Analytical expressions for the concentrations of substrate, oxygen and mediator in an amperometric enzyme electrode

The theoretical model of Martens and Hall [N. Martens, E.A.H. Hall, Model for an immobilized oxidase enzyme electrode in the presence of two oxidants, Anal. Chem. 66 (1994) 2763–2770] in an immobilized oxidase enzyme electrodes is discussed. This model contains a non-linear term related to enzyme reaction system. In this paper, we obtain approximate analytical solutions for the non-linear equations under steady-state condition by using the homotopy perturbation method (HPM) and homotopy analysis method (HAM). Simple and approximate polynomial expressions for the concentration of substrate, oxygen, reduced mediator and current were obtained in terms of Thiele moduli and the normalized surface concentrations of species. 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.