Flagellated bacteria swim in circles near a rigid wall.

The rotation of bacterial flagella driven by rotary motors enables the cell to swim through fluid. Bacteria run and reorient by changing the rotational direction of the motor for survival. Fluid environmental conditions also change the course of swimming; for example, cells near a solid boundary draw circular trajectories rather than straight runs. We present a bacterium model with a single flagellum that is attached to the cell body and investigate the effect of the solid wall on bacterial locomotion. The cell body of the bacterium is considered to be a rigid body and is linked via a rotary motor to the elastic flagellum which is modeled by the Kirchhoff rod theory. The hydrodynamic interaction of the cell near a solid boundary is described using the regularized Stokes formulation combined with the image system. We show that the trajectories of the bacteria near a solid boundary are influenced by the rotation rate of the motor, the shape of the cell body, helical geometry, and elastic properties of the flagellum.