Electrochemical modeling of steady-state diffusion-reaction processes with second-order irreversible kinetics

This work presents a mathematical model for steady-state mass transport in electrochemical systems involving isotropic diffusion and a second-order irreversible reaction within a porous particle of any geometry. The nonlinear governing equation reflects the interplay between diffusion and nonlinear kinetics, relevant to electrochemical reactors, porous electrodes, and biosensors. Two semi-analytical methods the Rajendran-Joy method (RJM) and Akbari-Ganji method (AGM) are employed to obtain approximate solutions, with trial functions optimized using electrochemical boundary conditions. Numerical simulations confirm the accuracy of the solutions. A parametric study explores the effects of reaction rates, isotropic diffusion, and geometry on concentration profiles, while sensitivity analysis identifies key parameters influencing transport-reaction behaviour. A simple and novel expression for the effectiveness factor, quantifying the interplay between reaction kinetics and mass transport within porous electrodes, is also presented. The results underscore the applicability of mathematical modeling in optimizing electrochemical system performance and advancing the understanding of nonlinear transport phenomena.