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.