Preface ...................................................... xiii
1 Introduction and Fundamental Concepts ........................ 1
1.1 Electrokinetic Mechanisms for Microfluidic and
Nanofluidic Transport ................................... 1
1.1.1 Introduction to Microfluidic and Nanofluidic
Systems .......................................... 1
1.1.2 Microscale and Nanoscale Electrokinetic
Transport ........................................ 5
1.1.3 Organization ..................................... 8
1.2 Electrostatics .......................................... 8
1.2.1 Coulomb's Law .................................... 9
1.2.2 Electric Field and Potential .................... 10
1.2.3 Charge Density .................................. 11
1.2.4 Electric-Field Vector Relationships ............. 11
1.2.5 Gauss' Law: The Flux of the Electric Field ...... 12
1.3 Fundamental Concepts of Electrokinetic Theories ........ 14
1.3.1 Constitutive Relations Governing Continuum
Hydrodynamics ................................... 14
1.3.2 Induced Dipoles, Interfacial Conditions, and
the Maxwell Stress Tensor ....................... 16
1.3.3 Electrokinetic Actuation of Dielectric
Liquids - Gradients in the Maxwell Pressure ..... 20
1.3.4 Constitutive Equation for Ion Transport ......... 29
2 Classical Equilibrium Theory Due to Surface Charges ......... 35
2.1 The Debye Double Layer ................................. 35
2.1.1 Surface Charging ................................ 35
2.1.2 Concentration Polarization of Ions -
The Screening Effect ............................ 36
2.2 Poisson-Boltzmann Distribution ......................... 36
2.2.1 The Poisson-Boltzmann Distribution and Surface
Electric Field .................................. 36
2.2.2 Osmotic Pressure, Conservative Force, and
Stability of the Poisson-Boltzmann
Distribution .................................... 39
2.2.3 Repulsive Forces Between Charged or Constant-
Potential Particles in Electrolytes Under
Poisson-Boltzmann Equilibrium ................... 41
2.3 The Debye-Huckel Theory ................................ 45
2.4 Nonlinear Analysis of the Poisson-Boltzmann
Equilibrium in the Debye Layer ......................... 47
2.5 Extensions to the Diffuse Double Layer Theory .......... 53
2.6 Attraction Between Identical Particles Due to
Symmetry Breaking ...................................... 56
2.7 Overlapping Double Layers in Nanopores: Pore
Conductance and Threshold Field for Electro-Osmotic
Flow ................................................... 65
2.8 Double Layer Formation and Relaxation Dynamics ......... 72
2.9 Equilibrium Double Layer Electrokinetic Phenomena ...... 73
3 Electro-Osmotic Transport ................................... 76
3.1 Electro-Osmosis ........................................ 76
3.2 Smoluchowski Slip in Microchannels ..................... 77
3.3 Electro-Osmotic Slip Velocity with Bulk Concentration
Gradients: Formal Asymptotics .......................... 81
3.4 Electro-Osmotic Flow in Nanochannels ................... 86
3.5 Mixed or Frustrated Flows .............................. 88
3.6 DC Electrokinetic Pumps ................................ 89
3.7 Electric Field and Hydrodynamic Streamline
Similarity ............................................. 97
3.8 Frustrated Flow and Vortex Formation Due to pH
Gradients .............................................. 99
3.9 Conductivity-Gradient-Driven Electrohydrodynamic
Instabilities ......................................... 103
3.9.1 Conductivity Gradients in the Direction of
the Applied Field .............................. 104
3.9.2 Conductivity Gradients Transverse to the
Direction of the Applied Field ................. 112
3.10 Hydrodynamic Dispersion and Channel Profiling ......... 116
3.11 Electro viscous Effects Due to the Streaming
Potential in a Finite-Length Nanochannel: The Zero-
Current Model ......................................... 122
4 Electrophoretic Transport and Separation ................... 128
4.1 Uniform Charge Electrophoresis: Classical Theory ...... 128
