Binary system with limited

Thermodynamic Description of a Binary System With Limited Miscibility. 

Kinetic Description of a Binary System With Limited Miscibility. The kinetic interpretation of a system with limited miscibility can be expressed in terms of the diffusion coefficient D of the system. At constant pressure and temperature, again three different states can be distinguished (4) ... 

Cho, T.-H. Ochi, K. Kojima, K. Isobaric vapor-liquid equilibria for binary systems with limited miscibiiity, water - n-amyi... 

Fig. C.4. Schematic phase diagram of a binary system with limited solubihty of the components...

In general, tests have tended to concentrate attention on the ability of a flux model to interpolate through the intermediate pressure range between Knudsen diffusion control and bulk diffusion control. What is also important, but seldom known at present, is whether a model predicts a composition dependence consistent with experiment for the matrix elements in equation (10.2). In multicomponent mixtures an enormous amount of experimental work would be needed to investigate this thoroughly, but it should be possible to supplement a systematic investigation of a flux model applied to binary systems with some limited experiments on particular multicomponent mixtures, as in the work of Hesse and Koder, and Remick and Geankoplia. Interpretation of such tests would be simplest and most direct if they were to be carried out with only small differences in composition between the two sides of the porous medium. Diffusion would then occur in a system of essentially uniform composition, so that flux measurements would provide values for the matrix elements in (10.2) at well-defined compositions. 

Because of the interest in its use in elevated-temperature molten salt electrolyte batteries, one of the first binary alloy systems studied in detail was the lithium-aluminium system. As shown in Fig. 1, the potential-composition behavior shows a long plateau between the lithium-saturated terminal solid solution and the intermediate P phase "LiAl", and a shorter one between the composition limits of the P and y phases, as well as composition-dependent values in the single-phase regions [35], This is as expected for a binary system with complete equilibrium. The potential of the first plateau varies linearly with temperature, as shown in Fig. 2. 

The distillation of binary mixtures is covered thoroughly in Volume 2, Chapter 11, and the discussion in this section is limited to a brief review of the most useful design methods. Though binary systems are usually considered separately, the design methods developed for multicomponent systems (Section 11.6) can obviously also be used for binary systems. With binary mixtures fixing the composition of one component fixes the composition of the other, and iterative procedures are not usually needed to determine the stage and reflux requirements simple graphical methods are normally used. 

The mass function, which is a pure combination of observables, is a lower limit to the possible mass of star 2 if the orbit is other than edge-on (that is, if % < 90°) or the observed star has mi > 0, then m2 > / Thus, observation of one star constrains the mass of the other star. Note, incidentally, that in a neutron star binary system with a high-mass companion (mi m2), / is low... 

Using a recent equation of state of the van der Waals type developed to describe non-polar components, a model is presented which considers water as a mixture of monomers and a limited number of polymers formed by association. The parameters of the model are determined so as to describe the pure-component properties (vapour pressure, saturated volumes of both phases) of water and the phase equilibria (vapour-liquid and/or liquid-liquid) for binary systems with water including selected hydrocarbons and inorganic gases. The results obtained are satisfactory for a considerable variety of different types of system over a wide range of pressure and temperature. 

Eutectic diagrams (from Greek svtt]ktoo- easily melted ) represent the T-x melting behavior for binary systems with completely immiscible solid phases a, /3. The solid a, /3 phases often correspond to (virtually) pure components A, B, respectively, so we may treat phase and component labels (rather loosely) as interchangeable in this limit. 

Figure 5.7 exhibits the prediction of the SS-LMBW/RISM-KHM theory for the site density profiles of the liquid/Iiquid interface in the binary system with partially miscible n-hexane and methanol at ambient conditions. The bulk limiting values of the n-hexane density in the phase rich in n-hexane (z —oo) and of the methanol density... 

Wilson equation Interaction method for the excess Gibb s energy suitable for totally miscible systems, not applicable for systems with limited miscibility since only the binary parameters are used, applicable to multicomponent systems only valid for small and medium operating pressures Wilson, G.M., J. Am. Chem. Soc. 86 (1964) 127. 

NRTL equation (non random two liquids) Method based on the Wilson equation with nonrandomness parameter which can be applied to systems with limited miscibility and nonideal systems use of binary parameters to calculate multicomponent data only valid for small and medium operating pressures Renon, H., and Prausnitz, J.M., AIChE. J. 14 (1968) 135. Renon, H., and Prausnitz, J.M., Ind. Eng. Chem. Dev. 8 (1969) 3, 413. 

