Comparison of numerical simulations of barrier membranes with impermeable flakes

Steady-state permeation through membranes filled with impermeable flakes has been simulated numerically using a three-dimensional finite element solver. These numerical results are compared to other published numerical results and the equations that are commonly used to estimate the increased membrane resistance. We discuss the conditions for which these equations fail to give good predictions and why. In comparison with other numerical results, predictions of barrier function by the published Monte Carlo simulations are of variable quality in both two and three dimensions. We present a rationale for layer independence of the results and the implications this has on both the design of membranes and how many layers are needed to produce a layer-independent result.