Jamming transition in two-dimensional hoppers and silos

Stochastic dynamics of granular hopper flows: A configurational mode controls the stability of clogs

Granular flows in small-outlet hoppers exhibit several characteristic but poorly understood behaviors: temporary clogs (pauses) where flow stops before later spontaneously restarting, permanent clogs that last indefinitely, and non-Gaussian, nonmonotonic flow-rate statistics. These aspects have been studied independently, but a model of hopper flow that explains all three has not been formulated. Here, we introduce a phenomenological model that provides a unifying dynamical mechanism for all three behaviors: coupling between the flow rate and a hidden mode that controls the stability of clogs. In the theory, flow rate evolves according to Langevin dynamics with multiplicative noise and an absorbing state at zero flow, conditional on the hidden mode. The model fully reproduces the statistics of pause and clog events of a large (>40000 flows) experimental dataset, including nonexponentially distributed clogging times and non-Gaussian flow rate distribution, and explains the stretched-exponential growth of the average clogging time with outlet size. Further, we identify the physical nature of the hidden mode in microscopic configurational features, including size and smoothness of the static arch structure formed during pauses and clogs. Our work provides a unifying framework for several poorly understood clogging phenomena, and suggests numerous new paths toward further understanding of this complex system.

Experimental measurements of the granular density of modes via impact

The jamming transition is an important feature of granular materials, with prior work showing an excess of low-frequency modes in the granular analog to the density of states, the granular density of modes. In this work, we present an experimental method for acoustically measuring the granular density of modes using a single impact event to excite vibrational modes in an experimental, three-dimensional, granular material. We test three different granular materials, all of which are composed of spherical beads. The first two systems are monodisperse collections of either 6 mm or 8 mm diameter beads. The third system is a bidisperse mixture of the previous two bead sizes. During data collection, the particles are confined to a box; on top of this box, and resting on the granular material, is a light, rigid sheet onto which pressure can be applied to the system. To excite the material, a steel impactor ball is dropped on top of the system. The response of the granular material to the impact pulse is recorded by piezoelectric sensors buried throughout the material, and the density of modes is computed from the spectrum of the velocity autocorrelation of these sensors. Our measurements of the density of modes show more low-frequency modes at low pressure, consistent with previous experimental and numerical results, as well as several low-frequency peaks in the density of modes that shift with applied pressure. Our method represents an experimentally simple technique for investigating the granular density of modes and may increase the accessibility and number of such measurements.

Anchoring Effect of an Obstacle in the Silo Unclogging Process

Contrary to the proven beneficial role that placing an obstacle above a silo exit has in clogging prevention, we demonstrate that, when the system is gently shaken, this passive element has a twofold effect in the clogging destruction process. On one side, the obstacle eases the destruction of weak arches, a phenomenon that can be explained by the pressure screening that it causes in the outlet proximities. But on the other side, we discover that the obstacle presence leads to the development of a few very strong arches. These arches, which dominate in the heavy tailed distributions of unclogging times, correlate with configurations where the number of particles contacting the obstacle from below are higher than the average; hence suggesting that the obstacle acts as an anchoring point for the granular packing. This finding may help one to understand the ambiguous effect of obstacles in the bottleneck flow of other systems, such as pedestrians evacuating a room or active matter in general.

Soft particles facilitate flow of rigid particles in a 2D hopper

The flow of granular materials through narrow openings governs flow and process efficiency in a variety of industrial settings. As the use of soft particles and other soft micro-materials becomes more widespread in consumer products, we seek to understand characteristics of granular flows beyond powder flows. We study clogging through a 2D hopper in systems consisting of a combination of soft and rigid particles of different sizes and mixing fractions. Our experimental results show that soft particles play a lubricating role in the flow of rigid spheres due to their deformability and slick surface, but the size of rigid particles influences clogging more than the size of soft ones. We simulate our results using a modification of the Durian bubble model to accommodate mixtures of particles of different softness. Without any adjustable parameters, the simulation results capture the clogging probability of soft-rigid particle mixtures through a 2D hopper.

Collisional regime during the discharge of a two-dimensional silo

The present work reports an investigation into the collisional dynamics of particles in the vicinity of the outlet of a two-dimensional silo using molecular dynamics simulations. Most studies on this granular system focus in the bulk of the medium. In this region, contacts are permanent or long-lived, so continuous approximations are able to yield results for velocity distributions or mass flow. Close to the exit, however, the density of the medium decreases and contacts are instantaneous. Thus, the collisional nature of the dynamics becomes significant, warranting a dedicated investigation as carried out in this work. More interesting, the vicinity of the outlet is the region where the arches that block the flow for small apertures are formed. It is found that the transition from the clogging regime (at small apertures) to the continuous flow regime is smooth in collisional variables. Furthermore, the dynamics of particles as reflected by the distributions of the velocities is as well unaffected. This result implies that there is no critical outlet size that separates both regimes, as had been proposed in the literature. Instead, the results achieved support the alternative picture in which a clog is possible for any outlet size.

