A model describing the variation in free energy in compound and single phase regions in binary systems containing miscibility gaps

1965 ◽  
Vol 18 (12) ◽  
pp. 1897
Author(s):  
JD Esdaile
Keyword(s):  
Experimental Data ◽  
Free Energy ◽  
Binary Systems ◽  
Atomic Fraction ◽  
Two Phase ◽  
Phase Fields ◽  
Isothermal Diagram ◽  
Integral Free Energy ◽  
Miscibility Gaps ◽  
Straight Lines

A model is derived to represent the variation of free energy of combination of one gram-atom of two components, represented by A and B, in intermediate single, or compound, phases in a binary system as a function of composition at constant temperature, and with a minimum of experimental data. The derivation of the model involves the, assumption that the straight lines representing the free energy of the two phase fields adjacent to a compound phase, on an isothermal integral free energy against atomic fraction diagram, intersect at the mid-point of the compound phase. A relation between logaA, logaB, and the atomic fraction NB is developed so as to conform with the preceding requirement and yield an almost horizontal tangent to the curve representing the compound phase at NB = � for a hypothetical symmetrical isothermal diagram. The equations developed on these bases are extended to non-symmetrical systems. These are shown to be successful in predicting the variation in free energy of compound phases, as a function of composition, in binary systems for which experimental data are available.

scholarly journals Statistical mechanics of binary systems

1942 ◽  
Vol 179 (978) ◽  
pp. 340-361 ◽  
Keyword(s):  
Phase Transition ◽  
Solid Solution ◽  
Partition Function ◽  
Binary Systems ◽  
Binary Solution ◽  
Phase Region ◽  
Atomic Fraction ◽  
Phase Boundaries ◽  
Binary Solid Solution ◽  
Two Phase

Mayer’s method for the expansion of the partition function of a gas is adapted to the calculation of the partition function of a binary solid solution. The partition function is expanded in powers of the atomic fraction. Singularities in this expansion correspond to a phase transition. The singularity can be calculated in the simplest case of a binary solution with a two-phase region. This case is treated in full; the limits of solubility and the specific heat are obtained. The latter is discontinuous at the phase boundaries.

Correlation of Surface and Interfacial Tension of Light Hydrocarbons in the Critical Region

1961 ◽  
Vol 1 (04) ◽  
pp. 259-263 ◽  
Author(s):  
E.W. Hough ◽  
G.L. Stegemeier
Keyword(s):  
Experimental Data ◽  
Surface Tension ◽  
Interfacial Tension ◽  
Critical Pressure ◽  
Binary Systems ◽  
Gas Oil ◽  
Light Hydrocarbons ◽  
Two Phase ◽  
Component Systems ◽  
Two Phases

Abstract Empirical equations for surface tension of propane and normal butane as functions of reduced temperature are obtained from experimental data. Another correlation relating surface tension to enthalpy of vaporization is given for these two compounds. In addition, new parachor numbers are calculated for the normal paraffin hydrocarbons. These numbers are utilized for the calculation of interfacial tension of two-component systems as functions of pressure and temperature, using a modified form of Weinaug-Katz equation. The experimental data for two binary systems are approximated by the correlation. From these results it is found that the inter facial tension in the high-pressure region remains extremely low at large pressure decrements below the critical pressure. Thus, it appears that condensate systems may have flow characteristics almost like single-phase conditions even though the pressure is within the two-phase region. Experimental data have shown that interfacial tension divided by density difference approaches zero as the critical pressure is approached. A calculation of wetting-phase saturations indicates that the saturation gradient at the two-phase contact becomes increasingly abrupt as the critical pressure is approached. Discussion Prediction of the surface and interfacial tension of the light hydrocarbons and of two-component hydrocarbon mixtures at various temperatures and pressures may be made if other physical properties are known. Extensive experimental work on single-component and binary systems is the basis for the correlations outlined in this paper. Interfacial tension is defined as the specific surface-free energy between two phases of unlike fractional composition, while surface tension is defined as the specific surface-free energy between two phases of the same fractional composition. The usual definitions relating interfacial tension to a liquid-liquid interface and surface tension to a gas-liquid interface are not clearly defined when the critical region is included, and there is no sharp distinction between a gas and a liquid phase. Interfacial tension is probably the most important single force that makes one-half to one-third of the total oil actually in place in a reservoir rock unrecoverable by conventional gas-drive or waterflood methods. A rough estimate of this figure for the United States is 100 billion bbl. Interfacial tension presently is used by petroleum engineers in the estimation of saturation gradients at the gas-oil contact and at the oil-water contact. The data in this paper should prove useful for estimates of reserves involving gas-oil contacts. Relative permeability undoubtedly is influenced by interfacial tension, for sufficiently small values. These data should be useful in determining how small the values are. In addition, these data should eventually add to our fundamental knowledge of surfaces. At the critical point, all surface excesses approach zero and the thickness becomes very large. SINGLE-COMPONENT SYSTEMS It has been observed that the following relationships are good approximations to the physical properties of propane and n-butane. For propane, For n-butane, Guggenheim's values for these constants, not specifically for hydrocarbons, are SPEJ P. 259^

scholarly journals Kinetics and thermodynamic properties related to the drying of 'Cabacinha' pepper fruits

