A finite Re slender body theory

The effects of fluid inertia on the settling motion of fibers is studied theoretically. Khayat \& Cox (1989) were the first to give a theory of hydrodynamic forces and torques on a slender body when fluid inertia is non-zero. Their theory uses a matched asymptotic expansion with a viscous inner flow and Oseen’s approximation for the outer flow. This restricts the analysis to cases where Re defined based on fiber diameter ($Re_D$) is zero. We develop a novel finite Re slender body theory that allows the inner flow to be described by steady Navier-Stokes and thus provide better comparisons of drag and torque with realistic scenarios where the $Re_D\neq0$.