The University of Southampton
University of Southampton Institutional Repository

Time-dependent modelling and asymptotic analysis of electrochemical cells

Time-dependent modelling and asymptotic analysis of electrochemical cells
Time-dependent modelling and asymptotic analysis of electrochemical cells
A (time-dependent) model for an electrochemical cell, comprising a dilute binary electrolytic solution between two flat electrodes, is formulated. The method of matched asymptotic expansions (taking the ratio of the Debye length to the cell width as the small asymptotic parameter) is used to derive simplified models of the cell in two distinguished limits and to systematically derive the Butler–Volmer boundary conditions. The first limit corresponds to a diffusion-limited reaction and the second to a capacitance-limited reaction. Additionally, for sufficiently small current flow/large diffusion, a simplified (lumped-parameter) model is derived which describes the long-time behaviour of the cell as the electrolyte is depleted. The limitations of the dilute model are identified, namely that for sufficiently large half-electrode potentials it predicts unfeasibly large concentrations of the ion species in the immediate vicinity of the electrodes. This motivates the formulation of a second model, for a concentrated electrolyte. Matched asymptotic analyses of this new model are conducted, in distinguished limits corresponding to a diffusion-limited reaction and a capacitance-limited reaction. These lead to simplified models in both of which a system of PDEs, in the outer region (the bulk of the electrolyte), matches to systems of ODEs, in inner regions about the electrodes. Example (steady-state) numerical solutions of the inner equations are presented.
butler–volmer equation, electrolyte, matched asymptotic expansions
0022-0833
239-275
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
King, J.R.
97bc791f-b608-4adb-a69a-ae992574b7b2
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
King, J.R.
97bc791f-b608-4adb-a69a-ae992574b7b2

Richardson, Giles and King, J.R. (2007) Time-dependent modelling and asymptotic analysis of electrochemical cells. Journal of Engineering Mathematics, 59 (3), 239-275. (doi:10.1007/s10665-006-9114-6).

Record type: Article

Abstract

A (time-dependent) model for an electrochemical cell, comprising a dilute binary electrolytic solution between two flat electrodes, is formulated. The method of matched asymptotic expansions (taking the ratio of the Debye length to the cell width as the small asymptotic parameter) is used to derive simplified models of the cell in two distinguished limits and to systematically derive the Butler–Volmer boundary conditions. The first limit corresponds to a diffusion-limited reaction and the second to a capacitance-limited reaction. Additionally, for sufficiently small current flow/large diffusion, a simplified (lumped-parameter) model is derived which describes the long-time behaviour of the cell as the electrolyte is depleted. The limitations of the dilute model are identified, namely that for sufficiently large half-electrode potentials it predicts unfeasibly large concentrations of the ion species in the immediate vicinity of the electrodes. This motivates the formulation of a second model, for a concentrated electrolyte. Matched asymptotic analyses of this new model are conducted, in distinguished limits corresponding to a diffusion-limited reaction and a capacitance-limited reaction. These lead to simplified models in both of which a system of PDEs, in the outer region (the bulk of the electrolyte), matches to systems of ODEs, in inner regions about the electrodes. Example (steady-state) numerical solutions of the inner equations are presented.

Text
Journal_of_Engineering_Mathematics_2007_Richardson.pdf - Other
Download (635kB)

More information

Published date: 2007
Keywords: butler–volmer equation, electrolyte, matched asymptotic expansions

Identifiers

Local EPrints ID: 156353
URI: http://eprints.soton.ac.uk/id/eprint/156353
ISSN: 0022-0833
PURE UUID: fdde3017-6fef-422e-ba67-4d0167352a33

Catalogue record

Date deposited: 03 Jun 2010 09:25
Last modified: 08 Jan 2022 08:38

Export record

Altmetrics

Contributors

Author: J.R. King

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×