Preface xi
1 Introduction to Capillarity and Wetting Phenomena 1
1.1 Surface Tension and Surface Free Energy 2
1.1.1 The Microscopic Origin of Surface Energies 2
1.1.2 Macroscopic Definition of Surface Energy and Surface Tension 5
1.2 Youngâ"Laplace Equation: The Basic Law of Capillarity 7
1.2.1 Laplaceâs Equation and the Pressure Jump Across Liquid Surfaces 7
1.2.2 Applications of the Youngâ"Laplace Equation: The Rayleighâ"Plateau Instability 11
1.3 Youngâ"Dupr© Equation: The Basic Law of Wetting 13
1.3.1 To Spread or Not to Spread: From Solid Surface Tension to Liquid Spreading 13
1.3.2 Partial Wetting: The Young Equation 16
1.4 Wetting in the Presence of Gravity 19
1.4.1 Bond Number and Capillary Length 21
1.4.2 Case Studies 22
1.4.2.1 The Shape of a Liquid Puddle 22
1.4.2.2 The Pendant Drop Method: Measuring Surface Tension by Balancing Capillary and Gravity Forces 24
1.4.2.3 Capillary Rise 25
1.5 Variational Derivation of the Youngâ"Laplace and the Youngâ"Dupr© Equation 26
1.6 Wetting at the Nanoscale 29
1.6.1 The Effective Interface Potential 30
1.6.2 Case Studies 32
1.6.2.1 The Effective Interface Potential for van der Waals Interaction 32
1.6.2.2 Equilibrium Surface Profile Near the Three-Phase Contact Line 34
1.7 Wetting of Heterogeneous Surfaces 35
1.7.1 Youngâ"Laplace and Youngâ"Dupr© Equation for Heterogeneous Surfaces 35
1.7.2 Gibbs Criterion for Contact Line Pinning at Domain Boundaries 37
1.7.3 From Discrete Morphology Transitions to Contact Angle Hysteresis 38
1.7.4 Optimum Contact Angle on Heterogeneous Surfaces: The Laws of Wenzel and Cassie 43
1.7.5 Superhydrophobic Surfaces 45
1.7.6 Wetting of Heterogeneous Surfaces in Three Dimensions 48
1.7.7 Wetting of Complex Surfaces in Three Dimensions: Morphology Transitions, Instabilities, and Symmetry Breaking 50
1.A Mechanical Equilibrium and Stress Tensor 55
Problems 56
References 58
2 Electrostatics 61
2.1 Fundamental Laws of Electrostatics 61
2.1.1 Electric Fields and the Electrostatic Potential 61
2.1.2 Specific Examples 64
2.2 Materials in Electric Fields 66
2.2.1 Conductors 66
2.2.2 Dielectrics 68
2.2.3 Dielectric Liquids and Leaky Dielectrics 73
2.3 Electrostatic Energy 76
2.3.1 Energy of Charges, Conductors, and Electric Fields 76
2.3.2 Capacitance Coefficients and Capacitance 78
2.3.3 Thermodynamic Energy of Charged Systems: Constant Charge Versus Constant Potential 80
2.4 Electrostatic Stresses and Forces 82
2.4.1 Global Forces Acting on Rigid Bodies 82
2.4.2 Local Forces: The Maxwell Stress Tensor 83
2.4.3 Stress Boundary Condition at Interfaces 85
2.5 Two Generic Case Studies 87
2.5.1 Parallel Plate Capacitor 87
2.5.2 Charge and Energy Distribution for Two Capacitors in Series 90
Problems 92
References 93
3 Adsorption at Interfaces 95
3.1 Adsorption Equilibrium 96
3.1.1 General Principles 96
3.1.2 Langmuir Adsorption 96
3.1.3 Reduction of Surface Tension 99
3.2 Adsorption Kinetics 101
3.3 Surface-Active Solutes: From Surfactants to Polymers, Proteins, and Particles 105
3.A A StatisticalMechanics Model of Interfacial Adsorption 107
Problems 110
References 110
4 From Electric Double Layer Theory to Lippmannâs Electrocapillary Equation 113
4.1 Electrocapillarity: the Historic Origins 113
4.2 The Electric Double Layer at Solidâ"Electrolyte Interfaces 115
4.2.1 Poissonâ"Boltzmann Theory and Gouyâ"Chapman Model of the EDL 116
4.2.2 Total Charge and Capacitance of the Diffuse Layer 120
4.2.3 Voltage Dependence of the Free Energy: Electrowetting 122
