Electrowetting

Frieder Mugele is the head of the Physics of Complex Fluids group at the University of Twente in Enschede, The Netherlands. Having obtained his academic degrees in physics at the University of Konstanz, Germany, he spent several years at the University of California in Berkeley, USA, and the University of Ulm, Germany, before his present appointment in Twente. Professor Mugele's research focuses on various aspects of solid-liquid interfaces and the properties of liquids on the micro- and nanoscale. He has been active in electrowetting since the late 1990s contributing in particular to the theoretical understanding and to fundamental concepts of electrowetting-driven microfluidics. Jason Heikenfeld is a Professor and Assistant Vice President for Commercialization at the Univ. of Cincinnati. He directs the Novel Devices Laboratory which has established highly-focused international leadership roles in an emergent technological paradigms including electrowetting, electronic paper, and most recently sweat biosensing technology. Prof. Heikenfeld's research approach centers on discovering and addressing the hidden challenges that can hinder the transition of innovative science into commercial application. Professor Heikenfeld is also a prolific inventor and serial entrepreneur, and during his teaching years was the highest-rated STEM educator at the University of Cincinnati.

• Preface xi1 Introduction to Capillarity and Wetting Phenomena 11.1 Surface Tension and Surface Free Energy 21.1.1 The Microscopic Origin of Surface Energies 21.1.2 Macroscopic Definition of Surface Energy and Surface Tension 51.2 Young–Laplace Equation: The Basic Law of Capillarity 71.2.1 Laplace’s Equation and the Pressure Jump Across Liquid Surfaces 71.2.2 Applications of the Young–Laplace Equation: The Rayleigh–Plateau Instability 111.3 Young–Dupré Equation: The Basic Law of Wetting 131.3.1 To Spread or Not to Spread: From Solid Surface Tension to Liquid Spreading 131.3.2 Partial Wetting: The Young Equation 161.4 Wetting in the Presence of Gravity 191.4.1 Bond Number and Capillary Length 211.4.2 Case Studies 221.4.2.1 The Shape of a Liquid Puddle 221.4.2.2 The Pendant Drop Method: Measuring Surface Tension by Balancing Capillary and Gravity Forces 241.4.2.3 Capillary Rise 251.5 Variational Derivation of the Young–Laplace and the Young–Dupré Equation 261.6 Wetting at the Nanoscale 291.6.1 The Effective Interface Potential 301.6.2 Case Studies 321.6.2.1 The Effective Interface Potential for van der Waals Interaction 321.6.2.2 Equilibrium Surface Profile Near the Three-Phase Contact Line 341.7 Wetting of Heterogeneous Surfaces 351.7.1 Young–Laplace and Young–Dupré Equation for Heterogeneous Surfaces 351.7.2 Gibbs Criterion for Contact Line Pinning at Domain Boundaries 371.7.3 From Discrete Morphology Transitions to Contact Angle Hysteresis 381.7.4 Optimum Contact Angle on Heterogeneous Surfaces: The Laws of Wenzel and Cassie 431.7.5 Superhydrophobic Surfaces 451.7.6 Wetting of Heterogeneous Surfaces in Three Dimensions 481.7.7 Wetting of Complex Surfaces in Three Dimensions: Morphology Transitions, Instabilities, and Symmetry Breaking 501.A Mechanical Equilibrium and Stress Tensor 55Problems 56References 582 Electrostatics 612.1 Fundamental Laws of Electrostatics 612.1.1 Electric Fields and the Electrostatic Potential 612.1.2 Specific Examples 642.2 Materials in Electric Fields 662.2.1 Conductors 662.2.2 Dielectrics 682.2.3 Dielectric Liquids and Leaky Dielectrics 732.3 Electrostatic Energy 762.3.1 Energy of Charges, Conductors, and Electric Fields 762.3.2 Capacitance Coefficients and Capacitance 782.3.3 Thermodynamic Energy of Charged Systems: Constant Charge Versus Constant Potential 802.4 Electrostatic Stresses and Forces 822.4.1 Global Forces Acting on Rigid Bodies 822.4.2 Local Forces: The Maxwell Stress Tensor 832.4.3 Stress Boundary Condition at Interfaces 852.5 Two Generic Case Studies 872.5.1 Parallel Plate Capacitor 872.5.2 Charge and Energy Distribution for Two Capacitors in Series 90Problems 92References 933 Adsorption at Interfaces 953.1 Adsorption Equilibrium 963.1.1 General Principles 963.1.2 Langmuir Adsorption 963.1.3 Reduction of Surface Tension 993.2 Adsorption Kinetics 1013.3 Surface-Active Solutes: From Surfactants to Polymers, Proteins, and Particles 1053.A A StatisticalMechanics Model of Interfacial Adsorption 107Problems 110References 1104 From Electric Double Layer Theory to Lippmann’s Electrocapillary Equation 1134.1 Electrocapillarity: the Historic Origins 1134.2 The Electric Double Layer at Solid–Electrolyte Interfaces 1154.2.1 Poisson–Boltzmann Theory and Gouy–Chapman Model of the EDL 1164.2.2 Total Charge and Capacitance of the Diffuse Layer 1204.2.3 Voltage Dependence of the Free Energy: Electrowetting 1224.3 Shortcomings of Poisson–Boltzmann Theory and the Gouy–Chapman Model 1244.4 Teflon–Water Interfaces: a Case Study 1254.A StatisticalMechanics Derivation of the Governing Equations 127Problems 130References 1305 Principles of Modern Electrowetting 1335.1 The Standard Model of Electrowetting (on Dielectric) 1335.1.1 Electrowetting Phenomenology 1335.1.2 Macroscopic EW Response 1365.1.3 Microscopic Structure of the Contact Line Region 1385.2 Interpretation of the StandardModel of EW 1455.2.1 The Electromechanical Interpretation 1455.2.2 StandardModel of EW Versus Lippmann’s Electrocapillarity 1455.2.3 Limitations of the Standard Model: Nonlinearities and Contact Angle Saturation 1495.3 DC Versus AC Electrowetting 1515.3.1 General Principles 1515.3.2 Application Example: Parallel Plate Geometry 153Problems 156References 1576 Elements of Fluid Dynamics 1596.1 Navier–Stokes Equations 1596.1.1 General Principles: from Newton to Navier–Stokes 1606.1.2 Boundary Conditions 1636.1.3 Nondimensional Navier–Stokes Equation: The Reynolds Number 1666.1.4 Example: Pressure-Driven Flow Between Two Parallel Plates 1676.2 Lubrication Flows 1706.2.1 General Lubrication Flows 1706.2.2 Lubrication Flows with a Free Liquid Surface 1736.2.3 Application I: Linear Stability Analysis of aThin Liquid Film 1746.2.4 Application II: Entrainment of Liquid Films 1766.3 Contact Line Dynamics 1796.3.1 Tanner’s Law and the Spreading of Drops on Macroscopic Scales 1796.3.2 Surface Profiles on the Mesoscopic Scale: The Cox–Voinov Law 1816.3.3 Dynamics of the Microscopic Contact Angle: The Molecular Kinetic Picture 1826.3.4 Comparison to Experimental Results 1836.4 SurfaceWaves and Drop Oscillations 1856.4.1 SurfaceWaves 1876.4.2 Oscillating Drops 1886.4.3 Example: Electrowetting-Driven Excitation of Eigenmodes of a Sessile Drop 1926.4.4 General Consequences 193Problems 194References 1967 Electrowetting Materials and Fabrication 1977.1 Practical Requirements 1977.2 Electrowetting Deviation: Caused by Non-obvious Materials Behavior 1987.2.1 Commonly Observed Temporal Deviations 1997.2.1.1 Dielectric Failure (Leakage Current) 1997.2.1.2 Dielectric Charging 2017.2.1.3 Charges into the Oil 2027.2.1.4 Oil Relaxation 2027.2.1.5 Surfactant Diffusion (Interface Absorption) 2037.2.1.6 Oil Film Trapping 2037.2.2 Commonly Observed Nontemporal Deviation 2047.2.2.1 Unexpected Young’s Angles: Gravity Effects 2047.2.2.2 Unexpected Young’s Angles: Surface and Interface Fouling 2047.2.2.3 Unexpected Young’s Angles: Dielectric Charging 2057.2.2.4 Wetting Hysteresis 2057.2.3 Deviation That Is Often Both Highly Temporal and Nontemporal 2067.2.3.1 Chemical/Surface Potentials 2067.3 Electrowetting Saturation 2077.4 The Invariant Onset of Deviation or Saturation and Lack of a Universal Theory for This Invariance 2087.4.1 The Invariance of Saturation for Aqueous Conducting Fluids 2087.4.2 The Invariance of the Onset of Deviation or Saturation for All Types of Conducting Fluids with 𝛾ci > 5 mNm−1 2097.4.3 