Conformations, hydrodynamic interactions, and instabilities of sedimenting semiflexible filaments

TL;DR

This study investigates how semiflexible filaments behave under gravitational fields, revealing shape instabilities, transitions to non-planar forms, and hydrodynamic interactions that influence their motion and interactions.

Contribution

It provides a combined numerical and analytical analysis of shape transitions and hydrodynamic effects in sedimenting semiflexible filaments, highlighting new non-planar shapes and interaction mechanisms.

Findings

Filaments undergo shape instabilities with increasing external field.

Non-planar shapes lead to sideways drift and helical trajectories.

Hydrodynamic interactions cause effective repulsion and influence relative velocities.

Abstract

The conformations and dynamics of semiflexible filaments subject to a homogeneous external (gravitational) field, e.g., in a centrifuge, are studied numerically and analytically. The competition between hydrodynamic drag and bending elasticity generates new shapes and dynamical features. We show that the shape of a semiflexible filament undergoes instabilities as the external field increases. We identify two transitions that correspond to the excitation of higher bending modes. In particular, for strong fields the filament stabilizes in a non-planar shape, resulting in a sideways drift or in helical trajectories. For two interacting filaments, we find the same transitions, with the important consequence that the new non-planar shapes have an effective hydrodynamic repulsion, in contrast to the planar shapes which attract themselves even when their osculating planes are rotated with respect to each other. For the case of planar filaments, we show analytically and numerically that the relative velocity is not necessarily due to a different drag of the individual filaments, but to the hydrodynamic interactions induced by their shape asymmetry.