Fluid mixtures

In this section we describe the common stability behavior displayed by binary mixtures ( 8.4.1), including a scheme for classifying that behavior ( 8.4.2). Then we show how models can be used to test for the observability of one-phase binary mixtures first we consider PvTx models ( 8.4.3 and 8.4.4) and then models for the excess Gibbs energy ( 8.4.5). 

Ultimately, we want to develop a computational procedure for determining the observability of a state proposed for a binary fluid. The motivation is that we want to avoid trying to solve phase-equilibrium problems that do not exist. Therefore we first test for observability, and if multiphase situations are observable, then we solve for phase compositions, if they are required. In this section we consider situations in which the proposed state is identified by specifying values for T, P, and Xp Such a state could be in any one of three observable conditions (a) a stable single phase, (b) a stable multiphase equilibrium, or (c) a metastable single phase. Some metastable phases can only relax to a stable single phase, but other metastable phases can split into multiple phases. Multiphase equilibria in binaries are predominantly two-phase situations, so we will restrict our attention to those possibilities here however, three and four-phase binaries are also possible. 

The middle envelope is the spinodal the set of states that separate metastable states from unstable states. Recall from 8.3 that one-phase mixtures become diffusionally unstable before becoming mechanically unstable. Therefore, the mixture spinodal is the locus of points at which the diffusional stability criterion (8.3.14) is first violated that is, it is the locus of points having 

Between the spinodal and the saturation envelope, mixtures may exist as metastable one-phase systems or as stable two-phase systems. The spinodal cannot cross the saturation envelope, but the spinodal becomes tangent to the saturation envelope at the critical point. 

For binary mixtures it is conventional to express the conditions for the critical point in terms of the change in Gibbs energy on mixing (3.7.38)  

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Hicks, C. P. Bibliography of Thermodynaunic Quantities for Binary Fluid Mixtures, "Chemical Thermodynamics", Vol. 2, Chap. 9, edited by M. L. McGlashan, Chemical Society, London, 1978. 

Hiza, M. J., A. J. Kidnay, and R. C. Miller "Equilibrium Properties of Fluid Mixtures—A Bibliography of Data on Fluids of Cryogenic Interest," NSRDS Bibliographic Series. Plenum, New York, 1975. 

Two generally accepted models for the vapor phase were discussed in Chapter 3 and one particular model for the liquid phase (UNIQUAC) was discussed in Chapter 4. Unfortunately, these, and all other presently available models, are only approximate when used to calculate equilibrium properties of dense fluid mixtures. Therefore, any such model must contain a number of adjustable parameters, which can only be obtained from experimental measurements. The predictions of the model may be sensitive to the values selected for model parameters, and the data available may contain significant measurement errors. Thus, it is of major importance that serious consideration be given to the proper treatment of experimental measurements for mixtures to obtain the most appropriate values for parameters in models such as UNIQUAC. 

As pointed out previously, the separation of homogeneous fluid mixtures requires the creation or addition of another phase. The most common method is by repeated vaporization and condensation— distillation. The three principal advantages of distillation are... 

Separation of mixtures of condensable and non-condensable components. If a fluid mixture contains both condensable and noncondensable components, then a partial condensation followed by a simple phase separator often can give a food separation. This is essentially a single-stage distillation operation. It is a special case that deserves attention in some detail later. 

Distillation is by far the most commonly used method for the separation of homogeneous fluid mixtures. The cost of distillation varies with operating pressure, which, in turn, is mainly determined by the molecular weight of the materials being separated. Its widespread use can be attributed to its ability to... 

Kirkwood J G 1935 Statistical mechanics of fluid mixtures J. Chem. Phys. 3 300 Kirkwood J G 1936 Statistical mechanics of liquid solutions Chem. Rev. 19 275... 

Exponent values derived from experiments on fluids, binary alloys, and certain magnets differ substantially from all those derived from analytic (mean-field) theories. Flowever it is surprising that the experimental values appear to be the same from all these experiments, not only for different fluids and fluid mixtures, but indeed the same for the magnets and alloys as well (see section A2.5.5). 

