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

TL;DR

This paper proves that the diffuse-interface model cannot describe static two-dimensional sessile drops, but quasi-static states may still be observed under certain conditions, with some configurations remaining possible.

Contribution

It establishes a nonexistence theorem for static 2D sessile drops in the diffuse-interface model, clarifying the model's limitations for certain fluid phenomena.

Findings

DIM does not admit static 2D sessile drop solutions.

Quasi-static states are possible when vapor-to-liquid density ratio is small.

Axisymmetric drops near a wall are not ruled out by the theorem.

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.