Solid-liquid-vapor systems

The power of the phase rule is immediately evident in that the solid/liquid/vapor system is characterized by the same amount of variance as was the solid/vapor system. As a result, the arguments made regarding the pressure-temperature curves of the former system can be extended to apply to the latter system, except that the liquid phase takes the place of the anhydrate phase. 

The degree of wetting is characterized by the contact angle 0 that depends on the various interfacial energies for the solid-liquid-vapor system and is usually referred to a droplet of liquid on a flat solid surface (Fig. 10.4). If the specific energies of the liquid-vapor, solid-vapor, and solid-liquid inta-faces are yiv, 7sv, and yah respectively, then by the principle of virtual work... 

Johnson RE (1959) Conflicts between Gibbsian thermodynamics and recent treatments of interfacial energies in solid-liquid-vapor systems. J Phys Chem 63 1655-1658... 

Figu re I. I. The pressure-temperature projection of a typical binary solvent-solute system. See text for discussion. SLV, solid/liquid/vapor LCEP, lower critical end point UCEP, upper critical end point. 

In recent years, studies of the phase behavior of salt-water systems have primarily been carried out by Russian investigators (headed by Prof. Vladimir Valyashko) at the Kurnakov Institute in Moscow, particularly for fundamental understanding of the phase behavior of such systems. Valyashko [37,39,42,43], Ravich [38], Urosova and Valyashko [40], and Ravich et al. [41] have given a classification of the existence of two types of salts, depending on whether the critical behavior is observed in saturated solutions. Type 1 does not exhibit critical behavior in saturated solutions. The classic example of Type 1 is the NaCl-water system and has been studied by many authors [36,37,44-47]. The Type 2 systems exhibit critical behaviors in saturated solutions, and therefore have discontinuous solid-liquid-vapor equilibria. Table 1 shows the classification of binary mixtures of salt-water systems. 

For a liquid-vapor system, a vapor-solid system, and a liquid-solid system, AV = Vv-V1 = Vv, AV = Vv - Vs = Vv, and AV = V, - Vs = M(P -p 1), respectively, where M and p are the molecular weight and density of the substance, respectively. Substituting these relationships into Equation (1.88) along with the ideal gas law and integrating the resulting equation yields ... 

Therefore, we designed and built a new apparatus, capable of investigating liquid-liquid-vapor equilibria (LLVE) and solid-liquid-vapor equilibria (SLVE) of complex systems with non-volatile components such as drugs or polymers. 

Brewer, J., N. Rodewald, and F. Kurata. 1961. "Phase Equilibria of the Propane-Hydrogen Sulfide System from the Cricondentherm to Solid-Liquid-Vapor Region", AIChE J. 7 13-16. 

A similar treatment may be given to a system where a single substance may exist in the three forms solid, liquid, vapor, and when the fusion is accompanied by an increase in volume. In this case the curve of fusing-points F F (Fig. 50) rises from left to right. 

The processes on solid/vapor interfaces (or solid surfaces) and solid/liquid interfaces differ sufficiently from the liquid/vapor systems. Due to huge relaxation times in the solid phase, the atoms or molecules in the interior are not capable of moving to the surface to accommodate the new area created, as in the case of liquid surfaces. It was noted in [1,48] that the excess stress at solid surfaces and solid/liquid interfaces can have opposite sign. However, there was no clear explanation of that fact. The relation between the surface stress a, and solid surface free energy 7sv, was first pointed out by Shuttleworth [49],... 

For ascertaining the process conditions of RESS and PGSS, it is essential to have knowledge of the equilibrium solubility of the solute in dense gas (SCF phase) and vice versa, and also the P-T trace for the solid-liquid-vapor (S-L-V) phase transition of the drug substance. If all three phases coexist, there is only a single degree of freedom for a binary system, and a P-T trace of the S-L-V equilibrium is sufficient to determine the phase equilibrium compositions. 

Mukhopadhyay M, Dalvi SV. A new thermodynamic method for solid-liquid-vapor equilibrium in Ternary systems from binary data for antisolvent crystallization. Proceedings of the 6th International Symposium, France, April 2003. 

The pressure-temperature phase diagrams also serve to highlight the fact that the polymorphic transition temperature varies with pressure, which is an important consideration in the supercritical fluid processing of materials in which crystallization occurs invariably at elevated pressures. Qualitative prediction of various phase changes (liquid/vapor, solid/vapor, solid/liquid, solid/liquid/vapor) at equilibrium under supercritical fluid conditions can be made by reference to the well-known Le Chatelier s principle. Accordingly, an increase in pressure will result in a decrease in the volume of the system. For most materials (with water being the most notable exception), the specific volume of the liquid and gas phase is less than that of the solid phase, so that... 

Some of the liquid vaporizes and some freezes, so that a solid-liquid-vapor mixture is present. Thus, the system is at the triple point at equilibrium. [The energy released in solidification of the water goes to heat the system up to 0°C, the triple point temperature.]... 

Since the sublimation and vapor pressures below the normal melting point are so far below the total system pressure of 1 atm (1.013 bar), we do not have to consider either solid-vapor or solid-liquid-vapor equilibrium. 

The equilibrium condition for a solid-liquid-vapor (SLV) system at a specified temperature and pressure may be written in terms of the fugacities of the solid-forming component as... 

Figure 2. Experimental and predicted solid-liquid-vapor locus for the methane-carbon dioxide system (O), Davis et al. (13) (A), Donnelly ir Katz (14) ( ), Sobocinski 6- Kurata (15) (-), P-R prediction.

Figure 3. Liquid composition at the solid-liquid-vapor condition in the methane-ethane-carbon dioxide ternary system ( ), —84.9°F (A), -90°F (M), —100°F ( ), -I29.9°F ( ), -I<50°F.

The development of SCF processes involves a consideration of the phase behavior of the system under supercritical conditions. The influence of pressure and temperature on phase behavior in such systems is complex. For example, it is possible to have multiple phases, such as liquid-liquid-vapor or solid-liquid-vapor equilibria, present in the system. In many cases, the operation of an SCF process under multiphase conditions may be undesirable and so phase behavior should first be investigated. The limiting case of equilibrium between two components (binary systems) provides a convenient starting point in the understanding of multicomponent phase behavior. 

When one component is present in three phases at equilibrium, the phase rule states that the system is invariant and possesses no degrees of freedom. This implies that such a system at equilibrium can only exist at one definite temperature and one definite pressure, which is termed the triple point. For instance, the solid/liquid/vapor triple point of water is found at a temperature of 273.16K and a pressure of 4.58 torr. 

Although the solid/liquid/vapor triple point is the most commonly encountered, the existence of other solid phases yields additional triple points. The number of triple points possible to a polymorphic system increases very rapidly with the number of potential solid phases. 

This review will present the basic surface chemical and rheological principles involved in the spreading of polymers. First, the case of static drops or films of liquids in equilibrium on solid surfaces is discussed. Secondly, we discuss systems where the solid/liquid/vapor interfacial forces are not in equilibrium and the liquid is free to spread spontaneously. Finally, we deal as best we can with the much more difficult problem of a liquid being spread by an external force, i.e., forced spreading. 

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