Dynamics of Mass Polar Spheroids During Sedimentation

TL;DR

This study investigates the sedimentation dynamics of mass polar spheroids, revealing that particle shape and mass distribution influence effective long-range interactions, with experimental results aligning with theoretical models.

Contribution

The paper provides experimental validation of theoretical predictions on how particle shape and mass asymmetry affect sedimentation interactions in polar spheroids.

Findings

Prolate particles exhibit stronger repulsion than oblate ones.

Separation scales with aspect ratio and mass offset as ~$(-1)/\u03c7^{0.39}$.

Particles with positive mass offset distribute more uniformly in 3D.

Abstract

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.