Hydrodynamically induced rhythmic motion of optically driven colloidal particles on a ring

We experimentally study the motion of optically driven colloidal particles on a circular path by varying their number N. Although an identical driving force is applied to each particle, their equally spaced configuration is hydrodynamically unstable, and a doublet configuration is spontaneously formed. In small-N systems, the angular difference between neighboring particles exhibits oscillatory or nonoscillatory behavior. The number of oscillatory modes that appear depends on the maximum number of doublets that the system can contain. Frequent switching between different modes was observed with increasing N. The characteristic frequencies of the oscillatory modes are discussed theoretically by linear stability analysis of the equations that govern the motion of hydrodynamically coupled particles. The evaluated frequencies of the slowest modes exhibit reasonably good agreement with those of the mainly observed modes in experiments. The relationship between the characteristic frequencies and specific configurations is confirmed experimentally by setting a specific initial configuration for the particles. An increase in N also enhances the mean angular velocity of the particles owing to the reduced effective viscosity in large-N systems.