SIMULATION OF SPERM SWIMMING IN AMBIENT FLUID

Abstract

Sperm swimming in a viscous fluid is simulated numerically by the immersed boundary method. The sperm is modeled by an elliptical head attached by a line flagellum in the present work. Both the familiar travelling-wave and the asymmetric parabola flagellum beatings are simulated. First, the simulation is validated by comparing the sperm swimming speed and the rate of working with the theoretical perturbation solutions. Then, a sperm swimming in a channel is discussed in detail. The traveling-wave beating drives the sperm to move forward, while the asymmetric beating leads the sperm to change its swimming direction. When the channel half height is less than the wavelength, the wall effect on the sperm motion becomes significant, which can be expressed by a function only of the ratio of the channel half height to the wavelength. A sperm offset from the channel centerline moves toward the near wall. The relationships of the swimming speed, the angular velocity and the rate of working with the beating parameters are also obtained.