Density, fluid mixture

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

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. 

We introduce, for the sake of convenience, species indices 5 and c for the components of the fluid mixture mimicking solvent species and colloids, and species index m for the matrix component. The matrix and both fluid species are at densities p cr, Pccl, and p cr, respectively. The diameter of matrix and fluid species is denoted by cr, cr, and cr, respectively. We choose the diameter of solvent particles as a length unit, = 1. The diameter of matrix species is chosen similar to a simplified model of silica xerogel [39], cr = 7.055. On the other hand, as in previous theoretical works on bulk colloidal dispersions, see e.g.. Ref. 48 and references therein, we choose the diameter of large fluid particles mimicking colloids, cr = 5. As usual for these dispersions, the concentration of large particles, c, must be taken much smaller than that of the solvent. For all the cases in question we assume = 1.25 x 10 . The model for interparticle interactions is... 

This is an important system in chemical processing. The effect of apparent density (liquid plus gas) as the fluid mixture enters the impeller is quite pronounced on the system horsepo ver. The horsepower falls off with increased gas flow which may lead to the danger of underpowering the unit. The absorption coefficient is a func-... 

For application to gas sorption in polymers, we have modified the Prigogine-Flory formalism to apply to low- and high-density fluids and their mixtures (12). The modified equation of state has the form... 

Thermodynamic Equation of State for Classical Fluid Mixtures of Molecules Interacting with Alpha-exponential-six Pair Potentials up to High Densities. 

The effect of hills is interesting, in that no credit can be taken for the downhill side of the pipeline. The sum of all the uphill elevations appears as a pressure loss in actual operating practice. Baker includes an elevation correction factor which attempts to allow for the fact that the fluid-mixture density in the inclined uphill portion of the line is not accurately known. The gas mass-velocity seems to be the major variable affecting this correction factor, although liquid mass-velocity, phase properties. 

The values of the chemical potentials in each phase, together with their pressure derivatives (available through the measured number densities), can be exploited to home in on the coexistence pressure. The method has been successfully applied to calculate the phase diagrams of a number of simple fluids and fluid mixtures [79, 80]. 

Step 3. The Reynolds number Re is calculated in this step. Dukler developed experimental data determining liquid holdup in two-phase flow systems. Re values above 200,000 are free of liquid slugs and holdup. If Re is greater than 200,000, then the flow is in the froth zone, or it is simply homogeneous flow as a mixture. For homogeneous flow, the average density of the two-phase flow fluid mixture is ... 

Consider an inhomogeneous fluid mixture of polyatomic species with the density distributions Pa(r) of interaction sites a in an external field with the site potential M (r). Minimization of the Helmholtz free energy with respect to variations performed analogously to Refs. [34,35] yields the relation... 

Jossi et al. (1962) presented a generalized correlation for the viscosity of high density fluids as a function of the reduced density via a corresponding states method. This method was discussed earlier. Among the gases that Jossi et al. (1962) used to build their correlation were carbon dioxide, methane, ethane, and propane. This gives us some confidence that this approach should be satisfactory for our acid gas mixtures. 

From another point of view, air is the term we use to define a more complex structure known as the atmosphere, that is, the relatively thin layer of a low-density fluid a few hundred kilometers high surrounding our planet. On a scale of cubic meters, air can be considered as a homogeneous mixture of constant composition, but on a larger scale the atmosphere cannot be considered uniform. Where does the atmosphere end This is a difficult question, but practically all of its mass (i.e., an estimated annual mean of 5.13 x 1021 g) is within 100 kilometers. 

For a pure supercritical fluid, the relationships between pressure, temperature and density are easily estimated (except very near the critical point) with reasonable precision from equations of state and conform quite closely to that given in Figure 1. The phase behavior of binary fluid systems is highly varied and much more complex than in single-component systems and has been well-described for selected binary systems (see, for example, reference 13 and references therein). A detailed discussion of the different types of binary fluid mixtures and the phase behavior of these systems can be found elsewhere (X2). Cubic ecjuations of state have been used successfully to describe the properties and phase behavior of multicomponent systems, particularly fot hydrocarbon mixtures (14.) The use of conventional ecjuations of state to describe properties of surfactant-supercritical fluid mixtures is not appropriate since they do not account for the formation of aggregates (the micellar pseudophase) or their solubilization in a supercritical fluid phase. A complete thermodynamic description of micelle and microemulsion formation in liquids remains a challenging problem, and no attempts have been made to extend these models to supercritical fluid phases. 

Whiting, W. B. Prausnitz, J. M. Equations of state for strongly nonideal fluid mixtures apphcation of local compositions toward density-dependent mixing rules. Fluid Phase Equilib. 1982, 9, 119-147. 

In general for a /-component fluid mixture one has a (z/ + 3 l 1)-component set p yd of dynamic variables, containing //-component of the number densities / k,a, the three components of the total current density Jk, and the total energy density E. However, as follows from the symmetric properties, the number ttk.a and energy densities are coupled only with the longitudinal component of Jk, directed along k. This is due to the space isotropy of the system. As a result, one may split the set of the hydrodynamic variables into two separate subsets ... 

In addition to density, diffusivity of the supercritical fluids is higher than that of liquid solvents, and can be easily varied. For typical conditions, diffusivity in supercritical fluids is of the order of lO cm /sec as compared to 10 for gases and 10 for liquids. Typical viscosity of supercritical fluids is of the order of 10 g/cm/sec, similar to that of gases, and about 100-fold lower than that of liquids. High diffusivity and low viscosity provide rapid equilibration of the fluid to the mixture to be extracted, hence extraction can be achieved close to the thermodynamic limits. However, the main extraction benefit of supercritical fluids is their adjustable density that provides adjustable solvent strength. The compounds of choice can be dissolved/extracted in the supercritical fluid at high pressure and then this fluid mixture is carried to another vessel where simple lowering of the pressure... 

This process is further illustrated by the plots in Fig. 4.15(b) where the moan dorusity J> of thermodynamically stable confined pha.ses is plotted as a function of z (i.c., the pore width). Three different branches arc discernible. For small z < 8, p is relatively high indicating that the pore is filled with liquid. A corresponding plot of the local densities of a representative phase for z = 5 shows that this liquid consists locally of A- (or B-)rich, high-density fluid (because the two cannot be distinguished in a symmetric mixture). Hence, for 2 < 8, we observe (local) decomposition of liquid mixtures. 

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