A macroscopic model for hydrodynamic interactions of bacterial flagellar bundles

Flagellated bacteria such as E. coli swim by rotating a helical rod-shaped propeller composed of a bundle of multiple flagella. Although the swimming of flagellated bacteria has been extensively studied, the collective dynamics of individual flagella in a bundle dictated by complex hydrodynamic, elasto-hydrodynamic and steric interactions at short distances of tens of nanometers remain elusive. Here, we experimentally investigate the hydrodynamic interactions between flagella by constructing a macroscopic scale model of a flagellar bundle. Specifically, we fabricate centimeter-scaled metal helical filaments and use high-viscosity silicone oil as our working fluid. Slow rotation of filaments in the oil at various controlled distances allow us to explore the effect of hydrodynamic coupling on the rotational dynamics of filaments at low Reynolds numbers. We further image the flow field around rotating helical filaments via PIV and compare our results with the predictions of slender-body theory. Our study reveals the hydrodynamic principles governing the collective dynamics of bacterial flagella and provides new insights into the locomotion of flagellated bacteria.