Role of vibrations in the jamming and unjamming of grains discharging from a silo

We present experimental results of the jamming of noncohesive particles discharged from a flat bottomed silo subjected to vertical vibration. When the exit orifice is only a few grain diameters wide, the flow can be arrested due to the formation of blocking arches. Hence, an external excitation is needed to resume the flow. The use of a continuous gentle vibration is a usual technique to ease the flow in such situations. Even though jamming is less frequent, it is still an issue in vibrated silos. There are, in principle, two possible mechanisms through which vibrations may facilitate the flow: (i) a decrease in the probability of the formation of blocking arches and (ii) the breakage of blocking arches once they have been formed. By measuring the time intervals inside an avalanche during which no particles flow through the outlet, we are able to estimate the probability of breaking a blocking arch by vibrations. The result agrees with the prediction of a bivariate probabilistic model in which the formation of blocking arches is equally probable in vibrated and nonvibrated silos. This indicates that the second aforementioned mechanism is mainly responsible for improving the flowability in gently vibrated silos.

Figure 1

Experimental device. S: silo; V: pneumatic vibrator; N: damping and isolation system (air cushions and valves); P: photosensor; A: compressed air duct; B: box; S: scales. The inset shows a photograph (from the bottom) and a sketch of the cross section of the changeable part in which the hole is bored.

Figure 2

Signal from the photosensor at the silo exit: a value of 1 indicates that a particle is blocking the beam, zero means that the beam is unobstructed. (a) Nonvibrated silo. (b) Vibrated silo. (c) A zoom of the signal shown in (b) during the first three seconds, the same time stretch as in (a). All the data shown have been obtained for an orifice size $R=3.05$.

Figure 3

Probability $n_s\left(R,\Gamma \right)$ of finding an avalanche of size $s$ for an orifice size $R=3.02$, without vibration ($\Gamma =0$, $◼$) and with vibration ($\Gamma =0.22$, $○$). The solid lines correspond to fits using Eq. (4). For the nonvibrated silo, the fitting parameters are $p=0.981$ and $q=0$. For the vibrated silo $p=0.981$ and $q=0.836$.

Figure 4

Jamming probability $J_{100}\left(R,\Gamma \right)$, i.e., the probability that the silo gets jammed before 100 particles flow through the outlet, as a function of $R$, for the vibrated $(○)$ and the nonvibrated $(◼)$ silo. The lines correspond to a fit using Eq. (2). The “weak jamming” probability $J_{100}^{\text{w}}\left(R\right)$ for the avalanches within an avalanche is also shown $(△)$.

Figure 5

Mean avalanche $⟨s⟩$ versus the dimensionless radius $R$ for the vibrated $(○)$ and nonvibrated $(◼)$ silo. The solid lines correspond to fits using Eq. (1) with the parameters given in the text. The dotted line and the dashed line correspond to the values of $R_c$ used in the fits.

Figure 6

Probability $q$ that a blocking arch is destabilized due to the vertical vibration as a function of the opening size $R$. Results obtained with the probabilistic model, in which $p$ does not depend on $\Gamma$ (solid circles). Results obtained from the analysis of the weak jams (open squares). The data correspond to several sets of experiments; for some of them both methods were implemented, while for others only one of the measurements was performed.

Figure 7

Normalized histograms of the time intervals $\left(\Delta t\right)$ within an avalanche during which there are no particles flowing through the orifice. Closed (open) symbols represent the data obtained with the nonvibrated (vibrated) silo for the values of $R$ indicated in the legend. For each $R$, measurements have been carried out within, at least, 3000 avalanches.