Mathematical modeling of thin, adhesive, microbial biocatalytic coatings for high intensity oxidations in multi-phase microchannel bioreactors: Hyperbolic function method.

A mathematical model of a multi-phase microchannel bioreactor is discussed. Further, the effect of oxygen diffusion on the concentration profile and effectiveness response was examined. Analytical expressions about the oxygen concentration profile and effectiveness were reported for all possible values of the reaction diffusion and the saturation parameters. These analytical results were found to be in good agreement with numerical simulations (MATLAB). Moreover, here we employ the Hyperbolic function method to solve the non-linear reaction/diffusion equation. This method's main advantage is obtaining an accurate solution by simple algebraic calculations. The influence of the parameters on the concentration and effectiveness factor is also discussed. [ABSTRACT FROM AUTHOR]