1. A.P. Tran, J.H. Meldon, and E.D. Sontag. Transient diffusion into a bi-layer membrane with mass transfer resistance: Exact solution and time lag analysis. Frontiers in Chemical Engineering, 2:25, 2021. [PDF] Keyword(s): Bi-layer membrane, transient diffusion, heat conduction, mass transfer resistance. Abstract:

   Exact analytical and closed-form solutions to a problem involving transient diffusion in a bi-layer membrane with external transfer resistance are presented. In addition to the solutions of the transient response, the lead and lag times that are often of importance in the characterization of membranes and arise from the analysis of the asymptotic behavior of the mass permeated through the membrane are also provided. The solutions presented here are also compared to previously derived limiting cases of the diffusion in a bi-layer with an impermeable wall and constant concentrations at the upstream and downstream boundaries. Analysis of the time lag shows that this membrane property is independent of the direction of flow. Finally, an outline is provided of how these solutions, which characterize the response to a step function increase in concentration, can be also used to derive more complex input conditions. Adequately handling boundary layer effects has a wide array of potential applications such as the study of bi-layer undergoing phenomena of heat convection, gas film resistance, and absorption/desorption.

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