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Understanding how porosity gradients can make a better filter using homogenization theory

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

Authors

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

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

Maria Bruna bruna@maths.ox.ac.uk



Abstract

Filters whose porosity decreases with depth are often more efficient at removing solute from a fluid than filters with a uniform porosity. We investigate this phenomenon via an extension of homogenization theory that accounts for a macroscale variation in microstructure. In the first stage of the paper, we homogenize the problems of flow through a filter with a near-periodic microstructure and of solute transport owing to advection, diffusion and filter adsorption. In the second stage, we use the computationally efficient homogenized equations to investigate and quantify why porosity gradients can improve filter efficiency. We find that a porosity gradient has a much larger effect on the uniformity of adsorption than it does on the total adsorption. This allows us to understand how a decreasing porosity can lead to a greater filter efficiency, by lowering the risk of localized blocking while maintaining the rate of total contaminant removal.

Journal Article Type Article
Publication Date Sep 23, 2015
Journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print ISSN 1364-5021
Electronic ISSN 1471-2946
Publisher Royal Society, The
Peer Reviewed Peer Reviewed
Volume 471
Issue 2182
APA6 Citation Dalwadi, M. P., Griffiths, I. M., & Bruna, M. (2015). Understanding how porosity gradients can make a better filter using homogenization theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2182), doi:10.1098/rspa.2015.0464
DOI https://doi.org/10.1098/rspa.2015.0464
Keywords homogenization, advection–diffusion–reaction, porous-media flow, depth filtration, porosity-graded filter, multi-scale modelling
Publisher URL http://rspa.royalsocietypublishing.org/content/471/2182/20150464
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../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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