Biofilm modeling in evolving porous media with Beavers‐Joseph condition

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2019-03, Vol.99 (3), p.n/a
• Main Author: Schulz, Raphael
• Format: Article
• Language: English
• Subjects: 35B27; 35R37; 74F10; 74Q15; 76S05; 76Zxx; Biofilms; Boundary conditions; Channels; Computational fluid dynamics; Darcys law; Evolution; Fluid flow; Porous media; Transport equations; Viscosity
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201800123

In this article, we derive an effective model for biofilm growth in a saturated porous medium. Several experimental investigations found out that biomass is in general very heterogeneous and contains in particular channels filled with fluid. These channels facilitate the transport of nutritive substances within the biofilm by advection. Referring to this, we model the biofilm itself at the pore‐scale as a porous medium. Hence the starting point at the pore‐scale is a Darcy‐Stokes system, where the Beavers‐Joseph boundary condition at the corresponding interface is proposed. 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. Based on the assumption of uniform evolve of the underlying pore geometry, solvability in a weak sense global in time or at least up to a possible clogging phenomenon is stated. In this article, we derive an effective model for biofilm growth in a saturated porous medium. Several experimental investigations found out that biomass is in general very heterogeneous and contains in particular channels filled with fluid. These channels facilitate the transport of nutritive substances within the biofilm by advection. Referring to this, we model the biofilm itself at the pore‐scale as a porous medium. Hence the starting point at the pore‐scale is a Darcy‐Stokes system, where the Beavers‐Joseph boundary condition at the corresponding interface is proposed. 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. Based on the assumption of uniform evolve of the underlying pore geometry, solvability in a weak sense global in time or at least up to a possible clogging phenomenon is stated.