Figure 2.
The effect of shear on computed sperm trajectories in a background flow with a surface repulsion potential, specified by the parameters of table 2. The virtual sperm has a symmetric flagellar envelope, Γ = ∞, with α = −0.2, corresponding to human sperm chirality, or α = +0.2, corresponding to the opposite chirality found in mouse, while the initial attack angle is θinit = 0.2π and the sperm is initially located at X(s = 0, t = 0) = (0, 0, 0.1). Other parameters are given in table 1. Given the initial conditions, we are observing virtual sperm behaviour in the vicinity of the origin of the repulsive surface potential at z = 0 and the trajectories are presented in terms of their projection onto the x–y plane, thus representing paths that would be observed in the focal plane of a microscope when viewed from above. The trajectory labelled Blakelet gives the predicted path of this sperm near a no-slip surface, whereas the trajectory labelled Imagelet is the prediction for this sperm near a surface of fixed tangential stress and no normal velocity. The predictions for the Stokeslet correspond to the absence of hydrodynamic wall effects, though the surface repulsion potential is still included in the model. (Online version in colour.)