Shape and stability of levitated viscous drops

A drop of molten glass can be levitated above a porous spherical mould by air injection. Owing to the viscosity contrast, the float height for a given shape is established on a much shorter time scale than the subsequent deformation of the drop under gravity, surface tension and the lubrication pressure. The set of solution branches for equilibrium, non-deforming shapes is surprisingly complicated and shows a rich bifurcation structure in $(Bo, Ca)$ space (drop volume, injection velocity). The stability of equilibria is determined using a novel boundary- integral representation that factors out the rapid adjustment of the float height.