Load-dependent resistive-force theory for helical filaments

The passive rotation of rigid helical filaments is the propulsion strategy used by flagellated bacteria and some artificial microswimmers to navigate at low Reynolds numbers. In a classical 1976 paper, Lighthill calculated the 'optimal' resistance coefficients in a local (logarithmically accurate) resistive-force theory that best approximates predictions from the non-local (algebraically accurate) slender-body theory for force-free swimming of a rotating helix without an attached load (e.g. no cell body). These coefficients have since been widely applied, often beyond the conditions for which they were originally derived. Here, we revisit the problem for the case where a load is attached to the rotating filament, such as the cell body of a bacterium or the head of an artificial swimmer. We show that the optimal resistance coefficients depend in fact on the size of the load, and we quantify the increasing inaccuracy of Lighthill's coefficients as the load grows. Finally, we provide a physical explanation for the origin of this unexpected load-dependence.This article is part of the theme issue 'Biological fluid dynamics: emerging directions'.