2016 ◽  
Vol 20 (2) ◽  
pp. 174-180 ◽  
Author(s):  
Hellismar W. da Silva ◽  
Renato S. Rodovalho ◽  
Marya F. Velasco ◽  
Camila F. Silva ◽  
Luís S. R. Vale
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Free Energy ◽  
Thermodynamic Properties ◽  
Gibbs Free Energy ◽  
Removal Rate ◽  
Effective Diffusion ◽  
Drying Time ◽  
Three Samples ◽  
Different Temperatures

ABSTRACT The objective of this study was to determine and model the drying kinetics of 'Cabacinha' pepper fruits at different temperatures of the drying air, as well as obtain the thermodynamic properties involved in the drying process of the product. Drying was carried out under controlled conductions of temperature (60, 70, 80, 90 and 100 °C) using three samples of 130 g of fruit, which were weighed periodically until constant mass. The experimental data were adjusted to different mathematical models often used in the representation of fruit drying. Effective diffusion coefficients, calculated from the mathematical model of liquid diffusion, were used to obtain activation energy, enthalpy, entropy and Gibbs free energy. The Midilli model showed the best fit to the experimental data of drying of 'Cabacinha' pepper fruits. The increase in drying temperature promoted an increase in water removal rate, effective diffusion coefficient and Gibbs free energy, besides a reduction in fruit drying time and in the values of entropy and enthalpy. The activation energy for the drying of pepper fruits was 36.09 kJ mol-1.

Development and Validation of a Three-Dimensional Multiphase Flow CFD Analysis for Journal Bearings in Steam and Heavy Duty Gas Turbines

2012 ◽  
Author(s):  
Stephan Uhkoetter ◽  
Stefan aus der Wiesche ◽  
Michael Kursch ◽  
Christian Beck
Keyword(s):  
Experimental Data ◽  
Multiphase Flow ◽  
Gas Turbines ◽  
High Speed ◽  
Three Dimensional ◽  
Air Entrainment ◽  
Journal Bearings ◽  
Heavy Duty ◽  
Present Contribution ◽  
Two Phase

The traditional method for hydrodynamic journal bearing analysis usually applies the lubrication theory based on the Reynolds equation and suitable empirical modifications to cover turbulence, heat transfer, and cavitation. In cases of complex bearing geometries for steam and heavy-duty gas turbines this approach has its obvious restrictions in regard to detail flow recirculation, mixing, mass balance, and filling level phenomena. These limitations could be circumvented by applying a computational fluid dynamics (CFD) approach resting closer to the fundamental physical laws. The present contribution reports about the state of the art of such a fully three-dimensional multiphase-flow CFD approach including cavitation and air entrainment for high-speed turbo-machinery journal bearings. It has been developed and validated using experimental data. Due to the high ambient shear rates in bearings, the multiphase-flow model for journal bearings requires substantial modifications in comparison to common two-phase flow simulations. Based on experimental data, it is found, that particular cavitation phenomena are essential for the understanding of steam and heavy-duty type gas turbine journal bearings.

scholarly journals An experimental and theoretical investigation of diffusion in a two-phase alloy

1948 ◽  
Vol 192 (1031) ◽  
pp. 575-592 ◽  
Keyword(s):  
Free Energy ◽  
Single Phase ◽  
Phase State ◽  
Theoretical Treatment ◽  
Research Association ◽  
Essential Difference ◽  
Two Phase ◽  
Two Factors ◽  
Order Of Magnitude ◽  
The Difference

The present paper describes an investigation of diffusion in the solid state. Previous experimental work has been confined to the case in which the free energy of a mixture is a minimum for the single-phase state, and diffusion decreases local differences of concentration. This may be called ‘diffusion downhill’. However, it is possible for the free energy to be a minimum for the two-phase state; diffusion may then increase differences of concentration; and so may be called ‘diffusion uphill’. Becker (1937) has proposed a simple theoretical treatment of these two types of diffusion in a binary alloy. The present paper describes an experimental test of this theory, using the unusual properties of the alloy Cu 4 FeNi 3 . This alloy is single phase above 800° C and two-phase at lower temperatures, both the phases being face-centred cubic; the essential difference between the two phases is their content of copper. On dissociating from one phase into two the alloy develops a series of intermediate structures showing striking X-ray patterns which are very sensitive to changes of structure. It was found possible to utilize these results for a quantitative study of diffusion ‘uphill’ and ‘downhill’ in the alloy. The experimental results, which can be expressed very simply, are in fair agreement with conclusions drawn from Becker’s theory. It was found that Fick’s equation, dc / dt = D d2c / dx2 , can, within the limits of error, be applied in all cases, with the modification that c denotes the difference of the measured copper concentration from its equilibrium value. The theory postulates that D is the product of two factors, of which one is D 0f the coefficient of diffusion that would be measured if the alloy were an ideal solid solution. The theory is able to calculate D/D 0 , if only in first approximation, and the experiments confirm this calculation. It was found that in most cases the speed of diffusion—‘uphill’ or ‘downhill’—has the order of magnitude of D 0 . * Now with British Electrical Research Association.

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