The effect of flake orientational order on the permeability of barrier membranes: numerical simulations and predictive models

• A new analytical model for membrane diffusion is proposed.
• The model accounts for the effects of flake volume fraction, aspect ratio, orientation and orientational order.
• The model results after the assimilation of the order parameter proposed by Bharadwaj into the model by Lape et al.

This work presents results of numerical simulations along with the development of simple analytical forms aimed at predicting diffusivity in barrier membranes with randomly dispersed flakes. Simulations are performed using Boundary Element models of representative volume elements that account for the barrier microstructures with high level of detail. Microstructural features such as flake aspect ratio (αα) and volume fraction (ϕϕ) are varied in the range of practical interest (0.1≤αϕ≤50.1≤αϕ≤5). Numerical simulations also address the effects of the flake orientational order. Simulation results are used to develop a new model that predicts the elements of the diffusivity matrix as a function of flake arrangement. The basic idea behind the proposed model is to assimilate the parameter proposed by Bharadwaj to describe flake orientational order into the diffusivity model by Lape, which was originally developed for uniformly oriented flakes. The model predictions are shown to be consistent with theoretical limiting behaviors and with those of other models in the literature. The proposed model is among the few ones that accounts for the disorder in the flake orientation, which is found to have a noticeable impact on diffusivity in the direction parallel to the flake orientation.