Trap Model for Clogging and Unclogging in Granular Hopper Flows

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.

Discharge Flow of a Cohesive Granular Media from a Silo

Cohesion can dramatically affect the flow of granular media. In this Letter, thanks to a cohesion-controlled granular material, we propose to investigate experimentally the effect of the cohesion on the discharge from a silo. We use two geometries, a cylindrical silo and a thin rectangular silo, with an adjustable bottom to control the size of the orifice. Similarly to cohesionless granular material, the mass flow rate is mostly controlled by the diameter of the outlet D, however, we observe that the cohesion tends to decrease the flow rate. We show that this effect is controlled by a cohesive length, based on the cohesive yield stress and gravity acceleration, which acts as an effective particle size. This cohesive length is also found to control the onset of flow.

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.

Numerical study of granular flow in a slit funnel with a novel structure to avoid particle clogging

To solve the problem of particle clogging in slit funnels and to obtain a stable discharge flow rate, we proposed a new funnel structure, namely the slit baffle funnel. We conducted a systematic investigation using the discrete element method (DEM) to study the effects of funnel half-angle θ, outlet width W, and baffle height H on flow rate and flow pattern. We found that the proposed structure could effectively avoid particle clogging and guarantee a continuous and stable flow rate with small outlet width. Under the condition of H >3 d, a bigger flow rate was obtained at a smaller funnel half-angle. This new funnel structure could be applied to solve clogging problems associated with granular matter in the slit geometry in mining, agriculture, food, and pharmaceuticals.

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.

Measuring Dynamics in Evacuation Behaviour with Deep Learning

Bounded rationality is one crucial component in human behaviours. It plays a key role in the typical collective behaviour of evacuation, in which heterogeneous information can lead to deviations from optimal choices. In this study, we propose a framework of deep learning to extract a key dynamical parameter that drives crowd evacuation behaviour in a cellular automaton (CA) model. On simulation data sets of a replica dynamic CA model, trained deep convolution neural networks (CNNs) can accurately predict dynamics from multiple frames of images. The dynamical parameter could be regarded as a factor describing the optimality of path-choosing decisions in evacuation behaviour. In addition, it should be noted that the performance of this method is robust to incomplete images, in which the information loss caused by cutting images does not hinder the feasibility of the method. Moreover, this framework provides us with a platform to quantitatively measure the optimal strategy in evacuation, and this approach can be extended to other well-designed crowd behaviour experiments.

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.

On the broad tails in breaking time distributions of vibrated clogging arches

Flowing grains can clog an orifice by developing arches, an undesirable event in many cases. Several strategies have been put forward to avoid this. One of them is to vibrate the system in order to undo the clogging. Nevertheless, the time taken to break an arch under a constant vibration has a distribution displaying a heavy tail. This can lead to a situation where the average breaking time is not well defined. Moreover, it has been observed in some experiments that these tails tend to flatten for very long times, exacerbating the problem. Here we will review two conceptual frameworks that have been proposed to understand the phenomenon and discuss their physical implications.

Nonergodicity in silo unclogging: Broken and unbroken arches

We report an experiment on the unclogging dynamics in a two-dimensional silo submitted to a sustained gentle vibration. We find that arches present a jerking motion where rearrangements in the positions of their beads are interspersed with quiescent periods. This behavior occurs for both arches that break down and those that withstand the external perturbation: Arches evolve until they either collapse or get trapped in a stable configuration. This evolution is described in terms of a scalar variable characterizing the arch shape that can be modeled as a continuous-time random walk. By studying the diffusivity of this variable, we show that the unclogging is a weakly nonergodic process. Remarkably, arches that do not collapse explore different configurations before settling in one of them and break ergodicity much in the same way than arches that break down.

Friction-mediated flow and jamming in a two-dimensional silo with two exit orifices

We show that the interparticle friction coefficient significantly influences the flow and jamming behavior of granular materials exiting through the orifice of a two-dimensional silo in the presence of another orifice located in its vicinity. The fluctuations emanating from a continuous flow through a larger orifice results in an intermittent flow through the smaller orifice consisting of sequential jamming and flowing events. The mean time duration of jammed and flow events, respectively, increase and decrease monotonically with increasing interparticle friction coefficient. The frequency of unjamming instances (n_{u}), however, shows a nonmonotonic behavior comprising an increase followed by a decrease with increasing friction coefficient. The decrease on either side of the maximum, then, represents a system moving progressively towards a permanently jammed or a permanently flowing state. The overall behavior shows a systematic dependence on the interorifice distance, which determines the strength of the fluctuations reaching the smaller orifice leading to unjamming instances. The probability distributions of jamming and flowing times are nearly similar for different combinations of friction coefficients and interorifice distances studied and, respectively, exhibit exponential and power-law tails.

Effect of hopper angle on granular clogging

We present experimental results of the effect of the hopper angle on the clogging of grains discharged from a two-dimensional silo under gravity action. We observe that the probability of clogging can be reduced by three orders of magnitude by increasing the hopper angle. In addition, we find that for very large hopper angles, the avalanche size (〈s〉) grows with the outlet size (D) stepwise, in contrast to the case of a flat-bottom silo for which 〈s〉 grows smoothly with D. This surprising effect is originated from the static equilibrium requirement imposed by the hopper geometry to the arch that arrests the flow. The hopper angle sets the bounds of the possible angles of the vectors connecting consecutive beads in the arch. As a consequence, only a small and specific portion of the arches that jam a flat-bottom silo can survive in hoppers.

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.