Homogenization of a porous intercalation electrode with phase separation
- Heida, Martin
- Landstorfer, Manuel
- Liero, Matthias
2020 Mathematics Subject Classification
- 78A57 35Q92 35B27 78M40 80A22
- Battery, homogenization, two-scale convergence, porous electrode, non-equilibrium thermodynamics, phase separation
In this work, we derive a new model framework for a porous intercalation electrode with a phase separating active material upon lithium intercalation. We start from a microscopic model consisting of transport equations for lithium ions in an electrolyte phase and intercalated lithium in a solid active phase. Both are coupled through a Neumann--boundary condition modeling the lithium intercalation reaction. The active material phase is considered to be phase separating upon lithium intercalation. We assume that the porous material is a given periodic microstructure and perform analytical homogenization. Effectively, the microscopic model consists of a diffusion and a Cahn--Hilliard equation, whereas the limit model consists of a diffusion and an Allen--Cahn equation. Thus we observe a Cahn--Hilliard to Allen--Cahn transition during the upscaling process. In the sense of gradient flows, the transition goes in hand with a change in the underlying metric structure of the PDE system.