WETTING PHENOMENA AND CONSTANT MEAN CURVATURE SURFACES WITH BOUNDARY

Abstract

In a microscopic scale or microgravity environment, interfaces in wetting phenomena are usually modeled by surfaces with constant mean curvature (CMC surfaces). Usually, the condition regarding the constancy of the contact angle along the line of separation between different phases is assumed. Although the classical capillary boundary condition is the angle made at the contact line, configurations also occur in which a Dirichlet condition is appropriate. In this article, we discuss those with vanishing boundary conditions, such as those that occur on a thin flat portion of a plate of general shape covered with water. In this paper, we review recent works on the existence of CMC surfaces with non-empty boundary, with a special focus on the Dirichlet problem for the constant mean curvature equation.