Spheroid particles

A new description of slurry-cast propellants ( Plastisol Propellants ) has been given by Camp (44]. Fine particle spheroidal nitrocellulose is the base of the... 

The most conunon choice for a reference system is one with hard cores (e.g. hard spheres or hard spheroidal particles) whose equilibrium properties are necessarily independent of temperature. Although exact results are lacking in tluee dimensions, excellent approximations for the free energy and pair correlation fiinctions of hard spheres are now available to make the calculations feasible. 

As pointed out earlier (Section 3.5), certain shapes of hysteresis loops are associated with specific pore structures. Thus, type HI loops are often obtained with agglomerates or compacts of spheroidal particles of fairly uniform size and array. Some corpuscular systems (e.g. certain silica gels) tend to give H2 loops, but in these cases the distribution of pore size and shape is not well defined. Types H3 and H4 have been obtained with adsorbents having slit-shaped pores or plate-like particles (in the case of H3). The Type I isotherm character associated with H4 is, of course, indicative of microporosity. 

The Stokes-Einstein equation has already been presented. It was noted that its vahdity was restricted to large solutes, such as spherical macromolecules and particles in a continuum solvent. The equation has also been found to predict accurately the diffusion coefficient of spherical latex particles and globular proteins. Corrections to Stokes-Einstein for molecules approximating spheroids is given by Tanford. Since solute-solute interactions are ignored in this theory, it applies in the dilute range only. 

Heywood [Heywood, Symposium on Paiticle Size Analysis, lust. Chem. Engrs. (1 7), Suppl. 25, 14] recognized that the word shape refers to two distinc t charac teiistics of a particle—form and proportion. The first defines the degree to which the particle approaches a definite form such as cube, tetr edron, or sphere, and the second by the relative proportions of the particle which distinguish one cuboid, tetrahedron, or spheroid from another in the same class. He replaced historical quahtative definitions of shape by numerical shape coefficients. 

Onion-like graphitic clusters have also been generated by other methods (a) shock-wave treatment of carbon soot [16] (b) carbon deposits generated in a plasma torch[17], (c) laser melting of carbon within a high-pressure cell (50-300 kbar)[l8]. For these three cases, the reported graphitic particles display a spheroidal shape. 

In particular, the laser melting experiment produced two well-differentiated populations of carbon clusters (a) spheroidal diamond particles with a radial texture... 

Type I Mg powder shall consist of shavings, turnings, flakes, plates or any combination of these which meets the granulation requirement. Type II Mg powder shall consist of oblong chip-like particles with rounded edges. Type III Mg powder shall consist of granular or spheroidal particles... 

Note that the values of h depends upon the material and the mechanism of sintering. Also, these values depend upon r and x, the radii of the particles and the radius of joining. These equations apply only to spheroids and a shape factor must be considered as well. 

At this point, we are most interested in the size of particles and how the other factors relate to the question of size. The next most important factor is shape. Most of the particles that we will encounter are spheroidal or oblong in shape, but if we discover that we have needle-like (acicular) particles, how do we define their average diameter Is it an avereige of the sum of length plus cross-section, or what ... 

Now we focus our attention on the conditions of equilibrium for a fluid spheroid rotating about a constant axis. In this case the mutual position of fluid particles does not change and all of them move with the same angular velocity, a>. As is well known, there is a certain relationship between the density, angular velocity, and eccentricity of an oblate spheroid in equilibrium. In studying this question we will proceed from the equation of equilibrium of a fluid, described in the first section. 

In a series of papers, Chhabra (1995), Tripathi et al. (1994), and Tripathi and Chhabra (1995) presented the results of numerical calculations for the drag on spheroidal particles in a power law fluid in terms of CD = fn(tVRe, ). Darby (1996) analyzed these results and showed that this function can be expressed in a form equivalent to the Dallavalle equation, which applies over the entire range of n and tVRe as given by Chhabra. This equation is... 

Tripathi A, RP Chhabra. Drag on spheroidal particles in dilatant fluids. AIChE J 41 728, 1995. 

Tripathi A, RP Chhabra, T Sundararajan. Power law fluid flow over spheroidal particles. Ind Eng Chem Res 33 403, 1994. 

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