Monte Carlo Modelling of the Effective Diffusivity in 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.
David J. Fisher
I. V. Belova and G. E. Murch, "Monte Carlo Modelling of the Effective Diffusivity in Composite Material", Defect and Diffusion Forum, Vols. 261-262, pp. 103-108, 2007