Derivation of Micro/Macro Lithium Battery Models from Homogenization

• Published in: Transport in porous media Vol. 88; no. 2; pp. 249 - 270
• Main Authors: Ciucci, Francesco, Lai, Wei
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2011; Springer; Springer Nature B.V
• Subjects: Asymptotic series; Civil Engineering; Classical and Continuum Physics; Conservation equations; Derivation; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Electrode materials; Electrokinetics; Engineering and environment geology. Geothermics; Exact sciences and technology; Geotechnical Engineering & Applied Earth Sciences; Homogenization; Homogenizing; Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; Liquid phases; Lithium; Lithium batteries; Lithium-ion batteries; Mathematical analysis; Mathematical models; Multiscale analysis; Pollution, environment geology; Rechargeable batteries; Transport; Homogenization; Lithium batteries; Newman’s model; Porous electrode; Poisson–Nernst–Planck; models; electrodes; liquid phase; electricity; storage; transport; electrolytes; lithium; Newman's model; homogenization; solid phase; microstructures; Poisson-Nernst-Planck; ions; porous media; theory
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-011-9738-5

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.