The Arrested Emulsion

Phase separation in passive mixtures follows a predictable trajectory. Small droplets dissolve, large droplets grow, and the system coarsens toward a single macroscopic domain. Ostwald ripening — the thermodynamic imperative that large things eat small things — drives this relentlessly. Arresting coarsening usually requires external intervention: surfactants, gelation, jamming at the interface.

Active emulsions arrest themselves.

The mechanism requires only two ingredients: two molecular species with different diffusivities, and active interconversion between them. When the faster-diffusing species accumulates inside droplets — drawn in by the same thermodynamics that drives phase separation — it creates a compositional gradient. The fast species leaks outward rapidly, screening incoming material from the surrounding bath. The droplet builds its own buffer zone.

The arrest is self-limiting. A droplet that grows larger accumulates more of the fast-diffusing species, which strengthens the outward flux that opposes further growth. A droplet that shrinks loses its buffer and becomes vulnerable to dissolution — but only until it reaches the size where the compositional feedback stabilizes again. The result is a characteristic length scale set by the ratio of diffusivities and the interconversion rate, not by the droplet’s history.

No interaction asymmetry between species is required. No special interfacial chemistry. Just the fact that the component the droplet preferentially attracts is also the component best positioned to leave. The system hoards what it cannot hold, and the hoarding is what prevents the holding from going to completion.

The principle is that a system can arrest its own coarsening when its preferred accumulation creates a leak that screens further accumulation. The size selection is not imposed from outside but emerges from the internal tension between attraction and escape — the droplet’s appetite produces exactly the resistance that limits its own growth.