Interfacial energy liquid-vapor

Problem 6.4. At 1800 K, the surface energy of alumina (AI2O3) is 8.5 X 10 J/cm. The surface energy for liquid nickel against its own vapor at 1800 K is 1.7 X 10 " J/cm. At the same temperature, the interfacial energy between liquid nickel and alumina is 1.8 x 10 " J/cm. From these data, calculate the contact angle of a droplet of liquid nickel on an alumina plate at 1800 K. 

Interfacial energies between the solid-liquid, solid-vapor, and vapor-liquid are represented by ysL, ysv, and ylv, respectively. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc. 

The three interfacial surface energies, as shown at the three-phase junction in Figure 2.29, can be used to perform a simple force balance. The liquid-solid interfacial energy plus the component of the liquid-vapor interfacial energy that lies in the same direction must exactly balance the solid-vapor interfacial energy at equilibrium ... 

Fig. 1. Schematic of a liquid drop on a sohd surface showing the contact angle, 0, as well as the liquid—sohd interfacial energy, ySL, the liquid—vapor...

Liquid-vapor interfacial energy dyn/cm dyn/cm CTj- Granule tensile strength kg/cm" ... 

FIO. 20-66 Contact angle on a powder surface, where y , y, y " are the solid-vapor, solid-liquid, and liquid-vapor interfacial energies, and 0 is the contact angle measured through the liquid. 

Over the last two decades the exploration of microscopic processes at interfaces has advanced at a rapid pace. With the active use of computer simulations and density functional theory the theory of liquid/vapor, liquid/liquid and vacuum/crystal interfaces has progressed from a simple phenomenological treatment to sophisticated ah initio calculations of their electronic, structural and dynamic properties [1], However, for the case of liquid/crystal interfaces progress has been achieved only in understanding the simplest density profiles, while the mechanism of formation of solid/liquid interfaces, emergence of interfacial excess stress and the anisotropy of interfacial free energy are not yet completely established [2],... 

We also have continuity of the energy fluxes across the vapor-liquid interface, liquid-wall and wall-coolant interfaces. If we adopt a one-dimensional (film) model of the transport processes, then all of these energy fluxes are equal. Changes in the interfacial area due to curvature have been ignored such differences may be accounted for with the corrections shown in Section 8.2.4. 

The function is the mass transfer rate equation for the vapor phase is the interfacial energy balance F3 is valid if the liquid phase may be assumed unmixed with... 

Tarazona and Navascues have proposed a perturbation theory based upon the division of the pair potential given in Eq. (3.5.1). In addition, they make a further division of the reference potential into attractive and repulsive contributions in the manner of the WCA theory. The resulting perturbation theory for the interfacial properties of the reference system is constructed through adaptation of a method developed by Toxvaerd in his extension of the BH perturbation theory to the vapor-liquid interface. The Tarazona-Navascues theory generates results for the Helmholtz free energy and surface tension in addition to the density profile. Chacon et al. have shown how the perturbation theories based upon Eq. (3.5.1) may be developed by a series of approximations within the context of a general density-functional treatment. 

Alternatively, thermodynamic phase equilibrium in a model system can be evaluated by beginning the simulation with two (or more) phases in the same simulation volume, in direct physical contact (i.e., with a solid-fluid interface). This approach has succeeded [79], but its application can be problematic. Some of the issues have been reviewed by Frenkel and McTague [80]. Certainly the system must be large (recent studies [79,81,82] have employed from 1000 up to 65,000 particles) to permit the bulk nature of both phases to be represented. This is not as difficult for solid-liquid equilibrium as it is for vapor-liquid, because the solid and liquid densities are much more alike (it is a weaker first-order transition) and the interfacial free energy is smaller. However, the weakness of the transition also implies that a system out of equilibrium experiences a smaller driving force to the equilibrium condition. Consequently, equilibration of the system, particularly at the interface, may be slow. 

The values of the evaporation and sublimation heats are usually quite close to each other, as well as the densities of solid substances and their melts, measured at the melting point. Consequently, the values of the surface energy at the liquid-vapor, aLV, and at the solid-vapor, osv, interfaces are nearly identical. Oppositely, the interfacial energy oSL at the interface between the solid phase and its melt is usually low oSL values normally do not exceed 1/10 of surface tension values of melt (note that the heats of melting are also on the order of -10% of those of evaporation). 

The laws governing the interfacial phenomena between condensed phases and their vapor (or air) in single- and two-component systems, described in previous chapters, are largely applicable to the interfaces between two condensed phases, i.e., between two liquids, two solids, or between a solid and a liquid. At the same time, these interfaces have some important peculiarities, primarily related to the partial compensation of the intermolecular interactions. The degree of saturation of the surface forces is determined by the similarity in the molecular nature of the phases in contact. When adsorption of surfactants takes place at such interfaces, it may substantially enhance the decrease in the interfacial energy. The latter is of great importance, since surfactants play a major role in the formation and degradation of disperse systems (see Chapters IV, VI-VIII). 

---