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.
Cite
@article{arxiv.2007.07968,
title = {Nonexistence of two-dimensional sessile drops in the diffuse-interface model},
author = {E. S. Benilov},
journal= {arXiv preprint arXiv:2007.07968},
year = {2021}
}