Activity-induced droplet propulsion and multifractality

TL;DR

This paper presents a minimal hydrodynamic model for active droplets containing contractile swimmers, revealing a transition from rectilinear to chaotic motion and multifractal interface fluctuations as activity increases.

Contribution

It introduces a novel scalar order parameter-based model capturing activity-induced droplet dynamics without orientational order.

Findings

At low activity, droplets self-propel with rectilinear motion.

Increasing activity leads to chaotic super-diffusive motion.

Droplet interfaces exhibit multifractal fluctuations with calculable spectra.

Abstract

We develop a minimal hydrodynamic model, without an orientational order parameter, for assemblies of contractile swimmers encapsulated in a droplet of a binary-fluid emulsion. Our model uses two coupled scalar order parameters, $\phi$ and $\psi$, which capture, respectively, the droplet interface and the activity of the contractile swimmers inside this droplet. These order parameters are also coupled to the velocity field $\bm u$. At low activity, our model yields a self-propelling droplet whose center of mass $(CM)$ displays rectilinear motion, powered by the spatiotemporal evolution of the field $\psi$, which leads to a time-dependent vortex dipole at one end of the droplet. As we increase the activity, this $CM$ shows chaotic super-diffusive motion, which we characterize by its mean-square displacement; and the droplet interface exhibits multifractal fluctuations, whose spectrum of exponents we calculate. We explore the implications of our results for experiments on active droplets of contractile swimmers.