From flagellar undulations to collective motion: predicting the dynamics of sperm suspensions

Abstract

Swimming cells and microorganisms are as diverse in their collective dynamics as they are in their individual shapes and propulsion mechanisms. Even for sperm cells, which have a stereotyped shape consisting of a cell body connected to a flexible flagellum, a wide range of collective dynamics is observed spanning from the formation of tightly packed groups to the display of larger-scale, turbulence-like motion. Using a detailed mathematical model that resolves flagellum dynamics, we perform simulations of sperm suspensions containing up to 1000 cells and explore the connection between individual and collective dynamics. We find that depending on the level of variation in individual dynamics from one swimmer to another, the sperm exhibit either a strong tendency to aggregate, or the suspension exhibits large-scale swirling. Hydrodynamic interactions govern the formation and evolution of both states. In addition, a quantitative analysis of the states reveals that the flows generated at the time-scale of flagellum undulations contribute significantly to the overall energy in the surrounding fluid, highlighting the importance of resolving these flows.

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• Swimming in Complex Fluids
• Methods for suspensions of passive and active filaments
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• The pairwise hydrodynamic interactions of synchronized spermatozoa
• Detailed dynamics of discrete Gaussian semiflexible chains with arbitrary stiffness along the contour
• A numerical method for suspensions of articulated bodies in viscous flows
• Passively parallel regularized stokeslets
• Regularised non-uniform segments and efficient no-slip elastohydrodynamics
• How environment affects active particle swarms: a case study
• Undulatory swimming in suspensions and networks of flexible filaments