Scaled-up Modeling of Individual and Collective Rotation Dynamics of Flagella*

Bacteria like E. coli are propelled by a bundle of helical flagella driven by rotary motors which operate under a constant torque in the normal swimming condition. Although flagellated bacterial swimming has been extensively studied, the collective dynamics of interacting flagella in a bundle dictated by complex hydrodynamic, elasto-hydrodynamic and steric interactions is still not fully understood. To better understand this interplay, we designed an experimental macroscopic scaled-up model of flagellar bundles. We rotated our fabricated centimeter-scaled metal helical filaments of control spacing in high-viscosity silicon oils to explore the effect of hydrodynamic coupling on the rotational dynamics of the filaments at low Reynolds numbers. We imaged the flow field around rotating helical filaments via PIV and compared our results with the predictions of slender-body theory. Our study provides important insights into the macroscopic design of flagellated bacteria and sheds light onto the collective dynamics of flagella in a bundle driven by a constant torque.