Fluctuations of grains inside a discharging two-dimensional silo

Flow dynamics of different particle shapes in a rectangular silo

The present work investigates the effect of using six different particle shapes of equal volume on the discharge process of a rectangular silo with adjustable width, equipped with a flat bottom orifice opening of varying size. We find that the discharge rate decreases with the increasing aspect ratio of the particles for both lentil-shaped (oblate) and rice-shaped (prolate ellipsoidal) particles and macaroni-shaped particles show the lowest discharge rate among all the particle shapes. In addition, the silo width influences the discharge in such a way that the rates at which different particle shapes flow out from the system become more distinguishable at smaller silo widths. We observe that the velocity profile near the orifice opening becomes narrower and less sharp with increasing aspect ratio for both lentil- and rice-shaped particles. Moreover, the silo width does not have a significant influence on the velocity profile very near to the orifice, but, its influence becomes more noticeable with increasing height within the silo.

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.

Subdiffusion model for granular discharge in a submerged silo

Silo discharge has been extensively studied for decades although questions remain regarding the nature of the velocity field, particularly for submerged systems. In this work, fluid-driven granular drainage was performed in a quasi-two-dimensional silo with grains submerged in fluid. While the observed Gaussian velocity profiles were generally consistent with current diffusion models, the diffusion length was found to significantly decrease with height in contrast to the increases previously seen in dry silos. We propose a phenomenological anomalous diffusion model for the spreading of the flow upwards in the cell, with the fluid-driven flows we study here falling in the category of subdiffusive behavior. As the viscous characteristics of the system were amplified, the diffusion length increased and the shape of the flowing zone in the silo changed, deviating further from the parabolic form predicted by traditional normal diffusion models, in effect becoming more subdiffusive as quantified by a decreasing diffusion exponent.

Flow of anisometric particles in a quasi-two-dimensional hopper

The stationary flow field in a quasi-two-dimensional hopper is investigated experimentally. The behavior of materials consisting of beads and elongated particles with different aspect ratio is compared. We show, that while the vertical velocity in the flowing region can be fitted with a Gaussian function for beads, in the case of elongated grains the flowing channel is narrower and is bordered with sharper velocity gradient. For this case, we quantify deviations from the Gaussian velocity profile. Relative velocity fluctuations are considerably larger and slower for elongated grains.

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.

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].

Continuum simulation of the discharge of the granular silo: a validation test for the μ(I) visco-plastic flow law

Using a continuum Navier-Stokes solver with the μ(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 a quantitative comparison, but focus on the qualitative behavior of velocity and pressure at different locations in the flow. A good agreement for the velocity is obtained in the regions of rapid flows, while areas of slow creep are not entirely captured by the continuum model. The pressure field shows a general good agreement, while bulk deformations are found to be similar in both approaches. The influence of the parameters of the μ(I) flow law is systematically investigated, showing the importance of the dependence on the inertial number I to achieve quantitative agreement between continuum and discrete discharge. However, potential problems involving the systems size, the configuration and "non-local" effects, are suggested. Yet the general ability of the continuum model to reproduce qualitatively the granular behavior is found to be very encouraging.