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A Chemostat Model with Wall Attachment: The Effect of Biofilm Detachment Rates on Predicted Reactor Performance

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Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Abstract

We consider a previously introduced mathematical model of chemostat with suspended and wall attached growth and exchange of biomass via biofilm detachment and reattachment. In this study we investigate the role of the specific choice of a biomass detachment criterion. We find that this choice does greatly affect output parameters such as biomass in the system, but it does not affect strongly effluent concentration and hence the prediction of reactor performance.

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References

  1. Abbas, F., Eberl, H.J.: Investigation of the role of mesoscale detachment rate expressions in a macroscale model of a porous medium biofilm Reactor, Int. J. Biomath. Biostat. 2, 123–143 (2013)

    MATH  Google Scholar 

  2. Abbas, F., Sudarsan, R., Eberl, H.J.: Longtime behaviour of one-dimensional biofilm models with shear dependent detachment rates. Math. Biosci. Eng. 9, 215–239 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bester, E., Edwards, E.A., Wolfaardt, G.M.: Planktonic cell yield is linked to biofilm development. Can. J. Microbiol. 55, 1195–1206 (2009)

    Article  Google Scholar 

  4. Duddu, R., Chopp, D.L., Moran, B: A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment. Biotechnol. Bioeng. 103, 92–104 (2008)

    Article  Google Scholar 

  5. Emerenini, B.O., Hense, B.A., Kuttler, C., Eberl, H.J.: A mathematical model of quorum sensing induced biofilm detachment. PLoS ONE 10 (7), e0132385 (2015)

    Article  Google Scholar 

  6. Hunt, S.M., Hamilton, M.A., Sears, J.T., Harkin, G., Reno, J: A computer investigation of chemically mediated detachment in bacterial biofilms. J. Microbiol. 149, 1155–1163 (2003)

    Article  Google Scholar 

  7. Jones, D., Kojouharov, H.V., Le, D., Smith, H.L.: The Freter model: a simple model of biofilm formation. Math. Biol. 47, 137–152 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kommendal, R., Bakke, R.: Modeling Pseudomonas aeruginosa biofilm detachment. HIT Working Paper no 3/2003 (2003)

    Google Scholar 

  9. Masic, A., Eberl, H.J.: Persistence in a single species CSTR model with suspended flocs and wall attached biofilms. Bull. Math. Biol. 74, 1001–1024 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Morgenroth, E.: Detachment: an often-overlooked phenomenon in biofilm research and modeling. In: Wuertz, S., et al. (eds.) Biofilms in Wastewater Treatment, pp 246–290. IWA Publishing, London (2003)

    Google Scholar 

  11. Rittmann, B.E.: The effect of shear stress on biofilm loss rate. Biotechnol. Bioeng. 24, 501–506 (1982)

    Article  Google Scholar 

  12. Rittmann, B.E, McCarty, P.L.: Environmental Biotechnology. McGraw-Hill, Boston (2001)

    Google Scholar 

  13. Solano, C., Echeverz, M., Lasa, I.: Biofilm dispersion and quorum sensing. Curr. Opin. Microbiol. 18, 96–104 (2014)

    Article  Google Scholar 

  14. Stemmons, E.D., Smith, H.L.: Competition in a chemostat with wall attachment. SIAM J. Appl. Math. 61, 567–595 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Walter, W.: Gewöhnliche Differentialgleichungen, 7th edn. Springer-Verlag, Berlin (2000)

    Book  MATH  Google Scholar 

  16. Wanner, O., Gujer, W.: A multispecies biofilm model. Biotechnol. Bioeng. 28, 314–328 (1986)

    Article  Google Scholar 

  17. Wanner, O., Eberl, H., Morgenroth, E., Noguera, D.R., Picioreanu, C., Rittmann, B., van Loosdrecht, M.: Mathematical modeling of biofilms. Scientific and Technical Report No.18. IWA Publishing, London (2006)

    Google Scholar 

  18. Xavier, J.B., Picioreanu, C., van Loosdrecht, M.C.M: A general description of detachment for multidimensional modeling of biofilms. Biotechnol. Bioeng. 91, 651–669 (2005)

    Article  Google Scholar 

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Acknowledgements

HJE was supported by NSERC Canada through the Discovery Grant Program and through the Canada Research Chairs Program.

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Authors and Affiliations

  1. EAWAG, Überlandstrasse 133, 8600, Dübendorf, Switzerland

    Alma Mašić

  2. University of Guelph, 50 Stone Rd E, Guelph, ON, N1G2W1, Canada

    Hermann J. Eberl

Authors
  1. Alma Mašić
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  2. Hermann J. Eberl
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Corresponding author

Correspondence to Hermann J. Eberl .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Montreal, Montreal, Québec, Canada

    Jacques Bélair

  2. Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada

    Ian A. Frigaard

  3. Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada

    Herb Kunze

  4. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roman Makarov

  5. MS2Discovery Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roderick Melnik

  6. Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada

    Raymond J. Spiteri

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Mašić, A., Eberl, H.J. (2016). A Chemostat Model with Wall Attachment: The Effect of Biofilm Detachment Rates on Predicted Reactor Performance. In: Bélair, J., Frigaard, I., Kunze, H., Makarov, R., Melnik, R., Spiteri, R. (eds) Mathematical and Computational Approaches in Advancing Modern Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-30379-6_25

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