Figure A2.5.28. The coexistence curve and the heat capacity of the binary mixture 3-methylpentane + nitroethane. The circles are the experimental points, and the lines are calculated from the two-tenn crossover model. Reproduced from [28], 2000 Supercritical Fluids—Fundamentals and Applications ed E Kiran, P G Debenedetti and C J Peters (Dordrecht Kluwer) Anisimov M A and Sengers J V Critical and crossover phenomena in fluids and fluid mixtures, p 16, figure 3, by kind pemiission from Kluwer Academic Publishers.

Figure A2.5.30. Left-hand side Eight hypothetical phase diagrams (A through H) for ternary mixtures of d-and /-enantiomers with an optically inactive third component. Note the syimnetry about a line corresponding to a racemic mixture. Right-hand side Four T, x diagrams ((a) tlirough (d)) for pseudobinary mixtures of a racemic mixture of enantiomers with an optically inactive third component. Reproduced from [37] 1984 Phase Transitions and Critical Phenomena ed C Domb and J Lebowitz, vol 9, eh 2, Knobler C M and Scott R L Multicritical points in fluid mixtures. Experimental studies pp 213-14, (Copyright 1984) by pennission of the publisher Academic Press.

Syimnetrical tricritical points are predicted for fluid mixtures of sulfur or living polymers m certain solvents. Scott (1965) in a mean-field treatment [38] of sulfiir solutions found that a second-order transition Ime (the critical... 

Scott R L 1978 Critical exponents for binary fluid mixtures Specialist Periodical Reports, Chem. Thermodynam. 2 238-74... 

Anisimov M A and Sengers J V 2000 Critical and crossover phenomena in fluids and fluid mixtures Supercritical Fluids-Fundamentals and Applications ed E Kiran, P G Debenedetti and C J Peters (Dordrecht Kluwer) pp 1-33... 

Domb C and Lebowitz J (eds) 1984 Phase Transitions and Critical Phenomena vol 9 (London, New York Academic) oh 1. Lawrie I D and Sarbach S Theory of tricritical points oh 2. Knobler C M and Scott R L Multicritical points in fluid mixtures. Experimental studies. 

The enhanced concentration at the surface accounts, in part, for the catalytic activity shown by many solid surfaces, and it is also the basis of the application of adsorbents for low pressure storage of permanent gases such as methane. However, most of the important applications of adsorption depend on the selectivity, ie, the difference in the affinity of the surface for different components. As a result of this selectivity, adsorption offers, at least in principle, a relatively straightforward means of purification (removal of an undesirable trace component from a fluid mixture) and a potentially useflil means of bulk separation. 

Nitrogen in Multinutrient Fertilizers. Single-nutrient nitrogen materials suppHed over 85% of the fertilizer nitrogen used in the United States during the year ended June 30, 1990. The remaining 15% was suppHed as multinutrient materials (Fig. 3). This included 9% as ammonium phosphate, 2% as cogranulated mixtures, and 3% as fluid mixtures. 

Methyl- and dimethylnaphthalenes are contained in coke-oven tar and in certain petroleum fractions in significant amounts. A typical high temperature coke-oven coal tar, for example, contains ca 3 wt % of combined methyl- and dimethylnaphthalenes (6). In the United States, separation of individual isomers is seldom attempted instead a methylnaphtha1 ene-rich fraction is produced for commercial purposes. Such mixtures are used for solvents for pesticides, sulfur, and various aromatic compounds. They also can be used as low freezing, stable heat-transfer fluids. Mixtures that are rich in monomethyinaphthalene content have been used as dye carriers (qv) for color intensification in the dyeing of synthetic fibers, eg, polyester. They also are used as the feedstock to make naphthalene in dealkylation processes. PhthaUc anhydride also can be made from m ethyl n aph th al en e mixtures by an oxidation process that is similar to that used for naphthalene. 

