Droplet evolution in expanding flow of warm dense matter

We propose a simple, self-consistent kinetic model for the evolution of a mixture of droplets and vapor expanding adiabatically in vacuum after rapid, almost isochoric heating. We study the evolution of the two-phase fluid at intermediate times between the molecular and the hydrodynamic scales, focusing on out-of-equilibrium and surface effects. We use the van der Waals equation of state as a test bed to implement our model and study the phenomenology of the upcoming second neutralized drift compression experiment (NDCX-II) at Lawrence Berkeley National Laboratory (LBNL) that uses ion beams for target heating. We find an approximate expression for the temperature difference between the droplets and the expanding gas and we check it with numerical calculations. The formula provides a useful criterion to distinguish the thermalized and nonthermalized regimes of expansion. In the thermalized case, the liquid fraction grows in a proportion that we estimate analytically, whereas, in case of too rapid expansion, a strict limit for the evaporation of droplets is derived. The range of experimental situations is discussed.