Flow-induced phase separation: Boundaries determine the collective dynamics
How boundaries and confinement determine the collective dynamics of motile populations, such as biological flocks, robotic swarms, and synthetic active particles, remains largely unexplored. Here, combining experiments, theory and numerical simulations, we study the influence of boundaries on the fluid-mediated, dissipative, many-body forces and torques that determine the collective dynamics of self-propelled particles. Using experiments with active emulsion droplets whose motion is fully three-dimensional, we demonstrate that geometric confinement alters the far-field flow of the particles and, thereby, their hydrodynamic interactions. These changes give rise to distinct states of collective organization: two-dimensional crystals arrested at free interfaces, three-dimensional crystals stabilized by vorticity, and one-dimensional quasi-stable lines that travel in both two and three dimensions.
We rationalize these experimental results by computing the slow viscous flow produced by the droplets in the presence of boundaries. Numerical simulations based on the theory are in excellent agreement with experiment. Our work elucidates how macroscopic boundaries, by altering the microscopic interactions between constituents, influence the emergence of long-ranged order and long-lived structures in non-equilibrium systems. Our findings are relevant to the formation of biological aggregates at multiple scales and to the emerging field of geometric and topological synthetic active matter.