Spontaneous jamming and unjamming in a hopper with multiple exit orifices

We show that the flow of granular material inside a two-dimensional flat bottomed hopper is altered significantly by having more than one exit orifice. For hoppers with small orifice widths, intermittent flow through one orifice enables the resumption of flow through the adjacent jammed orifice, thus displaying a sequence of jamming and unjamming events. Using discrete element simulations, we show that the total amount of granular material (i.e., avalanche size) emanating from all the orifices combined can be enhanced by about an order of magnitude difference by simply adjusting the interorifice distance. The unjamming is driven primarily by fluctuations alone when the interorifice distance is large, but when the orifices are brought close enough, the fluctuations along with the mean flow cause the flow to unjam.

Figure 1

Sample snapshots of the flow occurrence in a two-orifice hopper for a specified $w$ and $D$. (a) Flow occurring through the left orifice while the right orifice is jammed. (b) Spontaneous flow reinitialization through the right orifice at a later time.

Figure 2

Jamming characteristics for varying distances $\left(w\right)$ between orifices of different widths $\left(D\right)$. (a) Mean avalanche size per unit orifice $\left(s_m\right)$ plotted against the interorifice distance $\left(w\right)$. The dashed lines correspond to the avalanche size $\left(s_0\right)$ for a hopper having a single orifice of width $D$. (b) Scaled mean avalanche size $\left(s_m/s_0\right)$ plotted against the interorifice distance $\left(w\right)$.

Figure 3

(a) Schematic of a single-orifice hopper of width $L$ and height $H$. (b) Variation of mean avalanche size $\left(s_0\right)$ for a hopper with a single orifice of width $D$. Variation of (c) mean velocity $v$, (d) rms velocity $u$, and (e) rms normal stress $T$ along the horizontal direction $\left(x\right)$ obtained over a region $3d$ in the $z$ direction for four different orifice widths. Please refer to the text for the method to obtain the mean and rms quantities. The mean velocity and rms velocity are measured in units of $d/\tau$, while the rms stress is measured in units of $mg/d^2$.

Figure 4

Correlation between the mean avalanche size per unit orifice width $\left(s_m\right)$ and (a) the rms velocity and (b) the rms normal stress. All quantities are obtained at distance $\left(w\right)$. The dashed lines show an exponential fit. (c), (d) Data in (a) and (b), respectively, after normalizing $s_m$ with the mean avalanche size $\left(s_0\right)$ for a hopper with a single orifice. The solid line in (c) and (d) shows an exponential fit.