Graham Morrison

Phase equilibria in polydisperse fluids

We present a new approach for solving phase equilibria problems in multicomponent systems together with several applications. A mathematical framework is developed that provides a method for generalizing the thermodynamics of a finite‐component system to that of a system with an infinite number of components—a polydisperse system. Two new functions, the mole fraction distribution function and the mole fraction density function, play a key role in our method. The phase equilibria conditions are written in terms of these functions and are formally solved. We illustrate the utility of our approach by solving, for a polydisperse generalization of the van der Waals model, three phase‐equilibria problems: (1) the fractionation of a polydisperse impurity dissolved in a solvent; (2) the shift of the critical temperature and density due to the presence of a polydisperse impurity; (3) the calculation of the cloud‐point surface and critical point of a completely polydisperse system.

Thermodynamic properties of two alternative refrigerants: 1,1-dichloro-2,2,2-trifluoroethane (R123) and 1,1,1,2-tetrafluoroethane (R134a)

Abstract This paper describes two different sets of measurements of the properties of two proposed alternative refrigerants, 1,1,1,2-tetrafluoroethane (R134a) 1 and 1,1-dichloro-2,2,2-trifluoroethane (R123) 1 . The first are vapor—liquid equilibrium measurements made in a simple variable-volume sapphire cell. The vapor pressures and saturation liquid densities were determined for both materials, between 268 K and the critical temperature for R134a and between 303 K and 373 K for R123. The saturation vapor density was also determined for R134a from 298 K to the critical point, where the critical conditions were measured. The second set of measurements were made with a vibrating tube densimeter from the saturation pressure to 5500 kPa for R134a and to 3500 kPa for R123 in the temperature range 278 K–368 K. These data are then compared with other determinations of similar properties.

Critical behavior in fluids and fluid mixtures

Abstract The presence of large fluctuations near a critical point leads to thermodynamic anomalies not present in classical, i.e., analytic equations, such as that of van der Waals. We introduce the concepts of universality, critical exponents, scaling laws, “field” and “density” variables, “strong” and “weak” directions. Experimental evidence for the presence of nonclassical critical behavior in fluids and fluid mixtures is presented. A scaled thermodynamic potential represents the thermodynamic data of steam, ethylene and isobutane accurately. It is valid up to 1.07 T c , and within ±30% from ρ c . Methods for joining it to an analytic equation are discussed. The generalization to a nonclassical description of fluid mixtures is described, and applications are given. The engineer may require the nonclassical description in custody transfer, design of supercritical power cycles and supercritical extraction. The classical approach is used here to explain peculiarities of dilute mixtures recently reported by several experimenters.

Thermodynamic behavior of supercritical fluid mixtures

The recent surge of interest in supercritical extraction has brought the unusual properties of supercritical mixtures into the focus of attention. We discuss some of the properties of binary mixtures in a range around the gas-liquid critical line from the point of view of supercritical solubility. The general thermodynamic relationships that govern the enhancement of supercritical solubility are readily derived by a mathematical method introduced by Ehrenfest. The enhancement is governed by a strong divergence centered at a critical end point. We give the classical and nonclassical power-law behavior of the solubility along the experimental paths of constant temperature or pressure. The factor multiplying the strong divergence contains the partial molar volume or enthalpy of the solute in the supercritical phase. These partials are quite anomalous, especially if the mole fraction of the solute is small. They diverge at the solvents critical point. We cite experimental evidence of these divergences, especially the results of recent experiments in dilute near-critical salt solutions. The anomalies found in these salt solutions are common to all dilute near-critical mixtures with a nonvolatile second component. We show that on experimentally convenient paths the solubility in a binary liquid mixture near its consolute points is not strongly enhanced. Finally, we sketch a nonclassical model based on the decorated lattice gas that can be used to describe supercritical solubility enhancement at low solubility, with the pure solvent used as a reference.

Compressed Liquid Densities and Saturation Densities of Pentafluoroethane (R125)

A vibrating tube densimeter was used to measure the density of pentafluoroethane, R125. Measurements were made between 275 and 369 K, and 1600 and 6300 kPa. Densities ranged between 0.2584 and 1.3484g cm−1 with an accuracy of ± 0.05% except in the near-critical region. A 32 parameter modified Benedict-Webb-Rubin equation of state (MBWR) was fit to the data.

