On mathematical modeling of filtration and drying in filter membranes

In this work, we formulate a coupled mathematical model for the filtration and drying dynamics in a porous medium occurring consecutively. Our model accounts for the porous medium internal morphology (internal structure, porosity, etc.), the contaminant deposition, and the evolution of dry-fluid interfaces due to evaporation. An asymptotic model is derived based on the small aspect ratio of the thin filter membrane. The reduced model provides insights to the overall porous medium evolution over cycles of filtration and drying processes and predicts the timeline to discard the filter based on its optimum performance. Given the complexity of fluid boundary movements due to the filtration and drying processes, the reduced model still acts as an efficient prediction tool offering a tremendous reduction in computational costs.