Fulford G R, Katz D F, Powell R L
School of Mathematics and Statistics, Australian Defence Force Academy, Canberra, ACT, Australia.
Biorheology. 1998 Jul-Oct;35(4-5):295-309. doi: 10.1016/S0006-355X(99)80012-2.
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.
针对在一般线性粘弹性流体中游动的精子，提出了一种修正的阻力理论。该理论基于鞭毛速度的傅里叶分解，这导致要用复粘度来求解斯托克斯流动方程。我们使用一个具有球形头部的模型精子，它沿其鞭毛传播小振幅正弦波。得到了自由游动精子的推进速度、做功速率以及固定精子所受推力的结果。与牛顿流体相比，粘弹性流体中的推进速度没有变化。然而，对于麦克斯韦流体，做功速率确实会改变，且随流体弹性的增加而降低。因此，该理论预测，在能量消耗相同的情况下，精子在麦克斯韦流体中能比在牛顿流体中游得更快。
