Speed-Dispersion Induced Alignment : a 1D model inspired by swimming droplets experiments

TL;DR

This paper introduces a 1D model inspired by experiments with self-propelled droplets, demonstrating how speed dispersion and lack of Galilean invariance induce alignment and collective motion, with transient condensation phenomena observed.

Contribution

The paper proposes a minimalistic 1D active particle model capturing speed dispersion and Galilean invariance effects, revealing a transition to collective motion and transient condensation.

Findings

Model exhibits a transition to collective motion in 1D.

Condensation occurs as a transient slowing down before alignment.

Analytical and numerical evidence support the dynamical behaviors.

Abstract

We investigate the collective dynamics of self-propelled droplets, confined in a one dimensional micro-fluidic channel. On one hand, neighboring droplets align and form large trains of droplets moving in the same direction. On the other hand, the droplets condensates, leaving large regions with very low density. A careful examination of the interactions between two "colliding" droplets demonstrates that local alignment takes place as a result of the interplay between the dispersion of their speeds and the absence of Galilean invariance. Inspired by these observations, we propose a minimalistic 1D model of active particles reproducing such dynamical rules and, combining analytical arguments and numerical evidences, we show that the model exhibits a transition to collective motion in 1D for a large range of values of the control parameters. Condensation takes place as a transient phenomena which tremendously slows down the dynamics, before the system eventually settles into a homogeneous aligned phase.