Monte Carlo calculation of effective diffusivities in two- and three-dimensional heterogeneous materials of variable structure
Mark R. Riley, Fernando J. Muzzio, Helen M. Buettner, Sebastián C. Reyes · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1994
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 ${\mathit{D}}_{\mathit{c}}$ distributed in a continuous phase with diffusivity ${\mathit{D}}_{0}$>${\mathit{D}}_{\mathit{c}}$. Two-dimensional simulations for various values of ${\mathit{D}}_{0}$/${\mathit{D}}_{\mathit{c}}$ 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.