  Most bacteria are driven by the cilia or flagella, consisting of a long
filament and a rotary molecular motor through a short flexible hook. The
beating pattern of these filaments shows synchronization properties from
hydrodynamic interactions, especially in low Reynolds number fluids. Here, we
introduce a model based on simple spherical oscillators which execute
oscillatory movements in one dimension by an active force, as a simplified
imitation of the movements of cilia or flagella. It is demonstrated that the
flow, measured by the net transportation of a test particle, is generated by a
chain of oscillators and enhanced by the hydrodynamic interactions between
beads, with supports from both perturbative and numerical results.
Transportation efficiency also highly correlates with hydrodynamic
interactions. Increments of bead numbers are generally expected to produce
stronger flow and efficiency, at least for small numbers of beads.
