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A multidimensional multispecies continuum model for heterogeneous biofilm development

Alpkvist, Erik LU and Klapper, Isaac (2007) In Bulletin of Mathematical Biology 69(2). p.765-789
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 species 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... (More)
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 species 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. (Less)
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
biofilm, continuum model, mathematical modeling, multidimensional, multiple species
in
Bulletin of Mathematical Biology
volume
69
issue
2
pages
765 - 789
publisher
Springer
external identifiers
  • scopus:33847334391
ISSN
1522-9602
DOI
10.1007/s11538-006-9168-7
language
English
LU publication?
no
id
204804c3-c341-4650-809f-e9ec6a64f1bc (old id 944886)
alternative location
http://www.springerlink.com/content/ngj4t5h2m6550445/fulltext.pdf
date added to LUP
2008-01-24 09:28:24
date last changed
2017-10-22 03:38:38
@article{204804c3-c341-4650-809f-e9ec6a64f1bc,
  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 species 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.},
  author       = {Alpkvist, Erik and Klapper, Isaac},
  issn         = {1522-9602},
  keyword      = {biofilm,continuum model,mathematical modeling,multidimensional,multiple species},
  language     = {eng},
  number       = {2},
  pages        = {765--789},
  publisher    = {Springer},
  series       = {Bulletin of Mathematical Biology},
  title        = {A multidimensional multispecies continuum model for heterogeneous biofilm development},
  url          = {http://dx.doi.org/10.1007/s11538-006-9168-7},
  volume       = {69},
  year         = {2007},
}