Pressure independence of granular flow through an aperture

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.

Clogging and avalanches in quasi-two-dimensional emulsion hopper flow

We experimentally and computationally study the flow of a quasi-two-dimensional emulsion through a constricting hopper shape. Our area fractions are above jamming such that the droplets are always in contact with one another and are in many cases highly deformed. At the lowest flow rates, the droplets often clog and thus exit the hopper via intermittent avalanches. At the highest flow rates, the droplets exit continuously. The transition between these two types of behaviors is a fairly smooth function of the mean strain rate. The avalanches are characterized by a power-law distribution of the time interval between droplets exiting the hopper, with long intervals between the avalanches. Our computational studies reproduce the experimental observations by adding a flexible compliance to the system (in other words, a finite stiffness of the sample chamber). The compliance results in continuous flow at high flow rates, and allows the system to clog at low flow rates leading to avalanches. The computational results suggest that the interplay of the flow rate and compliance controls the presence or absence of the avalanches.

Soft particle clogging in two-dimensional hoppers

We study the outflow of soft particles through quasi-two-dimensional hoppers with both experiments and simulations. The experiments utilize spheres made with hydrogel, silicone rubber, and glass. The hopper chamber has an adjustable exit width and tilt angle (the latter to control the magnitude of gravitational forcing). Our simulation mimics the experiments using purely two-dimensional soft particles with viscous interactions but no friction. Results from both simulations and experiments demonstrate that clogging is easier for reduced gravitational force or stiffer particles. For particles with low or no friction, the average number of particles in a clogging arch depends only on the ratio between hopper exit width and the mean particle diameter. In contrast, for the silicone rubber particles with larger frictional interactions, arches have more particles than the low friction cases. Additionally, an analysis of the number of particles left in the hopper when clogging occurs provides evidence for a hydrostatic pressure effect that is relevant for the clogging of soft particles, but less so for the harder (glass) or frictional (silicone rubber) particles.

Clogging of granular materials in a horizontal hopper: Effect of outlet size, hopper angle, and driving velocity

Due to the independence of the driving velocity and outlet size, it is possible to isolate geometrical and kinematic contributions to clogging in two-dimensional horizontal flow in a hopper driven by a conveyor belt. We experimentally investigate the geometric (outlet size and hopper angle) and kinematic effects (driving velocity) on the clogging in such a horizontal flow. Based on quantitative measurements and analysis of the avalanche size, blocking probability of a particle at the outlet, and other parameters, we show that the geometric factors can more effectively affect clogging. In addition, we find that the clogging tends to be alleviated with the increases of the driving velocity, suggesting a possible "fast is fast" behavior within a wide range of driving velocity. We borrow and modify a model from clogging in gravity-driven hoppers, which can accurately describe the shape of the clogging probability function in the conveyor belt driven flow, suggesting that these two systems could share some mechanisms for clogging.

Silo discharge of mixtures of soft and rigid grains

We study the outflow dynamics and clogging phenomena of mixtures of soft, elastic low-friction spherical grains and hard frictional spheres of similar size in a quasi-two-dimensional (2D) silo with narrow orifice at the bottom. Previous work has demonstrated the crucial influence of elasticity and friction on silo discharge. We show that the addition of small amounts, even as low as 5%, of hard grains to an ensemble of soft, low-friction grains already has significant consequences. The mixtures allow a direct comparison of the probabilities of the different types of particles to clog the orifice. We analyze these probabilities for the hard, frictional and the soft, slippery grains on the basis of their participation in the blocking arches, and compare outflow velocities and durations of non-permanent clogs for different compositions of the mixtures. Experimental results are compared with numerical simulations. The latter strongly suggest a significant influence of the inter-species particle friction.

Discharge of a 2D magnetic silo

We investigate experimentally the discharge of a 2D-silo, a Hele-Shaw cell, filled with a mono layer of ferromagnetic grains submitted to an external magnetic field B perpendicular to the cell plane. In this case the magnetic pair interactions are repulsive. We show that the granular flow rate decreases systematically with the amplitude of the external magnetic field applied. Interestingly, while the output flow rate remains constant during an experiment, we reveal very large spatio-temporal fluctuations of the packing density within the cell, particularly evident for magnetic field of high amplitudes.

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.

Decoupling Geometrical and Kinematic Contributions to the Silo Clogging Process

Based on the implementation of a novel silo discharge procedure, we are able to control the grains velocities regardless of the outlet size. This allows isolating the geometrical and kinematic contributions to the clogging process. We find that, for a given outlet size, reducing the grains velocities to extremely low values leads to a clogging probability increment of almost two orders of magnitude, hence revealing the importance of particle kinematics in the silo clogging process. Then, we explore the contribution of both variables, outlet size and grains velocity, and we find that our results agree with an already known exponential expression that relates clogging probability with outlet size. We propose a modification of such expression revealing that only two parameters are necessary to fit all the data: one is related with the geometry of the problem, and the other with the grains kinematics.

