弹性驱动系统的局部不稳定性与Spinodal分解
Localized Instabilities and Spinodal Decomposition in Driven Systems in the Presence of Elasticity
摘要：
我们研究数值和解析相分离的不稳定性在固体层上施加外部材料ux。第一个不稳定性是本地化的边界层在暴露的自由表面的过程类似于旋节分解。在极限静态的情况下，当没有材料ux时，相干旋节分解被恢复。在本问题中，时间依赖性和非均匀基态的稳定性分析以及完整控制方程的数值模拟被用来建立波长和不稳定性对参数设置及其瞬态性质的依赖性，因为图案最终粗化为一个在移动的前沿。第二种不稳定性与弹性条件下的Mullins-Sekerka不稳定性有关，当ux反转时，出现在两相之间的移动前沿。完整的模型和相应的尖锐界面模型的稳定性进行了分析和比较。我们的研究结果表明，如何界面和散装不稳定性可以在同一框架内进行分析，它允许识别和区分他们每个人清楚。详细了解两个不稳定性和它们在现实环境中的相互联系的相关性证明了锂离子电池的上下文中的锂化/脱锂过程建模的方程系统。
英文摘要：
We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material ux is imposed. The first instability is localized within a boundary layer at the exposed free surface by a process akin to spinodal decomposition. In the limiting static case, when there is no material ux, the coherent spinodal decomposition is recovered. In the present problem stability analysis of the time-dependent and non-uniform base states as well as numerical simulations of the full governing equations are used to establish the dependence of the wavelength and onset of the instability on parameter settings and its transient nature as the patterns eventually coarsen into a at moving front. The second instability is related to the Mullins- Sekerka instability in the presence of elasticity and arises at the moving front between the two phases when the ux is reversed. Stability analyses of the full model and the corresponding sharp-interface model are carried out and compared. Our results demonstrate how interface and bulk instabilities can be analysed within the same framework which allows to identify and distinguish each of them clearly. The relevance for a detailed understanding of both instabilities and their interconnections in a realistic setting are demonstrated for a system of equations modelling the lithiation/delithiation processes within the context of Lithium ion batteries.
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