Mathematical modelling of a biofilm: The Adomian decomposition method


A mathematical modelling by a biofilm under steady state conditions is discussed. The nonlinear differential Equations in biofilm reaction is solved using the Adomian decomposition method. Approximate analytical expressions for substrate concentration have been derived for all values of parameters δ and SL. These analytical results are compared with the available numerical results and are found to be in good agreement.

Share and Cite:

Muthukaruppan, S. , Eswari, A. and Rajendran, L. (2013) Mathematical modelling of a biofilm: The Adomian decomposition method. Natural Science, 5, 456-462. doi: 10.4236/ns.2013.54059.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Christensen, B.E. and Characklis, W.G. (1990) Physical and chemical properties of biofilms. In: Characklis, W.G. and Marshall, K.C., Eds., Biofilm, Wiley, New York, 93-130.
[2] Skorokhodov, V.D. and Shestakova, S.I. (2004) Protection of nonmetalic materials from biocorrosion. Vysshaya Shkola, Moscow.
[3] Rittmann, B.E. and McCarty, P. L. (2000) Environmental biotechnology: Principles and applications. McGraw-Hill, Boston.
[4] Frank-Kamenetskii, D.A. (1987) Diffusion and heat transfer in chemical kinetics. Nauka, Moscow.
[5] Poltorak, O.M., Pryakhin, A.N. and Shhaitan, K.V. (1975) A general approach to solving kinetic problems. Vestnik Moskovskogo Universiteta, Seriya 2: Khimiya, 5, 536-543.
[6] Reznichenko, G.Yu. (2002) Lectures on mathematical models in biology. NITs Regulyarnaya i Khaoticheskaya Dinamika Part 1, Izhevsk.
[7] Dueck, J.H., Pyl’nik, S.V. and Min’kov, L.L. (2002) Modeling of the evolution of a biofilm with allowance for its erosion. In: Modeling of Processes in Synergetic Systems, Tomskogo Gosudarstvennogo Universiteta, Tomsk, 245-248.
[8] Dueck, J., Pylnik, S. and Minkov, L. (2004) Mathematical modelling of biofilm dynamics. In: Vestrate, W., Ed., Proceedings of European Symposium on Environmental Bio technology ESEB, Balkema, Belgium, Leiden, 545-547.
[9] Dueck, I.G., Pyl’nik, S.V. and Min’kov, L.L. (2005) Modeling the evolution of a water remediation biofilm with account for its erosion. Biophysics, 50, 445-453.
[10] Minkov, L.L., Pylnik, S.V. and Dueck, J.H. (2006) Steady state problem of substrate consumption in a biofilm for a square law of microbial death rate. Theoretical Foundations of Chemical Engineering, 40, 496-502. doi:10.1134/S004057950605006X
[11] Jaradat, O.K. (2008) Adomian decomposition method for solving Abelian differential equations. Journal of Applied Sciences, 8, 1962-1966. doi:10.3923/jas.2008.1962.1966
[12] Majid Wazwaz, A. and Gorguis, A. (2004) Solution of wave equation by Adomian decomposition method and the restrictions of the method. Applied Mathematics and Computation, 149, 807-814. doi:10.1016/S0096-3003(03)00186-3
[13] Makinde, O.D. (2007) Adomian decomposition approach to a SIR epidemic model with constant vaccination strategy. Applied Mathematics and Computation, 184, 842-848. doi:10.1016/j.amc.2006.06.074
[14] Siddiquia, A.M., Hameedb, M., Siddiquic, B.M. and Ghoric, Q.K. (2010) Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid. Communications in Nonlinear Science and Numerical Simulation, 15, 2388-2399. doi:10.1016/j.cnsns.2009.05.073
[15] Mohamed, M.A. (2010) Comparison differential trans formation technique with Adomian decomposition method for dispersive long-wave equations in (2+1)-dimensions. Applications & Applied Mathematics, 5, 148-166.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.