Rheomergy: collective behaviour mediated by active flow-based recruitment

The physics of signal propagation in a collection of organisms that communicate with each other both enables and limits how active excitations at the individual level reach, recruit and lead to collective patterning. Inspired by the spatio-temporal patterns in a planar swarm of bees that use pheromones and fanning flows to recruit additional bees, we develop a theoretical framework for patterning via active flow-based recruitment. Our model generalizes the well-known Patlak-Keller-Segel model of diffusion dominated aggregation and leads to an enhanced phase space of patterns spanned by two dimensionless parameters that measure the scaled stimulus/activity and the scaled chemotactic response. Together these determine the efficacy of signal communication via fluid flow (which we dub rheomergy) that leads to a variety of migration and aggregation patterns, consistent with observations.