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

Abstract

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

References in corpus (7)

• Evaporating pure, binary and ternary droplets: thermal effects and axial symmetry breaking
• Morphology changes in the evolution of liquid two-layer films
• Gravitational effect in evaporating binary microdroplets
• Relaxation of a dewetting contact line Part 1: A full-scale hydrodynamic calculation
• Long-wave theory of bounded two-layer films with a free liquid-liquid interface: Short- and long-time evolution
• Gradient dynamics models for liquid films with soluble surfactant
• Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration

Cited by in corpus (11)

• Drops on polymer brushes -- advances in thin-film modelling of adaptive substrates
• Stick-slip Dynamics in the Forced Wetting of Polymer Brushes
• Non-equilibrium configurations of swelling polymer brush layers induced by spreading drops of weakly volatile oil
• Bifurcation tracking on moving meshes and with consideration of azimuthal symmetry breaking instabilities
• Dynamics of particle aggregation in dewetting films of complex liquids
• Gradient dynamics approach to reactive thin-film hydrodynamics
• Drops of volatile binary mixtures on brush-covered substrates
• Mesoscopic hydrodynamic model for spreading, sliding and coarsening compound drops
• Gradient dynamics model for drops of volatile liquid on a porous substrate
• Chemomechanical motility modes of partially wetting liquid droplets
• Gradient dynamics model for chemically driven running drops