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Sketch of the magnetic swimmer with flexible tail. See text for notation.
Image sequence of a swimming cycle at frequency ω = 1 Hz in the Boger fluid (B2); time step between each image, Δt = 66.6 ms.
Position of the head along (○) and across ( ) the swimming direction as well as head angle (⋄); filled symbols (blue) show results for the Boger (B2) fluid while empty symbols (red) are for the Newtonian (N2) fluid.
Mean forward swimming speed, U (mm/s), as a function of the oscillating frequency, ω (Hz). Filled and empty symbols correspond to Boger and Newtonian fluids, respectively. □ (black): fluids N2 and B2, flexible swimmer; ▷ (blue): fluids N1 and B1, flexible swimmer; ○ (red): fluids N1 and B1, rigid tail swimmer. The error bars depict the standard deviation of the measurements for the N2 and B2 fluids which were repeated four times.
Normalized swimming speed, U/ωL, as a function of sperm number, . All symbols as in Fig. 5 .
Ratio of non-Newtonian (U NN ) to Newtonian (U N ) swimming speeds, U NN /U N , as a function of the Deborah number, . ■ (black): fluids N2 and B2; ▶ (blue): fluids N1 and B1. The dashed line is a linear fit to the data for all fluids.
PIV results for the flow field around the swimmer with a two-dimensional tail in fluid B2. (a) Vorticity (colors) and velocity (arrows) fields; (b) cycle-averaged magnitude, , of the rate-of-strain tensor, D. Vorticity and rate-of-strain fields are normalized by the oscillation frequency, ω. The white regions show the position of the swimmer at different instants throughout the cycle.
Superimposed shapes of the flexible tail at different instants throughout the oscillation cycle. The solid (red) and dashed (blue) lines display the tail shape for the Newtonian (N2) and Boger (B2) fluids, respectively. These measurements correspond to the data shown in Fig. 3 .
Properties of the fluids studied: composition, density, viscosity, power index, and mean relaxation time.
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