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Mathematical modeling of substrate consumption in a biofilm: Solutions arrived using Akbari-Ganji method

This paper reports the mathematical modelling of substrate consumption by a biofilm. This model is based on a nonlinear equation comprising a nonlinear term connected to a square law of microbial death rate. This paper applies a powerful analytical method to solve the nonlinear equation, known as Akbari-Ganji’s method. A simple closed-form of analytical expression concentration of substrate and flux in the biofilm has been derived. The impact of several parameters on concentration and flux is explored, including biofilm thickness and bulk concentration. Numerical simulation for the concentration profile for steady-state conditions was compared with our analytical results. It is also observed that a satisfactory agreement has been obtained.