Leveraging Electrical Network Models for Solving Fick's Second Law of Diffusion in Membrane Gas Permeation

The permeation of gases through membranes is a fundamental process with wide-ranging applications, from gas separation and fuel cell technology to respiratory physiology. Governed by Fick's second law of diffusion, the mathematical modelling of such transport processes often becomes analytically and computationally challenging, especially in heterogeneous, mixed matrix, or multilayered systems. To navigate these complexities, this study revisits and expands upon the use of electrical analogies as an intuitive and powerful modelling approach rooted in mid-20th-century analog computing. By leveraging the mathematical equivalence between diffusion and electrical conduction, we construct an equivalent electrical network that mirrors the transient behaviour of gas permeation across membranes. In this framework, concentration gradients are represented as voltage differences, diffusive fluxes as electrical currents, and diffusional resistances as circuit resistances. While traditional applications of electrical analogies have largely focused on steady-state phenomena, our approach enables dynamic analysis, offering conceptual clarity and computational efficiency. This methodology not only simplifies the solution of Fick's second law but also reinforces the enduring relevance of analogical thinking in modern engineering practice. Comparative results demonstrate that the equivalent electrical circuit closely aligns with both analytical and finite difference solutions, validating its effectiveness and accuracy.