Stability of Rotating Liquid Films

In this paper we consider a modified Young-Laplace-Gauss variational formulation that incorporates a van der Waals potential of adhesion and gives equilibrium configurations of a liquid in contact with a solid and a gas. This model is used to compute the shape of the liquid/gas interface in a coaxial cylindrical container, a configuration like that of the main liquid helium tank in Gravity Probe B and STEP (Satellite Test of Equivalence Principle) space experiments. We derive the Euler-Lagrange equations and study their rotationally symmetric solutions. Then we compute the second variation and analyze the stability of several configurations. In particular, we prove the existence of a Plateau-Rayleigh instability and curvature-driven instability for very small volume configurations. We compare our results with previous physical experiments, and we conclude that certain observed instabilities cannot be attributed to the above mechanisms.