ion-exchange doped glasses [50–52] within static fluid cells. This work extended these earlier studies in two critical ways which are required to accomplish the specific aims described above. Firstly the use of the evanescent field surrounding a
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waveguide to directly capture particles initially carried within a pressure driven flow in a microfluidic system and secondly through the stable capture of particles both perpendicular and opposite to an imposed pressure driven flow. As shown in Fig. 9, the platform used here is comprised of SU-8 epoxybased photonic structures, combined with poly (dimethylsiloxane) (PDMS) microfluidics on a fused silica substrate. The particles used in our experiment were polystyrene spheres with refractive index n =1.574 in a 100 mM phosphate buffer solution (PBS) with a regulated pH of 7.0. The light source used for testing was a fiber coupled laser diode module with a wavelength of λ = 975 nm. In this experiment the dielectric particles are convected along with the pressure driven flow in the main microfluidic channel. When a particle comes in contact with the optically excited waveguide it may be captured in the evanescent field and begin moving in the direction of optical propagation. Figure 9d–e shows time step images of the particle becoming trapped on the waveguide and propelled in the direction opposite the initial flow. This trapping exhibited a dependence on pressure driven flow speed and the waveguide optical power. In particular, a greater portion of the particles are captured at lower flow speeds and higher optical powers. Though not yet fully characterized, we expect that this is a result of slower particles having less momentum to overcome the attraction well of the evanescent field and the higher power increasing the trapping stability.
Figure 9. Optical trapping and transport in the evanescent field of an optical waveguide. (a, b) A particle flowing in a microchannel becomes captured in the evanescent field of the excited waveguide. (c) SEM of two waveguides. (d–f) Time step images showing transport of 3 μm polystyrene particles on a waveguide.
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3.7. EXTENSION TO TRAPPING OF NANOPARTICLES IN SILICON PHOTONIC STRUCTURES
The results above show good proof of principal for dielectric particles. In [47] we demonstrate trapping of particles as small as a 500 nm, though the system was optimized for transport and not trapping and thus smaller target sizes are likely possible. From Eq. (2) it is clear that in order to increase the trapping force, ∇Io must be increased. This can be done by either condensing the optical energy down to a smaller cross sectional area, increasing the “sharpness” of the gradient, or through local amplification of the field. The latter of these is the extension that is proposed here. As for the first two of these we have recently demonstrated trapping of particles as small as 75 nm in silicon “slot waveguides”. These devices consist of a standard single mode silicon waveguide with a sub-wavelength slot cut through the middle as shown in Fig. 10a. As has been demonstrated [53] this slot serves to concentrate the optical energy in the “hollow core” region of the waveguide. Figure 11b–d demonstrates the successful trapping of particles 75 nm in diameter in these structures. As can be seen in these experiments we optically excite the waveguide in TM mode with about 100 μW of power and flow the dielectric nanoparticles over. The channel height is about 3 μm tall to confine the particles as close to the waveguide as possible. After some time a large number of particles are shown to collect in the waveguide 6(b). When the power is turned off, the particles are released and flow downstream. Note that the excitation wavelength for these experiments is 1,550 nm coinciding with the range in which silicon is transparent.
Figure 10. Silicon “Slot waveguide” trapping structure. (a) Schematic of waveguide, (b) mode profile showing trapping location.
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This represents an important “proof-of-principal” demonstration for two reasons. First it demonstrates that we are capable of trapping dielectric particles smaller than those than can be trapped with regular optical tweezers using silicon nanophotonic structures. Secondly it also demonstrates that even though the 1,550 nm wavelength more strongly adsorbs in water than the 975 nm wavelength used in C.2. it does not negatively impede trapping. This is likely the result of the enhanced heat transfer in a chip based system as opposed to a free space one (see D.1.3). Further details on these experiments are detailed in our recent paper [54] (included in the appendix). Movies illustrating the trapping can also be obtained in the supplemental material available from the Nature website.
Figure 11. Trapping of nanoparticles inside a silicon “Slot Waveguide.” (a) SEM of 100 nm wide slot waveguide. (b–d) Demonstration of trapping and release of 75 nm dielectric nanoparticles from inside slot. These experiments were conducted with approximate 100 mW of excitation power at 1,550 nm.
3.8. EXTENSION TO TRAPPING OF BIOMOLECULES
The nanoscopic dielectric particles can be considered as coarse “proof-ofconcept” approximate models for the biological species we intent to work with here. In general however biomolecules are significantly more complex and thus the results above may not be sufficiently convincing that the technique will have biological applicability. To address this we have performed the experiments shown in Fig. 12 that illustrate how we have been able to both capture from solution and stably trap individual strands of YOYO-1 tagged 48 kb long λ-DNA molecules. As in the experiments above, trapping was done with 250 mW of optical power at 1,550 nm optical excitation however in this case we used a 60 nm slot waveguide. Though here we intend to focus on essentially point molecules, it is important to point out for more general applicability of the technique that these experiments were conducted under buffer and pH conditions in which the DNA is known to be in a partially extended state [39]. Although others
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have demonstrated the ability to optically trap λ-DNA at pHs where the molecule is known to be in a supercoiled state [39, 55], it has proven difficult to trap partially extended molecules because the focal point of a tightly focused tweezer can only interrogate a small portion of the molecule. The slot waveguide technique allows us to trap extended molecules since the confinement force is equivalently applied along a line. 3.9. COMMENTS ON EFFECTS OF FLOW ON TRAPPING
Prior to closing off this paper it is important to make a quick point regarding how the microfluidic flow and how it affects the trapping for all three of the above cases. In all these cases, the flow just serves just to transport particles to the trap site and does not play an active role in the trapping. This is illustrated in Figs. 11 and 12 by the fact that the trap breaks upon removal of the optical excitation and both the nanoparticles and DNA are released. Note that this is very clearly illustrated in by the movies included as supplemental material in our recent paper [54]. Additionally in a recent theoretical paper [56] we have shown that the flow actually acts to break the trap, not stabilize it.
Figure 12. Capture and trapping of λ-DNA. Images show individual YOYO tagged 48 kBb λ-DNA trapped and released over a 60 nm slot waveguide.
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Acknowledgements This work was supported by the Nanobiotechnology Center (NBTC), an STC Program of the National Science Foundation under Agreement No. ECS-9876771, the National Institutes of Health – National Institute of Biomedical Imaging and Bioengineering (NIH-NIBIB) under grant number R21EB007031 and the National Science Foundation (NSF) Nanoscale Interdisciplinary Research Team program under grant number CBET0708599. Additional support has also been provided by the Defense Advanced Research Projects Agency Microsystems Technology Office (DARPA-MTO) Young Faculty Award Program. Portions of this work were performed at the Cornell Nanoscale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECS-0335765).
References 1. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Photonicbandgap microcavities in optical waveguides. Nature 390: p. 143–145 (1997). 2. S. Mandal and D. Erickson, Nanoscale optofluidic sensor arrays. Optics Express 16: p. 1623–1631 (2008). 3. S. Mandal, J. Goddard, and D. Erickson, A multiplexed optofluidic biomolecular sensor for low mass detection. Lab on a Chip Accepted (accessible on-line) (2009). 4. P. G. Ganesan, X. Wang, and O. Nalamasu, Method for sensing the selfassembly of polyelectrolyte monolayers using scanning probe microscope cantilever. Applied Physics Letters 89: p. 213107–213113 (2006). 5. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, Shift of whispering-gallery modes in microspheres by protein adsorption. Optics Letters 28: p. 272–274 (2003). 6. C. Sauvan, G. Lecamp, P. Lalanne, and J. Hugonin, Modal-reflectivity enhancement by geometry tuning in Photonic Crystal microcavities. Optics Express 13: p. 245–255 (2005). 7. M. Notomi, E. Kuramochi, and H. Taniyama, Ultrahigh-Q Nanocavity with 1D Photonic Gap. Optics Express 16: p. 11095–11102 (2008). 8. F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, Multiplexed DNA Quantification by Spectroscopic Shift of Two Microsphere Cavities. Biophysical Journal 85: p. 1974–1979 (2003).
OPTOFLUIDICS
549
9. S. X. Leng, J. E. McElhaney, J. D. Walston, D. Xie, N. S. Fedarko, and G. A. Kuchel, ELISA and Multiplex Technologies for Cytokine Measurement in Inflammation and Aging Research. The Journals of Gerontology. Series A. Biological Sciences and Medical Sciences 63: p. 879–884 (2008). 10. A. J. A. Lambeck, A. P. G. Crijns, N. Leffers, W. J. Sluiter, K. A. ten Hoor, M. Braid, A. G. J. van der Zee, T. Daemen, H. W. Nijman, and W. M. Kast, Serum Cytokine Profiling as a Diagnostic and Prognostic Tool in Ovarian Cancer: A Potential Role for Interleukin 7. Clinical Cancer Research 13: p. 2385–2391 (2007). 11. B. Cordovez, D. Psaltis, and D. Erickson, Trapping and Storage of Particles in Electroactive Microwells. Applied Physics Letters 90: p. 024102 (2007). 12. Y. S. Huh, A. J. Chung, B. Cordovez, and D. Erickson, Enhanced on-chip SERS based biomolecular detection using electrokinetically active microwells. Lab on a Chip (Accepted) (2008). 13. Y. S. Huh, A. J. Lowe, A. D. Strickland, C. A. Batt, and D. Erickson, SurfaceEnhanced Raman Scattering Based Ligase Detection Reaction. Journal of the American Chemical Society 131: p. 2208–2213 (2009). 14. D . G. Grier, A revolution in optical manipulation. Nature 424: p. 810–816 (2003). 15. S. L. Neale, M. P. Macdonald, K. Dholakia, and T. F. Krauss, All-optical control of microfluidic components using form birefringence. Nature Materials 4: p. 530–533 (2005). 16. P. Y. Chiou, A. T. Ohta, and M. C. Wu, Massively parallel manipulation of single cells and microparticles using optical images. Nature 436: p. 370–372 (2005). 17. M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, Microfluidic sorting of mammalian cells by optical force switching. Nature Biotechnology 23: p. 83–87 (2005). 18. J. E. Curtis, B. A. Koss, and D. G. Grier, Dynamic holographic optical tweezers. Optics Communications 207: p. 169–175 (2002). 19. K. Svoboda and S. M. Block, Optical trapping of metallic Rayleigh particles. Optics Letters 19: p. 930–932 (1994). 20. K. C. Neuman and S. M. Block, Optical trapping. Review of Scientific Instruments 75: p. 2787–2809 (2004). 21. A. Ashkin and J. P. Gordon, Stability of radiation-pressure particle traps – an optical Earnshaw theorem. Optics Letters 8: p. 511–513 (1983). 22. M. P. MacDonald, G. C. Spalding, and K. Dholakia, Microfluidic sorting in an optical lattice. Nature 426: p. 421–424 (2003). 23. T. Hatano, T. Kaneta, and T. Imasaka, Application of optical chromatography to immunoassay. Analytical Chemistry 69: p. 2711–2715 (1997). 24. T. Imasaka, Optical chromatography. A new tool for separation of particles. Analusis 26: p. M53–M55 (1998). 25. J. Makihara, T. Kaneta, and T. Imasaka, Optical chromatography: Size determination by eluting particles. Talanta 48: p. 551–557 (1999).
550
D. ERICKSON
26. T. Kaneta, Y. Ishidzu, N. Mishima, and T. Imasaka, Theory of optical chromatography. Analytical Chemistry 69: p. 2701–2710 (1997). 27. S. J. Hart and A. V. Terray, Refractive-index-driven separation of colloidal polymer particles using optical chromatography. Applied Physics Letters 83: p. 5316–5318 (2003). 28. S. J. Hart, A. Terray, K. L. Kuhn, J. Arnold, and T. A. Leski, Optical chromatography of biological particles. American Laboratory 36: p. 13–+ (2004). 29. A. Terray, J. Arnold, and S. J. Hart, Enhanced optical chromatography in a PDMS microfluidic system. Optics Express 13: p. 10406–10415 (2005). 30. S. J. Hart, A. Terray, T. A. Leski, J. Arnold, and R. Stroud, Discovery of a significant optical chromatographic difference between spores of Bacillus anthracis and its close relative, Bacillus thuringiensis. Analytical Chemistry 78: p. 3221–3225 (2006). 31. B. S. Zhao, Y. M. Koo, and D. S. Chung, Separations based on the mechanical forces of light. Analytica Chimica Acta 556: p. 97–103 (2006). 32. L. N. Ng, B. J. Luf, M. N. Zervas, and J. S. Wilkinson, Forces on a Rayleigh particle in the cover region of a planar waveguide. Journal of Lightwave Technology 18: p. 388–400 (2000). 33. L. N. Ng, M. N. Zervas, J. S. Wilkinson, and B. J. Luff, Manipulation of colloidal gold nanoparticles in the evanescent field of a channel waveguide. Applied Physics Letters 76: p. 1993–1995 (2000). 34. M. Born and E. Wolf, Principles of Optics. 6 ed, London: Pergamon (2003). 35. S. M. Mansfield, W. R. Studenmund, G. S. Kino, and K. Osato, Highnumerical-aperture lens system for optical storage. Optics Letters 18: p. 305– 307 (1993). 36. J. Guerra, D. Vezenov, P. Sullivan, W. Haimberger, and L. Thulin, Near-field optical recording without low-flying heads: Integral near-field optical (INFO) media. Japanese Journal of Applied Physics Part 1-Regular Papers Short Notes & Review Papers 41: p. 1866–1875 (2002). 37. I. Ichimura, S. Hayashi, and G. S. Kino, High-density optical recording using a solid immersion lens. Applied Optics 36: p. 4339–4348 (1997). 38. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, Observation of a single-beam gradient force optical trap for dielectric particles. Optics Letters 11: p. 288–290 (1986). 39. D. T. Chiu and R. N. Zare, Biased diffusion, optical trapping, and manipulation of single molecules in solution. Journal of the American Chemical Society 118: p. 6512–6513 (1996). 40. A. S. Zelenina, R. Quidant, G. Badenes, and M. Nieto-Vesperinas, Tunable optical sorting and manipulation of nanoparticles via plasmon excitation. Optics Letters 31: p. 2054–2056 (2006). 41. P. J. Pauzauskie, A. Radenovic, E. Trepagnier, H. Shroff, P. D. Yang, and J. Liphardt, Optical trapping and integration of semiconductor nanowire assemblies in water. Nature Materials 5: p. 97–101 (2006).
OPTOFLUIDICS
551
42. A. E. Cohen and W. E. Moerner, Suppressing Brownian motion of individual biomolecules in solution. Proceedings of the National Academy of Sciences of the United States of America 103: p. 4362–4365 (2006). 43. A. E. Cohen and W. E. Moerner, Controlling Brownian motion of single protein molecules and single fluorophores in aqueous buffer. Optics Express 16: p. 6941–6956 (2008). 44. P. Prasad, Nanophotonics, Hoboken, NJ: Wiley (2004). 45. B. Saleh and M. Teich, Fundamentals of photonics, New York,: Wiley (1991). 46. C. Pollock and M. Lipson, Integrated photonics, Norwell, MA: Kluwer (2003). 47. B. S. Schmidt, A. H. J. Yang, D. Erickson, and M. Lipson, Optofluidic trapping and transport on solid core waveguides within a microfluidic device. Optics Express 15: p. 14322–14334 (2007). 48. A. J. H. Yang and D. Erickson, Stability analysis of optofluidic transport on solid-core waveguiding structures. Nanotechnology 19: p. 045704 (2007). 49. S. Kawata and T. Tani, Optically driven Mie particles in an evanescent field along a channeled waveguide. Optics Letters 21: p. 1768–1770 (1996). 50. T. Tanaka and S. Yamamoto, Optically induced propulsion of small particles in an evenescent field of higher propagation mode in a multimode, channeled waveguide. Applied Physics Letters 77: p. 3131–3133 (2000). 51. K. Grujic, O. G. Helleso, J. P. Hole, and J. S. Wilkinson, Sorting of polystyrene microspheres using a Y-branched optical waveguide. Optics Express 13: p. 1–7 (2005). 52. K. Grujic and O. G. Helleso, Dielectric microsphere manipulation and chain assembly by counter-propagating waves in a channel waveguide. Optics Express 15: p. 6470–6477 (2007). 53. C. A. Barrios and M. Lipson, Electrically driven silicon resonant light emitting device based on slot- waveguide. Optics Express 13: p. 10092–10101 (2005). 54. A. Yang, S. Moore, B. Schmidt, M. Klug, M. Lipson, and D. Erickson, Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides. Nature, Accepted (2008). 55. K. Hirano, H. Nagata, T. Ishido, Y. Tanaka, Y. Baba, and M. Ishikawa, Sizing of single globular DNA molecules by using a circular acceleration technique with laser trapping. Analytical Chemistry 80: p. 5197–5202 (2008). 56. A. J. H. Yang and D. Erickson, Stability analysis of optofluidic transport on solid-core waveguiding structures. Nanotechnology 19: p. 045704 (2008).
