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Open AccessArticle

Optimising Dead-End Cake Filtration Using Poroelasticity Theory

1
School of Mathematics and Statistics, University of Glasgow, 132 University Pl, Glasgow G12 8TA, UK
2
Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Oxford OX2 6GG, UK
*
Author to whom correspondence should be addressed.
Modelling 2021, 2(1), 18-42; https://doi.org/10.3390/modelling2010002
Received: 21 November 2020 / Revised: 20 December 2020 / Accepted: 21 December 2020 / Published: 9 January 2021
(This article belongs to the Section Modelling in Engineering Structures)
Understanding the operation of filters used to remove particulates from fluids is important in many practical industries. Typically the particles are larger than the pores in the filter so a cake layer of particles forms on the filter surface. Here we extend existing models for filter blocking to account for deformation of the filter material and the cake layer due to the applied pressure that drives the fluid. These deformations change the permeability of the filter and the cake and hence the flow. We develop a new theory of compressible-cake filtration based on a simple poroelastic model in which we assume that the permeability depends linearly on local deformation. This assumption allows us to derive an explicit filtration law. The model predicts the possible shutdown of the filter when the imposed pressure difference is sufficiently large to reduce the permeability at some point to zero. The theory is applied to industrially relevant operating conditions, namely constant flux, maximising flux and constant pressure drop. Under these conditions, further analytical results are obtained, which yield predictions for optimal filter design with respect to given properties of the filter materials and the particles. View Full-Text
Keywords: poroelasticity; filtration; heterogeneous media; caking poroelasticity; filtration; heterogeneous media; caking
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MDPI and ACS Style

Köry, J.; Krupp, A.U.; Please, C.P.; Griffiths, I.M. Optimising Dead-End Cake Filtration Using Poroelasticity Theory. Modelling 2021, 2, 18-42. https://doi.org/10.3390/modelling2010002

AMA Style

Köry J, Krupp AU, Please CP, Griffiths IM. Optimising Dead-End Cake Filtration Using Poroelasticity Theory. Modelling. 2021; 2(1):18-42. https://doi.org/10.3390/modelling2010002

Chicago/Turabian Style

Köry, J.; Krupp, A. U.; Please, C. P.; Griffiths, I. M. 2021. "Optimising Dead-End Cake Filtration Using Poroelasticity Theory" Modelling 2, no. 1: 18-42. https://doi.org/10.3390/modelling2010002

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