Slender body theories for rotating filaments

Slender fibres are ubiquitous in biology, physics and engineering, with prominent examples including bacterial flagella cytoskeletal fibres. In this setting, slender body theories (SBTs), which give the resistance on fibre asymptotically its slenderness $\epsilon$ , useful tools for both analysis computations. However, a difficulty arises when accounting twist cross-sectional rotation: because angular velocity of filament can vary depending order magnitude applied torque, asymptotic must accurate results rotational dynamics over range velocities. paper, we first survey challenges applying existing SBTs, based either singularity or full boundary integral representations, to rotating filaments, showing particular that they fail consistently treat rotation–translation coupling curved filaments. We then provide an alternative approach approximates three-dimensional via one-dimensional line Rotne–Prager–Yamakawa regularized singularities. While unable accurately resolve flow field near filament, gives grand mobility symmetric translation–rotation coupling, making it applicable broad To restore fidelity geometry, use our model inform simple empirical equation relates mean force torque along centreline translational cross-section. The single unknown coefficient is estimated numerically from calculations rotating, filament.