VIVO-FLUIDICS AND PROGRAMMABLE MATTER DAVID ERICKSON
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, 14850, USA,
[email protected]
Abstract. In this talk I will discuss two projects that appear very different but are uniquely unified by the fact that they both involve the use of microfluidics to enable physical control of complex systems. The first of these projects involves our work on Insect Cyborgs or living insects with implanted microdevices. There I will show how we can use implanted microfluidic elements to exert control over the nervous system, turning it on and off on command, by injecting controlled amounts of neurotransmitters. In the second project I will demonstrate how microfluidics can be used to control assembly processes ultimately enabling a new form of “programmable matter”. There I will show how controlling the strength and location of fluidic jets can provide control over fluidic assembly processes enabling affinity tuning, reconfiguration and error correction. 1. Vivo-Fluidics The first half of this work describes the intimate fusion of microsystems and physiology though the partial implantation of a microfluidic device into living insects, Manduca Sexta moth. This effort is a critical component in our development of “Insect-Micro Air Vehicles (I-MAVs)” which aim to fuse nanodevice technology with living organism. The specific goal of this system is to provide “on-command” chemically induced immobilization and subsequent reanimation of the otherwise autonomous insect by implanting a low power electrokinetic drug delivery device. In the below I will demonstrate locomotor activity control by releasing neurotransmitters into wing muscles. I will also provide results of our fully functioning adult survivability data for pupal stage implanted microdevices along with results from a comprehensive study of a low power electroactive drug delivery system. 1.1. OVERVIEW AND INTRODUCTION
As a result of the challenges in downscaling traditional aircraft designs, a number of researchers have looked to the natural world to develop bioinspired MAVs [1]; for instance mimicking the body shapes, wing shapes S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_26, © Springer Science + Business Media B.V. 2010
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and flapping patterns that are present in nature [2–7]. Emulating the vast complexity of nature however has proven to be an extremely difficult engineering problem and thus man-made systems are unlikely to outperform natural flyers (particularly in terms of flight dynamics and power efficiency) in the near future. Flying insects, for example, have evolved an aerodynamic shape that allows them to remain stable in turbulent air conditions and a complex wing flapping motion with an extremely energy efficient stroke [8]. A Microfluidic Device
B
Figure 1. Insect-Micro Air Vehicles and Micro-platform. (A) Live Insect-MAVs with microdevice. (B) A schematic view of the developmental stages of a Manduca sexta moth. Insertion of the microfluidic device is conducted at the pupal stage of development.
Recent microsystems technology has enabled the development of an array of biomedical devices which allow us to monitor biological systems and biomolecular events with extreme precision [9, 10]. While such technology, which is collectively referred to as lab-on-a-chip devices, is proving extremely successful, rarely has the extension been made to exerting active control over a living system. Therefore, instead of simply monitoring biological systems with common nanotechnology techniques, this work is designed to establish active control over them. This effort involves the intimate fusion of microfluidics and physiology though the implantation of a microscale payload into insects. Here, we are specifically focusing on the development of microfluidic systems that enable chemically-induced immobilization and subsequent reanimation. We present our results on the development of implanted microfluidic devices which allow such control
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over flying insects, namely Manduca Sexta moths. Large flying moths such as Manduca sexta or Ascalapha odorata are able to carry payloads well in excess of one gram without significant degradation of their natural flight mechanics [11, 12] and thus are ideal for I-MAVs. One application of such a hybrid-insect system is in the development of I-MAVs, which exploit the highly evolved aerodynamics of insects and power efficiency with recent advances in microdevice engineering. An overview illustrating the system integration is presented in Fig. 1. 1.2. IMPLANTATION/INJECTION EXPERIMENTS
As shown in Figs. 1 and 2, the microdevice platform is partially implanted within the insect at the dorsal thorax of the pupa. All inserting operations were done in this immature stage so that the wounds could heal during the natural process of molting. It is expected that this results in a smaller physiological footprint, since the device has been carried through a greater portion of the insect’s development. Figure 1B outlines the M. sexta lifecycle, illustrating the stage in its development at which the implantations done here were conducted. To determine the optimal implantation strategy that minimizes the physiological footprint and maximizes survivability, we performed a number of experiments varying the insertion timing and location. We found that the dorsal thorax is the best location for implantation, and 1 to 2 days prior to the insects’ emergence is the best timing for our current design. Figure 1 demonstrates the results of the successful emergence of an insect with fully developed wings. Final survivability rate and flight-capable insect rate are 96% and 36%, respectively (total sample size was 50). Injection experiments were conducted to determine the optimal drug, dosage and delivery site for inducing the fastest physiological response and most complete but reversible impact on the level of observable insect activity. Of the large number of chemicals-γ-aminobutyric acid, Taurine, β-alanine, N-methyl-D-aspartic acid, Atropine, Malathion, Scorpion venom milk (Hadrurus arizonensis), L-Aspartate acid potassium salt hemihydrates (LAA), and L-Glutamic acid potassium salt monohydrate (LGA)-and injection sites that were tested and varied; for instance, the amount of 5 μL of a 5.9 M solution of LGA, which is the excitatory transmitter at insect skeletal neuromuscular junctions, was injected into the thorax. The thorax was determined to be the optimal injection site because it favors dispersion of the drug since the whole ventral CNS is densely located there and the heart is nearby. Within a minute after, the insect was immobilized for approximately 2–3 h, after which the insect fully regained its pre-injection neuromuscular activity level. We found that the dorsal thorax is the best location for both implantation and injection.
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Figure 2. Insertion/injection experiment process insertion procedure. (A) Manduca Sexta Moth pupa. (B) Implantation of microchip. (C) After insertion. (D) Insertion examples Injection procedure. (E) Prior to injection the insect was stimulated to gauge its baseline activity level. (F) Various chemicals were injected into the thorax to determine the dosage effects on the degree and length of insect temporary paralysis. (G) The moth paralyzes about a minute after injecting 5 μL of LGA. (H) In a successful test, after 2–3 h, the moth recovers sufficiently to flap its wings.
1.3. DRUG DELIVERY SYSTEM
The device structure is a modification of that presented by Chung et al. [13], and based on the fusion of previous active implantable drug delivery technologies [14] with our recently developed electrokinetically active
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microwells [15]. Briefly, the drug is stored within a microwell defined in a silicon substrate and a macro PDMS reservoir, which are sealed from the exterior using electrically functionalized Pyrex. The electrical leads of the device were connected to thin copper wires (see Fig. 3C), and voltages were applied twice to actuate the device [10, 13, 16]. A
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Figure 3. Microfluidic Device. (A) Time lapse illustrating repulsion the ejection of 1.9 μm fluorescent polystyrene microsphere particles from an electroactive microwell. After dissolution of the membrane, the fluorescent particles can be seen in the well. White lines outline the gold electrodes features. Images are taken every 2 s (total of 10 s). (B) Schematic of the electroactive microwell drug delivery system developed here. Scale bar represents 2 mm. (C) Microfluidic device with electrical leads connected to thin copper wires. Inset: Magnified view of microchip from above looking at the region near the membrane. (D) To illustrate the electrokinetic transport processes involved in the ejection stage, a finite element analysis of time-dependent species transport of the system is shown. Images show cut view of species concentration every 60 s up to 300 s after the ejection process.
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In the first stage, an electric potential is applied between two electrode pads on top of the microchip serving to electrochemically dissolve the membrane. To electrokinetically eject the contents from the reservoir, in the second stage a potential field is applied between one of the upper electrodes and that on the Pyrex bottom substrate. Characterization of the electrokinetic transport processes involved in the ejection is presented as shown in Fig. 3D. When a dosage command is issued, potentials are applied to electrochemically dissolve the gold membrane, and expose the toxin by sequence. As described in detail in Chung et al. [10], the use of electrokinetic transport allows for a significant reduction in the amount of time required to eject the well contents over earlier diffusive transport based devices (from hours to minutes), simplifies device design since only electrical components are required, and minimizes the rate amount of energy required per injection. 1.4. IMMOBILIZATION/REANIMATION
Based on the results of the insertion experiments, the microfluidic devices were implanted in M. sexta pupae, approximately 1 or 2 days before the adult insects were scheduled to emerge. Prior to implantations, the reservoirs were filled with different chemicals-LGA, LAA, and PBS which served as a negative control-and only properly hatched moths (able to fly) were tethered and tested for immobilization/reanimation. A typical experiment is shown in Fig. 4, where as can be seen, the electrical leads from the device were connected to thin copper wires which lead to an overhanging boom supporting the insect in midair. When a dosage command was issued, the two stage injection process (described above) was initiated. We applied 15 V for 4 min and 20 V for 4 min for membrane dissolution and electrokinetic ejection stages, respectively. For both LGA and LAA a dramatic reduction in the wing motion (i.e. rate and amplitude of flapping strokes) was observed, 90 s after the injection command was issued. No observable difference was found for the PBS ejection experiments. In the negative control case the device was excised to visually confirm that it had been actuated. After the discharging of the applied potential, the drug-induced immobilization lasted one hour and 20 min, after which the moths regained activity level. To verify that the paralysis was not due to the applied potential, the same voltages were applied on a dummy chip. As expected, no immobilization was noticed.
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Figure 4. Microfluidically modulated insect activity. (A) Active Manduca Sexta moth adult. (B) Paralyzed moth after 1 min: Injection of 5 μL of a 5.9 M solution of LGA. (C) Remaining paralysis without applied potential. (D) Revived insect after 2–3 h of paralysis.
2. Programmable Matter Here I will describe a two of the areas into which we are performing research related to programmable matter. The goal of the first direction (Section 2.1) was to develop a better experimental understanding of the fluid-dynamical and fluid-structural processes involved in 3D cube assembly processes. In the second direction our goal is the development of two forms of thermorheologically enabled programmable matter systems (Section 2.2). 2.1. EXPERIMENTS RELATED TO THE DEVELOPMENT OF FLUID DYNAMICALLY DRIVEN 3D ASSEMBLY PROCESSES
As I describe below, our research conducted in this area is separated into three different subcategories. The first of these (Section 2.1.1) describes the assembly chamber and the docking procedure we developed based on the experimental and numerical results obtained under earlier work [17, 18]. The second section (Section 2.1.2) describes our work on developing of an optimal fluid structure interaction system that promotes cube alignment and docking. This was largely done by investigating different cube topologies
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and finding better ways of manipulating the fluidic conditions during assembly. We demonstrate in that section a robust procedure for obtaining perfect docking and alignment of cubes. Section 2.1.3 describes some of the quantitative results we have obtained including the ability to dock in the proper upright orientation over 80% of the time and median assembly rates of 5 s/block. 2.1.1. Improvements to the Assembly Chamber and Procedure A 3D assembly experimental setup has been developed in the Erickson Lab in order to facilitate study of cube docking and alignment. The setup is shown in Fig. 5 below. The assembly chamber is similar to that which has been previously demonstrated however we now incorporate two major modifications which have been found to dramatically improve the docking rate and cube alignment during docking. As can be seen in the upper image of Fig. 5 the bottom of the assembly chamber contains two circulation pumps (essentially fishtank circulation pumps) which provide a continuous swirl of fluid motion around the chamber without requiring very high input/output flow rates through the chamber. This reduced the required cube attraction pressure drop to below 2PSI which is something that can be easily modulated with thermorheological valves. The second major advancement was the incorporation of a single solenoid valve that controls the outlet flow from the chamber through the assembled structure. As will be expanded on in the next section, this allows for pulsation of the flow through the sink and increases the number of collisions that a new cube has with the previously assembled structure allowing it to settle down into its properly docked position. 2.1.2. Development of an Optimal Fluid Structure Interaction System That Promotes Cube Alignment and Docking The first experiments we conducted using the assembly chamber described above are shown in Fig. 6 below. These cubes were unevenly weighted cubes which have a buoyancy driven preferred orientation during assembly (the sliver line at the top of the cubes shows the light end). This is done to reduce the number of degrees of freedom during docking. The left image in Fig. 6 shows an example of an assembly event where the cube did dock properly (with the lighted part up) and the right image shows a case where it did not. We will expand on this in Section 2.1.3 but the orientation assembly success rate was 84% using this lighted block technique.
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Relay Outlet Solenoid Valve Figure 5. Erickson lab programmable matter apparatus for studying the dynamics of the assembly process. (Upper) Image shows overview of assembly chamber and associated infrastructure. Note the two circulation pumps at the bottom of the assembly chamber. The two pumps dramatically facilitate the generation of random motions within the tank. (Lower) Image shows electrical infrastructure associated with driving the solonoid valve. As will be demonstrated below the incorperation of an solonoid valve operating at 3 Hz during the attraction process enables us to obtain proper docking.
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Figure 6. Proper orientation by physical misalignment during docking using initial square cubes. Right image shows a block which has docked in the proper orientation (sliver line up) and the left image shows one which did not. In both cases however with purely square cubes, proper alignment does not occur. This result is directly predicted from simulation.
As can be seen from Fig. 6 while the orientation is correct most times the alignment of new cubes added to the structure is mostly not correct (a clear offset is shown in both images of the figure). In order to solve this problem a cube topography had to be developed that would (1) guide the assembly into place if docking is close (2) become stably latched to the structure upon contact (3) be able to be rejected upon reversal of the flow. Towards this end, several cube topographies were designed, manufactured and tested in the assembly chamber. Solid works files showing some of the cube designs that were tested are shown in Fig. 7. This extensive experimentation revealed that the cube design shown in the upper left hand corner yielded the best results.
Figure 7. Cube topographies designed, manufactured and tested in the last project month. The cube in the top right corner represents the final design used below.
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Generally speaking however it was found that simply optimizing the cube topography was not enough to ensure robust docking of the cubes onto a structure. A typical result is shown in image 1 of Fig. 8. As can be seen the cubes tended to dock with better alignment that the square cubes shown above but neither precise docking or latching could be obtained. To enable this we developed a “sink-cycling” technique which performed the final fluidic alignment after initial docking. Briefly, after initial docking was observed external valves on the chamber were switched so at to ensure most of the chamber flow was directed through the structure (rather than being used to promote chamber mixing (image 2 of Fig. 8). Simultaneously with this a solenoid valve which controls the exit flow through the chamber was engaged at 3 Hz with a 50% duty cycle (so the attraction flow through the structure was turned on and off three times a second half of the time on and half of the time off) using a function generator. It was found that this cycling motion (image 3 in Fig. 8) served to “bounce” the cube into the properly docked position (image 4 in Fig. 8). Attracted cubes could be aligned and docked approximately 70% of the time (i.e. 30% of cubes attracted to the pedestal had to be rejected). This represents an important advancement for us as it demonstrates a repeatable technique through which docking misalignments can be corrected. We expect that 70% alignment value could be greatly improved as the technique is optimized.
1) Cube attracted to pedastel but misaligned
2) After docking full suction is applied at the attraction point (convective flow turned off)
3) Attraction cycled by turning attraction pressure on-and-off using solonoid valve on exit line.
4) After several sections cube finds most stable point (alignment) and becomes fully docked.
Figure 8. Docking and proper alignment of cube using suction enhancement and solonoid based sink-cycling. Cube shown in image is the one from the upper right corner of Fig. 1.
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In addition to enabling the docking the “sink-cycling” technique was also sufficiently strong to promote latching between the cube and the structure. The latch design can be seen Fig. 7 however in the actual implementation shown in Fig. 7 we used only two latches per face (so four total latching interactions). The smaller number of latches allowed us to maintain sufficient strength so that the structure was stable but was still sufficient weak that
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(c) t ≈ 0.5 s Figure 9. Time lapse images a cube being released from the docked position: (a) initially, there is now flow in/out of the docking pedestal at t = 0 s flow out of the pedestal is initiated; (b) the flow rejects the block; (c) the blocks moves out into the bulk flow.
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reversing the flow enabled one to reject the cube from the structure (as shown in Fig. 9). This was critically important because it demonstrates our concept of structural error correction. Figure 10 below illustrates a mock up of the initial target structures we will build with the assembly tank. By selectively plugging some of the holes in the structures we can pre-valve them (while the “smart cubes” are being developed) and assembly multi-cube structures like the C & U structures shown in the figure. We note that the latches on the structures are sufficiently strong that they can support the weight of the structure after the assembly fluid is drained.
Figure 10. Docking and proper alignment of cube using suction enhancement and solonoid based sink-cycling. Cube shown in image is the one from the upper right corner of Fig. 1.
2.1.3. Initial Results for Docking Time Probabilities and Alignment Successes In Fig. 11 we show a histogram of the average docking time, or the time between assembly events for the 3D cubes. As can be seen the average docking time for the cubes using the chamber above was 11 s. As can also be seen in half of the 24 trials the assembly time was less than 5 seconds. Additionally, as mentioned above, 20 out of 24 cubes docked with the proper buoyancy corrected alignment. The amounted to a 84% orientation efficiency.
