Chiral sedimentation of extended objects in viscous media

TL;DR

This paper theoretically analyzes how generic rigid objects sedimenting in viscous fluids exhibit chiral, helical motion due to hydrodynamic interactions, with experimental validation on macroscopic objects.

Contribution

It introduces a theoretical framework for understanding chiral sedimentation of extended objects and characterizes the dependence of angular velocity on object configuration.

Findings

Objects follow a helical path with constant angular velocity.

Angular velocity remains nonzero as stokeslet radius approaches zero.

Largest angular velocities occur when objects are aligned along the forcing direction.

Abstract

We study theoretically the chirality of a generic rigid object's sedimentation in a fluid under gravity in the low Reynolds number regime. We represent the object as a collection of small Stokes spheres or stokeslets, and the gravitational force as a constant point force applied at an arbitrary point of the object. For a generic configuration of stokeslets and forcing point, the motion takes a simple form in the nearly free draining limit where the stokeslet radius is arbitrarily small. In this case, the internal hydrodynamic interactions between stokeslets are weak, and the object follows a helical path while rotating at a constant angular velocity $\omega$ about a fixed axis. This $\omega$ is independent of initial orientation, and thus constitutes a chiral response for the object. Even though there can be no such chiral response in the absence of hydrodynamic interactions between the stokeslets, the angular velocity obtains a fixed, nonzero limit as the stokeslet radius approaches zero. We characterize empirically how $\omega$ depends on the placement of the stokeslets, concentrating on three-stokeslet objects with the external force applied far from the stokeslets. Objects with the largest $\omega$ are aligned along the forcing direction. In this case, the limiting $\omega$ varies as the inverse square of the minimum distance between stokeslets. We illustrate the prevalence of this robust chiral motion with experiments on small macroscopic objects of arbitrary shape.