Pattern formation in oil-in-water emulsions exposed to a salt gradient

We describe a radial configuration where horizontal flows create regular patterns. In particular, we experimentally show that when a drop of an oil-in-water emulsion with high salt concentration in its aqueous phase is injected into a Hele-Shaw cell filled with salt solution with low concentration, the drop spreads and a “flower” pattern of the emulsion appears. We also conduct numerical simulations and the numerical results agree well with experimental results both qualitatively and quantitatively for describing the main features of this pattern-forming instability. The numerical results also confirm the hypothesis that the change of the fluid density caused by salt and oil is the key. Initially, the emulsion is denser than the ambient fluid, so it spreads along the bottom. However, as it spreads, salt diffuses much faster than the oil droplets so that the emulsion drop finally becomes less dense than the ambient fluid. This transport introduces an unstable vertical density gradient. We also describe the corresponding secondary flow, which is in the form of an azimuthal instability. The criterion for pattern formation, the growth rate of the instability, and the most unstable mode of the instability are also discussed.