  Flagellated microorganisms overcome the low-Reynolds-number time
reversibility by rotating helical flagella. For peritrichous bacteria, such as
Escherichia coli, the randomly distributed flagellar filaments align along the
same direction to form a bundle, facilitating complex locomotive strategies. To
understand the process of flagella bundling, especially the propulsion force,
we develop a multi-functional macroscopic experimental system and employ
advanced numerical simulations for verification. Flagella arrangements and
phase differences between helices are investigated, revealing the variation in
propulsion contribution from the individual helix. Numerically, we build a
time-dependent model to match the bundling process and study the influence of
hydrodynamic interactions. Surprisingly, it is found that the total propulsion
generated by a bundle of two filaments is constant at various phase differences
between the helices. However, the difference between the propulsion from each
helix is significantly affected by the phase difference, and only one of the
helices is responsible for the total propulsion at a phase difference equals to
pi. Through our experimental and computational results, we provide a new model
considering the propulsion contribution of each filament to better understand
microbial locomotion mechanisms, especially on the wobbling behavior of the
cell. Our work also sheds light on the design and control of artificial
microswimmers.
