Electrokinetically driven microfluidics and nanofluidics

Electrokinetics is currently the mechanism of choice for fluid actuation and bioparticle manipulation at microscale and nanoscale dimensions. There has recently been interest in the use of AC electric fields, given the many advantages it offers over DC electrokinetics. Nevertheless, a fundamental understanding of the governing mechanisms underlying the complex and nonlinear physicochemical hydrodynamics associated with these systems is required before practical microfluidic and nanofluidic devices can be engineered. This text aims to provide a comprehensive treatise on both classical equilibrium electrokinetic phenomena as well as the more recent non-equilibrium phenomena associated with both DC and AC electrokinetics in the context of their application to the design of microfluidic and nanofluidic technology. In particular, Leslie Yeo and Hsueh-Chia Chang discuss the linear and nonlinear theories underlying electroosmosis, electrophoresis, and dielectrophoresis pertaining to electrolytes as well as dielectric systems. Interfacial electrokinetic phenomena such as electrospraying, electrospinning, and electrowetting are also discussed.

Author Notes

Dr.Hsueh-Chia Chang is Byarer Professor in the Department of Chemical and Biomolecular Engineering and Director of the Center for Microfluidics and Medical Diagnostics at the University of Notre Dame. He received his Ph.D. from Princeton University, afther which he joined the University of California, Santa Barbara, as an Assistant professor and subsequently the University of Houston as an Associate professor. Dr.Chang has received numerous awards, including the National Science Foundation's Presidential Young Investigator's Award, the Sigma Xi Outstanding Research Award at the University of Notre Dame, and the American physical society Division of Fluid Dynamics Francois N. Frenkiel Award. In 1997, he was elected a Fellow of the American Physical Society. Dr. Chang is the founding editor-in-chief and co-editor of the American Institute of Physics journal Biomicrofluidics. He has also served on the editorial board of the SIAM Journal of Applied Mathematics and the International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. Dr. Chang's research has culminated in more than 200 journal publications and 12 patents. He is also coauthor of Complex Wave Dynomics on Thin Films. Dr. Chang has delivered more than 10 Keynote lectures and 100 seminars. His former ph.D. students and postdoctoral researchers currently hold positions at 18 universities worldwide and several major chemical and pharmaceutical research facilities.
Dr. Leslie Y.Yeo is currently an Australian Research Fellow and Associate Professor in the Department of Mechanical and Aerospace Engineering and Co-Director of the Micro/Nanophysics Rsearch Laboratory at Monash Universrity, Australia. He received his Ph.D. from Imperial College London in 2002, for which he was awarded the Dudley Newitt Prize for a computational/theoretical thesis of outstanding merit. Prior to Joining Monash University, he was a Mathematical Modeller at Det Norske Veritas UK and a postdoctoral research associate in the Department of Chemical and Biomolecular Engineering at the University of Notre Dame. Dr. Yeo was the recipient of the 2007 Young Tall Poppy Science Award from the Australian Institute for Policy and Science "in recognition of the achievements of outstanding young researchers in the sciences including physcial, biomedical, applied sciences, engineering and technology," and a finalist in the Austrilian Museum's 2008 Eureka Prize people's Choice Award. His Work has been featured widely in the media, for example, on the Austrialian Broadcasting Corporation's science television program catalyst, on the 3RRR radio broadcast Einstein-a-Go-Go, and in various articles in the Economist, the Washington Times the Age, New Scientist, ABC Science Online, and Discovery Channel Online. Dr. Yeo is the author of more than 80 research publications and more than 10 patent applications and is currently the co-editor of the American institute of physics journal Biomicrofluidics.

