Packing factor, constant

Fig. 24. Generalized method using log scales for estimating packed column flooding and pressure drop, AP, in kPa/m g = gravitational constant, 9.81 m/s t = kinematic viscosity in mm /s (= cSt) E, G have units of kg/(m s) are in kg/m and the packing factor, F, in can be found in...

For isothermal compressible flow of a gas with constant compressibility factor Z through a packed bed of granular solids, an equation similar to Eq. (6-114) for pipe flow may be derived ... 

Alternate driving force approximations, item 2B in Table 16-12, for solid diffusion, and item 3B in Table 16-12, for pore diffusion, provide somewhat more accurate results in constant pattern packed-bed calculations with pore or solid diffusion controlling for constant separation factor systems. 

Since selectivity in HPLC involves both the stationary and mobile phases [5-9,58-60], it is important to note that the solvent strength of the mobile phase, as compared to the stationary phase, (composed of mobile-phase components reversibly retained by the bonded phase and silica support) determines the elution order or k of the retained components. Unfortunately, the columns with the same stationary phase can exhibit significant variabilities from one manufacturer to another and even from the same manufacturer [5-8]. Based on discussions heard at various scientific meetings, this situation has not changed much. Variabilities can occur in the packing process even where all other conditions are supposedly constant. These factors have to be considered prior to developing an understanding as to how separations occur in HPLC. 

Robbins found that the constant Cj in Eq. (8.12) correlates directly with the packing factor. This observation permitted him to derive packing factors from dry pressure measurements [applying Eq. (8.12) with uL = 0]. He also found that the constant C2 in Eq. (8.12) correlates well with the square root of the packing factor and the liquid viscosity to the 0.1 power. These findings permitted Robbins to express the curves shown in Fig. 8.15 in a generalized form, giving the equation... 

F = Packing factor p = Viscosity of liquid, centipoise g = Gravitational constant = 32.2... 

The mass-transfer coefficient is sensitive to several factors, including Henry s constant of the contaminant, the packing factor, and the temperature of the ambient air and water to be treated. An HTU value, calculated at 20°C from Eq. (7), would require a fivefold increase if ambient water and air temperatures of 5°C and -12°C, respectively, were encountered (9). Therefore, the equations presented are recommended for initial design work and evaluation of pilot studies or field data. Data from pilot studies are required to provide dependable values for the mass-transfer coefficient and the effects on removal efficiencies produced by varying system parameters. An analytical program... 

Theory for Nafion. To apply the general theory quantitatively it is necessary to express explicitly the relationships between rh and nh, rc and nc, and the force constant Ke. A four-parameter model (fCe,pi,p2,p3) was formulated to accomplish this goal. First, we define three packing factors pi, p2, and p3 as pi = packing factor for water molecules in a purely aqueous hydration shell p2 = packing factor for water molecules in hydration shells containing a cation, for example, ion-dipole hydration shells and p3 = packing factor of hydration shells in a cluster. 

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