Sedimentation of polygonal tiles*

We study the stokesian sedimentation of planar shapes by experiments in which polygonal tiles are placed in a vertical plane and sedimented at low Reynolds number in a quasi-two-dimensional container. We first focus on the effect of shape-polarity by studying isosceles triangles of varying apex angles. Unlike nonpolar shapes, a triangle rotates as it sediments due to coupling between the orientational and translational degrees of freedom, and asymptotically approaches a stable orientation [Jayaweera, Mason, J. Fluid Mech. 22 (1965)]. For small apex angles the triangle is stable with apex pointing down along the gravity direction. As the apex angle is increased we find a transition at $\pi $/3 for which all orientations of the triangle are stable and for apex angles greater than $\pi $/3, the triangle is stable with apex pointing up. We understand the experimental results with a model of three stokeslets fixed to the vertices of a triangle. The transition described above, and the coupling of orientation to horizontal drift are captured by this model. We also test generalizations of this discrete-stokeslet model to other regular and irregular polygons and to concave shapes.