Book contents
- Frontmatter
- Contents
- Preface
- Nomenclature
- Introduction
- 1 Kinematics, Conservation Equations, and Boundary Conditions for Incompressible Flow
- 2 Unidirectional Flow
- 3 Hydraulic Circuit Analysis
- 4 Passive Scalar Transport: Dispersion, Patterning, and Mixing
- 5 Electrostatics and Electrodynamics
- 6 Electroosmosis
- 7 Potential Fluid Flow
- 8 Stokes Flow
- 9 The Diffuse Structure of the Electrical Double Layer
- 10 Zeta Potential in Microchannels
- 11 Species and Charge Transport
- 12 Microchip Chemical Separations
- 13 Particle Electrophoresis
- 14 DNA Transport and Analysis
- 15 Nanofluidics: Fluid and Current Flow in Molecular-Scale and Thick-EDL Systems
- 16 AC Electrokinetics and the Dynamics of Diffuse Charge
- 17 Particle and Droplet Actuation: Dielectrophoresis, Magnetophoresis, and Digital Microfluidics
- APPENDIX A Units and Fundamental Constants
- APPENDIX B Properties of Electrolyte Solutions
- APPENDIX C Coordinate Systems and Vector Calculus
- APPENDIX D Governing Equation Reference
- APPENDIX E Nondimensionalization and Characteristic Parameters
- APPENDIX F Multipolar Solutions to the Laplace and Stokes Equations
- APPENDIX G Complex Functions
- APPENDIX H Interaction Potentials: Atomistic Modeling of Solvents and Solutes
- Bibliography
- Index
16 - AC Electrokinetics and the Dynamics of Diffuse Charge
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Nomenclature
- Introduction
- 1 Kinematics, Conservation Equations, and Boundary Conditions for Incompressible Flow
- 2 Unidirectional Flow
- 3 Hydraulic Circuit Analysis
- 4 Passive Scalar Transport: Dispersion, Patterning, and Mixing
- 5 Electrostatics and Electrodynamics
- 6 Electroosmosis
- 7 Potential Fluid Flow
- 8 Stokes Flow
- 9 The Diffuse Structure of the Electrical Double Layer
- 10 Zeta Potential in Microchannels
- 11 Species and Charge Transport
- 12 Microchip Chemical Separations
- 13 Particle Electrophoresis
- 14 DNA Transport and Analysis
- 15 Nanofluidics: Fluid and Current Flow in Molecular-Scale and Thick-EDL Systems
- 16 AC Electrokinetics and the Dynamics of Diffuse Charge
- 17 Particle and Droplet Actuation: Dielectrophoresis, Magnetophoresis, and Digital Microfluidics
- APPENDIX A Units and Fundamental Constants
- APPENDIX B Properties of Electrolyte Solutions
- APPENDIX C Coordinate Systems and Vector Calculus
- APPENDIX D Governing Equation Reference
- APPENDIX E Nondimensionalization and Characteristic Parameters
- APPENDIX F Multipolar Solutions to the Laplace and Stokes Equations
- APPENDIX G Complex Functions
- APPENDIX H Interaction Potentials: Atomistic Modeling of Solvents and Solutes
- Bibliography
- Index
Summary
Equilibrium models of the EDL (Chapter 9) assume that the ion distribution is in equilibrium and use a Boltzmann statistical description to predict ion distributions. The equilibrium assumption is appropriate for the EDL at an electrically insulating surface such as glass or most polymers, because the ion distribution processes are typically fast relative to the phenomena that change the boundary condition ϕ0 (e.g., surface adsorption or changes in electrolyte concentration or pH).
In this chapter, we address the dynamics of diffuse charge. We focus primarily on the formation of thin double layers at electrodes with attention to the dynamics of doublelayer formation and equilibration. Unlike for the double layer formed at the surface of an insulator, the double-layer equilibration at an electrode (owing to the potential applied at that electrode) is not necessarily fast compared with the variation of the voltage at the electrode – high-frequency voltage sources can vary rapidly compared with double-layer equilibration. Thus the dynamic aspects of double-layer equilibration are critically pertinent.
A full continuum description of these phenomena comes from the Poisson, Nernst–Planck, and Navier–Stokes equations combined with boundary conditions describing electrode kinetics. Because such analysis is daunting, we approximate the problem as that of predicting surface electroosmosis with time-dependent electrokinetic potentials, and use 1D models of the EDL to form equivalent circuits that can be used to model the temporal response of ϕ0.
- Type
- Chapter
- Information
- Micro- and Nanoscale Fluid MechanicsTransport in Microfluidic Devices, pp. 355 - 372Publisher: Cambridge University PressPrint publication year: 2010