Bubble Formation in a Finite Cone: More Pieces to the Puzzle

Oiling-Out: Insights from Gibbsian Surface Thermodynamics by Stability Analysis

The crystallization process is a significant stage in the pharmaceutical industry. During the process of crystallization with cooling, it is possible for a secondary liquid phase to appear before the formation of crystals. This phenomenon is called "oiling out" or liquid-liquid phase separation (LLPS). In this article, we explore the oiling-out phenomenon in a binary system of water and vanillin using stability analysis based on Gibbsian surface thermodynamics. To obtain the full picture of oiling out, we investigated three cases: droplet-solute-lean liquid equilibrium (DLE), crystal-solute-rich liquid equilibrium (CL'E), and crystal-solute-lean liquid equilibrium (CLE). The phase diagram of the system is plotted using the NRTL model for activity coefficients, along with considering the effect of the interfacial curvature on the phase diagram. From the phase boundaries and free-energy diagram of each case, we showed that the occurrence of the oiling-out phenomenon is justified based on the lower energy barrier of the droplet formation compared to that of the crystal formation. However, the energy level of a stable crystal is significantly lower and hence more stable than that of a stable droplet. Finally, we have determined different regions for droplet and crystal formation in the metastable phase diagram based on their supersaturation and provide insight for the oiling-out phenomenon.

Thermodynamic Investigation of Droplet-Droplet and Bubble-Droplet Equilibrium in an Immiscible Medium

In the absence of external fields, interfacial tensions between different phases dictate the equilibrium morphology of a multiphase system. Depending on the relative magnitudes of these interfacial tensions, a composite system made up of immiscible fluids in contact with one another can exhibit contrasting behavior: the formation of lenses in one case and complete encapsulation in another. Relatively simple concepts such as the spreading coefficient (SC) have been extensively used by many researchers to make predictions. However, these qualitative methods are limited to determining the nature of the equilibrium states and do not provide enough information to calculate the exact equilibrium geometries. Moreover, due to the assumptions made, their validity is questionable at smaller scales where pressure forces due to curvature of the interfaces become significant or in systems where a compressible gas phase is present. Here we investigate equilibrium configurations of two fluid drops suspended in another fluid, which can be seen as a simple building block of more complicated systems. We use Gibbsian composite-system thermodynamics to derive equilibrium conditions and the equation acting as the free energy (thermodynamic potential) for this system. These equations are then numerically solved for an example system consisting of a dodecane drop and an air bubble surrounded by water, and the relative stability of distinct equilibrium shapes is investigated based on free-energy comparisons. Quantitative effects of system parameters such as interfacial tensions, volumes, and the scale of the system on geometry and stability are further explored. Multiphase systems similar to the ones analyzed here have broad applications in microfluidics, atmospheric physics, soft photonics, froth flotation, oil recovery, and some biological phenomena.

Surface thermodynamics at the nanoscale

Fluid interfaces with nanoscale radii of curvature are generating great interest, both for their applications and as tools to probe our fundamental understanding. One important question is what is the smallest radius of curvature at which the three main thermodynamic combined equilibrium equations are valid: the Kelvin equation for the effect of curvature on vapor pressure, the Gibbs-Thomson equation for the curvature-induced freezing point depression, and the Ostwald-Freundlich equation for the curvature-induced increase in solubility. The objective of this Perspective is to provide conceptual, molecular modeling, and experimental support for the validity of these thermodynamic combined equilibrium equations down to the smallest interfacial radii of curvature. Important concepts underpinning thermodynamics, including ensemble averaging and Gibbs's treatment of bulk phase heterogeneities in the region of an interface, give reason to believe that these equations might be valid to smaller scales than was previously thought. There is significant molecular modeling and experimental support for all three of the Kelvin equation, the Gibbs-Thomson equation, and the Ostwald-Freundlich equation for interfacial radii of curvature from 1 to 4 nm. There is even evidence of sub-nanometer quantitative accuracy for the Kelvin equation and the Gibbs-Thomson equation.

Thermodynamic Investigation of the Effect of Electric Field on Solid-Liquid Equilibrium

In this study, the thermal, mechanical, and chemical equilibrium conditions are derived for binary solid-liquid equilibrium under the effect of an electric field. As an example, the effect of an electric field on the water/glycerol solid-liquid phase diagram is computed over the complete mole fraction range. We show that the application of an electric field can affect the composition dependent freezing and precipitating processes, changing freezing and precipitating temperatures and changing the eutectic point temperature and mole fraction.

Gibbsian Surface Thermodynamics

Gibbsian composite-system thermodynamics is the framework governing the equilibrium of composite systems, including systems that at equilibrium have more than one value of pressure because of the action of surface tension, semipermeable membranes, or fields, and thus cannot be treated as simple systems. J. W. Gibbs's paper that lays out composite-system thermodynamics, "On the Equilibrium of Heterogeneous Substances", communicated in two parts in 1876 and 1878, is widely regarded as one of the most important pieces of scientific literature of its century. Many scientists adopted and stressed the importance of Gibbsian thermodynamics. In 1960, H. B. Callen wrote a textbook that made Gibbsian composite-system thermodynamics more accessible to thermodynamicists. However, Callen's book left out Gibbs's work on curved fluid interfaces and did not treat the complicated nonideal systems of interest to today's thermodynamicists. In this Feature Article, I have attempted to convey in a comprehensive manner the framework of Gibbsian composite-system thermodynamics including in detail the treatment of systems with interface effects and with nonideal, multicomponent phases. This work lays out the relationships between important equilibrium equations including the following: the Gibbs-Duhem equation, the Gibbs adsorption equation, the Young-Laplace equation, the Young equation, the Cassie-Baxter equation, the Wenzel equation, the Kelvin equation, the Gibbs-Thompson equation, and the Ostwald-Freundlich equation, including nonideal and multicomponent forms. Equations of state that are often useful for Gibbsian composite-system thermodynamics are reviewed including adsorption isotherms and our own work on two semiempirical equations of state: the Elliott et al. form of the osmotic virial equation and the Shardt-Elliott-Connors-Wright equation for the temperature and composition dependence of surface tension. I summarize the work of our group developing Gibbisan composite-system thermodynamics including new equations for such things as the curvature-induced depression of the eutectic temperature or the removal of azeotropes by nanoscale fluid interface curvature. Gibbsian composite-system thermodynamics has broad applications in biotechnology, nanostructured materials, surface textures and coatings, microfluidics, nanoscience, atmospheric and environmental physics, among others.