Variations in shape

CellgeometTy is governed predominantly by the final foam density and the external forces exerted on the cellular stmcture prior to its stabilization in the expanded state. In a foam prepared without such external forces, the cells tend to be spherical or ellipsoidal at gas volumes less than 70—80% of the total volume, and they tend toward the shape of packed regular dodecahedra at greater gas volumes. These shapes have been shown to be consistent with surface chemistry arguments (144,146,147). Photographs of actual foam cells (Fig. 2) show a broad range of variations in shape. 

Distribution and Octol Density Variation in Shaped Charge Warheads (Shillelagh, TOW, DRAGON) , FATM 2134 (April 1974)... 

The diversity of iiving forms includes variation in shape and form... 

Initial inspection of the as-grown crystals, revealed substantial variations in shape, thickness and crystal morphology. Examination with a light microscope showed large differences in surface topography, which were particularly pronounced in WSe2 samples. The main features, found on the surfaces were ... 

As an example of the variations in shape that can be exhibited by a single crystalline material, consider the forms of potassium sulfate shown in Fig. 8. Clearly, the processing characteristics and particulate properties of the differently shaped potassium sulfate crystals will vary. 

For most organic electroactive molecules, the variations in shape and solvation upon electron transfer are minimal, owing to the usually large delocalization. It follows that the diffusion coefficients relative to R and P are generally very close to their average value D, which is then used to introduce a simplification in the following derivations. 

The 8-membered P4N4 rings show considerable variation in shape in compounds P4N4X8. It is planar in (PNF2)4 with a rather shorter P-N bond (1-51 A) and angles P-N-P, 147°, and N-P-N, 123°, but in the stable form of... 

Estimates by Flanigen et al. [13] of free dimensions of windows in some AlPO s are given in Table 2. These estimates do not allow for the variations in shapes of windows, as seen in Table 2 for zeolites and zeosils. The values nevertheless show that windows in AlPO s have about the same range in free dimensions as in zeolites. 

Crystals show enormous variation in external shape or habit, although all these shapes arise from ordered stacking of unit cells. This is illustrated in Figure 15.5, which speaks for itself. Flowever, for a given unit cell, the angles between faces that can exist are fixed. This thus allows determination of the crystal system and of the dimensions of the unit cell from a crystal (if it is perfect and not too small). Figure 15.5 shows that considerable variation in shape can be encountered. Even far more intricate shapes are observed in ice crystals present in snow (which are formed by desublimation of water from the air). The variation in shape is caused by variation in the growth rate of the various faces of a crystal, which rates often depend on the composition of the solution see Section 15.2. 

Because of the wide variety of materials that are dried in commercial equipment and the many types of equipment that are used, there is no single theory of drying that covers all materials and dryer types. Variations in shape and size of stock,... 

In a detailed study of micronodules from various areas of the Pacific, Stoffers et al. (1984) showed that micronodules are characterized by regional variations in shape, texture, mineralogy and composition. Micronodules from the Southwestern Pacific Basin are most abundant in the dark brown clays of the central part of the basin. Mineralogically, these micronodules consist of 10 A manganate and 5Mn02 with traces of quartz, phillipsite, quartz and feldspar. They have Mn/Fe ratios of 2.4 and Ni+Cu contents of 1.3%. These Mn/ Fe ratios are somewhat higher than for the associated nodules but the Ni+Cu contents somewhat lower. The micronodules are botiyoidal with smooth surface texture. Under the SEM, the surfaces of the micronodules display a honeycomb texture. 

The overall shape of the curve shown in Figure 13.1 is typical for linear amorphous polymers in general, although the temperatures quoted are specific to polystyrene and will differ for other polymers. Variations in shape are found for different molar masses when the sample is cross-linked or partly crystalline. The value of the modulus provides a good indication of the state of the polymer and can be obtained from the curve. 

Hj is the adjustment factor for the effect of variation in shape and size of the channel cross section ... 

The heterofermentative strains normally have long rod-shaped cells but considerable variation in shape (pleomorphism) occurs, and short rods may develop. They grow best at SC C (86°F) and in the pH range 4-0-5-0. With an extended lag period, they can adapt to grow in a medium of lower pH, in the presence of hop resins and of ethanol. Beer may support growth when suitable nitrogenous compounds are present. The quantity of lactic acid produced usually reflects the concentration of carbohydrates in the beer available for assimilation by these organisms. 

An alternative way of treating this problem, one which does not separate the variation in shape of the fall-off from its shift with temperature, is to examine the variation of the activation energy for the reaction with changes in pressure. Here, the use of the term activation energy implies nothing more than a convenient way of labelling the magnitude of the variation in rate constant with temperature, viz. 

Compressible flows in this case, the velocity profile has a continuous variation in shape. This fact influences the convective heat transfer coefficient, since no fully developed temperature profile can occur if the flow is developing (see - Convective Heat Transfer in Microcharmels ). 

Calcination of the gel products at 1(X)0°C showed that only the sol composition containing the acetate as the source of Ba produced phase-pure BaTi03. Further acetate sols were therefore prepared with 2-25 vol% Span 80 in the support solvent (oil phase + surfactant), and the gel product calcined at 1000°C. The particles were not only large (tens to hundreds of nm width) but of a variety of shapes dependent on surfactant contents in the sols. The variations in shape with increasing surfactant content are described below ... 

Automated detection of masses poses challenges for CAD because they may appear as intraluminal types (lobulated, polypoid, or circumferential) or non-intraluminal types (mucosal wall-thickening type of growth pattern or masses that block the colon), both of which have a wide variation in shape characteristics. Only a few CAD schemes for the detection of colorectal cancers have addressed this challenge (Nappi et al. 2002b Nappi et al. 2004a). 

When considering antennae of different species, the variation in shape is striking. To understand the evolutionary development of variations in size and... 

When Mam > 0.3 the hypothesis of incompressibility no longer holds and the gas acceleration leads to changes in the velocity profile not only in magnitude but also in shape. The magnitude increments produce additional pressure drop while the shape changes alter the friction factor at the walls. The continuous variation in shape of the velocity profile means that neither fully developed nor locally fully developed flows occur. This fact influences the convective heat transfer coefficient since no fully developed temperature profiles can occur if the flow is developing and the experimental Nusselt numbers differ by the theoretical values for fully developed flow. It is possible to demonstrate numerically that when the Mach number increases the Nusselt number decreases along the... 

---