TY - JOUR
T1 - Nonexistence of two-dimensional sessile drops in the diffuse-interface model
AU - Benilov, E. S.
N1 - Publisher Copyright:
© 2020 American Physical Society.
PY - 2020/8
Y1 - 2020/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85090330362&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.102.022802
DO - 10.1103/PhysRevE.102.022802
M3 - Article
C2 - 32942467
AN - SCOPUS:85090330362
SN - 2470-0045
VL - 102
SP - 022802
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 2
M1 - 022802
ER -