  We study the linear stability with respect to lateral perturbations of free
surface films of polymer mixtures on solid substrates. The study focuses on the
stability properties of the stratified and homogeneous steady film states
studied in Part I [U. Thiele, S. Madruga and L. Frastia, Phys. Fluids 19,
122106 (2007)]. To this aim, the linearized bulk equations and boundary
equations are solved using continuation techniques for several different cases
of energetic bias at the surfaces, corresponding to linear and quadratic
solutal Marangoni effects.
  For purely diffusive transport, an increase in film thickness either
exponentially decreases the lateral instability or entirely stabilizes the
film. Including convective transport leads to a further destabilization as
compared to the purely diffusive case. In some cases the inclusion of
convective transport and the related widening of the range of available film
configurations (it is then able to change its surface profile) change the
stability behavior qualitatively.
  We furthermore present results regarding the dependence of the instability on
several other parameters, namely, the Reynolds number, the Surface tension
number and the ratio of the typical velocities of convective and diffusive
transport.
