Analytical Expressions for the Concentration and Current in the Reduction of Hydrogen Peroxide at a Metal-Dispersed Conducting Polymer Film

Abstract

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 Modelling and Application of Analytical Methods for A Non-Linear EC2E Mechanism in Rotating Disk Electrode

“…Eqns (19)(20) and Eqns (22)(23) are the approximate analytical expressions for non-linear steady-state reaction-convection-diffusion Eqns( 11)-( 13) in the EC2E mechanism obtained using Homotopy Perturbation Method and Taylor's Series Method. The computed numeric values are tabulated to check the efficiency of HPM and TSM solution with numerical result.…”

“…Non-linear problems are highly complex to solve analytically. Recently several analytical techniques have been used to solve non-linear equations like Homotopy Perturbation Method(HPM), the Variational iteration method, Taylor's series method(TSM) , the Akbari-Ganji method and the Hyperbolic function method [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Here we employed two methods HPM and TSM to solve Eqns(11-13).…”

“…Here bvp4c solver is used to developing the MATLAB program. Further, to check the efficiency of the method, the numerical solution is compared with the HPM solution and TSM solution given in Eqns (19)(20) and Eqns (22)(23), and the comparison results are tabulated as follows:…”

Mathematical Investigation of Non-Linear Reaction-Diffusion Equations on Multiphase Flow Transport in the Entrapped-Cell Photobioreactor Using Asymptotic Methods

“…Recent techniques for solving non-linear differential equations include using hyperbolic functions [21][22], Taylor's series approach [23][24], Adomian decomposition method [25], the homotopy analysis method [26], and variational iteration method [27]. Among these techniques, Ji-Huan's homotopy perturbation method (HPM) uses the linearization process to solve nonlinear equations [28][29][30]. This method would find and add a small parameter to the equation, utilizing the traditional perturbation method while eliminating its limitations.…”

Analytical Discussion and Sensitivity Analysis of Parameters of Magnetohydrodynamic Free Convective Flow in an Inclined Plate

“…Over the past two decades, HPM has been employed by many researchers to obtain approximate analytical solutions for many nonlinear engineering dynamical systems [7,18]. In this section, a modified homotopy perturbation method [23,28] is employed to obtain an analytical solution of the MHD free convective flow past an inclined plate under a steady state condition. The basic idea of the HPM is described in Appendix A.…”