Critical Transition between Intensive and Extensive Active Droplets

Most emulsions ripen with an average droplet size increasing in time. In chemically active emulsions, coarsening can be absent, leading to a nonequilibrium steady state with monodisperse droplet sizes. By considering a minimal model for phase separation and chemical reactions maintained away from equilibrium, we show that there is a supercritical transition controlled by the conserved quantity between two classes of chemically active droplets: intensive and extensive active droplets. While intensive droplets reach a stationary size mainly controlled by the interplay between reactions and diffusion, the size of an extensive active droplet scales with the system size. For intensive droplets, growth arrests at a finite size. Thus, they can be far apart from each other and evolve independently from other droplets in an active emulsion. The growth of extensive droplets, however, arrests due to the presence of other droplets in the emulsion. In both cases, monodisperse emulsions can emerge. We show how the supercritical transition between intensive and extensive active droplets affects shape instabilities, including the division of active droplets, paving the way for the observation of successive division events in chemically active emulsions.