Particle shape ellipticity

In practice, it is the viscosity that is experimentally determined, and the correlations are used to determine axial ratios and shape factors. The viscosity can be determined by any number of techniques, the most common of which is light scattering. In addition to ellipticity, solvation (particle swelling due to water absorption) can have an effect on... 

Kneule and Weinspach (1967) also measured the suspension characteristics of numerous stirrer types and agitated vessels. They found the optimum stirrer diameter d, and distance from the bottom H, to be given by dT/d, = 3.0-3.5 and Hj/d, = 0.3-0.5. The optimum shapes for the vessel bottom are hemispherical and elliptical a flat vessel bottom is unsuitable for particle suspension. For a vessel with an elliptical bottom, baffles, and a propeller stirrer installed at HJd = 0.2-0.8 pumping the liquid toward the floor, the constant b in Eq. (3.22) has the value b = 3.06. For a turbine stirrer with six paddles and Hj/d, = 0.3, the value is b = 1.21. In order to keep the particles in the same material system in suspension, the propeller stirrer must therefore operate at a rotational speed (3.06/1.21)1/2 = 1.59 times higher than a turbine stirrer of the same size. 

Figure 3.40 Calculated phase velocity of flexural plate waves vs ratio of plate thickness, d, to wavelength. A, for silicon nitride. Material is assumed to have the elastic properties of Si3N4 and no residual tension. The mode shapes ate illustrated at the right with a greatly enlarged vertical scale for clarity. Ellipses at left show the retrograde elliptical particle motions of the lowest S3rmmetric and antisymmetric modes for d/A = 0.03. (Reprinted with pemtission. See Ref. (621.)...

Church [39] proposed the use of the ratio of the expected values of Martin s and Feret s diameters as a shape factor for a population of elliptical particles. Cole [40] introduced an image-analyzing computer (the Quantimet 720) to compare longest chord, perimeter and area for a large number of particles. Other parameters have been proposed by Pahl el. al [7,41], Beddow [42] and Laird [29]. 

The shape of metal particles affects field enhancement magnitude in a manner that depends on both the identity of the metal and the wavelengths of both the laser and the Raman-shifted light. For example, spherical and elliptical particles have different radii of curvature for... 

Vacuole dilatation information itself is not simply interpreted. The data instead are best understood through models of microstruetural failure (1). Assuming a single size of spherical filler particles encompassed by elliptically shaped voids that form arbitrarily in strain, and once formed grow at a constant rate with further deformation, then one can readily separate vacuole growth from vacuole formation. Models such as the one described above have been substantiated by microscopic studies. The solution of such models (1) indicates that the first derivative of vacuole dilatation with respect to strain c, is directly proportional to the cumulative number of vacuoles per unit volume,n, that exist at any strain. The second derivative is then directly proportional to the instantaneous frequency distribution of vacuole formation. These two results can be expressed mathematically... 

Here a denotes the maximum field amplitude, rj is the ellipticity together with the pulse-shape function g(rj), which depends on the phase rj = (ot — k r. The laser beam is characterized by the frequency co and the wave vector k with ck = co. The transversality condition implies k A — 0. For a charged point particle interacting with this external electromagnetic field, the Hamilton-Jacobi equation reads... 

Analytical expressions similar to those for spherical particles have been derived for infinite-length cylinders in perpendicular incidence as well as in oblique incidence, for elliptic cylinders, and for spheroids (see Refs. 168 and 169). With increasing complexity of the shape of the particle, even with as little change as from sphere to spheroid, the analytical solution to the problem becomes formidable. Then, the use of numerical solution techniques may be preferable to analytical techniques. 

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