Shape dynamics of a thin loop sedimenting in a viscous fluid

Thin elastic filaments and chains in viscous fluids are idealizations of biological and polymeric systems. We consider the non-local shape evolution, due to hydrodynamic self-interaction, of a chain-like, locally inextensible loop settling under gravity in the creeping flow regime. We find that the rigid translation of a circle along its gravitationally-aligned axis is unstable. A recirculating blob and tail arrangement is explored as a possible attracting state of a long chain.