Gas-liquid transition of van der Waals fluid confined in fluctuating nano-space

Gas-liquid transition is generally a complex process, which involves nucleation of droplets and their growth by evaporation-condensation or collision-coalescence processes. Here, we focus on a microscopic system in which there is only one liquid droplet at most. In this case, we can develop an equilibrium theory for the formation of the droplet in the gas phase using the classical nucleation theory. We use the van der Waals fluid model with surface tension and calculate the size fluctuation of the droplet for various confinement conditions, NVT (in which the volume V of the system is fixed), NPT (in which the pressure P of the system is fixed), and NBT (in which the system is confined in a nano-bubble immersed in a host liquid, where both V and P can fluctuate). We show that in the NBT system, the size flexibility along with space confinement induces a wealth of properties that are not found in NVT and NPT. It exhibits richer phase behaviors: a stable droplet appears and coexists with the pure gas phase and/or pure liquid phase. When compared to the NVT system, the NBT system shows not only the oscillatory fluctuation between the two stable states but also a large fluctuation in the total volume and the pressure.