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. 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 long-wave 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 allows for a long-wave as well as a full-curvature formulation. Second, we compare results obtained with the mesoscopic long-wave 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.

Stick-slip dynamics in the forced wetting of polymer brushes

“…, by using a Flory–Huggins energy with χ ≠ 0), substrate elasticity, 23 or the effects of evaporation into an ambient vapour phase using, e.g. , the approach suggested by Hartmann et al 66 and Kap et al 86…”

“…60,61 This approach has been expanded to two-field systems as, for example, two-layer liquid films, 62,63 liquid drops/films covered by an insoluble surfactant, 64 drops on viscoelastic substrates, 23 films of liquid mixtures, 65 and drops of volatile liquids in a vapour-filled gap. 66 It also forms a central building block for models of biofilms 67 and drops of active liquids. 68…”

Drops on Polymer Brushes: Advances in Thin-Film Modeling of Adaptive Substrates

“…In past years, such gradient dynamics models have been proposed for the dewetting of two-layer films on solid substrates, ,,− for the dynamics of liquid films covered by insoluble and soluble surfactants, dewetting and decomposing films of binary mixtures, , and the coupled dynamics of shallow drops of volatile liquids and the resulting vapor . Although there the thermodynamic form sometimes only reformulates models already known in their hydrodynamic form, ,− it nevertheless allows one to easily thermodynamically validate the models and to identify possible (small and large) thermodynamic inconsistencies and reasons for observed unphysical behavior .…”

“…Technically, one eliminates the second column and second row from the mobility matrices (eq ) and (eq ) and removes f brush and all ζ-dependencies from eq , thereby reducing the model (eq ) to two dynamic equations, one for the liquid and one for the vapor. The resulting two-field model is developed and analyzed in ref . It allows for the study of drop evaporation in the full range of parameters from the phase transition-limited case (often covered by “one-sided models”) to the diffusion-limited case. A two-field model of a sessile drop of nonvolatile liquid on an adaptive brush-covered substrate with brush state-dependent interface and wetting energies is obtained in the limit ρ vap → 0 in the energy functional and the mobilities.…”

“…Here, we review how the gradient dynamics form of mesoscopic hydrodynamics is employed to extend the reach of thin-film models toward brush-covered substrates − and, in passing, as well show how for volatile liquids the vapor dynamics can be covered . In particular, the next section introduces the gradient dynamics approach for films/drops of nonvolatile simple liquids on rigid, smooth solid substrates, and then expands it to an arbitrary number of coupled scalar degrees of freedom.…”