Phase equilibria binary liquid-solid

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. 

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 ... 

So, for this binary solution of components A and B, which mix perfectly at all compositions, there is a two-phase region at which both solid and liquid phases can coexist. The uppermost boundary between the liquid and liquid + solid phase regions in Figure 2.3f is known as the liquidus, or the point at which solid first begins to form when a melt of constant composition is cooled under equilibrium conditions. Similarly, the lower phase boundary between the solid and liquid + solid phase regions is known as the solidus, or the point at which solidification is complete upon further equilibrium cooling at a fixed composition. 

Three-Phase Transformations in Binary Systems. Although this chapter focuses on the equilibrium between phases in binary component systems, we have already seen that in the case of a entectic point, phase transformations that occur over minute temperature fluctuations can be represented on phase diagrams as well. These transformations are known as three-phase transformations, becanse they involve three distinct phases that coexist at the transformation temperature. Then-characteristic shapes as they occnr in binary component phase diagrams are summarized in Table 2.3. Here, the Greek letters a, f), y, and so on, designate solid phases, and L designates the liquid phase. Subscripts differentiate between immiscible phases of different compositions. For example, Lj and Ljj are immiscible liquids, and a and a are allotropic solid phases (different crystal structures). 

In a binary system more than two fluid phases are possible. For instance a mixture of pentanol and water can split into two liquid phases with a different composition a water-rich liquid phase and a pentanol-rich liquid-phase. If these two liquid phases are in equilibrium with a vapour phase we have a three-phase equilibrium. The existence of two pure solid phases is an often occuring case, but it is also possible that solid solutions or mixed crystals are formed and that solids exists in more than one crystal structure. 

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],... 

The potential of supercritical extraction, a separation process in which a gas above its critical temperature is used as a solvent, has been widely recognized in the recent years. The first proposed applications have involved mainly compounds of low volatility, and processes that utilize supercritical fluids for the separation of solids from natural matrices (such as caffeine from coffee beans) are already in industrial operation. The use of supercritical fluids for separation of liquid mixtures, although of wider applicability, has been less well studied as the minimum number of components for any such separation is three (the solvent, and a binary mixture of components to be separated). The experimental study of phase equilibrium in ternary mixtures at high pressures is complicated and theoretical methods to correlate the observed phase behavior are lacking. 

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. 

Supercritical fluids are found in numerous applications thanks to their properties which vary with temperature and pressure. Supercritical fluids are put in contact with various compounds which also have physico-chemical properties dependant on temperature and pressure. Consequently, mixtures of these compounds with the supercritical solvent must be expected to behave in a complex way. For a binary mixture, for example, several types of phase equilibrium exist solid-fluid for low temperatures, solid-fluid-liquid when temperature rises, and liquid-fluid. 

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-... 

Different cubic equations of states have so far been used to model the solid-liquid-fluid phase equilibrium and the solubility of an organic solid solute in the fluid or liquid phase. These equations are listed elsewhere (11), along with the procedures for evaluating the binary parameters and adjustable interaction constants in them. These cubic equations of state (EOS) can be summarized as having the following general form ... 

For ascertaining the process conditions of RESS and PGSS, it is essential to have knowledge of the equilibrium solubility of the solute in dense gas (SCF phase) and vice versa, and also the P-T trace for the solid-liquid-vapor (S-L-V) phase transition of the drug substance. If all three phases coexist, there is only a single degree of freedom for a binary system, and a P-T trace of the S-L-V equilibrium is sufficient to determine the phase equilibrium compositions. 

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. 

This curve will, of course, lie in the plane formed by one face of the prism. In a similar manner we obtain the freezing-point curves Ak C and B gC. These curves give the composition of the binary liquid phases in equilibrium with one of the pure components, or, at the eutectic points, with a mixture of two solid components. If to the system represented say by the point ki, a small quantity of the third component, C, is added, the temperature at which the two solid phases A and B can exist in equilibrium with the liquid phase is lowered and this depression of the eutectic point is all the greater the larger the addition of C. In this way we obtain the curve which slopes inwards and downwards, and indicates the varying composition of the ternary liquid phase with which a mixture of solid A and B are in equilibrium. Similarly, the curves fegK and k K are the corresponding eutectic curves for A and C, and B and C in equilibrkim with ternary solutions. At the point K, the three solid components... 

Equilibrium Treatment of Solidification. As an example of liquid-solid phase change in solid-fluid flow systems with the assumption of local thermal equilibrium imposed, consider the formulation of solid-fluid phase change (solidification/melting or sublimation/frosting) of a binary mixture. For this problem, the equilibrium condition extends to the local thermodynamic equilibrium where the local phasic temperature (thermal equilibrium), pressure (mechanical equilibrium), and chemical potential (chemical equilibrium) are assumed to be equal between the solid and the fluid phases. This is stated as... 

The development of SCF processes involves a consideration of the phase behavior of the system under supercritical conditions. The influence of pressure and temperature on phase behavior in such systems is complex. For example, it is possible to have multiple phases, such as liquid-liquid-vapor or solid-liquid-vapor equilibria, present in the system. In many cases, the operation of an SCF process under multiphase conditions may be undesirable and so phase behavior should first be investigated. The limiting case of equilibrium between two components (binary systems) provides a convenient starting point in the understanding of multicomponent phase behavior. 

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