A theoretical approach to mathematical modeling of sperm swimming in viscoelastic Ellis fluid in a passive canal

This study aimed at investigating the biomechanics of sperm swimming through a passive channel. The spermatozoa are modeled as a Taylor's swimming sheet which is immersed in a viscoelastic Ellis fluid. A typical small size of microorganisms and their swimming protocol lead to negligible internal forces (or dominant viscous forces). The constitutive equations of sperm-driven flow are derived by employing the creeping flow and long-wavelength approximation. For some initial guesses of a flow rate and a swimming speed, the reduced differential equation is numerically solved via the MATLAB routine bvp5c for large values of the pertinent parameters. To find the unknowns (flow rate and sperm speed), Broyden's algorithm is employed in such a way that refines values of flow rate and swimming speed satisfying the dynamic equilibrium conditions. Using these refined values, one gets the energy diminution. The swimming speed, flow rate, power expended by the swimmer, streamlines pattern and velocity profiles are displayed in graphical figures.

Automated summary

This study investigated the biomechanics of sperm swimming through a passive channel. The spermatozoa were modeled as a Taylor's swimming sheet immersed in a viscoelastic Ellis fluid. By employing the creeping flow and long-wavelength approximation, the constitutive equations of sperm-driven flow were derived. The numerical solution of the reduced differential equation was obtained using Broyden's algorithm to refine the flow rate and swimming speed satisfying dynamic equilibrium conditions. Graphical figures displayed the swimming speed, flow rate, power expended by the swimmer, streamlines pattern, and velocity profiles.