Simulation of small swimmer motions driven by tail/flagellum beating

Abstract

The motion of a small swimmer in a viscous fluid has been simulated numerically by using the immersed boundary method. The force of the interaction between the swimmer and the fluid was calculated with a feedback law. It was assumed that the fluid flow is governed by the incompressible Navier–Stokes equations and that the swimmer is propelled by the interaction force according to Newton’s second law. The swimmer was modeled as a rigid head attached to a line tail/flagellum. The simulation was validated for low Reynolds numbers by comparing the calculated waving sheet swimming speed and rate of work to theoretical perturbation solutions. The swimming of the small swimmer in a channel was then analyzed in detail. Both traveling-wave and asymmetric parabola flagellum beatings were simulated. Traveling-wave beating drives the swimmer forward, whereas asymmetric beating results in a change in its swimming direction. When the channel half height is less than the wavelength, the effects of a wall on the swimmer’s motion are significant and can be described with a function that varies only with the ratio of the channel half height to the wavelength. If the swimmer’s position is offset from the channel centerline, it moves toward the near wall. When the swimmer’s size is increased, its motion becomes affected by the Reynolds number and the swimmer mass; further, the pitching motion is restrained and its swimming speed is increased.