Cluster formation in active emulsion.

This article focuses on the conditions for cluster formation in an active octane-in-water emulsion activated by ammonia, where droplet motion is driven by Marangoni flow resulting from surface tension gradients. Experimental results demonstrate that clusters form around immobile droplet nuclei when the average droplet velocity is below a critical value, which depends inversely on droplet density in the emulsion. The study presents a phenomenological kinetic model showing that the rate of droplet attachment to clusters is proportional to droplet velocity, while detachment rate scales with the square of velocity, explaining the existence of the critical velocity threshold for cluster growth. These findings contribute to understanding the collective behavior of active droplets in emulsions and the interplay between droplet velocity and density in cluster dynamics.