Rolling waves on the surface of a thin layer of viscous liquid at phase transition

The mathematical model, describing the flow of a thin liquid film over a vertical wall with consideration of condensation and evaporation at the interface under the regime of rolling waves, was developed. The families of exact and numerical generalized solutions, where the traveling waves conjugate with each other or with a “residual” thickness through the strong and weak discontinuity, were constructed. Time evolution of these exact generalized solutions was studied. The maps of flow regimes on a vertical heat exchange surface were plotted.