Motion of grains in a vibrated U-tube

TL;DR

This study experimentally explores how the growth rate of a granular column in a vibrated U-tube varies with vibration intensity, revealing three distinct behavioral regimes analogous to phase transitions.

Contribution

It identifies and characterizes three different growth behaviors of grains in a vibrated U-tube as a function of vibration amplitude, providing a new understanding of granular dynamics under shaking.

Findings

Zero growth at low vibration, transitioning smoothly to growth.

Sigmoidal growth behavior at intermediate vibrations.

Abrupt cessation of growth at high vibration levels.

Abstract

We investigate experimentally the behavior of the rate of growth of a column of grains, in a partially filled vertically shaken U-tube. For the set of frequencies used we identify three qualitatively different behaviors for the growth rate $\gamma$ as a function of the dimensionless acceleration $\Gamma$: 1) an interval of zero growth for low $\Gamma$ with a smooth change to nonzero growth, analogous to a continuous phase transition; 2) a sigmoidal region for $\gamma$ at intermediate values of the dimensionless acceleration $\Gamma$; and 3) an abrupt change from high values of $\gamma$ to zero growth at high values of $\Gamma$, similar to a first order phase transition. We obtain that our data is well described by a simple differential equation for the change of the growth rate with the dimensionless acceleration of the vertical vibrations.