Simulation of a pending drop at a capillary tip

We derive four different numerical schemes to compute the shape of axisymmetric drops at the tip of a capillary for a given drop volume and a given Bond number. Small drop volumes show a convex shape, however increasing the drop volume a point of inflection appears and at a critical drop volume (depending from the Bond number) the drop detaches from its capillary. One of the four schemes produces drop shapes completely different from the others. We show that these shapes are unstable by solving numerically the free boundary value problem for the transient Navier-Stokes equations.