Granular flow through an aperture: pressure and flow rate are independent

Self-similarity of pressure profiles during forced granular flows

We present measurements of the vertical stress profile σ on the base of flat-bottomed cylindrical silos discharged through an orifice centered on its base. An overweight forces the material on top of the free surface. The mean bottom pressure σ(z,D,W), with z the height of the granular column, D the silo diameter, and W the mass of the overweight, increases significantly at the end of the discharge. Inspired by early models of stress distribution, we show that σ measured at z=0 can be rescaled to yield a collapse of the data, as a function of z/D, for all D and W explored. We also show that the profile σ(r) is self-similar as a function of the radial coordinate r and can be rescaled to collapse the data for different z,D, and W. Although the model correctly predicts the functional dependences, it fails in quantitative terms. These results challenge our understanding of free and forced granular flows through orifices.

Unjamming strongly compressed rafts: Effects of the compression direction

We experimentally study the unjamming dynamics of strongly compressed particle rafts confined between two fixed walls and two movable barriers. The back barrier is made of an elastic band, whose deflection indicates the local stress. The front barrier is pierced by a gate, whose opening triggers local unjamming. Prior to gate opening, the rafts are quasistatically compressed by moving only one of the two barriers, in the vicinity of which folds form. Using high-speed imaging, we follow the raft relaxation with folded, jammed, and unjammed areas and measure the velocity fields inside and outside the confined domain. Two very different behaviors develop. For rafts compressed by the back barrier, only partial unjamming occurs. At the end of the process, many folds remain and the back stress does not relax. The flow develops mostly along the compression axis and the particles passing the gate form a dense raft whose width is the gate width. For rafts compressed at the front, quasitotal unjamming is observed. Almost no folds persist and only minimal stress remains, if any. The particles flow along the compression axis but also normally to it and form a rather circular and not dense assembly. Both the force chain network orientation and the initial fold location could cause the unjamming difference. Other effects, such as a different pressure field or simple steric hindrance, cannot be excluded.

Velocity scaling in the region of orifice influence in silo draining under gravity

This study utilizes computations based on a soft-particle discrete element method for investigating the scaling of velocity in the region of orifice influence situated directly above and in proximity to the outlet in a two-dimensional silo. The velocity at the exit scales with the outlet size (D), in striking agreement with the earlier studies. However, the scaling of velocity upstream of the outlet with D as the length scale does not exist. Consequently, we present a scaling with a length parameter h_{e} being the height of an equi-inertial curve, which is defined to be a curve on which the inertial number is constant, thereby consolidating the coexisting different flow regimes in a discharging silo. The velocity corresponding to an equi-inertial curve, when measured relative to the velocity at the outlet, scales very well with h_{e} for low inertial numbers belonging to the dense flow regime. However, such scaling does not hold for high inertial numbers corresponding to the rapid flow regime in the region located closer to the orifice. We tie this scaling breakdown to the velocity fluctuations in light of the similarity between the profiles of scaled relative velocity and the scaled kinetic pressure, suggesting h_{e} to be a promising candidate for unifying the kinematics of granular flow near the outlet in the silo.

Granular flow through an aperture: Influence of obstacles near the outlet

We study how the presence of obstacles in a confined system of monodisperse disks affects their discharge through an aperture. The disks are driven by a horizontal conveyor belt that moves at constant velocity. The mean packing fraction at the outlet decreases as the distance between the obstacles and the aperture decreases. The obstacles organize the dynamics of the stagnant zones in two characteristic behaviors that differ mainly in the magnitude of the fluctuations of the fraction of stagnant disks in the system. It is shown that the effective aperture is reduced by the presence of obstacles.

Flux of granular particles through a shaken sieve plate

We experimentally investigate a discharging flux of granular particles through a sieve plate subject to vertical vibrations. The mean mass flux shows a non-monotonic relation with the vibration strength. High-speed photography reveals that two stages, the free flight of the particles’ bulk over the plate and the adhesion of the particles’ bulk with the plate, alternately appear, where only the adhesion stage contributes to the flow. With two independent methods, we then measure the adhesion time under different vibration conditions, and define an adhesion flux. The adhesion flux monotonically increases with increasing vibration strength. By rescaling the adhesion flux, we find that the adhesion flux is approximately determined by the peak vibration velocity of the shaker. The conclusion is examined with other sieve geometries.

Granular flow through an aperture: influence of the packing fraction

For the last 50 years, the flow of a granular material through an aperture has been intensely studied in gravity-driven vertical systems (e.g., silos and hoppers). Nevertheless, in many industrial applications, grains are horizontally transported at constant velocity, lying on conveyor belts or floating on the surface of flowing liquids. Unlike fluid flows, that are controlled by the pressure, granular flow is not sensitive to the local pressure but rather to the local velocity of the grains at the outlet. We can also expect the flow rate to depend on the local density of the grains. Indeed, vertical systems are packed in dense configurations by gravity, but, in contrast, in horizontal systems the density can take a large range of values, potentially very small, which may significantly alter the flow rate. In the present article, we study, for different initial packing fractions, the discharge through an orifice of monodisperse grains driven at constant velocity by a horizontal conveyor belt. We report how, during the discharge, the packing fraction is modified by the presence of the outlet, and we analyze how changes in the packing fraction induce variations in the flow rate. We observe that variations of packing fraction do not affect the velocity of the grains at the outlet, and, therefore, we establish that flow-rate variations are directly related to changes in the packing fraction.

