Breakup of a liquid film, falling gown a vertical, uniformly heated wall

摘要

An analytical expression is developed for the minimum thickness at the breakup of a thin liquid film, flowing down a vertical wall, for both evaporating and non-evaporating conditions. This expression, derived based on the minimization of the total energy of a stable liquid rivulet forming following the film breakup, required solving for the rivulet profile and the two-dimensional velocity field in the rivulet. Results showed that the minimum liquid film thickness (MLFT) is a complex function of Marangoni number, vapor Reynolds number, liquid Prandtl number, physical properties of liquid and vapor, wall thermal conductivity, and the equilibrium contact angle of the liquid on the wall at zero heat flux, e0. As the wall heat flux increases, or the vapor pressure decreases, MLFT increases. At am wall heat flux, MLFT equals that for a non-evaporating film. The value of MLFT for an evaporating liquid film is independent of the thickness of the underlying, heated wall, but depends on the wall thermal conductivity < 100 W/m·K. At high heat flux, MLFT is independent of the wall thermal conductivity above 100 W/m·K and of θ{sub}0. The present expression for MLFT is in reasonable agreement with reported data for the breakup of evaporating water films on glass and stainless steel.