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A simple model of biofilm growth in a porous medium that accounts for detachment and attachment of suspended biomass and their contribution to substrate degradation

Part of: Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  12 April 2018

HARRY J. GAEBLER  and
HERMANN J. EBERL
HARRY J. GAEBLER
Affiliation:
Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, CanadaN1G2W1 email: gaeblerh@uoguelph.ca, heberl@uoguelph.ca
HERMANN J. EBERL
Affiliation:
Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, CanadaN1G2W1 email: gaeblerh@uoguelph.ca, heberl@uoguelph.ca
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Abstract

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We derive a macroscopic model for biofilm formation in a porous medium reactor to investigate the role of suspended bacteria on reactor performance. The starting point is the mesoscopic one-dimensional Wanner–Gujer biofilm model. The following processes are included: hydrodynamics and transport of substrate in the reactor, biofilm and suspended bacteria growth in the pore space, attachment of suspended cells to the biofilm, and detachment of biofilm cells. The mesoscopic equations are up-scaled from the biofilm scale to the reactor scale, yielding a stiff system of balance laws, which we study numerically. We find that suspended bacteria and attachment can have a significant effect on biofilm reactor performance.

Keywords

Balance lawsbiofilmporous medium

MSC classification

Secondary: 35Q92: PDEs in connection with biology and other natural sciences 68U20: Simulation 92D25: Population dynamics (general)
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Special Issue 6: Biofilms , December 2018 , pp. 1110 - 1140
Copyright
Copyright © Cambridge University Press 2018 

Footnotes

†This study was financially supported through an Ontario Graduate Scholarship and an Arthur D. Latornell Graduate Scholarships awarded to HJG, and through an NSERC Discovery Grant (HJE). Computing resources were made available by an NSERC Research Tool and Infrastructure Grant awarded to HJE.

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