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A thin film model for crystal growth and dissolution in confinement

Banff International Research Station for Mathematical Innovation and Discovery

Crystal growth is a model system for non-equilibrium physics. As a consequence, it has been widely studied, and in particular the nonlinear dynamics giving rise to complex shapes such as those of snow flakes have attracted much interest. However until now, most of these studies have been devoted to free growth, i.e. gowth in infinite systems. Confinement, which breaks translation invariance, gives rise to a novel class of nonlinear dynamics and morphologies, which are relevant in natural sciences such as geology â where crystal growth is often confined in small pores or faults of rocks, and for biomineralization, the process by which living organisms produce minerals (e.g. for their skeleton) â where growth is confined into a soft and complex environment. We propose a model for growth and dissolution of a crystal in confinement describing the non-equilibrium dynamics within the contact region using a continuum thin film equation [1]. Our model accounts self-consistently (in the lubrication regime) for surface tension effects, for the disjoining pressure, and for non-equilibrium transport processes such as diffusion and liquid convection. Based on this model, we study dissolution under a macroscopic load (pressure solution) [1] and growth under an applied supersaturation (crystallisation force) [2,3]. In pressure solution [1], the functional form of the crystal-substrate interaction potential appears to influence strongly the dynamics. For example, a divergent repulsion leads to flat contacts, and to a dissolution rate which increases indefinitely with the applied load. In contrast, a finite repulsion implies a sharp pointy contact shape, and a dissolution rate independent from the applied load. In confined growth it is well known that crystals can produce forces on their environment, and can exhibit a rim in the contact region. Our model shows the generic formation and growth of a precursor cavity which ultimately leads to the formation of the rim. The results are supported by experiments on NaClO3 in the University of Oslo [2].  We show that the formation of the cavity can be supercritical or subcritical, depending on the functional form of disjoining pressure [3]. Finally, the production of forces close to and far from equilibrium is also discussed [4]. References: [1] Thin film modeling of crystal dissolution and growth in confinement L Gagliardi, O Pierre-Louis, Physical Review E 97 (1), 012802 (2018) [2] Cavity formation in confined growing crystals F Kohler, L Gagliardi, O Pierre-Louis, DK Dysthe PHYSICAL REVIEW LETTERS 121, 096101 (2018) [3] Crystal growth in nano-confinement: Subcritical cavity formation and viscosity effects L Gagliardi, O Pierre-Louis, to be published in Journal of Crystal Growth (2019) [4] The non-equilibrium crystallization force L Gagliardi, O Pierre-Louis, preprint (2019).

Mathematics; Fluid mechanics; Approximations and expansions; Fluid dynamics

video/mp4

Author affiliation: Université Claude Bernard Lyon 1

2019-10-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72121

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/