Evaporation-driven Contact Angles in a Pure-vapor Atmosphere : the Effect of Vapor Pressure Non-uniformity

Abstract

A small vicinity of a contact line, with well-defined (micro)scales (henceforth the “microstructure”), is studied theoretically for a system of a perfectly wetting liquid, its pure vapor and a superheated flat substrate. At one end, the microstructure terminates in a non-evaporating microfilm owing to the disjoining-pressure-induced Kelvin effect. At the other end, for motionless contact lines, it terminates in a constant film slope (apparent contact angle as seen on a larger scale), the angle being non-vanishing despite the perfect wetting due to an overall dynamic situation engendered by evaporation. Here we go one step beyond the standard one-sided model by incorporating the effect of vapor pressure non-uniformity as caused by a locally intense evaporation flow, treated in the Stokes approximation. Thereby, the film dynamics is primarily affected through thermodynamics (shift of the local saturation temperature and evaporation rate), the direct mechanical impact being rather negligible. The resulting integro-differential lubrication film equation is solved by handling the newly introduced effect (giving rise to the “integro” part) as a perturbation. In the ammonia (at 300 K) example dealt with here, it proves to be rather weak indeed: the contact angle decreases while the integral evaporation flux increases just by a few percent for a superheat of ~1 K. However, the numbers grow (roughly linearly) with the superheat.