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 γ s , γ E and m. The obtained analytical results are compared with the available limiting case results and are found to be in good agreement.