Analysis of Motion of Bacteria with Rotating Flagella

A method is proposed for analyzing the swimming motions of bacteria. It is assumed that a bacterium consists of a spherical cell body and several rotating flagella. The forces and torques exerted on each flagellum are evaluated in a coordinate system fixed to the flagellum, using the resistive force theory. They are transformed into a coordinate system fixed to the cell body. Then, the velocity and angular velocity of the cell body can be determined because the net force and torque on the bacterium are zero. This method is applicable to the motion of bacteria with rotating flagella in any form of curve attached at any point on the cell body. A numerical example shows that the trajectory of bacteria with a flagellum slanting from the radial direction of the cell body follows the pattern of a double helix. Another example shows that a doubly flagellated bacterium swims faster than a singly flagellated bacterium.