Topology controls flow patterns in active double emulsions.

Active emulsions and liquid crystalline shells are intriguing and experimentally realisable types of topological matter. Here we numerically study the morphology and spatiotemporal dynamics of a double emulsion, where one or two passive small droplets are embedded in a larger active droplet. We find activity introduces a variety of rich and nontrivial nonequilibrium states in the system. First, a double emulsion with a single active droplet becomes self-motile, and there is a transition between translational and rotational motion: both of these regimes remain defect-free, hence topologically trivial. Second, a pair of particles nucleate one or more disclination loops, with conformational dynamics resembling a rotor or chaotic oscillator, accessed by tuning activity. In the first state a single, topologically charged, disclination loop powers the rotation. In the latter state, this disclination stretches and writhes in 3D, continuously undergoing recombination to yield an example of an active living polymer. These emulsions can be self-assembled in the lab, and provide a pathway to form flow and topological patterns in active matter in a controlled way, as opposed to bulk systems that typically yield active turbulence.