Swimming of spermatozoa in a linear viscoelastic fluid.
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.
Fulford
G R
GR
School of Mathematics and Statistics, Australian Defence Force Academy, Canberra, ACT, Australia. g-fulford@adfa.edu.au
Katz
D F
DF
Powell
R L
RL
D000818:Animals; D004548:Elasticity; D006801:Humans; D008297:Male; D008954:Models, Biological; D012661:Semen; D013081:Sperm Motility / Q000502:physiology*; D013094:Spermatozoa / Q000502:physiology*; D014783:Viscosity