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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.

Nanoscale polymeric thin films are widely used in diverse applications such as energy devices, flexible electronics and biosensors, where a satisfactory mechanical performance is of vital importance to realize their full functionality. It has been evidenced that the elastic properties of polymer films are often strongly affected by their thickness; however, the underlying mechanism of this phenomenon, especially a thorough understanding at the microscopic level, has yet to be achieved. Here we established a coarse-grained molecular dynamics (CGMD) based computational framework, combining with experimental verifications, aiming to reveal the conformational origin of the stiffening behavior of crosslinked polymeric thin films. By imposing systematic controls over the polymer network structures, we found that the bi-axial modulus changes are essentially consequent of the alteration of polymer conformations. A unified theory was then proposed, to quantitatively clarify the correlation between the elastic properties of the system and the distributional variations of the chain end-to-end distances, with predicting a significant hardening effect on top of the conventional entropic elasticity with largely uncoiled chains. Adopting processing protocols inspired by the modeling, our experiments showed that PDMS films at approximately the same thickness may exhibit a two order of magnitude difference in their moduli. The good agreement between experiments and simulations illustrated our findings as an effective guideline for tailoring the elastic properties of polymer films at nanoscale.