Liquid-liquid phase-separated pattern propagation in ternary mixtures*

Ternary mixtures can undergo liquid-liquid phase separation in response to concentration changes. It is observed that a ternary mixture of oil-water-ethanol in a microchannel with water and surfactant leads to the formation of a phase separating front, leaving alternating oil- and water-rich stripes in its wake due to ethanol diffusion out of the mixture [Moerman et al. PNAS 2018, 115 (12), 3599-3604]. We model these dynamics via a system with an initially stable ternary mixture (oil-water-ethanol) and a stable single-component phase (water) in contact. Letting ethanol preferentially diffuse out of the ternary mixture causes the mixture to undergo spinodal decomposition from the interface. We recast the Flory-Huggins free energy – assuming that the interaction parameters involving ethanol are zero – to get an effective binary mixture description, parameterized by ethanol concentration. This makes the ternary mixture likely to become unstable below a cut-off ethanol concentration. Using Cahn-Hilliard dynamics, we explore features of diffusion-mediated phase-separated patterns such as length scale, phase composition, and front velocity. Extension of this idea can help understand how to control phase separation in co-flow systems, where advection can affect phase-separated patterns.