  Interaction of motile microrganisms with a nearby solid substrate is a well
studied phenomenon. However, the effects of hydrodynamic slippage on the
substrate have received a little attention. In the present study, within the
framework of the squirmer model, we impose a tangential velocity at the swimmer
surface as a representation of the ciliatory propulsion and subsequently obtain
exact solution of the Stokes equation based on a combined analytical-numerical
approach. We illustrate how the near-wall swimming velocities are non-trivially
altered by the interaction of wall slip and hydrodynamic forces. We report a
characteristic transition of swimming trajectories for both puller and pusher
type microswimmers by hydrodynamic slippage if the wall-slip length crosses a
critical value. In case of puller microswimmers that are propelled by a
breast-stroke like action of their swimming apparatus ahead of their cell body,
the wall slip can cause wall-bound trapping swimming states, either as periodic
or damped periodic oscillations which would otherwise escape from a no slip
wall. The associated critical slip length has a non-monotonic dependence on the
initial orientation of the swimmer which is represented by novel phase
diagrams. Pushers, which get their propulsive thrust from posterior flagellar
action, also show similar swimming state transitions but in this case the wall
slip mediated reorientation dynamics and the swimming modes compete in a
different fashion to that of the pullers. The present results pave the way for
understanding the motion characteristic of biological microswimmers near
confinements with hydrophobic walls or strategize the design of microfluidic
devices used for sorting and motion rectification of artificial swimmers by
tailoring their surface wettability.
