Discrete solution of the electrokinetic equations

TL;DR

This paper introduces a robust numerical scheme combining lattice-Boltzmann and discrete convection-diffusion methods to solve electrokinetic equations, enabling accurate simulations of electro-osmotic flows and sedimentation without linearization assumptions.

Contribution

The novel approach integrates lattice-Boltzmann with discrete convection-diffusion to solve electrokinetic equations, avoiding linearization and handling a wide Peclet number range.

Findings

Successfully computes sedimentation velocity of charged spheres.

Accurately models electro-osmotic flows with no spurious fluxes.

Handles large Peclet numbers without linearization.

Abstract

We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete solution of the convection-diffusion equation for the different charged and neutral species that compose the fluid. The method is based on identifying the elementary fluxes between nodes, which ensures the absence of spurious fluxes in equilibrium. We show how the model is suitable to study electro-osmotic flows. As an illustration, we show that, by introducing appropriate dynamic rules in the presence of solid interfaces, we can compute the sedimentation velocity (and hence the sedimentation potential) of a charged sphere. Our approach does not assume linearization of the Poisson-Boltzmann equation and allows us for a wide variation of the Peclet number.