Kepler orbits of settling discs
Abstract
The collective dynamics of objects moving through a viscous fluid is complex and counterintuitive. A key to understanding the role of nontrivial particle shape in this complexity is the interaction of a pair of sedimenting spheroids. We report experimental results on two discs settling at negligible Reynolds number (), finding two classes of bound periodic orbits, each with transitions to scattering states. We account for these dynamics, at leading far-field order, through an effective Hamiltonian in which gravitational driving endows orientation with the properties of momentum. This leads to a precise correspondence with the Kepler problem of planetary motion for a wide range of initial conditions, and also to orbits with no Keplerian analogue. This notion of internal degrees of freedom manifesting themselves as an effective inertia is potentially a more general tool in Stokesian driven systems.
Cite
@article{arxiv.1803.10269,
title = {Kepler orbits of settling discs},
author = {Rahul Chajwa and Narayanan Menon and Sriram Ramaswamy},
journal= {arXiv preprint arXiv:1803.10269},
year = {2019}
}