Lattice Boltzmann Method for mixtures at variable Schmidt number

TL;DR

This paper introduces a modified Lattice Boltzmann Method that independently controls mutual diffusivity and viscosity in multicomponent mixtures, validated through simulations of neutral and charged systems.

Contribution

It proposes a novel modification to the multicomponent BGK equations by adding separate timescales for mass and momentum diffusion, enabling independent control of diffusivity.

Findings

Accurate simulation of neutral binary and charged ternary mixtures.

Observed deviations from Helmholtz-Smoluchowski prediction at high diffusivity.

Validated method for bulk and slit channel conditions.

Abstract

When simulating multicomponent mixtures via the Lattice Boltzmann Method, it is desirable to control the mutual diffusivity between species while maintaining the viscosity of the solution fixed. This goal is herein achieved by a modification of the multicomponent Bhatnagar-Gross-Krook (BGK) evolution equations by introducing two different timescales for mass and momentum diffusion. Diffusivity is thus controlled by an effective drag force acting between species. Numerical simulations confirm the accuracy of the method for neutral binary and charged ternary mixtures in bulk conditions. The simulation of a charged mixture in a charged slit channel show that the conductivity and electro-osmotic mobility exhibit a departure from the Helmholtz-Smoluchowski prediction at high diffusivity.