A semianalytical method for simulating mass transport at channel electrodes

Abstract

A method for simulating electrode reactions in channel flow is developed and efficiently implemented in the symbolic algebra program Maple™. The steady-state convective diffusion equation for fully developed 2-D laminar (Poiseuille) flow past one or more electrodes in a channel is considered for a charge-transfer electrode reaction between two soluble species. The case where axial diffusion (along the channel, x direction) is neglected and the diffusivities are equal has an exact solution as an infinite series, in which each term is the product of an exponential in x and a confluent hypergeometric function in y (across the channel). The practical implementation consists of evaluating a finite number of terms and numerically evaluating the two parameters in each term. Sturm–Liouville (eigenfunction) theory is used to reliably find the parameters for arbitrary values of the rate constants. Comparison is made with results from a commercial software package that uses a finite-element method.