Energetics of synchronization for model flagella and cilia

Synchronisation is often observed in the swimming of flagellated cells, either for multiple appendages on same organism or between flagella nearby cells. Beating cilia are also seen to synchronise their dynamics. In 1951, Taylor showed that in-phase beating co-swimming spermatozoa was consistent with minimisation energy dissipated surrounding fluid. Here we revisit Taylor's hypothesis three models and cilia: (1) waving sheets both longitudinal transverse modes, as relevant flexible flagella; (2) spheres orbiting above a no-slip surface model interacting cilia; (3) whirling rods address interaction nodal cilia. By calculating flow fields explicitly, show rate working minimised our phase difference depending separation precise kinematics; opposite-phase motion relative position orientation spheres; rods. These results will be useful future probing dynamics synchronisation these setups.