Knotting semi-flexible filaments in strong fields with hydrodynamics

Knots appear spontaneously across length scales, from headphone cords and Christmas lights at the macroscale to polymers, proteins, and DNA filaments inside bacteriophages or in microfluidic setups. The probability with which different knots emerge provides insight into the forces and constraints governing their formation. Here, we uncover how hydrodynamic interactions and body forces cooperate to induce and stabilize knots in semi-flexible filaments. Using Brownian dynamics simulations with hydrodynamics, we show that field-driven sedimentation generates toroidal flows that guide the filament into knotted configurations. The resulting hydrodynamic tension between the leading knotted head and the trailing tail tightens the structure, producing a hierarchy of metastable knots whose stability increases with topological complexity. Consequently, the filament undergoes an annealing-like sequence of transitions between simple and complex knots, ultimately reaching stabilization.