标题： 颗粒在二维和三维中的堵塞量纲分析 显示英文标题

标题： Dimensional analysis for clogging of grains in two and three dimensions

摘要： 我们进行标准的量纲分析（Vaschy--Buckingham$\Pi$-定理）以确定当颗粒通过并堵塞在平底料仓底部的小孔时的平均雪崩大小$\langle s \rangle$。 我们考虑颗粒直径$d$、小孔直径$D$、颗粒密度$\rho$、颗粒杨氏模量$E$和重力加速度$g$的影响。 我们既进行离散元方法模拟，又整理文献中的可用数据以采样参数空间。 我们发现，我们在多个实验和模拟中对摩擦颗粒的模拟和数据与标度方程$\ln (\langle s \rangle+1) = A_\alpha (D/d-1)^{\alpha} + B_\alpha \sqrt{\rho g d / E}$一致，其中$A_\alpha$和$B_\alpha$是经验常数，$\alpha$是系统的维度（$\alpha=2$和$\alpha=3$分别对应二维和三维）。 该表达式成功地综合了多种相关堵塞系统的堵塞行为，并激发了对未来扩展到更复杂配置的研究，例如涉及非常低摩擦粒子或外部振动的情况。 显示英文摘要

摘要： We conduct standard dimensional analysis (Vaschy--Buckingham $\Pi$-theorem) for the mean avalanche size $\langle s \rangle$ when particles flow through, and clog at, a small orifice on the base of a flat-bottomed silo. We consider the effect of particle diameter $d$, orifice diameter $D$, particle density $\rho$, particle Young's modulus $E$ and acceleration of gravity $g$. We both perform discrete element method simulations and compile available data in the literature in order to sample the parameter space. We find that our simulations and data across many experiments and simulations of frictional grains are consistent with the scaling equation $\ln (\langle s \rangle+1) = A_\alpha (D/d-1)^{\alpha} + B_\alpha \sqrt{\rho g d / E}$, where $A_\alpha$ and $B_\alpha$ are empirical constants and $\alpha$ is the dimensionality of the system ($\alpha=2$ and $\alpha=3$ for 2D and 3D, respectively). This expression successfully synthesizes the clogging behavior of a number of related clogging systems and motivates future extensions to more complex configurations involving, for example, very low friction particles or external vibrations.