Fig 7. Influence of the viscosity of the background fluid on the swimming characteristic is determined for fluids with viscosities of 0.1 Pa.s, 1 Pa.s, 5 Pa.s, and 10 Pa.s.

Helical flagellar propulsion is more efficient than planar flagellar propulsion at relatively low actuation frequency regardless to the viscosity of the fluid. (a) At low viscosity (μ = 0.1 Pa.s), optimal sperm number of 2.1 is approached at high actuation frequency (> 50 Hz). (b) At μ = 1 Pa.s, the optimal actuation frequencies are 20 Hz and 50 Hz for helical and planar flagellar propulsion, respectively. (c) At μ = 5 Pa.s, the optimal actuation frequencies are 4 Hz and 11 Hz for helical and planar flagellar propulsion, respectively. (d) Helical and planar flagellar propulsion have optimal swimming speed at 2 Hz and 6 Hz, respectively (S5 Dataset).