Synchronization of driven oscillators is a key aspect of flow generation in artificial and biological filaments such as cilia. Previous theoretical and numerical studies have considered the "rotor" model of a cilium in which the filament is coarse grained into a colloidal sphere driven with a given force law along a predefined trajectory to represent the oscillating motion of the cilium. These studies pointed to the importance of two factors in the emergence of synchronization: the modulation of the driving force around the orbit and the deformability of the trajectory. In this work it is shown via experiments, supported by numerical simulations and theory, that both of these factors are important and can be combined to produce strong synchronization (within a few cycles) even in the presence of thermal noise.

In this article we consider the complete set of synchronized and phase-locked states available to pairs of hydrodynamically coupled colloidal rotors, consisting of spherical beads driven about circular paths in the same, and in opposing senses. Oscillators such as these have previously been used as coarse grained, minimal models of beating cilia. Two mechanisms are known to be important in establishing synchrony. The first involves perturbation of the driving force, and the second involves deformation of the rotor trajectory. We demonstrate that these mechanisms are of similar strength, in the regime of interest, and interact to determine observed behavior. Combining analysis and simulation with experiments performed using holographic optical tweezers, we show how varying the amplitude of the driving force perturbation leads to a transition from synchronized to phase-locked states. Analogies with biological systems are discussed, as are implications for the design of biomimetic devices.

No abstract

No abstract

No abstract