Summary 2097.5 Choosing Materials: Large Young’s Angle and LowWetting Hysteresis 2107.5.1 Conventional Ultralow Surface Energy Coatings (Fluoropolymers) 2117.5.2 Hydrophilic Coatings Made HydrophobicThrough Proper Choice of Insulating Fluid 2137.5.3 Superhydrophobic Coatings: Larger Young’s Angle in Air but Small Modulation Range 2137.6 Choosing Materials: the Electrowetting Dielectric (Capacitor) 2157.6.1 Current State of the Art for Low Potential Electrowetting:Multilayer Dielectrics 2187.6.2 A Note of Critical Importance for the Topcoat in a Multilayer System 2197.6.3 Carefully Choosing the Best Materials for Each Individual Layer of the Dielectric Stack 2197.6.3.1 First Layer: Inorganic Dielectrics 2197.6.3.2 Second Layer: Organic Dielectrics 2207.6.3.3 Third Layer: Fluoropolymer 2207.6.3.4 The Simplest Approaches Available to Electrowetting Practitioners 2207.7 Choosing Materials: Insulating and Conducting Fluids 2217.7.1 The Insulating Fluid 2217.7.2 The Conducting Fluid 2217.7.2.1 Ionic Content 2227.7.2.2 Don’t UseWater! 2237.8 Summary of General Best Practices 2247.9 Mitigating Surface Fouling in Biological Applications 2247.10 Additional Issues for Complex or Integrated Devices 226Acknowledgement 2277.A Trapped Charge Derivation 227Problems 229References 2318 Fundamentals of Applied Electrowetting 2358.1 Introduction and Scope 2358.2 Droplet Transport 2358.2.1 Basic Force Balance Interpretation of Droplet Transport 2358.2.2 Advanced Droplet Transport Physics:Threshold and Velocity 2378.2.2.1 Advanced Droplet Transport Physics: Flow Field 2398.2.3 Additional Practical Notes on Implementation of Basic Droplet Transport 2408.3 Droplet Transport for Splitting, Dosing, Merging, and Mixing 2408.3.1 Simple Experimental Examples 2418.3.2 Fundamentals of Droplet Splitting 2418.3.2.1 Influence of Vertical Radii of Curvature 2428.3.2.2 Influence of Horizontal Radii of Curvature 2428.3.3 Fundamentals of Droplet Dosing (Dispensing) 2438.3.4 Fundamentals of Droplet Mixing 2448.4 Stationary Droplet Oscillation, Jumping, and Mixing 2448.4.1 Droplet Oscillation 2448.4.2 Droplet Oscillation and Jumping 2458.4.3 Droplet Oscillation and Hysteresis 2458.4.4 Droplet Oscillation and Mixing 2468.5 Gating, Valving, and Pumping 2478.5.1 Fundamentals 2478.6 Generating Droplets and Channels 2498.6.1 Fundamentals for Droplet Generation 2498.6.2 Fundamentals for Channel Generation 2508.7 Shape Change in a Channel 2518.7.1 Fundamentals 2518.8 Control of Meniscus Curvature 2528.8.1 Fundamentals 2528.8.2 Additional Notes on Implementation 2538.9 Control of Meniscus Surface Area/Coverage 2538.9.1 Fundamentals 2538.9.2 Additional Notes on Implementation 2548.10 Control of Film Breakup and Oil Entrapment 2558.10.1 Fundamentals 2558.11 1D, 2D, and 3D Control of Rigid Objects 2578.11.1 Fundamentals 2578.12 Reverse Electrowetting and Energy Harvesting 258Problems 260References 2619 Related and Emerging Topics 2659.1 Introduction and Scope 2659.2 Dielectrophoresis and Dielectrowetting 2659.2.1 Basic Dielectrophoresis 2659.2.2 Dielectrowetting 2679.3 Innovations in Liquid Metal Electrowetting and Electrocapillarity 2699.3.1 Electrowetting of GaInSn Liquid Metal Alloys 2699.3.2 Giant Electrochemical Changes in Liquid Metal Interfacial Surface Tensions 2709.4 Nonequilibrium Electrical ControlWithout Contact Angle Modulation 2719.4.1 Some Limitations of Conventional Electrowetting 2719.4.2 ElectrowettingWithoutWetting 272Problems 273References 274Appendix Historical Perspective of Modern Electrowetting: Individual Testimonials 277Introduction and Scope 277“CJ” Kim 277Authors Note from Heikenfeld 278Johan Feenstra 278Tom Jones 279FriederMugele 280Richard Fair 281Author’s Note from Heikenfeld 282Bruno Berge 282Glen McHale 285Stein Kuiper 286Jason Heikenfeld 288Kwan Hyung Kang: An Appreciation by T. B. Jones 289Author’s Note from Mugele 290References 290Index 293