This study utilizes computations based on soft-particle discrete element method for investigating the scaling of velocity in a two-dimensional silo draining under gravity. We focus on the region situated directly above and in proximity to the outlet, referred to as the region of orifice influence (ROI). The velocity at the exit scales with the outlet size, in agreement with previous studies. The velocity in the ROI upstream of the outlet, however, does not collapse to a single curve when scaled with the outlet size. We show that the height of an $\textit{equi-inertial}$ curve, which is defined to be a curve on which the inertial number is constant, can be employed for scaling the velocity in the ROI. The velocity corresponding to an equi-inertial curve, when measured relative to the outlet velocity, is considered for scaling. Results show that the scaling holds very well for low inertial number corresponding to the dense flow regime, whereas it breaks down for high inertial number region.
We investigate the mixing characteristics of dry granular material while draining down a silo with multiple exit orifices. The mixing in the silo, which otherwise consists of noninteracting stagnant and flow regions, is observed to improve significantly when the flow through specific orifices is stopped intermittently. This momentary stoppage of flow through the orifice is either controlled manually or is chosen by the system itself when the orifice width is small enough to cause spontaneous jamming and unjamming. We observe that the overall mixing behavior shows a systematic dependence on the…
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 …
Granular material in a silo with two openings can display a `flow rate dip', where a non-monotonic relationship between flow rate and orifice separation occurs. In this paper we study continuum modelling of the silo with two openings. We find that the $μ(I)$ rheology can capture the flow rate dip if physically relevant friction parameters are used. We also extend the model by accounting for wall friction, dilatancy, and non-local effects. We find that accounting for the wall friction using a Hele-Shaw model better replicates the qualitative characteristics of the flow rate dip seen in experime…
For granular materials falling through a circular exit at the bottom of a silo, no continuous flow can be sustained when the diameter D of the exit is less than 5 times the characteristic size of the grains. If the bottom of the silo rotates horizontally with respect to the wall of the silo, finite flow rate can be sustained even at small D. We investigate the effect of bottom rotation to the flow rate of a cylindrical silo filled with mono-disperse plastic beads of d = 6 mm diameter. We find that the flow rate W follows Beverloo Law down to D = 1.2d and that W increases with the rotation rate…
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…
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 ($y_t$)…
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, …
We measure the flow of granular materials inside a quasi-two dimensional silo as it drains and compare the data with some existing models. The particles inside the silo are imaged and tracked with unprecedented resolution in both space and time to obtain their velocity and diffusion properties. The data obtained by varying the orifice width and the hopper angle allows us to thoroughly test models of gravity driven flows inside these geometries. All of our measured velocity profiles are smooth and free of the shock-like discontinuities ("rupture zones") predicted by critical state soil mechanic…
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…
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…
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…
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 regi…
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…
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…
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…
