Abstract
The swimming motion of a bacterium model consisting of a spherical cell body and a rotating helical flagellum is discussed. In order to calculate the speed and efficiency, we adopt the slender body theory (SBT) developed by Higdon. The effect of flagellar dimensions on the swimming motion is elucidated. The results are compared with those of the boundary element method (BEM), which is expected to provide more accurate results. The agreement is excellent, and the computational time of the SBT is about 1/400 of the time of the BEM. From the viewpoint of fluid dynamics, the optimal flagella for speed and effciency are both illustrated. The difference between the two shapes is apparent in the radius of the flagellar helix. The reason for this is explained taking into account the roles of the force and torque produced by the flagellar motion. In addition, the two flagella are compared to the flagellum in the real world. The bacterial flagellum resembles in shape the most efficient flagellum rather than the fastest one.
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