Sessile drop evaporation in a gap – crossover between diffusion-limited and phase transition-limited regime

We consider the time evolution of a sessile drop volatile partially wetting liquid on rigid solid substrate. The evaporates under strong confinement, namely, it sits one two parallel plates that form narrow gap. First, we develop an efficient mesoscopic long-wave description in gradient dynamics form. It couples diffusive vertically averaged vapour density gap to equation for profile drop. underlying free energy functional incorporates wetting, interface and bulk energies gas entropy. model allows us investigate transition between diffusion-limited phase transition-limited evaporation shallow droplets. Its character as well full-curvature formulation. Second, compare results obtained with corresponding direct numerical simulations solving Stokes coupled diffusion selected experiments. In passing, discuss influence contact line pinning.