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On a Multiphase Multicomponent Model of Biofilm Growth

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Abstract

Biofilms are formed when free-floating bacteria attach to a surface and secrete polysaccharide to form an extracellular polymeric matrix (EPS). A general model of biofilm growth needs to include the bacteria, the EPS, and the solvent within the biofilm region Ω(t), and the solvent in the surrounding region D(t). The interface between the two regions, Γ(t), is a free boundary. In this paper, we consider a mathematical model that consists of a Stokes equation for the EPS with bacteria attached to it, a Stokes equation for the solvent in Ω(t) and another for the solvent in D(t). The volume fraction of the EPS is another unknown satisfying a reaction-diffusion equation. The entire system is coupled nonlinearly within Ω(t) and across the free surface Γ(t). We prove the existence and uniqueness of a solution, with a smooth surface Γ(t), for a small time interval.

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Authors and Affiliations

  1. Mathematical Biosciences Institute, and Department of Mathematics, Ohio State University, Columbus, OH, 43210, USA

    Avner Friedman & Chuan Xue

  2. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Bei Hu

Authors
  1. Avner Friedman
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  2. Bei Hu
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  3. Chuan Xue
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Correspondence to Chuan Xue.

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Communicated by D. Kinderlehrer

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Friedman, A., Hu, B. & Xue, C. On a Multiphase Multicomponent Model of Biofilm Growth. Arch Rational Mech Anal 211, 257–300 (2014). https://doi.org/10.1007/s00205-013-0665-1

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  • DOI: https://doi.org/10.1007/s00205-013-0665-1

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