Dynamics of Mass Polar Spheroids During Sedimentation

The dynamics of sedimenting particles under gravity are surprisingly complex due to the presence of effective long-ranged forces. When the particles are polar with a well-defined symmetry axis and non-uniform density, recent theoretical predictions suggest that prolate objects will repel and oblate ones will weakly attract. We tested these predictions using mass polar proalte spheroids, which are composed of 2 mm spheres glued together. We probed different aspect rations ($\kappa$) and center of mass offsets ($\chi$) by combining spheres of different densities. Experiments were done in both quasi-two-dimensional (2D) and three=dimensional (3D) chambers. By optically tracking the motion of single particles, we found that the dynamics were well-described by a reduced mobility matrix model that could be solved analytically. Pairs of particles exhibited an effective repulsion, and their separation roughly scaled as ~$(\kappa-1)/\chi^{0.39}$, i.e. particles that were more prolate or had smaller mass asymmetry had stronger repulsion effects. In 3D, particles with $\chi>0$ were distributed more uniformly than $\chi=0$ particles, and the degree of uniformity increased with $\kappa$, indicating that the effective 2-body repulsion manifests for a large number of particles.