Bounded and unbounded capillary surfaces in a cusp domain

Abstract

We study asymptotic behavior of the height of a static liquid surface in a cusp domain as modelled by the Laplace‐Young capillary surface equation. We introduce a new form of an asymptotic expansion in terms of the functions defining the boundary curves forming a cusp. We are able to address the asymptotic behavior of the capillary surface in cusp domains not previously considered, such as an exponential cusp. In addition, we have shown that the capillary surface in a cusp domain is bounded if the contact angles of the boundary walls forming a cusp are supplementary angles, which implies the continuity of the capillary surface at the cusp.