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2.2. THERMORHEOLOGICAL PROGRAMMABLE MATTER
The second area of research we are performing is on the development of the thermo-optically programmable surfaces and assemblies. In the below I focus on the accomplishments related to direct optical control the mechanical properties of a thermo-rheological fluid using the technique illustrated in Fig. 12. In the below we show the capability to dynamically modulate the properties of the fluid from liquid to solid on time scales of less than 1s using only low intensity light. As shown in Fig. 12 the basic premise is that light is shined on a surface which contains a photothermal conversion layer (various types of light absorbing layers are used below) which converts the light to heat and locally gels up the fluid. In this section we report the results in the context of developing a technique for dynamically reconfigurable microfluidics. After that we report further results relating this work to the assembly of 2D tiles. In both this section and section 3.0 the thermorheological fluid used in our experiments here is a 15% (w/w) aqueous solution of Pluronic F127 (BASF) with a gelation temperature of approximately 30°C. 2.2.1. Demonstration of Thermooptically Controlled Flow and Localized Gelling As mentioned above, the first set of experiments we conducted towards developing the thermooptically programmable material described above were aimed at characterizing the optical conditions which would lead to localized gelation. A schematic describing the apparatus used to conduct these experiments is shown in Fig. 13. The microfluidic chip we used consisted of an upper part containing a patterned microchannel that is bonded to a
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substrate with a coating on it that absorbs light. Analogous to what is shown in Fig. 12, by selectively illuminating the absorbing substrate with a laser light, we are able to convert the optical energy to thermal energy and gel the thermorheological fluid flowing in the channel.
Figure 12. Overview of envisioned thermooptically programmable materials. Left image shows experimental arrangement and process by which optically triggered spatial distributions in gellation (and hence material properties) occur. Right image shows 3D overview of technique.
To demonstrate the effect we performed “Opto-thermorheological” valving in a T-shaped microfluidic channel as shown in Fig. 13. Initially, the flow rate through each of the bifurcating channels was the same. On illuminating one of the channels with laser light (405 nm, 40 mW power) through a 20X objective, we were able to reduce and eventually stop the flow in this channel and direct all the flow into the other one as shown in Fig. 14a. The same objective was also used to image the sample, and the flow was visualized by seeding the fluid with 1.5 μm silica particles (Duke Scientific). As shown in Fig. 14b, when a non-absorbing plain glass substrate was used, no such gellation or valving was observed. The insets in each image of the figure show a zoomed up view of flow velocity in the valved channel. The microfluidic channels used here were fabricated using standard soft lithography techniques with poly(dimethylsiloxane) (PDMS) (Ellsworth Adhesives). We used two different kinds of absorbing substrates for these experiments; a plain glass substrate with gold sputter deposited on it and a cover slip coated with indium tin oxide (ITO) (Sigma-Aldrich) as well as a nonabsorbing plain glass substrate for control experiments. We also looked at the effect of varying channel width on the valving and considered channels of widths 25 and 50 μm. The height of the channels was kept constant at 25 μm. The results in Fig. 14a are for an ITO coated substrate with a channel width of 50 μm, though we saw similar results for our other chips as well. Further details on these experiments are provided in our recent paper [19].
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Figure 13. Schematic demonstrating valving technique with a laser and a microfluidic chip with an absorbing substrate.
Figure 14. Demonstration of valving in a microfluidic channel (Media 1). (a) ITO coated substrate (valving occurs). (b) Plain glass substrate (no valving).
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To characterize the temperature rise at the gellation point, in situ temperature measurements using Rhodamine B were also carried for different channel geometries and substrates as described in [19]. The results here do indicate channel temperatures on the order of the sol–gel transition temperature; however we found that flow in the valved channel was not completely stopped. We expect this is because the yield stress of the gel formed in the channel is not sufficient to fully withstand the applied pressure. We attempted to improve the flow valving by increasing the beam power as well as changing the beam waist by using different magnification objectives, but found that higher beam powers and smaller beam waists resulted in bubble formation due to evaporation while larger beam waists resulted in too little heating and no subsequent gelation. These temperature measurements also show that the ITO coated substrate had higher temperatures over a wider region of the channel compared to the gold coated substrate. This indicates that the absorption of the ITO coated substrate is better than that of the sputtered gold substrate at the wavelength used in our experiments here (405 nm). We also found that the 25 μm channel with the ITO coated substrate had a higher temperature compared to the corresponding 50 μm channel which we expect is due to the lower thermal conductivity of the PDMS sidewalls compared to the aqueous pluronic solution in the channel (about 0.18 W/mK for PDMS compared to about 0.6 W/mK for water). 2.2.2. Directed Assembly of Programmable Matter Surfaces with Hydrodynamically Switchable Affinities Self-assembly [20, 21] has been used to create structures at the micro- and nanoscales using techniques such as chemical bonding [22–24], fluid and surface tension based attraction [25–29], geometric interactions [30, 31] and magnetic fields [32, 33] as the assembly driving mechanism. Most of these self-assembly processes create either highly regular structures such as colloidal crystals [34], or small scale complex structures comprised of, for example, DNA polymers [35]. Recently Chung et al. [29] have developed a guided fluidic self-assembly process that allows for the assembly of relatively large irregular structures. Using this technique, the authors were able to design the assembling components on-the-fly and transport them on a railed network to the assembly site. While this technique is very flexible in the shape of the components, their motion is confined by the pre-defined rail networks on which these components move. A hurdle to exploiting the potential of self-assembly is the inability of current techniques to assemble complex structures comprising large numbers of particles in non-regular, non-predefined geometries. One of the reasons for this is the use of static interactions, or affinities between the assembling components to drive the assembly process. For example, in nucleic-acid driven assembly, the final structure is governed by the predefined base-pair
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sequence [22, 36]. As a result, the assembling components and their affinities need to be specifically designed a priori for a given target structure. Since each affinity sequence corresponds to a specific target structure, assembled structures are also not generally reconfigurable. Similar arguments can be made for many hydrophobic/hydrophilic [26, 27, 37] and geometric/surface tension interactions [30, 31]. One way to address the above issues is to develop a means to dynamically (i.e. during assembly) tune affinities between assembling components. The concept of affinity switching has been demonstrated at the centimeter scale using mechanical and magnetic switching [38–42]. These methods however are difficult to implement at the microscale due to fabrication constraints and energy limitations.
Figure 15. Schematic demonstrating the use of dynamically tunable affinities to create arbitrary, programmable and reconfigurable structures. (a) Shows the attraction of a subelement moving stochastically in the fluid to the substrate. The sub-elements are unpowered while in the fluid, but once they are attached to the substrate they can draw power to switch their affinities. (b, c) Depict the building of an arbitrary target structure by dynamically switching the affinities within the structure and controlling the local attraction basin around the structure. (d) Shows the final assembled structure. (e) Shows reconfiguration of the assembled structure by switching affinities. (f) Shows error correction to reject an incorrectly assembled component. Inset: inset shows image of flow valving using a thermorheological fluid (a) off state (b) on state.
The 3rd area of research we are pursuing is related to the development of programmable matter surfaces which exploit hydrodynamically tunable affinity switching. This builds on the initial silicon tile work we have recently published [18, 43]. Our process for affinity switching is shown in the schematic in Fig. 15. In the process, locally restricting the flow near one face of the structure limits the probability of another component being attracted to that face. Hence that part of the structure has no affinity for an approaching component, while other parts of the structure are still positive affinity regions. Figure 15 shows the use of affinity switching by flow
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modulation to create irregular structures, reconfigure structures and carry out error correction. Each of these moves was demonstrated using 2D silicon tiles in the previous report. We note that this affinity switching process is the same as the technique currently being used in 3D and the results obtained here are equivalently transferable to that work. Here we report the development of the technique for manufacturing the tiles with embedded microchannels and to come up with a technique for assembling an arbitrary structure from them. The basic assembly strategy we intend to follow is shown in Fig. 16 and provides one of the main motivations for pursuing the opto-thermorheologically modulated material system described above. As shown in Fig. 16 we intend here to use a DMD system to direct both the far field directed assembly (left image) of the tiles and perform the near field affinity tuning (right image). As is shown through global heating of the fluid we can create temporary “tracks” through which the tile motion of the assembly elements can be guided and through local heating in the embedded channels we can perform the affinity tuning. Although we plan to initially focus on demonstrating this in 2D, this technique could also be extended to 3D assembly.
Figure 16. Thermorheological control of assembly process for both (a) far-field directed assembly and (b) near field directed assembly.
A number of fabrication techniques were developed and tested. For these initial experiments we have decided to use polymer based tiles, rather than silicon ones as was done in the previous experiments, to facilitate the fabrication. The final procedure we decided on is shown in Fig. 17. The 3-D tile structure was fabricated by stacking three layer consisting of lower SU-8, HFE-processable negative tone photoresist, and top SU-8. First, the silicon wafer was coated with OmnicoatTM at 3,000 rpm and 200°C for 1 min prior to applying the SU-8 resist. The OmniCoat™ was used as a SU8 release layer. Following this, the 20 μm thick SU-8 was spun at 4,000 rpm for 30 s. The coated wafer was exposed to 120 mJ/cm2 of contact aligner through a bottom-layer mask of the 3-D tile. After post-baking, it was dip developing solution for 60 s, rinsed in a IPA(isopropyl alcohol), and dried with N2 gas. To improve the adhesion between second layer (HFE-processable negative tone photoresist) and SU-8 layer, the wafer was activated with oxygen plasma for 1 min. Following this, HFE-processable
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negative tone photoresist was coated with spin speed at 2,000 rpm and baked 75°C for 2 min. Following UV exposure (84 mJ/cm2), bake (at 70°C), and development in HFE-7500, the fluid layer (second layer) features were generated on the SU-8 patterned substrate. In this experiment, we have fabricated the polymer-based 3-D tile by using the fluorous solvent to make fluid channel in the tile. This is because fluorous solvents are poor solvents for nonfluorinated organic materials. Among the variety of fluorous solvents, segregated hydrofluoroethers (HFEs) attracted our attention because of their nonflammability noncracking, and other unfavorable physical or chemical damage of organic materials. For the third layer, another 25 μm thick SU-8 was patterned on fluid layer using the same procedures of first SU-8. To penetrate fluids into the internal channel of tile, the HFE-processable negative tone photoresist of the second layer was removed by HFE-7500 solvents (3M Company). After completion, the tiles were detached from the wafer with 1,165 photoresist stripper (Shipley Microposit) for overnight. As can be seen from Fig. 18 (which shows the actual tiles during representative stages of the fabrication process), we have been able to manufacture the successful 3-D tiles based on the SU-8 polymer.
Figure 17. Schematic showing details of fabrication procedure developed for making the “3D” tiles with embedded microchannels.
To ensure continuity of the microchannels through the tiles we performed a series of initial dye doped fluid infusion experiments. The results of these experiments are shown in Fig. 18. The image shows that the channels are indeed free, clear and leak free since the due can be seen to infuse through the structure tracking out only the microchannels. The major challenges with the 3D tiles that we will tackle in the short term are: increasing the channel height (the current height is only 2.5 μm and thus the flow through them is relatively slow), releasing them from the substrate (we do not expect that release will be difficult but we have not accomplished it yet) and
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Figure 18. Images showing 3D tiles at various stages during the fabrication procedure. (a) Base layer deposited; (b) after patterning of microchannel layer and upper substrate; (c) after hard bake of upper substrate; (d) after developing of channels. The red cross in part (b) shows the location of the embedded channel.
Figure 19. Pattern for 3D Polymer tiles with embedded microchannels and latches.
dispersing them in solution (we have demonstrated this with the silicon tiles but are unsure of how the polymer tiles will be behave). In addition to the above we have also fabricated a series of polymer tiles with different latching mechanisms as shown in Fig. 19. We will begin experimentation with these tiles in parallel with those to be conducted using the flow through tiles. Acknowledgements This work was supported by the DARPA, Microsystems Technology Office, Hybrid Insect MEMS (HI-MEMS) program, through the Boyce Thompson Institute for Plant Research and the Defense Sciences Office, Programmable
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Matter Program. Distribution unlimited. Fundamental research exempt from prepublication controls.
References 1. R. Dudley, BIOMECHANICS:Enhanced: Unsteady Aerodynamics. Science 284: p. 1937–1939 (1999). 2. N. Franceschini, F. Ruffier, and J. Serres, A bio-inspired flying robot sheds light on insect piloting abilities. Curr Bio 17: p. 329–335 (2007). 3. R. J. Wood, Liftoff of a 60mg flapping-wing MAV. Proc IEEE/RSJ Int Conf Intelli Rob Sys: p. 1889–1894 (2007). 4. R. J. Wood, The first takeoff of a biologically inspired at-scale robotic insect. IEEE Trans Robotics 24: p. 341–347 (2008). 5. R. J. Wood, S. Avadhanula, R. Sahai, E. Steltz, and R. S. Fearing, Microrobot design using fiber reinforced composites. J Mech Design 130: p. 052304 (2008). 6. H. Tanaka, K. Hoshino, K. Matsumoto, and I. Shimoyama, Flight dynamics of a butterfly-type ornithopter. Proc IEEE/RSJ Int Conf Intelli Rob Sys: p. 2706– 2711 (2005). 7. E. Steltz, S. Avadhanula, and R. S. Fearing, High lift force with 275 Hz wing beat in MFI. Proc IEEE/RSJ Int Conf Intelli Rob Sys: p. 3987–3992 (2007). 8. S. P. Sane, The aerodynamics of insect flight. J Exp Biol 206: p. 4191–208 (2003). 9. D. Erickson and D. Q. Li, Integrated microfluidic devices. Analytica Chimica Acta 507: p. 11–26 (2004). 10. A. J. Chung and D. Erickson, Engineering insect flight metabolics using immature stage implanted microfluidics. Lab on a Chip 9: p. 669–676 (2009). 11. J. H. Marden, Maximum Lift Production during Takeoff in Flying Animals. J Exp Biol 130: p. 235–258 (1987). 12. J. H. Marden, Scaling of maximum net force output by motors used for locomotion. J Exp Biol 208: p. 1653–1664 (2005). 13. A. J. Chung, D. Kim, and D. Erickson, Electrokinetic microfluidic devices for rapid, low power drug delivery in autonomous microsystems. Lab on a Chip 8: p. 330–338 (2008). 14. J. T. Santini, M. J. Cima, and R. Langer, A controlled-release microchip. Nature 397: p. 335–338 (1999). 15. B. Cordovez, D. Psaltis, and D. Erickson, Trapping and storage of particles in electroactive microwells. Appl Phys Lett 90: p. 024102 (2007). 16. A. J. Chung, Y. S. Huh, and D. Erickson, A robust, electrochemically driven microwell drug delivery system for controlled vasopressin release. Biomed Microdev 11: p. 861–867 (2009). 17. M. Krishnan, M. T. Tolley, H. Lipson, and D. Erickson, Increased robustness for fluidic self-assembly. Phys Fluids 20: p. 1–16 (2008). 18. 18. M. T. Tolley, M. Krishnan, D. Erickson, and H. Lipson, Dynamically programmable fluidic assembly. Appl Phys Lett 93: p. 1–13 (2008).
