Composition dependence

For liquid-liquid systems, the separations are isothermal and the objective function is one-dimensional, consisting of Equation (7-17). However, the composition dependence of the... 

An important industrial example of W/O emulsions arises in water-in-crude-oil emulsions that form during production. These emulsions must be broken to aid transportation and refining [43]. These suspensions have been extensively studied by Sjoblom and co-workers [10, 13, 14] and Wasan and co-workers [44]. Stabilization arises from combinations of surface-active components, asphaltenes, polymers, and particles the composition depends on the source of the crude oil. Certain copolymers can mimic the emulsion stabilizing fractions of crude oil and have been studied in terms of their pressure-area behavior [45]. 

If the value of the asymptote is indeed found to be independent of x(0) and x(L), as equation (10.14) predicts, this tells us something about Che composition dependence of the matrix element in equation... 

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. 

In this section we have seen that the copolymer composition depends to a large extent on the four propagation constants, although it is sufficient to consider these in terms of the two ratios ri and r2. In the next section we shall examine these ratios in somewhat greater detail. 

There are physical—chemical differences between fats of the same fatty acid composition, depending on the placement of the fatty acids. For example, cocoa butter and mutton tallow share the same fatty acid composition, but fatty acid placement on the glycerin backbone yields products of very different physical properties. 

Fire Resista.nce. Many fillers, particularly inorganic oxides, are noncombustible and provide a measure of passive fire resistance to filled plastics by reducing the volume of combustible matter in the filled composition. Depending on their density, they may also serve as insulation. 

Fig. 1. Phase diagram for mixtures (a) upper critical solution temperature (UCST) (b) lower critical solution temperature (LCST) (c) composition dependence of the free energy of the mixture (on an arbitrary scale) for temperatures above and below the critical value.

Over 50 acidic, basic, and neutral aluminum sulfate hydrates have been reported. Only a few of these are well characterized because the exact compositions depend on conditions of precipitation from solution. Variables such as supersaturation, nucleation and crystal growth rates, occlusion, nonequilihrium conditions, and hydrolysis can each play a role ia the final composition. Commercial dry alum is likely not a single crystalline hydrate, but rather it contains significant amounts of amorphous material. 

Acylated Protein Hydrolysates. These surfactants are prepared by acylation of proteia hydrolysates with fatty acids or acid chlorides. The hydrolysates are variable ia composition, depending on the degree of hydrolysis. CoUagen from leather (qv) processiag is a common proteia source. Acylated proteia hydrolysates (Maypoa, by laotex Chemical Company) are mild surfactants recommended for personal-care products (see Cosmetics). 

Composition. Molasses composition depends on several factors, eg, locality, variety, sod, climate, and processing. Cane molasses is generally at pH 5.5—6.5 and contains 30—40 wt % sucrose and 15—20 wt % reducing sugars. Beet molasses is ca 7.5—8.6 pH, and contains ca 50—60 wt % sucrose, a trace of reducing sugars, and 0.5—2.0 wt % raffinose. Cane molasses contains less ash, less nitrogenous material, but considerably more vitamins than beet molasses. Composition of selected molasses products is Hsted in Table 7. Procedures for molasses analysis are avadable (59). 

Although PVT equations of state are based on data for pure fluids, they are frequently appHed to mixtures. 7h.e virial equations are unique in that rigorous expressions are known for the composition dependence of the virial coefficients. Statistical mechanics provide exact mixing rules which show that the nxh. virial coefficient of a mixture is nxh. degree in the mole fractions ... 

For most LLE applications, the effect of pressure on can be ignored, and thus equation 228 constitutes a set of N equations relating equiUbrium compositions to each other and to temperature. Solution of these equations for a particular temperature requires a single expression for the composition dependence of suitable for both Hquid phases. Not all expressions for G suffice, even in principle, because some cannot represent Hquid—Hquid phase sphtting. 

Glassy phosphates (sodium polymetaphosphate [50813-16-6] sodium hexametaphosphate [10124-56-8J) vary in composition, depending upon the... 

The preparation of molecular composites by electropolymeriza tion of heterocycles in solution with polyelectrolytes is an extremely versatile technique, and many polyelectrolyte systems have been studied. The advantages of this method include the use of aqueous systems for the polymerization. Also, the physical and mechanical properties of the overall composite depend on the properties of the polyelectrolyte, so material tailorabiUty is feasible by selection of a polyelectrolyte with desirable properties. 

The density-series virial coefficients B, C, D,. . . , depend on temperature and composition only. The composition dependencies are given by the exact recipes... 

The application of cubic equations of state to mixtures requires expression of the equation-of-state parameters as func tions of composition. No exact theory like that for the virial coefficients prescribes this composition dependence, and empirical mixing rules provide approximate relationships. The mixing rules that have found general favor for the Redhch/Kwong equation are ... 

These are general equations that do not depend on the particular mixing rules adopted for the composition dependence of a and b. The mixing rules given by Eqs. (4-221) and (4-222) can certainly be employed with these equations. However, for purposes of vapor/liquid equilibrium calculations, a special pair of mixing rules is far more appropriate, and will be introduced when these calculations are treated. Solution of Eq. (4-232) for fugacity coefficient at given T and P reqmres prior solution of Eq. (4-231) for V, from which is found Z = PV/RT. 

A second advantage is that the procedure, applied for infinite dilution of each species, yields two values of kj from which a composition-dependent function can be generated, a simple linear relation proving fully satisfactory ... 

The two values kp and k are usually not very different, and kp is not strongly composition dependent. Nevertheless, the quadratic dependence of Z — a/RT) on composition indicated by Eq. (4-305) is not exactly preserved. Since this quantity is not a true second virial coefficient, only a value predicted by a cubic equation of state, a strict quadratic dependence is not required. Moreover, the composition-dependent kp leads to better results than does use of a constant value. 

Outlined below are the steps required for of a X T.E calciilation of vapor-phase composition and pressure, given the liquid-phase composition and temperature. A choice must be made of an equation of state. Only the Soave/Redlich/Kwong and Peng/Robinson equations, as represented by Eqs. (4-230) and (4-231), are considered here. These two equations usually give comparable results. A choice must also be made of a two-parameter correlating expression to represent the liquid-phase composition dependence of for each pq binaiy. The Wilson, NRTL (with a fixed), and UNIQUAC equations are of general applicabihty for binary systems, the Margules and van Laar equations may also be used. The equation selected depends on evidence of its suitability to the particular system treated. Reasonable estimates of the parameters in the equation must also be known at the temperature of interest. These parameters are directly related to infinite-dilution values of the activity coefficients for each pq binaiy. 

Polymers and glasses 10- 10-= 10- -10-" 10- -10- Approximate theories exist for dilute and concentrated limits strong composition dependence... 

Concentrated, Binary Mixtures of Nonelectrolytes Several correlations that predict the composition dependence of Dab. re summarized in Table 5-19. Most are based on known values of D°g and Dba- In fact, a rule of thumb states that, for many binary systems, D°g and Dba bound the Dab vs. Xa cuiwe. CuUinan s equation predicts dif-fusivities even in hen of values at infinite dilution, but requires accurate density, viscosity, and activity coefficient data. 

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