In the macroscopic heat-transfer term of equation 9, the first group in brackets represents the usual Dittus-Boelter equation for heat-transfer coefficients. The second bracket is the ratio of frictional pressure drop per unit length for two-phase flow to that for Hquid phase alone. The Prandd-number function is an empirical correction term. The final bracket is the ratio of the binary macroscopic heat-transfer coefficient to the heat-transfer coefficient that would be calculated for a pure fluid with properties identical to those of the fluid mixture. This term is built on the postulate that mass transfer does not affect the boiling mechanism itself but does affect the driving force. 

Work in the area of simultaneous heat and mass transfer has centered on the solution of equations such as 1—18 for cases where the stmcture and properties of a soHd phase must also be considered, as in drying (qv) or adsorption (qv), or where a chemical reaction takes place. Drying simulation (45—47) and drying of foods (48,49) have been particularly active subjects. In the adsorption area the separation of multicomponent fluid mixtures is influenced by comparative rates of diffusion and by interface temperatures (50,51). In the area of reactor studies there has been much interest in monolithic and honeycomb catalytic reactions (52,53) (see Exhaust control, industrial). Eor these kinds of appHcations psychrometric charts for systems other than air—water would be useful. The constmction of such has been considered (54). 

R. J. Sadus, High Pressure Phase Behaviour of Multicomponent Fluid Mixtures, Elsevier, Amsterdam, the Netherlands, 1992. 

Consider a closed, nonreacting PTT system containing n moles of a homogeneous fluid mixture. The mole numbers of the individual chemical species sum to... 

In many important cases of reactions involving gas, hquid, and solid phases, the solid phase is a porous catalyst. It may be in a fixed bed or it may be suspended in the fluid mixture. In general, the reaction occurs either in the liquid phase or at the liquid/solid interface. In fixed-bed reactors the particles have diameters of about 3 mm (0.12 in) and occupy about 50 percent of the vessel volume. Diameters of suspended particles are hmited to O.I to 0.2 mm (0.004 to 0.008 in) minimum by requirements of filterability and occupy I to 10 percent of the volume in stirred vessels. 

GLS Fluidized with a Stable Level of Catalyst Only the fluid mixture leaves the vessel. Gas and liquid enter at the bottom. Liquid is continuous, gas is dispersed. Particles are larger than in bubble columns, 0.2 to 1.0 mm (0.008 to 0.04 in). Bed expansion is small. Bed temperatures are uniform within 2°C (3.6°F) in medium-size beds, and neat transfer to embedded surfaces is excellent. Catalyst may be bled off and replenished continuously, or reactivated continuously. Figure 23-40 shows such a unit. 

Polymers can be used as surface coatings. Linear polymers are applied as a solution the solvent evaporates leaving a protective film of the polymer. Thermosets are applied as a fluid mixture of resin and hardener which has to be mixed just before it is used, and cures almost as soon as it is applied. 

Steady-state operation (i.e., accumulation in the reactor is zero) Constant fluid mixture density Stirrer input energy is neglected Wj,... 

Broth Complex fluid mixture in bioreactor, including cells, nutrients, substrate, antifoam, cell products, etc. 

Several colloidal systems, that are of practical importance, contain spherically symmetric particles the size of which changes continuously. Polydisperse fluid mixtures can be described by a continuous probability density of one or more particle attributes, such as particle size. Thus, they may be viewed as containing an infinite number of components. It has been several decades since the introduction of polydispersity as a model for molecular mixtures [73], but only recently has it received widespread attention [74-82]. Initially, work was concentrated on nearly monodisperse mixtures and the polydispersity was accounted for by the construction of perturbation expansions with a pure, monodispersive, component as the reference fluid [77,80]. Subsequently, Kofke and Glandt [79] have obtained the equation of state using a theory based on the distinction of particular species in a polydispersive mixture, not by their intermolecular potentials but by a specific form of the distribution of their chemical potentials. Quite recently, Lado [81,82] has generalized the usual OZ equation to the case of a polydispersive mixture. Recently, the latter theory has been also extended to the case of polydisperse quenched-annealed mixtures [83,84]. As this approach has not been reviewed previously, we shall consider it in some detail. 

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