Monte Carlo modelling of the effective diffusivity of a composite material

In this paper we perform a systematic Monte Carlo study of the effective diffusivity in a 2D composite in which the dispersed phase (squares) is arranged in square planar and brick-work patterns within the matrix phase. We focus on the commonly encountered case where the dispersed phase has a much lower diffusivity than the matrix and where the segregation of the diffusant favours the matrix phase. It is found that while the generalized Maxwell-Garnett Equation generally describes the effective diffusivity semi-quantitatively, in order to have an accurate representation of the effective diffusivity at moderate volume fractions of the dispersed phase, it is necessary to use a more refined Maxwell-Garnett Equation that takes into account the actual shape and geometry of the dispersed phase.