The evaporation/condensation transition of liquid droplets

The condensation of a supersaturated vapor enclosed in a finite system is considered. A phenomenological analysis reveals that the vapor is found to be stable at densities well above coexistence. The system size at which the supersaturated vapor condenses into a droplet is found to be governed by a typical length scale which depends on the coexistence densities, temperature and surface tension. When fluctuations are neglected, the chemical potential is seen to show a discontinuity at an effective spinodal point, where the inhomogeneous state becomes more stable than the homogeneous state. If fluctuations are taken into account, the transition is rounded, but the slope of the chemical potential versus density isotherm develops a discontinuity in the thermodynamic limit. In order to test the theoretical predictions, we perform a simulation study of droplet condensation for a Lennard-Jones fluid and obtain loops in the chemical potential versus density and pressure. By computing probability distributions for the cluster size, chemical potential, and internal energy, we confirm that the effective spinodal point may be identified with the occurrence of a first order phase transition, resulting in the condensation of a droplet. An accurate equation of state is employed in order to estimate the droplet size and the coexisting vapor density and good quantitative agreement with the simulation data is obtained. The results highlight the need of an accurate equation of state data for the Laplace equation to have predictive power.