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 ($\simeq 10^{-4}$), 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.

References in corpus (4)

• Are Steadily Moving Crystals Unstable?
• Screened and Unscreened Phases in Sedimenting Suspensions
• Screening, Hyperuniformity, and Instability in the Sedimentation of Irregular Objects
• Hydrodynamic Interactions between Two Forced Objects of Arbitrary Shape: I Effect on Alignment

Cited by in corpus (11)

• Stokes flows in three-dimensional fluids with odd and parity-violating viscosities
• A review of shaped colloidal particles in fluids: Anisotropy and chirality
• Waves, Algebraic Growth and Clumping in Sedimenting Disk Arrays
• Trading particle shape with fluid symmetry: on the mobility matrix in 3D chiral fluids
• Hindered stokesian settling of discs and rods
• Dynamics of Mass Polar Spheroids During Sedimentation
• From fluttering to drifting in inertialess sedimentation of achiral particles
• Dynamical modes of highly elastic loops settling under gravity in a viscous fluid
• Active Caustics
• Dynamics and clustering of sedimenting disc lattices
• Experimental investigations on the nonequilibrium dynamics of pattern formation in fluid and granular systems