Fluid phases

Selected References for Calculation of Multicomponent Fluid-Phase Equilibria... 

Prausnitz, J. M., "Molecular Thermodynamics of Fluid-Phase Equilibria," Prentice-Hall, Englewood Cliffs, N.J. (1969)... 

PRAUSNITZ J.M. MOLECULAR THERMODYNAMICS OF FLUID PHASE EQUILIBRIA, PRENTICE-HALL. ENGLEWOOD CLIFFS. N.J.I19691. 

In fact, it is often possible with stirred-tank reactors to come close to the idealized well-stirred model in practice, providing the fluid phase is not too viscous. Such reactors should be avoided for some types of parallel reaction systems (see Fig. 2.2) and for all systems in which byproduct formation is via series reactions. 

There has been extensive activity in the study of lipid monolayers as discussed above in Section IV-4E. Coexisting fluid phases have been observed via fluorescence microscopy of mixtures of phospholipid and cholesterol where a critical point occurs near 30 mol% cholesterol [257]. 

The CS pressures are close to the machine calculations in the fluid phase, and are bracketed by the pressures from the virial and compressibility equations using the PY approximation. Computer simulations show a fluid-solid phase transition tiiat is not reproduced by any of these equations of state. The theory has been extended to mixtures of hard spheres with additive diameters by Lebowitz [35], Lebowitz and Rowlinson [35], and Baxter [36]. 

Figure A2.5.26. Molar heat capacity C y of a van der Waals fluid as a fimction of temperature from mean-field theory (dotted line) from crossover theory (frill curve). Reproduced from [29] Kostrowicka Wyczalkowska A, Anisimov M A and Sengers J V 1999 Global crossover equation of state of a van der Waals fluid Fluid Phase Equilibria 158-160 532, figure 4, by pennission of Elsevier Science.

Levelt Sengers J M H 1999 Mean-field theories, their weaknesses and strength Fluid Phase Equilibria 158-160 3-17... 

Kostrowicka Wyczalkowska A, Anisimov M A and Sengers J V 1999 Global crossover equation of state of a van der Waals fluid Fluid Phase Equilibria 158-160 523-35... 

Panagiotopoulos A Z 1992 Direot determination of fluid phase equilibria by simulation in the Gibbs ensemble a review Mol. SImul. 9 1 -23... 

Panagiotopoulos A Z 1989 Exaot oaloulations of fluid-phase equilibria by Monte Carlo simulation in a new statistioal ensemble Int. J. Thermophys. 10 447-57... 

Figure C2.6.9. Phase diagram of charged colloidal particles. The solid lines are predictions by Robbins et al [85]. Fluid phase (open circles), fee crystal (solid circles) and bee crystal (triangles). is tire interaction energy at tire...

As shown in section C2.6.6.2, hard-sphere suspensions already show a rich phase behaviour. This is even more the case when binary mixtures of hard spheres are considered. First, we will mention tire case of moderate size ratios, around 0.6. At low concentrations tliese fonn a mixed fluid phase. On increasing tire overall concentration of mixtures, however, binary crystals of type AB2 and AB were observed (where A represents tire larger spheres), in addition to pure A or B crystals [105, 106]. An example of an AB2 stmcture is shown in figure C2.6.11. Computer simulations confinned tire tliennodynamic stability of tire stmctures tliat were observed [107, 1081. 

A second case to be considered is that of mixtures witli a small size ratio, <0.2. For a long time it was believed tliat such mixtures would not show any instability in tire fluid phase, but such an instability was predicted by Biben and Flansen [109]. This can be understood to be as a result of depletion interactions, exerted on the large spheres by tire small spheres (see section C2.6.4.3). Experimentally, such mixtures were indeed found to display an instability [110]. The gas-liquid transition does, however, seem to be metastable witli respect to tire fluid-crystal transition [111, 112]. This was confinned by computer simulations [113]. 

Catalysis in a single fluid phase (liquid, gas or supercritical fluid) is called homogeneous catalysis because the phase in which it occurs is relatively unifonn or homogeneous. The catalyst may be molecular or ionic. Catalysis at an interface (usually a solid surface) is called heterogeneous catalysis, an implication of this tenn is that more than one phase is present in the reactor, and the reactants are usually concentrated in a fluid phase in contact with the catalyst, e.g., a gas in contact with a solid. Most catalysts used in the largest teclmological processes are solids. The tenn catalytic site (or active site) describes the groups on the surface to which reactants bond for catalysis to occur the identities of the catalytic sites are often unknown because most solid surfaces are nonunifonn in stmcture and composition and difficult to characterize well, and the active sites often constitute a small minority of the surface sites. 

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

Initiation and Growth of Cells. The initiation or nucleation of cells is the formation of cells of such size that they are capable of growth under the given conditions of foam expansion. The growth of a hole or cell in a fluid medium at equiUbrium is controlled by the pressure difference (AP) between the inside and the outside of the cell, the surface tension of the fluid phase y, and the radius r of the cell ... 

The product must be formulated and frozen in a manner which ensures that there is no fluid phase remaining. To achieve this, it is necessary to cool the product to a temperature below which no significant Hquid—soHd phase transitions exist. This temperature can be deterrnined by differential scanning calorimetry or by measuring changes in resistivity (94,95). 

The fugacity coefficient of thesolid solute dissolved in the fluid phase (0 ) has been obtained using cubic equations of state (52) and statistical mechanical perturbation theory (53). The enhancement factor, E, shown as the quantity ia brackets ia equation 2, is defined as the real solubiUty divided by the solubihty ia an ideal gas. The solubiUty ia an ideal gas is simply the vapor pressure of the sohd over the pressure. Enhancement factors of 10 are common for supercritical systems. Notable exceptions such as the squalane—carbon dioxide system may have enhancement factors greater than 10. Solubihty data can be reduced to a simple form by plotting the logarithm of the enhancement factor vs density, resulting ia a fairly linear relationship (52). 

K. A. Bartscherer, H. Renon, andM. Minier, Fluid-Phase Equilibria, 107, 93 (1995). 

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