Maxwell-Stefan theory based lattice Boltzmann model for diffusion in multicomponent mixtures

TL;DR

This paper introduces a Maxwell-Stefan based lattice Boltzmann model for simulating diffusion in multicomponent mixtures, accurately recovering continuum equations and capturing complex diffusion phenomena with reduced computational cost.

Contribution

A novel multiple-relaxation-time lattice Boltzmann model based on Maxwell-Stefan equations for multicomponent diffusion, with simplified lattice structures and local collision processes.

Findings

Model accurately recovers Maxwell-Stefan continuum equations.

Simulations capture reverse, osmotic, and diffusion barrier phenomena.

Results agree well with existing studies.

Abstract

The phenomena of diffusion in multicomponent (more than two components) mixtures are very universal in both science and engineering, and from mathematical point of view, they are usually described by the Maxwell-Stefan (MS) based continuum equations. In this paper, we propose a multiple-relaxation-time lattice Boltzmann (LB) model for the mass diffusion in multicomponent mixtures, and also perform a Chapman-Enskog analysis to show that the MS based continuum equations can be correctly recovered from the developed LB model. In addition, considering the fact that the MS based continuum equations are just a diffusion type of partial differential equations, we can also adopt much simpler lattice structures to reduce the computational cost of present LB model. We then conduct some simulations to test this model, and find that the results are in good agreement with some available works. Besides, the reverse diffusion, osmotic diffusion and diffusion barrier phenomena are also captured. Finally, compared to the kinetic theory based LB models for multicomponent gas diffusion, the present model does not include any complicated interpolations, and its collision process can be still implemented locally. Therefore, the advantages of single-component LB method can also be preserved in present LB model.