  Flagellated bacteria exploiting helical propulsion are known to swim along
circular trajectories near surfaces. Fluid dynamics predicts this circular
motion to be clockwise (CW) above a rigid surface (when viewed from inside the
fluid) and counter-clockwise (CCW) below a free surface. Recent experimental
investigations showed that complex physicochemical processes at the nearby
surface could lead to a change in the direction of rotation, both at solid
surfaces absorbing slip-inducing polymers and interfaces covered with
surfactants. Motivated by these results, we use a far-field hydrodynamic model
to predict the kinematics of swimming near three types of interfaces: clean
fluid-fluid interface, slipping rigid wall, and a fluid interface covered by
incompressible surfactants. Representing the helical swimmer by a superposition
of hydrodynamic singularities, we first show that in all cases the surfaces
reorient the swimmer parallel to the surface and attract it, both of which are
a consequence of the Stokes dipole component of the swimmer flow field. We then
show that circular motion is induced by a higher-order singularity, namely a
rotlet dipole, and that its rotation direction (CW vs. CCW) is strongly
affected by the boundary conditions at the interface and the bacteria shape.
Our results suggest thus that the hydrodynamics of complex interfaces provide a
mechanism to selectively stir bacteria.
