Model for Density Waves in Gravity-Driven Granular Flow in Narrow Pipes

TL;DR

This paper presents a one-dimensional model for gravity-driven granular flow in narrow pipes, revealing how density waves form based on collision dissipation and how flow rate relates to wave structure.

Contribution

It introduces a simple criterion for density wave formation and analyzes the relationship between grain number per wave and flow dynamics.

Findings

Density waves form when wall collision dissipation exceeds inter-particle dissipation.

Maximum flow rate occurs when the number of grains per density wave is large.

Number of grains per wave approaches a constant as total particles increase.

Abstract

A gravity-driven flow of grains through a narrow pipe in vacuum is studied by means of a one-dimensional model with two coefficients of restitution. Numerical simulations show clearly how density waves form when a strikingly simple criterion is fulfilled: that dissipation due to collisions between the grains and the walls of the pipe is greater per collision than that which stems from collisions between particles. Counterintuitively, the highest flow rate is observed when the number of grains per density wave grows large. We find strong indication that the number of grains per density wave always approaches a constant as the particle number tends to infinity, and that collapse to a single wave, which was often observed also in previous simulations, occurs because the number of grains is insufficient for multiple wave formation.