Relaxation of a highly deformed elastic filament at a fluid interface

Abstract

We perform experiments to investigate the relaxation of a highly deformed elastic filament at a liquid-air interface. The dynamics for filaments of differing length, diameter and elastic modulus collapse to a single curve when the time-dependence is scaled by a time scale $\tau = 8 \pi \mu L_o^4/B$. The relaxation, however, is completed in a very small fraction of the time $\tau$. Even though the time scale $\tau$ can be obtained by balancing the linear bending and viscous forces, it appears to control the highly nonlinear regime of our experiments. Nonlinear numerical simulations show that the force due to tension along the filament is comparable to the bending force, producing a net elastic restoring force that is much smaller than either term. We perform particle image velocimetry at the liquid-air interface to support the results of the numerics. Finally, we find that when the filament is initialized in asymmetric shapes, it rapidly goes to a shape with symmetric stresses. This symmetrisation process is entirely non-linear; we show that the symmetric curvature state minimizes energy at arbitrarily large deformation.