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.
|Original language||English (US)|
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - May 12 2009|
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics