The transient current-potential response of the enzyme-catalyzed oxygen reduction reaction in biofuel cells is analyzed. The onedimensional nonlinear reaction-diffusion equation is solved analytically using the homotopy method for deriving the substrate concentrations and current densities pertaining to chronoamperometric response. The time required to obtain the steady state has been obtained and the influence of film thickness, diffusion coefficients, and enzyme characteristics has been deciphered. The equations are shown to be valid for experimental data on mediated electron transfer reactions of redox polymers containing osmium complexes. The substrate concentrations and current densities for supported, gas-diffusion and flow through electrodes are also reported.

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A mathematical model describing the reduction of Hydrogen peroxide (H 2 O 2 ) to water in a metal dispersed conducting polymer film is discussed. The model is based on a system of reaction-diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reaction. The approximate analytical expressions corresponding to the concentration of substrate and product for steady and non-steady state conditions have been obtained using a new approach to homotopy perturbation method (HPM). Approximate analytical expressions of the electrochemical oxidation current are also presented for steady and non-steady state conditions. The numerical simulation (Matlab program) response for concentration profiles was carried out and compared with the analytical results of this work and are found to be in good agreement. The influence of initial substrate concentration, the thickness of the film as well as the diffusion layer and kinetic parameters on the current response were investigated. A graphical procedure for estimating the kinetic parameters from the expression of the current response is also proposed.

Mathematical models of amperometric biosensors at three basic types of enzyme kinetics in nonstationary diffusion conditions are discussed. The models are based on nonstationary diffusion equations containing a linear term related to the first‐order and nonlinear term related to the Michaelis–Menten and ping–pong of the enzymatic reaction mechanism. In this paper, we obtain approximate closed‐form analytical solutions for the nonlinear equations under steady‐state condition by using the homotopy analysis method. Analytical expressions for concentrations of substrate and cosubstrate and corresponding current response have been derived for all possible values of parameters. Furthermore, in this work, the numerical simulation of the problem is also reported using Scilab/MATLAB program. An agreement between analytical and numerical results is noted.

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