This paper investigates the behavior of confined fluid in the gap between a sphere and a flat plate by examining the curve of free energy of the system versus size of the new phase. Four possible situations corresponding to new phase formation out of confined liquid or vapor at pressures above or below the saturation pressure are studied. Using surface thermodynamics, the feasible shape of the meniscus (concave/convex), the possibility of phase transition, as well as the number and the nature (unstable/stable) of equilibrium states have been determined for each of these four situations. The effects of equilibrium contact angle, separation distance of confinement surfaces, and sphere size have been studied. We show that the number and nature of equilibrium states, along with the effect of different parameters in these four possible situations, can be well described under two categories of new phase formation with (a) concave or (b) convex meniscus. Our results reveal that in the sphere-plate gap, stable coexistence of the liquid and vapor phases is only possible when the meniscus is concave (which corresponds to either capillary condensation or capillary evaporation), and when the sphere and plate are separated by a distance less than a critical amount (where that critical amount is always less than the Kelvin radius). With convex menisci, no stable coexistence of liquid and vapor phase is possible.

In this paper, we examine the thermodynamic stability of surface nanobubbles. The appropriate free energy is defined for the system of nanobubbles on a solid surface submerged in a supersaturated liquid solution at constant pressure and temperature, under conditions where an individual nanobubble is not in diffusive contact with a gas phase outside of the system or with other nanobubbles on the time scale of the experiment. The conditions under which plots of free energy versus the radius of curvature of the nanobubbles show a global minimum, which denotes the stable equilibrium state, are explored. Our investigation shows that supersaturation and an anomalously high contact angle (measured through the liquid) are required to have stable surface nanobubbles. In addition, the anomalously high contact angle of surface nanobubbles is discussed from the standpoint of a framework recently proposed by Koch, Amirfazli, and Elliott that relates advancing and receding contact angles to thermodynamic equilibrium contact angles, combined with the existence of a gas enrichment layer.

Thermodynamic phase behavior is affected by curved interfaces in micro- and nanoscale systems. For example, capillary freezing point depression is associated with the pressure difference between the solid and liquid phases caused by interface curvature. In this study, the thermal, mechanical, and chemical equilibrium conditions are derived for binary solid-liquid equilibrium with a curved solid-liquid interface due to confinement in a capillary. This derivation shows the equivalence of the most general forms of the Gibbs-Thomson and Ostwald-Freundlich equations. As an example, the effect of curvature on solid-liquid equilibrium is explained quantitatively for the water/glycerol system. Considering the effect of a curved solid-liquid interface, a complete solid-liquid phase diagram is developed over a range of concentrations for the water/glycerol system (including the freezing of pure water or precipitation of pure glycerol depending on the concentration of the solution). This phase diagram is compared with the traditional phase diagram in which the assumption of a flat solid-liquid interface is made. We show the extent to which nanoscale interface curvature can affect the composition-dependent freezing and precipitating processes, as well as the change in the eutectic point temperature and concentration with interface curvature. Understanding the effect of curvature on solid-liquid equilibrium in nanoscale capillaries has applications in the food industry, soil science, cryobiology, nanoporous materials, and various nanoscience fields.

The behavior of pure fluid confined in a cone is investigated using thermodynamic stability analysis. Four situations are explained on the basis of the initial confined phase (liquid/vapor) and its pressure (above/below the saturation pressure). Thermodynamic stability analysis (a plot of the free energy of the system versus the size of the new potential phase) reveals whether the phase transition is possible and, if so, the number and type (unstable/metastable/stable) of equilibrium states in each of these situations. Moreover we investigated the effect of the equilibrium contact angle and the cone angle (equivalent to the confinement's surface separation distance) on the free energy (potential equilibrium states). The results are then compared to our previous study of pure fluid confined in the gap between a sphere and a flat plate and the gap between two flat plates.1 Confined fluid behavior of the four possible situations (for these three geometries) can be explained in a unified framework under two categories based on only the meniscus shape (concave/convex). For systems with bulk-phase pressure imposed by a reservoir, the stable coexistence of pure liquid and vapor is possible only when the meniscus is concave.

We investigate the stability of bubble formation, starting with a convex or a concave meniscus, from a liquid solution (of water and a dissolved gas) inside a finite cone at constant temperature and constant liquid pressure (above the saturation pressure of the pure solvent). It is assumed that the dissolved gas (nitrogen) forms a dilute solution at equilibrium, which can be described by Henry's law. The number and nature of equilibrium states are determined with Gibbsian composite-system thermodynamics, both from the intersection of the equilibrium Kelvin radius with the geometry radius and from the extrema in the plot of free energy of the system versus size of the new phase. Bubble stability is studied along the whole growth path, as the bubble grows inside, gets pinned, and grows further outside the finite cone. The changes in the concentration of the liquid bulk phase and the vapor phase during the growth of the bubble are carefully incorporated in the equations. The effects of various parameters, including cone apex angle, cone half mouth radius, contact angle, total number of moles, and initial degree of saturation, on the stability of the bubble are also investigated. Stability of bubble formation from a liquid solution inside a confined geometry such as a finite cone is of interest in areas such as restoring underwater superhydrophobicity and adhesion of particles to the roughness of synthetic biomaterials.