Mathematical modeling of the thin liquid layer runoff process based on generalized conditions at the interface: parametric analysis and numerical solution

The problem of a thin layer of liquid flowing down an inclined substrate under conditions of a co-current gas flow is considered. Mathematical modeling is carried out on the basis of the Navier–Stokes and heat transfer equations, as well as generalized conditions at the thermocapillary boundary. Parametric analysis of the problem is made. An algorithm of numerical solution is constructed for the evolution equation determining the thickness of the liquid layer. A comparison of numerical calculations for ethanol and HFE-7100 liquids is presented. The influence of an additional term in the interface energy equation on the dynamics of the liquid layer is shown.