Sedimentation Dynamics of Bodies with Two Planes of Symmetry

Abstract

We show that bodies with two planes of symmetry can display a range of behaviors even without inertia. Any such body supports a conserved quantity in its dynamics, and is either a settler, a drifter or a flutterer, depending only on its shape. At large time, settlers and drifters, respectively, fall vertically and obliquely, while flutterers rotate forever while executing intricate patterns. The dynamics of flutterers decouples into a periodic and a Floquet part with different timescales, giving periodicity or quasiperiodicity. We design a set of bodies and use the boundary integral method to show that settlers, drifters, and flutterers, all lie in this set.

References in corpus (4)

• Lord Kelvin's isotropic helicoid
• Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries
• U-shaped disks in Stokes flow: Chiral sedimentation of a non-chiral particle
• Orientation dynamics of two-dimensional concavo-convex bodies

Cited by in corpus (4)

• From fluttering to drifting in inertialess sedimentation of achiral particles
• Dynamical modes of highly elastic loops settling under gravity in a viscous fluid
• Sedimenting rigid particles of certain shapes approach a stationary orientation
• Dynamics and clustering of sedimenting disc lattices