Fluid parameters, pure

The cross terms were expressed using pure fluid parameters... 

FIGURE 2.1 Experimental monomer fraction data for alcohols and NRHB predictions. Experimental data are from Refs. [71-73] and were used as they were transformed by von Solms et al. [70]. (NRHB pure fluid parameters were adapted from Tsivintzelis, I. et al., Ind. Eng. Chem. Res., 47, 5651, 2008.)... 

FIGURE 2.8 Solubility of benzoic acid in supercritical CO2 and supercritical ethane at 318 K. Experimental data [83] (points) and NRHB correlations (lines) with ky = -0.04417 for CO2 and -0.06974 for ethane. (Pure fluid parameters adapted from Tsivintzelis, I. et al., AIChE J., 55, 756, 2009.)... 

FIGURE 2.9 2-Butanol-poly(vinyl acetate) VLB. Experimental data [84] (points), NRHB predictions (dotted lines, = 0), and correlations (solid lines, = 0.01372). (Pure fluid parameters were adopted from Tsivintzelis and Kontogeorgis [68]). 

The value of We ranges from 0.03 to 0.4, suggesting that the value of drag coefficient in viscoelastic fluids can be up to four times larger than that in purely viscous fluids. However, more work is needed to generalize these observations over wider ranges of conditions, especially the non-Newtonian fluid parameters. No information is available concerning the severity of wall effects on nonspherical particles in viscoelastic media. 

If equation 25 is used to estimate the binary lattice fluid parameters, then the free energy. A, as a function of T, V and may be calculated from equation 19 using only pure component lattice fluid parameters. These parameters may be determined from pure component equilibrium properties such as P-V-T data or vapour pressure (12). 

The pure component lattice fluid parameters for PMMA, CO2 and C2H4 have been obtained using the P-V-T data reported in (77) for the polymer and in (18) for the penetrants. The parameters values obtained in this work for the Sanchez-Lacombe EOS are recorded in Table I. They are in good agreement with the values reported in the literature for the same components (79). 

The Sanchez and Lacombe theory for polymer mixtures is based on an appropriate mixing of rules, which allows for the prediction of the thermodynamic behaviour of a binary mixture, once the pure fluids parameters are known and an interaction parameter is determined. 

Appendix C presents properties and parameters for 92 pure fluids and characteristic binary-mixture parameters for 150 binary pairs. 

Although generalized correlations are based on data for pure fluids, they are frequently appHed to mixtures. The mole fraction is introduced as a variable through empirical recipes for the composition dependence of parameters upon which the correlation is based. The simplest such recipes provide pseudoparameters that are linear in mole fraction ... 

Equations of State. Equations of state having adjustable parameters are often used to model the pressure—volume—temperature (PVT) behavior of pure fluids and mixtures (1,2). Equations that are cubic in specific volume, such as a van der Waals equation having two adjustable parameters, are the mathematically simplest forms capable of representing the two real volume roots associated with phase equiUbrium, or the three roots (vapor, Hquid, sohd) characteristic of the triple point. 

For pure organic vapors, the Lydersen et al. corresponding states method is the most accurate technique for predicting compressibility factors and, hence, vapor densities. Critical temperature, critical pressure, and critical compressibility factor defined by Eq. (2-21) are used as input parameters. Figure 2-37 is used to predict the compressibihty factor at = 0.27, and the result is corrected to the Z of the desired fluid using Eq. (2-83). 

This information allows prediction of X T.E at 323.15 K and at the higher temperatures, 372.8, 397.7, and 422.6 K, for which measured X T.E values are given by Wilsak, et al. (Fluid Phase Equilibria, 28, pp. 13-37 [1986]). Values of In yX and hence of the Margules parameters at the higher temperatures are given by Eq. (4-325) with Cf = 0. The pure-species vapor pressures in all cases are the measured values reported with the data sets. Res lilts of these calculations are displayed in Table 4-1, where the parentheses enclose values from the gamma/ phi approach as reported in the papers cited. 

