Approximate solutions of transient reaction-diffusion equations for second-order regeneration at spherical microelectrodes via HPM

The purpose of this study is to investigate the transient behavior of a second-order regeneration reaction at spherical microelectrodes, where nonlinear reaction–diffusion dynamics govern the system response. The research is designed to capture the interplay between electrochemical electron transfer and the subsequent homogeneous chemical reaction that regenerates the electroactive species, a process of considerable importance in electrochemical sensors and catalytic systems. The methodology combines analytical and numerical approaches: the homotopy perturbation method (HPM) is applied to derive approximate solutions for non-steady-state concentrations and current responses, while numerical simulations are carried out using Scilab to ensure accuracy and reliability. The approach effectively manages the inherent nonlinearity of the governing equations, offering tractable expressions for system behavior. The findings demonstrate strong agreement between the HPM-based analytical solutions and numerical simulations, confirming the validity of the proposed approach. The study concludes that HPM is a robust and efficient tool for analyzing nonlinear electrochemical systems. The practical implications highlight its potential application in the modeling and optimization of electrochemical devices, such as biosensors, microelectrodes, and catalytic fuel cells, where transient dynamics and regeneration mechanisms play a critical role.