Extended Annular Capillary Surfaces

The height of the surface of a fluid in an annular tube is explored using a shooting method to solve a boundary value problem where the radii and the contact angles are given. The contact angles on the inner and outer tube surface need not be the same. These surfaces are then extended so that they are no longer graphs. The extended surfaces are shown to solve a boundary value problem over an annular base domain where given inclination angles are achieved at given radii.