Fluid enhancement factor

The numerator quantifies the effect of hydrostatic pressure on the fugacity of the solid phase. The exponential term is known as the Poynting correction (17). The denominator quantifies the fluid phase intermolecular interactions and density effects. Note that the enhancement factor is dependent on the solid volume as well as the interactions in the supercritical fluid. A solute with a large solid molar volume will have a larger enhancement factor than a solute with a smaller solid molar volume at the same temperature and pressure when the interactions in the supercritical phase are identical. To further understand the molecular interactions in supercritical fluids, it is interesting to decompose the enhancement factor into these two effects. We may define a fluid enhancement factor, Ep, and a Poynting enhancement factor, Ep,... 

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). 

Solid-Fluid Equilibria The solubility of the solid is very sensitive to pressure and temperature in compressible regions, where the solvent s density and solubility parameter are highly variable. In contrast, plots of the log of the solubility versus density at constant temperature often exhibit fairly simple linear behavior (Fig. 20-19). To understand the role of solute-solvent interactions on sofubilities and selectivities, it is instructive to define an enhancement factor E as the actual solubihty divided by the solubility in an ideal gas, so that E = ysP/Pf, where P is the vapor pressure. The solubilities in CO2 are governed primarily by vapor pressures, a property of the solid... 

When nano LC is combined with mass spectrometer detection, attamole detection can be achieved for low abundance components in biological fluids, drug metabolites, and natural products such as Chinese herb medicines. Nano LC-MS-MS has become an essential tool for complex biological and drug metabolite studies. Nano LC-MS presents two significant differences from conventional analytical HPLC (1) large enhancement factor for sample detection and (2) direct interface to MS without flow splitting. The enhancement in MS ion counts relative to a conventional 4.6 mm ID column is proportional to the ratio of the square of the column diameter ... 

Figure 23.4 The enhancement factor for fluid-fluid reactions as a function of Mf and modified from the numerical solution of van Krevelens and Hoftijzer (1954).

The solubility data for naphthalene in ethylene and in CO2 are consistent with the data in Figure 3. The proper way to make the comparison is to use the enhancement factor instead of the solubility. The enhancement factor equals y2P/P2 which is simply the actual solubility divided by the solubility in an ideal gas. The enhancement factor removes the effect of vapor pressure which is useful for comparing fluids at constant reduced temperature but at different actual temperatures. In terms of the fugacity coefficient of the solute, 2, the enhancement factor is given by... 

The high solubility of solid substances in supercritical fluids compared to those in ideal gases (enhancement factors of lO -lO are common) allows their use as solvents in pharmaceutical, biomedical and food industries. Sections 2.4-2.7 are devoted to predictions of the entrainer effect, and of solubility in supercritical fluids with and without entrainer. Reliable predictive methods for solid solubilities in mixtures of a supercritical solvent -i- cosolvent were developed (2.4-2.6). These apply not only to the usual cosolvents such as organic liquids (2.4-2.5), but also to cases in which the cosolvent is a gas or another supercritical fluid (2.6). Our methods provided good agreement with experimental data in all of these cases (2.4-2.6). 

For analysis of such coupled fluid-fluid systems it is useful to distinguish between three regimes of the reaction rate (see Figure 1) which are characterized by different values of the Hatta number Ha (eqs. (2) and (3)) and the enhancement factor E (see below) ... 

The enhancement factors for solubility of compounds, over ideal solubility, in supercritical fluids is typically... 

Assuming that the COj-naphthalene mixture obeys the Peng-Robinson equation of state with C02-n = 0.103, estimate the.solubility of naphthalene in the CO2 supercritical fluid (SCF). Also compute the predicted enhancement factors and the contribution of the Poynting factor to the enhancement factor. 

By factoring out solute volatility, the enhancement factor allows comparison of solvent and secondary solute effects. Empirically, there is a linear relationship between the log of the enhancement factor and solvent density. For nonpolar and polar solutes in supercritical carbon dioxide, plots of enhancement factor coincide, indicating that differences in solubility are primarily due to vapor-pressure differences. Nonlinear behavior is noted in the case of high solubilities. The enhancement m pure fluids is relatively independent of solute structure but is sensitive to solvent polarity and density. 

Characterization of the solvent power of supercritical fluids is often quantified by the enhancement factor. The enhancement factor is the ratio of the actual solubility to the ideal gas solubility at the same temperature... 

This chapter provides an introduction to supercritical fluid behavior. As a tutorial, qualitative fluid behavior is stressed rather than quantitative description. Solubilities in solid-fluid systems are interpreted with a simple fluid model. Enhancement factors are introduced to demonstrate the importance of repulsive forces. Intermolecular interactions in cosolvent systems are discussed. Liquid-fluid phase behavior and phase transitions in liquid-fluid and solid-fluid systems are briefly presented. Transport properties are briefly presented to stress their density dependence. 

Solubility of some substances in the supercritical fluids, among different parameters, mostly depends on the vapor pressure, the substance polarity, and substance molar mass. Compounds of smaller molar mass and a higher vapor pressure at supercritical condition are more soluble in SFs, compared to other with lower vapor pressure and higher molar mass. An enhancement factor (dimensionless parameter) is defined as the ratio of solubility of substances in the SF (solvent) compared to its solubility in the ideal gas. Usually, this parameter has the common value between 10" and 10 [3]. Different mechanisms reported in the literature have been used for explaining the enhancement of solute solubility in supercritical fluids. They included the hydrogen bonding, the charge transfer complex formation, dipole-dipole noninduced and induced interactions, and solute-solvent with and without cosolvent interactions. 

The film theory has an important drawback. Although, the value of 6 is not known, one should regard it as uniquely dete mined by the hydrodynamics of the liquid phase. On the basis, Eq.l2 would predict k to be proportional to the diffusivity D. Empiri cal mass transfer coefficient correlations available in the lit rature for a liquid in contact with a gas consistently indicate that in fact k is proportional to the square root of D. Therefore, analyses based on the film theory model are not expected to predict correctly the influence of diffusivity values on the enhancement factor I. Therefore, one is lead to a more complex model of the fluid mechanics involved, the penetration theory model. This model leads, in its several variations, to the correct prediction of the... 

Film Theory and Gas-Liquid and Liquid-Liquid Mass Transfer. The history and literature surrounding interfacial mass transfer is enormous. In the present context, it suffices to say that the film model, which postulates the existence of a thin fluid layer in each fluid phase at the interface, is generally accepted (60). In the context of coupled mass transfer and reaction, two common treatments involve 1) the Hatta number and (2) enhancement factors. Both descriptions normally require a detailed model of the kinetics as well as the mass transfer. The Hatta number is perhaps more intuitive, since the numbers span the limiting cases of infinitely slow reaction with respect to mass transfer to infinitely fast reaction with respect to mass transfer. In the former case all reaction occurs in the bulk phase, and in the latter reaction occurs exclusively at the interface with no bulk reaction occurring. Enhancement factors are usually categorized in terms of reaction order (61). In the context of nonreactive systems, a characteristic time scale (eg, half-life) for attaining vapor-liquid equilibrium and liquid-liquid equilibrium, 6>eq, in typical laboratory settings is of the order of minutes. 

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