Spherical shape

In the converse situation free of gravity, a drop assumes a perfectly spherical shape. At one point, the U.S. Space program tested this idea with the solidification of ball bearings from molten metal drops in microgravity conditions. 

The serum albumin molecule is known to have an approximately spherical shape (see Example 8.7) and is foundf to have an intrinsic viscosity in aqueous buffer solutions of 3.7 cm g". Using p = 1-34 g cm as the density of the... 

Inasmuch as friction conditions determine the flow characteristics of a powder, coarser powder particles of spherical shape flow fastest and powder particles of identical diameter but irregular shape flow more slowly. Finer particles may start to flow, but stop after a short time. Tapping is needed in order to start the flow again. Very fine powders (fine powder particles to coarser ones may increase the apparent density, but usually decreases the flow quality. Metal powders having a thin oxide film may flow well. When the oxide film is removed and the friction between the particles therefore increases, these powders may flow poorly. 

A weU-known feature of olefin polymerisation with Ziegler-Natta catalysts is the repHcation phenomenon ia which the growing polymer particle mimics the shape of the catalyst (101). This phenomenon allows morphological control of the polymer particle, particularly sise, shape, sise distribution, and compactness, which greatiy influences the polymerisation processes (102). In one example, the polymer particle has the same spherical shape as the catalyst particle, but with a diameter approximately 40 times larger (96). 

Fig. 2. Compression strength of agglomerates formed into spherical shape by tumbling where = mean disperse particle diameter (8). To convert kPa to...

Types ofSCT Catalysts. The catalysts used in the SCR were initially formed into spherical shapes that were placed either in fixed-bed reactors for clean gas apphcations or moving-bed reactors where dust was present. The moving-bed reactors added complexity to the design and in some appHcations resulted in unacceptable catalyst abrasion. As of 1993 most SCR catalysts are either supported on a ceramic or metallic honeycomb or are direcdy extmded as a honeycomb (1). A typical honeycomb block has face dimensions of 150 by 150 mm and can be as long as one meter. The number of cells per block varies from 20 by 20 up to 45 by 45 (39). 

David W. Taylor Model Basin, Washington, September 1953 Jackson, loc. cit. Valentin, op. cit.. Chap. 2 Soo, op. cit.. Chap. 3 Calderbank, loc. cit., p. CE220 and Levich, op. cit.. Chap. 8). A comprehensive and apparently accurate predictive method has been publisned [Jami-alahamadi et al., Trans ICE, 72, part A, 119-122 (1994)]. Small bubbles (below 0.2 mm in diameter) are essentially rigid spheres and rise at terminal velocities that place them clearly in the laminar-flow region hence their rising velocity may be calculated from Stokes law. As bubble size increases to about 2 mm, the spherical shape is retained, and the Reynolds number is still sufficiently small (<10) that Stokes law should be nearly obeyed. 

With a spherical-shaped anode of radius, r, which is immersed very deep in an electrolyte t > Kq), the current radiates uniformly outward in all directions. Between this spherical anode and the infinitely large and distant remote ground, a voltage U is applied which involves a current 7 = UIR. R is the grounding resistance. 

The majority of particles in the atmosphere are spherical in shape because they are formed by condensation or cooling processes or they contain core nuclei coated with liquid. Liquid surface tension draws the material in the particle into a spherical shape. Other important particle shapes exist in the atmosphere e.g., asbestos is present as long fibers and fly ash can be irregular in shape. 

CP-1 was assembled in an approximately spherical shape with the purest graphite in the center. About 6 tons of luanium metal fuel was used, in addition to approximately 40.5 tons of uranium oxide fuel. The lowest point of the reactor rested on the floor and the periphery was supported on a wooden structure. The whole pile was surrounded by a tent of mbberized balloon fabric so that neutron absorbing air could be evacuated. About 75 layers of 10.48-cm (4.125-in.) graphite bricks would have been required to complete the 790-cm diameter sphere. However, criticality was achieved at layer 56 without the need to evacuate the air, and assembly was discontinued at layer 57. The core then had an ellipsoidal cross section, with a polar radius of 209 cm and an equatorial radius of309 cm [20]. CP-1 was operated at low power (0.5 W) for several days. Fortuitously, it was found that the nuclear chain reaction could be controlled with cadmium strips which were inserted into the reactor to absorb neutrons and hence reduce the value of k to considerably less than 1. The pile was then disassembled and rebuilt at what is now the site of Argonne National Laboratory, U.S.A, with a concrete biological shield. Designated CP-2, the pile eventually reached a power level of 100 kW [22]. 

Hertz [27] solved the problem of the contact between two elastic elliptical bodies by modeling each body as an infinite half plane which is loaded over a contact area that is small in comparison to the body itself. The requirement of small areas of contact further allowed Hertz to use a parabola to represent the shape of the profile of the ellipses. In essence. Hertz modeled the interaction of elliptical asperities in contact. Fundamental in his solution is the assumption that, when two elliptical objects are compressed against one another, the shape of the deformed mating surface lies between the shape of the two undeformed surfaces but more closely resembles the shape of the surface with the higher elastic modulus. This means the deformed shape after two spheres are pressed against one another is a spherical shape. 

Fig. I. High-resolution electron micrographs of graphitic particles (a) as obtained from the electric arc-deposit, they display a well-defined faceted structure and a large inner hollow space, (b) the same particles after being subjected to intense electron irradiation (note the remarkable spherical shape and the disappearance of the central empty space) dark lines represent graphitic layers.

The very first stage of flame propagation upon ignition, during which the flame has a spherical shape, mainly determines the blast peak overpressure produced by the entire vapor cloud explosion. 

Fireball A burning fuel-air cloud whose energy is emitted primarily in the form of radiant heat. The inner core of the cloud consists almost completely of fuel, whereas the outer layer (where ignition first occurs) consists of a flammable fuel-air mixture. As the buoyancy forces of hot gases increase, the burning cloud tends to rise, expand, and assume a spherical shape. 

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