Droplet and cluster formation in freely falling granular streams

TL;DR

This study uses molecular dynamics simulations to explore how inelastic collisions and attractive forces influence the formation of droplets and clusters in freely falling granular streams, revealing regimes from gas-like to liquid-like behaviors.

Contribution

It introduces a detailed simulation-based analysis of granular stream behaviors, highlighting the impact of energy dissipation and cohesion on structure formation, and proposes a simple energy balance model.

Findings

Inelastic collisions collimated the granular stream.

Short-range attractions led to droplet and cluster formation.

Identified a new regime with small aggregate capture from the gas phase.

Abstract

Particle beams are important tools for probing atomic and molecular interactions. Here we demonstrate that particle beams also offer a unique opportunity to investigate interactions in macroscopic systems, such as granular media. Motivated by recent experiments on streams of grains that exhibit liquid-like breakup into droplets, we use molecular dynamics simulations to investigate the evolution of a dense stream of macroscopic spheres accelerating out of an opening at the bottom of a reservoir. We show how nanoscale details associated with energy dissipation during collisions modify the stream's macroscopic behavior. We find that inelastic collisions collimate the stream, while the presence of short-range attractive interactions drives structure formation. Parameterizing the collision dynamics by the coefficient of restitution (i.e., the ratio of relative velocities before and after impact) and the strength of the cohesive interaction, we map out a spectrum of behaviors that ranges from gas-like jets in which all grains drift apart to liquid-like streams that break into large droplets containing hundreds of grains. We also find a new, intermediate regime in which small aggregates form by capture from the gas phase, similar to what can be observed in molecular beams. Our results show that nearly all aspects of stream behavior are closely related to the velocity gradient associated with vertical free fall. Led by this observation, we propose a simple energy balance model to explain the droplet formation process. The qualitative as well as many quantitative features of the simulations and the model compare well with available experimental data and provide a first quantitative measure of the role of attractions in freely cooling granular streams.