Mathematical analysis of non-linear boundary-value problems in reaction-diffusion model of chitosan-alginate microsphere using asymptotic methods

Abstract

This article describes the non-linear reaction-diffusion model, which depicts the behaviour of hydrogen peroxide production and glucose oxidation in the chitosan-alginate microsphere. Analytical solutions of glucose, oxygen, gluconic acid and hydrogen peroxide concentrations in planar coordinates under steady-state circumstances are obtained for all reaction-diffusion parameters. The non-linear boundary value problem's approximate analytical expressions are obtained using asymptotic techniques based on the homotopy perturbation and Akbari-Ganji method. The exact and commonly used MATLAB program provided a numerical simulation. It is demonstrated that the resulting analytical expressions strongly agree with the numerical outcomes reported in the literature. Furthermore, determining hydrogen peroxide flux and pH profiles within the microspheres are also discussed. The theoretical findings make it possible to forecast and enhance the efficiency of enzyme kinetics.