Settling of shaped solids

The gravitational settling of particles in a viscous fluid is a confounding problem in many-body physics, owing to the long-range flow fields set up by each falling particle. Here I will present experimental and theoretical results that show qualitatively new behaviour when the particles have non-trivial shape and orientational degrees of freedom, as do snowflakes, plankton, crystals, and other natural sediment. As examples of the richness that emerges from shape, I will discuss unusual phenomena in the sedimentation of individual polar and polygonal objects, of pairs of apolar and polar objects, and of a one-dimensional lattice of apolar discs. For instance, a pair of spheres falls with constant separation vector, whereas pairs of discs either fall into bound states with periodic twirling in the orientation, or fall into scattering states, in exact analogy with Keplerian orbits [1]. A line of spheres is unstable to small density perturbations, whereas a line of discs can alternatively display wave-like excitations of position and orientation[2]. Underlying these behaviours is a Hamiltonian description where orientation plays the role of an effective inertia. In the example of a sedimenting lattice, we also find a clean example of an unusual route to instability: while the system is linearly stable, there is transient growth in perturbations until nonlinear mechanisms can take over.

This work was done in collaboration with Rahul Chajwa, Alyssa Conway, Rama Govindarajan and Sriram Ramaswamy.

1. R. Chajwa et al. Kepler Orbits in Pairs of Disks Settling in a Viscous Fluid. Phys. Rev. Lett. 122, p.224501. 2019
2. R. Chajwa et al Waves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays Phys. Rev. X 10, 041016 (2020)