Contact line singularity at partial wetting during evaporation driven by substrate heating

Abstract

We present a theoretical investigation of the evaporation of a liquid on a solid substrate into the atmosphere of its pure vapor. The evaporation is provoked by the overheating of the substrate above the saturation temperature. At partial wetting, the liquid forms a wedge ending at the triple liquid-vapor-solid contact line (CL). The wedge region is extremely important in all evaporation geometries (bubble, drop, meniscus in a capillary) for two reasons. First, in this region a significant part of the evaporative heat flux is spent to compensate the latent heat. Second, a strong meniscus curvature that occurs in this region leads to the apparent contact angle larger than its actual microscopic value. We show that unlike the conventional diffusive evaporation models, the evaporation rate at the CL is bounded and is defined by the CL velocity. In particular the evaporation rate vanishes at the CL when it is immobile. This means that the slip length is not essential for the contact line singularity relaxation. The pressure boundary conditions at the CL are also derived. An analytic expression for the apparent contact angle (valid in the asymptotic limit of vanishing overheating) is derived. It is compared to numerical results.