LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
Departamento de Física y Matemática Aplicada, Facultad de Ciencias, Universidad de Navarra, 31080 Pamplona, Spain.
Phys Rev Lett. 2018 May 11;120(19):198002. doi: 10.1103/PhysRevLett.120.198002.
Granular flows through narrow outlets may be interrupted by the formation of arches or vaults that clog the exit. These clogs may be destroyed by vibrations. A feature which remains elusive is the broad distribution p(τ) of clog lifetimes τ measured under constant vibrations. Here, we propose a simple model for arch breaking, in which the vibrations are formally equivalent to thermal fluctuations in a Langevin equation; the rupture of an arch corresponds to the escape from an energy trap. We infer the distribution of trap depths from experiments made in two-dimensional hoppers. Using this distribution, we show that the model captures the empirically observed heavy tails in p(τ). These heavy tails flatten at large τ, consistently with experimental observations under weak vibrations. But, here, we find that this flattening is systematic, which casts doubt on the ability of gentle vibrations to restore a finite outflow forever. The trap model also replicates recent results on the effect of increasing gravity on the statistics of clog formation in a static silo. Therefore, the proposed framework points to a common physical underpinning to the processes of clogging and unclogging, despite their different statistics.
细颗粒通过狭窄出口的流动可能会由于拱或拱顶的形成而中断，这些拱或拱顶会堵塞出口。这些堵塞物可能会被振动破坏。一个难以捉摸的特征是在恒定振动下测量的堵塞物寿命 τ 的广泛分布 p(τ)。在这里，我们提出了一个简单的拱破坏模型，其中振动在 Langevin 方程中形式上等效于热涨落；拱的破裂对应于从能量陷阱中逃脱。我们从二维料斗中的实验推断出陷阱深度的分布。使用这个分布，我们表明该模型捕获了实验观测到的 p(τ)中的重尾分布。这些重尾在 τ 较大时变平，与弱振动下的实验观察一致。但是，在这里，我们发现这种变平是系统的，这使得温和振动永远恢复有限流出的能力受到怀疑。该陷阱模型还复制了最近关于增加重力对静态筒仓中堵塞形成统计的影响的结果。因此，尽管它们的统计数据不同，但所提出的框架指出了堵塞和解堵过程的共同物理基础。
