Porosity and tortuosity relations as revealed by a mathematical model of biofilm structure

Journal of Theoretical Biology

Volumn 233, Issue 2, 2005, Pages 245-251

  Zacarias, G D ^a   Ferreira, C P ^a   Velasco Hernandez J X ^a  

^a INSTITUTO MEXICANO DEL PETRÓLEO   (Mexico)

Author keywords

Biofilm model; Biofilm porosity; Biofilm streamlines; Biofilm structure

Indexed keywords

BIOFILM;

ARTICLE; BIOFILM; CHEMICAL STRUCTURE; GEOMETRY; MATHEMATICAL MODEL; POROSITY; PRIORITY JOURNAL; VISCOSITY;

ANIMALS; BIOFILMS; COMPUTER SIMULATION; MODELS, BIOLOGICAL; POROSITY; VISCOSITY;

EID: 11144263563     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jtbi.2004.10.006     Document Type: Article

References (33)

1. Adler, P.M., Thovert, J.-F. 1998. Real porous media: local geometry and macroscopic properties. Appl. Mech. Rev. 51 (9), 537-585.
2. H. Aref Stirring by chaotic advection J. Fluid Mech. 143 1 1984
3. H. Aref The development of chaotic advection Phys. Fluids 14 4 2002 1315
4. Arks, M.A., Straube, A.V., 1996. Steady stokes flow with long-range correlations, fractal Fourier spectrum, and anomalus transport. Phys. Rev. Lett. 89 (24), 244101-1-244101-4.
5. G. Beer Programming the Boundary Element Method 2001 Wiley New York
6. Bishop, P.L., Rittman, B.E., 1995. Modelling heterogeneity in biofilms: report of the discussion session. Water Sci. Technol. 32 (8), 263-265.
7. Butkov, E., 1973. Mathematical Physics. Addison-Wesley Publishing Company, Reading, MA, pp. 520-547.
8. E.L. Cussler Diffusion Mass Transfer in Fluid Systems 1997 Cambridge University Press Cambridge
9. De Beer, D., Stoodley, P., 1995. Relation between the structure of an aerobic biofilm and transport phenomena. Water Sci. Technol. 32 (8), 11-18.
10. Dockery, J., Klapper, I., 2002. Finger formation in biofilm layers. Accelerated Electron. J. Soc. Ind. Appl. Math. 62 (3), 853-869.
11. Garcia López, L.A., Velga, M.C., Nogueira, R., Aparicio, A., Melo, L.F., 2003. A technique using a membrane flow cell to determine average mass transfer coefficients and tortuosity factors in biofilms. Water Sci. Technol. 47 (5), 61.
12. Heydorn, A., Kjaer, B.E., Hentzer, M., Parsek, M.R., Givskov, M., Molin, S., 2000. Experimental reproducibility in flow-chamber biofilms. Microbiology 146, 2409-2415.
13. Islas-Juarez, R., 2003. Effective diffusion in porous media. Master's Thesis, Universidad Autónoma de México.
14. Jayaraman, A., Mansfeld, F.B., Wood, T.K., 1999. Inhibiting sulfate-reducing bacteria in biofilms by expressing the antimicrobial peptides indolicidin and bactenecin. J. Ind. Microbiol. Biotechnol. 22, 167-175.
15. Koponen, A., Kataja, M., Timonen, J., 1996. Tortuous flow in porous media. Phys. Rev. E 54 (1), 406.
16. Koponen, A., Kataja, M., Timonen, J., 1997. Permeability and effective porosity of porous media. Phys. Rev. E 56 (3), 3319.
17. Kwok, W.K., Picioreanu, C., Ong, S.L., Van Loosdrecht, M.C.M., Ong, W.J., Heijnen, J.J., 1998. Influence of biomass production and detachment forces on biofilm structures in a biofilm airlift suspension reactor. Biotechnol. Bioeng. 58, 400-407.
18. Lewandowski, Z., Stoodley, P., Altobelli, S., Fukushima, E., 1994. Hydrodynamics and kinetics in biofilm systems recent advances and new problems. Water Sci. Technol. 29 (10-11), 223-229.
19. Ornek, D., Jayaraman, A., Syrett, B.C., Hsu, C.-H., Mansfeld, F.B., Wood, T.K., 2002. Pitting corrosion inhibition of aluminum 2024 by bacillus biofilms secreting polyaspartate or γ - xspolyglutamate. Appl. Micribiol Biotechnol. 58, 651-657.
20. Ornek, D., Wood, T.K., Hsu, C.-H., Mansfeld, F.B., 2002. Corrosion control using regenerative biofilms (ccurb) on brass in different media. Corros. Sci. 44, 2291-2302.
21. Picioreanu, C., Van Loosdrecht, M.C.M., Heijnen, J., 1998. A new combined differential-discrete cellular automaton approach for biofilm modeling: application for growth in gel beds. Biotechnol. Bioeng. 57 (6), 718-731.
22. Picioreanu, C., Van Loosdrecht, M.C.M., Heijnen, J., 1999. Discrete-differential modeling of biofilm structure. Water Sci. Technol. 39 (7), 115-122.
23. C. Picioreanu, and M.H.J. Van Loosdrecht A theoretical study on the effect of surface roughness on mass transport and transformation in biofilms Biotechnol. Bioeng. 68 4 2000 355 369
24. Picioreanu, C., Van Loosdrecht, M.C.M., Heijnen, J., 2000b. Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study. Biotechnol. Bioeng. 69 (5), 504-515.
25. Picioreanu, C., Van Loosdrecht, M.C.M., Heijnen, J., 2000c. Two-dimensional model of biofilm detachment caused by internal stress form liquid flow. Biotechnol. Bioeng. 72 (2), 205-218.
26. Raissa, M., D'Souza, Margolus, N.H., Smith, M.A., 2002. Dimension-splitting for simplifying diffusion in lattice-gas models. J. Statist. Phys. 107 (112), 401-422.
27. Ramanujan, S., Pluen, A., 2002. Diffusion and convection in collagen gels: implications for transport in the tumor interstitium. Biophys. J. 83, 1650.
28. Thurnheer, T., Gmur, R., Shapiro, S., Guggenheim, B., 2003. Mass transport of macro-molecules within an in vitro model of supragingival plaque. Adv. Eng. Mater. 69 (3), 1702.
29. Van Loosdrecht, M.C.M., Eikelboom, D., Gjaltema, A., Mulder, A., Tijhuis, L., Heijnen, J.J., 1995. Biofilm structure. Water Sci. Technol. 32 (8), 35-43.
30. Veldsink, J.W., Van Damme, R.M.J., 1995. The use dusty gas model for the description of mass transport with chemical reaction in porous media. Chem. Eng. J. 57, 115.
31. H.A. Videla Manual of Biocorrosion 1996 Lewis Publishers, Inc. Boca Raton
32. Wanner, O., Gujer, W., 1986. A multispecies biofilm model. Biotechnol. Bioeng. 28, 314-328.
33. Watnick, P., Kolter, R., 2000. Biofilm, city of microbes. J. Bacteriolo. 182 (10), 2675-2679.