Particle clustering dynamics

McMillan J, Shaffer F, Gopalan B, et al Particle cluster dynamics during fluidization, Chem Eng Sci 100 39-51, 2013. 

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]. 

Consideration of particle clustering effects is of relevance to the modeling of the hydro-dynamic behavior in the riser. Thus, when the cluster properties are known for a given riser operation, models based on the concept of clusters can be applied. 

Nauchitel and Pertsin have studied the melting properties of 13-, 19-, and 55-particle Lennard-Jones clusters.Questioning the validity of results obtained from free-volume simulations of such systems, they have used hard-sphere boundaries to constrain their clusters to finite volumes. The results of Nauchitel and Pertsin are most interesting for the 55-particle cluster. For certain ranges of temperature and mean density, structural evidence for surface melting was obtained projections of the cluster s coordinates, and radial density distribution functions, like those given in Fig. 17, characterize the cluster as a 13-particle icosahedral core surrounded by a fluidlike shell. However, dynamic calculations like those described for other clusters in the previous section have yet to be obtained to determine how fluidlike these outer atoms really are. 

M.B. Sevryuk, A. Lombardi, and V. Aquilanti, Hyperangular momenta and energy partitions in multi-dimensional many-particle classical mechanics the invariance approach to cluster dynamics. Phys. Rev. A, 72 033201, 2005. 

Dudowicz, J., Freed, K.F., Douglas, J. Lattice model of living polymerization. 111. Evidence for particle clustering from phase separation properties and "rounding" of the dynamical clustering transition. J. Chem. Phys. 2000,113,434. 

Gonzalez-Ortiz LJ, Asua JM. Development of particle morphology in emulsion polymerization. 1. Cluster dynamics. Macromolecules 1995 28 3135-3145. 

Fig. 13 Number of equal-sized primary particles per agglomerate as a function of the averaged radius of gyration including its extreme deviation (horizontal bars) as well as a the particle Stokes number St and b the particle Reynolds number Rep. Results obtained by LBM-based direct numerical simulations (DNS, open symbols) and numerical predictions for agglomerates formed by particle-cluster (P-C, solid line) and cluster-cluster (C-C, dashed line) collisions based on Langevin dynamics [4]...

Dynamic simulation approaches to model kinetic percolation are difficult to implement because of the inherent complexity of the problem, which requires intensive computation. As with any kinetic modd, the duration of the simulation must be commensruate with the critical timescales of the experiments. An early study to investigate the effeas of interactions on the percolation threshold was conducted by Bug et al. Here, a continuum Monte Carlo algorithm was used to modd a small system of 500 spherical particles undergoing Brownian motion. More recently, advanced simulation approaches such as Dissipative Particle Dynamics (DPD) have been applied to study kinetic percolation in composite sys-tems. " DPD is an off-lattice simulation technique similar to molecular dynamics, but applied to the supramolecular scale. Here, the larger-scale dynamics of a system are studied by monitoring the motion of particle clusters in response to pairwise, dissipative, and random forces. ... 

Figure 6 Snapshots of the dynamic pattern of solid volume fractions indicative of particle clusters, in a gas-particle flow, as calculated by means of a DSMC by Tanaka et al (1995). Reprinted from Tanaka et al (7995) with permission from the ASME.

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