Network and Stochastic Modeling of Membrane Filtration with Multiple Fouling Modes
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Membrane filters are in widespread daily use, and there are commercial incentives to optimize their filtration performance (improve impurity retention while increasing lifetime, for example). We present a simple model of a membrane filter, in which the interior pore structure is represented as a randomly generated network of cylindrical pores. Impurity-laden feed solution passes through the pore network and deposits its impurity particles via two distinct fouling mechanisms: (i) small particles are transported and attracted to pore walls, shrinking the pores; and (ii) large particles are transported by flow through the network until they reach a pore too small to transit (which is then blocked). Our study focuses on how the geometric details of the pore network (e.g. porosity, tortuosity, pore size distribution) influence filter performance. We present statistically-averaged simulations showing how filter performance changes as key design features of the pore network are changed, and in particular, how a pore size gradient in the depth of the filter may be harnessed to optimize filtration outcomes.
