Phase fluctuations in a confined fluid

Abstract

Fluid phase equilibrium depends on the external constraints imposed on a system. In a closed system with fixed volume, depending on the average density, a vapor bubble may be stable, metastable, or unstable, with respect to the homogeneous liquid phase. In the case where the bubble is metastable, we study its lifetime, i.e. the average waiting time needed to observe bubble collapse, and the corresponding lifetime of the homogeneous liquid. For the smallest systems, we predict the possibility to observe phase flipping, when the fluid oscillates between states with and without bubble. We provide an example of phase flipping in a simulation of a Lennard-Jones fluid.

Figures (15)

• Figure 1: Berthelot-Laplace length as a function of temperature for pure water.
• Figure 2: Reduced free energy as a function of reduced bubble volume for pure water at $T=\qty{20}{\degreeCelsius}$. The black curves show reduced densities $\delta_0=0.9984$, $0.9980$, and $0.9976$, correspondings to regimes (i), (ii), and (iii), respectively. The red and blue curves correspond to the spinodal ($\delta_\mathrm{0,sp}\approx0.99815$) and binodal ($\delta_\mathrm{0,eq} \approx 0.99789$) curves, respectively.
• Figure 3: Snapshot of a typical bubble created following the protocol reported in the text. The bubble is depicted as yellow while the LJ particles are shown in red. Note that the size of the LJ particles was decreased for a better view of the bubble.
• Figure 4: Characteristic bubble volumes as a function of reduced average density. The metastable and critical bubble volumes correspond to the upper and lower portion of the curves, respectively. Here the cavity volume is $V=\qty{1}{\mu m^3}$, and the temperature is $T=\qty{20}{\degreeCelsius}$ (solid curve) or 300℃ (dotted curve). The corresponding locations of the binodals and spinodals are indicated with arrows.
• Figure 5: Energy barrier for bubble collapse as a function of reduced average density for various cavity volumes (as given by the labels in $\unit{\mu m^3})$, at $T=\qty{20}{\degreeCelsius}$ (solid curves) or $\qty{300}{\degreeCelsius}$ (dotted curves). Each curve starts at the corresponding $\delta_\mathrm{0,eq}$. The inset shows the case $V=10^{-5}\unit{\mu m^3}$, $T=\qty{20}{\degreeCelsius}$, on a linear scale.