Stochastic Modeling of Filtration with Sieving in Graded Pore Networks

TL;DR

This paper develops a stochastic model for filtration in graded pore networks, capturing the interplay of sieving and adsorption fouling mechanisms, revealing how pore size gradients and particle dynamics influence filter performance and lifetime.

Contribution

It introduces a coupled continuum-discrete model for fouling in graded pore filters, highlighting the impact of sieving and adsorption interactions on flux decline and filter lifetime.

Findings

Sieving alters the flux decline rate qualitatively.

Pore size differences influence fouling competition.

A phase transition in filter lifetime occurs with increased sieving particle arrival.

Abstract

We model filtration of a feed solution, containing both small and large foulant particles, by a membrane filter. The membrane interior is modeled as a network of pores, allowing for the simultaneous adsorption of small particles and sieving of large particles, two fouling mechanisms typically observed during the early stages of commercial filtration applications. In our model, first-principles continuum partial differential equations model transport of the small particles and adsorptive fouling in each pore, while sieving particles are assumed to follow a discrete Poisson arrival process with a biased random walk through the pore network. Our goals are to understand the relative influences of each fouling mode and highlight the effect of their coupling on the performance of filters with a pore-size gradient (specifically, we consider a banded filter with different pore sizes in each band). Our results suggest that, due to the discrete nature of pore blockage, sieving alters qualitatively the rate of the flux decline. Moreover, the difference between sieving particle sizes and the initial pore size (radius) in each band plays a crucial role in indicating the onset and disappearance of sieving-adsorption competition. Lastly, we demonstrate a phase transition in the filter lifetime as the arrival frequency of sieving particles increases.