Azeotropy in refrigerant mixtures: Azéotropie dans les mélanges de frigorigènes

Abstract Azeotropic mixtures are attractive as refrigerants because they behave very nearly as pure materials. A simple correlative scheme that allows one to judge whether or not an azeotrope is likely in a binary refrigerant mixture is developed. The existence of 65 azeotropes in the 300 possible binary mixtures of 25 selected refrigerants is predicted. Of those, 23 have been reported in extensive compilations of such information. Among the remainder, for which there is apparently no experimental information, are mixtures that might offer promise as alternative refrigerants.

Interaction coefficients for 15 mixtures of flammable and non-flammable components

Abstract Bubble pressures were measured for 15 binary mixtures, each composed mainly of one flammable and one non-flammable component. The mixtures were trichlorofluoromethane + isopentane, pentafluoroethane + 1,1,1-trifluoroethane, 1,1-dichloro-2,2,2-trifluoroethane+{1,1-dichloro-1-fluoroethane or isopentane}, 1,1,1,2-tetrafluoroethane+{1,1-difluoroethane or propane or cyclopropane or isobutane}, difluoromethane +{pentafluoroethane or 1,1,1,2-tetrafluoroethane or 1,1-difluoroethane}. Also studied were mixtures of 1,1-difluoroethane+{cyclopropane or propane or butane or isobutane}, which comprise two flammable components. The measurements were made at approximately equimolar compositions using either a vapour-liquid equilibrium apparatus over a range of temperatures, or a static pressure measurement at 273.15K. The bubble pressures were used to determine interaction coefficients that characterize the non-ideal behaviour of these fluid mixtures. The interaction coefficients are used in equation-of-state models for the thermodynamic properties of refrigerant mixtures.

Thermodynamic properties of CHF2-O-CHF2, bis(difluoromethyl) ether

Abstract Defibaugh, D.R., Gillis, K.Aa Moldover M.R., Morrison, G. and Schmidt, J.W., 1992. Thermodynamic properties of CHF2-O-CHF2, bis(difluoromethyl) ether. Fluid Phase Equilibria, 81: 285–305. We have measured the thermodynamic properties of bis(difluoromethyl) ether, CHF2-O- CHF2, a candidate alternative refrigerant that is also known as E134. From the data we obtained the coefficients of a Carnahan-Starling-DeSantis equation of state and a polyno- mial representation of the ideal-gas heat capacity. This representation of the thermodynamic properties of E134 is consistent with the computer package REFPROP distributed by the National Institute of Standards and Technology to represent the properties of many candidate refrigerants. The representation is based on measurements of the refractive index of the saturated liquid and vapor, and the speed of sound of the dilute vapor. These measurements provide the boiling point, critical parameters, and the ideal-gas heat capacity of E134. Measurements on less pure samples were used to estimate the density of saturated liquid E134 and compressed liquid E134, and the interfacial tension. The pure samples appeared to be stable during the measurements; under similar conditions impure samples were not. Azeotropy in mixtures of E134 with CHF2CH2F (also known as R143) was discovered.

Modelling aqueous solutions near the critical point of water

We review the thermodynamic properties of dilute solution near the critical point of the solvent. Two examples are discussed, a solution of a non-electrolyte and a solution of an electrolyte. The limiting behavior of the electrolyte solutions is modelled with a Debye-Huckel term in the Helmholtz free energy. The partial molar properties, in particular the volume and isobaric thermal expansion are examined in detail. The derivation of these properties is introduced by considering the geometry of the thermodynamic surfaces near to and far from the critical point of the solvent. We conclude that the properties of solutions near the solvent critical point are dominated by that feature; solution properties cannot be adequately modelled without including the functional forms associated with the critical point.

The shape of the temperature-entropy saturation boundary

Abstract The phase diagram in temperature-entropy space plays an important role in the visualization, design and analysis of operating cycles in refrigerators and heat pumps. The shape of the phase boundary in this space varies dramatically from one material to another. The origin of these differences is shown to be a consequence of molecular structure. Relationships of varying accuracy are developed to estimate the slope of the vapour branch of the T - S diagram.