Binary mixtures, phase behavior

An occurrence of several critical points for monocomponent fluid leads to complication of binary mixture phase behavior. Following Varchenko s approach", generic phenomena encountered in binary mixtures when the pressure p and the temperature T change, correspond to singularities of the convex envelope (with respect to the x variable) of the front (a multifunction of the variable x) representing the Gibbs potential G(p,T,x). Pressure p and temperature T play the role of external model parameters like ki2. A total... 

For a comprehensive discussion of binary fluid-phase behavior, see J. S. Rowlinson and F. L. Swinton, Liquids and Liquid Mixtures, 3d ed., Butterworth Scientific, London, 1982. 

We have studied one-fluid model of binary fluids with polyamorphic components and found that multicritical point scenario gives opportunity to consider the continuous critical lines as the pathways linking isolated critical points of components on the global equilibria surface of binary mixture. It enhances considerably the landscape of mixture phase behavior in a stable region at the account of hidden allocation of other critical points in metastable region. 

The phase behavior of single-component systems has been discussed as part of thepVT relationship presented in Section 4.2.1. Examiifing the phase behavior of mixtures, we observe that, with mixtures, phase behavior remains one facet of the pVT relationship. But a new phenomenon is encountered with mixtures phases at equilibrium are generally of different compositions. These mixtures show a great variety of phase behavior that can often be exploited to make separations. We examine in broad terms the qualitative features of the phase behavior of binary mixtures of various types. Experience has shown a wealth of phenomena displayed by binary mixtures. 

Similarly to the phase diagrams for binary systems, the main types for fluid phase diagrams of ternary mixtures should not have an intersection of critical curves and inunis-cibUity regions with a crystallization surface in them. Combination of four main types of binary fluid phase behavior la, lb, Ic and Id (Figure 1.2) for constituting binary subsystems gives six major classes of ternary fluid mixtures with one volatile component, two binary subsystems (with volatile component) complicated by the immiscibility phenomena and the third binary subsystem (consisted from two nonvolatile components) of type la with a continuous solid solutions. These six classes of ternary fluid mixtures can be referred as ternary class I (with binary subsystems Ib-lb-la), ternary class II (with binary subsystems Ic-lc-la), ternary class III (with binary subsystems Id-ld-la), or ternary class IV (with binary subsystems Ib-ld-la), ternary class V (with binary subsystems Ib-lc-la) and ternary class VI (with binary subsystems Ic-ld-la). 

In the area of applications, an important goal for research in coming years will be to develop a set of pure component group-based potentials and combining rules that can be used for general predictions of both pure component and mixture phase behavior. Early results for realistic mixtures [117] suggest that relatively simple intermolecular potential models can be used to predict the phase behavior of broad classes of binary systems. For mixtures with large differences in polar character of the components. 

Ternary Blends. Discussion of polymer blends is typically limited to those containing only two different components. Of course, inclusion of additional components may be useful in formulating commercial products. The recent Hterature describes the theoretical treatment and experimental studies of the phase behavior of ternary blends (10,21). The most commonly studied ternary mixtures are those where two of the binary pairs are miscible, but the third pair is not. There are limited regions where such ternary mixtures exhibit one phase. A few cases have been examined where all three binary pairs are miscible however, theoretically this does not always ensure homogeneous ternary mixtures (10,21). 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (soHd line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, C , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are CO2—/ -hexane and CO2—benzene. More compHcated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (Hquid—Hquid) immiscihility lines, and even three-phase (Hquid—Hquid—gas) immiscihility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include CO2—hexadecane and CO2—H2O Class IV, CO2—nitrobenzene Class V, ethane—/ -propanol and Class VI, H2O—/ -butanol. 

Figure 7.2 A three-dimensional phase diagram for a Type I binary mixture (here, CO2 and methanol). The shaded volume is the two-phase liquid-vapor region. This is shown ti uncated at 25 °C for illustration purposes. The volume surrounding the two-phase region is the continuum of fluid behavior.

For helium, a = 2.56 A and e/k = 10.22°K, where k is Boltzmann s constant. For xenon, e/k = 221 °K and a = 4.10. Because of symmetry, the subscript 1 may refer to either helium or xenon from the assumption of corresponding-states behavior, v°2 should be independent of the component chosen for subscript 1. Equation (108) is an equation of state for the binary mixture, and from it the phase behavior can be calculated without further assumptions. 

Wilding, N. B. Schmid, F. Nielaba, P., Liquid-vapor phase behavior of a symmetrical binary fluid mixture, Phys. Rev. E 1998, 58, 2201-2212... 

Two-constant equation of state phase behavior calculations for aqueous mixtures often require the use of temperature dependent binary interaction parameters. The methods used for evaluating these parameters for some of the typical aqueous binary pairs found in coal gasification and related process streams are described. Experimental and predicted phase compositions based on these methods are illustrated for aqueous pairs containing CO2. H2S, NH3, and other gases. 

Schwahn, D. Willner, L. Phase Behavior and Flory-Huggins Interaction Parameter of Binary Polybutadiene Copolymer Mixtures with Different Vinyl Content and Molar Volume. Macromolecules 2002,35, 239-247. 

The thermotropic behavior and phase diagrams of binary mixtures of copper and gold complexes of the type [MX(CNR)] (X = anionic ligand, R = p-alkoxyaryl group) have been studied [32] and the main results are ... 

The phase map shown in Figure IB represents the skin permeation enhancement activity of the formulations containing binary mixtures of lauryl sarcosinate and sorbitan monolaurate at different concentrations and compositions. The region of maximum activity lies in a very narrow range of compositions. For such a nonlinear activity-composition behavior, it is very important to probe the binary phase map at as fine a resolution as possible, thus increasing the experimentation volume. 

Figure 4.26 shows a flow reactor of diameter D in which the downstream portion of the walls is catalytic. Assume that there is no gas-phase chemistry and that there is a single chemically active gas-phase species that is dilute in an inert carrier gas. For example, consider carbon-monoxide carried in air. Assume further a highly efficient catalyst that completely destroys any CO at the surface in other words, the gas-phase mass fraction of CO at the surface is zero. Upstream of the catalytic section, the CO is completely mixed with the carrier (i.e., a flat profile). The CO2 that desorbs from the catalyst is so dilute in the air that its behavior can be neglected. Thus the gas-phase and mass-transfer problem can be treated as a binary mixture of CO and air. The overall objective of this analysis is to... 

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