Weak clogging in constricted channel flow

We investigate simple models of a monodisperse system of soft, frictionless disks flowing through a two-dimensional microchannel in the presence of a single or a double constriction using Brownian dynamics simulation. After a transient time, a stationary state is observed with an increase in particle density before the constriction and a depletion after it. For a constriction width to particle diameter ratio of less than 3, the mean particle velocity is reduced compared to the unimpeded flow and it falls to zero for ratios of less than 1. At low temperatures, the particle mean velocity may vary nonmonotonically with the constriction width. The associated intermittent behavior is due to the formation of small arches of particles with a finite lifetime. The distribution of the interparticle exit times rises rapidly at short times followed by an exponential decay with a large characteristic time, while the cascade size distribution displays prominent peaks for specific cluster sizes. Although the dependence of the mean velocity on the separation of two constrictions is not simple, the mean flow velocity of a system with a single constriction provides an upper envelope for the system with two constrictions. We also examine the orientation of the leading pair of particles in front of the constriction(s). With a single constriction in the intermittent regime, there is a strong preference for the leading pair to be orientated perpendicular to the flow. When two constrictions are present, orientations parallel to the flow are much more likely at the second constriction.

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.

Characterization of the Clogging Transition in Vibrated Granular Media

The existence of a transition from a clogged to an unclogged state has been recently proposed for the flow of macroscopic particles through bottlenecks in systems as diverse as colloidal suspensions, granular matter, or live beings. Here, we experimentally demonstrate that, for vibrated granular media, such a transition genuinely exists, and we characterize it as a function of the outlet size and vibration intensity. We confirm the suitability of the "flowing parameter" as the order parameter, and we find out that the rescaled maximum acceleration of the system should be replaced as the control parameter by a dimensionless velocity that can be seen as the square root of the ratio between kinetic and potential energy. In all the investigated scenarios, we observe that, for a critical value of this control parameter S_{c}, there seems to be a continuous transition to an unclogged state. The data can be rescaled with this critical value, which, as expected, decreases with the orifice size D. This leads to a phase diagram in the S-D plane in which clogging appears as a concave surface.

Discharge of elongated grains from silo with rotating bottom

We study the flow of elongated grains (wooden pegs of length L=20 mm with circular cross section of diameter d_{c}=6 and 8 mm) from a silo with a rotating bottom and a circular orifice of diameter D. In the small orifice range (D/d<5) clogs are mostly broken by the rotating base, and the flow is intermittent with avalanches and temporary clogs. Here d≡(3/2d_{c}^{2}L)^{1/3} is the effective grain diameter. Unlike for spherical grains, for rods the flow rate W clearly deviates from the power law dependence W∝(D-kd)^{2.5} at lower orifice sizes in the intermittent regime, where W is measured in between temporary clogs only. Instead, below about D/d<3 an exponential dependence W∝e^{κD} is detected. Here k and κ are constants of order unity. Even more importantly, rotating the silo base leads to a strong-more than 50%-decrease of the flow rate, which otherwise does not depend significantly on the value of ω in the continuous flow regime. In the intermittent regime, W(ω) appears to follow a nonmonotonic trend, although with considerable noise. A simple picture, in terms of the switching from funnel flow to mass flow and the alignment of the pegs due to rotation, is proposed to explain the observed difference between spherical and elongated grains. We also observe shear-induced orientational ordering of the pegs at the bottom such that their long axes in average are oriented at a small angle 〈θ〉≈15^{∘} to the motion of the bottom.

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.

