An evaluation of models and computational approaches for the barrier properties of coatings containing flakes of high aspect ratio

Abstract

We report on the results of a comprehensive two-dimensional computational study of diffusion across disordered flake composites. Our objective is (1) the evaluation of existing literature models for the effect of flake orientation and (2) the evaluation of the influence of boundary conditions and unit-cell types on the predicted barrier properties. Flake orientation is an important parameter affecting barrier properties in flake-filled composites, as the barrier efficacy of such systems depends significantly on the extent to which the flakes have been oriented as close as possible to being perpendicular to the direction of macroscopic diffusion. Our comparisons rely on an extensive set of computational results in two-dimensional, doubly periodic unit cells, each containing up to 3000 individual unidirectional flake cross-sections which are randomly placed and with their axes forming an angle (π/2 − θ) with the direction of macroscopic diffusion. A unique feature of our study is the consideration of high aspect ratio (α) systems with α = 100 and 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. In addition, we show that the use of adiabatic boundary conditions produces erroneous results at high flake concentrations. Comparison of our results with existing theoretical models revealed several shortcomings of the latter concerning both the effect of flake concentration (αφ) and the effect of the orientation angle (θ). The principal reason for the latter shortcoming is the fact that said models do not respect the rotational invariance of the diffusivity tensor. © 2018, American Coatings Association.