Localized instabilities and spinodal decomposition in driven systems in the presence of elasticity

Abstract

We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material flux 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 flux, 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 flat moving front. The second instability is related to the MullinsSekerka instability in the presence of elasticity and arises at the moving front between the two phases when the flux 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.

Phase separation in swelling and deswelling hydrogels with a free boundary

“…For experimental comparisons with the results here, it may be possible to suppress these instabilities by choosing a small enough length scale for the lateral confinement but, in general, corrugations of the one-dimensional solutions will trigger a more complex evolution of the transition boundary. In this context, it would also be exciting to further explore the analogy with lithium intercalation in battery electrodes and the instabilities observed there [37][38][39]. It would be interesting to know if stress relaxation at the free surface also promotes phase transitions [40] in a swelling hydrogel.…”

How do degenerate mobilities determine singularity formation in Cahn-Hilliard equations?

“…These applications exploit the fact that in a phase-field model, the interfaces are represented by a thin layer over which the order parameter varies rapidly but continuously. Examples of such processes are surface diffusion and electromigration in crystals and alloys [24,67,21,36,16,8,9], motion of immiscible fluids with free boundaries [35,1,44,18,66], polymer blends [54,34,25], tumour growth models [28,59,51] or lithiation in battery electrodes [55], to name just a few.…”