Drop Behavior Influenced by the Correlation Length on Noisy Surfaces

Can a liquid drop on a substrate be in equilibrium with saturated vapor?

It is well known that liquid and saturated vapor, separated by a flat interface in an unbounded space, are in equilibrium. One would similarly expect a liquid drop, sitting on a flat substrate, to be in equilibrium with the vapor surrounding it. Yet, it is not: as shown in this work, the drop evaporates. Mathematically, this conclusion is deduced using the diffuse-interface model, but it is also reformulated in terms of the maximum-entropy principle, suggesting model independence. Physically, evaporation of drops is due to the so-called Kelvin effect, which gives rise to a liquid-to-vapor mass flux if the boundary of the liquid phase is convex.

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

The diffuse-interface model (DIM) is a widely used tool for modeling fluid phenomena involving interfaces, such as 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-for example, for water at room temperature-the ridges can still be observed as quasistatic 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.

Dependence of the surface tension and contact angle on the temperature, as described by the diffuse-interface model

Four results associated with the diffuse-interface model (DIM) for contact lines are reported in this paper. First, a boundary condition is derived, which states that the fluid near a solid wall must have a certain density ρ_{0} depending on the solid's properties. Unlike previous derivations, the one presented here is based on the same physics as the DIM itself and does not require additional assumptions. Second, asymptotic estimates are used to check a conjecture lying at the foundation of the DIM, as well as all other models of contact lines, that liquid-vapor interfaces are nearly isothermal. It turns out that, for water, they are not, although, for a more viscous fluid, they can be. The nonisothermality occurs locally, near the interface, but can still affect the contact-line dynamics. Third, the DIM coupled with a realistic equation of state for water is used to compute the dependence of the surface tension σ on the temperature T, which agrees well with the empirical σ(T). Fourth, the same framework is used to compute the static contact angle of a water-vapor interface. It is shown that, with increasing temperature, the contact angle becomes either 180^{∘} (perfect hydrophobicity) or 0^{∘} (perfect hydrophilicity), depending on whether ρ_{0} matches the density of saturated vapor or liquid, respectively. Such behavior presumably occurs in all fluids, not just water, and for all sufficiently strong variations of parameters, not just that of the temperature, as corroborated by existing observations of drops under variable electric field.