Local drag of a slender rod parallel to a plane wall in a viscous fluid

The viscous drag on a slender rod by wall is important to many biological and industrial systems. This critically depends the separation between can be approximated asymptotically in specific regimes, namely far from, or very close to, wall, but typically determined numerically for general separations. In this note we determine an asymptotic representation of local parallel which valid all possible through matching behaviour from wall. We show that leading order both these regimes has been known since 1981 they used produce composite contrast sphere above where no simple uniformly exists. estimate error as increases, discuss how results could resistive-force theory demonstrate their use two-hinged swimmer