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Understanding rapid charge and discharge in nano-structured lithium iron phosphate cathodes

Part of: Equations and systems of special type Representations of solutions Optics, electromagnetic theory - General Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  01 March 2021

M. CASTLE Open the ORCID record for M. CASTLE [Opens in a new window] ,
G. RICHARDSON  and
J. M. FOSTER
M. CASTLE
Affiliation:
School and Mathematics and Physics, University of Portsmouth, Lion Terrace, PO1 3HF, UK email: michael.castle@port.ac.uk
G. RICHARDSON
Affiliation:
Mathematical Sciences, University of Southampton, University Rd., SouthamptonSO17 1BJ, UK email: g.richardson@soton.ac.uk The Faraday Institution, Quad One, Becquerel Avenue, Harwell Campus, Didcot OX11 0RA, UK email: jamie.michael.foster@gmail.com
J. M. FOSTER
Affiliation:
School and Mathematics and Physics, University of Portsmouth, Lion Terrace, PO1 3HF, UK email: michael.castle@port.ac.uk The Faraday Institution, Quad One, Becquerel Avenue, Harwell Campus, Didcot OX11 0RA, UK email: jamie.michael.foster@gmail.com
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Abstract

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A Doyle–Fuller–Newman (DFN) model for the charge and discharge of nano-structured lithium iron phosphate (LFP) cathodes is formulated on the basis that lithium transport within the nanoscale LFP electrode particles is much faster than cell discharge, and is therefore not rate limiting. We present some numerical solutions to the model and show that for relevant parameter values, and a variety of C-rates, it is possible for sharp discharge fronts to form and intrude into the electrode from its outer edge(s). These discharge fronts separate regions of fully utilised LFP electrode particles from those that are not. Motivated by this observation an asymptotic solution to the model is sought. The results of the asymptotic analysis of the DFN model lead to a reduced order model, which we term the reaction front model (or RFM). Favourable agreement is shown between solutions to the RFM and the full DFN model in appropriate parameter regimes. The RFM is significantly cheaper to solve than the DFN model, and therefore has the potential to be used in scenarios where computational costs are prohibitive, e.g. in optimisation and parameter estimation problems or in engineering control systems.

Keywords

Lithium-ion batteryPorous Electrode TheoryNewman ModelMatched Asymptotic ExpansionsReduced Order ModelLithium Iron Phosphate

MSC classification

Primary: 78A57: Electrochemistry
Secondary: 35C20: Asymptotic expansions 35M33: Initial-boundary value problems for systems of mixed type 65M20: Method of lines
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 2 , April 2022 , pp. 328 - 368
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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