A lattice Boltzmann model for coupled diffusion

Diffusion coupling between different chemical components can have significant effects on the distribution of chemical species and can affect the physico-chemical properties of their supporting medium. The coupling can arise from local electric charge conservation for ions or from bound components forming compounds. We present a new lattice Boltzmann model to account for the diffusive coupling between different chemical species. In this model each coupling is added as an extra relaxation term in the collision operator. The model is tested on a simple diffusion problem with two coupled components and is in excellent agreement with the results obtained through a finite difference method. Our model is observed to be numerically very stable and unconditional stability is shown for a class of diffusion matrices. We further develop the model to account for advection and show an example of application to flow in porous media in two dimensions and an example of convection due to salinity differences. We show that our model with advection loses the unconditional stability, but offers a straight-forward approach to complicated two-dimensional advection and coupled diffusion problems.