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

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

Pipe transport in underground mining: an experimental approach

Transport of material through pipes or channels in mines or gravel quarries seems to be a simple and economic form of conveying blasted ore between different levels. Despite the apparent advantages of moving the material by means of the gravity force, there exists an important problem that makes the applicability of this method more difficult: the election of the pipe diameter to prevent clogging of the stones. It was R. Kvapil in the sixties who extended the ideas of granular flows in silos to underground mining. Nevertheless, after his pioneering works there are only a few manuscripts focused on this topic, and many questions remain unsolved. In this work, we present experimental results about the flow of particles (gravel) driven by gravity through tilted tubes. The amount of material discharged between clogs shows that the probability of clogging can be estimated by the same procedures introduced for silos. Finally, by changing the ratio between the tube diameter and the typical particle size, we discuss about the existence or not of a critical size beyond which clogging is not possible

Jamming and critical outlet size in the discharge of a two-dimensional silo

We present an experimental study of jamming in the discharge of grains through an opening in a two-dimensional silo. For a wide range of outlet sizes, we obtain the size distribution of avalanche defined as the number of grains that fall between two consecutive jams. From these distributions, we obtain the probability that the silo jams before N particles pass through the orifice. Then a simple model of arch formation is proposed that predicts the shape of the jamming probability function and reveals that it does not exist a critical size of the orifice above which there is not 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

Clogging and unclogging of many-particle systems passing through a bottleneck

When a group of discrete particles pass through a narrowing, the flow may become arrested due to the development of structures that span over the size of the aperture. Then, it is said that the system is clogged. Here, we will discuss about the existence of a phase diagram for the clogged state that has been recently proposed, arguing on its usefulness to describe different systems of discrete bodies ranging from granular materials, to colloidal suspensions and live beings. This diagram is built based on the value of a flowing parameter which characterizes the intermittent flow observed in all these discrete systems provided that there is an external or internal energy supply. Such requirement, which is necessary to destabilize the clogging arches, is absent in a standard static silo, which is therefore examined as a particular case. This view will help to understand some a priori inconsistencies concerning the role of driving force in the clogging process that have been found in the last years

Disentangling the free-fall arch paradox in silo discharge

Several theoretical predictions of the mass flow rate of granular media discharged from a silo are based on the spontaneous development of a free-fall arch region, the existence of which is still controversial. In this Letter, we study experimentally and numerically the particle flow through an orifice placed at the bottom of 2D and 3D silos. The implementation of a coarse-grained technique allows a thorough description of all the kinetic and micromechanical properties of the particle flow in the outlet proximities. Though the free-fall arch does not exist as traditionally understood—a region above which particles have negligible velocity and below which particles fall solely under gravity action—we discover that the kinetic pressure displays a well-defined transition in a position that scales with the outlet size. This universal scaling explains why the free-fall arch picture has served as an approximation to describe the flow rate in the discharge of silos

Velocity and density scaling at the outlet of a silo and its role in the expression of the mass flow rate

The role of density and velocity profiles in the flow of particles through apertures has been recently put on evidence in a two-dimensional experiment (Phys. Rev. Lett. 108, 248001). For the whole range of apertures studied, both velocity and density profiles are selfsimilar and the obtained scaling functions allow to derive the relevant scales of the problem. Indeed, by means of the functionality obtained for these profiles, an exact expression for the mass flow rate was proposed. Such expression showed a perfect agreement with the experiential data. In this work, we generalize this study to the three dimensional case. We perform numerical simulations of a 3D silo in which the velocity and volume fraction profiles are determined. Both profiles shows that the scaling obtained for 2D can be generalized to the 3D case. Finally, the scaling of the mass flow rate with the outlet radius is discussed

Silo clogging reduction by placing an obstacle above the outlet

We present an experimental study of the effect that an obstacle above the outlet of a silo has on the clogging probability. Both, the size of the ori ce and the obstacle position are varied for a chosen obstacle size and shape. If the position of the obstacle is properly selected the clogging probability can be importantly reduced. Indeed, as the outlet size is increased – and we approach the critical size above which there is not clogging – the obstacle effect is enhanced. For the largest outlet size studied, the clogging probability is reduced by a factor of more than one hundred. We will show, using numerical simulations, that the physical parameter behind the reduction of the silo clogging seems to be the decrease of the vertical pressure at the outlet proximities

Flow-rate fluctuations in the outpouring of grains from a two-dimensional silo

We present experimental results obtained with a two-dimensional silo discharging under gravity through an orifice at the flat bottom. High-speed measurements provide enough time resolution to detect every single bead that goes out and this allows the measurement of the flow rate in short-time windows. Two different regimes are clearly distinguished: one for large orifices, which can be described by Gaussian fluctuations, and another for small orifices, in which extreme events appear. The frontier between those two regimes coincides with the outlet size below which jamming events are frequent. Moreover, it is shown that the power spectrum of the flow-rate oscillations is not dominated by any particular frequency