Basic and extendable framework for effective charge transport in electrochemical systems

Jeta Molla, Markus Schmuck

Research output: Contribution to journalArticle

Abstract

We consider basic and easily extendible transport formulations for lithium batteries consisting of an anode (Li-foil), a separator (polymer electrolyte), and a composite cathode (composed of electrolyte and intercalation particles). Our mathematical investigations show the following novel features: (i) complete and very basic description of mixed transport processes relying on a neutral, binary symmetric electrolyte resulting in a non-standard Poisson equation for the electric potential together with interstitial diffusion approximated by classical diffusion; (ii) upscaled and basic composite cathode equations allowing to take geometric and material features of electrodes into account; (iii) the derived effective macroscopic model can be numerically solved with well-known numerical strategies for homogeneous domains and hence does not require to solve a high-dimensional numerical problem or to depend on computationally involved multiscale discretization strategies where highly heterogeneous and realistic, nonlinear, and reactive boundary conditions are still unexplored. We believe that the here proposed basic and easily extendible formulations will serve as a basic and simple setup towards a systematic theoretical and experimental understanding of complex electrochemical systems and their optimization, e.g. Li-batteries.
Original languageEnglish
Pages (from-to)85-91
Number of pages7
JournalApplied Mathematics Letters
Volume95
Early online date25 Mar 2019
DOIs
Publication statusPublished - Sep 2019

Fingerprint

electrolytes
cathodes
formulations
composite materials
lithium batteries
separators
Poisson equation
intercalation
electric batteries
foils
interstitials
anodes
boundary conditions
optimization
electrodes
polymers
electric potential

Keywords

  • Butler–Volmer equations
  • Electrode design
  • Homogenization
  • Lithium batteries
  • Multiscale modelling

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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abstract = "We consider basic and easily extendible transport formulations for lithium batteries consisting of an anode (Li-foil), a separator (polymer electrolyte), and a composite cathode (composed of electrolyte and intercalation particles). Our mathematical investigations show the following novel features: (i) complete and very basic description of mixed transport processes relying on a neutral, binary symmetric electrolyte resulting in a non-standard Poisson equation for the electric potential together with interstitial diffusion approximated by classical diffusion; (ii) upscaled and basic composite cathode equations allowing to take geometric and material features of electrodes into account; (iii) the derived effective macroscopic model can be numerically solved with well-known numerical strategies for homogeneous domains and hence does not require to solve a high-dimensional numerical problem or to depend on computationally involved multiscale discretization strategies where highly heterogeneous and realistic, nonlinear, and reactive boundary conditions are still unexplored. We believe that the here proposed basic and easily extendible formulations will serve as a basic and simple setup towards a systematic theoretical and experimental understanding of complex electrochemical systems and their optimization, e.g. Li-batteries.",
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Basic and extendable framework for effective charge transport in electrochemical systems. / Molla, Jeta; Schmuck, Markus.

In: Applied Mathematics Letters, Vol. 95, 09.2019, p. 85-91.

Research output: Contribution to journalArticle

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AU - Schmuck, Markus

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AB - We consider basic and easily extendible transport formulations for lithium batteries consisting of an anode (Li-foil), a separator (polymer electrolyte), and a composite cathode (composed of electrolyte and intercalation particles). Our mathematical investigations show the following novel features: (i) complete and very basic description of mixed transport processes relying on a neutral, binary symmetric electrolyte resulting in a non-standard Poisson equation for the electric potential together with interstitial diffusion approximated by classical diffusion; (ii) upscaled and basic composite cathode equations allowing to take geometric and material features of electrodes into account; (iii) the derived effective macroscopic model can be numerically solved with well-known numerical strategies for homogeneous domains and hence does not require to solve a high-dimensional numerical problem or to depend on computationally involved multiscale discretization strategies where highly heterogeneous and realistic, nonlinear, and reactive boundary conditions are still unexplored. We believe that the here proposed basic and easily extendible formulations will serve as a basic and simple setup towards a systematic theoretical and experimental understanding of complex electrochemical systems and their optimization, e.g. Li-batteries.

KW - Butler–Volmer equations

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