  We present a second order numerical scheme to compute capillary bridges
between arbitrary solids by minimizing the total energy of all interfaces. From
a theoretical point of view, this approach can be interpreted as the
computation of generalized minimal surfaces using a Newton-scheme utilizing the
shape Hessian. In particular, we give an explicit representation of the shape
Hessian for functionals on shells involving the normal vector without reverting
back to a volume formulation or approximating curvature. From an algorithmic
perspective, we combine a resolved interface via a triangulated surface for the
liquid with a level set description for the constraints stemming from the
arbitrary geometry. The actual shape of the capillary bridge is then computed
via finite elements provided by the FEniCS environment, minimizing the shape
derivative of the total interface energy.
