  Flow of a thin viscous film down a flat inclined plane becomes unstable to
long wave interfacial fluctuations when the Reynolds number based on the mean
film thickness becomes larger than a critical value (this value decreases as
the angle of inclination with the horizontal increases, and in particular
becomes zero when the plate is vertical). Control of these interfacial
instabilities is relevant to a wide range of industrial applications including
coating processes and heat or mass transfer systems. This study considers the
effect of blowing and suction through the substrate in order to construct from
first principles physically realistic models that can be used for detailed
passive and active control studies of direct relevance to possible experiments.
Two different long-wave, thin-film equations are derived to describe this
system; these include the imposed blowing/suction as well as inertia, surface
tension, gravity and viscosity. The case of spatially periodic blowing and
suction is considered in detail and the bifurcation structure of forced steady
states is explored numerically to predict that steady states cease to exist for
sufficiently large suction speeds since the film locally thins to zero
thickness giving way to dry patches on the substrate. The linear stability of
the resulting nonuniform steady states is investigated for perturbations of
arbitrary wavelengths, and any instabilities are followed into the fully
nonlinear regime using time-dependent computations. The case of small amplitude
blowing/suction is studied analytically both for steady states and their
stability. Finally, the transition between travelling waves and non-uniform
steady states is explored as the suction amplitude increases.
