Mathematical analysis of non-linear boundary-value problems in reaction-diffusion model of chitosan-alginate microsphere using homotopy perturbation and Akbari-Ganji methods

• Published in: Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters 2024-09, Vol.11, p.100809, Article 100809
• Main Authors: Reena, A., Swaminathan, R.
• Format: Article
• Language: English
• Subjects: Akbari-Ganji method; Chitosan-alginate microsphere; Enzyme kinetics; Homotopy perturbation method; Mathematical modelling; Non-linear equations; Reaction-diffusion
• ISSN: 2666-8181; 2666-8181
• DOI: 10.1016/j.padiff.2024.100809

•Non-linear boundary-value problems in reaction-diffusion model of chitosan-alginate microsphere is discussed.•The model depicts the behaviour of hydrogen peroxide production and glucose oxidation in the chitosan-alginate microsphere in planar coordinates.•Approximate analytical expressions for the concentration of substrates glucose, oxygen, gluconic acid and hydrogen peroxide were derived.•The impact of reaction-diffusion and saturation parameters on concentrations and determination of flux and pH profiles are also investigated.•Asymptotic methods of homotopy perturbation and Akbari-Ganji methods are used to derive the analytical solutions. 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. [Display omitted]