Triphase Separation of a Ternary Symmetric Highly Viscous Mixture

Abstract

We discuss numerical results of diffusion-driven separation into three phases of a symmetric, three-component highly viscous liquid mixture after an instantaneous quench from the one-phase region into an unstable location within the tie triangle of its phase diagram. Our theoretical approach follows a diffuse-interface model of partially miscible ternary liquid mixtures that incorporates the one-parameter Margules correlation 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 3D, showing the segregation kinetics in terms of basic segregation statistics, such as the integral scale of the pair-correlation function and the separation depth for each component. Based on the temporal evolution of the integral scales, phase separation takes place via the simultaneous growth of three phases up until a symmetry-breaking event after which one component continues to separate quickly, while phase separation for the other two seems to be delayed. However, inspection of the separation depths reveals that there can be no symmetry among the three components at any instant in time during a triphase segregation process.

Continuum-scale modelling of polymer blends using the Cahn–Hilliard equation: transport and thermodynamics

“…However, there are a variety of more-advanced thermodynamic models that are better suited for specific systems or enable more-accurate modelling of complex systems that can be employed. To date, only a handful of studies have explored more-complex thermodynamic models, such as CALPHAD-based free-energy functions 16 , the comparatively simple activity-coefficient model Non-random Two-Liquid (NRTL) 17,18 and free-energy functions suitable for mineralic systems 19 , within the Cahn-Hilliard equation.…”

Impact of Particle Arrays on Phase Separation Composition Patterns

“…Numerical simulations of phase separation in ternary (A:B:C) mixtures have taken several approaches, including Cahn-Hilliard-type [26,[46][47][48][49][50][51], molecular dynamics [52,53], Monte Carlo [54], lattice Boltzmann [28], and others [27,55,56]. In this paper, we characterize the ternary mixture, which consists of particles (C) embedded in a matrix (A:B), through a Cahn-Hilliard-based phase-field model, as described in Sec.…”