Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 471, Issue 2182, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2015.0464
Keywords
homogenization; advection-diffusion-reaction; porous-media flow; depth filtration; porosity-graded filter; multi-scale modelling
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Funding
- EPSRC [EP/K503769/1]
- Royal Society
- St Johns College, Oxford
- 2020 Science programme - EPSRC Cross-Disciplinary Interface Programme [EP/I017909/1]
- EPSRC [EP/I017909/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/I017909/1, EP/K503769/1] Funding Source: researchfish
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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.
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