Shape transition and propulsive force of an elastic rod rotating in a viscous fluid

TL;DR

This study investigates how flexible rods deform and generate propulsion when rotating in viscous fluids, revealing a shape transition from gentle bending to a helical form at a critical torque, supported by experiments and theory.

Contribution

It provides a combined experimental and theoretical analysis of shape transitions and propulsion in rotating elastic rods in viscous fluids, highlighting a critical torque-induced shape change.

Findings

Rod bends gently at low torque with small propulsion.

At a critical torque, the rod forms a helix with increased propulsion.

Theory and experiments show good agreement on shape transition.

Abstract

The deformation of thin rods in a viscous liquid is central to the mechanics of motility in cells ranging from \textit{Escherichia coli} to sperm. Here we use experiments and theory to study the shape transition of a flexible rod rotating in a viscous fluid driven either by constant torque or at constant speed. The rod is tilted relative to the rotation axis. At low applied torque, the rod bends gently and generates small propulsive force. At a critical torque, the rotation speed increases abruptly and the rod forms a helical shape with much greater propulsive force. We find good agreement between theory and experiment.