Storage of sperm in the female reproductive tract occurs across species that reproduce by internal fertilization, modulating availability and preserving fertility. For instance, the sperm of the insects from the family Drosophilidae are stored in and released from the seminal receptacle—a long, slender, coiled tube. The sperm flagella, longer than any straight portion of the tube, must be flexible enough to navigate the twists and turns of these tightly coiled organs. As a step towards studying the coupled system of fluid, tube geometry, and flexible flagella, we present here a framework to study flagellar motion in tubular enclosures. The basic swimmer is modeled as a flexible Kirchhoff rod comprised of regularized Stokeslet segments, while the rigid surfaces that constitute the enclosure are represented by regularized Stokeslet surfaces. Swimming kinematics is not prescribed, but emerges from time-varying preferred curvatures. This approach allows for swimmer-wall interactions and, in turn, the evolution of swimming behavior near rigid boundaries. We first investigate the effects of flagellar bending rigidity, beat frequency, and the presence of inactive flagellar regions on swimming performance in free space. Next, we study the effect of confinement levels on swimming performance inside straight tubes. We find that swimming speed increases as the tube diameter decreases, with a more pronounced boost in speed for stiffer flagella. We also find that the swimmers, whose preferred beat is planar, drift towards the tube walls if the diameter of the tube is large enough. Finally, our work demonstrates that the model flagellum can navigate through a curved tube, which will enable studies aimed at understanding the coevolution of female reproductive tracts and sperm morphology in different organisms.

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• Biological fluid dynamics
• Low Reynolds number flows
• Microswimmers
• Flagella
• Stokes equations