Sedimentation of geometrically polar shapes

We study the effect of shape-polarity on the stokesian sedimentation dynamics of particles by experiments in which isosceles triangles of varying apex angles, are placed in a vertical plane and sedimented at low Reynolds number in a quasi-two-dimensional container. Unlike an nonpolar shape the triangle rotates as it sediments - due to coupling between the orientational and translational degrees of freedom -- and asymptotically approaches a stable configuration either pointing along or away from gravity [Jayaweera, Mason, J. Fluid Mech. 22 (1965)]. For small apex angles the triangle is stable with apex pointing down. As the apex angle is increased we find a transition at π/3 for which all orientations of the triangle are stable and for apex angles greater than π/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. Adding polarity to the particles introduces an effective damping term in the equations of motion, thus making it not amenable to an effective hamiltonian treatment constructed for apolar particles [R. Chajwa et. al. arXiv:1803.10269 (2018)].