The locomotion of microorganisms in viscoelastic fluids at finite Reynolds numbers

The locomotion of microorganisms in complex fluids at low Reynolds numbers has been widely studied by ignoring fluid inertia. Here, we combine the asymptotic analysis and numerical simulations to explore the effect of fluid inertia on the dynamic mechanism of microorganisms swimming through viscoelastic fluids using Taylor’s swimming sheet model, undergoing small-amplitude undulations. Surprisingly, fluid inertia can enhance the speed and efficiency of the infinite-length sheet in viscoelastic fluids at finite Reynolds numbers, in stark contrast to the previous results found in Newtonian fluids. Moreover, speed and efficiency slightly exceed those Newtonian values at the small Weissenberg number due to a passive inertial response of the sheet. We associate this with the magnitude of the hydrodynamic force increasing at finite Reynolds numbers. These insights contribute to a deeper understanding of the inertial effect on the locomotion of microorganisms through complex fluids.