Flow rate of particles through apertures obtained from self-similar density and velocity profiles

Discharge of rice-shaped particles from a monolayer flat-bottom silo

In this work, we performed experiments regarding the outflow of spheres and two different types of rice-shaped particles in a quasi-two-dimensional monolayer silo with a flat bottom. We investigate the velocity and solid fraction profiles at the orifice and test whether the profiles for nonspherical particles have similar self-similar properties as in the spherical case. We find that the magnitude and shape of the velocity profiles for all three particle types are in a similar range. In contrast, the solid fraction at the orifice has a dome-shaped profile for both rice particles, whereas the profile for spherical particles is rather flat. The discharge rate determined from the velocity and solid fraction profiles describes the independently measured experimental discharge rate very well for all three investigated particle types.

Fabric-based jamming phase diagram for frictional granular materials

A jamming phase diagram maps the phase states of granular materials to their intensive properties such as shear stress and density (or packing fraction). We investigate how different phases in a jamming phase diagram of granular materials are related to their fabric structure via three-dimensional discrete element method simulations. Constant-volume quasi-static simple shear tests ensuring uniform shear strain field are conducted on bi-disperse spherical frictional particles. Specimens with different initial solid fractions are sheared until reaching steady state at a large shear strain (200%). The jamming threshold in terms of stress, non-rattler fraction, and coordination numbers (Z's) of different contact networks is discussed. The evolution of fabric anisotropy (F) of each contact network during shearing is also examined. By plotting the fabric data in the F-Z space, a unique critical fabric surface (CFS) becomes apparent across all specimens, irrespective of their initial phase states. Through the correlation of this CFS with fabric signals corresponding to jamming transitions, we introduce a novel jamming phase diagram in the fabric F-Z space, offering a convenient approach to distinguish the various phases of granular materials solely through the direct observation of geometrical arrangements of particles. This jamming phase diagram underscores the importance of the microstructure underlying the conventional jamming phenomenon and introduces a novel standpoint for interpreting the phase transitions of granular materials that have been exposed to processes such as compaction, shearing, and other complex loading histories.

Self-similarity of pressure profiles during forced granular flows

We present measurements of the vertical stress profile σ on the base of flat-bottomed cylindrical silos discharged through an orifice centered on its base. An overweight forces the material on top of the free surface. The mean bottom pressure σ(z,D,W), with z the height of the granular column, D the silo diameter, and W the mass of the overweight, increases significantly at the end of the discharge. Inspired by early models of stress distribution, we show that σ measured at z=0 can be rescaled to yield a collapse of the data, as a function of z/D, for all D and W explored. We also show that the profile σ(r) is self-similar as a function of the radial coordinate r and can be rescaled to collapse the data for different z,D, and W. Although the model correctly predicts the functional dependences, it fails in quantitative terms. These results challenge our understanding of free and forced granular flows through orifices.

Nonlinear effect of grain elongation on the flow rate in silo discharge

By means of two-dimensional numerical simulations based on contact dynamics, we present a systematic analysis of the joint effects of grain shape (i.e., grain elongation) and system size on silo discharge for increasing orifice sizes D. Grains are rounded-cap rectangles whose aspect ratio are varied from 1 (disks) to 7. In order to clearly isolate the effect of grain shape, the mass of the grains is keeping constant as well as the condition of the discharge by reintroducing the exiting grains at the top of the silo. In order to quantify the possible size effects, the thickness W of the silos is varied from 7 to 70 grains diameter, while keeping the silos aspect ratio always equal to 2. We find that, as long as size effects are negligible, the flow rate Q increases as a Beverloo-like function with D, also for the most elongated grains. In contrast, the effects of grain elongation on the flow rate depend on orifice size. For small normalized orifice sizes, the flow rate is nearly independent with grain elongation. For intermediate normalized orifice sizes the flow rate first increases with grain elongation up to a maximum value that depends on the normalized size of the orifice and saturates as the grains become more elongated. For larger normalized orifice size, the flow rate is an increasing function of grains' aspect ratio. Velocity profiles and packing fraction profiles close to the orifice turn out to be self-similar for all grain shapes and for the whole range of orifice and system sizes studied. Following the methodology introduced by Janda et al. [Phys. Rev. Lett. 108, 248001 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.248001], we explain the nonlinear variation of Q with grain elongation, and for all orifice sizes, from compensation mechanisms between the velocity and packing fraction measured at the center of the orifice. Finally, an equation to predict the evolution of Q as a function of the aspect ratio of the grains is deduced.

