Sphere walls

All the spheres in a layer were supported by two spheres of the layer below and the column wall, creating a stable packing structure. As the tube-to-particle diameter ratio of the bed was only four, the entire packing structure was controlled by the influence of the wall. Nevertheless, the packing was divided into an immediate wall layer and a central section, but this should not be taken to imply that the central structure was not wall influenced. Although a three-sphere planar structure would almost fit within the nine-sphere wall layer, there was just not enough room at the same axial coordinate. When, however, the... 

The data from the WS model in some cases deviated slightly from the full-bed models. This could be explained by the slightly different layout of the WS model. Some spheres had to be relocated in the WS model to create a two-layer periodicity from the six-layer periodicity in the full-bed models. The differences in velocity magnitudes were mainly found in the transition area between the wall layers and the center layers. The effect of slightly larger gaps between spheres from the nine-sphere wall layers and the three-sphere central layers, due to the sphere relocations, had a noticeable effect on the velocity profile. Differences were also found in the central layer area where the sphere positions were not identical. 

Overall the spheres were of good quality judging from images obtained and could be used for filling with sodium alanate. However, to confirm through wall open porosity formation across the spheres wall, approximately 900 A cross section was made across a sphere wall and SEM and elemental mapping was conducted and Fig. 3 shows the results obtained. 

Figure 3 900 A sphere wall cross section following acid leaching...

Figure 6 Spheres wall cross section after filling with sodium alanate...

For an externally applied pressure, a compression-compression stress field is obtained with a thick-walled sphere. If the sphere wall is thin, a biaxial field is produced. If the pressure is applied internally, a triaxial tension-tension-compression state is generated. A nearly uniform stress field is produced over the entire specimen. The supporting tube is surrounded with a low modulus material to avoid stress concentration and... 

Source From KPW 1978. The "E" subscript here is for the "easy approximation" in that paper "NSE" is for "not so easy." The coefficient for Eq. [1] differs because of the substitution of summation over = (2jrkT/ti)n for integration with a consequent factor 2ir kT/ti. Original many-body formulation in L1974 and L1971. Numbers in [ ] correspond to those in KPW 1978. Sphere-wall interactions are also treated in J. D. Love, "On the van der Waals force between two spheres or a sphere and a wall," J. Chem. Soc. Faraday Trans. 2, 73, 669-688 (1977). 

This simple and appealing result shows that, for H 1 /k, the sphere-wall interaction depends linearly on the charge densities of each surface, and decays exponentially with the separation distance. The result does not depend on whether the surfaces are considered to be constant charge density or constant potential, because the potentials of an isolated wall and sphere were used in its derivation. Phillips [13] has compared Eq. (24) with a numerical solution of the linear Poisson-Boltzmann equation, and shows that it errs by less than about 10% for xh>3 when 0.5 [Pg.257]

Before considering detailed comparisons between various levels of approximation, we introduce the nonlinear Derjaguin approximation as an alternative, simple expression for sphere-wall interactions that is valid when kci S> 1 and h/a < C 1. The result for the force on the sphere is given by... 

Recently, KIEFER et al. [5.102] have published their relatively easily calculated approximations of the general homogeneous sphere-sphere and sphere-wall interactions that simplify the results of LANGBEIN [5.34,94]. 

Double-beam instruments may compare the spectral response of a specimen in the sample beam to the diffuse white coating on the sphere wall. See also the discussion on instrument limitations. If the sample is primarily a specular reflector or transmitter the reference beam should contain a similar type... 

The interior walls of the integrating sphere are coated with a white, highly reflective material. In Fig. 2, light from an external source is collimated and strikes the sample surface at normal incidence. A photodetector responds proportionally to the internal illumination produced on the sphere wall. A baffle prevents direct illumination of the detector after scattering from the sample. The incident beam flux is recorded initially without the sample in place to determine the measurement baseline. 

In June 1993, faults were detected on expansion tank n 3 on welds subject to thermal fatigue. After careful examination and removal of the secondary pumps and thermal insulation, similar faults were found on the other tanks. Replacement (under argon atmosphere) of the coimection flange to the inlet pipe and parts of the sphere wall were undertaken and are still in progress. 

In the rotational core, used in HRE-1, the flow pattern tends to produce isotherms which are vertical cylinders. These are perturbed by boundary-layer mixing at the sphere walls. The temperature generally increases in the direction of the central axis, whieh is at outlet temperature. The gas bubbles are centrifuged rapidly into a gas void which forms at the center axis and from wliich gas can be removed. The gas void is quite stable in cores up to about 2 ft in diameter, l)ut in larger. spheres the pumping requirements to stabilize the void arc excessive [5]. The pressure drop through a rotational core is a function of the particular sj stem, but is usually above 5 inlet-velocity heads. 

In this equation, I, is the integrated emission spectmm of the sphere with the excitation bean hitting the sample, is the integrated emission spectmm of the sphere with the sample with the excitation beam hitting the sphere wall but not the sample, and is the integrated excitation spectmm of the integrating sphere with the sample holder. The absorption coefficient a of the sample is defined as... 

Here, is the integrated excitation spectrum of the sphere with the sample with the excitation beam hitting the sphere wall but not the sample and is the integrated excitation... 

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