Computational analysis of transport across flake-filled composites of realistic microstructure

Abstract

In this paper we present the results of a computational study of diffusion across disordered flake composites in which the flakes are misaligned with respect to the direction of bulk diffusion. We evaluate the effect of flake orientation as well as the influence of boundary conditions and unit-cell types on the predicted barrier properties. Flake orientation impacts very significantly on the barrier properties in flake-filled composites, and usually the key objective in their fabrication is to orient them as close as possible to being perpendicular to the direction of macroscopic diffusion. Our computations are carried out in two-dimensional, doubly-periodic unit cells, each containing up to 3000 individual flake cross-sections. We consider high aspect ratio (α) systems with α=1000, from the dilute (αφ=0.01) and into the very concentrated (αφ=40) regime. The effective diffusivity of the corresponding unit cells is computed from the imposed concentration difference and the computed mass flux, using Fick's Law. We show that use of cyclic boundary conditions and doubly-periodic unit cells results in effective diffusivities which are in agreement with theory and invariant of the shape of the unit cell. We also show that the use of adiabatic boundary conditions produces erroneous results at high flake concentrations. Finally we compare our results to the predictions of existing literature models and find that the latter deviate significantly from computation at high flake concentrations.