Memory effects in active droplets

Marangoni-driven self-propelled droplets have attracted considerable attention as a platform to study active soft matter and collective behavior. The speed of active drops is generally assumed to be determined by instantaneous diameter and solubilization rate, which together dictate the spontaneously generated interfacial tension gradients across the drop surface and induce propulsion; the history of the droplet has not before been considered. Here, we report that active droplets can exhibit a type of memory wherein the temporal history of the droplet, particularly the starting diameter, influences the droplet speed. For example, two droplets of identical instantaneous diameter in the same local chemical environment can exhibit dramatically different instantaneous velocities depending upon their initial diameter. This effect is observed for a range of droplet oils and common ionic surfactants. The relationships between drop diameter, velocity, and solubilization rate were examined for several ionic and nonionic surfactants and suggest that droplet motility only is present when solubilization is interfacially limited, as opposed to diffusion limited. Oil droplets in ionic surfactant solutions also undergo a transition from motile to non-motile, where the diameter at the transitionary point depends upon initial drop diameter. We hypothesize that this memory behavior may result from an interfacial phase transition, as hinted at by observed visual deformations on drop interfaces under some circumstances. We believe this work provides insight as to how memory may be imparted in active droplet systems, highlights the importance of non-equilibrium phenomena in active materials, and offers valuable insights for the design of adaptive, dynamic droplet systems.