Dissolution or Growth of a Liquid Drop Embedded in a Continuous Phase of Another Liquid via a Phase-Field Ternary Mixture Model based on the NRTL (Non-Random Two Liquid) equation.

We simulate the diffusion-driven dissolution or growth of a single-component drop embedded in a continuous phase of a binary liquid (or viceversa). Our theoretical approach follows a phase field model of partially miscible ternary liquid mixtures, which is based on a regular solution assumption together with a Cahn-Hilliard representation of the nonlocal components of the Gibbs free energy of mixing. In addition, the excess free energy is modeled with either a Flory-Huggins or an NRTL model equation. Based on 2D simulation results, we show 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 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. Similar results are obtained in the case of an isolated two-component drop embedded in a continuous phase of a single-component liquid. Finally, we show that the results obtained using the two excess free energy models are virtually identical to each other.