Bend It Like A Flagellum

Flagellar motion at low Reynolds number presents a wide variety of mathematical problems that have been addressed over past decades. Swimming dynamics and navigation through tubular confined spaces present challenges in modeling, because, unlike confinements by infinite planes or spheres, fundamental solutions to Stokes equations are not readily expressed. In this work, we present a framework to study flagellar motion in narrow and tortuous tubular enclosures. The basic swimmer is modeled using Kirchhoff rods with regularized Stokeslet segments while the rigid surfaces that constitute the enclosure are represented by regularized Stokeslet surfaces. Swimming kinematics is not prescribed, rather is emergent from time-varying local prescribed curvatures. This approach allows for swimmer-wall interactions and in turn, the evolution of swimming behavior near rigid boundaries of arbitrary shapes. We also investigate the effects of changing environmental variables (fluid viscosity, tube diameter, etc.) and flagellum parameters (e.g., length, stiffness, etc.) on swimming performance and navigational success through bends. Both aspects have profound implications for understanding the coevolution of female reproductive tracts and sperm morphology and kinematics in different organisms.