Twists, tumbles, and orbits during the sedimentation of shaped particles

Sedimentation is a fundamental process across many natural systems, from atmospheric aerosols and marine snow to the locomotion of microorganisms against gravity. The shape of a particle crucially determines its sedimentation behavior, often leading to complex rotational and orbital trajectories. These dynamics are governed by the particle's hydrodynamic mobility tensor, which captures the coupling between translational and rotational motion in viscous flow. In this work, we develop an efficient numerical framework to compute the full mobility tensor directly from the three-dimensional geometry of an arbitrary particle. Starting with a 3D model of the particle, such as an .stl file, the method discretizes the particle surface into distributed stokeslets and applies six independent rigid-body motions to extract all tensor components. We validate our results against analytical solutions for simple geometries and experimental measurements for asymmetric and helical particles, demonstrating that the method accurately captures both symmetric and asymmetric hydrodynamic couplings relevant to sedimentation dynamics. Moreover, our method can serve as a predictive tool for tuning locomotive properties in viscous fluids, and responses to an array of external forces.