Finite Element Simulation of Modified Poisson-Nernst-Planck/Navier-Stokes Model for Compressible Electrolytes under Mechanical Equilibrium

TL;DR

This paper develops a finite element method for a modified Poisson-Nernst-Planck/Navier-Stokes model tailored for compressible electrolytes under mechanical equilibrium, enabling analysis of both compressible and incompressible regimes with practical applications.

Contribution

It introduces a numerical scheme capable of handling compressible electrolytes and reduces the system to a modified Poisson-Boltzmann form for efficient simulation.

Findings

The scheme accurately captures electrolyte behavior under various conditions.

It demonstrates seamless transition between compressible and incompressible regimes.

Numerical results align with theoretical expectations for limiting behaviors.

Abstract

This work presents a finite element method for a modified Poisson-Nernst-Planck/Navier-Stokes (PNP/NS) model under the mechanical equilibrium, developed for compressible electrolytes. Another key contribution of this work is the reduction of the equilibrium system to a modified Poisson-Boltzmann system. The proposed numerical scheme is capable of handling both compressible and incompressible regimes by employing a bulk modulus parameter, which governs the fluid's compressibility and enables seamless transition between these regimes. To emphasize practical relevance, we discuss the implications of compressible electrolytes in the context of double-layer capacitance behavior. We also conduct numerical simulations over various domains to demonstrate its applicability under various operating conditions, including temperature fluctuations and variations in the bulk modulus. The numerical results validate the accuracy and robustness of our computational scheme and demonstrate that the observed limiting behavior for the incompressible regime aligns with the theoretical trends anticipated by Dreyer et al. [39].