Tuning the motility of self-propelled droplets: from persistent to stochastic*

Active droplets produce isotropic concentration gradients in the solution. These solute-mediated interactions depend on the size of the droplet and on the composition of the solvent, as shown in the case of di-ethyl phthalate (DEP) droplets in an aqueous solution of sodium dodecyl sulphate (SDS) [P. G. Moerman et al. PRE 96, 032607 (2017)]. When the fluctuations of these interactions are sufficient to break the symmetry of this dissolution gradient, a self-sustained motion is initiated. These droplets exhibit different motility profiles, from ballistic to diffusive. We use the rotational diffusion model to describe the motility of these swimmers. For a given droplet size, we tune the concentration of surfactant in the solution in order to control the droplet solubility. We show that contrary to Janus particles, the persistence length of the trajectory decreases when adding more fuel (surfactant) in the system: the sensitivity to fluctuations of local fuel concentration increases.