Eliminating friction with friction: 2D Janssen effect in a friction-driven system

The Janssen effect is a unique property of confined granular materials experiencing gravitational compaction in which the pressure at the bottom saturates with an increasing filling height due to frictional interactions with side walls. In this Letter, we replace gravitational compaction with frictional compaction. We study friction-compacted 2D granular materials confined within fixed boundaries on a horizontal conveyor belt. We find that even with high-friction side walls the Janssen effect completely vanishes. Our results demonstrate that gravity-compacted granular systems are inherently different from friction-compacted systems in at least one important way: vibrations induced by sliding friction with the driving surface relax away tangential forces on the walls. Remarkably, we find that the Janssen effect can be recovered by replacing the straight side walls with a sawtooth pattern. The mechanical force introduced by varying the sawtooth angle θ can be viewed as equivalent to a tunable friction force. By construction, this mechanical friction force cannot be relaxed away by vibrations in the system.

Continuum simulation of the discharge of the granular silo: a validation test for the μ(I) visco-plastic flow law

Using a continuum Navier-Stokes solver with the μ(I) flow law implemented to model the viscous behavior, and the discrete Contact Dynamics algorithm, the discharge of granular silos is simulated in two dimensions from the early stages of the discharge until complete release of the material. In both cases, the Beverloo scaling is recovered. We first do not attempt a quantitative comparison, but focus on the qualitative behavior of velocity and pressure at different locations in the flow. A good agreement for the velocity is obtained in the regions of rapid flows, while areas of slow creep are not entirely captured by the continuum model. The pressure field shows a general good agreement, while bulk deformations are found to be similar in both approaches. The influence of the parameters of the μ(I) flow law is systematically investigated, showing the importance of the dependence on the inertial number I to achieve quantitative agreement between continuum and discrete discharge. However, potential problems involving the systems size, the configuration and "non-local" effects, are suggested. Yet the general ability of the continuum model to reproduce qualitatively the granular behavior is found to be very encouraging.

Orifice jamming of fluid-driven granular flow

The three-dimensional jamming of neutrally buoyant monodisperse, bidisperse, and tridisperse mixtures of particles flowing through a restriction under fluid flow has been studied. During the transient initial accumulation of particles at the restriction, a low probability of a jamming event is observed, followed by a transition to a steady-state flowing backlog of particles, where the jamming probability per particle reaches a constant. Analogous to the steady-state flow in gravity-driven jams, this results in a geometric distribution describing the number of particles that discharge prior to a jamming event. We develop new models to describe the transition from an accumulation to a steady-state flow, and the jamming probability after the transition has occurred. Predictions of the behavior of the geometric distribution see the log-probability of a jam occurring proportionally to (R(2)(2)-1), where R(2) is the ratio of opening diameter to the second moment number average particle diameter. This behavior is demonstrated to apply to more general restriction shapes, and collapses for all mixture compositions for the restriction sizes tested.

Jamming of particles in a two-dimensional fluid-driven flow

The jamming of particles under flow is of critical importance in a broad range of natural and industrial settings, such as the jamming of ice in rivers, or the plugging of suspended solids in pipeline transport. Relatively few studies have been carried out on jamming of suspended particles under flow, in comparison to the many studies on jamming in gravity-driven flows that have revealed various features of the jamming process. Fluid-driven particle flows differ in several aspects from gravity-driven flows, particularly in being compatible with a range of particle concentrations and velocities. Additionally, there are fluid-particle interactions and hydrodynamic effects. To investigate particle jamming in fluid-driven flows, we have performed both experiments and computer simulations on the flow of circular particles floating over water in an open channel with a restriction. We determined the flow-rate boundary for a dilute-to-dense flow transition, similar to that seen in gravity-driven flows. The maximum particle throughput increased for larger restriction sizes consistent with a Beverloo equation form over the entire range of particle mixtures and restriction sizes. The exponent of ~3/2 in the Beverloo equation is consistent with approximately constant acceleration of grains due to fluid drag in the immediate region of the opening. We verified that the jamming probability from the dense flow gave a geometric distribution in the number of particles escaping before a jam. The probability of jamming in both experiments and simulations was found to be dependent on the ratio of channel opening to particle size, but only weakly dependent on the fluid flow velocity. Flow entrance effects were measured and observed to affect the jamming probability, and dependence on particle friction coefficient was determined from simulation. A comprehensive model for the jamming probability integrating these observations from the different flow regimes was shown to be in good agreement for experimental data on average times before jamming.

Flow and clogging in a silo with an obstacle above the orifice

In a recent paper [Zuriguel et al., Phys. Rev. Lett. 107, 278001 (2011)] it has been shown that the presence of an obstacle above the outlet can significatively reduce the clogging probability of granular matter pouring from a silo. The amount of this reduction strongly depends on the obstacle position. In this work, we present new measurements to analyze different outlet sizes, extending foregoing results and revealing that the effect of the obstacle is enhanced as the outlet size is increased. In addition, the effect of the obstacle position on the flow rate properties and in the geometrical features of arches is studied. These results reinforce previous evidence of the pressure reduction induced by the obstacle. In addition, it is shown how the mean avalanche size and the average flow rate are not necessarily linked. On the other hand, a close relationship is suggested between the mean avalanche size and the flow rate fluctuations.

Evolution of pressure profiles during the discharge of a silo

We report measurements of the pressure profile in the outlet plane of a discharging silo. We observe that, whatever the preparation of the granular system, a dynamic Janssen effect is at play: the apparent mass of the grains (i.e., the part of their mass sustained by the base) is significantly smaller than their actual mass because of the redirection of the weight to the lateral wall of the container. The pressure profiles reveal a significant decrease in pressure in the vicinity of the outlet as the system discharges, whereas the flow rate remains constant. The measurements are thus a direct experimental proof that the flow rates of granular material through an aperture are not controlled by the local stress conditions.