Length scale of density waves in the gravitational flow of fine grains in pipes

TL;DR

This paper investigates the length scale of density waves in the gravitational flow of fine grains in pipes, using a one-dimensional model and stability analysis, and compares the results with experimental data.

Contribution

It introduces a linear stability analysis of a new one-dimensional model to estimate the density wave length scale in granular pipe flow.

Findings

Identification of long-wavelength instability in density waves

Estimation of the density wave length scale from a cut-off wavenumber

Model validation through comparison with experimental data

Abstract

Gravitational flow of grains in pipes is frequently encountered in industry. When the grains and pipes are size-constrained, granular flow may result in density waves consisting of alternate high- and low-compactness regions. This paper discusses the length scale of density waves that appear when fine grains fall vertically in pipes. A one-dimensional model and a linear stability analysis of the model are presented. The analysis suggests the presence of long-wavelength instability for the most unstable mode, moreover, a cut-off wavenumber from which the length scale is estimated. Finally, the model results are compared to experimental data.