Institute of Physics, Academia Sinica, Taipei 115, Taiwan.
Phys Rev E. 2017 Sep;96(3-1):032906. doi: 10.1103/PhysRevE.96.032906. Epub 2017 Sep 14.
When grains flow out of a silo, flow rate W increases with exit size D. If D is too small, an arch may form and the flow may be blocked at the exit. To recover from clogging, the arch has to be destroyed. Here we construct a two-dimensional silo with movable exit and study the effects of exit oscillation (with amplitude A and frequency f) on flow rate, clogging, and unclogging of grains through the exit. We find that, if exit oscillates, W remains finite even when D (measured in unit of grain diameter) is only slightly larger than one. Surprisingly, while W increases with oscillation strength Γ≡4π^{2}Af^{2} as expected at small D, W decreases with Γ when D≥5 due to induced random motion of the grains at the exit. When D is small and oscillation speed v≡2πAf is slow, temporary clogging events cause the grains to flow intermittently. In this regime, W depends only on v-a feature consistent to a simple arch breaking mechanism, and the phase boundary of intermittent flow in the D-v plane is consistent to either a power law: D∝v^{-7} or an exponential form: D∝e^{-D/0.55}. Furthermore, the flow time statistic is Poissonian whereas the recovery time statistic follows a power-law distribution.
当谷物从筒仓流出时，流量$W$随出口尺寸$D$的增加而增加。如果$D$太小，可能会形成拱形，出口处的流动可能会被堵塞。为了从堵塞中恢复，拱形必须被破坏。在这里，我们构建了一个带有可移动出口的二维筒仓，并研究了出口振荡（幅度为$A$，频率为$f$）对通过出口的谷物流量、堵塞和疏通的影响。我们发现，即使当$D$（以谷物直径为单位测量）仅略大于 1 时，出口振荡也能使$W$保持有限。令人惊讶的是，虽然当$D\lt5$时，$W$随着预期的振荡强度$\Gamma≡4\pi^{2}Af^{2}$的增加而增加，但当$D\geq5$时，由于出口处的谷物随机运动，$W$随$\Gamma$的增加而减小。当$D$较小且振荡速度$v≡2\pi Af$较慢时，暂时的堵塞事件会导致谷物间歇性流动。在这种情况下，$W$仅取决于$v-a$，这与一个简单的拱形破坏机制一致，并且在$D-v$平面上的间歇性流动的相边界与幂律：$D∝v^{-7}$或指数形式：$D∝e^{-D/0.55}$一致。此外，流动时间统计是泊松分布，而恢复时间统计遵循幂律分布。
