Approximate Models of Microbiological Processes in a Biofilm Formed on Fine Spherical Particles

This paper concerns the dynamical modeling of the microbiological processes that occur in the biofilms that are formed on fine inert particles. Such biofilm forms e.g. in fluidized-bed bio-reactors, expanded bed biofilm reactors and biofilm air-lift suspension reactors. An approximate model that is based on the Laplace-Carson transform and a family of approximate models that are based on the concept of the pseudo-stationary substrate concentration profile in the biofilm were proposed. The applicability of the models to the microbiological processes was evaluated following Monod or Haldane kinetics in the conditions of dynamical biofilm growth. The use of approximate models significantly simplifies the computations compared to the exact one. Moreover, the stiffness that was present in the exact model, which was solved numerically by the method of lines, was eliminated. Good accuracy was obtained even for large internal mass transfer resistances in the biofilm. It was shown that significantly higher accuracy was obtained using one of the proposed models than that which was obtained using the previously published approximate model that was derived using the homotopy analysis method.

Automated summary

This paper focuses on the dynamical modeling of microbiological processes in biofilms formed on fine inert particles. Approximate models based on the Laplace-Carson transform and a family of approximate models based on the concept of pseudo-stationary substrate concentration profiles were proposed. The models were evaluated for their applicability to microbiological processes using Monod or Haldane kinetics under conditions of dynamic biofilm growth. The use of approximate models simplifies computations and eliminates stiffness compared to the exact model. The proposed models achieved higher accuracy than the previously published approximate model derived using the homotopy analysis method.