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We report impact properties for the binary collisions of small spheres. The impacts are modeled in terms of three coefficients. The first is the coefficient of normal restitution. The second represents the frictional properties of the contact surfaces. The last

Computer simulations of two-dimensional rapid granular flows of uniform smooth inelastic disks under simple shear reveal a dynamic microstructure characterized by the local, spatially anisotropic agglomeration of disks. A spectral analysis of the concentration field suggests that the formation of this inelastic microstructure is correlated with the magnitude of the'total stresses in the flow. The simulations confirm the theoretical results of Jenkins and Richman [J. Fluid Mech. 192, 3 13 ( 1988) ] for the kinetic stresses in the dilute limit and for the collisional stresses in the dense limit, when the size of the periodic domain used in the simulations is a small multiple of the disk diameter. However, the kinetic and, to a lesser extent, collisional stresses both increase significantly with the size of the periodic domain, thus departing from the predictions of the theory that assumes spatial homogeneity and isotropy.

We study fully developed, steady granular flows confined between parallel flat frictional sidewalls using numerical simulations and experiments. Above a critical rate, sidewall friction stabilizes the underlying heap at an inclination larger than the angle of repose. The shear rate is constant and independent of inclination over much of the flowing layer. In the direction normal to the free surface, the solid volume fraction increases on a scale equal to half the flowing layer depth. Beneath a critical depth at which internal friction is invariant, grains exhibit creeping and intermittent cage motion similar to that in glasses, causing gradual weakening of friction at the walls.

A model of dilute gas-solid flow in vertical risers is developed in which the particle phase is treated as a granular material, the balance equations for rapid granular flow are modified to incorporate the drag force from the gas, and boundary conditions, based on collisional exchanges of momentum and energy at the wall, are employed. In this model, it is assumed that the particle fluctuations are determined by inter-particle collisions only and that the turbulence of the gas is unaffected by the presence of the particles. , et al. (1984), and an explanation for the enhancement of turbulence that they observed.

We consider dense, relatively shallow flows of 3 mm glass spheres moving down a chute with a flat, frictional base of 3.6 m length. Sustained flows are observed at inclinations corresponding to an effective friction between the static and dynamic friction of individual grains. A capacitance instrument records the formation of waves with a dominant component traveling upstream. Simultaneous measurements of granular temperature at the base using a load cell reveal that the waves are accompanied by substantial reduction in granular agitation. A theory incorporating contributions from impulsive and enduring interactions with the base produces quantitative predictions for the range of sustained flows observed in the experiments. Closure of the theory is achieved using a balance between the production and dissipation of angular momentum in a narrow basal shear layer. A linear stability analysis of the corresponding hydraulic equations further suggests the origin of the waves.

ABSTRACT--The authors report impact properties for collisions of small, nearly spherical particles that present interesting experimental challenges. They consider difficulties arising with surface reflectivity, slight asphericity, surface damage and collisions with particles affixed to a rigid plate. To measure these impact properties, the authors refine the experimental technique of Foerster et aL To permit straightforward incorporation in rapid granular theories, the impacts are described with three coefficients. The first is the Newtonian coefficient of normal restitution. The second represents the frictional properties of the contact surfaces. The last characterizes the restitution of the tangential component of the contact point velocity for impacts that involve negligible sliding.

We consider dense flows of spherical grains down an inclined plane on which spherical bumps have been affixed. We propose a theory that models stresses as the superposition of a rate-dependent contribution arising from collisional interactions and a rate-independent part related to enduring frictional contacts among the grains. We show that dense flows consist of three regions. The first is a thin basal layer where grains progressively gain fluctuation energy with increasing distance from the bottom boundary. The second is a core region where the solid volume fraction is constant and the production and dissipation of fluctuation energy are nearly balanced. The last is a thin collisional surface layer where the volume fraction abruptly vanishes as the free surface is approached. We also distinguish basal flows with the smallest possible height, in which the core and surface layers have disappeared. We derive simple closures of the governing equations for the three regions with insight from the numerical simulations of Silbert et al. [Phys. Rev. E64, 051302 (2001)] and the physical experiments of Pouliquen [Phys. Fluids 11, 542 (1999)]. The theory captures the range of inclination angles at which steady, fully developed flows are observed, the corresponding shape of the mean and fluctuation velocity profiles, the dependence of the flow rate on inclination, flow height, interparticle friction, and normal restitution coefficient, and the dependence of the height of basal flows on inclination.

Unlike most fluids, granular materials include coexisting solid, liquid or gaseous regions, which produce a rich variety of complex flows. Dense flows down inclines preserve this complexity but remain simple enough for detailed analysis. In this review we survey recent advances in this rapidly evolving area of granular flow, with the aim of providing an organized, synthetic review of phenomena and a characterization of the state of understanding. The perspective that we adopt is influenced by the hope of obtaining a theory for dense, inclined flows that is based on assumptions that can be tested in physical experiments and numerical simulations, and that uses input parameters that can be independently measured. We focus on dense granular flows over three kinds of inclined surfaces: flat-frictional, bumpy-frictional and erodible. The wealth of information generated by experiments and numerical simulations for these flows has led to meaningful tests of relatively simple existing theories.

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