Nonlinear electrochemical relaxation around conductors

TL;DR

This paper investigates the nonlinear electrochemical relaxation of uncharged conductors in electrolyte solutions under strong electric fields, using the Poisson-Nernst-Planck equations to analyze surface and bulk ion transport effects.

Contribution

It develops a comprehensive analysis of nonlinear electrochemical relaxation beyond the circuit approximation, deriving boundary conditions and solving equations numerically and asymptotically.

Findings

Bulk concentration gradients form under strong fields.

Surface conduction significantly influences relaxation dynamics.

New dimensionless parameters generalize existing transport ratios.

Abstract

We analyze the simplest problem of electrochemical relaxation in more than one dimension - the response of an uncharged, ideally polarizable metallic sphere (or cylinder) in a symmetric, binary electrolyte to a uniform electric field. In order to go beyond the circuit approximation for thin double layers, our analysis is based on the Poisson-Nernst-Planck (PNP) equations of dilute solution theory. Unlike most previous studies, however, we focus on the nonlinear regime, where the applied voltage across the conductor is larger than the thermal voltage. In such strong electric fields, the classical model predicts that the double layer adsorbs enough ions to produce bulk concentration gradients and surface conduction. Our analysis begins with a general derivation of surface conservation laws in the thin double-layer limit, which provide effective boundary conditions on the quasi-neutral bulk. We solve the resulting nonlinear partial differential equations numerically for strong fields and also perform a time-dependent asymptotic analysis for weaker fields, where bulk diffusion and surface conduction arise as first-order corrections. We also derive various dimensionless parameters comparing surface to bulk transport processes, which generalize the Bikerman-Dukhin number. Our results have basic relevance for double-layer charging dynamics and nonlinear electrokinetics in the ubiquitous PNP approximation.