Lattice Boltzmann method for continuum, multi-component mass diffusion in complex 2D geometries

Abstract

Multi-component gas diffusion in the continuum flow regime is often modelled using the Stefan–Maxwell (SM) equations. Recent advances in lattice Boltzmann (LB) mass diffusion models have made it possible to directly compare LB predictions with solutions to the SM equations. In this work, one-dimensional (1D) and two-dimensional (2D), equi-molar counter-diffusion of two gases in the presence of a third, inert gas is studied. The work is an extension and validation of a recently proposed binary LB model for components having dissimilar molecular weights. The treatment of inflow and outflow boundary conditions (for specifying species mole fractions or mole flux) is developed via the averaging of component velocities before and after collisions. Results for one and two spatial dimensions have been compared with analytic and numerical solutions to the SM equations and good agreement has been found for a wide range of parameters and for large variations in molecular weights. A novel molecular weight tuning strategy for increasing the accuracy has been demonstrated. The model developed can be used to model continuum, multi-component mass transfer in complex geometries such as porous media without empirical modification of diffusion coefficients based on porosity and tortuosity values. An envisioned application of this technique is to model gas diffusion in porous solid oxide fuel cell electrodes.