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A Multidimensional Multispecies Continuum Model for Heterogeneous Biofilm Development

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An Erratum to this article was published on 30 June 2007

An Erratum to this article was published on 30 June 2007

Abstract

We propose a multidimensional continuum model for heterogeneous growth of biofilm systems with multiple species and multiple substrates. The new model provides a deterministic framework for the study of the interactions between several spe1cies and their effects on biofilm heterogeneity. It consists of a system of partial differential equations derived on the basis of conservation laws and reaction kinetics. The derivation and key assumptions are presented. The assumptions used are a combination of those used in the established one dimensional model, due to Wanner and Gujer, and for the viscous fluid model, of Dockery and Klapper. The work of Wanner and Gujer in particular has been extensively used through the years, and thus this new model is an extension to several spatial dimensions of an already proven working model. The model equations are solved using numerical techniques, for purposes of simulation and verification. The new model is applied to two different biofilm systems in several spatial dimensions, one of which is equivalent to a system originally studied by Wanner and Gujer. Dimensionless formulations for these two systems are given, and numerical simulation results with varying initial conditions are presented.

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Authors and Affiliations

  1. Applied Mathematics Group, School of Technology and Society, Malmö University, SE-205 06, Malmö, Sweden

    Erik Alpkvista

  2. Department of Mathematical Sciences, Montana State University, Bozeman, MT, 59717, USA

    Isaac Klapper

  3. Center for Biofilm Engineering, Montana State University, Bozeman, MT, 59717, USA

    Isaac Klapper

Authors
  1. Erik Alpkvista
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  2. Isaac Klapper
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Correspondence to Erik Alpkvista.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s11538-007-9212-2

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Alpkvista, E., Klapper, I. A Multidimensional Multispecies Continuum Model for Heterogeneous Biofilm Development. Bull. Math. Biol. 69, 765–789 (2007). https://doi.org/10.1007/s11538-006-9168-7

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  • DOI: https://doi.org/10.1007/s11538-006-9168-7

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