Derivation and analysis of an effective model for biofilm growth in evolving porous media

The present article deals with the growth of biofilms produced by bacteria within a saturated porous medium. Starting from the pore‐scale, the process is essentially described by attachment/detachment of mobile microorganisms to a solid surface and their ability to build biomass. The increase in bio...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2017-05, Vol.40 (8), p.2930-2948
Main Authors: Schulz, Raphael, Knabner, Peter
Format: Article
Language:English
Subjects:
biofilm growth
Biofilms
Biomass
Darcys law
Differential equations
evolving microstructure
Fluid dynamics
Fluid flow
fluid‐solid interactions
formal homogenization
Mathematical analysis
Ordinary differential equations
Parameters
Porosity
Porous media
Solid surfaces
Transport equations
weak solutions
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Summary:The present article deals with the growth of biofilms produced by bacteria within a saturated porous medium. Starting from the pore‐scale, the process is essentially described by attachment/detachment of mobile microorganisms to a solid surface and their ability to build biomass. The increase in biomass on the surface of the solid matrix changes the porosity and impedes flow through the pores. Using formal periodic homogenization, we derive an averaged model describing the process via Darcy's law and upscaled transport equations with effective coefficients provided by the evolving microstructure at the pore‐scale. Assuming, that the underlying pore geometry may be described by a single parameter, for example, porosity, the level set equation locating the biofilm‐liquid interface transforms into an ordinary differential equation (ODE) for the parameter. For such a setting, we state significant analytical and algebraic properties of these effective parameters. A further objective of this article is the analytical investigation of the resulting coupled PDE–ODE model. In a weak sense, unique solvability either global in time or at least up to a possible clogging phenomenon is shown. Copyright © 2016 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4211