Approximate Solution to the Diffusion-Reaction Problem with Nonlinear Kinetics in Transient Systems

Abstract

A method to obtain the approximate solution to the diffusion- reaction problem with nonlinear kinetics in transient systems is presented. The analytical solution to the equation that governs the process is based on the linearization of the kinetics expression through the Taylor series expansion above the surface particle concentration of the key component, which includes a critical radius to avoid negative concentration values. The present results for the average concentration were compared with the numerical solution of the exact problem and the error was less than ten percent for the power-law and Monod kinetics equation.