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3-D Numerical Simulations of Biofilm Flows

Published online by Cambridge University Press:  28 May 2015

Chen Chen ,
Mingming Ren ,
Ashok Srinivansan  and
Qi Wang
Chen Chen
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29063, USA
Mingming Ren
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29063, USA Beijing Computational Science Research Center, Beijing, 100084, China
Ashok Srinivansan
Affiliation:
Department of Computer Science, Florida State University, Tallahassee, FL 32302, USA
Qi Wang*
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29063, USA
*
Corresponding author. Email: wangq@mailbox.sc.edu
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Abstract

We study the biofilm-flow interaction resulting in biofilm growth and deformation in a water channel in a 3-D setting using the phase field model developed recently. In this biofilm model, the biofilm made up of the EPS, bacteria and solvent is tracked using a biofilm volume fraction which vanishes outside the biofilm region. The interface between the biofilm and the solvent is marked by the zero level surface of the volume fraction measured from the biofilm to the solvent. The growth of the biofilm and the solvent-biofilm interaction with the top nutrient feeding condition is simulated in the viscous regime (growth regime) of the biofilm-solvent mixture flow. In quiescent flows, the model predicts growth patterns consistent with experimental findings for single or multiple adjacent biofilm colonies, in which the known mushroom shape growth pattern is obtained. Shear induced deformation in biofilms is simulated in a shear cell, providing a viable numerical evidence for using simulation tool to study biofilm growth and interaction dynamics in aqueous environment.

Keywords

65M0676D0576A0576T3076Z0592C05BiofilmCahn-Hilliard equationphase filedfinite difference methodmultiphase flow
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 1 , Issue 3 , August 2011 , pp. 197 - 214
Copyright
Copyright © Global-Science Press 2011

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References

[1]Beris, A. N. and Edwards, B., Thermodynamics of Flowing Systems, Oxford Science Publications, New York, 1994.Google Scholar
[2]Bird, R. B., Armstrong, R. C., Hassager, O., Dynamics of Polymeric Liquids, vol. 1 & 2, John Wiley and Sons, New York, 1987.Google Scholar
[3]Cahn, J. W. and Hilliard, J. E., Free energy of a nonuniform system. I: interfacial free energy, J. Chem. Phys., 28 (1958), 258–267.Google Scholar
[4]Cahn, J. W., Free energy of a nonuniform system. II. Thermodynamic basis, J. Chem. Phys., 30(5) (1959), 1121–1124.Google Scholar
[5]Cahn, J. W. and Hilliard, J. E., Free energy of a nonuniform system. III. Nucleation in a two- component incompressible fluid, J. Chem. Phys., 31 (1959), 688–699.Google Scholar
[6]Cogan, N. and Keener, J, The role of biofilm matrix in structural development, Math. Medicine Biol., 21(2) (2004),147–166.Google Scholar
[7]Costerton, B., Medical Biofilm Microbiology: The Role of Microbial Biofilms in Disease, Chronic Infections, and Medical Device Failure, CD-ROM, Montana State University, 2003.Google Scholar
[8]Doi, M. and Edwards, S. F., The Theory of Polymer Dynamics, Oxford Science Publications, Oxford, 1986.Google Scholar
[9]Doi, M., Introduction to Polymer Physics, Oxford Science Publications, Oxford, 1995.Google Scholar
[10]Flory, P. J., Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953.Google Scholar
[11]Hassett, D. J., Limbach, P. A., Hennigan, R. F., Klose, K. E., Hancock, R. E., Platt, M. D., Hunt, D. F., Bacterial biofilms of importance to medicine and bioterrorism: Proteomic techniques to identify novel vaccine components and drug targets, Expert Opin. Biol. Ther., 3(8) 2003, 1201-7.CrossRefGoogle ScholarPubMed
[12]Larson, R. G., The Rheology of Complex Fluids, Oxford University Press, New York, 1998.Google Scholar
[13]Lima, C. A. A., Ribeiro, R., Foresti, E., Zaiat, M., Morphological study of biomass during the start-up period of a fixed-bed anaerobic reactor treating domestic sewage, Brazilian Arch. Biol. Tech., 48(5) (2005), 841–849.Google Scholar
[14]Cogan, N. G. and Keener, J., Channel formation in gels, SIAM J. Appl. Math., 65(6) (2005), 1839–1854.Google Scholar
[15]Klapper, I., Effect of heterogeneous structure in mechanically unstressed biofilms on overall growth, Bull. Math. Biol., 66 (2004), 809–824.Google Scholar
[16]Alpkvist, E. and Klapper, I., A multidimensional multispecies continuum model for heterogeneous biofilm development, Bull. Math. Biol., 69(2) (2007), 765–789.Google Scholar
[17]Klapper, I, Rupp, C. J., Cargo, R., Purvedorj, B., Stoodley, P., Viscoelastic fluid description of bacterial biofilm material properties, Biotechnol. Bioeng., 80(3) (2002), 289–296.Google Scholar
[18]Klapper, I. and Dockery, J., Role of cohesion in the material description of biofilms, Phys. Rev. E, 74 (2006), 031902.Google Scholar
[19]Dockery, J. and Klapper, I., Finger formation in biofilm layers, SIAM J. Appl. Math., 62 (2002), 853–869.Google Scholar
[20]Laspidou, C. S. and Rittmann, B. E., Modeling biofilm complexity by including active and inert biomass and extracelluar polymeric substances, Biofilm, 1 (2004), 285–291.CrossRefGoogle Scholar
[21]Picioreanu, C., Loosdrecht, M. van, Heijnen, J., Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach, Biotechnol. Bioeng., 58 (1998), 101–116.Google Scholar
[22]Picioreanu, C., Loosdrecht, M. van, Heijnen, J., Multidimensional modelling of biofilm structure, Biotech. Microbial Biosystems: New Frontiers, Proceedings of the 8th International Symposium on Microbial Ecology, CR, Bell, Brylinsky, M., Johnson-Green, P. (eds), Atlantic Canada Society for Microbial Ecology, Halifax, Canada, 1999.Google Scholar
[23]Picioreanu, C., Kreft, M. J-U, Loosdrecht, M. van, Particle-based multidimensional multispecies biofilm models, Appl. Environ. Microbiol., May (2004), 3024–3040.Google Scholar
[24]Picioreanu, C., Xavier, J. B., Loosdrecht, M. van, Advances in mathematical modeling of biofilm structure, Biofilm, 1 (2004), 337–349.Google Scholar
[25]Pyo, J.-H. and Shen, J., Gauge-Uzawa methods for incompressible flows with variable density, J. Comp. Phys., 221 (2007), 181–197.Google Scholar
[26]Tanaka, H., Viscoelastic model of phase separation, Phys. Rev. E, 56(4) (1997), 4451–4462.Google Scholar
[27]Wolgemuth, C., Hoiczyk, E., Kaiser, D., Oster, G., How myxobacteria glide, Curr. Biol., 12 (2002), 369–377.Google Scholar
[28]Zhang, T., Cogan, N., Wang, Q., Phase-field models for biofilms. I. Theory and 1-D simulations, SIAM J. Appl. Math., 69(3) (2008), 641–669.Google Scholar
[29]Zhang, T. Y., Cogan, N., Wang, Q., Phase field models for biofilms. II. 2-D numerical simulations of biofilm-flow interaction, Commun. Comput. Phys., 4 (2008), 72–101.Google Scholar