Monte Carlo calculation of effective diffusivities in two- and three-dimensional heterogeneous materials of variable structure

A Monte Carlo technique that simulates tracer diffusion in multiphase materials of arbitrary complexity has been developed. Effective diffusivities are calculated for structures consisting of either overlapping or nonoverlapping inclusions with diffusivity Dc distributed in a continuous phase with diffusivity D0>Dc. Two-dimensional simulations for various values of D0/Dc generate normalized diffusivities that correspond closely to their three-dimensional counterparts; they nearly collapse to a common curve when a simple scaling relation is applied.