Synchronization and Collective Dynamics in a Carpet of Microfluidic Rotors

We study synchronization of an array of rotors on a substrate that are coupled by hydrodynamic interaction. Each rotor, which is modeled by an effective rigid body, is driven by an internal torque and exerts an active force on the surrounding fluid. The long-ranged nature of the hydrodynamic interaction between the rotors causes a rich pattern of dynamical behaviors including phase ordering and self-proliferating spiral waves. Our results suggest strategies for designing controllable microfluidic mixers using the emergent behavior of hydrodynamically coupled active components.