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An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube
NORCE, Nygardsgaten 112, N-5008 Bergen, Norway.;Univ Bergen, Fac Math & Nat Sci, Dept Math, Allegaten 41,POB 7803, N-5020 Bergen, Norway..
NORCE, Nygardsgaten 112, N-5008 Bergen, Norway..
Karlstad Univ, Dept Math & Comp Sci, Univ Gatan 2, S-651 88 Karlstad, Sweden..
Univ Bergen, Fac Math & Nat Sci, Dept Math, Allegaten 41,POB 7803, N-5020 Bergen, Norway.;Hasselt Univ, Fac Sci, Campus Diepenbeek,Agoralaan Bldg D, B-3590 Diepenbeek, Belgium..
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2020 (English)In: Transport in Porous Media, ISSN 0169-3913, E-ISSN 1573-1634, Vol. 132, no 1, p. 83-112Article in journal (Refereed) Published
Abstract [en]

In this paper, we derive upscaled equations for modeling biofilm growth in porous media. The resulting macroscale mathematical models consider permeable multi-species biofilm including water flow, transport, detachment and reactions. The biofilm is composed of extracellular polymeric substances (EPS), water, active bacteria and dead bacteria. The free flow is described by the Stokes and continuity equations, and the water flux inside the biofilm by the Brinkman and continuity equations. The nutrients are transported in the water phase by convection and diffusion. This pore-scale model includes variations in the biofilm composition and size due to reproduction of bacteria, production of EPS, death of bacteria and shear forces. The model includes a water-biofilm interface between the free flow and the biofilm. Homogenization techniques are applied to obtain upscaled models in a thin channel and a tube, by investigating the limit as the ratio of the aperture to the length epsilon of both geometries approaches to zero. As epsilon gets smaller, we obtain that the percentage of biofilm coverage area over time predicted by the pore-scale model approaches the one obtained using the effective equations, which shows a correspondence between both models. The two derived porosity-permeability relations are compared to two empirical relations from the literature. The resulting numerical computations are presented to compare the outcome of the effective (upscaled) models for the two mentioned geometries.

Place, publisher, year, edition, pages
SPRINGER , 2020. Vol. 132, no 1, p. 83-112
Keywords [en]
Biofilm, Bioclogging, Mathematical model, Homogenization, Porosity-permeability relationships
Identifiers
URN: urn:nbn:se:kau:diva-77247DOI: 10.1007/s11242-020-01381-5ISI: 000513451300004OAI: oai:DiVA.org:kau-77247DiVA, id: diva2:1414215
Available from: 2020-03-12 Created: 2020-03-12 Last updated: 2020-03-12

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