| Summary: | Some microorganisms swim in the fluid by rotating their helical flagella rigidly, and many studies have been focused on the mechanics of their swimming in purely viscous Newtonian fluid such as water. Recently, attention has been paid to the effects of viscoelasticity on the swimming of microorganisms, since many microorganisms commonly swim in viscoelastic fluid environments such as mucus gels and biofilms. In this study, we focused on the effect of viscoelastic Mach numbers M = V/c, where V is the speed of an object through a fluid and c is the speed of shear waves in the fluid, to which not much attention has been paid in the literature. We examined experimentally the effect of viscoelastic Mach numbers on the propulsive forces of a rotating model helical flagellum in subcritical (M < 1) and supercritical (M > 1) conditions. Helical flagellum models with different pitches and helical diameters were used for this study. The models were rotated in some viscoelastic fluids with different damping characteristics of the shear waves (such as wormlike micelle solutions and polymer solutions). In the fluid with lower damping characteristics, the force measurement results show that the rotating speed dependence changes significantly at the speed whose Mach number (defined as the ratio of helical wave speed to shear wave speed) is unity. It is also found that the propulsive forces are the function of only the tangential velocity along the helix when the tangential velocity is relatively high. The velocity fields obtained by a particle image velocimetry show that the flow patterns around a model helix changes between subcritical and supercritical conditions and the damping characteristics of the shear waves in the fluid play an important role in the flows generated around the model helix. These results suggest the importance of considering viscoelastic Mach numbers and damping characteristics of shear waves in the fluid.
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