An approach combining the lattice Boltzmann method and Maxwell–Stefan equation for modeling multi-component diffusion

Abstract

The lattice Boltzmann method is an appropriate mesoscopic-scale tool for investigating the diffusion processes. However, since the state-of-the-art multi-component diffusion lattice Boltzmann (LB) models are based on the kinetic theory and start from the lattice Bhatnagar–Gross–Krook model, some defects cannot be avoided: they are only suitable for steady flow and there are limitations for setting the velocity and viscosity in lattice units. We devise a new incompressible LB model for ideal gases in solid oxide fuel cells (SOFCs), which is based on the advection–diffusion equation and coupled with the Maxwell–Stefan (M–S) equation by relaxation time. The coupled M–S equation is used for correction, considering the driving force in a multi-component diffusion system. Our LB model is implemented to predict the concentration overpotentials of a porous anode in a SOFC. The overpotentials are calculated from an H2–H2O–Ar ternary mass transport simulation and compared to the corresponding experimental results and several published continuum-scale and LB computations, demonstrating that our model offers a better consistency with the experimental measurement. Moreover, a Stefan tube is simulated for benchmarking against the local parameters; this is compared with the related experimental data and demonstrates the accuracy of our LB model.