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A multiscale method to calculate filter blockage

Dalwadi, Mohit P.; Bruna, Maria; Griffiths, Ian M.

Authors

Mohit P. Dalwadi mohit.dalwadi@nottingham.ac.uk

Maria Bruna bruna@maths.ox.ac.uk

Ian M. Griffiths griffiths@maths.ox.ac.uk



Abstract

Filters that act by adsorbing contaminant onto their pore walls will experience a decrease in porosity over time, and may eventually block. As adsorption will generally be greater towards the entrance of a filter, where the concentration of contaminant particles is higher, these effects can also result in a spatially varying porosity. We investigate this dynamic process using an extension of homogenization theory that accounts for a macroscale variation in microstructure. We formulate and homogenize the coupled problems of flow through a filter with a near-periodic time-dependent microstructure, solute transport due to advection, diffusion and filter adsorption, and filter structure evolution due to the adsorption of contaminant. We use the homogenized equations to investigate how the contaminant removal and filter lifespan depend on the initial porosity distribution for a unidirectional flow. We confirm a conjecture made by Dalwadi et al. (Proc. R. Soc. Lond. A, vol. 471 (2182), 2015, 20150464) that filters with an initially negative porosity gradient have a longer lifespan and remove more contaminant than filters with an initially constant porosity, or worse, an initially positive porosity gradient. In addition, we determine which initial porosity distributions result in a filter that will block everywhere at once by exploiting an asymptotic reduction of the homogenized equations. We show that these filters remove more contaminant than other filters with the same initial average porosity, but that filters which block everywhere at once are limited by how large their initial average porosity can be.

Citation

Dalwadi, M. P., Bruna, M., & Griffiths, I. M. (in press). A multiscale method to calculate filter blockage. Journal of Fluid Mechanics, 809, https://doi.org/10.1017/jfm.2016.656

Journal Article Type Article
Acceptance Date Oct 5, 2016
Online Publication Date Nov 8, 2016
Deposit Date Oct 6, 2016
Publicly Available Date Nov 8, 2016
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Electronic ISSN 1469-7645
Publisher Cambridge University Press (CUP)
Peer Reviewed Peer Reviewed
Volume 809
DOI https://doi.org/10.1017/jfm.2016.656
Keywords Low-Reynolds-number flows, Porous media, Suspensions
Public URL http://eprints.nottingham.ac.uk/id/eprint/37382
Publisher URL https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/a-multiscale-method-to-calculate-filter-blockage/E1872752B049B760A9AED88188377F73
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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