Binary Solid-Liquid Equilibria

Only the solid and liquid phases are of interest in most crystallization processes therefore, the vapor phase will generally be ignored in the following discussion. Furthermore, pressure has little effect on the properties of condensed phases, and will also be ignored in most of what follows. 

What does all this mean In the simplest terms, we can express these choices graphically as follows  

As can be seen, the two standard-state choices correspond to the limiting Raoult s law [P° (I)] or Henry s law [P° (II)] dashed lines at x, = 1. Accordingly, for solving problems involving activities, we can always use the equation 

For ideal solutions, these two conventions become equivalent (P° = Pj = A Henry)5 but for real solutions the distinction between solvent (Pa) and solute (Pg) standard states must be kept in mind. 

The T-x diagrams for binary solid-liquid systems can be categorized into four primary types  

We shall first describe representative behavior for each type (Sections 7.4.1-7.4.4), then sketch how continuous changes in intermolecular interactions are expected to lead continuously from one type of T-x behavior to another (Section 7.4.5), including rather uncommon features such as solid-solid consolute points. 

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The case of binary solid-liquid equilibrium permits one to focus on liquid-phase nonidealities because the activity coefficient of solid component ij, Yjj, equals unity. Aselage et al. (148) investigated the liquid-solution behavior in the well-characterized Ga-Sb and In-Sb systems. The availability of a thermodynamically consistent data base (measurements of liquidus, component activity, and enthalpy of mixing) provided the opportunity to examine a variety of solution models. Little difference was found among seven models in their ability to fit the combined data base, although asymmetric models are expected to perform better in some systems. 

Knoester, M., De Bruijne, P., and van den Tempel, M. (1972). The solid-liquid equilibrium of binary mixtures of triglycerides with palmitic and stearic chains. Chem. Phys. Lipids. 9,309-319. 

To obtain the values of kaa for the binary mixture PH (1) + NA (2), the solid-liquid equilibrium data for this system [22] were used. The mole fraction of component a in the liquid phase was expressed through the modihed Schroder equation [23],... 

Now consider the case depicted in figure 3.20c, an isotherm at the UCEP temperature (see figure 3.19). At the UCEP pressure there is a vapor-liquid critical point in the presence of solid. This requires the solid-liquid equilibrium curve to intersect the liquid-gas envelope precisely at the binary liquid-gas critical point and, hence, exhibit a negative horizontal inflection, i.e., (dPldx)T = 0. Notice that the vapor-liquid envelope has not shrunk to a point, as it did at the naphthalene-ethylene UCEP. The solid curve shown in figure 3.20d is the solubility isotherm obtained if a flow-through apparatus is used and only the solubility in the SCF phase is determined. This solid curve has the characteristics of the 55°C biphenyl-carbon dioxide isotherm shown in figure 3.17. So the 55°C isotherm represents liquid biphenyl solubilities at pressures below 475 bar and solid biphenyl solubilities at pressures above 475 bar. 

FIGURE 9.26 The thermodynamic equilibrium phase diagram for a binary solid-liquid system. The eutectic temperature and species A mass fraction and a dendritic temperature and liquidus and solidus species A mass fractions are also shown. 

AC or BC, which melts at a higher temperature than either of the pure elements (except for the InSb-Sb case). The binary phase diagram consists of two simple eutectic systems on either side of the compound (e.g., the A-AC and the AC-C systems). The third binary phase diagram represents solid-liquid equilibrium between elements from the same group. In Figure 1 the A-B portion of the ternary phase diagram is depicted as being isomorphous... 

The solid-liquid equilibrium state of the A-B-C ternary system is calculated by equating the temperature and pressure of each phase as well as the chemical potentials of each of the species present in both phases. In addition to these equations, a constraint of stoichiometry is placed on the solid solution the sum of the mole fractions of the Group III elements must be equal to the sum of the mole fractions of the Group V elements. Because of this constraint, the chemical potentials of the three species are not independently variable in the solid. The ternary solid solution A B C can be treated as if it were a binary solution of components and BC. The requirement of equal chemical potentials of each of the species present in both phases then becomes... 

Costa, M. C., Experimental determination of solid-liquid equilibrium for binary systems of saturated fatty acids a study detailed of the solid phase, D.Sc. Thesis, University of Campinas, Campinas, 2008. 

Besides the pure component parameters, in particular the mixture parameters, for example of a g -model or an equation of state, should be checked carefully prior to process simulation. The procedure is shown in Figure 11.4 for the binary system acetone-cyclohexane, which may be one of the binary key systems of a multicomponent mixture. From the results shown in Figure 11.4, it can be concluded that the VLE behavior of the binary system can be reliably described in the temperature range 0-50 C with the Wilson parameters used. But from the poor -results, it seems that an extrapolation to higher or lower temperature may be dangerous, as already can be seen from the solid-liquid equilibrium (SLE) results of the eutectic system in the temperature range 0 to —lOO C and also from the incorrect temperature dependence of the calculated azeotropic data. 

Gibilaro, L. G., di Felice, R. and Waldram, S. P. A predictive model for the equilibrium composition and inversion of binary-solid liquid fluidized beds. Chem. Engng Sci. 41, 379-387 (1986). 

Domanska, U. Lachwa, J. Thermodynamics of binary mixtures of N-methyl-2-pyrrolidinone and ketone. Experimental results and modelling of the (solid + liquid) equilibrium and the (vapour + liquid) equilibrium. The modified UNIFAC (Do) model characterization J. Chem. Thermodyn. 2005,37, 692-704... 

