Formal analysis of isothermal reaction/diffusion in a defined general geometry
MEG Lyons, R. Joy Salomi, L. Rajendran
Abstract
Theoretical investigation into the steady-state amperometric response of a polymer-modified electrode system with Michaelis-Menten kinetics is presented and discussed. The interplay between substrate diffusion within the polymer matrix and substrate reaction at the catalytic polymer sites is generally investigated. An approximate analytical expression for the substrate concentration profiles in terms of modified Bessel functions for a general geometry (planar, cylindrical and spherical) and the accompanying current response and effectiveness factor is produced. It has been revealed that the modified Bessel function solution can represent the effectiveness factor for a catalyst pellet for an irreversible reaction regardless of the pellet's shape. The geometric shape parameter, which describes the shape of the pellet, determines the order of the Bessel function. Various kinetic cases for different limiting circumstances are also discussed. For all connected regions of the pellet, the geometrical form parameter values are within the range of 0 - 2. The amperometric current response and substrate concentration predicted from the theoretical model are in excellent agreement with the obtained numerical results