Cohesion number

Both arguments can be mathematically expressed in terms of a dimensionless cohesion number ffc... 

A powder will flow when the stresses exceed the cohesive strength of a material. The cohesion number (tTc) is one metric that could be of assistance when scaling up blending processes for cohesive materials (4). This metric is calculated according to the following equation ... 

In a chiral solution that is not a racemic mixture, however, the chiral molecules present in greater numbers are configurationally equivalent to each other, and therefore each possesses identical electron clouds to its molecular twins. As such, each interaction between light and one of these majority molecule s electron clouds will result in rotations of identical magnitude and direction. When these billions of billions of interactions are summed together into one cohesive number, they do not cancel one another as racemic and achiral solutions tend to do - rather, the chiral solution as a whole is observed to rotate polarized light in one particular direction due to its molecular properties. 

In terms of the limit of behavior between A and C powders, a dimensionless Group known as cohesion number Coh, is defined as... 

Equation 2.4 is, actually, the product of the inverse of the cohesion number and another dimensionless group known as the Archimedes number Ar, and thus... 

Oltrogge (2 ) and Verloop (2 ) introduce in their derivations of equation (1) a stabilizing elastic behaviour of the bed which is ascribed to the hydro-dyneunics of the flow of a fluid through particle layers. However, this explanation cannot be valid for the low Reynolds numbers encountered in homogeneous gas-solids fluidization as was recently shown by Mutsers and Rietema (21 ). Rietema ( ) showed the essential role of interpartical contact in fluidization. This contact cem be demonstrated e.g. by electrical conductivity measurements. Due to this contact, particles exert cohesion forces on each other. For particles with d < 100 pm the cohesion number ... 

The solubility parameter is not calculated directly. It is calculated as the square root of the cohesive energy density. There are a number of group additivity techniques for computing cohesive energy. None of these techniques is best for all polymers. 

When a sample of ca 100 g has been obtained, a representative sample for use in size characterization equipment must then be taken. Some of the more modem methods of size characterization require as Htde as 1 mg of powder, thus obtaining a representative sample can be quite difficult. If the powder flows weU and does not contain too many fines, a device known as the spinning riffler (Fig. 4c) can be used. A spinning riffler consists of a series of cups that rotate under the powder supply. The time of one rotation divided into the time of total powder flow should be as large a number as possible. Although this device has been shown to be very efficient, problems can be encountered on very small (1 mg) samples, and the powder must be processed several times. Moreover, in order to avoid cross-contamination, cleanup after each of the sampling processes can be quite difficult. Furthermore, if the powder is cohesive and does not flow weU, the equipment is not easy to use. A siUca flow agent can be added to the powder to enable the powder to flow... 

The permachor method is an empirical method for predicting the permeabiUties of oxygen, nitrogen, and carbon dioxide in polymers (29). In this method a numerical value is assigned to each constituent part of the polymer. An average number is derived for the polymer, and a simple equation converts the value into a permeabiUty. This method has been shown to be related to the cohesive energy density and the free volume of the polymer (2). The model has been modified to liquid permeation with some success. 

A number of general principles govern the selection of crushers [Riley, Chem. Proce.ss Eng. (January 1953)]. When the rock contains a predominant amount of material that has a tendency to be cohesive when moist, such as clay, any form of repeated pressure crusher will show a tendency for the fines to pack in the outlet of the crushing zone and prevent free discharge at fine settings. Impact breakers are then... 

Visually, failure was mostly eohesive within the adhesive (see Figs. 34 and 46). However, there was a small area of apparent interfacial failure ( initiation zone ) located at one end of each substrate. Line scans were eondueted aeross the initiation zone, from the edge of the substrate to the area of cohesive failure within the adhesive. From the line scans, it was apparent that there were patehes of polymer present in the initiation zone, even when failure appeared to be interfaeial (see Fig. 46). SIMS images of the initiation zone were constructed for various mass numbers (see Figs. 47-49). The images showed well-defined cation-rieh... 

APAOs has limited their utility in a number of applications. The broad MWD produces poor machining and spraying, and the low cohesive strength causes bond failures at temperatures well below the softening point when minimal stress is applied. To address these deficiencies, metallocene-polymerized materials have been developed [17,18]. These materials have much narrower MWDs than Ziegler-Natta polymerized materials and a more uniform comonomer distribution (see Table 3). Materials available commercially to date are better suited to compete with conventional EVA and EnBA polymers, against which their potential benefits have yet to be realized in practice. 

Table I. Cohesive energies of shallow tori the parameters n, and ii, are the number of hexagons along the outer and inner eirele, respeetively (see Fig. 6). Here Af is the tiumber of atoms in a torus...

The diameters of the inside and outside circles, the pitch length, and the cohesive energy per atom for helices are given in Table 2. The number of pentagons. 

Fujiwara et al. used the CMC values of sodium and calcium salts to calculate the energetic parameters of the micellization [61]. The cohesive energy change in micelle formation of the a-sulfonated fatty acid methyl esters, calculated from the dependency of the CMC on the numbers of C atoms, is equivalent to that of typical ionic surfactants (Na ester sulfonates, 1.1 kT Ca ester sulfonates, 0.93 kT Na dodecyl sulfate, 1.1 kT). The degree of dissociation for the counterions bound to the micelle can be calculated from the dependency of the CMC on the concentration of the counterions. The values of the ester sulfonates are also in the same range as for other typical ionic surfactants (Na ester sulfonates, 0.61 Ca ester sulfonates, 0.70 Na dodecyl sulfate, 0.66). 

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