An Investigation of the Breakup of an Evaporating Liquid Film, Falling Down a Vertical, Uniformly Heated Wall

Abstract

The breakup of an evaporating, thin liquid film falling down a vertical, uniformly heated wall is of interest in many applications. Analytical expressions are developed for predicting the thickness of an evaporating liquid film and the corresponding wetting rate at breakup, which are in good agreement with experimental data for water. These expressions, derived from minimizing the total energy of a stable liquid rivulet forming immediately following the film breakup, required solving for the rivulet profile and the two-dimensional velocity field in the rivulet. The total energy of the rivulet is the sum of the kinetics energy of the liquid, the surface energies at the liquid-vapor and the solid-liquid interfaces, and those due to evaporation and the thermocapillary force along the liquid-vapor interface. The liquid film thickness at breakup is a function of Marangoni number, vapor Reynolds number, liquid and vapor properties, equilibrium contact angle of the liquid with underlying wall material, and the wall thermal conductance <3×104 W/m2K. For a wall conductance <3×104 W/m2K, the film thickness at breakup, when the wall is heated uniformly at its inner surface, is higher than when the wall is heated at its outer surface, but both are identical when the wall conductance ⩾3×104 W/m2K. The contribution of the equilibrium contact angle diminishes, but the thickness of the liquid film at breakup increases, as the wall heat flux increases.