Localized Instabilities and Spinodal Decomposition in Driven Systems in the Presence of Elasticity

TL;DR

This paper investigates localized boundary layer instabilities and spinodal decomposition in driven elastic systems, revealing how phase separation patterns depend on external flux and elastic effects, with implications for lithium-ion battery modeling.

Contribution

It introduces a combined analytical and numerical framework to analyze interface and bulk instabilities in driven elastic systems, linking them to phase separation in battery materials.

Findings

Localized instabilities occur at free surfaces due to spinodal decomposition.

Instability wavelength and onset depend on system parameters.

Interface and bulk instabilities are distinguishable within the same framework.

Abstract

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.