Fluid systems, phase equilibrium

In practice, colloidal systems do not always reach tlie predicted equilibrium state, which is observed here for tlie case of narrow attractions. On increasing tlie polymer concentration, a fluid-crystal phase separation may be induced, but at higher concentration crystallization is arrested and amorjihous gels have been found to fonn instead [101, 102]. Close to the phase boundary, transient gels were observed, in which phase separation proceeded after a lag time. 

All these processes are, in common, liquid-gas mass-transfer operations and thus require similar treatment from the aspects of phase equilibrium and kinetics of mass transfer. The fluid-dynamic analysis ofthe eqmpment utihzed for the transfer also is similar for many types of liquid-gas process systems. 

Fig. 2.37. Phase diagram for Ca0-Na20 Si02-(Al203)-H20 system in equilibrium with quartz at 400°C and 400 bars. Plagioclase solid solution can be represented by the albite and anorthite fields, whereas epidote is represented by clinozoisite. Note that the clinozoisite field is adjacent to the anorthite field, suggesting that fluids with high Ca/(H+) might equilibrate with excess anorthite by replacing it with epidote. The location of the albite-anorthite-epidote equilibrium point is a function of epidote and plagioclase composition and depends on the model used for calculation of the thermodynamic properties of aqueous cations (Berndt et al., 1989).

There are numerous sources of phase equilibrium data available that serve as a database to those developing or improving equations of state. References to these databases are widely available. In addition, new data are added mainly through the Journal of Chemical and Engineering Data and the journal Fluid Phase Equilibria. Next, we give data for two systems so that the reader may practice the estimation methods discussed in this chapter. 

Optimizing solvents and solvent mixtures can be done empirically or through modeling. An example of the latter involves a single Sanchez-Lacombe lattice fluid equation of state, used to model both phases for a polymer-supercritical fluid-cosolvent system. This method works well over a wide pressure range both volumetric and phase equilibrium properties for a cross-linked poly(dimethyl siloxane) phase in contact with CO2 modified by a number of cosolvents (West et al., 1998). 

The model provides a good approach for the biotransformation system and highlights the main parameters involved. However, prediction of mass transfer effects on the outcome of the process, through evaluation of changes in the mass transfer coefficients, is rather difficult. A similar mass transfer reaction model, but based on the two-film model for mass transfer for a transformation occurring in the bulk aqueous phase as shown in Figure 8.3, could prove quite useful. Each of the films presents a resistance to mass transfer, but concentrations in the two fluids are in equilibrium at the interface, an assumption that holds provided surfactants do not accumulate at the interface and mass transfer rates are extremely high [36]. 

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 basic for developing a high pressure liquid extraction unit is the phase equilibrium for the (at least) ternary system, made up of compound A and compound B, which have to be separated by the supercritical fluid C. Changing pressure and temperature influences on one hand the area of the two phase region, where extraction takes place, and on the other hand the connodes, representing the equilibrium between extract and raffinate phase. 

The equilibrium interfaces of fluid systems possess one variant chemical potential less than isolated bulk phases with the same number of components. This is due to the additional condition of heterogeneous equilibrium and follows from Gibbs phase rule. As a result, the equilibrium interface of a binary system is invariant at any given P and T, whereas the interface between the phases a and /3 of a ternary system is (mono-) variant. However, we will see later that for multiphase crystals with coherent boundaries, the situation is more complicated. 

Consider a two-component, two-phase fluid system. Let (3 be a spherical fluid droplet of radius r surrounded by a, the second fluid phase. The equilibrium conditions are... 

The phase rule specifies the number of intensive properties of a system that must be set to establish all other intensive properties at fixed values (3), without providing information about how to calculate values for these properties. The field of applied engineering thermodynamics has grown out of the need to assign numerical values to thermodynamic properties within the constraints of the phase rule and fundamental laws. In the engineering disciplines there is a particular demand for physical properties, both for pure fluids and mixtures, and for phase equilibrium data (4,5). 

G. Schneider, Phase Equilibriums in Liquid Systems at High Pressures , Ber. Bunsenges. Physik. Chem., 70, 497-520 (1966). G. M. Schneider, Phase Equilibria in Fluid Mixtures at High Pressures , Adv. Chem. Phys. 17, 1-42 (1970). G. M. Schneider, "Gas-Gas Equilibrium. Fluid Mixtures Under Pressure , Fortschr. Chem. Forsch. 13, 559-600 (1970). G. M. Schneider, Phase Behavior and Critical Phenomena in Fluid Mixtures Under Pressure , Ber. Bunsenges. Physik. Chem. 76, 325-331 (1972). G. M. Schneider in Water A Comprehensive Treatise, Vol II, F. Franks, ed.. Plenum Press, New York, 1973, Ch. 6. 

Chapters 17 and 18 use thermodynamics to describe solutions, with nonelectrolyte solutions described in Chapter 17 and electrolyte solutions described in Chapter 18. Chapter 17 focuses on the excess thermodynamic properties, with the properties of the ideal and regular solution compared with the real solution. Deviations from ideal solution behavior are correlated with the type of interactions in the liquid mixture, and extensions are made to systems with (liquid + liquid) phase equilibrium, and (fluid -I- fluid) phase equilibrium when the mixture involves supercritical fluids. 

Vejrosta, J., Novak, J., and Jonsson, J.A. 1992. A method for measuring infinite-dilution partition coefficients of volatile compounds between the gas and liquid phases of aqueous systems. Fluid Phase Equilibrium 8, 25-35. 

In these systems, the interface between two phases is located at the high-throughput membrane porous matrix level. Physicochemical, structural and geometrical properties of porous meso- and microporous membranes are exploited to facilitate mass transfer between two contacting immiscible phases, e.g., gas-liquid, vapor-liquid, liquid-liquid, liquid-supercritical fluid, etc., without dispersing one phase in the other (except for membrane emulsification, where two phases are contacted and then dispersed drop by drop one into another under precise controlled conditions). Separation depends primarily on phase equilibrium. Membrane-based absorbers and strippers, extractors and back extractors, supported gas membrane-based processes and osmotic distillation are examples of such processes that have already been in some cases commercialized. Membrane distillation, membrane... 

Keywords Carbon dioxide Polyethylene glycol Phase behavior Biphasic solvent system Supercritical fluids Phase equilibrium... 

Lopes JA, Gourgouillon D, Pereira PJ et al (2000) On the effect of polymer fractionation on phase equilibrium in C02 + poly(ethylene glycol)s systems. J Supercrit Fluids 16(3) 261-267... 

Weidner E, Wiesmet V, Knez Z et al (1997) Phase equilibrium (solid-liquid-gas) in polyethylene glycol-carbon dioxide systems. J Supercrit Fluids 10(3) 139-147... 

A recirculation apparatus for the determination of high pressure phase equilibrium data for mixtures of water, polar organic liquids and supercritical fluids was constructed and operated for binary and ternary systems with supercritical carbon dioxide. 

The system carbon dioxide - acetone - water was investigated at 313 and 333 K. The system demonstrates several of the general characteristics of phase equilibrium behavior for ternary aqueous systems with a supercritical fluid. These include an extensive LLV region that appears at relatively low pressures. Carbon dioxide exhibits a high selectivity for acetone over water and can be used to extract acetone from dilute aqueous solutions. 

For the design of a process for formation of solid particles using supercritical fluids, data on solid - liquid and vapour - liquid phase equilibrium are essential. PGSS process is only possible for systems where enough gas is solubilized in the liquid. 

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. 

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