Phase separation can induce pattern propagation in ternary mixtures

Ternary mixtures can undergo liquid-liquid phase separation in response to concentration changes. In experiments, 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 diffusing out of the mixture [Moerman et al. PNAS 2018, 115 (12), 3599-3604]. To understand these observations, we model 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. Recasting the Flory-Huggins free energy – assuming that the interaction parameters involving ethanol are zero – gives an effective binary mixture description, parameterized by ethanol concentration. The ternary mixture is then likely to become unstable below a cut-off ethanol concentration. Using Cahn-Hilliard dynamics, we examine the length scale, phase composition, and front velocity of the phase-separated patterns and compare them to results from marginal stability analysis used to study front propagation. Extensions of this idea can help understand phase separation in co-flow systems, where advection can also affect phase-separated patterns.