  Slip-boundary effects on the polar liquid film motor (PLFM) -- a novel
micro-fluidic device with important implications for advancing knowledge on
liquid micro-film's structure, dynamics, modeling and technology -- are
studied. We develop a mathematical model, under slip boundary conditions,
describing electro-hydro-dynamical rotations in the PLFMs induced either by
direct current (DC) or alternating current (AC) fields. Our main results are:
(i) rotation characteristics depend on the ratio $k=l_{s}/D$ ($l_{s}$ denotes
the slip length, resulting from the interface's impact on the structure of the
liquid and $D$ denotes the film's diameter). (ii) As $k$ ($k>-1/2$) increases:
(a) PLFMs subsequently exhibit rotation characteristics under "negative-",
"no-", "partial-" and "perfect-" slip boundary conditions; (b) the maximum
value of the linear velocity of the steady rotating liquid film increases and
its location approaches the film's border; (c) the decay of the angular
velocities' dependency on the distance from the center of the film slows down,
resulting in a macroscopic flow near the boundary. (iii) In addition to $k$,
the rotation characteristics of the AC PLFM depend on the magnitudes, the
frequencies, and the phase difference of the AC fields. (iv) Our analytical
derived rotation speed distributions are consistent with the existing
experimental ones.
