Tuning active emulsion dynamics via surfactants and topology

. We study water-in-oil emulsion droplets, running the Belousov-Zhabotinsky reaction, that form a new type of synthetic active matter unit. These droplets, stabilised by surfactants dispersed in the oil medium, are capable of internal chemical oscillations and self-propulsion. Here we present studies of networks of such self-propelled chemical oscillators and show that the resulting dynamics depend strongly on the topology of the active matter units and their connections. The chemical oscillations can couple via the exchange of promoter and inhibitor type of reaction intermediates across the droplets under precise conditions of surfactant bilayer formation between the droplets. The self-emerging synchronization dynamics are then characterized by the topology of the oscillator networks. Further, we show that the chemical oscillations inside the droplets cause oscillatory speed variations in the motion of individual droplets, extending our previous studies on such swimmers. Finally, we demonstrate that qualitatively new types of self-propelled motion can occur when simple droplet networks, for example two droplets connected by a bilayer, are set into motion. Altogether, these results lead to exciting possibilities in future studies of autonomous active matter. Graphical abstract