A mathematical model for wetting and drying in filter membranes*

A filter membrane may be frequently used during its lifetime, with wetting and drying processes occurring in the porous medium for several cycles. During these cycles, the concentration distribution of molecules or contaminants and the medium morphology evolve. As a consequence, the filter performance ultimately deteriorates after several cycles. In this work, we formulate a coupled mathematical model for the wetting 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/wet interfaces due to evaporation. The model provides insights to the overall porous medium evolution over cycles of wetting and drying processes and predicts the timeline to discard the filter based on its optimum performance.