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19. M. Krishnan, J. Park, and D. Erickson, Optothermorheological flow manipulation. Optics Lett 34: p. 1976–1978 (2009). 20. D. Philp and J. F. Stoddart, Self-assembly in natural and unnatural systems. Angew Chem 35: p. 1155–1196 (1996). 21. G. M. Whitesides and B. Grzybowski, Self-assembly at all scales. Science 295: p. 2418–2421 (2002). 22. E. Winfree, F. R. Liu, L. A. Wenzler, and N. C. Seeman, Design and selfassembly of two-dimensional DNA crystals. Nature 394: p. 539–544 (1998). 23. B. Olenyuk, J. A. Whiteford, A. Fechtenkötter, and P. J. Stang, Selfassembly of nanoscale cuboctahedra by coordination chemistry. Nature 398: p. 796–799 (1999). 24. P. W. K. Rothemund, Folding DNA to create nanoscale shapes and patterns. Nature 440: p. 297–302 (2006). 25. N. Bowden, A. Terfort, J. Carbeck, and G. M. Whitesides, Self-assembly of mesoscale objects into ordered two-dimensional arrays. Science 276: p. 233– 235 (1997). 26. N. Bowden, F. Arias, T. Deng, and G. M. Whitesides, Self-assembly of microscale objects at a liquid/liquid interface through lateral capillary forces. Langmuir 17: p. 1757–1765 (2001). 27. U. Srinivasan, D. Liepmann, and R. T. Howe, Microstructure to substrate selfassembly using capillary forces. J MEMS 10: p. 17–24 (2001). 28. J. H. Chung, W. Zheng, T. J. Hatch, and H. O. Jacobs, Programmable reconfigurable self-assembly: Parallel heterogeneous integration of chip-scale components on planar and nonplanar surfaces. J MEMS 15: p. 457–464 (2006). 29. S. E. Chung, W. Park, S. Shin, S. A. Lee, and S. Kwon, Guided and fluidic self-assembly of microstructures using railed microfluidic channels. Nature Mater 7: p. 581–587 (2008). 30. H. J. Yeh and J. S. Smith, Fluidic Self-assembly for the integration of GaAs light-emitting diodes on Si substrates. IEEE Photon Technol Lett 6: p. 706– 708 (1994). 31. W. Zheng and H. O. Jacobs, Shape-and-solder-directed self-assembly to package semiconductor device segments. Appl Phys Lett 85: p. 3635–3637 (2004). 32. M. Golosovsky, Y. Saado, and D. Davidov, Self-assembly of floating magnetic particles into ordered structures: a promising route for the fabrication of tunable photonic band gap materials. Appl Phys Lett 75: p. 4168–4170 (1999). 33. M. Tanase, D. M. Silevitch, A. Hultgren, L. A. Bauer, P. C. Searson, G. J. Meyer, and D. H. Reich, Magnetic trapping and self-assembly of multicomponent nanowires. J App Phys 91: p. 8549–8551 (2002). 34. S. C. Glotzer, M. J. Solomon, and N. A. Kotov, Self-assembly: from nanoscale to microscale colloids. AIChE J 50: p. 2978–2985 (2004). 35. Y. G. Li, Y. D. Tseng, S. Y. Kwon, L. D'Espaux, J. S. Bunch, P. L. McEuen, and D. Luo, Controlled assembly of dendrimer-like DNA. Nature Mater. 3: p. 38–42 (2004). 36. H. Yan, S. H. Park, G. Finkelstein, J. H. Reif, and T. H. LaBean, DNAtemplated self-assembly of protein arrays and highly conductive nanowires. Science 301: p. 1882–1884 (2003).
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D. ERICKSON
37. H. L. Chen, R. Schulman, A. Goel, and E. Winfree, Reducing facet nucleation during algorithmic self-assembly. Nano Lett 7: p. 2913–2919 (2007). 38. S. Murata, H. Kurokawa, and S. Kokaji. Self-assembling machine. In Proc. IEEE international conference on robotics and automation (ICRA94). San Diego, CA (1994). 39. P. White, K. Kopanski, and H. Lipson. Stochastic self-reconfigurable cellular robotics. In Proc. IEEE international conference on robotics and automation (ICRA04). New Orleans, LA (2004). 40. S. Griffith, D. Goldwater, and J. M. Jacobson, Robotics – self-replication from random parts. Nature 437: p. 636–636 (2005). 41. S. C. Goldstein, J. D. Cambell, and T. C. Mowry, Programmable matter. Computer 38: p. 99–101 (2005). 42. E. Klavins, Programmable self-assembly. IEEE Cont Syst Mag 27: p. 43–56 (2007). 43. M. Krishnan, M. T. Tolley, H. Lipson, and D. Erickson, Hydrodynamically tunable affinities for fluidic assembly. Langmuir 25: p. 3769–3774 (2009).
HYDROPHORETIC SEPARATION METHOD APPLICABLE TO BIOLOGICAL SAMPLES SUNGYOUNG CHOI AND JE-KYUN PARK Department of Bio and Brain Engineering, College of Life Science and Bioengineering, KAIST, Daejeon 305-701, Korea,
[email protected]
Abstract. Isolating target particles of biological samples as a complex mixture is of fundamental importance in clinical and biomedical applications. Conventional separation methods are well established, but restrictive due to operational complexity and large size. Recent technical advances of microfluidic devices for separation provide new capabilities for accurate and fast separation of a small number of particles. We herein review hydrophoretic separation as a representative principle for size separation, comparing its advantages and disadvantages with other methods. 1. Introduction 1.1. SIZE MATTERS IN BIOLOGY
The size of biological particles varies greatly with their environment and biological function. Keeping a cell’s organelles or itself the right size is an important matter of life or death. The relationship between cell size and cell division has been extensively studied in yeast and is currently being investigated in mammalian cells [1, 2]. In addition, indentifying a minute change of cellular and molecular size is an important matter for biology researches. One microliter of blood contains several millions of blood cells, proteins, glucose, ions and hormones suspended in blood plasma. For transfusion, each blood component such as red blood cells (RBCs), platelets and plasma should be separated completely removing white blood cells (WBCs), which can cause febrile transfusion reactions and infections [3]. Purifying WBCs or their subsets in rapid and noninvasive ways is essential for inflammation studies and immunological evaluation. Separation by size at molecular level is a fundamental, analytical and preparative technique in forensics, molecular biology, genetics, and microbiology. Nucleic acid, ribonucleic acid, or protein molecules are routinely separated through a
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gel matrix in which an electric current is applied. Separated molecules in the gel matrix can be used for further characterization such as mass spectrometry, polymerase chain reaction, cloning and sequencing. 1.2. SIZE SEPARATION IN MICROFLOWS
Size-based separation is widely used in biotechnology, from cell separation to multianalyte, flow-assisted immunoassays [4−6]. For these purposes, conventional field-flow separation techniques and their microfabricated counterparts have been developed, such as field-flow fractionation (FFF) and hydrodynamic chromatography [7−9]. Both techniques use a parabolic flow profile in which analytes are distributed differentially according to their size, mass, and other physical properties. In this way, particles have different retention times along different velocity paths. Among the various FFF methods, sedimentation FFF, gravitational FFF (GrFFF), and their combination method with dielectrophoresis (DEP-FFF) have been used for applications of micron-sized particles, providing biocompatible and sterilized protocols. However, particle separation in GrFFF and DEP-FFF is not conducted in a continuous manner, which gives some disadvantages of both restricted amounts of samples within separation chamber volumes and relatively long separation times. Microfluidic methods for continuous size separation can be categorized into field-based and field-free, flow-assisted separation. Many physical fields have been used for separation of microparticles such as cells and bacteria, including dielectrophoretic (DEP), optical, and acoustic fields [10−12]. In these field-based methods, the physical force acting on particles is typically proportional to their volume. The field gradient perpendicular to particle flows pushes particles along the gradient direction and differentially deflects them according to their size. The electric-field gradient at a pinched channel region under a direct-current bias between inlets and outlets allows the separation of microbeads, blood cells and human breast adenocarcinoma cancer cell line (MCF-7) [13]. The acoustic radiation force is also used for separation of lipid particle contaminants from erythrocytes [14]. However, the level of the force acting on macromolecules is several femto-Newtons or less, which is insufficient to manipulate nucleic acids, proteins, or small bacteria cells in flows. Dielectrophoretic trapping of DNA toward the highfield region has been proposed using dielectric constrictions and nanotubes, but these methods are limited by difficult sample recovery and low sample throughput [15, 16]. Flow-assisted methods typically utilize steric hindrance mechanisms in which microchannels or microstructures form barriers to move particles out of their streamlines and into a desired equilibrium position. The steric hindrance mechanism allows size separation of micron and submicron
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particles. Seki and coworkers developed ‘pinched flow fractionation’ that particles are pushed and aligned by a sheath flow toward a pinched channel wall [17]. The smaller the particles are, the closer their distance from the wall is. This size-dependent alignment allows differently-sized particles to flow into different positions across the channel. Austin and colleagues demonstrated size separation through deterministic lateral displacement that particles interact with a large array of pillars, repeating similar hindrance processes with pinched flow fractionation in many times [18]. By the repeated sieving processes, Austin and coworkers demonstrated the continuous, high-resolution size separation of microbeads and blood cells [18, 19]. However, these methods require the precise sheath control of a sample flow to prevent particles from flowing on multiple paths. To overcome these limitations imposed on conventional and microfluidic methods for size separation, hydrophoretic methods have been developed. Here we provide a review of the methods for continuous size separation of microparticles, blood cells and cell-cycle synchrony, and for sheathless focusing of cells without external fields and sheath flows in microfluidic devices. We describe details of the separation mechanism and its application to particle and cell manipulation, comparing its advantages and disadvantages with other microfluidic methods. Finally, we present some challenges of the hydrophoretic technology. 2. Principle of Hydrophoretic Separation 2.1. STERIC HINDRANCE
Hydrophoresis that refers to the movement of suspended particles under the influence of a microstructure-induced pressure field utilizes steric hindrance mechanism for size separation, as many of other separation methods such as FFF, pinched flow fractionation, and deterministic lateral displacement work [7, 17−19]. Steric effects commonly arise when atoms within a molecule are brought too close together. Since the atoms occupy a certain amount of space, they should form a certain preferred order without overlapping. The same principle works in microscale physics. As particles of a given size are driven directly to the channel wall to be bumped, the particles form different shear layers according to size. Larger particles can be affected by high shear layers of the parabolic flow profile. To induce this particle ordering by steric hindrance, the driving force to the channel wall is inevitably required, such as gravitational force and sheath flow. The use of the driving force makes these separation systems complicate in their fabrication and operation. Hydrophoresis eliminates the need of the external driving force using convective flows induced by regularly patterned obstacles with an anisotropic resistance with respect to the fluid flow (Fig. 1) [20]. Upon application of a
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fluid flow along the y-axis, the anisotropic fluidic resistance of the obstacles generates rotational fluid streams as shown in Fig. 1b, c. The channels for simulation were 50 μm wide (Wch) and 38 μm deep (Hch) with Hob = 18 μm, θ = 10°, Lob = 12 μm, and Dob = 21 μm. These convective flows work as the inherent driving force that pushes particles to the obstacle surface. As particles (D in diameter) reach near the right sidewall, the rotational flows push them upward, thereby forcing them to align to the groove surface. Steric hindrance occurs when the obstacles prevent rotational flows of large particles that are observed in relatively smaller particles as illustrated in Fig. 1d. The particle−obstacle interaction deflects the large particle downward and makes the particle diffused out of the rotational streamlines. The particle thus follows stream 1 in Fig. 1c and stay near the right sidewall without deviation. The height of the obstacle gap (Hg = Hch − Hob) determines whether particles assume hydrophoretic ordering [20]. For D/Hg ≥ 0.5, the obstacle gap begins to hinder the rotational flow of particles induced by the anisotropic obstacles and leads to hydrophoretic ordering. In contrast, the smaller particle will deviate from the right sidewall following stream 2 in Fig. 1c, sorted from the large particle (Fig. 1d).
Figure 1. Hydrophoretic separation principle. (a) Schematic showing a hydrophoretic device with anisotropic microfluidic obstacles. (b and c) Simulated streamlines in the device. The slanted groove patterns on the channel generate rotational flows by using a steady axial pressure gradient. (d) Different particle ordering according to particle size by steric hindrance mechanism. (Reproduced with permission from Ref. [20]; Copyright 2009, American Chemical Society.)
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2.2. THREE-DIMENSIONAL MEASUREMENT OF HYDROPHORETIC ORDERING
The convective flows as the driving force of hydrophoresis show spatially varying characteristics in three dimensions. Therefore, it is inevitable to measure particle motions in three dimensions for exact characterization of hydrophoresis, although its separation results exhibit two-dimensional (2D) characteristics. Figure 2a–c show two orthogonal-axis images of a grooved microchannel for hydrophoretic particle ordering. These images were taken through a mirror-embedded microchannel. Details about the imaging principle can be found elsewhere [21]. As shown in Fig. 2, particles have spatially varying trajectories both in lateral and vertical directions, but different according to their size. Following the above ordering condition of D/Hg ≥ 0.5, the steric effect makes 15 μm beads diffused out of the rotational streams, thereby staying near sidewall 1 (Fig. 2c). The steric effect also enables the three-dimensional (3D) focusing of the 15 μm beads. Their focusing position was (y, z) = (17.2 ± 3.1, 22.8 ± 0.8 μm) in the channel of 50 μm in width, 37 μm in height, and 19 μm in height of obstacle gap (Hg). This result well supports that the steric effect confines the large particles in a certain position of the z-axis as well as y-axis. In contrast, 4 μm beads obeying the ordering condition continuously go back and forth between sidewall 1 and sidewall 2, following the transverse flows of the rotational flows without particle ordering (Fig. 2a, b). The hydrophoresis mechanism also verified with a computational modeling. The numerical functions for steric effect were defined, as treating particles as a point mass and assuming that they follow the velocity vector at the particle center, but continuously checking whether the particles collide with the grooves. Especially for the 15 μm bead, the collision occurs around the front edge of the groove. At that time, its position was shifted along the slant groove to the distance that is larger than its radius. This correction forces the bead to be aligned to the top surface of the groove that makes it diffused out of its rotational streams (Fig. 2d). In contrast, the 4 μm bead goes upward and approaches near the top surface of the channel, following the upward flows without aligning to the top surface of the groove. After reaching the channel surface, the 4 μm bead crosses the channel from sidewall 1 to sidewall 2, following the transverse flows of the rotational flows. After crossing the channel, the bead goes downward and crosses the channel again in the opposite direction. These results clearly revealed that hydrophoresis is governed by both convective vortices and steric hindrance.
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Figure 2. 3D particle ordering by hydrophoresis. (a) Fluorescence micrograph of 4 μm-sized beads passing through the grooved channel. (b) Trajectory of a single 4 μm-sized bead in the channel. (c) Fluorescence micrograph of 15 μm-sized beads assuming hydrophoretic selfordering. (d and e) Simulated particle trajectories of 15 and 4 μm-sized beads, respectively. (Reproduced with permission from Ref. [21]; Copyright 2009, Wiley-VCH Verlag GmbH & Co. KGaA.)
3. Particle and Cell Manipulation by Hydrophoresis Hydrophoresis offers advantages of a sheathless method, passive operation, and single channel. These advantages can make this separation technique a solution to the challenging problem of conventional separation methods. Here, we provide a detailed review of hydrophoretic methods for particle and cell manipulation, comparing their advantages and disadvantages with other microfluidic methods. 3.1. SIZE SEPARATION OF MICROPARTICLES
Size separation has been successfully demonstrated in many of microfluidic separation approaches of a continuous mode. In the field-based separation such as DEP, acoustic, and optical methods, the force acting on particles is proportional to their volume and corresponding native physical properties, including dielectric susceptibility, particle compressibility, and refractive index, respectively [10−12]. In many applications, target and non-target particles, however, exhibit similar responses to the acting force that precludes sorting particles based on intrinsic phenotypes. On the other hand, the
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volume dependence of the acting force in the field-based separation enables selective separation of microparticles by particle size. Kralj et al. demonstrated continuous separation of 4- and 6-μm beads using slanted, planar, interdigitated electrodes [22]. Kim et al. utilized the scattering force in the direction of laser beam propagation for lateral separation of 5- and 10-μm beads [23]. In field-free, flow-assisted separation, steric hindrance mechanism enables more precise size separation [7, 17, 18]. Seki and coworkers have employed splitting and recombining microchannel networks to continuously sort 1-, 2-, and 3-μm beads, so called hydrodynamic filtration [24]. Small particles in the networks readily flowed out through the branch channels, while larger particles formed thicker layers along a sidewall and the steric barrier forced the particles flow through the main channel. The deterministic lateral displacement (DLD) array, pioneered by Austin and colleagues, utilizes a kind of steric hindrance mechanism in which particles interact with a large array of pillars, repeating similar hindrance processes with hydrodynamic filtration [18]. Inglis et al. employed the repeated physical alignment of particles in the DLD array for separation of 2.3- to 15.0-μm beads [25]. Despite the successful demonstration of these methods, many of them are still limited by either low-resolution separation or narrow sizerange for separation. Although the DLD array sorted the particles of 0.8, 0.9, and 1.0 μm with a resolution of ≈10 nm, their efficacy in several or several tens of micrometers should be demonstrated. Hydrophoresis enables precise size separation in the size range from 8 to 15 μm compatible to mammalian cells in diameter (Fig. 3) [26]. On a microscale level, the diameter of particles assuming hydrophoretic ordering affects their ordering paths. Particles in the diameter range 8−15 μm were clearly resolved into their own equivalent positions (Fig. 3a, b). The coefficients of variance (CVs) of the lateral positions for 11, 12, and 15 μm particles showed similar values to the ≈2% CV for their sizes. This uncertainty of the lateral positions is attributed to the inhomogeneity of their sizes. The size selectivity values for 11 and 12 μm particles were ≈300 and 80 nm, respectively. With this high size-selectivity, the hydrophoretic sizing of 10.4 μm particles with a high CV of 8.7% was successfully demonstrated, compared with a conventional laser diffraction method. The selectivity, however, is not maintained as downscaling the range into a submicrometer scale [20]. Even in that range, the hydrophoretic device can separate particles in binary mode: large particles in hydrophoretic ordering are sorted from relatively smaller particles in free flow (Fig. 3c). The purity of the 0.52 μm beads after separation was increased to 99.6% from the initial value of 72.2%, while the purity of the 1.1 μm beads was enhanced from 27.8% to 41.7%. The particle size range for hydrophoretic
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ordering can be modulated by the height of the obstacle gap. The rule for hydrophoretic ordering, D/Hg ≥ 0.5 still hold even in a sub-micrometer scale (Fig. 3d, e). For application to biomolecular separation, the efficacy of the hydrophoretic ordering should be demonstrated as the obstacle gap is reduced in nanoscale.