4.3 Shortcomings of Poissonâ"Boltzmann Theory and the Gouyâ"Chapman Model 124
4.4 Teflonâ"Water Interfaces: a Case Study 125
4.A StatisticalMechanics Derivation of the Governing Equations 127
Problems 130
References 130
5 Principles of Modern Electrowetting 133
5.1 The Standard Model of Electrowetting (on Dielectric) 133
5.1.1 Electrowetting Phenomenology 133
5.1.2 Macroscopic EW Response 136
5.1.3 Microscopic Structure of the Contact Line Region 138
5.2 Interpretation of the StandardModel of EW 145
5.2.1 The Electromechanical Interpretation 145
5.2.2 StandardModel of EW Versus Lippmannâs Electrocapillarity 145
5.2.3 Limitations of the Standard Model: Nonlinearities and Contact Angle Saturation 149
5.3 DC Versus AC Electrowetting 151
5.3.1 General Principles 151
5.3.2 Application Example: Parallel Plate Geometry 153
Problems 156
References 157
6 Elements of Fluid Dynamics 159
6.1 Navierâ"Stokes Equations 159
6.1.1 General Principles: from Newton to Navierâ"Stokes 160
6.1.2 Boundary Conditions 163
6.1.3 Nondimensional Navierâ"Stokes Equation: The Reynolds Number 166
6.1.4 Example: Pressure-Driven Flow Between Two Parallel Plates 167
6.2 Lubrication Flows 170
6.2.1 General Lubrication Flows 170
6.2.2 Lubrication Flows with a Free Liquid Surface 173
6.2.3 Application I: Linear Stability Analysis of aThin Liquid Film 174
6.2.4 Application II: Entrainment of Liquid Films 176
6.3 Contact Line Dynamics 179
6.3.1 Tannerâs Law and the Spreading of Drops on Macroscopic Scales 179
6.3.2 Surface Profiles on the Mesoscopic Scale: The Coxâ"Voinov Law 181
6.3.3 Dynamics of the Microscopic Contact Angle: The Molecular Kinetic Picture 182
6.3.4 Comparison to Experimental Results 183
6.4 SurfaceWaves and Drop Oscillations 185
6.4.1 SurfaceWaves 187
6.4.2 Oscillating Drops 188
6.4.3 Example: Electrowetting-Driven Excitation of Eigenmodes of a Sessile Drop 192
6.4.4 General Consequences 193
Problems 194
References 196
7 Electrowetting Materials and Fabrication 197
7.1 Practical Requirements 197
7.2 Electrowetting Deviation: Caused by Non-obvious Materials Behavior 198
7.2.1 Commonly Observed Temporal Deviations 199
7.2.1.1 Dielectric Failure (Leakage Current) 199
7.2.1.2 Dielectric Charging 201
7.2.1.3 Charges into the Oil 202
7.2.1.4 Oil Relaxation 202
7.2.1.5 Surfactant Diffusion (Interface Absorption) 203
7.2.1.6 Oil Film Trapping 203
7.2.2 Commonly Observed Nontemporal Deviation 204
7.2.2.1 Unexpected Youngâs Angles: Gravity Effects 204
7.2.2.2 Unexpected Youngâs Angles: Surface and Interface Fouling 204
7.2.2.3 Unexpected Youngâs Angles: Dielectric Charging 205
7.2.2.4 Wetting Hysteresis 205
7.2.3 Deviation That Is Often Both Highly Temporal and Nontemporal 206
7.2.3.1 Chemical/Surface Potentials 206
7.3 Electrowetting Saturation 207
7.4 The Invariant Onset of Deviation or Saturation and Lack of a Universal Theory for This Invariance 208
7.4.1 The Invariance of Saturation for Aqueous Conducting Fluids 208
7.4.2 The Invariance of the Onset of Deviation or Saturation for All Types of Conducting Fluids with ð¾ci > 5 mNmâ'1 209
7.4.3 Summary 209
7.5 Choosing Materials: Large Youngâs Angle and LowWetting Hysteresis 210
7.5.1 Conventional Ultralow Surface Energy Coatings (Fluoropolymers) 211
7.5.2 Hydrophilic Coatings Made HydrophobicThrough Proper Choice of Insulating Fluid 213
7.5.3 Superhydrophobic Coatings: Larger Youngâs Angle in Air but Small Modulation Range 213
7.6 Choosing Materials: the Electrowetting Dielectric (Capacitor) 215
7.6.1 Current State of the Art for Low Potential Electrowetting:Multilayer Dielectrics 218
