Helical beating of actuated elastic filament

A possible propulsion mechanism at low Reynolds number is the rotation of a flexible filament, tilted with respect to its rotation axis. Using a simple linear model, we establish the non linear torque-force relations for two torque-driven actuation modes. When the rotation of the filament is induced by two perpendicular transverse oscillating torques, the propulsive force increases monotonically with the torque amplitude. However, when a constant torque directed along the rotation axis is applied to the filament, an unstable branch appears in the torque-force characteristics, leading to a discontinuous transition in the shape of the filament. We characterize this shape transition using two geometrical parameters, quantifying the wrapping around and the collapse on the axis of the filament, both experimentally and theoretically. PACS numbers: 2008, 2008 Submitted to: J. Phys.: Condens. Matter Helical beating of actuated flagella 2