Figure 3. Size separation of microparticles by hydrophoresis. (a) Different distributions of particle streams according to particle size in the hydrophoretic device with Hg of 23 μm. (b) Lateral position of particles as a function of particle size. (Reproduced with permission from Ref. [26]; Copyright 2007, The Royal Society of Chemistry.) (c) Size separation of 0.52 and 1.1 μm beads in the device with Hg of 1.4 μm. (d) Hydrophoretic ordering of 0.52 μm beads in the device with Hg of 0.65 μm. (e) The ratio of particle diameter assuming hydrophoretic ordering to Hg as a function of Hg. (Reproduced with permission from Ref. [20]; Copyright 2009, American Chemical Society.)
3.2. BLOOD CELL SEPARATION
Precise and rapid isolation of blood cells is of fundamental importance in clinical and biomedical researches. Since blood is a very complex mixture containing RBCs, WBCs, and platelets, blood samples need to be separated prior to analysis. To address this need, many of microfluidic principles for particle separation above mentioned have been utilized. Pommer et al. isolated platelets from diluted whole blood, by exploiting the fact that are
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the smallest cell type in blood and the volume dependence of the DEP force [27]. Magnetophoresis utilizes the magnetic susceptibility difference between WBCs and RBCs for separation: the relative magnetic susceptibilities of deoxyhemoglobin RBCs and WBCs are about 3.9 × 10−6 and −0.13 × 10−6 in water, respectively [28]. The deterministic bump array separated WBCs from RBCs with an enrichment ratio of 110-fold using asymmetric bifurcation of laminar flow under which RBCs follow streamlines, and WBCs are bumped the array and laterally moved by hydrodynamic lateral drag [19]. A microfluidic network with splitting channels isolated WBCs in a continuous manner with an enrichment ratio of 29-fold [29]. Many of current microfluidic devices for blood cell separation exploit differences in the size and geometry between blood cells. However, RBCs and WBCs in suspension have a similar diameter that make it difficult to separate two cell types only based on their diameter. Therefore, it is important to identify and utilize the small thickness of RBCs in the range 1.7−2.6 μm especially in flow-assisted separation methods. To solve this challenge, the hydrophoretic filtration method has been proposed, by modifying the slant groove with a filtration pore (Fig. 4a) [30]. The gap height of the filtration obstacles was set between the thickness of RBCs (2−3 μm) and the diameter of WBCs (6−10 μm) to identify and utilize the thickness of RBCs for separation. Blood cells passing through the hydrophoretic channel structure are divided into two groups. WBCs larger than the gap height of the filtration obstacles collide against the obstacles and move into the filtration pore. In contrast, RBCs are aligned parallel to the obstacle due to their small thickness and deformability, thereby freely passing through the obstacle gap. By using this principle, the hydrophoretic filtration device enriched WBCs to ≈210-fold from RBCs in just a single round of separation, while ≈85% of WBCs was recovered compared with their initial concentration [30]. This higher enrichment ratio supports that the hydrophoretic filtration device well identifies and utilizes the small thickness of RBCs and their deformability for separation. However, the effort to simultaneously discriminate more cell types such as platelets and WBC subsets, and plasma molecules should be addressed for complete blood separation. The deterministic bump array has demonstrated multiplecell sorting with RBCs and WBC subsets [19]. To expand the separation range of hydrophoresis, more design variations and optimization are still needed.
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Figure 4. Blood cell separation by hydrophoretic filtration. (a) Principle of hydrophoretic filtration. A flow direction is along the y-axis. WBCs (D in diameter) and RBCs (d in thickness) having a smaller size than the gap height (H) of the slanted obstacles freely pass through the gap and are focused to the sidewall by hydrophoretic ordering. In the filtration region, the gap height (h) of the filtration obstacle is set between two cell types, thereby sorting WBCs from RBCs by hydrophoretic filtration. (b) Optical image of hydrophoretic filtration device. (c and d) Bright-field (left) and fluorescence (right) images showing blood cells before and after hydrophoretic filtration, respectively. (Reproduced with permission from Ref. [30]; Copyright 2007, The Royal Society of Chemistry.)
3.3. CELL CYCLE SYNCHRONIZATION
Indentifying a minute change of cell size is an important matter for biology researches. Although there are many arguable points on a size-sensing
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mechanism of animal cells, it is obvious that a normal cell maintains its right size during its cell-cycle progression, called homeostasis and alteration of cell size can manifest as disease [1]. The successful synchronization of cell cycle phase or separation of cell cycle synchrony is an important factor for continuous advancement in the fields of cell cycle regulation and cancer to understand the physiological roles of regulatory molecules involved in each phase of the cell cycle, and their relationship with oncogenes and tumor suppressor genes. Synchronization methods especially based on physical separation exploits the fact that cells have different nucleus size or cell mass according to cell-cycle phases. Centrifugal elutriation has been used for cell cycle synchronization through balancing between the elutriation flow and the centrifugal force against the flow direction [31]. Dielectrophoresis (DEP) has been recently employed for the selection of cells at a specific phase by exploiting the dependence of the DEP force on a particle volume [32]. Although they showed impressive results, they require a complicated equipment setup of a centrifuge, rotor assembly, separationand elutriation-chamber, or relatively complex fabrication processes such as metal-electrode patterning. Hydrophoretic size separation has been used as a simple, low-cost, and noninvasive means for cell cycle synchronization (Fig. 5) [33]. To ensure the hydrophoretic size separation of U937 cells whose diameters vary between 11 and 22 μm, the hydrophoretic device was engineered with Hg = 24 μm. In the device, U937 cells were clearly resolved into their own equivalent positions according to their size (Fig. 5b). Hydrophoretic size separation of U937 cells showed that there exists a linear correlation between the cell size and lateral distribution with the linear regression coefficient of −1.6 μm/μm2 (Fig. 5c). A minute change of cell size by chemical interference was also measured by hydrophoresis, with nocodazole, a synchronizing agent that arrests cells at or prior to mitosis (Fig. 5d). Compared with the control, asynchronous cells, the treated cells with nocodazole have an average change in both the cell area of 40.3 μm2 and lateral position of −95.3 μm. The robustness of the hydrophoretic method for practical applications was demonstrated by sorting cells in the G0/G1 and G2/M phases out of the original, asynchronous cells with a high level of synchrony of 95.5% and 85.2%, respectively. Differently from current separation approaches, hydrophoresis has advantages of passive, sheath-less, and high-resolution within the size range of mammalian cells that facilitate easy integration and provide gentle, effective separation in cells-on-chips [34]. Further efforts to integrate hydrophoresis with cell analysis units and to find out more meaningful applications are needed.
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Figure 5. Cell cycle synchronization by hydrophoresis. (a) Schematic of hydrophoretic device where cells in the G0/G1 and G2/M phases are separated. (b) Optical micrograph showing asynchronous cells distributed to their size in the outlet region of the hydrophoretic device with Hg = 24 μm. (c) Scatter plot of the lateral position in the outlet region versus the area of the asynchronous cells. (d) Scatter plot of the lateral position in the outlet region versus the area of nocodazole-treated cells. The horizontal and vertical dashed lines in parts c and d denote the mean values for the lateral position and cell area, respectively. (Reproduced with permission from Ref. [33]; Copyright 2009, American Chemical Society.)
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3.4. SHEATHLESS PARTICLE FOCUSING
Focusing particles in a fluid stream is critical to the performance of a flow cytometer for counting, analyzing, and sorting microscopic particles. The channel designs for 2D or 3D hydrodynamic focusing typically require at least four inlets and their individual control to fully sheathe a sample flow [35, 36]. This focusing approach makes microflow cytometers more complex, requiring well-controlled fluidics. To overcome the limitations by conventional hydrodynamic focusing methods, microfluidic sheathless focusing methods have been developed for miniaturizing flow cytometers. The driving forces and mechanisms for particle manipulation that are used in the separation methods above mentioned are also applicable for sheathless particle focusing. Yu et al. investigated the electrode arrays on the circumference of a round microchannel for the purpose of 3D focusing of microparticles by DEP [37]. Shi et al. utilized standing surface acoustic waves for 3D focusing of 1.9 μm particles, generated from interdigitated transducers deposited on a piezoelectric substrate [38]. Seki and coworkers have employed splitting and recombining channel networks for sheathless focusing of 5 μm particles by hydrodynamic filtration [39]. The DLD array, pioneered by Austin and colleague, was utilized for focusing of 2.7 μm particles by steric hindrance mechanism [40]. However, these sheathless focusing devices have an inherent weakness that the focusing efficiency of the devices largely depends on particle size. This limitation still holds in hydrophoretic devices for sheathless focusing [41]. The obstacles for hydrophoresis were designed in shape of the letter V, thereby generating lateral flows toward the channel center. However, due to the size-dependent behaviors of particles, the obstacles are still more effective for particle separation than for particle focusing. To fix this, the V-shaped obstacles were modified with extended geometries from the obstacles that have the isotropic resistance to the applied fluid flow (Fig. 6a, b) [42]. By repeating the extension step, the ratio of the width of the focused particle stream to the channel width becomes smaller, while the focusing efficiency increases. At every extension, the extension width should be carefully modulated, thereby allowing particles to flow only in the channel region of V-shaped patterns. With this principle, the sheathless focusing of Jurkat cells within the standard deviation of 8.7 μm in 1 mm-wide channels was achieved (Fig. 6c, d) [42].
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Figure 6. Hydrophoretic device for sheathless particle focusing. (a) Optical micrographs of the hydrophoretic device with five step extensions. (b) Simulated pressure fields and streamlines around bent obstacles showing that there are no significant variations of the pressure intensity in the extended region due to its isotropic fluidic resistance to the fluid flow. (c) Optical micrograph showing the focusing stream of Jurkat cells in the outlet region of 1 mm width. (d) Measured focusing profiles of Jurkat cells. (Reproduced with permission from Ref. [42]; Copyright 2008, American Chemical Society.)
4. Challenges of Hydrophoresis Recent advances in microfluidics have overcome many drawbacks of conventional particle manipulation techniques by taking advantage of accurate particle control without turbulent disturbance due to laminar flow at low Reynolds number and high process efficiency even with a small number of particles. However, there are still limitations to be solved, such as operational complexity from requirements of sheath flows and external fields. Hydrophoresis can be a solution to this challenging problem with advantages of a sheathless method, passive operation, and single channel, thereby realizing ‘plug-and-sort’ and ‘plug-and-focus’ without any calibration of flow conditions. However, there are several practical considerations for real, practical applications of hydrophoresis. The first is the limited size range for separation as mentioned before. Hydrophoresis has a high size-
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selectivity of ≈80–300 nm in the size range from 8 to 15 μm compatible to mammalian cells, but this selectivity is not maintained as downscaling the range into a sub-micrometer scale. Thereby, hydrophoresis is more suitable for size separation of mammalian cells than molecular separation. This limited range for size separation can be a hindrance to the widespread use of hydrophoresis to apply to a broad range of different biological samples. Therefore, further efforts to widen the size range for separation should be needed through more design variations and optimization. The second consideration for practical applications of hydrophoresis arises from the fact that there is no special application that hydrophoresis can be best used. This problem will be applicable to the other microfluidic separation methods. Although microfluidic separation methods including hydrophoresis can provide unique advantages as mentioned above, other well-established techniques such as FFF and centrifugal elutriation have been shown to be superior in characterizing biological samples. Thus, continued efforts should be addressed to solve this problem by coupling microfluidic separation units with other comprehensive analytical units. In highly integrated microdevices, microfluidic separation techniques can find out their more widespread and versatile roles. 5. Conclusions Microfluidics holds the potential to miniaturize and enhance the way in which conventional laboratory functions have been conducted significantly. One important challenge is the sample preparation such as separation to make biological samples available for analysis. While significant improvement has been shown in this field, there are still many more challenges for future development. The real integration of microfluidic separation devices with comprehensive analytical units has yet to be achieved. However, once this integration is completely realized, microfluidic separation units can save time required for off-chip sample preparation and offer high process efficiency even with a small sample volume. Acknowledgments This research was supported by the National Research Laboratory (NRL) Program grant (R0A-2008-000-20109-0) and by the Nano/Bio Science and Technology Program grant (2008-00771) funded by the Korea government (MEST). The authors thank the Chung Moon Soul Center for BioInformation and BioElectronics at KAIST.
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References 1. L. J. Saucedo and B. A. Edgar, Why size matters: Altering cell size, Current Opinion in Genetics & Development, 12(5), 565–571 (2002). 2. P. Jorgensen and M. Tyers, How cells coordinate growth and division, Current Biology, 14, R1014–R1027 (2004). 3. E. P. Dellinger and D. A. Anaya, Infectious and immunologic consequences of blood transfusion, Critical Care, 8, S18–S23 (2004). 4. P. Sethu, A. Sin and M. Toner, Microfluidic diffusive filter for apheresis (leukapheresis), Lab on a Chip, 6, 83–89 (2006). 5. D. Melucci, M. Guardigli, B. Roda, A. Zattoni, P. Reschiglian and A. Roda, A new method for immunoassays using field-flow fractionation with on-line, continuous chemiluminescence detection, Talanta, 60, 303–312 (2003). 6. P. Reschiglian, A. Zattoni, D. Melucci, B. Roda, M. Guardigli and A. Roda, Flow field-flow fractionation with chemiluminescence detection for flowassisted, multianalyte assays in heterogeneous phase, Journal of Separation Science, 26, 1417–1421 (2003). 7. P. Reschiglian, A. Zattoni, B. Roda, E. Michelini and A. Roda, Field-flow fractionation and biotechnology, Trends in Biotechnology, 23, 475–483 (2005). 8. Bernard, B. Paulet, V. Colin and P. J. P. Cardot, Red blood cell separations by gravitational field-flow fractionation: Instrumentation and applications, Trends in Analytical Chemistry, 14, 266–273 (1995). 9. P. Reschiglian, A. Zattoni, B. Roda, S. Casolari, M. H. Moon, J. Lee, J. Jung, K. Rodmalm and G. Cenacchi, Bacteria sorting by field-flow fractionation. Application to whole-cell Escherichia coli vaccine strains, Analytical Chemistry, 74, 4895–4904 (2002). 10. X. Hu, P. H. Bessette, J. Qian, C. D. Meinhart, P. S. Daugherty and H. T. Soh, Marker-specific sorting of rare cells using dielectrophoresis, Proceedings of the National Academy of Sciences of the United States of America, 102, 15757–15761 (2005). 11. M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand and W. F. Butler, Microfluidic sorting of mammalian cells by optical force switching, Nature Biotechnology, 23, 83–87 (2005). 12. F. Petersson, L. Åberg, A.-M. Swärd-Nilsson and T. Laurell, Free flow acoustophoresis: Microfluidic-based mode of particle and cell Separation, Analytical Chemistry, 79, 5117–5123 (2007). 13. Y. Kang, D. Li, S. A. Kalams and J. E. Eid, DC-Dielectrophoretic separation of biological cells by size, Biomedical Microdevices, 10, 243–249 (2008). 14. F. Petersson, A. Nilsson, C. Holm, H. Jönsson and T. Laurell, Separation of lipids from blood utilizing ultrasonic standing waves in microfluidic channels, The Analyst, 129, 938–943 (2004). 15. C.-F. Chou, J. O. Tegenfeldt, O. Bakajin, S. S. Chan, E. C. Cox, N. Darnton, T. Duke and R. H. Austin, Electrodeless dielectrophoresis of single- and double-stranded dNA, Biophysical Journal, 83, 2170–2179 (2002). 16. S. Tuukkanen, J. J. Toppari, A. Kuzyk, L. Hirviniemi, V. P. Hytönen, T. Ihalainen and P. Törmä, Carbon nanotubes as electrodes for dielectrophoresis of DNA, Nano Letters, 6, 1339–1343 (2006).
