Sedimentation of Elastic Filaments

Experiments have shown that a straight elastic filament bends as it settles under gravity in a viscous fluid. Previous theoretical studies have argued that the observed bending is due to nonlocal hydrodynamic interactions between different parts of the filament. In this talk, we propose an alternative mechanism that does not rely on nonlocal effects. We employ a simpler, local model based on the Resistive Force Theory, where hydrodynamic forces depend on the local orientation and velocity along the filament. We focus on steady states, in which case our model involves a single dimensionless compliance parameter, η. Irrespective of η, the model predicts two trivial solutions, corresponding to perfectly horizontal and vertical filaments. However, for η above a critical value, a new branch of solutions emerges, corresponding to filaments exhibiting non-trivial shapes. The theoretical shapes are in good agreement with those observed in experiments. To gain further insight into our predictions, we consider the limit of flexible filaments (large η) and derive closed-form asymptotic formulae for the filament shape and settling speed.