Analytical solution of the nonlinear initial value problem in one-stage thermophilic bioremediation process for the treatment of cheese whey

A mathematical model for thermophilic cheese whey bioremediation in a one- stage process is presented. The model is based on system of reaction diffusion equations containing a nonlinear term related to Michaelis-Menten kinetics of the enzymatic reaction. We present the approximate analytical solution the nonlinear differential equations that describe the rate of reaction coupled with a Michaelis-Menten kinetics law. The simple and closed form of analytical expressions for the concentrations of biomass, lactose, lactate, acetate have been derived by using new homotopy perturbation method for all values of parameter.  These results are compared with simulation results and are found to be in good agreement. The obtained results are valid for the whole solution domain.