Calculation of the effective diffusivity of heterogeneous media using the lattice-Boltzmann method

The effective diffusivity of a heterogeneous medium is calculated numerically as a function of the inclusion fraction using the lattice-Boltzmann approach. Effective diffusivities are calculated for structures consisting of either permeable or nonpermeable inclusions distributed in a continuous phase. Two-dimensional simulations show good agreement with results obtained by means of Monte Carlo simulations of tracer diffusion. Numerical results are shown that are in agreement with the predictions of Maxwell's equation, for small inclusion fractions.