Derivation of Micro/Macro Lithium Battery Models from Homogenization |
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Authors: | Francesco Ciucci Wei Lai |
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Institution: | (1) Celgard, LLC, 13800, South Lakes Dr, Charlotte, NC 28273, USA |
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Abstract: | In this article, we develop a micro–macroscopic coupled model aimed at studying the interplay between electrokinetics and
transport in lithium ion batteries. The system studied consists of a solid (electrode material) and a liquid phase (electrolyte)
with periodic microscopic features. In this work, homogenization of generalized Poisson–Nernst–Planck (PNP) equation set leads
to a micro/macro formulation similar in nature to the one developed in Newman’s model for lithium batteries. Underlying conservation
equations are derived for each phase using asymptotic expansions and mathematical tools from homogenization theory, starting
from a PNP micromodel, and in particular Newman’s model is obtained as a corollary of the micro/macro approach developed here.
The advantage of homogenization lies in the fact that effective parameters can be derived directly from the analysis of the
periodic microstructure and from the application of the theory developed in this article. In addition, the advantages of using
homogenization in Lithium ion battery modeling are outlined. Lastly, this work is a necessary step toward more general homogenized
models and toward mathematical proofs, and it is also needed preliminary analysis for multiscale computational schemes. |
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