A new mathematical model for effectiveness factors in biofilm under toxic conditions

Abstract

A mathematical model for biofilms inhibition for steady-state conditions is discussed. The model involves the reaction–diffusion equations which have variety of non-linear reaction rate functions for various types of inhibition. Simple and an approximate polynomial expression of concentration and effectiveness factor are derived for general non-linear monod kinetics models. Comparison of the analytical results and numerical simulation is also presented. A good agreement between theoretical predictions and numerical results is observed. The concentrations and the effectiveness factors are also computed for the limiting cases of monod kinetics models. The optimum value of the parameters for effectiveness factors is also discussed.

Keywords

• Biofilms
• New approach to Homotopy perturbation method
• Mathematical modeling
• Non-linear reaction/diffusion equations
• Simulation