4/3-Law of Granular Particles Flowing through a Vertical Pipe

TL;DR

This study investigates density waves in granular flow through a vertical pipe, revealing a power-law frequency spectrum with an exponent of 4/3, supported by experiments, simulations, and theoretical modeling.

Contribution

It introduces a simple one-dimensional model that reproduces the 4/3 exponent observed in granular flow density waves.

Findings

Density waves exhibit a power-law spectrum with exponent ~4/3.

The model successfully reproduces the observed spectral behavior.

Experimental and simulation results are consistent with theoretical analysis.

Abstract

Density waves of granular material (sand) flowing through a vertical pipe have been investigated. Clear density waves emerge when the cock attached to bottom end of the pipe is closed. The FFT power spectra were found to show a stable power-law form $ P(f) \sim f^{-\alpha}. $ The value of the exponent was evaluated as $\alpha \cong 4/3$. We also introduce a simple one-dimensional model which reproduces $\alpha = 4/3$ from both simulation and theoretical analysis. (to be published in Phys.Rev.Lett.)