4.2 Combined Electrophoresis and Electro-Osmotic
Convection ............................................ 131
4.3 Electroviscous Effects ................................ 132
4.4 Cellular Electrophoresis Involving a Conducting
Layer of Charges ...................................... 133
4.5 Electrophoresis with Surface Charge Migration and
Counterion Condensation Effects ....................... 137
4.6 Other Conductive Electrophoresis Theories -
Conducting Stern Layer and Convective Current
Effects ............................................... 139
4.7 A General Electrophoresis Theory in the Debye-Huckel
Limit ................................................. 141
4.8 Capillary Electrophoresis: Applications ............... 143
4.8.1 Capillary Zone Electrophoresis ................. 146
4.8.2 Capillary Gel Electrophoresis .................. 147
4.8.3 Micellar Electrokinetic Chromatography ......... 148
4.8.4 Capillary Isotachophoresis ..................... 149
4.8.5 Capillary Isoelectric Focusing ................. 149
4.8.6 Capillary Electrochromatography ................ 150
4.8.7 End-Labeled Free-Solution Electrophoresis ...... 152
5 Field-Induced Dielectric Polarization ...................... 155
5.1 Nonequilibrium Electrokinetics ........................ 155
5.2 Dielectric Polarization ............................... 156
5.2.1 Dielectric Materials and Dipole Formation ...... 156
5.2.2 Polarization Mechanisms ........................ 160
5.2.3 Impedance Characterization of Relaxation
Times .......................................... 161
5.3 Interfacial Polarization .............................. 168
5.3.1 Interfacial Polarizability - The Clausius-
Mossotti Factor ................................ 168
5.3.2 Dielectric Dispersion .......................... 177
5.3.3 Bacterial Growth Detection Through Reactance
Measurements ................................... 180
6 DC Nonlinear Electrokinetics Due to Field-Induced Double
Layer Polarization ......................................... 184
6.1 DC Nonlinear Electrokinetics .......................... 184
6.2 Electrokinetic Flow Manipulation Using Field
(Capacitance) Effects ................................. 185
6.3 Concentration Polarization at Nearly Insulated
Wedges ................................................ 188
6.4 Electrokinetic Phenomenon of the Second Kind .......... 200
6.5 Extended Polarized Layer: Current-Voltage
Relationship .......................................... 208
6.6 Dukhin's Model and Tangential Convection Effects ...... 215
6.6.1 Low Peclet Numbers - The Dukhin Theory ......... 215
6.6.2 High Peclet Numbers - Tangential Convection
Enhancement of the Normal Flux ................. 217
6.7 Electrokinetic Vortex Generation for Micromixing ...... 221
6.8 Dynamic Superconcentration at Critical-Point Double
Layer Gates ........................................... 225
6.9 Vortex Instability of Extended Polarized Layers and
Selection of Overlimiting Currents .................... 233
6.10 Nonlinear Current-Voltage Characteristics of
Nanopores ............................................. 239
7 AC Nonlinear Electro-Osmosis Due to Field-Induced Double
Layer Polarization ......................................... 251
7.1 AC Nonlinear Electrokinetics .......................... 251
7.2 Derivation of the AC Electro-Osmotic Slip Velocity .... 257
7.2.1 Double Layer Electrostatic Model ............... 258
7.2.2 Hydrodynamic Model ............................. 261
7.2.3 Bulk Potential ................................. 263
7.2.4 Flow Reversal .................................. 263
7.3 Planar Converging Stagnation Flow on Symmetric
Coplanar Electrodes ................................... 268
7.4 Normal Double Layer Charging of Passive Metal
Surfaces .............................................. 276
7.5 Electrothermal AC Electro-Osmosis ..................... 280
8 Dielectrophoresis and Electrorotation - Double Layer
Effects .................................................... 284
8.1 Ponderomotive Forces .................................. 284
