Analytical solution of system of coupled non-linear reaction diffusion equations. Part II: Direct reaction of substrate at underlying microdisc surface

An analysis of the reaction and diffusion within polymer-modified ultramicroelectrodes is presented. This analysis contains a non-linear term related to Michaelis–Menten kinetics. In this paper, we obtain approximate analytical solutions for the non-linear equations that describe diffusion and the reaction within the polymer-modified ultramicroelectrode by employing the Homotopy perturbation method (HPM). Approximate analytical expressions for substrate and mediator concentration have been derived for all values of parameter γs,γEγs,γE and m. The obtained analytical results are compared with the available limiting case results and are found to be in good agreement.