Time-dependent ion transport in heterogeneous permselective systems

TL;DR

This paper develops analytical and numerical models to study time-dependent ion transport in two-dimensional heterogeneous permselective systems, revealing how voltage response and ion depletion are affected by system geometry.

Contribution

It extends previous one-dimensional models to two-dimensional systems, providing analytical solutions and numerical comparisons for transient ion transport and voltage response.

Findings

Voltage varies between initial Ohmic and steady-state responses.

Field-focusing accelerates ion depletion at interfaces.

Analytical and numerical solutions agree well.

Abstract

The current study extends previous analytical and numerical solutions of chronopotentiometric response of one-dimensional systems consisting of three layers to the more realistic two-dimensional heterogeneous ion-permselective medium. An analytical solution for the transient concentration-polarization problem, under the local electro-neutrality approximation and ideal permselectivity, was obtained using the Laplace transform and separation of variables. Then the two-dimensional electric potential was obtained numerically and was compared to the full Poisson-Nernst-Planck solution. It was then shown that the resultant voltage drop across the system varies between the initial Ohmic response and that of the steady-state accounting for concentration-polarization. Also, field-focusing effect in a two-dimensional system is shown to result in a faster depletion of ions at the permselective interface.