Analysis of mass transfer in composite materials with irregular interfaces

We present a theoretical analysis of permeation through composite bi-layer materials with an irregular interface. The conservation of mass equation for the permeating species is solved using both approximate analytic and numerical techniques. The approximate analytic solution is valid for small deviations of the interface from planarity. To assess the accuracy of the analytic solution, the analytic solution is compared to numerical approximations for a wide range of composite geometries and relative material permeabilities. The analytic solution proves to be accurate and easy to use. The analysis demonstrates that a composite material with an irregular interface possesses a higher permeability and slightly lower selectivity than an equivalent composite with a flat interface. Furthermore, the changes in permeability depend strongly on the magnitude of the interface irregularity but are relatively insensitive to the relative thickness of the two layers.