Breaking symmetries in chiral sedimentation

We experimentally study the design of chiral shapes to optimize translation-rotation coupling in Stokes flow. Helical ribbons serve as a simple reference geometry which is co-centered and has strong translation-rotation coupling. During sedimentation, helical ribbons follow periodic orbits in orientation with complex quasi-periodic orbits in space. Adding a center of mass offset by inserting metal spheres in the 3D printed ribbons breaks co-centered symmetry and produces a wide range of dynamics including closed orbits, convergence to attracting orientations, and limit cycles. In experiments and numerical simulations, we measure the stability balloon in the space of 3D center-of-mass offsets where a bifurcation occurs that separates particles with complex dynamics from those with larger center of mass offsets that converge to a single orientation in tilt-spin space.