Investigating the roles of topology and geometry in pore network 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. We modify previous theoretical work to model the internal structure of membrane filters as a network of initially cylindrical pores whose radii are drawn from a log-normal 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 quantify membrane filter performance, using metrics such as total throughput and accumulated foulant concentration in the filtrate. In the presented work, we investigate the correlation between the performance of such pore networks and their topological properties, in order to discover optimal pore topologies for membrane filter design. We apply persistent homology as our principal tool, using super-level thresholding on the radii of a network's pores to represent the birth and death of key topological features as 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 identify a strong, purely topological effect on total throughput, which does not reduce to the effect of other, more well-understood pore network properties, such as pore radius distribution or number of pores.