7.6.2 A Note of Critical Importance for the Topcoat in a Multilayer System 219
7.6.3 Carefully Choosing the Best Materials for Each Individual Layer of the Dielectric Stack 219
7.6.3.1 First Layer: Inorganic Dielectrics 219
7.6.3.2 Second Layer: Organic Dielectrics 220
7.6.3.3 Third Layer: Fluoropolymer 220
7.6.3.4 The Simplest Approaches Available to Electrowetting Practitioners 220
7.7 Choosing Materials: Insulating and Conducting Fluids 221
7.7.1 The Insulating Fluid 221
7.7.2 The Conducting Fluid 221
7.7.2.1 Ionic Content 222
7.7.2.2 Donât UseWater! 223
7.8 Summary of General Best Practices 224
7.9 Mitigating Surface Fouling in Biological Applications 224
7.10 Additional Issues for Complex or Integrated Devices 226
Acknowledgement 227
7.A Trapped Charge Derivation 227
Problems 229
References 231
8 Fundamentals of Applied Electrowetting 235
8.1 Introduction and Scope 235
8.2 Droplet Transport 235
8.2.1 Basic Force Balance Interpretation of Droplet Transport 235
8.2.2 Advanced Droplet Transport Physics:Threshold and Velocity 237
8.2.2.1 Advanced Droplet Transport Physics: Flow Field 239
8.2.3 Additional Practical Notes on Implementation of Basic Droplet Transport 240
8.3 Droplet Transport for Splitting, Dosing, Merging, and Mixing 240
8.3.1 Simple Experimental Examples 241
8.3.2 Fundamentals of Droplet Splitting 241
8.3.2.1 Influence of Vertical Radii of Curvature 242
8.3.2.2 Influence of Horizontal Radii of Curvature 242
8.3.3 Fundamentals of Droplet Dosing (Dispensing) 243
8.3.4 Fundamentals of Droplet Mixing 244
8.4 Stationary Droplet Oscillation, Jumping, and Mixing 244
8.4.1 Droplet Oscillation 244
8.4.2 Droplet Oscillation and Jumping 245
8.4.3 Droplet Oscillation and Hysteresis 245
8.4.4 Droplet Oscillation and Mixing 246
8.5 Gating, Valving, and Pumping 247
8.5.1 Fundamentals 247
8.6 Generating Droplets and Channels 249
8.6.1 Fundamentals for Droplet Generation 249
8.6.2 Fundamentals for Channel Generation 250
8.7 Shape Change in a Channel 251
8.7.1 Fundamentals 251
8.8 Control of Meniscus Curvature 252
8.8.1 Fundamentals 252
8.8.2 Additional Notes on Implementation 253
8.9 Control of Meniscus Surface Area/Coverage 253
8.9.1 Fundamentals 253
8.9.2 Additional Notes on Implementation 254
8.10 Control of Film Breakup and Oil Entrapment 255
8.10.1 Fundamentals 255
8.11 1D, 2D, and 3D Control of Rigid Objects 257
8.11.1 Fundamentals 257
8.12 Reverse Electrowetting and Energy Harvesting 258
Problems 260
References 261
9 Related and Emerging Topics 265
9.1 Introduction and Scope 265
9.2 Dielectrophoresis and Dielectrowetting 265
9.2.1 Basic Dielectrophoresis 265
9.2.2 Dielectrowetting 267
9.3 Innovations in Liquid Metal Electrowetting and Electrocapillarity 269
9.3.1 Electrowetting of GaInSn Liquid Metal Alloys 269
9.3.2 Giant Electrochemical Changes in Liquid Metal Interfacial Surface Tensions 270
9.4 Nonequilibrium Electrical ControlWithout Contact Angle Modulation 271
9.4.1 Some Limitations of Conventional Electrowetting 271
9.4.2 ElectrowettingWithoutWetting 272
Problems 273
References 274
Appendix Historical Perspective of Modern Electrowetting: Individual Testimonials 277
Introduction and Scope 277
âCJâ Kim 277
Authors Note from Heikenfeld 278
Johan Feenstra 278
Tom Jones 279
FriederMugele 280
Richard Fair 281
Authorâs Note from Heikenfeld 282
Bruno Berge 282
Glen McHale 285
Stein Kuiper 286
Jason Heikenfeld 288
Kwan Hyung Kang: An Appreciation by T. B. Jones 289
Authorâs Note from Mugele 290
References 290
Index 293
