Numerical investigation of the evolution and breakup of an evaporating liquid film on a structured wall

This paper examines the evolution and rupture of a thin liquid film evaporating on a structured wall and the concomitant heat and mass transport. The heat is supplied either from the side of the wall or from the hot ambient gas. An evolution equation for the film thickness is derived in the framework of the long-wave theory under the assumption that the film thickness is small compared to the length scale of film deformation. The resulting fourth order partial differential equation is solved numerically employing a finite difference scheme using a MATLAB code. The results show that, in the case of a hot wall, the film breakup may occur even in the absence of evaporation. The reason for this breakup is Marangoni convection driven by uneven temperature distribution at the liquid-gas interface due to the wall structure. With increasing evaporation rate the rupture time decreases and the position at which the rupture occurs is shifted towards the crests of the wall topography. Additionally, it is found that the wave length of the wall structure has a non-monotonous effect on rupture time. If the film is heated by the ambient gas, the liquid-gas interface tends to follow the wall topography shape.