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Charge transport modelling of lithium ion batteries

Charge transport modelling of lithium ion batteries
Charge transport modelling of lithium ion batteries
This paper presents the current state of mathematical modelling of the electrochemical behaviour of lithium-ion batteries as they are charged and discharged. It reviews the models developed by Newman and co-workers, both in the cases of dilute and moderately- concentrated electrolytes and indicates the modelling assumptions required for their de- velopment. Particular attention is paid to the interface conditions imposed between the electrolyte and the active electrode material; necessary conditions are derived for one of these, the Butler-Volmer relation, in order to ensure physically realistic solutions. Insight into the origin of the differences between various models found in the literature is revealed by considering formulations obtained by using different measures of the electric potential. Materials commonly used for electrodes in lithium ion batteries are considered and the various mathematical models used to describe lithium transport in them discussed. The problem of up-scaling from models of behaviour at the single electrode particle scale to the cell scale is addressed using homogenisation techniques resulting in the pseudo 2D model commonly used to describe charge transport and discharge behaviour in lithium-ion cells. Numerical solution to this model is discussed and illustrative results for a common device are computed.
Lithium batteries, charge transport, modelling, P2D model, Newman model, Butler-Volmer equation, homogenisation
0956-7925
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Foster, Jamie
63b20d93-5aaa-4ee3-b63e-6c1e245093bb
Ranom, Rahifa
4d0388d2-9c91-415b-8eb9-4a68222ee66b
Please, Colin
24f463d8-2feb-4280-b27a-e98396d8a684
Ramos, Angel
3282ddba-497f-4019-995c-7f70eac9a2e3
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Foster, Jamie
63b20d93-5aaa-4ee3-b63e-6c1e245093bb
Ranom, Rahifa
4d0388d2-9c91-415b-8eb9-4a68222ee66b
Please, Colin
24f463d8-2feb-4280-b27a-e98396d8a684
Ramos, Angel
3282ddba-497f-4019-995c-7f70eac9a2e3

Richardson, Giles, Foster, Jamie, Ranom, Rahifa, Please, Colin and Ramos, Angel (2021) Charge transport modelling of lithium ion batteries. European Journal of Applied Mathematics. (In Press)

Record type: Article

Abstract

This paper presents the current state of mathematical modelling of the electrochemical behaviour of lithium-ion batteries as they are charged and discharged. It reviews the models developed by Newman and co-workers, both in the cases of dilute and moderately- concentrated electrolytes and indicates the modelling assumptions required for their de- velopment. Particular attention is paid to the interface conditions imposed between the electrolyte and the active electrode material; necessary conditions are derived for one of these, the Butler-Volmer relation, in order to ensure physically realistic solutions. Insight into the origin of the differences between various models found in the literature is revealed by considering formulations obtained by using different measures of the electric potential. Materials commonly used for electrodes in lithium ion batteries are considered and the various mathematical models used to describe lithium transport in them discussed. The problem of up-scaling from models of behaviour at the single electrode particle scale to the cell scale is addressed using homogenisation techniques resulting in the pseudo 2D model commonly used to describe charge transport and discharge behaviour in lithium-ion cells. Numerical solution to this model is discussed and illustrative results for a common device are computed.

Text
LiB_rev_revised_final - Accepted Manuscript
Restricted to Repository staff only until 7 March 2022.
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More information

Accepted/In Press date: 7 September 2021
Keywords: Lithium batteries, charge transport, modelling, P2D model, Newman model, Butler-Volmer equation, homogenisation

Identifiers

Local EPrints ID: 451390
URI: http://eprints.soton.ac.uk/id/eprint/451390
ISSN: 0956-7925
PURE UUID: 2bff5d3e-cf05-49b5-9f44-b1f0a0916dab

Catalogue record

Date deposited: 23 Sep 2021 16:39
Last modified: 23 Sep 2021 16:39

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Contributors

Author: Jamie Foster
Author: Rahifa Ranom
Author: Colin Please
Author: Angel Ramos

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