Chiral sedimentation of extended objects in viscous media

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 ω about a fixed axis. This ω 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 ω 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 ω are aligned along the forcing direction. In this case, the limiting ω 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.

Hydrodynamic interactions between two forced objects of arbitrary shape. I. Effect on alignment

“…To make your way through this richness it is important to make two distinctions between types of trajectories. The first distinction is between constant forcing (as in sedimentation), which can make the objects only partially aligned without synchronizing their phases of rotation 5,9 , and a time-dependent forcing protocol, which is known to lock the phase of an individual object onto that of the force 10,11 . The main issue examined below is how the presence of hydrodynamic interaction affects these two behaviors.…”

“…9. The sum of the stokeslets and the corresponding total torque must be equal to the external generalized forces applied on the objects.…”

“…For example, applying a torque by a rotating uniform magnetic field was used to achieve efficient transport of chiral magnetic objects 8 . Another example, which is the main issue of the present work, is the ability to achieve orientational alignment of asymmetric objects by applying an external force [9][10][11] .…”

Predicting tensorial electrophoretic effects in asymmetric colloids

“…The qualitative tensorial behavior is known from our prior study of sedimentation [6,37,38]. However, electrophoresis is much more experimentally convenient.…”

“…We have begun to explore cases of asymmetric objects that show the potential for the striking behaviors anticipated in Refs. [5,37] from the surface of the object. For this we may consider stationary stokeslets distributed through a shell of finite thickness d cloaking the object surface [20,39].…”