On the Bifurcation and Stability of Rigidly Rotating Inviscid Liquid Bridges

Journal of Nonlinear Science

Volumn 8, Issue 2, 1998, Pages 215-232

  Kruse, H P ^a   Scheurle, J ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000968358     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003329900049     Document Type: Article

References (34)

1. Abraham R. and Marsden J. E., Foundations of Mechanics, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass., 1978.
2. Arnold V. I., Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier, Grenoble 16(1) (1966), 319-361.
3. Concus P. and Finn R., The shape of a pendent liquid drop, Philos. Trans. Roy. Soc. London Ser. A, 292 (1979), 307-340.
4. Concus P. and Finn R., Capillary surfaces in microgravity, in Low-Gravity Fluid Mechanics and Transport Phenomena, J. N. Koster and R. L. Sani, eds., Progress in Astronautics and Aeronautics 130, AIAA, Washington, DC, 1990, 183-206.
5. Crandall M. G. and Rabinowitz P. H., Bifurcation from simple eigenvalues, J. Funct. Anal. 8 (1971), 321-340.
6. Crandall M. G. and Rabinowitz P. H., Bifurcation, perturbation of simple eigenvalues and linearized stability. Arch. Ratl. Mech. Anal. 52 (1973), 161-180.
7. Fermigier M. and Jenffer, P., An experimental investigation of the dynamic contact angle in liquid-liquid systems, J. Coloid Interface Sci. 146(1) (1991), 226-241.
8. Finn R., Equilibrium Capillary Surfaces. Springer-Verlag, New York, 1986.
9. Finn R. and Vogel T. I., On the volume infimum for liquid bridges, Z. Anal. Anw. 11 (1992), 3-23.
10. Kruse H.-P., Flüssigkeitstropfen zwischen parallelen Platten: Hamiltonsche Struktur, Existenz von Lösungen und Stabilität, Doctoral thesis, Universität Hamburg, 1992.
11. Kruse H.-P., The Hamiltonian structure of the equations of motion of a liquid drop trapped between two plates, Preprint, 1994.
12. Kruse H.-P., Mahalov A., and Marsden J. E., On the three-dimensional instabilities of rotating liquid bridges, Preprint 1995.
13. Kruse H.-P., Marsden J. E., and Scheurle J., On uniformly rotating fluid drops trapped between two parallel plates, Lect. Appl. Math. 29 (1993), 307-317.
14. Lewis D., Nonlinear stability of a rotating planar liquid drop, Arch. Ratl. Mech. Anal. 106 (1989), 287-333.
15. Lewis D., Lagrangian Block Diagonalization, J. Dyn. Diff. Eq. 4(1) (1992), 1-41.
16. Lewis D., Bifurcations of liquid drops, Nonlinearity 6 (1993), 491-522.
17. Lewis D., Marsden J. E., Montgomery R., and Ratiu T. S., The Hamiltonian structure for dynamic free boundary problems, Physica D 18 (1986), 391-404.
18. Lewis D., Marsden J. E., and Ratiu T. S., Stability and bifurcation of a rotating planar liquid drop, J. Math. Phys. 28 (1987), 2500-2515.
19. Lewis, D. and Simo J. C., Nonlinear stability of rotating pseudo-rigid bodies, Proc. Roy. Soc. London A 427 (1990), 281-319.
20. Marsden J. E., Lectures on Mechanics, London Math. Soc. Lect. Note Series, Vol. 174, Cambridge Univ. Press, Cambridge, 1992.
21. Marsden J. E., Simo J. C., Lewis D., and Posbergh T. A., A block diagonalization theorem in the energy momentum method, Cont. Math. AMS 97 (1989), 297-313.
22. Oh, Y. G., A stability criterion for Hamiltonian systems with symmetry, Geom. Phys. 4 (1987), 163-182.
23. Patrick G. W., Relative equilibria of Hamiltonian systems with symmetry: Linearization, smoothness, and drift, J. Nonl. Sci. 5(5) (1995), 373-418.
24. Scheurle J., Some aspects of successive bifurcations in the Couette-Taylor problem, in Pattern Formation: Symmetry Methods and Applications, J. Chadam, M. Golubitsky, W. F. Langford, and B. Wetton, eds., Fields Inst. Comm. 5 (1996), 335-345.
25. Simo J. C., Lewis D., and Marsden J. E., Stability of relative equilibria. Part 1: The reduced energy momentum method, Arch. Ratl. Mech. Anal. 115 (1991), 15-59.
26. Simo J. C., Posbergh T. A., and Marsden J. E., Stability of coupled rigid bodies and geometrically exact rods: Block diagonalization and the energy-momentum method, Phys. Reports 193 (1990), 279-360.
27. Simo J. C., Posbergh T. A., and Marsden J. E., Stability of relative equilibria. Part II: Application to nonlinear elasticity, Arch. Ratl. Mech. Anal. 115 (1991), 61-100.
28. Smale S., Topology and mechanics, Inv. Math. 10 (1970), 305-331; 11 (1970), 45-64.
29. Smale S., Topology and mechanics, Inv. Math. 10 (1970), 305-331; 11 (1970), 45-64.
30. Thompson P. and Robbins M., Simulations of contact-line motion: Slip and the dynamic contact angle, Phys. Rev. Lett. 63(7) (1989), 766-769.
31. Thompson P. and Robbins M., To slip or not to slip?, Physics World, November 1990, 35-38.
32. Vogel T. I., Stability of a liquid drop trapped between two parallel planes, SIAM J. Appl. Math. 47 (1987), 516-525.
33. Vogel T. I., Stability of a liquid drop trapped between two planes II: General contact angles, SIAM J. Appl. Math. 49 (1989), 1009-1028.
34. Zhou L., On the volume intimum for liquid bridges, Z. Anal. Anw. 12 (1993), 629-642.