The effective diffusivity in two-phase material

In this paper we employ Monte Carlo computer simulation to test the extended Maxwell-Garnett expression for the effective diffusivity in a simple model of a two phase material. We determine the effective diffusivity in f.c.c., b.c.c. and s.c. type arrangements of dispersed spheres at variable densities and for cases where the diffusivity in the dispersed phase was less than, and greater than, the diffusivity in the matrix phase. It is shown that the above equation agrees very well with the simulation data for all densities up to where the spheres of the dispersed phase touch and over six orders of magnitude in the ratio of the diffusivity of the dispersed phase to the diffusivity of the matrix phase.