Stochastic Modeling of Sieving in Membrane Filters

Membrane filtration of fluids is ubiquitous, and there is increasing interest from industrial practitioners in mathematical models that capture the complex nature of the process. Previous theoretical efforts include studies on material features of the membrane structure, and their connection to fluid mechanical properties and filtering efficiency. In this work, we focus on filtration through membranes whose internal structure is a network of pores through which foulant-laden fluid flows, with two modes of fouling operating simultaneously -- adsorption and sieving. Adsorption involves a slow accretion of foulant particles far smaller than pore sizes on the pore wall, while sieving concerns much larger particles that block pore entrances on a faster time scale. We model sieving as a stochastic process on the network with both a simulation-based approach and a mean-field probabilistic approach. Using each method, we investigate how the two fouling mechanisms interact and affect measures of membrane filter performance such as total throughput and accumulated foulant concentration in the filtrate. In addition, we show how the behavior changes when network geometric parameters are varied.