  We combine experiments with simulations to investigate the fluid-structure
interaction of a flexible helical rod rotating in a viscous fluid, under low
Reynolds number conditions. Our analysis takes into account the coupling
between the geometrically nonlinear behavior of the elastic rod with a
non-local hydrodynamic model for the fluid loading. We quantify the resulting
propulsive force, as well as the buckling instability of the originally helical
filament that occurs above a critical rotation velocity. A scaling analysis is
performed to rationalize the onset of this instability. A universal phase
diagram is constructed to map out the region of successful propulsion and the
corresponding boundary of stability are established. Comparing our results with
data for flagellated bacteria suggests that this instability may be exploited
in nature for physiological purposes.
