Worm-like emulsion droplets

Forming an interface between immiscible fluids incurs a free-energy cost that usually favors minimizing the interfacial area. An emulsion droplet of fixed volume therefore tends to form a sphere, and pairs of droplets tend to coalesce. Surfactant molecules adsorbed to the droplets' surfaces stabilize emulsions by providing a kinetic barrier to coalescence. Here, we show that the bound surfactants' osmotic pressure also competes with the droplet's intrinsic surface tension and can reverse the sign of the overall surface free energy. The onset of negative surface tension favors maximizing surface area and therefore favors elongation into a worm-like morphology. Analyzing this system in the Gibbs grand canonical ensemble reveals a phase transition between spherical and worm-like emulsions that is governed by the chemical potential of surfactant molecules in solution. Predictions based on this model agree with the observed behavior of an experimental model system composed of lipid-stabilized silicone oil droplets in an aqueous surfactant solution.