Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach

Abstract

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which shows the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems. © 2014 AIP Publishing LLC. [http://dx

Direct simulations of homogeneous bubble nucleation: Agreement with classical nucleation theory and no local hot spots

“…[31]), while the larger bubbles are roughly spherical. The vapor-liquid transitions are smooth and wide, as found in DFT [17] and square gradient [18] calculations. Comparisons with bubble density profiles show that our volume estimates V based on the number of lowdensity cells are reliable: The resulting spherical radii r MD = (3V /4π ) 1/3 lie only slightly below the equimolar radii, which would be the radius of a constant density bubble with a sharp interface (where the density jumps from the central value ρ V to the bulk liquid value ρ L ) and the same integrated mass [13].…”

“…More recently density functional theory (DFT) [12,17], square gradient theory [18] and some modifications of the classical theory [19,20] have been employed to model the bubble nucleation process. Measuring bubble nucleation rates in a perfectly homogeneous liquid is very challenging in laboratory experiments [21], but can be achieved in principle in computer simulations, both with the Monte Carlo method [22] and with molecular dynamics (MD) [11,[23][24][25][26][27][28][29][30][31][32][33].…”

Communication: Superstabilization of fluids in nanocontainers

“…For small bubbles, the negative pressure in the Laplace equation becomes so large, that the liquid phase will stretch to fill the entire container, thereby collapsing the bubble. 24,31 For droplet condensation, this situation happens because droplet formation occurs at the expenses of the surrounding vapor. For sufficiently small systems, the formation of the liquid drop can deplete the supersaturation so much that sufficiently large droplets cannot form.…”

“…It holds irrespective of any capillary approximation or assumption of a constant surface tension, as evidenced by the fact that it also appears in density functional calculations in closed volumes. 24,31,35 At these conditions, that are experimentally feasible, it would be possible to control and prevent the explosive boiling of liquids, the cavitation of overstretched fluids, and to measure accurate equations of state for fluids in deeply metastable regions. This would thus have striking consequences in a wide variety of scientific and industrial phenomena.…”

“…To analyze the peculiarities of nucleation in small systems, we use the modified bubble/droplet model 23 that has been shown to give very similar predictions for the properties of the critical cluster/bubble as more advanced theories, e.g., density functional theory. 24 This model considers the potential formation of a bubble or droplet of n molecules at the center of the container. The bubble/droplet and the exterior phase are both assumed to have the thermodynamic properties of a homogeneous phase separated by an interface at r with constant surface tension, σ .…”