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In this paper we report measurements of collisional properties of spheres using high-speed video analysis. These results agree with a simple collision operator. We study the size and velocity dependences of the coefficient of restitution in the normal direction. The experimental data are compared with the relevant models of energy dissipation and show the existence of two dissipation regimes. For large impact velocities a plastic deformation model is in good agreement with our measurements, while for smaller velocities a model of viscoelastic dissipation gives qualitative agreement.

Segregation of particulate mixtures is a problem of great consequence in industries involved with the handling and processing of granular materials in which homogeneity is generally required. While there are several factors that may be responsible for segregation in bulk solids, it is well accepted that nonuniformity in particle size is a fundamental contributor. When the granular material is exposed to vibrations, the question of whether or not convection is an essential ingredient for size segregation is addressed by distinguishing between the situation where vibrations are not sufficiently energetic to promote a mean flow of the bulk solid, and those cases where a convective flow does occur. Based on experimental and simulation results in the literature, as well as dynamical systems analysis of a recent model of a binary granular mixture, it is proposed that "void-filling" beneath large particles is a universal mechanism promoting segregation, while convection essentially provides a means of mixing enhancement.

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Three-dimensional granular dynamics simulations are carried out to investigate macroscopic behavior of granular materials subjected to vibrations. Particles, idealized as smooth inelastic, uniform spheres, are gravitationally loaded into a rectangular periodic cell having an open top and plane floor. Vibrations to the bed are subsequently imposed through the sinusoidally oscillated floor. Significant differences in the character of the bed are found, depending on the strength of the applied floor accelerations Γ=aω2, even if the boundary input energy is fixed. At high acceleration values, a dense upper region is supported on a fluidized low-density region near the floor. The temperature is maximum at the floor and monotonically attenuates upward, while the solids fraction profile peaks at some intermediate depth. When lower accelerations are applied, the granular temperature no longer decreases monotonically from the bottom to the top and the solids fraction depth profile bulges at approximately three diameters from the floor. The surface of the bed appears chaotic and fluidized, where a low solids fraction and high temperature occurs. The bed height, which remains almost constant below 1.2g, undergoes a pronounced expansion when 1.2g≤Γ≤2.0g, and subsequently flattens out at Γ≂2.8g. Computed granular temperature and solids fraction depth profiles are in good agreement with recent kinetic theory predictions when the acceleration is large enough, while bed expansion at lower accelerations is quantitatively consistent with existing experimental data.