FIG. 1 Density profile of a liquid-vapor interface as a function of height z showing the interfacial region with the location of the dividing surface.

A very important feature of the surface is its curvature. Any point on the surface is characterized by two radii of curvature, R1 and R2. The radius of curvature at a certain point along a certain direction is defined as the radius of the sphere with which the surface can be locally approximated such that the first and second derivatives in that direction are equal to those of the sphere. Together with this definition, one needs to determine the sign of the radius of curvature, since the curvature can be directed toward either the liquid or the vapor phase. The usual convention, the one that we will also adopt here, is to define curvature toward the liquid phase (or in general, toward the denser phase) as positive.