Chapter 16
AC electrokinetics and the dynamics of diffuse charge

At this point, we need to put our previous discussions of electrical double layers in context. We started by considering a relatively simple equilibrium model (Chapter 9) of the electrical double layer that assumed that the system was in steady-state, the geometry was one-dimensional, and the reservoir of fluid was considered infinite. The equilibrium assumption was appropriate for the electrical double layer at an electrically insulating surface such as glass or most polymers, because the ion distribution processes are typically fast as compared to the phenomena that change the boundary condition φ₀ (e.g., surface adsorption or changes in electrolyte concentration or pH). Further, the one-dimensional geometry was appropriate because most engineering systems have radii of curvature larger than λ_D (i.e., microchannels) or exhibit approximate spherical symmetry (micro/nanoparticles). Assuming that the bulk fluid reservoir is infinite works well if double layers are thin or if the geometry is simple.

This picture of the electrical double layer, combined with the 1D Navier-Stokes analysis in Chapter 6, led to a solution for the fluid velocity for electroosmosis in the presence of a transverse electric field, in the limit where ion transport was ignored and equilibrium ion concentrations were assumed to apply throughout.

One situation in which this treatment breaks down is for the interface between low-surface area, thin double layer regions and high-surface area, thick double layer regions, as discussed in Chapter 15—there, we saw that ion transport must be considered when the geometry becomes more complex and when the reservoir of ions in the bulk can no longer be assumed infinite.

In this chapter, we address the dynamics of diffuse charge. We focus primarily on the formation of double layers at electrodes with attention to the dynamics of double layer formation and equilibration. Unlike for the double layer formed at the surface of an insulator (owing to chemical reactions at the surface and the attendant surface potential), the double layer equilibration at an electrode (owing to the potential applied at that electrode) is not necessarily fast as compared to the variation of the voltage at the electrode—high frequency voltage sources can vary rapidly as compared to double layer equilibration. Thus the dynamics of double layer equilibration are critically pertinent.

In addition to the characteristic times of double layer equilibration, the geometries of interest are different and usually more complex when considering flow induced by the potential at a conducting surface. In particular, the straightforward geometry employed in our early discussion of electroosmosis—a potential at an insulating surface inducing an electric field normal to the surface, and a largely uncoupled extrinsically applied electric field parallel to the surface—is not possible at a conducting surface since the conducting surface precludes the existence of the parallel electric field. The basic system we use to introduce the material (ion motion normal to two parallel electrodes) can be used to calculate the characteristic equilibration times, but this system does not induce fluid flow. The geometries that do induce fluid flow are typically not one-dimensional, and numerical solution is typically required.

By considering a more complicated picture of double layer dynamics, we can identify a number of interesting flow phenomena, some of which have been termedAC electroosmosis andinduced-charge electroosmosis. We focus on the dynamics ofelectrical double layers for a 1D geometry and focus on equivalent circuit models of this process. By stressing dynamics, we imply that our central goal is to identify not just the steady-state nature of the double layer, but also the characteristic time required for the double layer to achieve steady-state upon experiencing a change in surface potential. By identifying this characteristic time, we can describe the response of the system to AC signals and predict a variety of AC phenomena.

Diffuse charge is not generated solely near surfaces. If the properties of a fluid are nonuniform, the spatial variation in electrical conductivity and permittivity lead to a perturbation in the electric field and the net charge density field. The net charge density created leads to an electrostatic body force, which also leads to fluid flow. These flows are usually called electrothermal flows, because thermal inhomogeneity is its most common source.

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