Analytical expression of concentrations of adsorbed CO molecules, O atoms and oxide oxygen

Chinnasamy Thangapandi,Lakshmanan Rajendran

doi:10.4236/ns.2013.53045

Abstract

A mathematical model of the oscillatory regimes of CO oxidation over plantinum-group metal catalysts are discussed. The model is based on nonstationary diffusion equation containing a nonlinear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents the analytical and numerical solution of the system of non-linear differential equations. Here the Homotopy perturbation method (HPM) is used to find out the analytical expressions of the concentration of CO molecules, O atom and oxide oxygen respectively. A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical and numerical results is observed.

Highlights

Rate auto-oscillations in a heterogeneous catalytic reaction were first discussed more than two decades ago [1,2,3]
Various mathematical models are used in detailed analysis of the mechanism of the rate oscillations in catalytic CO oxidation
Microscopic stochastic models by using the Monte Carlo method [13,14,15,16,17,18] one of the most interesting in theoretical investigation of the dynamics of fluctuating reaction systems. These stochastic models are based on detailed information concerning the elementary steps of the reaction, the structure of the catalyst surface, and the mobility of species in the adsorption layer

Summary

INTRODUCTION

Rate auto-oscillations in a heterogeneous catalytic reaction were first discussed more than two decades ago [1,2,3]. Various mathematical models are used in detailed analysis of the mechanism of the rate oscillations in catalytic CO oxidation These models are based on a set of nonlinear ordinary differential equations [4,5,6,7,8,9,10,11,12]. Microscopic stochastic models by using the Monte Carlo method [13,14,15,16,17,18] one of the most interesting in theoretical investigation of the dynamics of fluctuating reaction systems These stochastic models are based on detailed information concerning the elementary steps of the reaction, the structure of the catalyst surface, and the mobility of species in the adsorption layer. The purpose of the communication is to derive the analytical expression of θCO (t ) , θO (t ) , and θO∗ (t ) by solving the system of non-linear differential equation using Homotopy perturbation method

MATHEMATICAL FORMULATION OF BOUNDARY VALUE PROBLEM

STOCHASTIC AND DETERMINISTIC MODELS

ANALYTICAL EXPRESSION OF CONCENTRATION FOR STEADY STATE CONDITION

NUMERICAL SOLUTION

DISCUSSION

CONCLUSION