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Rittmann, B.E and McCarty, P.L. (1981) Substrate flux into biofilms of any thickness. Journal of Environmental Engineering, 107, 831-849.

has been cited by the following article:

• TITLE: Approximate analytical solution of non-linear reaction diffusion equation in fluidized bed biofilm reactor

  AUTHORS: Seetharaman Usha, Shanmugarajan Anitha, Lakshmanan Rajendran

  KEYWORDS: Fluidized Bed Biofilm Reactor; Non-Linear Reaction Diffusion Equation; Phenol; Effectiveness Factor; Modified Adomian; Decomposition Method

  JOURNAL NAME: Natural Science, Vol.4 No.12, December 13, 2012

  ABSTRACT: A mathematical model for the fluidized bed biofilm reactor (FBBR) is discussed. An approximate analytical solution of concentration of phenol is obtained using modified Adomian decomposition method (MADM). The main objective is to propose an analytical method of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Theoretical results obtained can be used to predict the biofilm density of a single bioparticle. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation.