Flow and clogging in a silo with an obstacle above the orifice

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 features of arches is studied. These results reinforce previous evidence of the pressure reduction induced by the obstacle. In addition, it is shown how the mean avalanche size and the average flow rate are not necessarily linked. On the other hand, a close relationship is suggested between the mean avalanche size and the flow rate fluctuations.

Figure 1

Photograph of an arch formed above the outlet. The dashed horizontal segment marks the line where the crossing of each bead is scored to compute passage times. $R$ is the length (size) of the outlet and $h$ is the distance from the bottom of the obstacle to the outlet. Particles forming the arch are indicated by crosses and particles forming the base of the arch are indicated by circles.

Figure 2

(a) Mean avalanche size vs $h$ for $R=3.13$ mm ($\diamond$), $R=4.20$ mm ($\circ$), and $R=4.55$ mm ($\square$). Horizontal lines indicate the values of $\langle s\rangle$ when $h\to \infty$. (b) Same results as in panel (a), but the mean avalanche size is divided by the mean avalanche size at $h\to \infty$ corresponding to each value of $R$.

Figure 3

(a) Average flow rate vs $h$ for $R=3.13$ mm ($\diamond$), $R=4.20$ mm ($\circ$), and $R=4.55$ mm ($\square$). Error bars are confidence intervals at $95\%$. Horizontal lines indicate the values of $\langle q\rangle$ when $h\to \infty$. (b) Same results as in panel (a) but dividing the average flow rate by the average flow rate at $h\to \infty$ corresponding to each value of $R$.

Figure 4

Time series of the flow rate q (beads per unit time as measured at nonoverlapping time windows of 30 ms) for an orifice size $R=4.2$ and an obstacle of 10 mm diameter placed at (a) $h\to \infty$ and (b) $h=4.20$ mm. In panels (c)–(e) the normalized histograms of the flow rate values are presented for different obstacle positions, namely (c) $h\to \infty$, (d) $h=9.04$ mm, (e) $h=4.82$ mm, and (f) $h=4.20$ mm.

Figure 5

Coefficient of variation, i.e., standard deviation of the values obtained for the flow rate $q$ rescaled by $\langle q\rangle$, vs the obstacle position for $R=3.13$ mm ($\diamond$), $R=4.20$ mm ($\circ$), and $R=4.55$ mm ($\square$). The horizontal lines indicate the values of ${\sigma }_q/\langle q\rangle$ for $h\to \infty$ for each value of $R$.

Figure 6

(a) Mean avalanche size, (b) average flow rate, and (c) coefficient of variation for different obstacle diameters ($D_I$). In all the graphs $D_I=0$ represents the values obtained for the silo without obstacle. All the obstacles were placed at $h=3.05\pm 0.07$ mm in a silo where the outlet size was $R=3.13\pm 0.05$ mm. Error bars [which are too small to be perceived in panel (a)] are confidence intervals at $95\%$.

Figure 7

(a) Normalized histogram of the size of the arches measured in number of beads ($\eta$). (b) Normalized histogram of the arch height (note the semilogarithmic scale). (c) Normalized histogram of the arch span (in semilogarithmic scale). (d) Normalized histogram (in semilogarithmic scale) of the aspect ratios ($A$) of the arches, defined as half the span divided by the height. In all the graphs measurements have been carried out in a silo with an outlet size $R=4.2$ mm, without an obstacle ($\square$) and with a 10-mm-diameter obstacle placed at $h=4.2$ mm ($\circ$).

Figure 8

Average aspect ratio for arches as a function of their number of particles ($\eta$). As in Fig. 7, the measurements have been carried out in a silo with an outlet size $R=4.2$ mm, without an obstacle ($\square$) and with a 10-mm-diameter obstacle placed at $h=4.2$ mm ($\circ$). The error bars are the $95\%$ confidence intervals.