A hybrid differencing scheme for mass transport in electrochemical systems

Abstract

Purpose

To present a new hybrid differencing scheme for the numerical solution of an electromigration‐diffusion equation. The value of this work is evidenced by demonstrated improvement in the simulation of the Fu and Chan experiment when using the hybrid scheme.

Design/methodology/approach

A hybrid differencing scheme is developed which is based upon the solution of the pseudo‐steady state electromigration‐diffusion equation. In this scheme, a weighting parameter is calculated that varies the relative influence of the upwind node (relative to the direction of electromigration). This scheme significantly enhances the accuracy of electrochemical system mass transport models.

Findings

The hybrid scheme was compared to the upwind scheme. Use of the new hybrid scheme improved the accuracy of the model predictions by as much as 87 percent compared to the upwind scheme. However, use of the new scheme also increased the simulation time by between 6 and 43 percent. Deviations from electroneutrality and the presence of an activity coefficient gradient were detrimental to the stability of the hybrid scheme.

Research limitations/implications

This scheme is presented in the paper as an one‐dimensional (1D) scheme. However, it could be extended to more than 1D but some artificial viscosity may result.

Practical implications

The hybrid scheme developed and demonstrated herein is useful for researchers developing mass transport models of electrochemical systems. It has been proven capable of improving the accuracy of electrolyte mass transport models.

Originality/value

This is the first hybrid differencing scheme designed for the special characteristics of electrochemical mass transport systems. It greatly improves the accuracy of simulation results. This work is useful to those who mathematically model electrochemical systems.

Citation

Heppner, K.L. and Evitts, R.W. (2005), "A hybrid differencing scheme for mass transport in electrochemical systems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 15 No. 8, pp. 842-862. https://doi.org/10.1108/09615530510625110