Emergence of Cilia Synchronization and Circulating Flows in Spherical Cavities

Collective synchronization plays a fundamental role in biological systems. In particular, densely packed motile cilia can self-organize through hydrodynamic interactions to generate directional fluid transport. Previous studies using dynamic rotor models have shown that spontaneous metachronal waves can emerge and drive fluid pumping on planar or open-boundary systems. However, in many systems, such as in the Kuppfer's vesicle, cilia are confined within a curved and bounded geometry. The question of how global curvature and confinement shape synchronization and flows remains largely unexplored. In this work, we study a simplified yet illustrative model of dynamic rotors lie on the inner boundary of a spherical geometry enclosing a low–Reynolds–number (Stokes) fluid. Through numerical simulations and analysis, we found that hydrodynamic coupling between the rotors leads to spontaneous synchronization in the form of spiral waves that propagate on the inner boundary of the sphere and generate directional recirculating flows within the spherical cavity. These findings provide a mechanistic understanding of how geometry and hydrodynamic coupling shape collective dynamics in confined biological systems.