HYDROPHORESIS FOR BIOLOGICAL APPLICATIONS
593
17. M. Yamada, M. Nakashima and M. Seki, Pinched flow fractionation: Continuous size separation of particles utilizing a laminar flow profile in a pinched microchannel, Analytical Chemistry, 76, 5465–5471 (2004). 18. L. R. Huang, E. C. Cox, R. H. Austin and J. C. Sturm, Continuous particle separation through deterministic lateral displacement, Science, 304, 987–990 (2004). 19. J. A. Davis, D. W. Inglis, K. J. Morton, D. A. Lawrence, L. R. Huang, S. Y. Chou, J. C. Sturm and R. H. Austin, Deterministic hydrodynamics: Taking blood apart, Proceedings of the National Academy of Sciences of the United States of America, 103, 14779–14784 (2006). 20. S. Choi, S. Song, C. Choi and J.-K. Park, Hydrophoretic sorting of micrometer and submicrometer particles using anisotropic microfluidic obstacles, Analytical Chemistry, 81, 50–55 (2009). 21. S. Choi and J.-K. Park, Optically coated mirror-embedded microchannel to measure hydrophoretic particle ordering in three dimensions, Small, 5, 2205– 2211 (2009). 22. J. G. Kralj, M. T. W. Lis, M. A. Schmidt and K. F. Jensen, Continuous dielectrophoretic size-based particle sorting, Analytical Chemistry, 78, 5019– 5025 (2006). 23. S. B. Kim, S. Y. Yoon, H. J. Sung and S. S. Kim, Cross-type optical particle separation in a microchannel, Analytical Chemistry, 80, 2628–2630 (2008). 24. M. Yamada and M. Seki, Microfluidic particle sorter employing flow splitting and recombining, Analytical Chemistry, 78, 1357–1362 (2006). 25. D. W. Inglis, J. A. Davis, T. J. Zieziulewicz, D. A. Lawrence, R. H. Austin and J. C. Sturm, Determining blood cell size using microfluidic hydrodynamics, Journal of Immunological Methods, 329, 151–156 (2008). 26. S. Choi and J.-K. Park, Continuous hydrophoretic separation and sizing of microparticles using slanted obstacles in a microchannel, Lab on a Chip, 7, 890–897 (2007). 27. M. S. Pommer, Y. Zhang, N. Keerthi, D. Chen, J. A. Thomson, C. D. Meinhart and H. T. Soh, Dielectrophoretic separation of platelets from diluted whole blood in microfluidic channels, Electrophoresis, 29, 1213–1218 (2008). 28. K.-H. Han and A. B. Frazier, Paramagnetic capture mode magnetophoretic microseparator for high efficiency blood cell separations, Lab on a Chip, 6, 265–273 (2006). 29. M. Yamada and M. Seki, Hydrodynamic filtration for on-chip particle concentration and classification utilizing microfluidics, Lab on a Chip, 5, 1233–1239 (2005). 30. S. Choi, S. Song, C. Choi and J.-K. Park, Continuous blood cell separation by hydrophoretic filtration, Lab on a Chip, 7, 1532–1538 (2007). 31. M. F. Heil, J. M. Wu and J. W. Chiao, Cell-cycle differences of HL-60 leukemia cells fractionated by centrifugal elutriation, Biochimica et Biophysica Acta, 845, 17–20 (1985). 32. U. Kim, C.-W. Shu, K. Y. Dane, P. S. Daugherty, J. Y. J. Wang and H. T. Soh, Selection of mammalian cells based on their cell-cycle phase using dielectrophoresis, Proceedings of the National Academy of Sciences of the United States of America, 104, 20708–20712 (2007).
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33. S. Choi, S. Song, C. Choi and J.-K. Park, Microfluidic self-sorting of mammalian cells to achieve cell cycle synchrony by hydrophoresis, Analytical Chemistry, 81, 1964–1968 (2009). 34. J. El-Ali, P. K. Sorger and K. F. Jensen, Cells on chips, Nature, 442, 403–411 (2006). 35. C. Simonnet and A. Groisman, High-throughput and high-resolution flow cytometry in molded microfluidic devices, Analytical Chemistry, 78, 5653– 5663 (2006). 36. N. Sundararajan, M. S. Pio, L. P. Lee and A. A. Berlin, Three-dimensional hydrodynamic focusing in polydimethylsiloxane (PDMS) microchannels, Journal of Microelectromechanical Systems, 13, 559–567 (2004). 37. C. Yu, J. Vykoukal, D. M. Vykoukal, J. A. Schwartz, L. Shi and P. R. C. Gascoyne, A three-dimensional dielectrophoretic particle focusing channel for microcytometry applications, Journal of Microelectromechanical Systems, 14, 480–487 (2005). 38. J. Shi, X. Mao, D. Ahmed, A. Colletti and T. J. Huang, Focusing microparticles in a microfluidic channel with standing surface acoustic waves (SSAW), Lab on a Chip, 8, 221–223 (2008). 39. R. Aoki, M. Yamada, M. Yasuda and M. Seki, In-channel focusing of flowing microparticles utilizing hydrodynamic filtration, Microfluidics and Nanofluidics, 6, 571–576 (2009). 40. K. J. Morton, K. Loutherback, D. W. Inglis, O. K. Tsui, J. C. Sturm, S. Y. Chou and R. H. Austin, Hydrodynamic metamaterials: Microfabricated arrays to steer, refract, and focus streams of biomaterials, Proceedings of the National Academy of Sciences of the United States of America, 105, 7434– 7438 (2008). 41. S. Choi, S. Song, C. Choi and J.-K. Park, Sheathless focusing of microbeads and blood cells based on hydrophoresis, Small, 4, 634–641 (2008). 42. S. Choi and J.-K. Park, Sheathless hydrophoretic particle focusing in a microchannel with exponentially increasing obstacle arrays, Analytical Chemistry, 80, 3035–3039 (2008).
PROGRAMMABLE CELL MANIPULATION USING LAB-ON-A-DISPLAY HYUNDOO HWANG AND JE-KYUN PARK Department of Bio and Brain Engineering, College of Life Science and Bioengineering, KAIST, Daejeon 305-701, Korea,
[email protected]
Abstract. Programmable manipulation of particles or cells plays an important role in many biological and medical applications. Here a new programmable micro manipulator, named lab-on-a-display, in which particles are manipulated by optically induced electrokinetic forces generated from an optoelectronic tweezers on a liquid crystal display, is introduced. This optoelectrofluidic platform has been utilized to manipulate various kinds of cells such as blood cells, oocytes, and motile bacteria for several biotechnological applications. 1. Introduction Tools for manipulation of microparticles play an important role in many areas of biotechnology, biomedical research, and colloidal science. Microscopic particle or cell handling, such as transporting, trapping, concentrating, and sorting, is essential to perform several biomedical and chemical applications, including immunoassays, cellular interaction, cell transfection, biological physics, microbiology, embryology, tissue engineering, and in vitro fertilization. For these purposes, several mechanisms such as optical [1], electrokinetic [2], magnetic [3], acoustic [4], and hydrodynamic [5] forces have been utilized. Since optical tweezers, which uses optical forces induced by a transfer of photonic momentum from incident light to target particles, was first reported by Ashkin and his coworkers in 1970 [6], it has become a powerful tool for trapping cells and probing physical properties of biological polymers [7, 8]. For stable trapping of microparticles, the incident light should have high power and diverge rapidly enough away from a focal point via an objective lens, which has high numerical aperture [1]. In addition, high optical power, which is proportional to the number of particles, and complicated optical components for scanning or splitting light beam are required for multiple traps [9−11]. These limitations make the optical tweezers difficult to be applied for massive parallel manipulation of microparticles. S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_28, © Springer Science + Business Media B.V. 2010
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Electrokinetics, which includes dielectrophoresis (DEP), electrophoresis, and ac electroosmosis (ACEO), has also been widely used for particle manipulation in a microfluidic device. Since any modification of target particles is not required as well as parallel manipulation in a large area with low power consumption is possible by patterning microelectrode array, this mechanism has been emerged as one of the most favorable tools for manipulation of cells [2, 12−15]. In 2003, Maranesi and his colleagues demonstrated two dimensional (2D) manipulation of individual cells using a programmable DEP platform based on a complementary metal-oxide semiconductor (CMOS) circuit [16]. By addressing and activating individual electrodes in the 2D electrode array, parallel manipulation of single cells, which are trapped with reconfigurable virtual DEP cages, was possible without any microfluidic and optical components. However, the integration of CMOS circuits increases the cost for manufacturing such the devices, making it less attractive for disposable applications. The wiring and interconnecting of the large number of electrodes also remained challenging issues. Optoelectrofluidics has appeared to deal with the limitations of typical platforms for microparticle manipulation, especially based on optics and electrokinetics. It refers to the study of the motions of particles or molecules and their interactions with surrounding fluid and electric field, which is induced or perturbed in an optical manner [17]. As shown in Fig. 1, this concept includes electrokinetic principles such as electrophoresis, DEP, ACEO, and electrothermal flow, which are induced by combination of optical and electrical fields or optical-to-electrical energy transfer. In 1995, Mizuno et al. observed concentration of microparticles and molecules by strong vortices driven by laser-induced local heating of fluid in an electric field [18]. Hayward and his colleagues also demonstrated electrophoretic patterning of colloidal particles using an ultraviolet (UV) light pattern projected onto an indium tin oxide (ITO) electrode [19]. When the UV micropattern was projected, the number of electron-hole pairs due to oxidation−reduction reaction on the interface between water and the electrode becomes increased, resulting in a perturbation of an applied electric field. After that, many researchers have been trying to apply a photoconductive material deposited on a plate electrode to induce a nonuniform electric field, which results in the electrokinetic motion of particles and fluids, only with a weak white light source [17, 20−33] or a conventional laser [34−38]. Optoelectrofluidics provides a solution for disposability and interconnection issues in the parallel manipulation of multiple cells using
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Figure 1. Principles of optoelectrofluidics [39].
electrokinetic forces. Moreover, the optoelectrofluidic platforms require much lower optical power and offer much larger manipulation area than the typical optical mechanism such as optical tweezers. In this chapter, recent research progresses in the optoelectrofluidic manipulation platform for biotechnological applications developed in our group are described. 2. Lab-on-a-Display: An LCD-based Optoelectrofluidic Platform 2.1. ESSENTIAL COMPONENTS FOR LAB-ON-A-DISPLAY
To construct an optoelectrofluidic platform, a device composed of such a photoconductive layer and a sample solution, a light source projected to the device to induce an electric field in the sample solution by forming virtual electrodes, a display device for modulating the light pattern, and a power supply for applying a voltage are essential. Optical components such as lenses and mirrors also play a crucial role in the optoelectrofluidic system, but it depends on the display device and the light source. In this section, we will explain at length about the essential components for the optoelectrofluidic platform. In 2005, Chiou et al. first introduced an optoelectronic tweezers (OET) device, which is composed of ITO plate electrodes for the application of a voltage and hydrogenated amorphous silicon (a-Si:H) as a photoconductive layer deposited on the plate electrode [34]. Since the intrinsic a-Si:H has
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shorter carrier diffusion length and higher optical absorption coefficient than crystalline silicon, it is a good photoconductive material to make virtual electrode patterns of high resolution [40]. The OET device based on a-Si:H is simple and easy to fabricate using a plasma enhanced chemical vapor deposition (PECVD) method. In general, a triple layer of (i) heavily doped a-Si:H for lowering contact resistance, (ii) intrinsic a-Si:H for high photoconductivity, and (iii) silicon nitride (or silicon oxide) for passivation was sequentially deposited onto the ITO-coated glass substrate in a single chamber reactor [22]. After that, some regions were etched by reactive ion etch (RIE) to expose the ITO surface for applying an operating voltage. The fabricated OET device is shown in Fig. 2a. Finally, a bare ITO-coated glass substrate as a ground electrode is turned upside down and put on the fabricated photoconductive layer as sandwiching a sample solution containing target microparticles and cells with a certain gap height using spacers as shown in Fig. 2b. Display device is also one of the important components in the optoelectrofluidic platform. Sometimes, a mask with a fixed pattern [19], a diaphragm [31−33], or only a focused laser spot [36−38] has been applied for projecting a light onto a partial area of the photoconductive layer, but a display device, which is controllable by a computer, is necessary for programmable manipulation of light-activated virtual electrodes. As a display device, three types of device have been used: (i) a digital micromirror device (DMD) [34, 35]; (ii) a beam projector [28−30]; and (iii) a liquid crystal display (LCD) [17, 20−27]. In the case of the DMD and the beam projector, they always require well-aligned and relatively complicated optical setup for generating and focusing light patterns, limiting the system integration for user-friendly and portable applications. Choi and his coworkers reported an LCD-based optoelectrofluidic platform, named lab-on-a-display in 2007 [20]. There is no optical component between an LCD and an OET device, thus a light pattern generated from an LCD is directly transferred onto the OET device as shown in Fig. 3a. It offers the simplest structure and the largest manipulation area among the optoelectrofluidic platforms, which have been reported previously. In addition, the lab-on-a-display platform is very thin and tolerant to vibrations due to the elimination of lens and optical alignment, providing more suitable form for portable applications. However, the lens-less structure causes a blurred image due to diffraction of a light, limiting the minimum size of virtual electrodes and the performance of particle manipulation.
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To overcome those limitations of each platform, Hwang et al. proposed a lens-integrated type of an LCD-based optoelectrofluidic platform as shown in Fig. 3b [22]. In this platform, an LCD module is installed on an illumination of a conventional microscope. A condenser lens, which is integrated in the microscope, condenses and focuses the light passed through the LCD module onto the photoconductive layer of the OET device on the microscope stage. This lens-integrated type of lab-on-a-display provides much simpler and easier way to use in practice than the DMDand the projector-based platforms, as well as much higher manipulation performances and virtual electrode resolution than the lens-less lab-on-adisplay platform.
Figure 2. Pictures of (a) a fabricated photoconductive layer [39] and (b) a set optoelectrofluidic device on a microscope stage.
The optoelectrofluidic platform basically requires a light source, whose intensity is much lower than that for typical optical tweezers system. Therefore, we do not have to care about photonic and thermal damages of biological samples seriously. Practically, however, the light source is closely connected with the optical components in a whole system and the display device. When we apply a laser source, many optical components are required to project, to spatially modulate, and to focus the light pattern onto the photoconductive surface whatever the display device used. On the other hand, in the case of a white light source such as halogen lamp, the optical components are not always required or not so complicated if we utilize an LCD as a display device. It provides higher flexibility on the optoelectrofluidic system according to the target application.
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Figure 3. Schematics of lab-on-a-display platform. (a) Lens-less type and (b) lens-integrated type. (Reproduced with permission from Ref. [22]; Copyright 2008, Wiley-VCH Verlag GmbH & Co. KGaA.)
2.2. PHYSICAL PHENOMENA IN LAB-ON-A-DISPLAY
As we mentioned above, the electrokinetic mechanisms, which includes electrophoresis, DEP, ACEO, electrothermal effect, and electro-orientation, are main driving force for particle manipulation using an optoelectrofluidic device. In addition, we could also observe the electrostatic interactions due to the polarization of dielectric particles like cells. Electrophoresis, the movement of charged objects in an electric field, is originated from the Coulomb force, which is defined by:
FColumb = qE
,
(1)
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where q is the net charge of the particle and E is the applied electric field. In general, most cells have functional groups, of which charge is negative at neutral pH [41]. Therefore, we can manipulate and separate different cells according to their zeta potentials by applying dc or ac electric field of extremely low frequency below about 10 Hz. Hayward et al. have patterned polystyrene microbeads based on the optically induced electrophoresis using a UV light pattern which is projected onto an ITO electrode [19]. DEP, one of the most widely applied principles for optoelectrofluidic manipulation [20−22, 26−29, 34−37], is the movement of dielectric objects under a nonuniform electric field driven by forces arising from the interaction between an induced electric dipole of the particle and the applied electric field [42]. The DEP force acting on a spherical particle is given by:
FDEP = 2πr ε m Re[ f CM ]∇ E 3
2
, (2)
where r is the radius of the particles; εm is the permittivity of the suspending medium. Re[fCM] is the real part of the Clausius–Mossotti factor which is described as below: , ε *p − ε m* fCM = * (3) ε p + 2ε m* where εp* and εm* are the complex permittivities of the particle and the medium, respectively. The value of Re[fCM] depends on the frequency of applied ac voltage and the conductivity of particles and medium, varying between +1 and −0.5. In the optoelectrofluidic device, the particles are repelled from the light pattern, where the electric field is relatively higher than other region, if Re[fCM] is negative (negative DEP). If Re[fCM] is positive, the particles move toward the light pattern (positive DEP). Since most cells and molecules show the positive DEP motion in low-conductivity media, they are trapped within and moved along dynamic image patterns in an optoelectrofluidic device [22, 28, 34, 36]. The DEP force is proportional to the volume of particle and the square of the electric field gradient. This nature of DEP force limits the rapid manipulation of submicro-/nanoscale particles existing far from the edge of the virtual electrodes. Due to the limitation of DEP, the optically induced ACEO, which is a fluidic motion generated by the motion of ions within the electric double layer due to the tangential electric field, have been applied for rapid concentration of microparticles, nanoparticles and molecules using lab-on-a-display [17, 30−32]. When we project an LCD image onto the photoconductive layer, the microparticles suspended around the image
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pattern are rapidly moved to the illuminated area by the optically induced ACEO flow. The particles, which have been staying far away from the virtual electrodes, are also driven by the globally occurred flows [17]. The fluids around the partially illuminated area in the optoelectrofluidic device flow along the surface of the photoconductive layer with a rectified slip velocity defined as:
vslip
t
=
, 1 λD Re[σ q Et* ] 2 η
(4)
where λD is the Debye length and η is the fluid viscosity. The charges contained in the Debye layer (σq) and the tangential electric field (Et) vary sinusoidally and can be evaluated as σq = εmζ/λD and Et = –α∂ζ/∂y, respectively, where ζ is the zeta potential, which is the voltage drop across the Debye layer, and α is a geometry factor [43]. In addition to these electrokinetic phenomena, electrostatic interactions among the microparticles due to their induced dipole are also observable [23]. The electrostatic interaction force, Fdipole = r6εmRe[fCM]2E2 [44], can make the particles form a structure like perl chain by attractive forces in the direction of an electric field, and a crystalline structure with a regular distances among the particles by repulsive forces in the plane perpendicular to the electric field. These electrostatic attractive and repulsive interactions can interfere with the precise control of microparticles using lab-on-adisplay. On the other hand, we can utilize these phenomena for several applications such as a manufacture of self-assembled micropattern structures, a study about interactions between two cells, and a bead-based immunoassay. In general, the ACEO flow occurs dominantly at the ac frequency relatively lower than that for DEP. Based on this frequency dependency of electrokinetics, rapid and selective concentration of microbeads according to their size has been demonstrated using lab-on-a-display as shown in Fig. 4 [17]. At 10 kHz frequency, 1-µm-diameter beads were concentrated into the illuminated area by ACEO flows, while 6-µm-diameter beads were repelled from the area due to relatively strong negative DEP forces. As a consequence, the 1 µm beads could be simultaneously separated from the mixture. At the ac frequencies below 1 kHz, both different sized particles were concentrated into the illuminated area by hydrodynamic drag forces by ACEO flows, which is much stronger than the DEP forces. At such an extremely low frequency, it has been known that not only the global flows by ACEO around the light pattern, but also local induced-charge electroosmosis (ICEO) along the surface of particles and the electrostatic forces affect the behavior of particles in significance.
