Stability of freely falling granular streams

TL;DR

This paper investigates the stability and breakup of freely falling granular streams using simulations and hydrodynamics, revealing how cohesive energy influences droplet formation and flow stability over time.

Contribution

It provides a combined simulation and theoretical analysis of granular stream breakup, highlighting the stability conditions and pattern formation over time.

Findings

Stream breaks into droplets with size depending on cohesive energy

Flow is stable initially but becomes unstable at long times

Perturbation growth depends on the timing of fluctuations

Abstract

A freely falling stream of weakly cohesive granular particles is modeled and analysed with help of event driven simulations and continuum hydrodynamics. The former show a breakup of the stream into droplets, whose size is measured as a function of cohesive energy. Extensional flow is an exact solution of the one-dimensional Navier-Stokes equation, corresponding to a strain rate, decaying like 1/t from its initial value, gammaDot0. Expanding around this basic state, we show that the flow is stable for short times (gammaDot0 * t << 1), whereas for long times (gammaDot0 * t >> 1) perturbations of all wavelength grow. The growthrate of a given wavelength depends on the instant of time when the fluctuation occurs, so that the observable patterns can vary considerably.