Nonexistence of two-dimensional sessile drops in the diffuse-interface model

Abstract

The diffuse-interface model (DIM) is a widely used tool for modeling fluid phenomena involving interfaces -- such as, for example, sessile drops (liquid drops on a solid substrate, surrounded by saturated vapor) and liquid ridges (two-dimensional sessile drops). In this work, it is proved that, surprisingly, the DIM does not admit solutions describing static liquid ridges. If, however, the vapor-to-liquid density ratio is small -- as, for example, for water at room temperature -- the ridges can still be observed as quasi-static states, as their evolution is too slow to be distinguishable from evaporation. Interestingly, the nonexistence theorem cannot be extended to axisymmetric sessile drops and ridges near a vertical wall, which are not ruled out.

References in corpus (7)

• Disjoining Potential and Spreading of Thin Liquid Layers in the Diffuse Interface Model Coupled to Hydrodynamics
• Decomposition driven interface evolution for layers of binary mixtures: I. Model derivation and stratified base states
• Moving contact line dynamics: from diffuse to sharp interfaces
• The contact line behaviour of solid-liquid-gas diffuse-interface models
• Dependence of the surface tension and contact angle on the temperature, as described by the diffuse-interface model
• Asymptotic reductions of the diffuse-interface model, with applications to contact lines in fluids
• The dynamics of liquid films, as described by the diffuse-interface model

Cited by in corpus (5)

• Capillary condensation of saturated vapor in a corner formed by two intersecting walls
• The multicomponent diffuse-interface model and its application to water/air interfaces
• Dynamics of a drop floating in vapor of the same fluid
• The dynamics of liquid films, as described by the diffuse-interface model
• Can a liquid drop on a substrate be in equilibrium with saturated vapor?