Elongated particles discharged with a conveyor belt in a two-dimensional silo

The flow of elliptical particles out of a two-dimensional silo when extracted with a conveyor belt is analyzed experimentally. The conveyor belt-placed directly below the silo outlet-reduces the flow rate, increases the size of the stagnant zone, and it has a very strong influence on the relative velocity fluctuations as they strongly increase everywhere in the silo with decreasing belt speed. In other words, instead of slower but smooth flow, flow reduction by belt leads to intermittent flow. Interestingly, we show that this intermittency correlates with a strong reduction of the orientational order of the particles at the orifice region. Moreover, we observe that the average orientation of the grains passing through the outlet is modified when they are extracted with the belt, a feature that becomes more evident for large orifices.

Discharge of elongated grains in silos under rotational shear

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 with 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 with our earlier experimental findings [Phys. Rev. E 103, 062905 (2021)2470-004510.1103/PhysRevE.103.062905]. With the help of the coarse-graining methodology we obtain the spatial distribution of the macroscopic density, velocity, kinetic pressure, and orientation fields. This allows us detecting a transition from funnel to mass flow pattern caused by the external shear. Additionally, averaging these fields in the region of the orifice reveals that the strong initial decrease in Q is mostly attributed to changes in the flow velocity, while the weakly increasing trend at higher rotation rates is related to increasing packing fraction. Similar analysis of the grain orientation at the orifice suggests a correlation of the flow rate magnitude with the vertical orientation and the packing fraction at the orifice with the order of the grains. Lastly, the vertical profile of mean acceleration at the center of the silo denotes that the region where the acceleration is not negligible shrinks significantly due to the strong perturbation induced by the moving wall.

Role of cohesion in the flow of active particles through bottlenecks

We experimentally and numerically study the flow of programmable active particles (APs) with tunable cohesion strength through geometric constrictions. Similar to purely repulsive granular systems, we observe an exponential distribution of burst sizes and power-law-distributed clogging durations. Upon increasing cohesion between APs, we find a rather abrupt transition from an arch-dominated clogging regime to a cohesion-dominated regime where droplets form at the aperture of the bottleneck. In the arch-dominated regime the flow-rate only weakly depends on the cohesion strength. This suggests that cohesion must not necessarily decrease the group's efficiency passing through geometric constrictions or pores. Such behavior is explained by "slippery" particle bonds which avoids the formation of a rigid particle network and thus prevents clogging. Overall, our results confirm the general applicability of the statistical framework of intermittent flow through bottlenecks developed for granular materials also in case of active microswimmers whose behavior is more complex than that of Brownian particles but which mimic the behavior of living systems.

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.

Challenges, opportunities and recent advances in near infrared spectroscopy applications for monitoring blend uniformity in the continuous manufacturing of solid oral dosage forms

Near infrared (NIR) spectroscopy has been widely recognized as a powerful PAT tool for monitoring blend uniformity in continuous manufacturing (CM) processes. However, the dynamic nature of the powder stream and the fast rate at which it moves, compared to batch processes, introduces challenges to NIR quantitative methods for monitoring blend uniformity. For instance, defining the effective sample size interrogated by NIR, selecting the best sampling location for blend monitoring, and ensuring NIR model robustness against influential sources of variability are challenges commonly reported for NIR applications in CM. This article reviews the NIR applications for powder blend monitoring in the continuous manufacturing of solid oral dosage forms, with a particular focus on the challenges, opportunities for method optimization and recent advances with respect three main aspects: effective sample size measured by NIR, probe location and method robustness.

Flow-induced surface crystallization of granular particles in cylindrical confinement

An interesting phenomenon that a layer of crystallized shell formed at the container wall during an orifice flow in a cylinder is observed experimentally and is investigated in DEM simulation. Different from shear or vibration driven granular crystallization, our simulation shows during the flow the shell layer is formed spontaneously from stagnant zone at the base and grows at a constant rate to the top with no external drive. Roughness of the shell surface is defined as a standard deviation of the surface height and its development is found to disobey existed growth models. The growth rate of the shell is found linearly proportional to the flow rate. This shell is static and served as a rough wall in an orifice flow with frictionless sidewall, which changes the flow profiles and its stress properties, and in turn guarantees a constant flow rate.

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.

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.

Quantitative measurement of solid fraction in a silo using SPRITE

The purpose of this study is to develop MRI methods to measure the solid fraction in granular flows quantitatively. It is increasingly recognised that solid fraction plays a key role in granular rheology, but experimental characterisation of it during flow is challenging. Here centric sectoral-SPRITE imaging is applied to image mustard seeds discharging from a 3D-printed hopper. Quantitative images are obtained after considering and correcting artefacts that may arise from flow and relaxation. The image intensity is then further corrected for spatial variations in the B₁ field. Various maps of nominally homogeneous samples were tested to correct for variations in the B₁ field. The B₁ field was found to be sensitive to the geometry of the sample and the material in the sample. Hence, here static images of the seeds in the hopper were used to correct for B₁ field variations. Moreover, small signal variations were observed from measurements performed on different days owing to subtle differences in the spectrometer operation. Here an internal standard was used to scale the signal intensity and correct for these variations. Following these corrections, a linear correlation (R² = 0.999) was observed between the scaled image intensities and the known solid fractions of packed samples with solid fractions between 0.55 and 0.64. This correlation was used as a calibration of the 3D image of the hopper to extract quantitative time-averaged spatial maps of solid fraction during steady flow. The measurements were confirmed to be quantitative by also measuring the velocity of the particles. Together these measurements were used to calculate a mass flow rate in the hopper, which was consistent with the mass flow measured gravimetrically.

