On correlating topology and performance of pore networks in membrane filters*

Membrane filtration is an important and ubiquitous process in industrial applications, and there is a growing body of mathematical models that capture this complex process. Previous theoretical work models the internal structure of membrane filters as a network of cylindrical pores whose radii are drawn from a uniform distribution, with fouling modeled as an adsorption process; i.e. the gradual accretion of fouling particles on the inner walls of the pores. Simulation-based approaches are used to measure membrane filter performance, using metrics such as total throughput and accumulated foulant concentration. In the present work, we investigate the correlation between the performance of these networks and their topological properties, in order to discover optimal pore topologies for membrane filter design. We use persistent homology as our principal tool for quantifying topological features, where the radii of a network's pores are represented by a collection of two-dimensional points known as a persistence diagram. The data encoded in these persistence diagrams are then statistically correlated with the performance metrics, particularly with total throughput. We also compare the performance of uniformly and log-normally distributed pore radii, since real membrane filters are believed to have pores of log-normally distributed width. Previous findings for uniformly-distributed radii, relating total throughput to membrane porosity and accumulated foulant concentration to tortuosity, respectively, are compared to new findings with log-normally distributed radii.