Influence of topology on performance of pore networks in membrane filters

Membrane filtration, a crucial and widely used industrial process, has attracted significant attention in mathematical modeling. Previous theoretical endeavors have posited the internal structure of membrane filters as a network of cylindrical pores, with fouling characterized as the gradual accumulation of fouling particles on the inner walls of these pores. Subsequently, membrane filter performance was evaluated employing metrics such as total throughput and accumulated foulant concentration throughout the filter's lifespan; and the correlation between such metrics and certain network properties, such as porosity and tortuosity, was analyzed. In this work, we analyze the correlation between the performance of such networks and their topological characteristics, with the objective of identifying the most pertinent topological features for membrane filter design for a fixed porosity setup. Persistent homology serves as our primary instrument for quantifying topological features. Specifically, we generate persistence diagrams for the pore networks utilizing thresholding based on the pore radii. The data encoded in these persistence diagrams are then statistically correlated with the performance metrics. We identify a strong correlation between total throughput and our topological measures and demonstrate explicitly that membrane topology significantly influences filtration performance, distinct from the effects of membrane geometry. We also report a strong positive correlation between total throughput and accumulated foulant concentration and find that, for fixed porosity setups as used in this work, tortuosity does not provide a useful measure for permeability.