Particle velocity measurement within a free-falling particle curtain using microscopic shadow velocimetry

We report an optical method for particle velocity measurement that is suitable for the measurement of particle velocities within dense particle-laden flows with high spatial resolution. The technique is based on particle shadow velocimetry with the use of a long-distance microscopic lens for images collection. The narrow depth of field of the lens allows particles within the focal plane to have much higher pattern intensities than those outside it on the collected images. Data processing was then employed to remove particles from outside the focal plane based on the gradient of the signal and a threshold. Following this, particle velocity was calculated from two successive images in the usual way. The technique was successfully demonstrated in a free-falling particle curtain with volume fractions in the four-way coupling regime of near-spherical micro-particles falling under gravity. The method was successfully employed to measure the transverse velocity profile through the curtain, which is the first time that such a measurement has been performed. Other highly-fidelity experimental data, which is also well suited to model development and validation, include the particle mass flow rate, curtain thickness and opacity.

The effect of cohesion on the discharge of a granular material through the orifice of a silo

We present the results of both experimental and numerical investigations of the silo discharge for a cohesive granular material. In our study, thanks to a cohesion-controlled granular material (CCGM) we propose to investigate the effect of the cohesive length lc, on the discharge of a silo for two different configurations, one axisymmetrical, and one quasi-2D rectangular silo. In both configurations, an adjustable bottom is used to control the size of the orifice. As observed for cohesionless granular material by previous studies, the mass flow rate and the density through an orifice are mostly controlled by the diameter of the orifice D. The experimental results of the quasi-2D silo are compared with continuum numerical simulations.

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.

Discharge of a granular silo under mechanical vibrations

In this paper, we study the flow rate of model granular material in a silo under the influence of mechanical vibrations. Experimental measurements and discrete element simulations (DEM) are performed in a quasi-2D silo. The influence on the flow rate of the opening size and the vibration applied on the entire silo is studied. Two distinct regimes are evidenced, governed by the Froude number Fr and the relative frequency Ω. In the first regime, a decreased flow rate is observed when increasing the vibration intensity. This behavior is explained by the presence of reorganizations induced by the vibration, leading to a more homogeneous but also slower flow. In the second regime, an increased flow rate is evidenced when increasing the vibration intensity. We find this behavior comes from the intermittent nature of the flow, where the flow rate is directly controlled by the propagation of shock waves all along the silo.

Velocity scaling in the region of orifice influence in silo draining under gravity

This study utilizes computations based on a soft-particle discrete element method for investigating the scaling of velocity in the region of orifice influence situated directly above and in proximity to the outlet in a two-dimensional silo. The velocity at the exit scales with the outlet size (D), in striking agreement with the earlier studies. However, the scaling of velocity upstream of the outlet with D as the length scale does not exist. Consequently, we present a scaling with a length parameter h_{e} being the height of an equi-inertial curve, which is defined to be a curve on which the inertial number is constant, thereby consolidating the coexisting different flow regimes in a discharging silo. The velocity corresponding to an equi-inertial curve, when measured relative to the velocity at the outlet, scales very well with h_{e} for low inertial numbers belonging to the dense flow regime. However, such scaling does not hold for high inertial numbers corresponding to the rapid flow regime in the region located closer to the orifice. We tie this scaling breakdown to the velocity fluctuations in light of the similarity between the profiles of scaled relative velocity and the scaled kinetic pressure, suggesting h_{e} to be a promising candidate for unifying the kinematics of granular flow near the outlet in the silo.

Discharge of a silo through a lateral orifice: Role of the bottom inclination versus friction

In this work we propose to identify the relative role of the inclination of gravitational acceleration and friction on the discharge flow rate of a granular media from a rectangular silo by varying the silo geometry thanks to an inclined bottom which ends up at a lateral outlet. The study is motivated by a nuclear safety problem: a fuel rod (modeled by an elongated silo) accidentally releases fuel fragments (modeled by grains). We performed experiments where we independently measured the mass flow rate and the velocity profiles, together with discrete particle simulations and continuum simulations with a frictional rheology described by a μ(I) constitutive law and taking into account the wall friction. We study monolayer flows and three-dimensional flows, and we propose an analytical model that predicts the discharge flow rate of particles from a rectangular silo with an inclined bottom according to its outlet aspect ratio and the bottom inclination angle.

