We report interferometric measurements on 0.1...1 mm thick films of su
per-fluid He-3-B. The menisci of three different rotational states of
the superfluid were observed and analyzed theoretically using two-flui
d hydrodynamics: These are (i) the equilibrium vortex state in which t
he superfluid and the normal components corotate (solid body rotation)
, (ii) the vortex-free state (the Landau state), in which only the nor
mal component rotates, and (iii) the quasistationary vortex state in w
hich only the superfluid fraction rotates (pure superfluid rotation).
The Landau state manifested itself by a reduced parabolic meniscus at
rotations speeds below the critical angular velocity Omega(c) less tha
n or similar to 0.2 rad/s for vortex formation. Transition from the La
ndau state to the equilibrium vortex state yielded a sudden deepening
of the meniscus when Omega(c) was exceeded. After a rapid halt of the
cryostat, we observed a novel meniscus which was produced by th superf
luid rotation while the normal component was at rest. The enhanced dep
th of this meniscus is governed by the reactive and for thermomechanic
al excitation, we measured the response of a thin superfluid layer to
a heat pulse and analyzed it within the theory of two-fluid hydrodynam
ics. The data were employed, using the dispersion relation for thin fi
lm oscillations, to deduce the second viscosity coefficient zeta(3) cl
ose to T-c.