Twirling, whirling, and overwhirling revisited: Viscous dynamics of rotating filaments and ribbons

Paul M. Ryan, Charles W. Wolgemuth

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


When an initially straight filament is immersed in a viscous fluid and rotated at one end, the fluid resists the rotational motion and causes a buildup of twist in the object. At a critical turning frequency, the object buckles due to the elastic stresses in the material. While this instability has been extensively studied over the past 25 years, these analyses have focused narrowly on filaments with circular cross sections near the onset of the instability. Here we explore the phase diagram for twirling filaments as a function of cross-sectional aspect ratio and rotational frequency. We find a large range of dynamic behaviors and even find that while filaments with circular cross sections transition directly from twirling to overwhirling, ribbonlike objects undergo a twirl-to-whirl transition, similar to what was originally predicted for rodlike objects. We show that the linear stability for rotating ribbons is equivalent to first order to that of cylindrical filaments. Hysteresis is also common, suggesting that there are multiple stable states in these systems. Finally, by comparing simulations using resistive force theory to immersed boundary methods, we identify the reason that these two methods have historically not agreed on the value of the critical turning frequency.

Original languageEnglish (US)
Article number113101
JournalPhysical Review Fluids
Issue number11
StatePublished - Nov 2022

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Fluid Flow and Transfer Processes


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