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

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.

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Cited by in corpus (4)

• Optimal error estimates of coupled and divergence-free virtual element methods for the Poisson--Nernst--Planck/Navier--Stokes equations
• Phase Field Modeling and Numerical Algorithm for Two-Phase Dielectric Fluid Flows
• Finite Element Simulation of Modified Poisson-Nernst-Planck/Navier-Stokes Model for Compressible Electrolytes under Mechanical Equilibrium
• A finite element solver for a thermodynamically consistent electrolyte model