Packing volume

The maximum packing volume of a filler can be calculated for different geometrical arrangements, determined after the filler is dispersed in a liquid media (e.g. oil). It is calculated by dividing the tamped bulk density by specific gravity of filler. Table 5.8 compares the data obtained from calculation for monodispersed spheres in different arrangements with determined values. 

In polymeric systems, particle size has to be corrected for the thickness of the occluded polymer layer. This can be done by the use of the volume coefficient of separation, a, given by the following equation  

Spatial configuration or fillers in different media Maximum packing volume fraction 

Surface treated ground calcium carbonate (1 pm) in mineral oil 0.77 

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Large active exposed surface area the specific surface area, e.g., the exposed surface area of the packing per cubic foot of packed volume, is important since larger specific area means a larger area available for contact between the liquid and the gas, resulting in more efficient scrubber operation. 

On the basis of this better performance of the Pall ring, a smaller diameter tower must be selected and the tower reevaluated based on the new mass flow rates with this packing. The economics require that the higher packing cost, smaller tower diameter, new total packing volume, and tower pressure drop be considered. 

Packing surface area/unit packing volume increases resulting in more efficient packing performance (lower HETP). For structured packing the more narrow passage-way between sheet components results in more efficient performance [90]. 

Liquid hold-up, ft /ft packed tower volume Operating hold-up for any liquid, ft /ff packing volume... 

Total hold-up, ft3 liquid/ft packing volume Enthalpy of air at any temperature higher than inlet, Btu/lb dry air note hj = exit air Enthalpy of inlet air to tower, equivalent to enthalpy of saturated air at wet bulb temperature, Btu/lb dry air from Moist Air Tables, ASHVTE Guide... 

Static hold-up for water, ft- /ft packing volume Water hold-up, ft liquid/ft tower volume Enthalpy of air saturated at bulk water temperature, Btu/lb dry air... 

Btu/ (hr) (ft tower packing volume) (enthalpy-difference between air and water)... 

The data for the fraction-steps can be in terms of numbers of particles, weight, %-weight or even a packed volume. We shall next Investigate parameters of distributions as a function of method of reporting data. 

In a typical situation, as illustrated in Figure 24.3, the composition and flow rate of each feed stream (gas at the bottom and liquid at the top) are specified, directly or indirectly this enables evaluation of the quantities pAin, cAin, cB in, L, and G. The unknown quantities to be determined, in addition to h (or I, the packed volume), are Pa,out and c, our The determination involves use of the rate law developed in Section 9.2 for an appropriate kinetics regime (1) reaction in bulk liquid only (relatively slow intrinsic rate of reaction), or (2) in liquid film only (relatively fast reaction), or (3) in both bulk liquid and liquid film. For case (2), cA = 0 throughout the bulk liquid, and the equations developed below for the more general case (3), cA 0, are simplified accordingly. 

Absorber (packed) Diameter, height, internal pressure, material of construction, packing type, packing volume... 

Assuming the reaction to occur within the wet packing volume Vs, the liquid phase balance for MEK is... 

Table 4.29 Packing volume fractions for various types of atomic packing...

The mass transfer coefficients considered so far - namely, kQ,kj, KQ,andKj - are defined with respect to known interfacial areas. However, the interfacial areas in equipment such as the packed column and bubble column are indefinite, and vary with operating conditions such as fluid velocities. It is for this reason that the volumetric coefficients defined with respect to the unit volume of the equipment are used, or more strictly, the unit packed volume in the packed column or the unit volume of liquid containing bubbles in the bubble column. Corresponding to /cg, Kq, and we define k a, k, a, K, /i, and K a, all of which have units of (kmol h m )/(kmol m ) - that is, (h ). Although the volumetric coefficients are often regarded as single coefficients, it is more reasonable to consider a separately from the Ar-terms, because the effective interfacial area per unit packed volume or unit volume of liquid-gas mixture a (m m ) varies not only with operating conditions such as fluid velocities but also with the types of operation, such as physical absorption, chemical absorption, and vaporization. 

With regards to handling data on industrial apparatus for gas-liquid mass transfer (such as packed columns, bubble columns, and stirred tanks), it is more practical to use volumetric mass transfer coefficients, such as KqU and K a, because the interfacial area a cannot be well defined and will vary with operating conditions. As noted in Section 6.7.2, the volumetric mass transfer coefficients for packed columns are defined with respect to the packed volume - that is, the sum of the volumes of gas, liquid, and packings. In contrast, volumetric mass transfer coefficients, which involve the specific gas-liquid interfacial area a (L L 5), for liquid-gas bubble systems (such as gassed stirred tanks and bubble columns) are defined with respect to the unit volume of gas-liquid mixture or of clear liquid volume, excluding the gas bubbles. In this book, we shall use a for the specific interfacial area with respect to the clear liquid volume, and a for the specific interfacial area with respect to the total volume of gas-liquid mixture. 

In a trayed tower, vapor-liquid contact occurs, only on the 5 or 6 in above the tray deck, and the majority of the tower s volume is not used to exchange heat or mass between vapor and liquid. In a packed tower, the entire packed volume is used for this vapor-liquid contacting. 

Incubate 1 mL of cell lysate ( 3 x 106 cells) with either 10 pg of MAb or 100 pL (packed volume) Ab-beads overnight at 4°C... 

When soluble MAb is used, add 50 pL (packed volume) of protein A-beads or anti-Ig beads, and incubate for a further hour at 4°C. 

Note 1 As was mentioned in Note 1 under item B the US MIL-STD-650 (Ref 21) does not make any distinction betw Bulk Apparent Densities. It defines them in Method 201.1 as "weight per unit of outside volume, which may include voids in Method 201.2 as "weight per unit of apparent volume and in Method 201.3 as "weight per unit of packed volume , which means that the specimen is dropped and tapped to dispel voids Note 2 Accdg to Ref 13, p 877, "It is not always possible to say whether a given measurement refers to bulk specific gravity, to apparent specific gravity, or to some intermediate value, since the determination of solid volume depends on the nature of the substance used to permeate the voids and on the nature of the pores in the solid ... 

The two-phase composite of microspheres and voids only (i.e. packed spheres without any binding resin) has also a minimum limit. Cubic packing (volume fraction 0.53) is the lower limit, below which the structure is not selfsupporting any more, and some resin is required to fill in between the spheres. S). 

Column Chromatography. Sepharose beads containing covalently linked gangliosides (0.2 ml packed volume) were placed into a pasteur pipette containing a small amount of glass wool. Columns were washed with HEM containing 50 ug/ml bovine serum albumin (3 ml). Interferon solutions in MEM-albumin (1 ml) were placed on the columns, which were eluted with MEM-albumin at a flow rate of no more than one drop per minute. Fractions of 1 ml were collected and interferon titers determined in each fraction after serial two-fold dilution. Columns onto which mouse fibroblast interferon had been loaded, were eluted with MEM-albumin first, then with 0.07 M N-acetylneuraminyl lactose at pH 2. 

In order to generalize the expression of S for various packing materials, S is redefined as the total surface area per unit packed volume and is expressed by... 

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