Shock waves in two-dimensional granular flow: effects of rough walls and polydispersity

We have studied the two-dimensional flow of balls in a small angle funnel, when either the side walls are rough or the balls are polydisperse. As in earlier work on monodisperse flows in smooth funnels, we observe the formation of kinematic shock waves/density waves. We find that for rough walls the flows are more disordered than for smooth walls and that shock waves generally propagate more slowly. For rough wall funnel flow, we show that the shock velocity and frequency obey simple scaling laws. These scaling laws are consistent with those found for smooth wall flow, but here they are cleaner since there are fewer packing-site effects and we study a wider range of parameters. For pipe flow (parallel side walls), rough walls support many shock waves, while smooth walls exhibit fewer or no shock waves. For funnel flows of balls with varying sizes, we find that flows with weak polydispersity behave qualitatively similar to monodisperse flows. For strong polydispersity, scaling breaks down and the shock waves consist of extended areas where the funnel is blocked completely.Comment: 11 pages, 15 figures; accepted for PR

Thixotropy in macroscopic suspensions of spheres

An experimental study of the viscosity of a macroscopic suspension, i.e. a suspension for which Brownian motion can be neglected, under steady shear is presented. The suspension is prepared with a high packing fraction and is density-matched in a Newtonian carrier fluid. The viscosity of the suspension depends on the shear rate and the time of shearing. It is shown for the first time that a macroscopic suspension shows thixotropic viscosity, i.e. shear-thinning with a long relaxation time as a unique function of shear. The relaxation times show a systematic decrease with increasing shear rate. These relaxation times are larger when decreasing the shear rates, compared to those observed after increasing the shear. The time scales involved are about 10000 times larger than the viscous time scale and about 1000 times smaller than the thermodynamic time scale. The structure of the suspension at the outer cylinder of a viscometer is monitored with a camera, showing the formation of a hexagonal structure. The temporal decrease of the viscosity under shear coincides with the formation of this hexagonal pattern

Granular discharge and clogging for tilted hoppers

We measure the flux of spherical glass beads through a hole as a systematic function of both tilt angle and hole diameter, for two different size beads. The discharge increases with hole diameter in accord with the Beverloo relation for both horizontal and vertical holes, but in the latter case with a larger small-hole cutoff. For large holes the flux decreases linearly in cosine of the tilt angle, vanishing smoothly somewhat below the angle of repose. For small holes it vanishes abruptly at a smaller angle. The conditions for zero flux are discussed in the context of a {\it clogging phase diagram} of flow state vs tilt angle and ratio of hole to grain size

Partially fluidized shear granular flows: Continuum theory and MD simulations

The continuum theory of partially fluidized shear granular flows is tested and calibrated using two dimensional soft particle molecular dynamics simulations. The theory is based on the relaxational dynamics of the order parameter that describes the transition between static and flowing regimes of granular material. We define the order parameter as a fraction of static contacts among all contacts between particles. We also propose and verify by direct simulations the constitutive relation based on the splitting of the shear stress tensor into a``fluid part'' proportional to the strain rate tensor, and a remaining ``solid part''. The ratio of these two parts is a function of the order parameter. The rheology of the fluid component agrees well with the kinetic theory of granular fluids even in the dense regime. Based on the hysteretic bifurcation diagram for a thin shear granular layer obtained in simulations, we construct the ``free energy'' for the order parameter. The theory calibrated using numerical experiments with the thin granular layer is applied to the surface-driven stationary two dimensional granular flows in a thick granular layer under gravity.Comment: 20 pages, 19 figures, submitted to Phys. Rev.

Plastic Flow in Two-Dimensional Solids

A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field \bi u and the lattice velocity {\bi v}=\p {\bi u}/\p t. Damping is assumed to arise from the shear viscosity in the momentum equation. The elastic energy density is a periodic function of the shear and tetragonal strains, which enables formation of slips at large strains. In this work we neglect defects such as vacancies, interstitials, or grain boundaries. The simplest slip consists of two edge dislocations with opposite Burgers vectors. The formation energy of a slip is minimized if its orientation is parallel or perpendicular to the flow in simple shear deformation and if it makes angles of $\pm \pi/4$ with respect to the stretched direction in uniaxial stretching. High-density dislocations produced in plastic flow do not disappear even if the flow is stopped. Thus large applied strains give rise to metastable, structurally disordered states. We divide the elastic energy into an elastic part due to affine deformation and a defect part. The latter represents degree of disorder and is nearly constant in plastic flow under cyclic straining.Comment: 16pages, Figures can be obtained at http://stat.scphys.kyoto-u.ac.jp/index-e.htm