Phase behavior involving solid-liquid equilibrium is the basis for crystallization in chemical and materials engineering. Binary mixture systems can have up to three degrees of freedom according to the Gibbs phase rule. 

The following solid—liquid equilibrium data are available for a binary mixture of C and metastable y—F e. 

A brief discussion of sohd-liquid phase equihbrium is presented prior to discussing specific crystalhzation methods. Figures 20-1 and 20-2 illustrate the phase diagrams for binary sohd-solution and eutectic systems, respectively. In the case of binary solid-solution systems, illustrated in Fig. 20-1, the liquid and solid phases contain equilibrium quantities of both components in a manner similar to vapor-hquid phase behavior. This type of behavior causes separation difficulties since multiple stages are required. In principle, however, high purity... 

In the case of a unary or one-component system, only temperature and pressure may be varied, so the coordinates of unary phase diagrams are pressure and temperature. In a typical unary diagram, as shown in Figure 3.11, the temperature is chosen as the horizontal axis by convention, although in binary diagrams temperature is chosen as the vertical axis. However, for a one-component system, the phase rule becomes F=l-P+2 = 3-P. This means that the maximum number of phases in equilibrium is three when F equals zero. This is illustrated in Figure 3.11 which has three areas, i.e., solid, liquid, and vapour In any... 

Taking Simultaneous Micellizadon and Adsorption Phenomena into Consideration In the presence of an adsorbent in contact with the surfactant solution, monomers of each species will be adsorbed at the solid/ liquid interface until the dual monomer/micelle, monomer/adsorbed-phase equilibrium is reached. A simplified model for calculating these equilibria has been built for the pseudo-binary systems investigated, based on the RST theory and the following assumptions ... 

The data for the phase equilibrium solid-liquid for the binary system cocoa butter-CC>2 and for the equilibrium solubility data of CO2 in the liquid phase of cocoa butter have been presented [70],... 

Solubilities of meso-tetraphenylporphyrin (normal melting temperature 444°C) in pentane and in toluene have been measured at elevated temperatures and pressures. Three-phase, solid-liquid-gas equilibrium temperatures and pressures were also measured for these two binary mixtures at conditions near the critical point of the supercritical-fluid solvent. The solubility of the porphyrin in supercritical toluene is three orders of magnitude greater than that in supercritical pentane or in conventional liquid solvents at ambient temperatures and pressures. An analysis of the phase diagram for toluene-porphyrin mixtures shows that supercritical toluene is the preferred solvent for this porphyrin because (1) high solubilities are obtained at moderate pressures, and (2) the porphyrin can be easily recovered from solution by small reductions in pressure. 

However, for mixtures of TPP and toluene, a third (liquid) phase forms in the presence of the gas and the solid, at pressures well below the critical pressure of toluene. At higher pressures, gas-liquid and solid-liquid equilibria were observed, rather than gas-solid equilibrium. Thus, phase compositions for gas-liquid equilibrium were measured for this binary mixture to give TPP solubilities in each of the fluid phases. Pressures and temperatures for three-phase, solid-liquid-gas equilibrium were also measured for both binary mixtures. 

Types of Phases in Binary Systems.—A two-component system, like a system with a single component, can exist in solid, liquid, and gaseous phases. The gas phase, of course, is perfectly simple it is simply a mixture of the gas phases of the two components. Our treatment of chemical equilibrium in gases, in Chap. X, includes this as a special case. Any two gases can mix in any proportions in a stable way, so long as they cannot react chemically, and we shall assume only the simple case where the two components do not react in the gaseous phase. 

A new developed process PGSS (Particles from Gas Saturated Solutions) was applied for generation of powder from polyethyleneglycols. Principle of PGSS process is described and phase equilibrium data for the binary systems PEG-CO2 for the vapour-liquid and the solid-liquid range are presented in a master diagram . The influence of the process parameters on particle size, particle size distribution, shape, bulk density and crystallinity is discussed. 

Several authors [3-9] studied the solubility of polymers in supercritical fluids due to research on fractionation of polymers. For solubility of SCF in polymers only limited number of experimental data are available till now [e.g. 4,5,10-12], Few data (for PEG S with molar mass up to 1000 g/mol) are available on the vapour-liquid phase equilibrium PEG -CO2 [13]. No data can be found on phase equilibrium solid-liquid for the binary PEG S -CO2. Experimental equipment and procedure for determination of phase equilibrium (vapour -liquid and solid -liquid) in the binary system PEG s -C02 are presented in [14]. It was found that the solubility of C02 in PEG is practically independent from the molecular mass of PEG and is influenced only by pressure and temperature of the system. 

Two early studies of the phase equilibrium in the system hydrogen sulfide + carbon dioxide were Bierlein and Kay (1953) and Sobocinski and Kurata (1959). Bierlein and Kay (1953) measured vapor-liquid equilibrium (VLE) in the range of temperature from 0° to 100°C and pressures to 9 MPa, and they established the critical locus for the binary mixture. For this binary system, the critical locus is continuous between the two pure component critical points. Sobocinski and Kurata (1959) confirmed much of the work of Bierlein and Kay (1953) and extended it to temperatures as low as -95°C, the temperature at which solids are formed. Furthermore, liquid phase immiscibility was not observed in this system. Liquid H2S and C02 are completely miscible. 

A brief discussion of solid-liquid phase equilibrium is presented prior to discussing specific crystallization methods. Figures 22-1 and 22-2 illustrate the phase diagrams for binary solid-solution and eutec-... 

The thermodynamic relationships for equilibrium between a binary solid solution and a binary liquid solution are given by... 

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