Propulsion and instability of a flexible helical rod rotating in a viscous fluid

TL;DR

This study combines experiments and simulations to analyze how a flexible helical rod propels and buckles in a viscous fluid at low Reynolds numbers, revealing stability boundaries and biological implications.

Contribution

It introduces a coupled fluid-structure model for flexible helical rods and maps out stability and propulsion regimes through experiments, simulations, and scaling analysis.

Findings

Identified the critical rotation velocity for buckling instability.

Mapped the phase diagram of propulsion versus stability.

Suggested biological relevance of the instability in bacteria.

Abstract

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.