Singularities of meniscus at the V-shaped edge

• We classified the cases when the meniscus on a V-shaped edge cannot be smooth.
• A wetting diagram is considered in 3D space of the V-angle and two contact angles.
• Wetting tetrahedrons in the 3D phase diagram are discovered.
• Particular examples of chemically inhomogeneous plates, blades, square corners, and Janus V-shaped edges were discussed.

An understanding of the capillary rise of the meniscus formed on the V-shaped fibers is crucial for many applications. We classified the cases when the meniscus cannot be smooth by analyzing the local behavior of the solutions to the Laplace equation of capillarity near the sharp edge. The V-angle and two contact angles that the meniscus forms on two chemically different sides of the fiber form a 3D phase space. Smooth menisci constitute a special domain in this 3D space. The constructed diagram allows one to separate the solutions with smooth and non-smooth menisci. The obtained criteria were illustrated using chemically inhomogeneous plates, blades, square corners, and Janus V-shaped edges.