Command of active droplets in a nematic liquid crystal by an electric field

A water droplet placed in a thermotropic nematic liquid crystal creates a topological point-defect in its vicinity, a so-called hyperbolic hedgehog, when the director is anchored normally to the interface. When such a droplet contains active bacteria, the dipolar configuration of the director field enables its unidirectional propulsion by rectifying the flows caused by the bacteria. Here we report real-time control of both the propulsion direction and the speed of active droplets in a nematic by an ac electric field. The dielectric torque on the director leads to two effects: (i) realignment of the overall director outside the droplet and (ii) transformation of the point-defect into a disclination ring. The first effect redirects the trajectory of the active droplet when the direction of the electric field changes. The second effect decreases the speed since the disclination ring reduces the asymmetry of director field around the droplet. When the disclination expands to an equatorial ring with a quadrupolar symmetry, the droplet stops. The real-time control of the direction and speed of active colloids is a step forward as compared to the current approaches in which the trajectories are predesigned, and no control over speed is present.