Transient electrohydrodynamic flow with concentration dependent fluid properties: modelling and energy-stable numerical schemes

TL;DR

This paper develops a thermodynamically consistent continuum model for electrohydrodynamic flow with concentration-dependent properties, and introduces energy-stable numerical schemes for efficient simulation of the coupled system.

Contribution

It presents a generalized Navier-Stokes-Poisson-Nernst-Planck model with concentration-dependent fluid properties and proposes decoupled, energy-stable numerical schemes for its simulation.

Findings

Numerical schemes satisfy the energy dissipation law.

Decoupled schemes improve computational efficiency.

Simulations demonstrate the effectiveness of the proposed methods.

Abstract

Transport of electrolytic solutions under influence of electric fields occurs in phenomena ranging from biology to geophysics. Here, we present a continuum model for single-phase electrohydrodynamic flow, which can be derived from fundamental thermodynamic principles. This results in a generalized Navier-Stokes-Poisson-Nernst-Planck system, where fluid properties such as density and permittivity depend on the ion concentration fields. We propose strategies for constructing numerical schemes for this set of equations, where solving the electrochemical and the hydrodynamic subproblems are decoupled at each time step. We provide time discretizations of the model that suffice to satisfy the same energy dissipation law as the continuous model. In particular, we propose both linear and non-linear discretizations of the electrochemical subproblem, along with a projection scheme for the fluid flow. The efficiency of the approach is demonstrated by numerical simulations using several of the proposed schemes.