Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 77, Issue 5, Pages 1653-1677Publisher
SIAM PUBLICATIONS
DOI: 10.1137/16M108817X
Keywords
biofilm growth; chemotaxis; porous media; fluid-solid interactions; evolving microstructure; parabolic PDE
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The article concerns the growth of biofilms made by chemotactical bacteria within a saturated porous media. The increase of a biomass on the surface of the solid matrix changes the porosity and impedes the flow through the pores. By formal periodic homogenization we derive an averaged model describing the process via Darcy's law and upscaled transport equations with effective coefficients given by the evolving microstructure at the pore-scale. Based on the assumption of uniform evolve of the underlying pore geometry and slight self-diffusivity of the bacteria, solvability in a weak sense global in time or at least up to a possible clogging phenomenon is shown in the two-dimensional case. Furthermore,
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