Particle flow rate in silos under rotational shear

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 [Phys. Rev. E 100, 012906 (2019)10.1103/PhysRevE.100.012906]. 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 nonmonotonic behavior is confirmed. Furthermore, using a coarse-graining technique, we compute the macroscopic density, momentum, and the stress tensor fields. These results show conclusively that changes in the discharge process are directly related to changes in the flow pattern from funnel flow to mass flow. Moreover, by decomposing the mass flux (linear momentum field) at the orifice into two main factors, macroscopic velocity and density fields, we obtain that the nonmonotonic behavior of the linear momentum is caused by density changes rather than by changes in the macroscopic velocity. In addition, by analyzing the spatial distribution of the kinetic stress, we find that for small orifices increasing rotational shear enhances the mean kinetic pressure 〈p^{k}〉 and the system dilatancy. This reduces the stability of the arches, and, consequently, the volumetric flow rate increases monotonically. For large orifices, however, we detected that 〈p^{k}〉 changes nonmonotonically, which might explain the nonmonotonic behavior of Q when varying the rotational shear.

Differential equation for the flow rate of discharging silos based on energy balance

Since the early work of Hagen [G. H. L. Hagen, Ber. Verhandl. K. Preuss. Akad. Wiss. Berlin 17, 35 (1852)] and Beverloo et al. [W. Beverloo et al., Chem. Eng. Sci. 15, 260 (1961)CESCAC0009-250910.1016/0009-2509(61)85030-6], 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 to 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 due to a compensation of energy terms. Moreover, this equation can be used to explore different conditions for silo discharges. In particular, we show how the effect of friction on the flow rate can be predicted. The theory is validated using discrete element method simulations.

Alveolar leak develops by a rich-get-richer process in ventilator-induced lung injury

Acute respiratory distress syndrome (ARDS) is a life-threatening condition for which there are currently no medical therapies other than supportive care involving the application of mechanical ventilation. However, mechanical ventilation itself can worsen ARDS by damaging the alveolocapillary barrier in the lungs. This allows plasma-derived fluid and proteins to leak into the airspaces of the lung where they interfere with the functioning of pulmonary surfactant, which increases the stresses of mechanical ventilation and worsens lung injury. Once such ventilator-induced lung injury (VILI) is underway, managing ARDS and saving the patient becomes increasingly problematic. Maintaining an intact alveolar barrier thus represents a crucial management goal, but the biophysical processes that perforate this barrier remain incompletely understood. To study the dynamics of barrier perforation, we subjected initially normal mice to an injurious ventilation regimen that imposed both volutrauma (overdistension injury) and atelectrauma (injury from repetitive reopening of closed airspaces) on the lung, and observed the rate at which macromolecules of various sizes leaked into the airspaces as a function of the degree of overall injury. Computational modeling applied to our findings suggests that perforations in the alveolocapillary barrier appear and progress according to a rich-get-richer mechanism in which the likelihood of a perforation getting larger increases with the size of the perforation. We suggest that atelectrauma causes the perforations after which volutrauma expands them. This mechanism explains why atelectrauma appears to be essential to the initiation of VILI in a normal lung, and why atelectrauma and volutrauma then act synergistically once VILI is underway.

Friction controls even submerged granular flows

We investigate the coupling between the interstitial medium and granular particles by studying the hopper flow of dry and submerged systems experimentally and numerically. In accordance with earlier studies, we find that the dry hopper empties at a constant rate. However, in the submerged system we observe the surging of the flow rate. We model both systems using the discrete element method, which we couple with computational fluid dynamics in the case of a submerged hopper. We are able to match the simulations and the experiments with good accuracy by fitting the particle-particle contact friction for each system separately. Submerging the hopper changes the particle-particle contact friction from μ_vacuum = 0.15 to μ_sub = 0.13, while all the other simulation parameters remain the same.

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.

Silo discharge of binary granular mixtures

We present numerical and experimental results on the mass flow rate during the discharge of three-dimensional silos filled with a bidisperse mixture of grains of different sizes. We analyzed the influence of the ratio between coarse and fine particles on the profile of volume fraction and velocity across the orifice. By using numerical simulations, we have shown that the velocity profile has the same shape as that in the monodisperse case and is insensitive to the composition of the mixture. On the contrary, the volume fraction profile is strongly affected by the composition of the mixture. Assuming that an effective particle size can be introduced to characterize the mixture, we have shown that previous expression for the mass flow rate of monodisperse particles can be used for binary mixtures. A comparison with Beverloo's correlation is also presented.