Dynamics of dense sheared granular flows. Part 1. Structure and diffusion

Abstract

Shear flows of inelastic spheres in three dimensions in the volume fraction range 0.4-0.64 are analysed using event-driven simulations. Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution en (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e_t (negative of the ratio of post- and pre-collisional velocities perpendicular to the line joining the centres). Here, we have considered both e_t = +1 and e_t = e_n (rough particles) and e_t = -1 (smooth particles), and the normal coefficient of restitution e_n was varied in the range 0.6-0.98. Care was taken to avoid inelastic collapse and ensure there are no particle overlaps during the simulation. First, we studied the ordering in the system by examining the icosahedral order parameter Q₆ in three dimensions and the planar order parameter q₆ in the plane perpendicular to the gradient direction. It was found that for shear flows of sufficiently large size, the system continues to be in the random state, with Q₆ and q₆ close to 0, even for volume fractions between φ = 0.5 and φ = 0.6; in contrast, for a system of elastic particles in the absence of shear, the system orders (crystallizes) at φ = 0.49. This indicates that the shear flow prevents ordering in a system of sufficiently large size. In a shear flow of inelastic particles, the strain rate and the temperature are related through the energy balance equation, and all time scales can be non-dimensionalized by the inverse of the strain rate. Therefore, the dynamics of the system are determined only by the volume fraction and the coefficients of restitution. The variation of the collision frequency with volume fraction and coefficient of restitution was examined. It was found, by plotting the inverse of the collision frequency as a function of volume fraction, that the collision frequency at constant strain rate diverges at a volume fraction φ_ad (volume fraction for arrested dynamics) which is lower than the random close-packing volume fraction 0.64 in the absence of shear. The volume fraction φ_ad decreases as the coefficient of restitution is decreased from e_n = 1; φ_ad has a minimum of about 0.585 for coefficient of restitution e_n in the range 0.6-0.8 for rough particles and is slightly larger for smooth particles. It is found that the dissipation rate and all components of the stress diverge proportional to the collision frequency in the close-packing limit. The qualitative behaviour of the increase in the stress and dissipation rate are well captured by results derived from kinetic theory, but the quantitative agreement is lacking even if the collision frequency obtained from simulations is used to calculate the pair correlation function used in the theory.