An Energetic Variational Approach for ion transport

TL;DR

This paper employs an energetic variational approach to derive and analyze the coupled Poisson-Nernst-Planck-Navier-Stokes system, providing a unified framework for ion transport with applications to electrokinetics.

Contribution

It introduces a variational derivation of the coupled system, incorporating physics through energy laws and transport, and discusses boundary conditions and Onsager's relation.

Findings

Derivation of coupled force balance equations via variational methods

Validation of Onsager's relation in electrokinetics near initial conditions

Framework applicable to diverse boundary conditions

Abstract

The transport and distribution of charged particles are crucial in the study of many physical and biological problems. In this paper, we employ an Energy Variational Approach to derive the coupled Poisson-Nernst-Planck-Navier-Stokes system. All physics is included in the choices of corresponding energy law and kinematic transport of particles. The variational derivations give the coupled force balance equations in a unique and deterministic fashion. We also discuss the situations with different types of boundary conditions. Finally, we show that the Onsager's relation holds for the electrokinetics, near the initial time of a step function applied field.