Numerical analysis of bacterium motion based on the slender body theory

Abstract

We calculated the speed and efficiency of bacterium swimming motion by use of the slender body theory developed by Higdon. A bacterium model consists of a spherical cell and a rotating helical flagellum is adopted. The results agree well with those of the boundary element method. The computational time of the slender body theory is about 1/400 of that of the boundary element method. We also carried out optimization of the shape of the flagellum with respect to the highest speed and the most efficient swimming. The difference of these two shapes is apparent in the radii of the flagellar helices, and associates with counter rotation of each cell that is keeping torque balance. The flagellar shape of the highest efficiency resembles the observed data for Vibrio alginolylicus. Flagella of the bacterium seem to be optimized for efficiency rather than swimming speed.