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.
A mathematical model of an ideal biotrickling filter (BF) system that inoculates a recently identified strain of Chelatococcus daeguensis TAD1 and brings about efficient nitrogen oxide treatment is discussed. The proposed model is based on nonlinear mass transport equations at the gas–biofilm interface. Using Akbari–Ganji’s technique, approximate analytical expressions for the nitric oxide concentration in the gaseous and biofilm phases were developed for all feasible system parameters. In addition, to investigate the dynamic behaviour of the system, a numerical analysis of the problem is provided using MATLAB tools. To demonstrate this new approach, graphical data are provided and quantitatively discussed. This theoretical result has good agreement with the numerical simulation (MATLAB) results for the experimental values of parameters.
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