Motility-induced droplet self-propulsion and multifractal interface fluctuations*

We develop a minimal phase-field model to study phase separation in an assembly of contractile micro-swimmers confined to a binary-emulsion droplet. Our model uses two scalar order parameters: one to capture the droplet's interface and another to capture the density of the contractile swimmers. Our model reveals, at low activity, straight-line motion of the centre-of-mass (CM) of the droplet powered by an emergent vortex dipole. With increasing activity, the CM displays chaotic super-diffusive motion, which we characterize by its mean-square-displacement; the active field generates low-Reynolds-number turbulence inside the droplet, which leads to multifractal interfacial deformations.