Involatile nanodroplets: an asymptotic analysis

The structure of nanometer-scale droplets of weakly volatile liquids arises through the interplay of strong intermolecular attraction, and core intermolecular repulsion, interfacial forces, and the large, negative chemical potential of the low density vapor with which it is in equilibrium. Using a van der Waals equation of state and a mesoscopic multiphase model, the structure of such nanodroplets is determined via an asymptotic analysis in terms of the ambient to critical temperature ratio. The structure of a spherical droplet is obtained as the solution of a simple "shooting" problem. The intradroplet pressure profile and a minimal droplet size are determined. The high pressure in the core of the droplet gives evidence for the preferred melting there for systems like water with a negative volume of melting. Our methodology can be generalized to multiphase droplets, as well as to composite structures wherein viruses or other nanoparticles are embedded.