Mathematical Modeling of Adsorption and Sieving in Membrane Pore Networks

In this work, we model membrane filtration in a network of pores with simultaneous adsorption and sieving, the two fouling mechanisms typically observed during the early stages of commercial filtration applications. In our model, first-principle partial differential equations model adsorptive fouling and species transport in the continuum in each pore, whereas sieving particles are assumed to follow a discrete Poisson arrival process. Our goal is to not only understand the individual influence of each fouling mode but also highlight the effect of their coupling on the performance of pore-radius graded banded filters. Our results suggest that, due to the discrete nature of pore blockage, sieving alters the convexity of the flux decline. Moreover, the difference between sieving particle sizes and the initial pore 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 filter lifetime as a function of the arrival frequency of sieving particles.