Clogging of soft particles in two-dimensional hoppers

Using experiments and simulations, we study the flow of soft particles through quasi-two-dimensional hoppers. The first experiment uses oil-in-water emulsion droplets in a thin sample chamber. Due to surfactants coating the droplets, they easily slide past each other, approximating soft frictionless disks. For these droplets, clogging at the hopper exit requires a narrow hopper opening only slightly larger than the droplet diameter. The second experiment uses soft hydrogel particles in a thin sample chamber, where we vary gravity by changing the tilt angle of the chamber. For reduced gravity, clogging becomes easier and can occur for larger hopper openings. Our simulations mimic the emulsion experiments and demonstrate that softness is a key factor controlling clogging: with stiffer particles or a weaker gravitational force, clogging is easier. The fractional amount a single particle is deformed under its own weight is a useful parameter measuring particle softness. Data from the simulation and hydrogel experiments collapse when compared using this parameter. Our results suggest that prior studies using hard particles were in a limit where the role of softness is negligible, which causes clogging to occur with significantly larger openings.

Flow and clog in a silo with oscillating exit

When grains flow out of a silo, flow rate W increases with exit size D. If D is too small, an arch may form and the flow may be blocked at the exit. To recover from clogging, the arch has to be destroyed. Here we construct a two-dimensional silo with movable exit and study the effects of exit oscillation (with amplitude A and frequency f) on flow rate, clogging, and unclogging of grains through the exit. We find that, if exit oscillates, W remains finite even when D (measured in unit of grain diameter) is only slightly larger than one. Surprisingly, while W increases with oscillation strength Γ≡4π^{2}Af^{2} as expected at small D, W decreases with Γ when D≥5 due to induced random motion of the grains at the exit. When D is small and oscillation speed v≡2πAf is slow, temporary clogging events cause the grains to flow intermittently. In this regime, W depends only on v-a feature consistent to a simple arch breaking mechanism, and the phase boundary of intermittent flow in the D-v plane is consistent to either a power law: D∝v^{-7} or an exponential form: D∝e^{-D/0.55}. Furthermore, the flow time statistic is Poissonian whereas the recovery time statistic follows a power-law distribution.

The sands of time run faster near the end

Grains exiting an underwater silo exhibit an unexpected surge in discharge rate as they empty. This contrasts with the constant flow rate of dry granular hoppers and the decreasing flow rate of pure liquids. Here we find that this surge depends on hopper diameter and happens also in air. The surge can be turned off by fixing the rate of fluid flow through the granular packing. With no flow control, dye injected on top of the packing gets drawn into the grains. We conclude that the surge is caused by a self-generated pumping of fluid through the packing. The effect is modelled via a driving pressure set by the exit speed of the grains. This highlights a surprising and unrecognized role that interstitial fluid plays in setting the discharge rate, and perhaps in controlling clog formation, for granular hoppers whether in air or under water.

Hourglasses measure time because the discharge rate of dry sand is constant. Here Koivisto et al. show that when such a system contains water there is a surge in discharge because the fluid drains faster than the grains, which might help us understand the transport of grains in silos.

Role of particle size in the kinematic properties of silo flow

We experimentally analyze the effect that particle size has on the mass flow rate of a quasi two-dimensional silo discharged by gravity. In a previous work, Janda et al. [Phys. Rev. Lett. 108, 248001 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.248001] introduced a new expression for the mass flow rate based on a detailed experimental analysis of the flow for 1-mm diameter beads. Here, we aim to extend these results by using particles of larger sizes and a variable that was not explicitly included in the proposed expression. We show that the velocity and density profiles at the outlet are self-similar and scale with the outlet size with the same functionalities as in the case of 1-mm particles. Nevertheless, some discrepancies are evidenced in the values of the fitting parameters. In particular, we observe that larger particles lead to higher velocities and lower packing fractions at the orifice. Intriguingly, both magnitudes seem to compensate giving rise to very similar flow rates. In order to shed light on the origin of this behavior we have computed fields of a solid fraction, velocity, and a kinetic-stress like variable in the region above the orifice.

Intermittency and velocity fluctuations in hopper flows prone to clogging

We study experimentally the dynamics of granular media in a discharging hopper. In such flows, there often appears to be a critical outlet size D_{c} such that the flow never clogs for D>D_{c}. We report on the time-averaged velocity distributions, as well as temporal intermittency in the ensemble-averaged velocity of grains in a viewing window, for both D<D_{c} and D>D_{c}, near and far from the outlet. We characterize the velocity distributions by the standard deviation and the skewness of the distribution of vertical velocities. We propose a measure for intermittency based on the two-sample Kolmogorov-Smirnov D_{KS} statistic for the velocity distributions as a function of time. We find that there is no discontinuity or kink in these various measures as a function of hole size. This result supports the proposition that there is no well-defined D_{c} and that clogging is always possible. Furthermore, the intermittency time scale of the flow is set by the speed of the grains at the hopper exit. This latter finding is consistent with a model of clogging as the independent sampling for stable configurations at the exit with a rate set by the exiting grain speed [C. C. Thomas and D. J. Durian, Phys. Rev. Lett. 114, 178001 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.178001].

