Density Waves in the Flows of Granular Media

TL;DR

This paper investigates density waves in granular flows through tubes and hoppers using analytic models and molecular dynamics simulations, identifying kinetic and dynamic wave types and their conditions.

Contribution

It introduces a combined analytical and simulation approach to characterize density waves in granular media flows, including new conditions for wave existence.

Findings

Existence of kinetic and dynamic density waves in tubes and hoppers.

Reproduction of density waves in MD simulations for tubes.

Identification of kinetic waves based on flux-density relationships.

Abstract

We study density waves in the flows of granular particles through vertical tubes and hoppers using both analytic methods and molecular dynamics (MD) simulations. We construct equations of motion for quasi one-dimensional systems. The equations, combined with the Bagnold's law for friction, are used to describe the time evolutions of the density and the velocity fields for narrow tubes and hoppers. The solutions of the equations can have two types of density waves, kinetic and dynamic. For tubes, we can show the existence of kinetic waves, and obtain the condition for dynamic waves for tubes from the equations. For hoppers, we obtain the solutions of the equations up to the first order of the opening angle, which also show the existence of kinetic waves. We reproduce density waves in the MD simulations for tubes. The waves are believed to be kinetic based on a few evidences, including a well defined flux-density curve. In MD simulations of flows in hoppers, we find density waves, which are also believed to be kinetic.