Effect of External Flows on Sperm Flagellar Dynamics

The swimming sperm of many external fertilizing marine organisms face complex fluid flows during their search for egg cells. Aided by chemotaxis, relatively weak flows and marine turbulence enhance spermegg fertilization rates through hydrodynamic guidance and mixing. However, strong flows can mechanically inhibit flagellar motility through elastohydrodynamic interactions - a phenomenon that remains poorly understood. We explore the effects of flow on the buckling dynamics of sperm flagella in an extensional flow through detailed numerical simulations, which are informed by microfluidic experiments and high-speed imaging. Compressional fluid forces lead to rich buckling dynamics of the sperm flagellum beyond a critical dimensionless sperm number, Sp, which represents the ratio of viscous force to elastic force. For non-motile sperm, the maximum buckling curvature and the number of buckling locations, or buckling mode, increase with increasing sperm number. In contrast, motile sperm exhibit an intrinsic flagellar curvature due to the propagation of bending waves along the flagellum. In compressional flow, this preexisting curvature acts as a precursor for buckling, which enhances local curvature without creating new buckling modes and leads to asymmetric beating. However, in extensional flow, flagellar beating remains symmetric with a smaller head yawing amplitude due to tensile forces. We also explore sperm motility in different shear flows. In the presence of Poiseuille flow, the sperm moves downstream or upstream depending on the flow strength along with net movement toward the centerline.