Chiral sedimentation of extended objects in viscous media.
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.
Krapf
Nathan W
NW
Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA.
Witten
Thomas A
TA
Keim
Nathan C
NC