Skip to main content
SpringerLink
Log in

Numerical Simulation of Biofilm Formation in a Microchannel

  • Conference paper
  • First Online:
Numerical Mathematics and Advanced Applications ENUMATH 2017 (ENUMATH 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 126))

Included in the following conference series:

Abstract

The focus of this paper is the numerical solution of a mathematical model for the growth of a permeable biofilm in a microchannel. The model includes water flux inside the biofilm, different biofilm components, and shear stress on the biofilm-water interface. To solve the resulting highly coupled system of model equations, we propose a splitting algorithm. The Arbitrary Lagrangian Eulerian (ALE) method is used to track the biofilm-water interface. Numerical simulations are performed using physical parameters from the existing literature. Our computations show the effect of biofilm permeability on the nutrient transport and on its growth.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. E. Alpkvist, I. Klapper, A multidimensional multispecies continuum model for heterogeneous biofilm development. Bull. Math. Biol. 69, 765–789 (2007)

    Article  Google Scholar 

  2. G. Beavers, D. Joseph, Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30(1), 197–207 (1967)

    Article  Google Scholar 

  3. W. Deng et al., Effect of permeable biofilm on micro-and macro-scale flow and transport in bioclogged pores. Environ. Sci. Technol. 47(19), 11092–11098 (2013)

    Article  Google Scholar 

  4. J. Donea et al., Arbitrary Lagrangian–Eulerian methods. Encycl. Comput. Mech. 1(14), 413–437 (2004)

    Google Scholar 

  5. R.M. Donlan, Biofilms: microbial life on surfaces. Emerg. Infect. Dis. 8(9), 881–890 (2002)

    Article  Google Scholar 

  6. R. Duddu, D.L. Chopp, B. Moran, A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment. Biotechnol. Bioeng. 103, 92–104 (2009)

    Article  Google Scholar 

  7. H.C. Flemming, J. Wingender, The biofilm matrix. Nat. Rev. Microbiol. 8(9), 623–633 (2010)

    Article  Google Scholar 

  8. D. Landa-Marbán et al., A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments (2018, under review)

    Google Scholar 

  9. F. List, F.A. Radu, A study on iterative methods for solving Richards’ equation. Comput. Geosci. 20(341), 341–353 (2016)

    Article  MathSciNet  Google Scholar 

  10. A. Mikelic, W.Jäger, On the interface condition of Beavers, Joseph, and Saffman. SIAM J. Appl. Math. 60(4), 1111–1127 (2000)

    Article  MathSciNet  Google Scholar 

  11. I.S. Pop, F. Radu, P. Knabner, Mixed finite elements for the Richards equation: linearization procedure. J. Comput. Appl. Math. 168(1–2), 365–373 (2004)

    Article  MathSciNet  Google Scholar 

  12. F.A. Radu et al., A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media. J. Comput. Appl. Math. 289, 134–141 (2015)

    Article  MathSciNet  Google Scholar 

  13. P.G. Saffman, On the boundary condition at the surface of a porous medium. Stud. Appl. Math. 50(2), 93–101 (1971)

    Article  Google Scholar 

  14. R. Schulz, P. Knabner, Derivation and analysis of an effective model for biofilm growth in evolving porous media. Math. Meth. Appl. Sci. 40, 2930–2948 (2017)

    Article  MathSciNet  Google Scholar 

  15. T.L. van Noorden et al., An upscaled model for biofilm growth in a thin strip. Water Resour. Res. 46, W06505 (2010)

    Google Scholar 

  16. B. Vu et al., Bacterial extracellular polysaccharides involved in biofilm formation. Molecules 14(7), 2535–2554 (2009)

    Article  Google Scholar 

Download references

Acknowledgements

The work of DLM and FAR was partially supported by the Research Council of Norway through the projects IMMENS no. 255426 and CHI no. 255510. ISP was supported by the Research Foundation-Flanders (FWO) through the Odysseus programme (G0G1316N) and Statoil through the Akademia grant.

Author information

Authors and Affiliations

  1. University of Bergen, Bergen, Norway

    David Landa-Marbán, Iuliu Sorin Pop, Kundan Kumar & Florin A. Radu

  2. Faculty of Sciences, Hasselt University, Diepenbeek, Belgium

    Iuliu Sorin Pop

Authors
  1. David Landa-Marbán
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Iuliu Sorin Pop
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kundan Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Florin A. Radu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Landa-Marbán .

Editor information

Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Florin Adrian Radu

  2. University of Bergen, Bergen, Norway

    Kundan Kumar

  3. University of Bergen, Bergen, Norway

    Inga Berre

  4. University of Bergen, Bergen, Norway

    Jan Martin Nordbotten

  5. Hasselt University, Diepenbeek, Belgium

    Iuliu Sorin Pop

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Landa-Marbán, D., Pop, I.S., Kumar, K., Radu, F.A. (2019). Numerical Simulation of Biofilm Formation in a Microchannel. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_75

Download citation

Publish with us

Policies and ethics

Search

Navigation