Density, packing

Shown in Table 5.3 is the packing density of the commercially available inorganic membrane modules. The single plate geometry has a very low packing density. Single tubes typically also show a low packing density unless the membrane tube and the module both have small diameters which are not practical other than for laboratory 

Comparison of process-related characteristics of various module configurations of organic polymer membranes 

Characteristics Plate Frame Spiral-Wound Tube-in- shell Hollow-fiber 

Method of replacement As sheets As module assembly As tubes As entire module 

Replacement labor High Medium High Medium 

---

This is attributed to the different nature of the bonding of sulphur to silver as compared to gold and the slightly different packing density. The coherence length detennined with He atom diffraction was found to be 12 mn [162]. 

Samples can be concentrated beyond tire glass transition. If tliis is done quickly enough to prevent crystallization, tliis ultimately leads to a random close-packed stmcture, witli a volume fraction (j) 0.64. Close-packed stmctures, such as fee, have a maximum packing density of (]) p = 0.74. The crystallization kinetics are strongly concentration dependent. The nucleation rate is fastest near tire melting concentration. On increasing concentration, tire nucleation process is arrested. This has been found to occur at tire glass transition [82]. 

At potentials positive to the bulk metal deposition, a metal monolayer-or in some cases a bilayer-of one metal can be electrodeposited on another metal surface this phenomenon is referred to as underiDotential deposition (upd) in the literature. Many investigations of several different metal adsorbate/substrate systems have been published to date. In general, two different classes of surface stmetures can be classified (a) simple superstmetures with small packing densities and (b) close-packed (bulklike) or even compressed stmetures, which are observed for deposition of the heavy metal ions Tl, Hg and Pb on Ag, Au, Cu or Pt (see, e.g., [63, 64, 65, 66, 62, 68, 69 and 70]). In case (a), the metal adsorbate is very often stabilized by coadsorbed anions typical representatives of this type are Cu/Au (111) (e.g. [44, 45, 21, 22 and 25]) or Cu/Pt(l 11) (e.g. [46, 74, 75, and 26 ]) It has to be mentioned that the two dimensional ordering of the Cu adatoms is significantly affected by the presence of coadsorbed anions, for example, for the upd of Cu on Au(l 11), the onset of underiDotential deposition shifts to more positive potentials from 80"to Br and CE [72]. 

The term essentially a drag coefficient for the dust cake particles, should be a function of the median particle size and particle size distribution, the particle shape, and the packing density. Experimental data are the only reflable source for predicting cake resistance to flow. Bag filters are often selected for some desired maximum pressure drop (500—1750 Pa = 3.75-13 mm Hg) and the cleaning interval is then set to limit pressure drop to a chosen maximum value. 

Fig. 1. A, hoUow-fiber spool B, hoUow-fiber cartridge employed ia hemodialysis C, cartridge identical to item B demonstrating high packing density D, hoUow-fiber assembly employed for tissue ceU growth E, hoUow-fiber bundle potted at its ends to be inserted into a cartridge or employed ia a situation...

Inorganic membranes (29,36) are generaUy more stable than their polymeric counterparts. Mechanical property data have not been definitive for good comparisons. IndustriaUy, tube bundle and honeycomb constmctions predominate with surface areas 20 to 200 m. Cross-flow is generaUy the preferred mode of operation. Packing densities are greater than 1000 /m. Porous ceramics, sintered metal, and metal oxides on porous carbon support... 

DpopE related to SpQpp, which is in turn related to the closeness of packing of the powder. The number of particles adjacent to a given particle is represented by The maximum packing density for monosize spheres occurs at hexagonal close packing, where = 12 and = 0.2595 for... 

Compressibility. The bulk density of a soHd is an essential value used in the analysis of its flow properties, such as when calculating mass flow hopper angles, opening sizes, bin loads, etc. Loose and/or packed density values ate not sufficient. Bulk soHds exhibit a range of densities that vary as a function of consoHdating pressure. This range of densities, called the compressibiHty of the soHd, can often be expressed on a log—log plot as a line or relationship. 

Orientation sometimes leads to lower permeabiHty values (better barrier properties). Orientation can iacrease packing density, which lowers the diffusion coefficient D it can also iacrease the difficulty of hopping or diffusiag ia a direction perpendicular to the film. In the latter case, movement ia general may be fast, but movement through the film is limited. However, mere stretching does not always lead to orientation of the molecular chains. In fact, stretching can lead to void formation, which iacreases permeabiHty. 

A catalyst manufactured using a shaped support assumes the same general size and shape of the support, and this is an important consideration in the process design, since these properties determine packing density and the pressure drop across the reactor. Depending on the nature of the main reaction and any side reactions, the contact time of the reactants and products with the catalyst must be optimized for maximum overall efficiency. Since this is frequendy accompHshed by altering dow rates, described in terms of space velocity, the size and shape of the catalyst must be selected carehiUy to allow operation within the capabiUties of the hardware. 

Multilayer boards, which use multiple interior laminates of plastic and copper, now comprise over half of the value of production, though much less on a surface area basis. Surface mount technologies demand extreme flatness and reproducibiHty from surfaces. Greater packing density has led to commercial production of finer lines and holes, often less than 50 p.m and 500 p.m, respectively. Electroless gold over electroless nickel—phosphoms, or electroless nickel—boron alone, is often used as a topcoating for wire bonding or improved solderabiHty. 

The wet pan is used for developing plasticity or molding qualities in ceramic reed materials. The abrasive and kneading actions of the mullers blend finer particles with the coarser particles as they are crushed (Greaves-Walker, Am. Refract. Jnst. Tech. Bull. 64, 1937), and this is necessary so that a high packing density can be achieved to result in strength. 

Aromatic polyamide (aramid) membranes are a copolymer of 1-3 diaminobenzene with 1-3 and 1-4 benzenedicarboxylic acid chlorides. They are usually made into fine hollow fibers, 93 [Lm outer diameter by 43 [Lm inner diameter. Some flat sheet is made for spirals. These membranes are widely used for seawater desalination and to some extent for other process applications. The hollow fibers are capable of veiy high-pressure operation and have considerably greater hydrolytic resistance than does CA. Their packing density in hoUow-fiber form makes them veiy susceptible to colloidal fouling (a permeator 8 inches in diameter contains 3 M fibers), and they have essentially no resistance to chlorine. 

Metal atoms tend to behave like miniature ball-bearings and tend to pack together as tightly as possible. F.c.c. and c.p.h. give the highest possible packing density, with 74% of the volume of the metal taken up by the atomic spheres. However, in some metals, like iron or chromium, the metallic bond has some directionality and this makes the atoms pack into the more open b.c.c. structure with a packing density of 68%. 

Fig. 2.4. The structure of a typical grain boundary. In order to "bridge the gap" between two crystals of different orientation the atoms in the grain boundary have to be packed in a less ordered way. The packing density in the boundary is then as low as 50%.

LM Gregoret, FE Cohen. Effect of packing density on chain conformation. J Mol Biol 219 109-122, 1991. 

---