Enhancement of the flow of vibrated grains through narrow apertures by addition of small particles

We analyze the flow and clogging of circular grains passing through a small aperture under vibration in two dimensions. Via discrete element method simulations, we show that when grains smaller than the original ones are introduced in the system as an additive, the net flow of the original species can be significantly increased. Moreover, there is an optimal radius of the additive particles that maximizes the effect. This finding may constitute the basis for technological applications not only concerning the flow of granular materials but also regarding active matter, including pedestrian evacuation.

Figure 1

Sketch of the silo and hopper. The grey circles correspond to the original species and the black circles to the added particles.

Figure 2

Total particle flow rate $Q$ (a) and particle flow rate of the the original particles $\tilde{Q}$ (b) as a function of the size ratio $r$ for two mixing ratios $\chi =0.2$ and 0.4 using added particles. The plotted quantities are divided by $Q_P$, which is the flow rate of the pure system (original particles alone). The box-plots indicate the quantiles for $0.065\%,25\%,50\%$ (median), $75\%$ and $99.35\%$, and rhombuses indicate outliers calculated over 50 realizations. The horizontal lines correspond to the quantiles for $25\%$ (bottom orange-dashed), $50\%$ (blue-solid), and $75\%$ (top orange-dashed) for a system of pure original particles. The arrows indicate the theoretical limiting value $Q=Q_P/(1-\chi )$ for $r\to 0$ (see text).

Figure 3

Snapshots from a simulations with original particles (left) and with added particles of $r=0.4$ (right). These are long-lasting arches (more than 5 s) that needed to be removed. The branch vectors of the particles forming each arch are indicated with white segments. The large particle (indicated as “a”) presents branch vectors with an angle $\theta >{180}^{\circ }$ due to the neighboring small particle. This makes it especially unstable against vibrations [3].

Figure 4

Survival function for different values of (a) $\chi$ and (b) $r$. In both panels the black solid line corresponds to the pure system with no added particles.

Figure 5

(a) Number $N_{\mathrm{arch}}$ of long-lasting arches that block the aperture as a function of $r$ for $\chi =0.4$. Long lasting means $\tau >5$ s. The error bars correspond to the standard deviation over 50 realizations. (b) Number $N_a$ of small added particles per arch in long-lasting arches ($\tau >5$ s) as a function of $r$ for $\chi =0.4$.