  The hydrodynamics of a flagellated microorganism is investigated when
swimming close to a planar free-slip surface by means of numerical solu- tions
of the Stokes equations obtained via a Boundary Element Method. Depending on
the initial condition, the swimmer can either escape from the free-slip surface
or collide with the boundary. Interestingly, the mi- croorganism does not
exhibit a stable orbit. Independently of escape or attraction to the interface,
close to a free-slip surface, the swimmer fol- lows a counter-clockwise
trajectory, in agreement with experimental find- ings, [15]. The hydrodynamics
is indeed modified by the free-surface. In fact, when the same swimmer moves
close to a no-slip wall, a set of initial conditions exists which result in
stable orbits. Moreover when moving close to a free-slip or a no-slip boundary
the swimmer assumes a different orientation with respect to its trajectory.
Taken together, these results contribute to shed light on the hydrodynamical
behaviour of microorgan- isms close to liquid-air interfaces which are relevant
for the formation of interfacial biofilms of aerobic bacteria.
