Stability of rotating liquid films

Diogo Aguiar Gomes*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)327-343
Number of pages17
JournalQuarterly Journal of Mechanics and Applied Mathematics
Issue number3
StatePublished - Aug 2002
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported in part by the National Aeronautics and Space Administration under grant NAG3-1941, by the Programa Praxis XXI under grant BD 522895, and FCT (Portugal) through programs POCTI, POCTI/32931/MAT/2000. Part of the computational work was carried out at the Lawrence Berkeley National Laboratory facilities.

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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