Twirling, whirling, and tensioning: Plectoneme formation and suppression in flexible filaments

A high-aspect ratio flexible filament suspended in a viscous fluid is unstable to a symmetry-breaking whirling motion when axially rotated beyond a critical velocity. We present experiments of this behavior and uncover a rich diversity of plectoneme formation soon after the initial instability, including multiple plectonemes for especially long filaments. A physical model extending Timoshenko's theory of elastic instability is presented which captures the fundamental physics involved in the instability. Additionally, we consider the effects of an axial flow that acts to tension the filament and control the onset of whirling without adjusting the physical properties of the filament itself. Such a setup could be employed to selectively engineer plectoneme formation at specified locations and lengths, and in fibers with submicron diameters, potentially to create superelastic ropes and fabrics.