Published in Physical Review E, Volume 79, Issue 5, May 1, 2009, pages 056307-1-056307-14.
At the time of publication, author Nathan Keim was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1103/PhysRevE.79.056307.
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.
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