On mathemathical modeling of flow and fouling in elastic membrane filters*

In this work, we present a mathematical model of an elastic membrane filter with multi-layer bifurcating interior morphology. Two pervasive filtration forcing mechanisms are considered: (i) constant pressure drop; and (ii) constant flux through the membrane. We investigate how filtration behave under these two forcing mechanisms and describe the morphology change due to fouling coupled to membrane pore elasticity. Simulations are conducted under the constant flux condition and then switched to the constant pressure scenario after the pressure reaches a certain threshold. We also compare the results to membranes with no elasticity and analyze the filtration efficiency under different membrane materials.