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

Flow instabilities can occur in a fluid system with two components that have significantly different diffusivities and that have opposite effects on the fluid density, as is the scenario in traditional double-diffusive convection. Here, we experimentally show that an oil-in-water emulsion exposed to salt concentration gradients generates a flowerlike pattern driven by vertical and azimuthal instabilities. We also report numerical and analytical studies to elaborate on the mechanism, the instability criteria, and the most unstable modes that determine the details of the observed patterns. We find that the instability is driven by buoyancy and stems from the differential transport between the dissolved salt and the suspended oil droplets, which have opposing effects on the density of the medium. Consequently, we identify a criterion for the development of the instability that involves the relative densities and concentrations of the salt and oil droplets. We also argue that the typical wave number of the pattern formed scales with the Péclet number of the salt, which here is equivalent to the Rayleigh number since the flow is driven by buoyancy. We find good agreement of these predictions with both experiments and numerical simulations.