Twirling and Whirling: Viscous Dynamics of Rotating Elastica

Abstract

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by a novel pair of coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two dynamical regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.

To be published in Physical Review Letters

References in corpus (4)

• Self-organized Beating and Swimming of Internally Driven Filaments
• Trapping and Wiggling: Elastohydrodynamics of Driven Microfilaments
• The Viscous Nonlinear Dynamics of Twist and Writhe
• Local Writhing Dynamics

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