Knotting semi-flexible filaments with centrifugal forces*

The sedimentation of elastic filaments is a classical problem in fluid mechanics. In this context, hydrodynamic phenomena play a key role in the filaments' deformation, rotation, and translation while competing with elastic forces and thermal motion. Consequently, the interplay between gravitational, elastic, and thermal effects determines the filament's settling dynamics, which may follow intriguing complex paths or sediment in stable configurations. From Brownian Dynamics numerical simulations, we found that at high centrifugal accelerations, the semi-flexible filaments may acquire long-stable configurations characterized by a knotted leading head and a trailing stretched tail, revealing that stable configurations can also be intriguing. The stability of this configuration is conferred by the tightness of the knotted structure due to a hydrodynamically induced tension in the filament. We conducted a systematic study to understand the role of centrifugal acceleration and filament stiffness on the topological structure of the knots. Although further investigation is required, such long-live metastable knotted structures might be strongly associated with the anomalous decrease of the sedimentation factor in long polymers at high rotational speeds commonly observed in ultracentrifuge systems.