Swimming of spermatozoa in a linear viscoelastic fluid

Article type: Research Article

Authors: Fulford, Glenn R. | Katz, David F. | Powell, Robert L.

Affiliations: School of Mathematics and Statistics, Australian Defence Force Academy, Canberra, ACT, Australia | Department of Biomedical Engineering Duke University, Durham, USA | Chemical Engineering and Materials Science University of California, Davis, USA

Abstract: A modified resistive force theory is developed for a spermatozoon swimming in a general linear viscoelastic fluid. The theory is based on a Fourier decomposition of the flagellar velocity, which leads to solving the Stokes flow equations with a complex viscosity. We use a model spermatozoon with a spherical head which propagates small amplitude sinusoidal waves along its flagellum. Results are obtained for the velocity of propulsion and the rate of working for a free swimming spermatozoon and the thrust on a fixed spermatozoon. There is no change in propulsive velocity for a viscoelastic fluid compared to a Newtonian fluid. The rate of working does change however, decreasing with increasing elasticity of the fluid, for a Maxwell fluid. Thus the theory predicts that a spermatozoon can swim faster in a Maxwell fluid with the same expenditure of energy for a Newtonian fluid.

Keywords: Sperm motility, viscoelastic fluid, flagellar, spermatazoa

Journal: Biorheology, vol. 35, no. 4-5, pp. 295-309, 1998