Study of Clogging Phenomenon for a Conical Hopper: The Influence of Particle Bed Height and Hopper Angle

The granular flow is one of the principal issues for the design of pebble bed reactors. Particularly, the clogging phenomenon raises an important issue for pebble bed reactors. In this paper, we conduct experiments and discrete particle simulation of two-dimensional discharge granular flow from a conical hopper, to study the effect of the particle bed height $h$ and hopper angle $\alpha$ on the clogging phenomenon. In general, the clogging probability $J$ increases with height $h$ and starts to saturate when $h$ is larger than a critical value. The experimental result trends are supported by discrete simulations. To understand the underlying physical mechanism, we conduct discrete particle simulations for various $h$ values, focusing on the following parameters: the statistical averaging of the volume fraction, velocity, and contact pressure of particles near the aperture during the discharge. We found that, among all relevant variables, the contact pressure of particles is the main cause of the increasement of J when $h$ increases. An exponential law between the pebble bed $h$ and clogging probability J has been established based on these observations and Janssen model. As for hopper angle $\alpha$ , J shows an almost constant behavior for any rise in $\alpha$ followed by a sudden regression at $\alpha ={75}^{°}$ . Surprisingly, the effect of $\alpha$ is most obvious for intermediate values of $h$ , where we observe a sharp increasement of clogging probability. The same trend is observed in the two-dimensional discrete simulation results.

Non-monotonic dependence of avalanche durations on particle velocities in the discharge of a silo

The distributions of avalanche times between successive clog events are analyzed in a silo discharged with a conveyor belt. In a previous work [Phys. Rev. Lett. 121, 138001 (2018)], we measured the distribution of avalanche sizes (in number of particles) for the same experiment, finding a monotonous influence of both the outlet size and the velocity of particles in the clogging probability. Nonetheless, if avalanche durations are analyzed instead of avalanche sizes, a minimum is observed when representing the mean avalanche time as function of the velocity of particles. This phenomenon is explained using kinematic arguments, which are validated by experimental data. At the same time, this work aims at highlighting the importance of discerning between measuring clogging avalanches in terms of times or doing it in terms of number of particles.

Clogging-jamming connection in narrow vertical pipes

We report experimental evidence of clogging due to the spontaneous development of hanging arches when a granular sample composed of spherical particles flows down a narrow vertical pipe. These arches, akin to the ones responsible for silo clogging, can only be possible due to the role of frictional forces; otherwise they will be unstable. We find that, contrary to the silo case, the probability of clogging in vertical narrow tubes does not decrease monotonically with the ratio of the pipe-to-particle diameters. This behavior is related to the clogging prevention caused by the spontaneous ordering of particles apparent in certain aspect ratios. More importantly, by means of numerical simulations, we discover that the interparticle normal force distributions broaden in systems with higher probability of clogging. This feature, which has been proposed before as a distinctive feature of jamming in sheared granular samples, suggests that clogging and jamming are connected in pipe flow.

Granular flow from silos with rotating orifice

For dry granular materials falling through a circular exit at the bottom of a silo, no continuous flow can be sustained when the diameter D of the exit is less than five times the characteristic size of the grains. If the bottom of the silo rotates horizontally with respect to the wall of the silo, finite flow rate can be sustained even at small D. We investigate the effect of bottom rotation to the flow rate of monodisperse plastic beads of d=6mm diameter from a cylindrical silo of 19 cm inner diameter. We find that the flow rate W follows Beverloo law down to D=1.3d and that W increases with the rotation speed ω in the small exit regime. If the exit is at an off-center distance R from the axis of the silo, W increases with the rate of area swept by the exit. On the other hand, when the exit diameter is large, W decreases with increasing ω at small ω but increases with ω at large ω. Such nonmonotonic dependence of flow rate on rotation speed may be explained as a gradual change from funnel flow to mass flow due to the shear at the bottom of the silo.

Investigation on the impact of powder arching in small die filling

The flow of particulate materials is critical during processes such as mixing, compression and packing. Non-cohesive arching, a feature characteristic of coarse and free-flowing particles, has been studied extensively for silos and hoppers. However, the arching of powders during die fill has received much less attention. In this study, die fill performance of coarse and free-flowing nonpareils was evaluated using a specially designed die filling device in order to investigate the impact of non-cohesive arching during die fill under gravity flow. Through evaluating die fill performance, the arching phenomenon during dynamic conditions of die fill could be captured. Nonpareils with large particle size increased the likelihood of arching and caused poorer die fill performance for narrow orifices. In contrast, die fill in large orifices was generally better with larger particles due to reduced inter-particulate friction. Both particle size and size distribution influenced non-cohesive arching during die fill. Forced feeding did not appear to affect die fill performance and non-cohesive arching. A critical particle size range beyond which die fill performance would decrease, particularly for the narrow orifices, was identified. Findings from this study provided a better insight into non-cohesive arching during die fill.

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.

