Twirling and whirling: Viscous dynamics of rotating elastic filaments

Charles W. Wolgemuth, Thomas R. Powers, Raymond E. Goldstein

Research output: Contribution to journalArticlepeer-review

99 Scopus citations


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 coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two 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.

Original languageEnglish (US)
Pages (from-to)1623-1626
Number of pages4
JournalPhysical review letters
Issue number7
StatePublished - 2000

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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