Predicting Size and Velocity in Collectively Moving Active Droplets

Traditionally, the concept of size control has been discussed primarily in the context of reaction–diffusion systems, a class of active matter with dissipative chemical reactions between sticky and non-sticky polymers. Such models have been used to describe biomolecular condensates in which chemical modifications convert phase-separating molecules into non-phase-separating ones. However, many other types of active systems also exhibit finite-sized droplets. One notable example is the non-reciprocal Cahn–Hilliard model, a two-component field theory that breaks Newton's third law at the mesoscale due to asymmetric (off-diagonal) coupling in the linearized dynamics. Starting from a phase-separated state, increasing the strength of non-reciprocal coupling induces a phase transition to a collectively moving droplet phase. Within the collectively moving phase, we derive analytical expressions that describe how droplet size, number, and velocity depend on the strength of non-reciprocal coupling, and we verify these predictions with numerical simulations. The analysis reveals an inverse relationship between droplet size and both their velocity and number: smaller droplets move faster and occur in greater numbers. These findings expand the theoretical framework of active size control and suggest that it may be a general feature of nonequilibrium systems.