Radius, double mean

These values are valid only for loess particles with a double-mean radius" greater than 60 fjim. 

The relationship between adhesive force and sphericity factor, as determined by direct detachment of loess particles with a double-mean radius of 100-160 ixm is illustrated by the following data ... 

As the sphericity factor increases from 0.4 to 0.9, the adhesive force drops off because of the decrease in the actual contact area for irregularly shaped particles. We also find a greater scatter of values of adhesive force with irregular particles than with spherical particles. For example, in the case of particles with a double-mean radius of 180 juni, the force of adhesion varies over a range of 2.8- 10" to 1.4- 10" dyn. 

The double-mean radius is understood to be the arithmetic average of two measurements in mutually perpendicular directions. 

These data are only valid for loess particles for which the double mean radius exceeds 60 m. 

Figure III.15 shows the adhesive forces measured by the method of direct detachment for loess particles as a function of the sphericity factor. As the sphericity factor rises from 0,4 to 0,9, the adhesive force diminishes as a result of the reduction in the actual contact area of regularly shaped particles. For particles of irregular shape there is a greater spread of adhesive-force values than for spherical particles. Thus, for particles with a double mean radius of 180 M, the adhesive force varies between 2.8 10 and 1,4 10 dyn.

However, solubility, depending as it does on the rather small difference between solvation energy and lattice energy (both large quantities which themselves increase as cation size decreases) and on entropy effects, cannot be simply related to cation radius. No consistent trends are apparent in aqueous, or for that matter nonaqueous, solutions but an empirical distinction can often be made between the lighter cerium lanthanides and the heavier yttrium lanthanides. Thus oxalates, double sulfates and double nitrates of the former are rather less soluble and basic nitrates more soluble than those of the latter. The differences are by no means sharp, but classical separation procedures depended on them. 

For particles of small radius, a, with thick electric double layers, meaning that Ka< 1, it is assumed that Stokes law applies and the electrical force is equated to the frictional resistance of the particle,... 

Like the previous one, the subject of this patent is a double-flighted screw profile with different tip and core diameters. The different tip radiuses mean that the barrel is cleaned by just one tip. 

When the double layer remains at equilibrium but has a finite thickness, the interactions between the particles do exist. The numerical results obtained by Shugai et al. [57] showed that the pair-interaction contribution to the mean electrophoretic mobility of a suspension can be significant for values of the scaled particle radius Ka < 10. Ennis and White [56] used the reflection results to obtain a complicated expression for a as a function of m. Interested readers should be referred to their paper for the general formula. For large Ka, the asymptotic expression for a is... 

Earlier speculations about the effect of the curvature of space on elemental synthesis and the stability of nuclides (2.4.1) are consistent with the interface model. The absolute curvature of the closed double cover of projective space, and the Hubble radius of the universe, together define the golden mean as a universal shape factor [233], characteristic of intergalactic space. This factor regulates the proton neutron ratio of stable nuclides and the detail of elemental periodicity. The self-similarity between material structures at different levels of size, such as elementary particles, atomic nuclei, chemical... 

Summarizing, the far and near field differ in three respects. First they do so in range. Common double layer fields extend over distances of order x" in the absence of an external field such fields are radial for a spherical double layer, as shown In fig. 3.86,bl. On the other hand, the range of the far fields is of the order of the particle radius a, which for the case considered, means that they extend far beyond the double layer. In the second place they differ In magnitude, as already stated. Thirdly, the difference is that in the near field there exist local excess charges, whereas in the far field each volume element is electro-neutral. In mathematical language, p [r,0) = 0, where r and 6 are defined in fig. 3.87. Consequently, the Laplacian of the potential is also zero in the far field. 

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