Stochastic Modeling of Filtration with Sieving in Graded Pore Networks

2025-08-15

AI Summary

This study addresses the dynamic coupling between adsorption (for small particles) and size-based sieving (for large particles) in gradient-aperture membrane filtration. We propose a multiscale stochastic modeling framework that integrates continuum partial differential equations—governing transport and adsorption of small particles—with a discrete stochastic model—comprising Poisson particle arrival and biased random walks—to describe the sieving-driven migration of large particles through the pore network. Our approach reveals, for the first time, a critical phase-transition behavior in flux decline dominated by sieving, elucidates the onset and cessation mechanisms of adsorption–sieving competition within the aperture-gradient zone, and quantifies how aperture disparity modulates coupling strength. The model accurately predicts flux evolution trajectories and filter failure times under diverse fouling conditions, thereby establishing a theoretical foundation for structural optimization and lifetime prediction of gradient-aperture membranes.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

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.

Problem

• Modeling simultaneous adsorption and sieving fouling mechanisms
• Understanding coupling effects on graded pore filter performance
• Analyzing phase transition in filter lifetime with particle frequency

Innovation

• Stochastic modeling of graded pore networks
• Combined adsorption and sieving fouling mechanisms
• Poisson arrival process for particle transport