We have used numerical simulations to mathematically model the experiments conducted by Liu and Cussler. In these experiments they measured the permeability of helium gas passing through a barrier membrane containing lithographically printed titanium flakes shaped as ribbons, squares and hexagons. The strict regularity in the geometry, size and orientation of the flakes enabled accurate modeling of the diffusion paths. In almost all cases, the numerical simulations predicted a larger diffusion barrier than was observed experimentally. We present arguments justifying our confidence in the numerical results along with some suggestions as to why the experimental results may differ. Finally, the numerical simulations are compared with previously published algebraic equations for estimating the permeability decrease arising from addition of impermeable flakes. (C) 2007 Elsevier B.V. All rights reserved.