Asymptotic analysis of ion transport in a nonlinear regime around polarized electrodes under ac

Abstract

In this paper we present the asymptotic solutions of the Poisson-Nernst-Planck equations describing ion transport near a polarized electrode under ac. The solutions can be described in terms of the triple-layer (or quadruple-layer in the transient period) structure. In the thinnest inner layer outside the Stern layer, cations and anions show alternating charging with the same frequency as ac. Next to the inner layer is a buffer region or "middle layer" in which cations and anions exhibit the same behavior but with a frequency double that of the ac frequency. The outer layer shows quasisteady diffusion of ions expanding toward the bulk region and vanishes after the transient period. The potential drop occurs only through the inner layer, which together with the concentrations can be obtained by solving a simple dynamical equation. The asymptotic method is applied to the one-dimensional ion-transport within two parallel facing electrodes and the solutions compare well with the ones obtained with robust numerical methods for the original full equations at various ranges of parameters. We also considered the effect of ion adsorption at the interface between the Stern and inner layers on the ion transport and the virtual slip velocity for the case of facing electrodes.