Stationary bubble formation and cavity collapse in wedge-shaped hoppers

The hourglass is one of the apparatuses familiar to everyone, but reveals intriguing behaviors peculiar to granular materials, and many issues are remained to be explored. In this study, we examined the dynamics of falling sand in a special form of hourglass, i.e., a wedge-shaped hopper, when a suspended granular layer is stabilized to a certain degree. As a result, we found remarkably different dynamic regimes of bubbling and cavity. In the bubbling regime, bubbles of nearly equal size are created in the sand at a regular time interval. In the cavity regime, a cavity grows as sand beads fall before a sudden collapse of the cavity. Bubbling found here is quite visible to a level never discussed in the physics literature and the cavity regime is a novel phase, which is neither continuous, intermittent nor completely blocked phase. We elucidate the physical conditions necessary for the bubbling and cavity regimes and develop simple theories for the regimes to successfully explain the observed phenomena by considering the stability of a suspended granular layer and clogging of granular flow at the outlet of the hopper. The bubbling and cavity regimes could be useful for mixing a fluid with granular materials.

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.

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.

Breaking arches with vibrations: the role of defects

We present experimental and numerical results regarding the stability of arches against external vibrations. Two-dimensional strings of mutually stabilizing grains are geometrically analyzed and subsequently submitted to a periodic forcing at fixed frequency and increasing amplitude. The main factor that determines the granular arch resistance against vibrations is the maximum angle among those formed between any particle of the arch and its two neighbors: the higher the maximum angle is, the easier it is to break the arch. On the basis of an analysis of the forces, a simple explanation is given for this dependence. From this, interesting information can be extracted about the expected magnitudes of normal forces and friction coefficients of the particles composing the arches.

Flow rate of particles through apertures obtained from self-similar density and velocity profiles

"Beverloo's law" is considered as the standard expression to estimate the flow rate of particles through apertures. This relation was obtained by simple dimensional analysis and includes empirical parameters whose physical meaning is poorly justified. In this Letter, we study the density and velocity profiles in the flow of particles through an aperture. We find that, for the whole range of apertures studied, both profiles are self-similar. Hence, by means of the functionality obtained for them the mass flow rate is calculated. The comparison of this expression with the Beverloo's one reveals some differences which are crucial to understanding the mechanism that governs the flow of particles through orifices.

Phase transition in peristaltic transport of frictionless granular particles

Flows of dissipative particles driven by the peristaltic motion of a tube are numerically studied. A transition from a slow "unjammed" flow to a fast "jammed" flow is found through the observation of the flow rate at a critical width of the bottleneck of a peristaltic tube. It is also found that the average and fluctuation of the transition time, and the peak value of the second moment of the flow rate exhibit power-law divergence near the critical point and that these variables satisfy scaling relationships near the critical point. The dependence of the critical width and exponents on the peristaltic speed and the density is also discussed.

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.

Silo clogging reduction by the presence of an obstacle

We present experimental results on the effect that inserting an obstacle just above the outlet of a silo has on the clogging process. We find that, if the obstacle position is properly selected, the probability that the granular flow is arrested can be reduced by a factor of 100. This dramatic effect occurs without any remarkable modification of the flow rate or the packing fraction above the outlet, which are discarded as the cause of the change in the clogging probability. Hence, inspired by previous results of pedestrian crowd dynamics, we propose that the physical mechanism behind the clogging reduction is a pressure decrease in the region of arch formation.

Influence of a reduced gravity on the volume fraction of a monolayer of spherical grains

Centrifuge force is used to study granular materials in low gravity conditions. We consider a monolayer of noncohesive spherical grains placed on a plate. Reduced gravity conditions can be simulated in the plane by tilting or by rotating the plate. We compare both approaches experimentally. The volume fraction is found to increase with the apparent gravity and saturates. A model based on the exponential distribution of the Voronoi cell areas has been built and is in excellent agreement with the experimental data by extrapolating the fits of the data. Moreover, numerical simulations exhibit that more arches can be maintained at low apparent gravities than at high.

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

We simultaneously measure the flow rate and the normal force on the base, near the outlet, during the discharge through an orifice of a dense packing of monosized disks driven by a conveyor belt. We find that the normal force on the base decreases even when a constant flow rate is measured. In addition, we show, by changing the mass of the disks, that pressure can be changed while the flow rate remains constant. Conversely, we are able, by changing the belt velocity, to set different flow rates for the same pressure. The experiment confirms that, contrary to what has been implicitly assumed in numerous works, the flow rate through an aperture is not controlled by the pressure in the outlet region.

Flowers in flour: avalanches in cohesive granular matter

We report on the intermittent dynamics of the free surface of a cohesive granular material during a silo discharge. In absence of cohesion, one observes the formation and the growth of a conical crater whose angle is well defined and constant in time. When the cohesion is involved the free surface exhibits a complex dynamics and the crater, resulting from a series of individual avalanches, is no longer axisymmetric. However, in spite of the intermittent behavior of the free surface, the flow rate is observed to remain constant throughout the discharge.