Speed of a Taylor Swimmer in Newtonian and Viscoelastic Fluids

We demonstrate that the speed of an idealized Taylor swimmer with a prescribed waveform in a viscoelastic fluid can be greater or lesser than in a Newtonian fluid depending on their rheological properties. The measurements are performed using a cylindrical sheet immersed in a fluid inside a cylindrical tank under torque free conditions with traveling waves imposed in the azimuthal direction. Swimming speeds in the Newtonian case are found to be consistent with calculations using the Stokes equation. A faster swimming speed is found in a viscoelastic fluid which has a constant viscosity with shear rate. By contrast, a slower swimming speed is found with more complex shear thinning viscoelastic fluids which have multiple relaxation time scales. These results are compared with calculations with Olroyd-B fluids which find a decreasing swimming speed with Deborah Number given by the product of fluid elastic relaxation time scale and the driving frequency.