Preface	p. xiii
1 Introduction and Fundamental Concepts	p. 1
1.1 Electrokinetic Mechanisms for Microfluidic and Nanofluidic Transport	p. 1
1.1.1 Introduction to Microfluidic and Nanofluidic Systems	p. 1
1.1.2 Microscale and Nanoscale Electrokinetic Transport	p. 5
1.1.3 Organization	p. 8
1.2 Electrostatics	p. 8
1.2.1 Coulomb's Law	p. 9
1.2.2 Electric Field and Potential	p. 10
1.2.3 Charge Density	p. 11
1.2.4 Electric-Field Vector Relationships	p. 11
1.2.5 Gauss' Law: The Flux of the Electric Field	p. 12
1.3 Fundamental Concepts of Electrokinetic Theories	p. 14
1.3.1 Constitutive Relations Governing Continuum Hydrodynamics	p. 14
1.3.2 Induced Dipoles, Interfacial Conditions, and the Maxwell Stress Tensor	p. 16
1.3.3 Electrokinetic Actuation of Dielectric Liquids - Gradients in the Maxwell Pressure	p. 20
1.3.4 Constitutive Equation for Ion Transport	p. 29
2 Classical Equilibrium Theory Due to Surface Charges	p. 35
2.1 The Debye Double Layer	p. 35
2.1.1 Surface Charging	p. 35
2.1.2 Concentration Polarization of Ions - The Screening Effect	p. 36
2.2 Poisson-Boltzmann Distribution	p. 36
2.2.1 The Poisson-Boltzmann Distribution and Surface Electric Field	p. 36
2.2.2 Osmotic Pressure, Conservative Force, and Stability of the Poisson-Boltzmann Distribution	p. 39
2.2.3 Repulsive Forces Between Charged or Constant-Potential Particles in Electrolytes Under Poisson-Boltzmann Equilibrium	p. 41
2.3 The Debye-Hückel Theory	p. 45
2.4 Nonlinear Analysis of the Poisson-Boltzmann Equilibrium in the Debye Layer	p. 47
2.5 Extensions to the Diffuse Double Layer Theory	p. 53
2.6 Attraction Between Identical Particles Due to Symmetry Breaking	p. 56
2.7 Overlapping Double Layers in Nanopores: Pore Conductance and Threshold Field for Electro-Osmotic Flow	p. 65
2.8 Double Layer Formation and Relaxation Dynamics	p. 72
2.9 Equilibrium Double Layer Electrokinetic Phenomena	p. 73
3 Electro-Osmotic Transport	p. 76
3.1 Electro-Osmosis	p. 76
3.2 Smoluchowski Slip in Microchannels	p. 77
3.3 Electro-Osmotic Slip Velocity with Bulk Concentration Gradients: Formal Asymptotics	p. 81
3.4 Electro-Osmotic Flow in Nanochannels	p. 86
3.5 Mixed or Frustrated Flows	p. 88
3.6 DC Electrokinetic Pumps	p. 89
3.7 Electric Field and Hydrodynamic Streamline Similarity	p. 97
3.8 Frustrated Flow and Vortex Formation Due to pH Gradients	p. 99
3.9 Conductivity-Gradient-Driven Electrohydrodynamic Instabilities	p. 103
3.9.1 Conductivity Gradients in the Direction of the Applied Field	p. 104
3.9.2 Conductivity Gradients Transverse to the Direction of the Applied Field	p. 112
3.10 Hydrodynamic Dispersion and Channel Profiling	p. 116
3.11 Electroviscous Effects Due to the Streaming Potential in a Finite-Length Nanochannel: The Zero-Current Model	p. 122
4 Electrophoretic Transport and Separation	p. 128
4.1 Uniform Charge Electrophoresis: Classical Theory	p. 128
4.2 Combined Electrophoresis and Electro-Osmotic Convection	p. 131
4.3 Electroviscous Effects	p. 132
4.4 Cellular Electrophoresis Involving a Conducting Layer of Charges	p. 133
4.5 Electrophoresis with Surface Charge Migration and Counterion Condensation Effects	p. 137
4.6 Other Conductive Electrophoresis Theories - Conducting Stern Layer and Convective Current Effects	p. 139
4.7 A General Electrophoresis Theory in the Debye-Hückel Limit	p. 141
4.8 Capillary Electrophoresis: Applications	p. 143
4.8.1 Capillary Zone Electrophoresis	p. 146
4.8.2 Capillary Gel Electrophoresis	p. 147
4.8.3 Micellar Electrokinetic Chromatography	p. 148
4.8.4 Capillary Isotachophoresis	p. 149
4.8.5 Capillary Isoelectric Focusing	p. 149
4.8.6 Capillary Electrochromatography	p. 150
4.8.7 End-Labeled Free-Solution Electrophoresis	p. 152
5 Field-Induced Dielectric Polarization	p. 155
5.1 Nonequilibrium Electrokinetics	p. 155
5.2 Dielectric Polarization	p. 156
5.2.1 Dielectric Materials and Dipole Formation	p. 156
5.2.2 Polarization Mechanisms	p. 160
5.2.3 Impedance Characterization of Relaxation Times	p. 161
5.3 Interfacial Polarization	p. 168
5.3.1 Interfacial Polarizability - The Clausius-Mossotti Factor	p. 168
5.3.2 Dielectric Dispersion	p. 177
5.3.3 Bacterial Growth Detection Through Reactance Measurements	p. 180
6 DC Nonlinear Electrokinetics Due to Field-Induced Double Layer Polarization	p. 184
6.1 DC Nonlinear Electrokinetics	p. 184
6.2 Electrokinetic Flow Manipulation Using Field (Capacitance) Effects	p. 185
6.3 Concentration Polarization at Nearly Insulated Wedges	p. 188
6.4 Electrokinetic Phenomenon of the Second Kind	p. 200
6.5 Extended Polarized Layer: Current-Voltage Relationship	p. 208
6.6 Dukhin's Model and Tangential Convection Effects	p. 215
6.6.1 Low Péclet Numbers - The Dukhin Theory	p. 215
6.6.2 High Péclet Numbers - Tangential Convection Enhancement of the Normal Flux	p. 217
6.7 Electrokinetic Vortex Generation for Micromixing	p. 221
6.8 Dynamic Superconcentration at Critical-Point Double Layer Gates	p. 225
6.9 Vortex Instability of Extended Polarized Layers and Selection of Overlimiting Currents	p. 233
6.10 Nonlinear Current-Voltage Characteristics of Nanopores	p. 239
7 AC Nonlinear Electro-Osmosis Due to Field-Induced Double Layer Polarization	p. 251
7.1 AC Nonlinear Electrokinetics	p. 251
7.2 Derivation of the AC Electro-Osmotic Slip Velocity	p. 257
7.2.1 Double Layer Electrostatic Model	p. 258
7.2.2 Hydrodynamic Model	p. 261
7.2.3 Bulk Potential	p. 263
7.2.4 Flow Reversal	p. 263
7.3 Planar Converging Stagnation Flow on Symmetric Coplanar Electrodes	p. 268
7.4 Normal Double Layer Charging of Passive Metal Surfaces	p. 276
7.5 Electrothermal AC Electro-Osmosis	p. 280
8 Dielectrophoresis and Electrorotation - Double Layer Effects	p. 284
8.1 Ponderomotive Forces	p. 284
8.2 Dielectrophoresis	p. 285
8.2.1 Classical Maxwell-Wagner Theory	p. 286
8.2.2 Low-Conductivity Limit (a "¿D) - Conducting Stern and Diffuse Layer Correction	p. 288
8.2.3 Normal Capacitive Charging	p. 295
8.2.4 Intermediate Conductivity Limit (a

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