|Max Planck Institute for Dynamics and Self-Organization & University of Goettingen
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Particulate flows of dielectric grains are almost always plagued by contact or triboelectrification and the resulting long-range electrostatic interactions. Extensive experimental, but rare theoretical, work is ongoing at present to understand the underlying mechanisms of contact electrification, and its consequences on collective scales. Although the hard matter principles remain elusive, here an effort is made to theoretically understand the collective/many-body effects in granular gases arising due to this phenomena. This thesis is focused on understanding the aggregation and pattern formation in heterogeneously charged, globally charge conserving, and initially dilute granular gases; the gas is charged with simplified but physically valid charge-exchange recipes and the subsequent effects of the long-range forces on the dynamics and morphology are studied. Canonical observables, such as growth rates of the average cluster size, average fractal dimension, granular temperature, and charge variance are computed using granular molecular dynamics simulations. In addition, the size, velocity and charge distributions are also studied. The observations from the detailed numerical simulations are utilized to (i) modify the mean-field Smoluchowski's coagulation equation, and (ii) to provide a kinetic description taking care of restitution as well as aggregation. The onset of clustering instability and the competition between dissipation and electrostatics, on a macroscopic scale, is then studied via the linear stability analysis of the granular hydrodynamic equations. Finally, the alterations in the aggregate growth rates and the fractal dimension due to additional degrees of freedom, introduced by the grain polarizability, are briefed. Most important results, in general terms, from the thesis are as follows. The presence of electrostatics fundamentally changes the nature of clustering in a granular gas -- from dynamic clustering to actual aggregation/coagulation. The growth rates of the clusters are enhanced. The morphology of the emerging structures is self-similar and exhibits fractal nature at simulated length and time scales. However, it is found that the heterogeneous charges and aggregation have a negligible influence on the established statistical result of granular temperature decay -- the Haff's law. The presence of charges fetches the granular gas further far-from equilibrium relative to its neutral counterpart, suggested by a non-relaxing velocity distribution and some evidence of the charge-velocity correlations. In case of large scale charge separation in the gas, the spatial regions can be differentiated to (i) where the electrostatic origin of the onset of clustering instability is expected to be linear, and (ii) where it is in principle nonlinear. The grain polarizability affects the small-sized aggregate population; the fractal dimension of this subpopulation is lowered. ...