Mathematical modeling of low-frequency oscillations observed in the diffusion of a substance through a membrane

In the diffusion process of a substance through a membrane under external steady-state conditions, low-frequency oscillations in its concentration are observed experimentally. A theoretical explanation for this phenomenon is given, and the results of mathematical modeling are presented. Models based on local membrane conductivity as a function of solution concentration are examined. It is shown in this case that positive feedback develops between changes in the flows and concentrations, and this determines the development of oscillations in the diffusion process of a substance.