8.2 Dielectrophoresis ..................................... 285
8.2.1 Classical Maxwell-Wagner Theory ................ 286
8.2.2 Low-Conductivity Limit (α << λD)- Conducting
Stern and Diffuse Layer Correction ............. 288
8.2.3 Normal Capacitive Charging ..................... 295
8.2.4 Intermediate Conductivity Limit (α ~ λD) -
Normal Charging and Tangential Conduction in
Thick Double Layers ............................ 300
8.2.5 High-Conductivity Limit (α >> λD) - Double
Layer Polarization with Polar Charging and
Tangential Conduction .......................... 305
8.3 Dielectrophoretic Discrimination of Red Blood Cell
Age by Buffer Selection and Membrane Crosslinking ..... 311
8.3.1 Single-Shell Maxwell-Wagner Model for Blood
Cells .......................................... 313
8.3.2 Optimal Buffer Composition and Membrane
Crosslinking Agent ............................. 315
8.3.3 Dielectrophoretic Measurements of Aged Red
Blood Cells .................................... 317
8.4 Molecular and Genetic Bead Dielectrophoresis .......... 321
8.5 Electrorotation ....................................... 327
8.6 Integrated Dielectrophoretic Chip for Bioparticle
Sorting and Detection ................................. 329
8.7 Integrated Traveling-Wave Dielectrophoretic Chip ...... 332
8.8 AC Electro-Osmosis Enhanced Dielectrophoretic
Trapping .............................................. 334
8.9 Dynamic Particle Aggregation and Band Formation in
AC Electro-Osmotic Vortex Flows ....................... 336
8.10 AC Field-Enhanced Protein Crystallization ............. 338
9 Electrohydrodynamic Atomization, Electrospinning, and
Discharge-Driven Vortices .................................. 344
9.1 Interfacial Electrokinetics ........................... 344
9.2 DC Electrospraying .................................... 345
9.2.1 Mechanism and Spray Modes ...................... 345
9.2.2 Conical Solutions Due to Induced Dielectric
Polarization ................................... 351
9.2.3 Bulk Space Charge, Ionic Wind, and
Hydrodynamic Effects ........................... 354
9.2.4 Effects of the Jet Dynamics on Current and
Drop Diameter .................................. 356
9.3 AC Cones and Electrosprays ............................ 360
9.3.1 AC Electrospraying ............................. 360
9.3.2 AC Cones: Net Entrainment of Liquid Space
Charge ......................................... 374
9.4 DC Electrospinning .................................... 380
9.5 AC Electrospinning .................................... 386
9.6 Discharge-Driven Vortices ............................. 394
9.7 Colloid Deposition and DC Taylor Cone Harmonics ....... 402
10 Electrokinetically Driven Bubble and Drop Transport ........ 407
10.1 Microfluidic Drop and Bubble Transport ................ 407
10.2 Electrocapillarity and Electrowetting ................. 408
10.3 Static Electrowetting ................................. 411
10.3.1 Threshold Electrowetting Voltage and Local
Contact Angle Hysteresis ....................... 412
10.3.2 Contact Line Saturation and Dielectric
Breakdown ...................................... 414
10.3.3 Theoretical Analysis of Static
Electrowetting ................................. 417
10.3.4 Drop Velocities ................................ 421
10.4 Spontaneous Electrowetting ........................... 423
10.4.1 Parallel Line Electrodes ....................... 423
10.4.2 Parallel Plate Electrodes ...................... 432
10.5 Electrokinetic Bubble Transport: Equilibrium Double
Layer Effects ......................................... 438
10.6 AC Electrowetting on Electrodes: Dynamic Double
Layer Effects ......................................... 441
APPENDIX A: Units, Notation, and Physical Constants ........... 449
APPENDIX B: List of Symbols ................................... 451
Bibliography .................................................. 459
Index ......................................................... 475
Color plates follow page ...................................... 222
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