Tunable Persistent Random Walk in Swimming Droplets

Abstract

We characterize the motility of athermal swimming droplets within the framework of a persistent random walk. Just like active colloids, their trajectories can be modeled with a constant velocity V and a slow angular diffusion, but the random changes in direction are not thermally driven. Instead, V is determined by the interfacial tension gradient along the droplet surface, while reorientation of the surfactant gradient leads to changes in direction with a persistence time τ. We show that the origin of locomotion is the difference in the critical micellar concentration in the front and the back of the droplet, ΔCMC. Tuning this parameter by salt controls V from 3 to 15 diameters d/s. Surfactant concentration has little effect on speed, but leads to a dramatic decrease in τ over 4 orders of magnitude. The corresponding range of the persistence length ℓ=Vτ extends beyond the realm of synthetic or living swimmers, in which V is limited by fuel consumption and τ is set by thermal fluctuations or biological activity, respectively. Our tunable swimmers are ideal candidates for the study of the departure from equilibrium to high levels of activity. We show that their collective behavior exhibits the formation of active clusters of a well-defined size.