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 $d\equiv(\frac{3}{2}d_c^2L)^{1/3}$ is the effective grain diameter. Unlike for spherical grains, for rods the flow rate $W$ clearly deviates from the power law dependence $W\propto (D-kd)^{2.5}$ 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 $W\propto e^{κD}$ 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 non-monotonic 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 $\langleθ\rangle \approx 15^\circ$ to the motion of the bottom.
This paper is aimed at pursuing a recent discussion about the comparison between Self-Organised Criticality, the jamming process and the percolation theory in the problem of a silo discharge [I. Zuriguel, A. Garcimartin, D. Maza, L.A.Pugnaloni, J.M.Pastor, "Jamming during the discharge of granular matter from a silo", Phys.Rev.E 71, 051303 (2005)]. Statistics of blocking a silo is investigated from different models: percolation, self organised criticality..
When a granular material is freely discharged from a silo through an orifice at its base, the flow rate remains constant throughout the discharge. However, it has been recently shown that, if the discharge is forced by an overweight, the flow rate increases at the final stages of the discharge, in striking contrast to viscous fluids [Madrid et al. Europhys. Lett. (2018)]. {Although the general mechanism that drives this increase in the flow rate has been discussed, there exist yet a number of open questions regarding this phenomenon. One such questions is to what extent is the internal velocit…
The flow rate of water through an orifice at the bottom of a container depends on the hydrostatic pressure whereas for a dry granular material is nearly constant. But what happens during the simultaneous discharge of grains and liquid from a silo? By measuring the flow rate as a function of time, we found that: (i) different regimes appear, going from constant flow rate dominated by the effective fluid viscosity to a hydrostatic-like discharge depending on the aperture and grain size, (ii) the mixed material is always discharged faster than dry grains but slower than liquid, (iii) for the mixt…
We study experimentally gravity-driven granular discharges of laboratory scale silos, during the initial instants of the discharge. We investigate deformable wall silos around their critical collapse height, as well as rigid wall silos. We propose a criterion to determine a maximum time for the onset of the collapse and find that the onset of collapse always occurs before the grains adjacent to the wall are sliding down. We conclude that the evolution of the static friction toward a state of maximum mobilization plays a crucial role in the collapse of the silo.
The granular silo is one of the many interesting illustrations of the thixotropic property of granular matter: a rapid flow develops at the outlet, propagating upwards through a dense shear flow while material at the bottom corners of the container remains static. For large enough outlets, the discharge flow is continuous; however, by contrast with the clepsydra for which the flow velocity depends on the height of fluid left in the container, the discharge rate of granular silos is constant. Implementing a plastic rheology in a 2D Navier-Stokes solver (following the mu(I)-rheology or a constan…
Resistance force exerted on an obstacle in a gravity-driven slow granular silo flow is studied by experiments and numerical simulations. In a two-dimensional granular silo, an obstacle is placed just above the exit. Then, steady discharge flow is made and its flow rate can be controlled by the width of exit and the position of obstacle. During the discharge of particles, flow rate and resistance force exerting on the obstacle are measured. Using the obtained data, a dimensionless number characterizing the force balance in granular flow is defined by the relation between the discharge flow rate…
We report experimental observations of sound waves in a granular material during resonant silo discharge called silo music. The grain motion was tracked by high speed imaging while the resonance of the silo was detected by accelerometers and acoustic methods. The grains do not oscillate in phase at neighboring vertical locations, but information propagates upward in this system in the form of sound waves. We show that the wave velocity is not constant throughout the silo, but considerably increases towards the lower end of the system, suggesting increased pressure in this region, where the flo…
Jamming and avalanche statistics are studied in a simulation of the discharge of a polydisperse ensemble of disks from a 2-D silo. Exponential distributions are found for the avalanche sizes for all sizes of the exit opening, in agreement with reported experiments. The average avalanche size grows quite fast with the size of the exit opening. Data for this growth agree better with a critical divergence with a large critical exponent, as reported for 3-D experiments, than with the exponential growth reported for 2-D experiments.
We use Topological Data Analysis to study the post buckling behavior of laboratory scale cylindrical silos under gravity driven granular discharges. Thin walled silos buckle during the discharge if the initial height of the granular column is large enough. The deformation of the silo is reversible as long as the filling height does not exceed a critical value, $L_c$. Beyond this threshold the deformation becomes permanent and the silo often collapses. We study the dynamics of reversible and irreversible deformation processes, varying the initial filling height around $L_c$. We find that all re…
We present a differential equation for the flow rate of granular materials during the discharge of a silo. This is based in the energy balance of the variable mass system in contrast with the traditional derivations based on heuristic postulates such as the free fall arch. We show that this new equation is consistent with the well known Beverloo rule, providing an independent estimate for the universal Beverloo prefactor. We also find an analytic expression for the pressure under discharging conditions.