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Figure 4. Selective concentration of microparticles using frequency-dependency of ac electrokinetics in lab-on-a-display. (Reproduced with permission from Ref. [17]; Copyright 2009, The Royal Society of Chemistry.)
Figure 5. Change of distances among 3-µm-diameter microparticles concentrated within the illuminated area. Combination of several physical mechanisms including frequencydependent electrokinetics and electrostatic interaction forces affect the behavior of particles. (Reproduced with permission from Ref. [30]; Copyright 2009, American Chemical Society.)
Figure 5 shows that the distances among the 3-µm-diameter particles, which were concentrated into and assembled within the illuminated area, can be tuned by the combination of those forces against the applied ac frequency below 1 kHz [30]. At 100 Hz, the forces, which assemble and closely pack the particles, acting on the 6 µm beads, became larger than that acting on the 1 µm beads. As a result, only the 6 µm beads were concentrated and closely packed within the illuminated area, and the 1 µm beads were pushed out from the area and swept away by the vortices around there as shown in Fig. 4. This technique can be used in several biochemical
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applications for the rapid and massive manipulation of nanoparticles, cells and proteins, as well as the manufacturing technologies for photonic crystals and biochemical sensors. 3. Lab-on-a-Display: An LCD-based Optoelectrofluidic Platform 3.1. INTERACTIVE MANIPULATION OF BLOOD CELLS
Manipulation, detection, measurement, and analysis of single cell make it possible to observe inhomogeneous cellular response to an external stimulus, which have been averaged and completely neglected in the study with large amount of cells. The optoelectrofluidics can provide an efficient way to handle individual particles at the single cell level. Especially, interactive and parallel manipulation of individual cells based on the light-driven electrokinetics can be applied in a number of applications in life and physical sciences. A lens-integrated LCD-based optoelectrofluidic system was exploited for the interactive and parallel manipulation of individual blood cells [22]. When a dynamic image pattern is projected into a specific area of a photoconductive layer in an OET device, virtual electrodes are generated by spatially resolved illumination of the photoconductive layer, resulting in DEP of microparticles suspended in the liquid layer under a nonuniform electric field. As shown in Fig. 6, the optoelectrofluidic platform has been easily constructed with an OET device, an LCD and a condenser lens integrated in a conventional microscope. By using the condenser lens, both stronger DEP force and higher spatial resolution of the virtual electrodes compared with those of lens-less LCD-based optoelectrofluidic platform [20] could be obtained. On the basis of a real-time microscopic movie, we could selectively transport a target cell via positive DEP generated from the optically induced virtual electrode patterns. Figure 7a shows the trapping and transporting of individual RBCs using an optically induced virtual electrode array. One to three RBCs were trapped in each light spot by positive DEP. By programming the LCD image, only one column of the array was selectively moved. The trapped RBCs were transported in the upper direction with the velocity of about 5 μm/s in the application of a voltage of 7 Vpp at 200 kHz. In addition, we could find a target WBC among many RBCs through the real-time movie on the computer screen. After finding and selecting the target WBC, a virtual tweezers was generated and the selected WBC could be dragged out from many unwanted RBCs as shown in Fig. 7b. These all processes were performed by using an interactive control program under the same voltage condition and a light spot of 6 μm in diameter was used for trapping the WBC. The interactive single cell manipulation using this
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Figure 6. Schematic of lens-integrated LCD-based optoelectrofluidic platform for interactive manipulation. (Reproduced with permission from Ref. [22]; Copyright 2008, Wiley-VCH Verlag GmbH & Co. KGaA.)
Figure 7. Manipulation of blood cells using lab-on-a-display. (a) Parallel manipulation of single red blood cells using a programmed LCD image. (b) Interactive manipulation of single white blood cell using lab-on-a-display. (Reproduced with permission from Ref. [22]; Copyright 2008, Wiley-VCH Verlag GmbH & Co. KGaA.)
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platform can be applied to several single cell-based studies in biology and chemistry. For example, we can observe a blood sample from a patient through a monitor screen, and click a strange WBC. Then, we can drag it out from RBCs, and check its morphology with other normal samples or perform a bead-based assay of cell surface proteins by binding with proteincoated microparticles. Like this, this platform will be potentially very powerful to investigate blood samples for diagnostic purposes, such as haematological and serological studies. 3.2. DISCRIMINATION OF NORMAL OOCYTES
Selection of fertilizable oocytes is one of the most important issues in in vitro fertilization (IVF) process. To date, the oocyte selection has been manually conducted by a skillful expert with a labor-intensive and timeconsuming process. Recently, a new method for DEP-based separation of normal oocytes has been demonstrated using a microelectrode device [45]. The normal oocytes showed higher DEP velocity compared to the abnormal ones, which were cultured without medium for 3 days. This result shows that the DEP characteristics of oocytes can be a new criterion for selecting healthy oocytes in IVF. However, the conventional separation method based on the microfabricated electrodes has some limitation such as difficulty of manipulating samples before and after the selection processes. To develop a fully-automated system for the discrimination of normal oocytes for IVF, an LCD-based optoelectrofluidic platform, which allows the programmable cell manipulation based on the optically induced DEP and the image-driven virtual electrodes, has been utilized [26]. When we apply the optoelectrofluidic platform for manipulating microparticles including biological cells based on the optically induced DEP force, the vertical component of DEP force sometimes induces the adsorption of particles onto the electrode surface and the friction forces that interfere with the effective particle manipulation [21, 24]. If the target particles are heavy and sticky cells such as oocytes, the effects of the gravity and the particle– surface interactions become more dominant than other cases applying the typical animal cells. To deal with such a physical problem of the optoelectrofluidic device, an alternative method was demonstrated by combining the gravity effect with the optically induced positive DEP. In this method, the vertical component of the optically induced DEP force acting on the oocytes is toward opposite direction to the gravity as shown in Fig. 8a. In consequence, the vertical positive DEP force, which pulls up the oocytes, counterbalance the gravity, thus the vertical net force acting on the oocytes are minimized. On the basis of this method named anti-gravity optoelectrofluidic platform, the discrimination performance could be enhanced due to the reduction of friction force acting on the oocytes which are relatively
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large and heavy cells being affected by the gravity field. According to the experimental results, the normal oocytes were moved along the light patterns by the optically induced DEP, while the abnormal ones were not. The difference between the moving velocity of healthy oocytes and that of starved ones was larger in the anti-gravity optoelectrofluidic platform than in the conventional platform. This increased difference of the moving velocity between normal and starved abnormal oocytes allows us to efficiently discriminate the normal ones spontaneously under the moving patterns of LCD image as shown in Fig. 8b. This technique may be widely usable for automatic selection of oocytes with a good developmental potential in IVF.
Figure 8. Optoelectrofluidic manipulating of oocytes. (a) Simulated electric field distribution formed by an optically induced virtual electrode under the antigravity mode of optoelectrofluidic platform. (b) Selection of normal oocytes using optically induced positive DEP in the optoelectrofluidic device. (Reproduced with permission from Ref. [26]; Copyright 2009, American Institute of Physics.)
3.3. PROGRAMMABLE MANIPULATION OF MOTILE CELLS
Motility is a typical behavior of a biological cell, which refers to the spontaneous and independent movement. The measurement of the cell motility is important for the study of cellular behaviors and their fundamental mechanisms in basic biology. Here we select Tetrahymena pyriformis
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(T. pyriformis), which is free-living ciliate protozoan, as a model for motility testing. Because of their high motility, they can respond more quickly to external stimuli than any other organisms. In the case of nonspherical object such as RBC [22] and T. pyriformis [25], the induced dipole moment of the object makes it align along the electric field. This phenomenon is named electro-orientation [42]. On the basis of this principle, we could stand the rod-like bacteria in the direction perpendicular to the plane in which it swims, and trap it by applying a vertical electric field as shown in Fig. 9. To study the cell motility, we used a grayscale OET, which allows adjustment of the electric field strength in an optoelectrofluidic device using a grayscale image with a variable intensity value for each pixel of an LCD module as shown in Fig. 10 [25]. Figure 11 shows a cross-sectional view of the optoelectrofluidic device. Both lateral and vertical electric fields were calculated. The lateral electric field was 0–10 mVpp/μm, which was less than one third of the vertical electric field at any position. Therefore, we could neglect the effect of the lateral electric field on the motile cells.
Figure 9. Electro-orientation of Tetrahymena pyriformis in a uniform electric field. (Reproduced with permission from Ref. [25]; Copyright 2008, American Institute of Physics.)
Figure 10. Experimental setup of grayscale OET for the alignment of swimming cells.
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Figure 11. Simulated electric field distribution when a gradient image is projected into an optoelectrofluidic device. (Reproduced with permission from Ref. [25]; Copyright 2008, American Institute of Physics.)
Image-controlled cell alignment for motility assay is shown in Fig. 12. Using the computer-controlled LCD images, the experimental plane was divided into five regions which have different light contrasts. In consequence, the spatially different electric field enables many replicate experiments simultaneously. The percentage of aligned T. pyriformis increased as the light intensity increased. When the electric field was eliminated, the cells reoriented to its normal shape and swam freely again. We can investigate the kinetic energy of the motile cells by measuring the threshold voltage,
Figure 12. Cell motility assay using the computer-controlled LCD images. (a) An image to measure the ratio of Tetrahymena trap. Trapped cells were marked with black arrows. (b) The ratios of aligned Tetrahymena according to the light contrast. At least five replicates were conducted. (Reproduced with permission from Ref. [25]; Copyright 2008, American Institute of Physics.)
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which can trap the cells. Based on this method, we can measure the motility of the bacteria not only at the single cell level but also at the multiple cell level. This optoelectrofluidic platform would be useful to study fundamental processes of the cell behaviors such as a signaling pathway of the motile cells by an attractant or a blocker of a specific receptor. 4. Conclusions A novel programmable microfluidic platform, in which particles are manipulated by electrokinetic mechanisms, such as DEP or ACEO generated with a light, has been developed. When a dynamic image pattern was projected into a specific area of a photoconductive layer, virtual electrodes were generated, resulting in electrokinetic motions of particles and fluids under a nonuniform electric field. This new platform could be applied to develop an integrated system for programmable manipulation of micro/nano particles including living cells and biomolecules. In the immediate future, this optoelectrofluidic platform promises to be an innovative technology not only for the manipulation but also for the measurement and detection for biological and chemical applications in practice. Acknowledgments This research was supported by the National Research Laboratory (NRL) Program grant (R0A-2008-000-20109-0) and by the Nano/Bio Science and Technology Program grant (2008-00771) funded by the Korea government (MEST). The authors thank the Chung Moon Soul Center for BioInformation and BioElectronics at KAIST.
References 1. D.G. Grier, A revolution in optical manipulation, Nature, 424(6950), 810–816 (2003). 2. J. Voldman, Electrical forces for microscale cell manipulation, Annual Review of Biomedical Engineering, 8, 425–454 (2006). 3. J. Dobson, Remote control of cellular behaviour with magnetic nanoparticles, Nature Nanotechnology, 3(3), 139–143 (2008). 4. H.M. Hertz, Standing-wave acoustic trap for nonintrusive positioning of microparticles, Journal of Applied Physics, 78(8), 4845–4849 (1995). 5. A.M. Skelley, O. Kirak, H. Suh, R. Jaenisch and J. Voldman, Microfluidic control of cell pairing and fusion, Nature Methods, 6(2), 147–152 (2009).
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6. A. Ashkin, Acceleration and trapping of particles by radiation pressure, Physical Review Letters, 24(4), 156 (1970). 7. A. Ashkin and J.M. Dziedzic, Optical trapping and manipulation of viruses and bacteria, Science, 235(4795), 1517–1520 (1987). 8. M.D. Wang, H. Yin, R. Landick, J. Gelles and S.M. Block, Stretching DNA with optical tweezers, Biophysical Journal, 72(3), 1335–1346 (1997). 9. C. Mio, T. Gong, A. Terray and D.W.M. Marr, Design of a scanning laser optical trap for multiparticle manipulation, Review of Scientific Instruments, 71(5), 2196–2200 (2000). 10. J.E. Curtis, B.A. Koss and D.G. Grier, Dynamic holographic optical tweezers, Optics Communications, 207(1), 169–175 (2002). 11. W. Hossack, E. Theofanidou, J. Crain, K. Heggarty and M. Birch, High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay, Optics Express, 11(17), 2053–2059 (2003). 12. X.B. Wang, J. Yang, Y. Huang, J. Vykoukal, F.F. Becker and P.R.C. Gascoyne, Cell separation by dielectrophoretic field-flow-fractionation, Analytical Chemistry, 72(4), 832–839 (2000). 13. J. Voldman, M.L. Gray, M. Toner and M.A. Schmidt, A microfabricationbased dynamic array cytometer, Analytical Chemistry, 74(16), 3984–3990 (2002). 14. L. Altomare, M. Borgatti, G. Medoro, N. Manaresi, M. Tartagni, R. Guerrieri and R. Gambari, Levitation and movement of human tumor cells using a printed circuit board device based on software-controlled dielectrophoresis, Biotechnology and Bioengineering, 82(4), 474–479 (2003). 15. A.R. Minerick, R. Zhou, P. Takhistov and H.-C. Chang, Manipulation and characterization of red blood cells with alternating current fields in microdevices, Electrophoresis, 24(21), 3703–3717 (2003). 16. N.R. Manaresi, A. Medoro, G. Altomare, L. Leonardi, A. Tartagni, M. Guerrieri, R., A CMOS chip for individual cell manipulation and detection, IEEE Journal of Solid-State Circuits, 38(12), 2297–2305 (2003). 17. H. Hwang and J.-K. Park, Rapid and selective concentration of microparticles in an optoelectrofluidic platform, Lab on a Chip, 9(2), 199–206 (2009). 18. A. Mizuno, M. Nishioka, Y. Ohno and L.-D. Dascalescu, Liquid microvortex generated around a laser focal point in an intense high-frequency electric field, IEEE Transactions on Industry Applications, 31(3), 464–468 (1995). 19. R.C. Hayward, D.A. Saville and I.A. Aksay, Electrophoretic assembly of colloidal crystals with optically tunable micropatterns, Nature, 404(6773), 56–59 (2000). 20. W. Choi, S.-H. Kim, J. Jang and J.-K. Park, Lab-on-a-display: a new microparticle manipulation platform using a liquid crystal display (LCD), Microfluidics and Nanofluidics, 3(2), 217–225 (2007). 21. H. Hwang, Y. Oh, J.-J. Kim, W. Choi, S.-H. Kim, J. Jang and J.-K. Park, Optoelectronic manipulation of microparticles using double photoconductive layers on a liquid crystal display, Biochip Journal, 1(4), 234–240 (2007). 22. H. Hwang, Y.-J. Choi, W. Choi, S.-H. Kim, J. Jang and J.-K. Park, Interactive manipulation of blood cells using a lens-integrated liquid crystal display based optoelectronic tweezers system, Electrophoresis, 29(6), 1203–1212 (2008).
