An experiment to measure the properties of the collisions between two small spheres or between a small sphere and a semi-infinite flat wall are described. The apparatus releases the particles in a free-fall without initial spin. 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 characterizes the restitution of the tangential components of the velocity of the contact point for impacts that do not involve sliding. The coefficients are calculated from stroboscopic photographs of the ballistics of the particles near the collision. The results establish that the collision model provides an accurate description of the dynamics of the impacts.

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, 313 (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 analyse the dilute, steady, fully developed flow of relatively massive particles in a turbulent gas in the context of a vertical pipe. The idea is that the exchange of momentum in collisions between the grains and between the grains and the wall plays a significant role in the balance of forces in the particle phase. Consequently, the particle phase is considered to be a dilute system of colliding grains, in which the velocity fluctuations are produced by collisions rather than by the gas turbulence. 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. The turbulence of the gas is treated using a one-equation closure. A numerical solution of the resulting governing equations provides velocity and turbulent energy profiles in agreement with the measurements of Tsuji et al. (1984).

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.