Mathematical Modelling of the Evaporating Liquid Films on the Basis of the Generalized Interface Conditions

The two-dimensional films, flowing down an inclined, non-uniformly heated substrate are studied. The results contain the new mathematical models developed with the help of the long-wave approximation of the Navier-Stokes and heat transfer equations or Oberbeck-Boussinesq equations in the case, when the generalized conditions are formulated at thermocapillary interface. The evolution equations for the film thickness include the effects of gravity, viscosity, capillarity, thermocapillarity, additional stress effects and evaporation