Trap Model for Clogging and Unclogging in Granular Hopper Flows

Granular flows through narrow outlets may be interrupted by the formation of arches or vaults that clog the exit. These clogs may be destroyed by vibrations. A feature which remains elusive is the broad distribution p(τ) of clog lifetimes τ measured under constant vibrations. Here, we propose a simple model for arch breaking, in which the vibrations are formally equivalent to thermal fluctuations in a Langevin equation; the rupture of an arch corresponds to the escape from an energy trap. We infer the distribution of trap depths from experiments made in two-dimensional hoppers. Using this distribution, we show that the model captures the empirically observed heavy tails in p(τ). These heavy tails flatten at large τ, consistently with experimental observations under weak vibrations. But, here, we find that this flattening is systematic, which casts doubt on the ability of gentle vibrations to restore a finite outflow forever. The trap model also replicates recent results on the effect of increasing gravity on the statistics of clog formation in a static silo. Therefore, the proposed framework points to a common physical underpinning to the processes of clogging and unclogging, despite their different statistics.

Clogging in constricted suspension flows

The flow of a charged-stabilized suspension through a single constricted channel is studied experimentally by tracking the particles individually. Surprisingly, the behavior is found to be qualitatively similar to that of inertial dry granular systems: For small values of the neck-to-particle size ratio (D/d<3), clogs form randomly as arches of the particle span the constriction. The statistics of the clogging events are Poissonian as reported for granular systems and agree for moderate particle volume fraction (ϕ≈20%) with a simple stochastic model for the number of particles at the neck. For larger neck sizes (D/d>3), even at the largest ϕ(≈60%) achievable in the experiments, an uninterrupted particle flow is observed, which resembles that of an hourglass. This particularly small value of D/d(≃3) at the transition to a practically uninterrupted flow is attributed to the low effective friction between the particles, achieved by the particle's functionalization and lubrication.

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.

Outflow and clogging of shape-anisotropic grains in hoppers with small apertures

Outflow of granular material through a small orifice is a fundamental process in many industrial fields, for example in silo discharge, and in everyday's life. Most experimental studies of the dynamics have been performed so far with monodisperse disks in two-dimensional (2D) hoppers or spherical grains in 3D. We investigate this process for shape-anisotropic grains in 3D hoppers and discuss the role of size and shape parameters on avalanche statistics, clogging states, and mean flow velocities. It is shown that an increasing aspect ratio of the grains leads to lower flow rates and higher clogging probabilities compared to spherical grains. On the other hand, the number of grains forming the clog is larger for elongated grains of comparable volumes, and the long axis of these blocking grains is preferentially aligned towards the center of the orifice. We find a qualitative transition in the hopper discharge behavior for aspect ratios larger than ≈6. At still higher aspect ratios >8-12, the outflowing material leaves long vertical holes in the hopper that penetrate the complete granular bed. This changes the discharge characteristics qualitatively.

Clogging of granular materials in silos: effect of gravity and outlet size

By means of extensive numerical simulations we disclose the role of the driving force in the clogging of inert particles passing through a constriction. We uncover the effect of gravity and outlet size on the flow rate and kinetic energy within the system, and use these quantities to deepen our understanding of the blocking process. First, we confirm the existence of a finite avalanche size when the driving force tends to zero. The magnitude of this limit avalanche size grows with the outlet size, as expected due to geometrical reasons. In addition, there is an augment of the avalanche size when the driving force is increased, an effect that is enhanced by the outlet size. This phenomenology is explained by assuming that in order to get a stable clog developed, two conditions must be fulfilled: (1) an arch spanning the outlet size should be formed; (2) the arch should resist until the complete dissipation of the kinetic energy within the system. From these assumptions, we are able to obtain the probability that an arch gets destabilized, which is shown to primarily depend on the square root of the kinetic energy. A minor additional dependence of the outlet size is also observed which is explained in the light of recent results of the arch resistance in vibrated silos.

Stability of clogging arches in a silo submitted to vertical vibrations

We present experimental results on the endurance of arches that block the outlet of a two-dimensional silo when subjected to vertical vibration. In a recent paper [C. Lozano et al., Phys. Rev. Lett. 109, 068001 (2012)], it was shown that the arch resistance against vibrations is determined by the maximum angle among those formed between each particle in the bridge and its two neighbors: the larger the maximum angle is, the weaker the bridge. It has also been reported that the breaking time distribution shows a power-law tail with an exponent that depends on the outlet size, the vibration intensity, and the load [I. Zuriguel et al., Sci. Rep. 4, 7324 (2014)]. Here we connect these previous works, demonstrating the importance of the maximum angle in the arch on the exponent of the breaking time distribution. Besides, we find that the acceleration needed to break an arch does not depend on the ramp rate of the applied acceleration, but it does depend on the outlet size above which the arch is formed. We also show that high frequencies of vibration reveal a change in the behavior of the arches that endure very long times. These arches have been identified as a subset with special geometrical features. Therefore, arches that cannot be broken by means of a given external excitation might exist.

