Seventh Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 17 (2009), pp. 51-69.
A simple bioclogging model that accounts for spatial
spreading of bacteria
Laurent Demaret, Hermann J. Eberl, Messoud A. Efendiev,
Piotr Maloszewski
Abstract:
An extension of biobarrier formation and bioclogging models is presented
that accounts for spatial expansion of the bacterial population in the soil.
The bacteria move into neighboring sites if locally almost all of the
available pore space is occupied and the environmental conditions are
such that further growth of the bacterial population is sustained.
This is described by a density-dependent, double degenerate
diffusion-equation that is coupled with the Darcy equations and a
transport-reaction equation for growth limiting substrates.
We conduct computational simulations of the governing differential
equation system.
Published April 15, 2009.
Math Subject Classifications: 35K65, 35M10, 68U20, 76S05, 92D25.
Key Words: Bioclogging; biofilm; hydrodynamics; porous medium;
mathematical model; nonlinear-diffusion; simulation.
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Laurent Demaret
Institute of Biomathematics and Biometry,
Helmholtz Zentrum München
German Research Center for Environmental Health
Ingolstädter Landstr 1, 85764 Neuherberg, Germany
email: laurent.demaret@helmholtz-muenchen.de
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Hermann J. Eberl
Department of Mathematics and Statistics
University of Guelph, Guelph, ON, N1G 2W1, Canada
email: heberl@uoguelph.ca
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Messoud A. Efendiev
Institute of Biomathematics and Biometry,
Helmholtz Zentrum München
German Research Center for Environmental Health
Ingolstädter Landstr 1, 85764 Neuherberg, Germany
email: messoud.efendiyev@helmholtz-muenchen.de
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Piotr Maloszewski
Institute of Groundwater Ecology,
Helmholtz Zentrum München
German Research Center for Environmental Health
Ingolstädter Landstr 1, 85764 Neuherberg, Germany
email: maloszewski@helmholtz-muenchen.de
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