Comparing sperm collective swimming with flocking transition*

In viscoelastic fluid, bovine sperm are able to interact and align with their neighbors to swim in clusters. The formation of the polar liquid phase, or large flocks of sperm, however, did not solely depend on the number density and the alignment mediated by the fluid, but was strongly influenced by the initial conditions. If a pulse of flow was used to create an aligned initial condition, hundreds of sperm were able to form a flock swimming in the same direction. This suggests that the transition is first-order, with strong hysteresis. Analyzing these flocks, we found the decay of the orientation correlation function to be linear on a log-log plot. From our finite flock sizes, there was no indication that the correlation function decayed to a non-zero value, as suggested theoretically for the polar liquid phase. Further, the effective exponents of the correlation function were found to vary for the same flock at different time points, which made us wonder about some of the premises of continuum theoretical models. From tracking individually swimming sperm, we found that the rotational noise is an exponential decay, while the speed follows a Gamma distribution. Neither is commonly used in theoretical models.