Simulations of granular materials: kinetics and hydrodynamic phenomena

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2003

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Moon, Sung Joon

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Granular materials often exhibit fluid-like behavior in the presence of an external forcing. This dissertation deals with kinetics and hydrodynamic phenomena in granular fluids subject to two types of forcing, vertical oscillation and homogeneous bulk heating, using a molecular dynamics simulation of frictional inelastic hard spheres. The oscillated granular fluid is simulated to probe microscopic dynamics of the transition from a wave pattern to spatiotemporal chaos, and to reveal a new kind of convection, transport, and segregation mechanism that is induced by a kink (a boundary between domains oscillating out of phase by π). We also examine the role of friction in the wave pattern, and find that a pattern loses its stability without friction. Due to their dissipative nature, granular fluids are always far from equilibrium, and the velocity distributions deviate from the Maxwellian. The single particle distribution functions both in homogeneously heated and vertically oscillated granular gases are studied. High energy tails of the distributions are described by stretched exponentials ∼ exp(−Av α ), and the exponent α depends on the system and material parameters. Precollisional velocities are strongly correlated (up to 15% of the granular temperature), and the correlations decay algebraically with the distance from a grain (∼ r −(1+δ) , where 0.2 < δ < 0.3) in a three-dimensional system. The normal shock wave in vertically oscillated layers of frictionless inelastic hard spheres are studied, and the results are compared with a continuum model; the agreement is shown to be remarkably good, even with the failure of the molecular chaos assumption and mean-field approximation that are used in the derivation of the model. Continuum equations for realistic granular fluids might include friction and a velocity-dependent coefficient of restitution, and the derivation of the equations accounting for such properties is still far from complete. We show that the coarse-grained integration/bifurcation method can be successfully applied to granular fluids. This method enables the accomplishment of some of the tasks traditionally performed only by use of continuum equations, even without the knowledge of the equations.

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