Analytical solution for the integral contact line evaporative heat sink

Abstract

Heat transfer by evaporation from a thin film is studied theoretically. The film thickness decreases with position and approaches an asymptotic value. The film is influenced by long-range iniermolecular forces, in particular van der Waals forces. According to the model, as well as previous models, these forces may partially suppress evaporation, locally, but may draw fluid into the thin film from a bulk pool, generally. The insulation effect of the fluid is included, whereas, capillary and thermocapillary effects are not considered. Analytical expressions are presented for the film slope, curvature, and flow in terms of the film thickness. The film is semi-infinite and steady, therefore, the flow at some position is equal to evaporation from the portion of the film downstream of that position and is proportional to the integral heat sink. Curvature may become quite large for small film thicknesses. An expression for the film thickness as a function of position is presented for the special case of a relatively strong insulation effect. Also presented is an engineering model relating the integral heat sink to a reduction in the Laplace pressure driving force for porous media flow, through a dynamic contact angle.