Dissolution or growth of a liquid drop via phase-field ternary mixture model based on the non-random, two-liquid equation

Abstract

We simulate the diffusion-driven dissolution or growth of a single-component liquid drop embedded in a continuous phase of a binary liquid. Our theoretical approach follows a diffuse-interface model of partially miscible ternary liquid mixtures that incorporates the non-random, two-liquid (NRTL) equation as a submodel for the enthalpic (so-called excess) component of the Gibbs energy of mixing, while its nonlocal part is represented based on a square-gradient (Cahn-Hilliard-type modeling) assumption. The governing equations for this phase-field ternary mixture model are simulated in 2D, showing that, for a single-component drop embedded in a continuous phase of a binary liquid (which is highly miscible with either one component of the continuous phase but is essentially immiscible with the other), the size of the drop can either shrink to zero or reach a stationary value, depending on whether the global composition of the mixture is within the one-phase region or the unstable range of the phase diagram.