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arXiv · 1803.10269

Kepler orbits of settling discs

Rahul Chajwa·Narayanan Menon·Sriram Ramaswamy
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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 ($\simeq 10^{-4}$), 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.

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Rahul Chajwa, Narayanan Menon, Sriram Ramaswamy. 2018-03-27. Kepler orbits of settling discs. https://doi.org/10.1103/physrevlett.122.224501

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