Particle clustering

The important feature is that a three-dimensional gel network comes from the condensation of partially hydroly2ed species. Thus, the microstmcture of a gel is governed by the rate of particle (cluster) growth and their extent of crosslinking or, more specifically, by the relative rates of hydrolysis and condensation (3). 

Cluster emission is an exotic decay that has some commonalities with a-decay. In a-decay, two protons and two neutrons that are moving in separate orbits within the nucleus come together and leak out of the nucleus as a single particle. Cluster emission occurs when other groups of nucleons form a single particle and leak out. Several of the observed decays are shown in Table 10. The emitted clusters include C, Ne, Mg, and Si. The... 

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)... 

One of the recent advances in magnetic studies is that it enables not only the estimation of the average volume v of clusters from the LF and HF approximations of the Langevln function, but also enables to compute particle size distribution based on an assumed function. By judiciously combining the parameters of the Langevln and of the "log normal function, we obtained a particle (cluster) size distribution of Y Fe203 in ZSM-5. The essential features of such computation are shown in Fig. 6. 

To dissociate molecules in an adsorbed layer of oxide, a spillover (photospillover) phenomenon can be used with prior activation of the surface of zinc oxide by particles (clusters) of Pt, Pd, Ni, etc. In the course of adsorption of molecular gases (especially H2, O2) or more complex molecules these particles emit (generate) active particles on the surface of substrate [12], which are capable, as we have already noted, to affect considerably the impurity conductivity even at minor concentrations. Thus, the semiconductor oxide activated by cluster particles of transition metals plays a double role of both activator and analyzer (sensor). The latter conclusion is proved by a large number of papers discussed in detail in review [13]. The papers cited maintain that the particles formed during the process of activation are fairly active as to their influence on the electrical properties of sensors made of semiconductor oxides in the form of thin sintered films. 

Atoms of metals are more interesting tiian hydrogen atoms, because they can form not only dimers Ag2, but also particles with larger number of atoms. What are the electric properties of these particles on surfaces of solids The answer to this question can be most easily obtained by using a semiconductor sensor which plays simultaneously the role of a sorbent target and is used as a detector of silver adatoms. The initial concentration of silver adatoms must be sufficiently small, so that growth of multiatomic aggregates of silver particles (clusters) could be traced by variation of an electric conductivity in time (after atomic beam was terminated), provided the assumption of small electric activity of clusters on a semiconductor surface [42] compared to that of atomic particles is true. 

The above rate equations confirm the suggested explanation of dynamics of silver particles on the surface of zinc oxide. They account for their relatively fast migration and recombination, as well as formation of larger particles (clusters) not interacting with electronic subsystem of the semiconductor. Note, however, that at longer time intervals, the appearance of a new phase (formation of silver crystals on the surface) results in phase interactions, which are accompanied by the appearance of potential jumps influencing the electronic subsystem of a zinc oxide film. Such an interaction also modifies the adsorption capability of the areas of zinc oxide surface in the vicinity of electrodes [43]. 

Unlike the simulations which only consider particle-cluster interactions discussed earlier, hierarchical cluster-cluster aggregation (HCCA) allows for the formation of clusters from two clusters of the same size. Clusters formed by this method are not as dense as clusters formed by particle-cluster simulations, because a cluster cannot penetrate into another cluster as far as a single particle can (Fig. 37). The fractal dimension of HCCA clusters varies from 2.0 to 2.3 depending on the model used to generate the structure DLA, RLA, or LTA. For additional details, the reader may consult Meakin (1988). 

Lints, M. C., and Glicksman, L. R., Structure of Particle Clusters Near Wall of a Circulating Fluidized Bed, AIChE Symp. Series, 89(296) 35 47 (1993)... 

Figure 29 (Qin and Liu, 1982) shows the behavior of individual particles above the distributor recorded by video camera of small clusters of particles, coated with a fluorescent material and spot-illuminated by a pulse of ultra violet light from an optical fiber. The sequential images, of which Fig. 29 just represents exposures after stated time intervals, were reconstructed to form the track of motion of the particle cluster shown in Fig. 30. Neither this track nor visual observation of the shallow bed while fluidized, reveal any vestige of bubbles. Instead, the particles are thrown up by the high velocity jets issuing from the distributor orifices to several times their static bed height.

O Brien, T. J., and Syamlal, M Particle cluster effects in the numerical simulation of a circulating fluidized bed, in (A. Avidan, Ed.) Circulating Fluidized Bed Technology IV, Proceedings of the Fourth International Conference on Circulating Fluidized Beds, Hidden Valley Conference Center and Mountain Resort, August 1-5, 1993, Somerset, PA, (1993). 

The CFD model described above is adequate for particle clusters with a constant fractal dimension. In most systems with fluid flow, clusters exposed to shear will restructure without changing their mass (or volume). Typically restructuring will reduce the surface area of the cluster and the fractal dimension will grow toward d — 3, corresponding to a sphere. To describe restructuring, the NDF must be extended to (at least) two internal coordinates (Selomulya et al., 2003 Zucca et al., 2006). For example, the joint surface, volume NDF can be denoted by n(s, u x, t) and obeys a bivariate PBE. 

Relaxation dispersion data for water on Cab-O-Sil, which is a monodis-perse silica fine particulate, are shown in Fig. 2 (45). The data are analyzed in terms of the model summarized schematically in Fig. 3. The y process characterizes the high frequency local motions of the liquid in the surface phase and defines the high field relaxation dispersion. There is little field dependence because the local motions are rapid. The p process defines the power-law region of the relaxation dispersion in this model and characterizes the molecular reorientations mediated by translational displacements on the length scale of the order of the monomer size, or the particle size. The a process represents averaging of molecular orientations by translational displacements on the order of the particle cluster size, which is limited to the long time or low frequency end by exchange with bulk or free water. This model has been discussed in a number of contexts and extended studies have been conducted (34,41,43). 

Fig. 3. Schematic representation of the topological space of hydration water in silica fine-particle cluster (45). The processes responsible for the water spin-lattice relaxation behavior are restricted rotational diffusion about an axis normal to the local surface (y process), reorientations mediated by translational displacements on the length scale of a monomer (P process), reorientations mediated by translational displacements in the length scale of the clusters (a process), and exchange with free water as a cutoff limit.

The underlying questions with these clusters are What is the mechanism for their existence Where are the clusters formed and How do clusters affect entrainment rates Based on evidence from pilot and commercial scale plants along with highspeed video of a cold-flow fluidized bed, the mechanism of particle clustering in and above fluidized beds and its effect on entrainment were examined. 

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). 

Cocco et al. [27] used high-speed video (Phantom V7.1 camera) to clearly show that particle clustering was, at least in part, responsible for this behavior in the same... 

Figure 11.7 shows several frames of the video obtained for particles and clusters in the freeboard region. As expected, the FCC catalyst tended to cluster in the freeboard region. A statistical analysis of this video suggested that 30% of the FCC catalyst in the freeboard existed as particle clusters with an average size of 11 5.0 particles. 

Figures 11.6 and 11.7 reveal why lower than expected entrainment rates were observed for both these materials. As expected and postulated by Hays et al. [26], Geldart and Wong [14], Baeyens et al. [15] and Choi et al. [16], particle clustering results in particle sizes too large for the drag force to carry the particles out of the unit. Thus, individual fine particles that would have been easily entrained out of the unit now fall back to the fluidized bed after clustering has occurred. Clustering may not only be dependent on the fines level but the material itself Jayaweera et al. [3] and Fortes et al. [7] also reported of particle clustering with an FCC catalyst...

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