Equations packings

Equation Packing Characteristic length L c ill Volume Validity range with respect to References... 

If the surface tension of a liquid is lowered by the addition of a solute, then, by the Gibbs equation, the solute must be adsorbed at the interface. This adsorption may amount to enough to correspond to a monomolecular layer of solute on the surface. For example, the limiting value of in Fig. Ill-12 gives an area per molecule of 52.0 A, which is about that expected for a close-packed... 

Use Eq. Ill-15 and related equations to calculate and the energy of vaporization of argon. Take m to be eo of Problem 6, and assume argon to have a close-packed structure of spheres 3.4 A in diameter. 

An adsorption isotherm known as the Temkin equation [149] has the form tt = ofF /F where a is a constant and F" is the limiting surface excess for a close-packed... 

A more natural way to account for the anisotropy is to treat tire parairreters in an interatomic potential, such as equation (A 1.5.64). as fiurctioirs of the relative orientation of the interacting molecules. Comer [131] was perhaps the first to use such an approach. Pack [132] pointed out that Legendre expansions of the well depth e and equilibrium location of the interaction potential converge more rapidly tirair Legendre expansions of the potential itself... 

Pack R T and Hirschfelder J O 1968 Separation of rotational coordinates from the W-electron diatomic Schrddinger equation J. Chem. Phys. 49 4009... 

To minimize the multiple path and mass transfer contributions to plate height (equations 12.23 and 12.26), the packing material should be of as small a diameter as is practical and loaded with a thin film of stationary phase (equation 12.25). Compared with capillary columns, which are discussed in the next section, packed columns can handle larger amounts of sample. Samples of 0.1-10 )J,L are routinely analyzed with a packed column. Column efficiencies are typically several hundred to 2000 plates/m, providing columns with 3000-10,000 theoretical plates. Assuming Wiax/Wiin is approximately 50, a packed column with 10,000 theoretical plates has a peak capacity (equation 12.18) of... 

Equation 12.33 defines the packing material s exclusion limit. 

To use all of these equations, the heights of the transfer units or the mass transfer coefficients and must be known. Transfer data for packed columns are often measured and reported direcdy in terms of and and correlated in this form against and... 

Equimolar Counterdiffusion. Just as unidirectional diffusion through stagnant films represents the situation in an ideally simple gas absorption process, equimolar counterdiffusion prevails as another special case in ideal distillation columns. In this case, the total molar flows and are constant, and the mass balance is given by equation 35. As shown eadier, noj/g factors have to be included in the derivation and the height of the packing is... 

Experimental Mass Transfer Coefficients. Hundreds of papers have been pubHshed reporting mass transfer coefficients in packed columns. For some simple systems which have been studied quite extensively, mass transfer data may be obtained directiy from the Hterature (6). The situation with respect to the prediction of mass transfer coefficients for new systems is stiU poor. Despite the wealth of experimental and theoretical studies, no comprehensive theory has been developed, and most generalizations are based on empirical or semiempitical equations. 

Other correlations based partially on theoretical considerations but made to fit existing data also exist (71—75). A number of researchers have also attempted to separate from a by measuring the latter, sometimes in terms of the wetted area (76—78). Finally, a number of correlations for the mass transfer coefficient itself exist. These ate based on a mote fundamental theory of mass transfer in packed columns (79—82). Although certain predictions were verified by experimental evidence, these models often cannot serve as design basis because the equations contain the interfacial area as an independent variable. 

This type of equation has been found useful in correlating drop diameters in packed columns where the packing si2e exceeds the drop diameter (65). 

Ca.rma.n-KozenyEfjua.tion, Flow through packed beds under laminar conditions can be described by the Carman-Kozeny equation in the... 

The deviation from the Einstein equation at higher concentrations is represented in Figure 13, which is typical of many systems (88,89). The relative viscosity tends to infinity as the concentration approaches the limiting volume fraction of close packing ( ) (0 = - 0.7). Equation 10 has been modified (90,91) to take this into account, and the expression for becomes (eq. 11) ... 

The expanded version of the van Deem ter equation is used to help understand the relationships between the packing parameters and the gas flow. 

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