A hybrid discrete–continuum framework for modelling filtration

Griffiths, I. M. and Stewart, P. S. (2022) A hybrid discrete–continuum framework for modelling filtration. Journal of Membrane Science, 647, 120258. (doi: 10.1016/j.memsci.2022.120258)

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Typical mathematical frameworks for modelling the blocking behaviour of a filter due to particle deposition fall into one of two categories: a continuum approximation, whereby particle deposition is assumed to occur in such a way that all pores in the material are in the same state of blocking at any given time; or a discrete model, where blocking is treated as individual events in both space and time. While the former is computationally inexpensive, the latter allows for variation from pore to pore. This pore-to-pore variation has been shown to provide a qualitative change in the observed filtration behaviour that is essential to reproduce experimental observations. We present a hybrid model that describes the location of particle depositions in a continuum manner while retaining a discrete, stochastic component to capture the time at which a blocking event occurs. The model is able to grade between the aforementioned extreme continuum and discrete cases through a parameter that controls the spatial extent of a blocking event. This enables us to uncover the way in which the nature of the blocking process changes between these two pre-existing models. The model also captures the key ingredients of a fully discrete stochastic model at a fraction of the computational cost, making it ready to use to describe other complex filtration scenarios.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Stewart, Professor Peter
Authors: Griffiths, I. M., and Stewart, P. S.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Membrane Science
ISSN (Online):1873-3123
Published Online:22 January 2022
Copyright Holders:Copyright © 2022 Elsevier B.V.
First Published:First published in Journal of Membrane Science 647: 120258
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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