  It has been shown recently [PRL 102, 254503 (2009)] that in the plane-plane
configuration a mechanical resonator vibrating close to a rigid wall in a
simple fluid can be overdamped to a frozen regime. Here, by solving
analytically the Navier Stokes equations with partial slip boundary conditions
at the solid fluid interface, we develop a theoretical approach justifying and
extending these earlier findings. We show in particular that in the perfect
slip regime the above mentioned results are, in the plane-plane configuration,
very general and robust with respect to lever geometry considerations. We
compare the results with those obtained previously for the sphere moving
perpendicularly and close to a plane in a simple fluid and discuss in more
details the differences concerning the dependence of the friction forces with
the gap distance separating the moving object (i.e., plane or sphere) from the
fixed plane. Finally, we show that the submicron fluidic effect reported in the
reference above, and discussed further in the present work, can have dramatic
implications in the design of nano-electromechanical systems (NEMS).
