Particles sphericity

Fitzgerald et al. (1984) measured pressure fluctuations in an atmospheric fluidized bed combustor and a quarter-scale cold model. The full set of scaling parameters was matched between the beds. The autocorrelation function of the pressure fluctuations was similar for the two beds but not within the 95% confidence levels they had anticipated. The amplitude of the autocorrelation function for the hot combustor was significantly lower than that for the cold model. Also, the experimentally determined time-scaling factor differed from the theoretical value by 24%. They suggested that the differences could be due to electrostatic effects. Particle sphericity and size distribution were not discussed failure to match these could also have influenced the hydrodynamic similarity of the two beds. Bed pressure fluctuations were measured using a single pressure point which, as discussed previously, may not accurately represent the local hydrodynamics within the bed. Similar results were... 

Glicksman and Farrell (1995) constructed a scale model of the Tidd 70 MWe pressurized fluidized bed combustor. The scale model was fluidized with air at atmospheric pressure and temperature. They used the simplified set of scaling relationships to construct a one-quarter length scale model of a section of the Tidd combustor shown in Fig. 34. Based on the results of Glicksman and McAndrews (1985), the bubble characteristics within a bank of horizontal tubes should be independent of wall effects at locations at least three to five bubble diameters away from the wall. Low density polyurethane beads were used to obtain a close fit with the solid-to-gas density ratio for the combustor as well as the particle sphericity and particle size distribution (Table 6). 

Figure 8.9 Concentration (cA) and temperature (Z ) gradients (schematic) in a porous catalyst particle (spherical or end-on cylindrical)...

The scattering models employed in data processing invariably involve the assumption of particle sphericity. Size data obtained from the analysis of suspensions of asymmetrical particles using laser diffraction tend to be somewhat more ambiguous than those obtained by electronic particle counting, where the solid volumes of the particles are detected. 

This work was extended by De Michelis and Calvelo (1994) who measured dispersion coefficients for 1cm cubes and for 1cm x 1cm x 1.5 cm cuboids. The data were again correlated by an expression taking the form of equation 3.30, with similar exponents on bed height (2.46 and 2.58 for cubes and cuboids respectively) and gas velocity (3.13 and 3.34 respectively) but coefficients of 0.110 and 0.256 respecfively fhe coefficient in equation 3.30 increased with decreasing particle sphericity. 

The particle number remains the same in interval III as in interval II, but the monomer concentration decreases with time, since monomer droplets are no longer present. The decrease in 4>m is slower with the more water-soluble monomers as the monomer in solution acts as a reservoir. The presence of a gel effect continues in interval IE. The quantitative interplay of a decreasing monomer concentration with the gel effect determines the exact behavior observed in this interval (GF or H). Polymerization continues at a steadily decreasing rate as the monomer concentration in the polymer particles decreases. Final conversions of essentially 100% are usually achieved. The final polymer particles, spherical in shape, usually have diameters of 50-300 nm, which places them intermediate in size between the initial micelles and monomer droplets. 

H3, Tl), it is unimportant that the Reynolds number of the internal motion was rather large for many flow visualization studies which set out to verify the Hadamard-Rybczynski predictions, so long as the Reynolds number based on the continuous fluid properties was small and the fluid particle spherical. The observed streamlines show excellent qualitative agreement with theory, although quantitative comparison is difficult in view of refractive mdex differences and the possibility of surface contamination. When a trace of surface-active contaminant is present, the motion tends to be damped out first at the rear of... 

Stokes stream function for continuous phase relative to particle sphericity, — AJA... 

If Vs/Is is to be nonzero, either S34/Sn and Ums/Ims, or S44/S] i and Vms/Ims, or both, must not be zero. S34 is zero for nonabsorbing particles in the Rayleigh limit and for arbitrary particles in the Rayleigh-Gans approximation. Even for particles—spherical and nonspherical—of size comparable with the wavelength, however, 34 tends to be small, particularly in the forward direction (see Figs. 13.13 and 13.14). 

SI units should be used in these equations. Furthermore, the effect of particle sphericity is included. Here, dsph could be taken equal to the mean nominal diameter measured by sieve analysis (d.p). 

Single-bilayer phosphatidylcholine (14) vesicles Magnetic particles prepared in situ from Fe2+/Fe3+ by OH Particles were characterized by transmission electron microscopy, electron diffraction, and X-ray microanalysis morphologies of intravesicular particles (spherical or disk-shaped) differed from those precipitated in bulk (acircular) 791... 

Particle size is one of the principal determinants of powder behavior such as packing and consolidation, flow ability, compaction, etc., and it is therefore one of the most common and important areas of powder characterization. Typically, one refers to particle size or diameter as the largest dimension of its individual particles. Because a given powder consists of particles of many sizes, it is preferable to measure and describe the entire distribution. While many methods of size determination exist, no one method is perfect (5) two very common methods are sieve analysis and laser diffraction. Sieving is a very simple and inexpensive method, but it provides data at relatively few points within a distribution and is often very operator dependent. Laser diffraction is a very rapid technique and provides a detailed description of the distribution. However, its instrumentation is relatively expensive, the analytical results are subject to the unique and proprietary algorithms of the equipment manufacturer, and they often assume particle sphericity. The particle size distribution shown in Figure 1 was obtained by laser diffraction, where the curves represent frequency and cumulative distributions. 

Apolipoproteins ( apo designates the protein in its lipid-free form) combine with lipids to form several classes of lipoprotein particles, spherical complexes with hydrophobic lipids in the core and hydrophilic amino acid side chains at the surface (Fig. 21-39a). Different combinations of lipids and proteins produce particles of different densities, ranging from chylomicrons to high-density lipoproteins. These particles can be separated by ultracentrifugation (Table 21-2) and visualized by electron microscopy (Fig. 21-39b). 

As is seen from the micrographs, in the carbon structures there are multiple branched fibers, which consist of finer sub fibers (Fig. 2 d), sheaf-like bundles of particles, spherical, tubular and conical elements (Fig. 2 a,b,c)-... 

Shape of particle (spherical or irregular and ease of packing)... 

Another factor is the shape of the particles. Spherical particles such as Gilsocoke pack quite differently from the acicular needle coke. It is here that past experience is paramount. The blending of the coke fractions with the binder is a crucial step in the manufacture of any graphite. 

Kolmogoroff microscale of turbulence (m) Particle sphericity factor, i.e., ratio of surface area of a sphere of same volume as the particle to surface area of particle (-)... 

Figure 40. Standard set of shapes for the determination of particle sphericity according to Rittenhouse ...

---