Flow-induced synchronization in large arrays of micro-rotors*

Motile cilia cover many eukaryotic cells, from single-celled protozoa to mammalian epithelial surfaces, and play important roles in fluid transport and mixing across the cell surface. They typically beat in coordinated patterns across length scales much greater than the length of the individual cilium. Existing literature attributes the origin of this large-scale coordination to hydrodynamic interaction. However, the stability of this collective synchrony is not yet quantitatively understood.

Here, we model each cilium as a micro-rotor consisting of a rigid sphere moving along a circular trajectory in close proximity to a no-slip boundary. Using the modified Green-Oseen tensor to model the far-field interaction among rotors, we numerically investigate the long-time dynamics of over 20,000 rotors arranged in square and hexagonal lattices in doubly-periodic domains. Homogeneous and isotropic states are found to be unstable to small perturbations. More interestingly, this instability leads to robust large-scale metachronal coordination.