Thermodynamics of droplets undergoing liquid-liquid phase separation

We study the thermodynamics of binary mixtures wherein the volume fraction of the minority component is less than the amount required to form a flat interface. Based on an explicit microscopic mean field theory, we show that the surface tension dominated equilibrium phase of a polymer mixture forms a single macroscopic droplet. A combination of elastic interactions that renormalize the surface tension, and arrests phase separation for a gel-polymer mixture, stabilize a micro-droplet phase. We compute the droplet size as a function of the interfacial tension, Flory parameter, and elastic moduli of the gel. Our results illustrate the importance of the rheological properties of the solvent in dictating the thermodynamic phase behavior of biopolymers undergoing liquid-liquid phase separation.