Size Distribution of Fluidized Nanoparticle Agglomeratesfrom Agglomeration and Fragmentation: A Population Balance Study
In this contribution, we present a study of the size distribution of fluidized nanoparticle agglomerates based on a population balance model that incorporates at the same time (1) a multi-scale description of the agglomerates  and (2) a detailed account of the outcomes of collision events. In particular, our model builds on the works of Brilliantov et al.  on agglomeration and fragmentation and of Liu  on the kinetic theory of granular flow applied to fluidization.
By analysing data from literature, we find that the experimental size distribution of fluidized nanoparticle agglomerates at dynamic equilibrium is independent of the nanoparticle properties and operating conditions when the distribution is rescaled with respect to the average agglomerate size. This suggests a universal mechanism for breakage and agglomeration under standard operation conditions. The population balance proposed here captures this feature when the size of the fragments resulting from a collision event follows an exponential law. Our model also sheds light into why the agglomerate size distribution of some nanoparticles, such as TiO2 P25 (dp = 21 nm), is nearly independent of the type of surface, i.e. hydrophilic vs. hydrophobic, whereas the size distribution for other nanoparticles, e.g. Al2O3 AluC (dp = 13 nm) and SiO2 A130 (dp = 16 nm), is highly sensitive to the type of surface. We find that this is due to two combined factors: the high density of TiO2 nanoparticles, which results in a large granular energy, and the relatively large nanoparticle size for this material, which results in a smaller tensile strength of the agglomerates. The way these two variables affect the outcome of a collision event in the balance explains the observed experimental results. TiO2 fluidization is expected to be improved by using nanoparticles with smaller particle size and a hydrophobic coating. Such insights can be used to optimize and intensify nanopowder fluidization.
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