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Most bacteria are driven by the cilia or flagella, consisting of a longfilament and a rotary molecular motor through a short flexible hook. Thebeating pattern of these filaments shows synchronization properties fromhydrodynamic interactions, especially in low Reynolds number fluids. Here, weintroduce a model based on simple spherical oscillators which executeoscillatory movements in one dimension by an active force, as a simplifiedimitation of the movements of cilia or flagella. It is demonstrated that theflow, measured by the net transportation of a test particle, is generated by achain of oscillators and enhanced by the hydrodynamic interactions betweenbeads, with supports from both perturbative and numerical results.Transportation efficiency also highly correlates with hydrodynamicinteractions. Increments of bead numbers are generally expected to producestronger flow and efficiency, at least for small numbers of beads.

Transportation efficiency of hydrodynamically coupled spherical oscillators in low Reynolds number fluids