Modified Poisson-Nernst-Planck model with accurate Coulomb correlation in variable media

TL;DR

This paper develops a modified Poisson-Nernst-Planck model incorporating Coulomb correlation effects in media with variable dielectric properties, using asymptotic expansions and numerical methods to analyze ion transport.

Contribution

The paper introduces a new set of modified PNP equations that include Coulomb correlation effects derived from a free energy functional, with efficient numerical solutions.

Findings

Coulomb correlation significantly affects ion transport predictions.

Asymptotic expansions enable efficient numerical solutions.

Numerical results demonstrate the impact of Coulomb correlation.

Abstract

We derive a set of modified Poisson-Nernst-Planck (mPNP) equations for ion transport from the variation of the free energy functional which includes the many-body Coulomb correlation in media of variable dielectric coefficient. The correlation effects are considered through the Debye charging process in which the self energy of an ion is governed by the generalized Debye-H\"uckel equation. We develop the asymptotic expansions of the self energy taking the ion radius as the small parameter such that the multiscale model can be solved efficiently by numerical methods. It is shown that the variations of the energy functional give the self-energy-modified PNP equations which satisfy a proper weak formulation. We present numerical results from different asymptotic expansions with a semi-implicit conservative numerical method and investigate the effect of the Coulomb correlation.