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. The rotors that are modeled by an effective rigid body, are 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 turbulent spiral waves. The model provides a novel example of coupled oscillators with long-range interaction. Our results suggest strategies for designing controllable microfluidic mixers using the emergent behavior of hydrodynamically coupled active components.