612
H. HWANG AND J.-K. PARK
23. H. Hwang, J.-J. Kim and J.-K. Park, Experimental investigation of electrostatic particle-particle interactions in optoelectronic tweezers, The Journal of Physical Chemistry B, 112(32), 9903–9908 (2008). 24. H. Hwang, Y. Oh, J.-J. Kim, W. Choi, S.-H. Kim, J. Jang and J.-K. Park, Reduction of nonspecific surface-particle interactions in optoelectronic tweezers, Applied Physics Letters, 92(2), 024108 (2008). 25. W. Choi, S.-W. Nam, H. Hwang, S. Park and J.-K. Park, Programmable manipulation of motile cells in optoelectronic tweezers using a grayscale image, Applied Physics Letters, 93(14), 143901 (2008). 26. H. Hwang, D.-H. Lee, W. Choi and J.-K. Park, Enhanced discrimination of normal oocytes using optically induced pulling-up dielectrophoretic force, Biomicrofluidics, 3, 014103 (2009). 27. D.-H. Lee, H. Hwang and J.-K. Park, Droplet manipulation using opticallyinduced dielectrophoresis in a channel-integrated optoelectronic tweezers, The 13th International Conference on Miniaturized Systems for Chemistry and Life Sciences, November 1–5, 2009, Jeju Island, Korea. 28. Y. Lu, Y. Huang, J.A. Yeh and C. Lee, Controllability of non-contact cell manipulation by image dielectrophoresis (iDEP), Optics and Quantum Electronics, 37, 1385–1395 (2005). 29. J.-Y. Huang, Y.-S. Lu and J.A. Yeh, Self-assembled high NA microlens arrays using global dielectrophoretic energy wells, Optics Express, 14, 10779–10784 (2006). 30. H. Hwang, Y.-H. Park and J.-K. Park, Optoelectrofluidic control of colloidal assembly in an optically induced electric field, Langmuir, 25(11), 6010–6014 (2009). 31. H. Hwang and J.-K. Park, Optoelectrofluidic concentration and separation of nanoparticles and molecules for automated particle-based immunoassays, The 20th International Conferences on Molecular Electronics and Devices, May 22–23, 2009, Seoul, Korea. 32. H. Hwang and J.-K. Park, Dynamic light-activated control of local chemical concentration in a fluid, Analytical Chemistry, 81(14), 5865–5870 (2009). 33. H. Hwang and J.-K. Park, Diffusion measurement of biomolecules using rapid generation of black hole in a molecular solution by optoelectrofluidics, The 13th International Conference on Miniaturized Systems for Chemistry and Life Sciences, November 1–5, 2009, Jeju Island, Korea. 34. P.Y. Chiou, A.T. Ohta and M.C. Wu, Massively parallel manipulation of single cells and microparticles using optical images, Nature, 436(7049), 370– 372 (2005). 35. A. Jamshidi, P.J. Pauzauskie, P.J. Schuck, A.T. Ohta, P.-Y. Chiou, J. Chou, P. Yang and M.C. Wu, Dynamic manipulation and separation of individual semiconducting and metallic nanowires, Nature Photonics, 2(2), 86–89 (2008). 36. M. Hoeb, J.O. Radler, S. Klein, M. Stutzmann and M.S. Brandt, Light-induced dielectrophoretic manipulation of DNA, Biophysical Journal, 93(3), 1032– 1038 (2007). 37. S.L. Neale, M. Mazilu, J.I.B. Wilson, K. Dholakia and T.F. Krauss, The resolution of optical traps created by light induced dielectrophoresis (LIDEP), Optics Express, 15, 12619–12626 (2007).
CELL MANIPULATION USING LAB-ON-A-DISPLAY
613
38. H. Hwang, Y. Oh, K.-H. Jeong and J.-K. Park, Optoelectrofluidic enhancement of surface enhanced Raman scattering, Biotronics 2009, October 7, 2009, Seoul, Korea. 39. H. Hwang, M.S. Thesis, KAIST, Korea, 2007. 40. R. Schwarz, F. Wang and M. Reissner, Fermi level dependence of the ambipolar diffusion length in amorphous silicon thin film transistors, Applied Physics Letters, 63(8), 1083–1085 (1993). 41. J.N. Mehrishi and J. Bauer, Electrophoresis of cells and the biological relevance of surface charge, Electrophoresis, 23(13), 1984–1994 (2002). 42. T.B. Jones, Electromechanis of particles, Cambridge University Press, New York, 1995. 43. R.F. Probstein, Physicochemical hydrodynamics: an introduction, Wiley and Sons, New York, 1994. 44. J. Kadaksham, P. Singh and N. Aubry, Dynamics of electrorheological suspensions subjected to spatially nonuniform electric fields, Journal of Fluids Engineering, 126(2), 170–179 (2004). 45. W. Choi, J.-S. Kim, D.-H. Lee, K.-K. Lee, D.-B. Koo and J.-K. Park, Dielectrophoretic oocyte selection chip for in vitro fertilization, Biomedical Microdevices, 10(3), 337–345 (2008).
INDEX Conjugated heat transfer, 61–80 Constant voltage scaling, 291 Convection number, 92 Critical heat flux, 88, 107–118, 122, 123, 133
A AC electrokinetics, 273–283, 481–501, 507, 603 Amperometry, 403, 404, 410–412, 417, 422 Assembled microchannel setup, 70, 515 Axial dispersion, 222, 224, 230–233
D 3D cell culture chip, 449 Dean number, 261 Dielectric thickness, 287 Dielectrophoresis (DEP) forces, 196, 197, 273, 274, 276–277, 279, 281–283, 323, 331, 342, 343, 378, 482, 484–501, 507, 510, 516, 578, 582, 585, 587, 589, 596, 600–602, 604, 606, 607, 610 Dielectrophoretic trapping, 497, 578 Droplet actuation, 286, 288, 289 Droplet microfluidics, 164–165, 183, 476 Droplet splitting and merging, 295 Drug delivery system, 123, 553, 556–558 Duct flow, 250–255
B Bifurcating channels, 191, 567 Bioelectrocatalysis, 410, 411 Biot number, 40, 51, 52, 55, 57, 65 Boiling in micro-channel, 83–101, 107, 112, 113, 118 Boiling number, 91, 92 Brinkman number, 3, 4, 8–10, 18, 31 Brownian motion, 145, 222, 274, 275, 279–280, 282–283, 428, 487, 499, 500, 541 C Castellated electrode array, 492 Catalysis, 341, 463, 468 Cell motility, 608, 609 Cellular redox environment, 403, 405–416 Centrifugal microfluidic platform, 333–341, 355 Channel curvature, 224, 228–231, 233, 240, 330 Chaotic advection, 224, 259–261 Chemiluminescent assays, 297–299 Chip-scale DNA diagnostic sensors, 299 Classic lumped system analysis, 65 Clausius–Mossotti factor, 276, 277, 482–484, 487, 489–491, 508–510, 601 Colorimetric assays, 297, 339, 347 Complex permittivity, 482, 508, 509, 511, 517, 601 Computational fluid dynamics (CFD), 204, 221
E Eigenfunctions, 39, 41–44, 49–51, 57, 67 Electrochemical detection, 317, 401–405 Electrokinetic platform, 274, 275, 279, 307, 341–344, 353, 377, 385, 386, 388, 391–395, 481, 484, 501, 510, 541, 543, 553, 556–558, 595–597, 600, 602–604, 610 Electroosmosis, 260, 273, 275–276, 343, 344, 378, 596, 602 Electroosmotic flow, 260, 262, 263, 275, 342, 344, 378, 385 Electrophoresis, 164, 273, 278, 295, 301, 322, 324, 342–344, 352, 353, 378–380, 428, 596, 600, 601 Electrophoretic velocity, 378 615
616 Electrorotation, 482, 489–490, 507, 510 Electrowetting, 197, 285, 292–297, 300, 309, 345–348, 352, 355, 476 Electrowetting platform, 345, 347 Elongated bubble flow, 84, 90, 94–101 Eotvos number, 216, 236, 238 Exocytosis, 401, 403, 416–421, 428, 444 Extended Graetz problem, 66 F Fast M-sequence transform, 518 Field flow fraction (FFF), 472, 496–497, 501, 578, 579, 591 Flow boiling heat transfer, 85, 88, 98, 101 Flow cytometer, 378, 383–390, 395, 454, 589 Flow cytometry, 300, 322, 384, 507, 514 Flow pattern, 84, 98–100, 108–109, 112, 258, 260, 471, 475 Flowrate scaling, 246–250 Fluid delivery, 431, 436–437, 447 Fluorescence detection, 343, 400–401 Focusing particles, 589–590 Forced convection in a micropipe, 3–4, 8–9 Front-capturing method, 204, 240 Front-tracking method, 203–219, 221–240 G Generalized integral transform technique (GITT), 39, 43, 57, 62, 63, 66, 67, 73 Geometric optimization, 137 Gradient system, 445–446 H Hagen-Poiseuille law, 187 High-throughput system, 446–447 Hybrid-insect system, 555 Hydrophilic forces, 290, 295 Hydrophoresis, 577–591 Hydrophoretic filtration method, 585
INDEX I Immunoassay, 315, 328, 339, 340, 378, 390–395, 456–464, 533–536, 578, 595, 602 Intensity of segregation, 226, 227 Interdigitated electrode array, 488, 493–495 Interfacial energy, 165 In vitro cell culture, 427, 428, 431, 442, 444 In vitro fertilization, 606 K Kinetic monitoring, 536–539 Knudsen number, 2–5, 8–10, 17, 18, 243, 245, 246, 248, 249, 251 Kutateladze formula, 133 L Lagrangian grid, 207–211 Laminar flow platform, 322, 323, 355 Lateral flow test, 306, 315–319, 355 LCD-based optoelectrofluidic platform, 597–610 Linear actuated device, 318–321 Lippmann-Young equation, 287, 291–293 Loop heat pipe, 123 Lyapunov exponent, 260, 261, 265–266 M Magnetic cell manipulation, 454–455 Magnetic droplet, 476 Magnetic immunoassay, 456–463 Magnetic label, 463, 473, 474 Magnetic nanoparticle, 453, 455, 457, 463, 468, 469 Magnetic nucleic acid assay, 455, 456 Magnetic separator, 471 Magnetophoresis, 323, 324, 585 Markov chain, 45, 46, 50, 52–57 Martinelli parameter, 93, 102 Massively parallel analysis, 343, 350–354 Mass sensitivity, 531–533
INDEX Maximum length sequence (MLS), 518, 519 Maxwell model, 144 Mesoporous silica structure, 463 Metropolis-Hastings algorithm, 40, 45, 47 Microarrays, 236, 318, 343, 350–353, 390, 428, 446, 447 Microchannel heat sink, 15, 16 Microdevice platform, 555 Microfluidic differential resistive pulse sensor method, 388, 389 Microfluidic emulsification, 168–178 Microfluidic large scale integration, 325–328, 355 Microfluidic networks, 187, 189, 191, 193–196, 336, 340, 391, 393, 446, 585 Microfluidic platform, 286, 295, 297, 306–315, 318, 328, 329, 331, 333, 334, 338–340, 350, 353–356, 520, 610 Microfluidics, 122, 123, 163–179, 183–198, 204, 205, 215, 219, 221–223, 233, 240, 257–270, 275, 283, 285–301, 305–356, 377–395, 400–403, 418, 421, 428–434, 436–442, 444–449, 453–456, 463, 464, 467–477, 481, 501, 507–523, 531, 538, 539, 543, 544, 547, 553, 554, 557–559, 566–568, 578–580, 582, 584, 585, 589–591, 596, 610, 459, 461 Microfluidic toolkit, 293–295, 300 Micromixer, 222, 224, 258–261, 310, 336 Microtube, 3, 18–27, 33 Mixed convection, 3, 7–8, 10–13 Mixing, 110, 122, 184, 222, 224–233, 240, 257–270, 273, 287, 288, 291, 294–297, 310, 314, 319, 322, 325, 327, 330, 332, 336, 337, 339, 340, 343, 346, 349, 352, 353, 378, 429, 471, 475, 476, 538, 563 Mixing entropy, 226 Mixing index, 260, 266–270
617 Momentum accommodation factor, 19 Multiplexed detection, 531, 533, 534 Multipoles, 490–492 N Nanofluids thermal conductivity, 154 Nanophotonics, 541–543, 546 Nanoscale optofluidic transport, 539–547 Navier-Stokes equations, 262 Nernst equation, 406 Nondimensional energy equation, 20, 21 Non-uniform heat flux boundary, 116 Nucleate boiling, 84, 86, 89–94, 101, 102, 112, 113, 121 Nusselt number, 2–4, 6–10, 16, 18, 22–24, 30, 44, 49–51, 62, 63, 70, 73–75, 79, 80, 90, 97, 101 O On-chip storage and dispensing, 294 Optical trapping stability, 543 Optoelectrofluidics, 596–610 Optoelectronic tweezer (OET), 597–599, 604, 608 Optofluidic surface enhanced Raman spectroscopy, 537–539 P Particle-tracking algorithm, 214 PCR. See Polymerase chain reaction PDMS. See Polydimethylsiloxane Péclet number, 18, 23, 34, 62, 74, 163, 231–233, 258, 261, 430, 431 Perfusion based microfluidic cell culture chip, 400, 429–431, 444, 448 Photonic crystal resonator, 529, 530, 532, 534 Picowell plates, 351–353 PIN-structure, 124, 125, 133 Poincaré sections, 257, 260, 261, 263–265, 270 Polarizability, 273, 274, 276, 279, 280
618 Polydimethylsiloxane (PDMS), 197, 198, 259, 324, 326–328, 381, 385, 386, 391, 431, 437–440, 443, 537, 538, 544, 557, 567, 569 Polymerase chain reaction (PCR), 300, 309, 318, 322, 324, 325, 328, 340, 347, 349, 350, 378–383, 395, 455, 578 Polynomial electrodes, 495 Posterior probability density, 44–46 Prandtl number, 18, 42, 75, 133, 145 Programmable matter, 553–573 Propulsive forces, 539, 540 Q Quasistatic model of break-up, 174 R Rarefaction coefficient, 248, 250, 251 Restructuring, 208–210 Reverse meniscus, 124–131 S Sample dilution and purification, 295 Scaling, 175, 177, 184, 189, 243– 250, 253, 254, 270, 274, 275, 279–283, 285–301, 308, 334, 482, 490, 499–500 Segmented flow microfluidics, 329–333 Sensitivity matrix, 48, 52 Shear stress, 2, 95, 167, 168, 171, 173, 174, 176, 177, 432, 434, 444 Sheathless focusing, 579, 589, 590 Single cell impedance analysis, 511, 514, 515, 518, 519, 521 Single cell trapping, 497–499, 521 Sink-cycling technique, 563, 564 Size separation, 578–579, 582–584, 587, 591 Slip-flow, 2, 17, 22, 25, 30, 39 Slip velocity, 17, 19, 30, 244, 246 Steric hindrance mechanism, 578–580, 583, 589 Stokes-Einstein relation, 279 Stokes equation, 186, 187, 248, 262 Superparamagnetic nanoparticle, 469
INDEX Surface acoustic waves, 348–350, 352, 355 Surface roughness, 26–29, 34, 96, 99, 441 Surface tension force, 134, 210–211, 236, 349 Surfactant, 147, 148, 157, 169, 170, 189, 205, 206, 219, 222, 223, 233–235, 240, 329, 333, 346, 469, 520 T Thermal accommodation coefficient, 40, 42, 45, 57 Thermal boundary conditions, 2, 5, 62, 79 Thermal management, 122 Thermal spreader, 121–137 Thermo-hydraulic mode, 125 Thermooptically programmable material, 566, 567 Thermoplastics, 437–443 Thermorheological fluid, 566, 567, 570 Three zone evaporation model for slug flow, 94–98 T-junction, 168, 169, 174–177, 183, 184, 198, 330 V Velocity distribution, 4, 243–246, 254 Velocity profile, 3, 4, 7, 18, 20, 27, 42, 224, 243, 245, 246, 248, 254, 255, 322, 342 Vibro viscometer, 152, 155 Viscosity of nanofluids, 143, 152, 154–157 Viscous dissipation, 2, 8–10, 18, 20, 22–31, 33, 34, 39, 41, 61, 79, 173, 188, 189 W Weber number, 91, 97, 110, 111, 168 White noise stimulation, 517 3ω method, 149–151, 157
