Diameter Stokesian

Other samples of alkaline slurry were subjected to particle size analysis by sedimentation. With the —43 xm + 1.2 [im fraction this analysis was done in a 50-mm-diameter settling column of dilute slurry with a tared pan at the base to record continuously the mass of sedimented solid. The data were analyzed by the method of Oden (8), and the particle size distribution (Stokesian diameter), expressed on a mass percent basis, was calculated. 

A typical output from the sedimentation balance for —43 xm + 1.2 xm material is shown in Figure 1. The occurrence of distinct peaks indicates that groups of closely sized particles are present, the smallest being about 6 xm in effective (Stokesian) diameter. The frequent occur-... 

The particle size distribution for the humic acid fraction is depicted in Figure 4. No material sedimented out until the most extreme conditions were applied (40,000 rpm for 24 hr), when some lightening of color at the top of the solution was observed. The sedimented particles had a Stokesian diameter of around 2 nm, which means that a particle size gap of three orders of magnitude exists between these and the next largest particles detected (5 xm). From the experimentally determined coal particle density of 1.43 g/cm, it was calculated that a solid sphere of diameter 2 nm would have a molecular mass of 4000. If the molecules were rod-shaped, even smaller molecular masses would be predicted. Literature values of the molecular mass of regenerated humic acids range between 800 and 20,000, with the values clustering around 1,000 and 10,000 (i5, 16, 17). 

No particles exist in alkali-digested coal solutions between 6 xm and 2 nm Stokesian diameter. 

The aerodynamic diameter dj, is the diameter of spheres of unit density po, which reach the same velocity as nonspherical particles of density p in the air stream Cd Re) is calculated for calibration particles of diameter dp, and Cd(i e, cp) is calculated for particles with diameter dv and sphericity 9. Sphericity is defined as the ratio of the surface area of a sphere with equivalent volume to the actual surface area of the particle determined, for example, by means of specific surface area measurements (24). The aerodynamic shape factor X is defined as the ratio of the drag force on a particle to the drag force on the particle volume-equivalent sphere at the same velocity. For the Stokesian flow regime and spherical particles (9 = 1, X drag... 

Very central to cyclone technology is the dynamically equivalent particle diameter. This is the diameter of an equi-dense sphere that has the same terminal velocity as the actual particle. Calculating this can be difficult in the range of intermediate Reynolds numbers, or when the Cunningham correction is significant. In the region where Stokes drag law applies, we call it the Stokesian diameter. 

Fig. 2.3.2. Silhouettes of several different particle types along with their equivalent aerodynamic and Stokesian diameters from Kaye (1995)...

The particle sphericity mainly enters the analysis because it influences the particle terminal velocity. We can account for its effect if we use the Stokesian diameter as a measure of particle size x rather than, for instance, a volume or mass equivalent diameter. We recall from Chap. 2 that the Stokesian (or dynamically equivalent ) diameter is the diameter of a sphere having the same terminal settling velocity and density as the particle under consideration. 

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