Hydrodynamic analysis of flagellated bacteria swimming near one and between two no-slip plane boundaries

The motility of swimming bacteria near solid surfaces has implications in a wide range of scenarios, including water treatment facilities, microfluidics, and biomedical implants. Using the boundary element method to numerically solve the equations of low Reynolds number fluid flow, we investigate the dynamics of a model swimmer propelled by rotating a single helical flagellum. Building on previous simulation results for swimmers near a single plane boundary, we introduce a second, parallel boundary and show that the bacterial trajectories change as the two plates are brought closer together. Analysis of this dynamical system shows that the configuration in the center of the channel and parallel to the walls is an unstable equilibrium state for large plate separations, but it becomes the only stable position for swimmers when the plate separation is reduced to three to four times the cell width. Our model also predicts that transient trajectories, i.e., those not at steady states, can exhibit curvature in the opposite sense to that expected from the well-known explanation for circular bacterial paths near a single wall.