Soft smooth particles in silo discharge show peculiar characteristics, including, for example, non-permanent clogging and intermittent flow. This paper describes a study of soft, low-frictional hydro\-gel spheres in a quasi-2D silo. We enforce a more competitive behavior of these spheres during their discharge by placing an obstacle in front of the outlet of the silo. High-speed optical imaging is used to capture the process of discharge. All particles in the field of view are identified and tracked by means of machine learning software using a MASK R-CNN algorithm. With particle tracking velo…
Acceleration and sound measurements during granular discharge from silos are used to show that silo music is a sound resonance produced by silo quake. The latter is produced by stick-slip friction between the wall and the granular material in tall narrow silos. For the discharge rates studied, the occurrence and frequency of flow pulsations are determined primarily by the surface properties of the granular material and the silo wall. The measurements show that the pulsating motion of the granular material drives the oscillatory motion of the silo and the occurrence of silo quake does not requi…
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 orif…
The discharge of polydisperse grains in a two-dimensional silo, operating in a continuous-discharge mode, is studied with the help of soft-particle discrete element simulations. We find that the mass flow rate displays similar variation with vertical normal stress at the base and the transition-point in the bulk, signifying that the base normal stress can be considered as a representative of its bulk counterpart. The variation of the base and transition-point normal stresses with fill height follows the Janssen's model, with the former being larger than the latter. The transition-point ($y_t$)…
Using both a continuum Navier-Stokes solver, with the mu(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 quantitative comparison, but focus on the qualitative behavior of velocity and pressure at different locations in the flow. A good agreement is obtained in the regions of rapid flows, while areas of slow creep are not entirely …
We present a complete analysis of the density distribution of particles in a two dimensional silo after discharge. Simulations through a pseudo-dynamic algorithm are performed for filling and subsequent discharge of a plane silo. Particles are monosized hard disks deposited in the container and subjected to a tapping process for compaction. Then, a hole of a given size is open at the bottom of the silo and the discharge is triggered. After a clogging at the opening is produced, and equilibrium is restored, the final distribution of the remaining particles at the silo is analyzed by dividing th…
Soft, low-friction particles in silos show peculiar features during their discharge. The outflow velocity and the clogging probability both depend upon the momentary silo fill height, in sharp contrast to silos filled with hard particles. The reason is the fill-height dependence of the pressure at the orifice. We study the statistics of silo discharge of soft hydrogel spheres. The outflow is found to become increasingly fluctuating and even intermittent with decreasing orifice size, and with decreasing fill height. In orifices narrower than two particle diameters, outflow can stop completely, …
When rough grains in standard packing conditions are discharged from a silo, a conical depression with a single slope is formed at the surface. We observed that the increase of the volume fraction generates a more complex depression characterized by two angles of discharge: a lower angle close to the one measured for standard packing and a considerably larger upper angle. The change in slope appears at the boundary between a densely packed stagnant region at the periphery and the central flowing channel formed over the aperture. Since the material in the latter zone is always fluidized, the fl…
We investigate, at a laboratory scale, the collapse of cylindrical shells of radius $R$ and thickness $t$ induced by a granular discharge. We measure the critical filling height for which the structure fails upon discharge. We observe that the silos sustain filling heights significantly above an estimation obtained by coupling standard shell-buckling and granular stress distribution theories. Two effects contribute to stabilize the structure: (i) below the critical filling height, a dynamical stabilization due to granular wall friction prevents the localized shell-buckling modes to grow irreve…
During a typical silo discharge, the material flow rate is determined by the contact forces between the grains. Here, we report an original study concerning the discharge of a two-dimensional silo filled with repelling magnetic grains. This non-contact interaction leads to a different dynamics from the one observed with conventional granular materials. We found that, although the flow rate dependence on the aperture size follows roughly the power-law with an exponent $3/2$ found in non-repulsive systems, the density and velocity profiles during the discharge are totally different. New phenomen…
Granular flow out of a silo is studied experimentally and numerically. The time evolution of the discharge rate as well as the normal force (apparent weight) at the bottom of the container is monitored. We show, that particle stiffness has a strong effect on the qualitative features of silo discharge. For deformable grains with a Young's modulus of about $Y_m\approx 40$ kPa in a silo with basal pressure of the order of 4 kPa lowering the friction coefficient leads to a gradual change in the discharge curve: the flow rate becomes filling height dependent, it decreases during the discharge proce…
We present an experimental study of segregation of granular matter in a quasi-two dimensional silo emptying out of an orifice. Size separation is observed when multi-sized particles are used with the larger particles found in the center of the silo in the region of fastest flow. We use imaging to study the flow inside the silo and quantitatively measure the concentration profiles of bi-disperse beads as a function of position and time. The angle of the surface is given by the angle of repose of the particles, and the flow occurs in a few layers only near the top of this inclined surface. The f…
The discharge of elongated particles from a silo with rotating bottom is investigated numerically. The introduction of a slight transverse shear reduces the flow rate $Q$ by up to 70% compared to stationary bottom, but the flow rate shows a modest increase by further increasing the external shear. Focusing on the dependency of flow rate $Q$ on orifice diameter $D$, the spheres and rods show two distinct trends. For rods, in the small aperture limit $Q$ seems to follow an exponential trend, deviating from the classical power-law dependence. These macroscopic observations are in good agreement w…
Since the early work of Hagen in 1852 and Beverloo et al. in 1961, the flow rate of granular material discharging through a circular orifice from a silo has been described by means of dimensional analysis and experimental fits, and explained through the "free fall arch" model. Here, in contrast with the traditional approach, we derive a differential equation based on the energy balance of the system. This equation is consistent with the well known Beverloo rule thanks to a compensation of energy terms. Moreover, this new equation can be used to explore new conditions for silo discharges. In pa…
The present work reports a novel investigation into the collisional dynamics of particles in the vicinity of the outlet of a 2D 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 …
We conducted simple experiment and numerical simulation of two-dimensional granular discharge flow driven by gravity under the influence of an obstacle. According to the previous work (Zuriguel {\it et al.,\,Phys.\,Rev.\,Lett.}\,{\bf 107}: 278001, 2011), the clogging of granular discharge flow can be suppressed by putting a circular obstacle at a proper position. In order to investigate the details of obstacle effect in granular flow, we focused on particle dynamics in this study. From the experimental and numerical data, we found that the obstacle remarkably affects the horizontal-velocity di…
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 microscopic velocity field 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 in order to characterize the features of the advective motion (due to the gravity force) and the diffusive motion, which shows nontrivial behaviour.
