Dimensional analysis for clogging of grains in two and three dimensions

TL;DR

This study uses dimensional analysis and simulations to derive a scaling law for the mean avalanche size in granular clogging, unifying data across different experiments and dimensions.

Contribution

It introduces a universal scaling equation for clogging that incorporates particle and system parameters, validated by simulations and literature data.

Findings

The scaling law fits diverse experimental and simulation data.

The mean avalanche size depends on particle size, orifice size, density, gravity, and elasticity.

The model applies to both 2D and 3D granular systems.

Abstract

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.