Thrust and Hydrodynamic Efficiency of the Bundled Flagella

Abstract

The motility mechanism of prokaryotic organisms has inspired many untethered microswimmers that could potentially perform minimally invasive medical procedures in stagnant fluid regions inside the human body. Some of these microswimmers are inspired by bacteria with single or multiple helical flagella to propel efficiently and fast. For multiple flagella configurations, the direct measurement of thrust and hydrodynamic propulsion efficiency has been challenging due to the ambiguous mechanical coupling between the flow field and mechanical power input. To address this challenge and to compare alternative micropropulsion designs, a methodology based on volumetric velocity field acquisition is developed to acquire the key propulsive performance parameters from scaled-up swimmer prototypes. A digital particle image velocimetry (PIV) analysis protocol was implemented and experiments were conducted with the aid of computational fluid dynamics (CFD). First, this methodology was validated using a rotating single-flagellum similitude model. In addition to the standard PIV error assessment, validation studies included 2D vs. 3D PIV, axial vs. lateral PIV and simultaneously acquired direct thrust force measurement comparisons. Compatible with typical micropropulsion flow regimes, experiments were conducted both for very low and higher Reynolds (Re) number regimes (up to a Re number = 0.01) than that are reported in the literature. Finally, multiple flagella bundling configurations at 0°, 90° and 180° helical phase-shift angles were studied using scaled-up multiple concentric flagella thrust elements. Thrust generation was found to be maximal for the in-phase (0°) bundling configuration but with ~50% lower hydrodynamic efficiency than the single flagellum. The proposed measurement protocol and static thrust test-bench can be used for bio-inspired microscale propulsion methods, where direct thrust and efficiency measurement are required.

Magnetic miniature swimmers with multiple rigid flagella

“…The in-phase configuration (θ = 0) demonstrates, in this case, to generate insufficient propulsion force to get off the ground. Different from the result obtained in [6]. Finally, in figure 6.c stands for the optimal angular distribution of tails, being 180 degrees the most performant.…”

“…Besides, a direct proportion between the number of attached bacteria and the reached speed is proven as well. Notwithstanding these results, the bundle shapes was studied in [6] considering rigid millimetric prototypes using CFD simulations and PIV techniques. The authors observed that the most efficient configuration is for a single flagellum.…”

“…We study the bundle distribution of a 2-flagella swimmer finding an optimum distribution when tails are separated a phase angle of 180 0 . Moreover, the in-phase distribution (phase angle 0 0 ) is ineffective since the swimmer does not achieve to propel, confronting the results in [6] with the typical helical geometries. Furthermore, the proposed 2-flagella swimmer with 3-mm in tail height demonstrates to be susceptible to tail height variations.…”

Bacteria-inspired Robotic Propulsion from Bundling of Soft Helical Filaments at Low Reynolds Number

“…Inspired by the complexity of mechanics behind simple locomotion, mechanical engineers also tried to formulate the motion of multiflagellated bacteria. 15,[23][24][25] It was only until recently that the bundling behavior was shown to be a purely mechanical phenomenon that is due to the interaction of the soft helical structures and the viscous fluid. 15 Besides its complexity in physics, the multi-flagellated mechanism is important from both robotic and biological perspectives due to the following features : (1) directional stability , 2 (2) redundancy of actuation, 26 (3) chemical secretion using flagella, 27, 28 (4) improved efficiency in swarm and propagation 29,30 Prior works on soft robots actuated by flagella have considered both simulation and experiments.…”

A finite element method for simulating soft active non-shearable rods immersed in generalized Newtonian fluids

“…Another peculiarity of soft-bio-matter problems is that, as happens also in aerodynamics, the effect of the surrounding fluid on the solid bodies is much more consequential than simply energy dissipation. Swimmers, in particular, rely on the complex response of the fluid for their propulsion and guidance [16,17,18,19]. A quite accurate fluid model is thus necessary to approximate the motion of microscopic organisms.…”