论文标题
锂离子电池的Cahn-Hilliard反应模型的尖锐界面极限
Sharp Interface Limit of the Cahn-Hilliard Reaction Model for Lithium-ion Batteries
论文作者
论文摘要
我们提出了一个弱解决方案理论，该理论是Cahn-Hilliard反应模型的尖锐界面极限，这是一种用于锂离子电池的变异PDE。该模型的一个基本特征是将巴特勒 - 沃尔默动力学用于锂离子插入，该动力学是作为罗宾型边界条件而产生的，将化学电位的通量与反应速率相关的通量，本身就是化学电位和离子浓度的非线性功能。为了通过非线性随着界面宽度的消失，我们在漫射且尖锐的界面级别引入解决方案概念，主要根据最佳耗散不平等来描述动力学。使用此功能框架并在能量收敛假设下，我们表明Cahn-Hilliard反应模型的溶液会收敛到Mullins-Sekerka型几何进化方程。
We propose a weak solution theory for the sharp interface limit of the Cahn-Hilliard reaction model, a variational PDE for lithium-ion batteries. An essential feature of this model is the use of Butler-Volmer kinetics for lithium-ion insertion, which arises as a Robin-type boundary condition relating the flux of the chemical potential to the reaction rate, itself a nonlinear function of the chemical potential and the ion concentration. To pass through the nonlinearity as interface width vanishes, we introduce solution concepts at the diffuse and sharp interface level describing dynamics principally in terms of an optimal dissipation inequality. Using this functional framework and under an energy convergence hypothesis, we show that solutions of the Cahn-Hilliard reaction model converge to a Mullins-Sekerka type geometric evolution equation.
