Critical solutions near their

Equations III-10 and III-11 are, of course, approximations, and the situation has been examined in some detail by Cahn and Hilliard [9], who find that Eq. Ill-11 is also approximated by regular solutions not too near their critical temperature. 

In these examples, as one would expect, the interfacial tensions are small and diminish as the critical solution temperature is approached. The differences between the surface tensions of the two phases are generally too small to decide whether the interfacial tension approaches zero asymptotically in all cases although such appears to be the case in the phenol water system we notice however that the temperature coefficient is very small indeed, as is the case for surface tensions of liquids near their critical point, but to a still greater degree. 

The continuous critical line for systems such as NaCl + H20 offers a temperature window for studying the behavior of electrolyte solutions near their liquid-vapor transition. Pitzer [4,13,142,144] compiled much evidence that the nonclassical fluctuations in pure water are apparently suppressed when adding electrolytes. Thus, from the application s point of view, a classical EOS may be quite useful. The pressing question is to what degree these observations withstand more quantitative analysis. 

As a final observation, we note from Figure 18.7 that the effect of pressure on V and its derivatives is small at all except the highest temperatures and low molalities. These results are not unexpected, since condensed phases are not very compressible. At the temperature and molality conditions where pressure effects are significant, the solutions are dilute and the temperatures approach the critical temperature of water (Tc = 647.3 K). When liquids are at temperatures near their critical temperature, they become more compressible, and pressure will have a larger effect on quantities such as V and its derivatives. 

Since both ethylene and ethane have reduced temperatures nearly equal to unity at the extraction conditions of 20 C, (T =. 98) and ethylene (T = 1.04), their respective solvent capacities for butene should be about the same. This is the case as is reflected in the same values for the selectivity against butene for all pure solvent gases. One can conclude that the primary effect of the non-polar solvent is to increase the capacity of the "vapor" phase for the extracted solute near the critical. The influence of the second solvent provides only the option of modifying the physical parameters namely, pressure and temperature, under which the optimal extraction is to be conducted. The evidence for this is the effect of the ammonia on the selectivity as calculated by the EOS in Table V. The higher values for the selectivities in the ethylene mixtures are pronounced. It can be concluded that the solvent mixture interaction parameters must dominate the solubility of butene in the vapor phase. 

EHR Ehrlich, P. and Kurpen, J.J., Phase equilibria of polymer-solvent systems at high pressiue near their critical loci, polyethylene with n-alkanes, J. Polym. Sci. Part A, 1, 3217, 1963. 1965ALL Allen, G. and Baker, C.H., Lower critical solution phenomena in polymer-solvent systems,... 

First, for all reduced surfactants dissolved in solution at concentrations near their critical micelle concentrations (CMC), oxidation leads to an increase in the surface tension of the solution (Fig. 1). In the case of surfactants I and n, oxidation returns the surface tension of the solution to a value that is similar to the surfactant-free solution of electrolyte (approx. 72 mN/m). The excess surface concentration of surfactant, estimated using the Gibbs adsorption equation, decreases in the case of surfactant II from 10x10 to < 0.1 X10 mol/m upon oxidation. Clearly, oxidation drives the desorption of surfactant from the surface of the solution. The increase in surface tension of... 

Rowley, R. L. Excess enthalpy of four partially miscible binary liquid mixtures near their critical solution Chem. Eng. Data 1990,35, 334-338... 

Supercritical fluids (SCFs) are compounds that exist at a temperature and pressure that are above their corresponding critical values [70,71]. They exhibit the properties of both gases and Hquids. With gases, they share the properties of low surface tension, low viscosity, and high diffusivity. Their main Hquid-like feature is the density, which results in enhanced solubility of solutes compared with the solubility of gases. Furthermore, the solubility of solutes can be manipulated by changes in pressure and temperature near the critical point [72]. 

Studies on non-ionic surfactants as effective drag-reducing additives have been submitted by Zakin (1972). He studied various effects on three non-ionic surfactants formed from straight-chain alcohols and ethyleneoxide. These surfactants have an upper and a lower temperature limit for solubility in water and prove effective drag reducers near their upper critical solubility temperature or clouding point. The clouding point is the point at which a solution of a non-ionic agent in water becomes turbid as the temperature is raised. 

In eqs 2 and 3, V is the molar volume, z is the compressibility factor, n is the total number of moles in the system, and ni is the number of moles of component i. Equations 2 and 3 show that the fugacity coefficient their derivatives with respect to the number of moles of solute are known. While near the critical point the fluctuations are important and an EOS involving them should be used, we neglect for the time being their effect. 

There have been a number of modeling efforts that employ the concept of clustering in supercritical fluid solutions. Debenedetti (22) has used a fluctuation analysis to estimate what might be described as a cluster size or aggregation number from the solute infinite dilution partial molar volumes. These calculations indicate the possible formation of very large clusters in the region of highest solvent compressibility, which is near the critical point. Recently, Lee and coworkers have calculated pair correlation functions of solutes in supercritical fluid solutions ( ). Their results are also consistent with the cluster theory. 

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