Fig. 1-21. Pressure diagram (a), boiling diagram (b) and equilibrium diagram (c) of a binary mixture with a miscibility gap over the complete concentration range (left column) and a binary system with a limited miscibility gap (right column).

The region in which vapor and liquid may coexist in a binary system is limited by the vapor pressure curves of the pure components and the critical line. In Figure 5.9 the vapor pressure curves of the pure compounds of the system ethane-heptane are shown together with the PT-curves of different fixed compositions of the liquid and the vapor phase. The intersections of the dew point and the bubble point curve for a given temperature and pressure mark the VLE for the chosen compositions in the liquid and the vapor phase. The critical points of a binary system can be found where a loop in Figure 5.9 is tangential to the envelope critical curve, also called critical locus. 

Manley, D. B. A better method for calculating relative volatility. Hydrocarbon Proc. 51 (l 972) Nr. 1,113 Mertl, I. Liquid-vapor equilibrium. Prediction of multicomponent vapor-liquid equilibria from the binary parameters in systems with limited miscibility. Coll. Czech. Chem. Comm. 37 (1972) 375. 

FIG. 13-37 McCabe-Thiele diagrams for limiting cases, a) Minimum stages for a column operating at total reflux with no feeds or products, (h) Minimum reflux for a binary system of normal volatility. 

On the other hand, very few ncdels for nulticonponent systans have been reported in the literature. Apart from models for binary systems, usually restricted to "zero-one" systans (5) (6), the most detailed model of this type has been proposed by Hamielec et al. (7), with reference to batch, semibatch and continuous emilsion polymerization reactors. Notably, besides the usual kinetic informations (nonomer, conversion, PSD), the model allows for the evaluation of IWD, long and short chain brandling frequencies and gel content. Comparisons between model predictions and experimental data are limited to tulK and solution binary pwlymerization systems. 

Adsorption phenomena from solutions onto sohd surfaces have been one of the important subjects in colloid and surface chemistry. Sophisticated application of adsorption has been demonstrated recently in the formation of self-assembhng monolayers and multilayers on various substrates [4,7], However, only a limited number of researchers have been devoted to the study of adsorption in binary hquid systems. The adsorption isotherm and colloidal stabihty measmement have been the main tools for these studies. The molecular level of characterization is needed to elucidate the phenomenon. We have employed the combination of smface forces measmement and Fomier transform infrared spectroscopy in attenuated total reflection (FTIR-ATR) to study the preferential (selective) adsorption of alcohol (methanol, ethanol, and propanol) onto glass surfaces from their binary mixtures with cyclohexane. Om studies have demonstrated the cluster formation of alcohol adsorbed on the surfaces and the long-range attraction associated with such adsorption. We may call these clusters macroclusters, because the thickness of the adsorbed alcohol layer is about 15 mn, which is quite large compared to the size of the alcohol. The following describes the results for the ethanol-cycohexane mixtures [10],... 

In practice, VLE data are available as sets of isothermal measurements. The number of isotherms is usually small (typically 1 to 5). Hence, we are often left with limited information to perform interpolation with respect to temperature. On the contrary, one can readily interpolate within an isotherm (two-dimensional interpolation). In particular, for systems with a sparingly soluble component, at each isotherm one interpolates the liquid mole fraction values for a desired pressure range. For any other binary system (e.g., azeotropic), at each isotherm, one interpolates the pressure for a given range of liquid phase mole fraction, typically 0 to 1. 

After the discovery of the Al6Mn i-QC [1], development of QCs were limited for almost a decade to ternary systems with a major A1 constituent, such as Al-(Pd,Mn)-Si, Al-Zn-(Li,Mg), Al-Cu-TM (TM = Fe, Ru, Os), Al-Pd-(Mn,Re) [2,25,26], (This may be the reason why jargon such as Al-based QCs was coined.) After all, most QC discoveries were achieved by chemical additions to, or substitutions in, known compounds. From the mid-1990s to about 2000, QCs were also found in Zn-Mg-R (R = rare-earth-metal), Cd-Mg-R, and (Yb,Ca)-Cd systems, the last being the first stable binary i-QC at room temperature. Experience and insight are worth a lot — Tsai and coworkers produced 90% of these i-QCs [27],... 

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