Hydrodynamic induced deformation and orientation of a microscopic elastic filament

Abstract

We describe simulations of a microscopic elastic filament immersed in a fluid and subject to a uniform external force. Our method accounts for the hydrodynamic coupling between the flow generated by the filament and the friction force it experiences. While models that neglect this coupling predict a drift in a straight configuration, our findings are very different. Notably, a force with a component perpendicular to the filament axis induces bending and perpendicular alignment. Moreover, with increasing force we observe four shape regimes, ranging from slight distortion to a state of tumbling motion that lacks a steady state. We also identify the appearance of marginally stable structures. Both the instability of these shapes and the observed alignment can be explained by the combined action of induced bending and non-local hydrodynamic interactions. Most of these effects should be experimentally relevant for stiff micro-filaments, such as microtubules.