The dense flow of air bubbles in a two-dimensional silo (through an aperture D) filled with a liquid is studied experimentally. A particle tracking technique has been used to bring out the main properties of the flow: displacements of the bubbles, transverse and axial velocities. The behavior of the air bubbles is observed to present similarities with non-deformable solid grains in a granular flow. Nevertheless, a correlation between the bubble velocities and their deformations has been evidenced. Moreover, a new discharge law (Beverloo-like) must be considered for such a system, where the flo…
Very recently, To et al.~have experimentally explored granular flow in a cylindrical silo, with a bottom wall that rotates horizontally with respect to the lateral wall \cite{Kiwing2019}. Here, we numerically reproduce their experimental findings, in particular, the peculiar behavior of the mass flow rate $Q$ as a function of the frequency of rotation $f$. Namely, we find that for small outlet diameters $D$ the flow rate increased with $f$, while for larger $D$ a non-monotonic behavior is confirmed. Furthermore, using a coarse-graining technique, we compute the macroscopic density, momentum, a…
Granular material flowing through bottlenecks like the openings of silos tend to clog and to inhibit further flow. We study this phenomenon in a three-dimensional hopper for spherical and shape-anisotropic particles by means of X-ray tomography. The X-ray tomograms provide information on the bulk of the granular filling, and allows to determine the particle positions and orientations inside the silo. In addition, it allows to calculate local packing densities in different parts of the container. We find that in the flowing zone of the silo particles show a preferred orientation and thereby a h…
We present experimental results of the jamming of non-cohesive particles discharged from a flat bottomed silo subjected to vertical vibration. When the exit orifice is only a few grain diameter wide, the flow can be arrested due to the formation of blocking arches. Hence, an external excitation is needed to resume the flow. The use of a continuous gentle vibration is a usual technique to ease the flow in such situations. Even though jamming is less frequent, it is still an issue in vibrated silos. There are, in principle, two possible mechanisms through which vibrations may facilitate the flow…
We examine the gravity-induced flow of dry and cohesionless granular media through an outlet placed eccentrically in a planar silo, employing computations based on a soft-sphere discrete element method. The vertical velocity profiles, measured at the outlet, are self-similar when the eccentricity is given in terms of the gap ($s$) between the wall and the corner of the outlet nearest to the wall. On the other hand, the self-similarity of vertical velocity does not always hold for all eccentricities ($e$) given by the distance between the centers of an outlet and the silo base, which is a typic…
We experimentally demonstrate that the flow rate of granular material through an aperture is controlled by the exit velocity imposed to the particles and not by the pressure at the base, contrary to what is often assumed in previous works. This result is achieved by studying the discharge process of a dense packing of monosized disks through an orifice. The flow is driven by a conveyor belt. This two-dimensional horizontal setup allows to uncouple pressure and velocity and, therefore, to independently control the velocity at which the disks escape the horizontal silo and the pressure in the vi…
When suspended particles are pushed by liquid flow through a constricted channel they might either pass the bottleneck without trouble or encounter a permanent clog that will stop them forever. However, they may also flow intermittently with great sensitivity to the neck-to-particle size ratio D/d. In this work, we experimentally explore the limits of the intermittent regime for a dense suspension through a single bottleneck as a function of this parameter. To this end, we make use of high time- and space-resolution experiments to obtain the distributions of arrest times T between successive b…
This paper describes methods to measure flow rate and jamming onset of granules discharged through a flat-bottom cylindrical hopper with a circular orifice. The intrinsic jamming onset for ideal particles (spherical, monodisperse, smooth) is experimentally measured by two independent methods, with good agreement. For non-ideal particles, the normalized jamming onset increases with elongated granule shape, broadened size distribution and increased friction as measured by the drained angle of repose. An empirical model of the jamming onset is introduced to quantify these effects over the range o…
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, ve…
