© 2002 by Oxford University Press
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Stability of Rotating Liquid Films
( 1 Department of Mathematics, University of Texas at Austin, Austin TX 78712, USA and Instituto Superior Técnico, Lisbon, Portugal )
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 the satellite test of equivalence principle (STEP) space experiments.
We derive the Euler–Lagrange equations and study their rotationally symmetric solutions. Then we compute the second variation and analyse 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.
Received 14 September 1999. Revised 21 December 2000 and 4 June 2001.