A parameter indicating whether viscoelastic effects are important is the Deborah number, which is the ratio of the characteristic relaxation time of the fluid to the characteristic time scale of the flow. For small Deborah numbers, the relaxation is fast compared to the characteristic time of the flow, and the fluid behavior is purely viscous. For veiy large Deborah numbers, the behavior closely resembles that of an elastic solid. 

A variety of equations-of-state have been applied to supercritical fluids, ranging from simple cubic equations like the Peng-Robinson equation-of-state to the Statistical Associating Fluid Theoiy. All are able to model nonpolar systems fairly successfully, but most are increasingly chaUenged as the polarity of the components increases. The key is to calculate the solute-fluid molecular interaction parameter from the pure-component properties. Often the standard approach (i.e. corresponding states based on critical properties) is of limited accuracy due to the vastly different critical temperatures of the solutes (if known) and the solvents other properties of the solute... 

Panagiotopoulos et al. [16] studied only a few ideal LJ mixtures, since their main objective was only to demonstrate the accuracy of the method. Murad et al. [17] have recently studied a wide range of ideal and nonideal LJ mixtures, and compared results obtained for osmotic pressure with the van t Hoff [17a] and other equations. Results for a wide range of other properties such as solvent exchange, chemical potentials and activity coefficients [18] were compared with the van der Waals 1 (vdWl) fluid approximation [19]. The vdWl theory replaces the mixture by one fictitious pure liquid with judiciously chosen potential parameters. It is defined for potentials with only two parameters, see Ref. 19. A summary of their most important conclusions include ... 

X is the scalar distance between the solute molecule and the center of the imaginary membrane, with the LJ parameters of the solute used as reducing parameters. The residual chemical potential for a pure fluid (which would correspond to component 2 in its pure state at the state conditions of cell A) can then, for example, be found using the expression... 

Many of the new plastics, blends, and material systems require special, enhanced processing features or techniques to be successfully injection molded. The associated materials evolution has resulted in new plastics or grades, many of which are more viscoelastic. That is, they exhibit greater melt elasticity. The advanced molding technology has started to address the coupling of viscoelastic material responses with the process parameters. This requires an understanding of plastics as viscoelastic fluids, rather than as purely viscous liquids, as is commonly held... 

Parameters r, q and q are pure component molecular-structure constants depending on molecular size and external surface areas. For fluids other than water or lower alcohols, q = q. ... 

The most common and widely used supercritical fluid in SFC is carbon dioxide. It is inert, in that it is non-toxic and non-flammable, it also has mild critical parameters, a low critical temperature of 31.3°C and a critical pressure of 72.8 atm [1], Using pure, supercritical carbon dioxide eliminates organic solvent waste and with it waste disposal costs and concerns. This is extremely practical advantage in the industrial environment where the generation of waste requires special handling and significant cost. 

Whilst it is obviously valuable to measure the solubility of reagents in the SCF, it is important to be aware that the solubility in a multicomponent system can be very different from that in the fluid alone. It is also important to note that the addition of reagents and catalysts can have a profound effect on the critical parameters of the mixture. Indeed, at high concentrations of reactants, the mole fraction of C02 is necessarily lower and it may not be possible to achieve a supercritical phase at the temperature of interest. Increases in pressure (i.e. further additions of C02) could yield a single liquid phase (which would have a much lower compressibility than scC02). For example, the Diels-Alder reaction (see Chapter 7) between 2-methyl-1,3-butadiene and maleic anydride has been carried out a pressure of 74.5 bar and a temperature of 50 °C, assuming that this would be under supercritical conditions as it would if it were pure C02. However, the critical parameters calculated for this system are a pressure of 77.4bar and a temperature of 123.2 °C, far in excess of those used [41]. 

The authors noted that when their friction parameter M= (pG/,) 8/G is real, it is equivalent to the real slip parameter s = fe used by McHale et al. [14]. From this analysis, a real interfacial energy G /8 is related to the slip length b, for a purely viscous fluid, by... 

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