Fraction of clogging configurations sampled by granular hopper flow

We measure the fraction F of flowing grain configurations that precede a clog, based on the average mass discharged between clogging events for various aperture geometries. By tilting the hopper, we demonstrate that F is a function of the hole area projected in the direction of the exiting grain velocity. By varying the length of slits, we demonstrate that grains clog in the same manner as if they were flowing out of a set of smaller independent circular openings. The collapsed data for F can be fit to a decay that is exponential in hole width raised to the power of the system dimensionality. This is consistent with a simple model in which individual grains near the hole have a large but constant probability to precede a clog. Such a picture implies that there is no sharp clogging transition, and that all hoppers have a nonzero probability to clog.

Commentary on "Jamming transition in a two-dimensional open granular pile with rolling resistance"

A Commentary on the paper by C F M Magalhes et. al. [Pap. Phys. 6, 060007 (2014)]. Received: 10 October 2014, Accepted: 10 October 2014; Edited by: L. A. Pugnaloni; DOI: http://dx.doi.org/10.4279/PIP.060008Cite as: R. Arévalo, Papers in Physics 6, 060008 (2014)

Role of driving force on the clogging of inert particles in a bottleneck

We present numerical results of the effect that the driving force has on the clogging probability of inert particles passing through a bottleneck. When the driving force is increased by four orders of magnitude, the mean avalanche size remains almost unaltered (increases 1.6 times) while the flow rate and the avalanche duration display strong dependence on this magnitude. This indicates that in order to characterize the ability of a system to clog, the right variable to consider is the number of particles that pass through the outlet. The weak dependence of this magnitude on the driving force is explained in terms of the average kinetic energy of the flowing grains that has to be dissipated in order to get an arch stabilized.

Geometry dependence of the clogging transition in tilted hoppers

We report the effects of system geometry on the clogging of granular material flowing out of flat-bottomed hoppers with variable aperture size D and with variable angle θ of tilt of the hopper away from horizontal. In general, larger tilt angles make the system more susceptible to clogging. To quantify this effect for a given θ, we measure the distribution of mass discharged between clogging events as a function of aperture size and extrapolate to the critical size at which the average mass diverges. By repeating for different angles, we map out a clogging phase diagram as a function of D and θ that demarcates the regimes of free flow (large D, small θ) and clogging (small D, large θ). We do this for both circular holes and long rectangular slits. Additionally, we measure four types of grain: smooth spheres (glass beads), compact angular grains (beach sand), disklike grains (lentils), and rodlike grains (rice). For circular apertures, the clogging phase diagram is found to be the same for all grain types. For narrow slit apertures and compact grains, the shape is also the same as for circular holes when expressed in terms of projected area of the aperture against the average flow direction. For lentils and rice discharged from slits, the behavior differs and may be due to alignment between grain and slit axes.

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.

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.

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.

Fluctuations of grains inside a discharging two-dimensional silo

We present experimental data corresponding to a two-dimensional dense granular flow, namely, the gravity-driven discharge of grains from a small opening in a silo. We study the local velocity field at the scale of single grains at different places with the help of particle-tracking techniques. From these data, the velocity profiles can be obtained and the validity of some long-standing approaches can be assessed. Moreover, the fluctuations of the velocities are taken into consideration to characterize the features of the advective motion (due to the gravity force) and the diffusive motion, which shows nontrivial behavior.

Granular jet impingement on a fixed target

In this work discrete element modeling (DEM) was applied to the flow of granular jets against a target. The resulting sheetlike or conelike formations under different conditions are described and explained by means of kinetic analysis. A qualitative and quantitative comparison with experimental results [Cheng, Phys. Rev. Lett. 93, 188001 (2007)] provides interesting insights in the theoretical treatment of the head-on collision of granular jets. Results presented in this paper provide a theoretical description of this type of physical system. However, there still exist obstacles in obtaining quantitative results.

Shape of jamming arches in two-dimensional deposits of granular materials

We present experimental results on the shape of arches that block the outlet of a two-dimensional silo. For a range of outlet sizes, we measure some properties of the arches such as the number of particles involved, the span, the aspect ratio, and the angles between mutually stabilizing particles. These measurements shed light on the role of frictional tangential forces in arching. In addition, we find that arches tend to adopt an aspect ratio (the quotient between height and half the span) close to 1, suggesting an isotropic load. The comparison of the experimental results with data from numerical models of the arches formed in the bulk of a granular column reveals the similarities of both, as well as some limitations in the few existing models.