Hydrodynamic Bundling of Flexible Helical Filaments

Flagellated bacteria such as Escherichia coli propel themselves by rotating bundles of helical filaments. Efficient bundling, indispensable for bacterial motility and chemotaxis, requires that independently driven filaments synchronize their rotation and bending through near-field elasto-hydrodynamic and steric interactions. Despite its central role in cellular locomotion and fundamental interests in soft active matter physics, this collective process at nanometer scales remains poorly understood. We address this gap with a dynamically scaled experiment that resolves bundling dynamics and the associated hydrodynamics. Specifically, we construct a closed-loop torque-controlled motor system to drive two centimeter-scale flexible helices in high-viscosity silicone oil (Re ≲ 10^-4), mimicking the constant-torque output of the bacterial flagellar motor. A miniature universal joint is inserted to emulate the compliant hook between the motor and the filament. Volumetric imaging combined with particle image velocimetry capture filament shape and dynamics as well as the three-dimensional flow field surrounding the filaments. By systematically varying filament stiffness, applied torque, and geometric configuration, we uncover robust scaling laws for synchronization times, bundling onset, and steady rotation rates. Our study advances the understanding of the locomotion of flagellated bacteria and provides new insights into the design of bio‑inspired micro‑swimmers.