Phase separation in a binary mixture confined between symmetric parallel plates: Capillary condensation transition near the bulk critical point

TL;DR

This paper studies phase separation and capillary condensation in a near-critical binary mixture confined between symmetric plates, incorporating critical fluctuation effects and analyzing both static and dynamic behaviors including late-stage coarsening.

Contribution

It introduces a local functional theory to account for critical fluctuations and examines the static van der Waals loop and dynamic phase separation in confined geometries.

Findings

Van der Waals loop appears below the film critical temperature.

Lateral instability leads to accelerated coarsening.

Pancake domain formation in the film center during late-stage evolution.

Abstract

We investigate phase separation of near-critical binary mixtures between parallel symmetric walls in the strong adsorption regime. We take into account the renormalization effect due to the critical fluctuations using the recent local functional theory [J. Chem. Phys. 136, 114704 (2012)]. In statics, a van der Waals loop is obtained in the relation between the average order parameter $<psi>$ in the film and the chemical potential when the temperature $T$ is lower than the film critical temperature $T_c^{ca}$ (in the case of an upper critical solution temperature). In dynamics, we lower $T$ below the capillary condensation line from above $T_c^{ca}$. We calculate the subsequent time-development assuming no mass exchange between the film and the reservoir. In the early stage, the order parameter $psi$ changes only in the direction perpendicular to the walls. For sufficiently deep quenching, such one-dimensional profiles become unstable with respect to the fluctuations varying in the lateral directions. The late-stage coarsening is then accelerated by the hydrodynamic interaction. A pancake domain of the phase disfavored by the walls finally appears in the middle of the film.