  A dynamical model is proposed to describe the coupled decomposition and
profile evolution of a free surface film of a binary mixture. An example is a
thin film of a polymer blend on a solid substrate undergoing simultaneous phase
separation and dewetting. The model is based on model-H describing the coupled
transport of the mass of one component (convective Cahn-Hilliard equation) and
momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate
boundary conditions at the solid substrate and the free surface.
  General transport equations are derived using phenomenological
non-equilibrium thermodynamics for a general non-isothermal setting taking into
account Soret and Dufour effects and interfacial viscosity for the internal
diffuse interface between the two components. Focusing on an isothermal setting
the resulting model is compared to literature results and its base states
corresponding to homogeneous or vertically stratified flat layers are analysed.
