Particle clustering cases

Careful X-ray studies can indicate the validity of such a number, and, as well, reveal whether the catalyst particles cluster. In this case, the X-ray size will be much smaller than that indicated by chemisorption. This ctui also be done by comparing X-ray and electron microscopy results.(6)... 

Recently, Hays et al. [26] reported on of several cases where particle clustering was inferred in flnidized bed systems. In the first case, they attempted to reproduce why highly variable entrainment rates were observed in a commercial-scale fluidized bed even though steady-state was presumed. Tests were conducted in a 6 inch (15-cm) diameter fluidized column with a static bed height of 52 inches (132 cm) of the same Geldart Gronp A powder (dp5o of 55-60 microns) used in the commercial process. The test unit was operated in batch mode at a superficial gas velocity of 0.66 ft/sec (0.2 m/sec). 

Entrainment rates measured in a laboratory or pilot plant unit can also underpredict entrainment rates in commercial nnits if the solids tend to form clusters. This could be the case if the commercial-scale plant contains baffles and the laboratory or pilot plants do not. This was the case illnstrated in Fignre 11.10. Even the spacing of the baffles can have an effect on the entrainment rate. Adding baffles to a fluidized bed regenerator may actnally increase entrainment rates. As discussed above, particle clusters may need snfficient time in the emnlsion or bnbble region of the bed to form. Thus, a particle cluster may start growing near the bottom of the bed and continue to grow as it travels to the top of the bed. Baffles spaced... 

Remaining above all a physicist, Ya.B. always departs from a concrete physical problem. But in those cases where the results have a general mathematical character, they are also applicable to physical situations which go far beyond the boundaries of the original problem. Thus, for example, Ya.B. s analysis (1970) [34 ] of particle cluster formation in a dust medium in his theory of the formation of the large-scale structure of the Universe simultaneously describes the appearance of optical caustics, as was shown, in particular, in his article with A. V. Mamaev and S. F. Shandarin [63]. 

This equation shows that the net /-mer growth rate, what we called 7,>1/2, (Figure 10.1) is not constant for all values of / as in the particle-free case. 7,+1/2 exceeds 7, i/2 (the net rate at which clusters of / — 1 become /) by an amount equal to the quantity of /-mer scavenged by the foreign particles. As a result, an analytical solution for the nucleation rate is not possible. 

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