Activity-induced droplet propulsion and multifractality

We elucidate the crucial role that confinement plays in collective and emergent behaviors in active- or living-matter systems by developing 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 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 superdiffusive 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.