Elastoviscous Influences on Bend Navigation by Flagellar Microswimmers inside Tubular Confinements

Compared to most mammals, some insect sperm flagella are disproportionately long relative to their relatively small body volume. This, compounded by the coevolution of even longer, tightly coiled female reproductive tracts, poses an intriguing evolutionary puzzle. This confinement raises a key microscale fluid dynamics question: how can a beating flagellum navigate such tortuous bends? To address this question, we develop a computational framework for studying flagellar motility within tubular enclosures. The swimmer is modeled as a flexible Kirchhoff rod discretized into regularized Stokeslet segments, while rigid tube walls are represented by regularized Stokeslet surfaces. Swimming kinematics emerge dynamically from time-varying target curvatures, enabling natural swimmer-wall interactions and boundary-dependent behavior. We demonstrate that navigational success correlates directly with a non-dimensional effective flexibility enabling bending and buckling through tight turns. Furthermore, we introduce a quantitative measure incorporating bend angle, tube radius, and bend curvature alongside effective flexibility to predict navigation performance.