Mathematical Investigation of Non-Linear Reaction-Diffusion Equations on Multiphase Flow Transport in the Entrapped-Cell Photobioreactor Using Asymptotic Methods

A BSTRACT . The mathematical investigation of a multiphase flow transport model intended to clarify the interaction mechanism between reactions and diffusion processes in the gel granules containing the entrapped -cell photobioreactor Rhodopseudomonas palustris CQK 01 is presented in this research. The model uses two pertinent non-linear reaction -diffusion equations for biochemical interactions in the photobioreactor under steady-state circumstances to reflect the substrate and product concentration within the gel granules. The solid phase and liquid phase fluxes within the gel granules and their concentrations are analytically calculated using the asymptotic methods of the Akbari-Ganji method and the homotopy perturbation approach. Our analytical results and the numerical data obtained by MATLAB software are compared to determine accuracy. The analytical results agreed with the simulated results for all possible reaction -diffusion and saturation parameter values. In addition, the impacts of applying two limiting cases -saturated and unsaturated enzyme kinetics -were examined. The close correspondence between the simulated and analytical data demonstrates that the parameters in our suggested solution can be used to simulate the dynamic performance of a system.