Analytical expressions of concentration and current in homogeneous catalytic reactions at spherical microelectrodes: Homotopy perturbation approach

An analysis of reaction and diffusion within the homogeneous catalytic reactions at spherical microelectrodes are presented. This model contains a non-linear term related to reaction/diffusion parameters. The analytical expression of quasi-first- and second-order homogeneous catalytic reactions with equal diffusion coefficients at spherical microelectrodes under non-steady-state conditions are obtained by using Homotopy perturbation method. Simple and closed analytical expressions for concentration and current for short and medium time and small values of reaction/diffusion parameters are presented. He’s Homotopy perturbation method is used to give the approximate analytical solutions of coupled non-linear system of reaction–diffusion equations. The numerical solution of the problem is also reported using SCILAB software program. The analytical results are compared with our numerical results. A excellent agreement with simulation data is noted. The concentration and current for pseudo-first-order EC′ reaction at spherical electrode is also reported and compared with second-order homogeneous catalytic reactions.