Grain dynamics in a two-dimensional granular flow

Response to perturbations for granular flow in a hopper

We experimentally investigate the response to perturbations of circular symmetry for dense granular flow inside a three-dimensional right-conical hopper. These experiments consist of particle tracking velocimetry for the flow at the outer boundary of the hopper. We are able to test commonly used constitutive relations and observe granular flow phenomena that we can model numerically. Unperturbed conical hopper flow has been described as a radial velocity field with no azimuthal component. Guided by numerical models based upon continuum descriptions, we find experimental evidence for secondary, azimuthal circulation in response to perturbation of the symmetry with respect to gravity by tilting. For small perturbations we can discriminate between constitutive relations, based upon the agreement between the numerical predictions they produce and our experimental results. We find that the secondary circulation can be suppressed as wall friction is varied, also in agreement with numerical predictions. For large tilt angles we observe the abrupt onset of circulation for parameters where circulation was previously suppressed. Finally, we observe that for large tilt angles the fluctuations in velocity grow, independent of the onset of circulation.

Relationship between the flow rate and the packing fraction in the choke area of the two-dimensional granular flow

Two-dimensional granular flow in a channel with small exit is studied by both experiments and simulations. We first observe the time variation of the transition from dilute flow state to dense flow state by both experiments and simulations. Then we obtain a relationship between the local flow rate and the local packing fraction in the choke area by use of molecular dynamics simulations. The relationship is a continuous function rather than a discontinuous one. The flow rate has a maximum at a moderate packing fraction and the packing fraction is terminated at high value with negative slope. According to the relationship, four flow states--i.e., stable dilute flow state, metastable dilute flow state, unstable dense flow state, and stable dense flow state--are defined for fixed inflow rate. The discontinuities and the complex time variation behavior occurring in the transition between dilute and dense flow states can be attributed to the abrupt variation through unstable flow state.

Anomalous Richtmyer-Meshkov fingering in dissipative particle systems

We study the fingering instability induced by a shock that propagates across a perturbed interface that separates two types of discrete particles. If collisions between particles conserve energy, then the relative sizes and growth rates of the fingers are similar to those in the analogous shock-induced fingering instability in fluids. However, we show that energy loss during particle collisions, even when very small, causes the qualitative features of the finger growth to be completely opposite to the fluid case. The fingers formed by light particles grow faster and become longer and narrower than the fingers formed by heavy particles. In addition, the finger composed of light particles collapses into an extremely compact, tortuous filament, and diffusive mixing between particle types at the particle scale is heavily suppressed.

Jamming transition in two-dimensional hoppers and silos

Jamming of monodisperse metal disks flowing through two-dimensional hoppers and silos is studied experimentally. Repeating the flow experiment M times in a hopper or silo (HS) of exit size d, we measure the histograms h(n) of the number of disks n through the HS before jamming. By treating the states of the HS as a Markov chain, we find that the jamming probability J(d), which is defined as the probability that jamming occurs in a HS containing m disks, is related to the distribution function F(n) is identical with (1/M) sigma(s=n) to (s=infinity) h(s) by J(d) = 1 - F(m) = 1 - e(-(alpha(m - n(o))). The decay rate alpha, as a function of d, is found to be the same for both hoppers and silos with different widths. The average number of disks N is identical with 1/alpha = [n] passing through the HS can be fitted to N = A e(Bd2), N = A e(B/(d(c) - d))), or N = A (d(c) - d)(-gamma). The implications of these three forms for N to the stability of dense flow are discussed.

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.

Two-dimensional granular Poiseuille flow on an incline: multiple dynamical regimes

We investigate experimentally the flow of a monolayer of spherical beads through a channel on a smooth incline that is bounded by rough sidewalls. Using high-speed video imaging and particle tracking, we measure the positions and velocities of all particles in the field of view. We find that the flows are accelerating and dilute if the channel exit is open. On the other hand, if the exit is constricted, flows can reach a state in which the local time-averaged velocity is invariant along the stream. In the latter case, we find a continuous transition from an oscillatory two-phase flow (2PF) regime with wide density variations to a uniform dense flow regime, depending on the channel width and the mean flow speed. These two regimes exhibit distinct density variation, time regularity, and transverse profiles. The rough sidewalls are found to be necessary for the 2PF regime. In the dense regions of both flows, particles exhibit temporary arches, long-range correlated velocities, inhomogenuous propagation of disturbances, and hexagonal lattice structures. On the other hand, the dilute regions of the two-phase flow are nearly collisionless. Existing models can neither fully describe the dynamics of both the dense and the dilute regions nor explain the spontaneous switching between them.