Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction

Abstract

For highly charged dielectric surfaces, the asymptotic structure underlying electrokinetic phenomena in the thin-double-layer limit reshuffles. The large counterion concentration near the surface, associated with the Boltzmann distribution in the diffuse layer, supports appreciable tangential fluxes appearing as effective surface currents in a macroscale description. Their inevitable nonuniformity gives rise in turn to comparable transverse currents, which, for logarithmically large zeta potentials, modify the electrokinetic transport in the electroneutral bulk. To date, this mechanism has been studied only using a weak-field linearization. We present here a generic thin-double-layer analysis of the electrokinetic transport about highly charged dielectric solids, which is not restricted to weak fields. We identify the counterion concentration amplification with the emergence of an internal boundary layer--within the diffuse part of the double layer--characterized by distinct scaling of ionic concentrations and electric field. In this multiscale description, surface conduction is conveniently localized within the internal layer. Our systematic scheme thus avoids the cumbersome procedure of retaining small asymptotic terms which change their magnitude at large zeta potentials. The electrokinetic transport predicted by the resulting macroscale model is inherently accompanied by bulk concentration polarization, which in turn results in nonlinear bulk transport. A novel fundamental subtlety associated with this intrinsic feature, overlooked in the weak-field approximation, has to do with the ambiguity of the "particle zeta potential" concept: In general, even uniformly charged surfaces are characterized by a nonuniform zeta-potential distribution. This impairs the need for a careful identification of the dimensionless number representing the transition to large zeta potentials.