Skip to main content
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
1. G. I. Taylor, “The instability of liquid surfaces when accelerated in a direction perpendicular to their planesProc. R. Soc. London Ser. A 201, 192196 (1950).
2. L. Rayleigh, “Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density,” Proc. London Math. Soc. s1-14(1), 170177 (1882).
3. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 2004).
4. D. H. Sharp, “An overview of Rayleigh-Taylor instability,” Phys. D 12, 318 (1984).
5. J. D. Lindl and W. C. Mead, “Two-dimensional simulation of fluid instability in laser-fusion pellets,” Phys. Rev. Lett. 34, 1273 (1975).
6. G. A. Houseman and P. Molnar, “Gravitational Rayleigh-Taylor instability of a layer with non-linear viscosity and convective thinning of continental lithosphere,” Geophys. J. Intl. 128, 125150 (1997).
7. M. Fermigier, L. Limat, J. E. Wesfreid, P. Boudinet, and C. Quilliet, “Two-dimensional patterns in Rayleigh-Taylor instability of a thin layer,” J. Fluid Mech. 236, 349383 (1992).
8. A. A. King, L. J. Cummings, S. Naire, and O. E. Jensen, “Liquid film dynamics in horizontal and tilted tubes: Dry spots and sliding drops,” Phys. Fluids 19, 042102 (2007).
9. A. Indeikina, I. Veretennikov, and H.-C. Chang, “Drop fall-off from pendent rivulets,” J. Fluid Mech. 338, 173201 (1997).
10. R. Majeski, H. Kugel, R. Kaita, M. G. Avasarala, M. G. Bell, R. E. Bell, L. Berzak, P. Beiersdorfer, S. P. Gerhardt, E. Granstedt, T. Gray, C. Jacobson, J. Kallman, S. Kaye, T. Kozub, B. P. LeBlanc, J. Lepson, D. P. Lundberg, R. Maingi, D. Mansfield, S. F. Paul, G. V. Pereverzev, H. Schneider, V. Soukhanovskii, T. Strickler, D. Stotler, J. Timberlake, L. E. Zakharov, The NSTX and LTX Research Teams, “The impact of lithium wall coatings on NSTX discharges and the engineering of the Lithium Tokamak eXperiment (LTX),” Fus. Eng. Des. 85(7–9), 12831289 (2010).
11. R. Kaita, L. Berzak, D. Boyle, T. Gray, E. Granstedt, G. Hammett, C. M. Jacobson, A. Jones, T. Kozub, H. Kugel, B. Leblanc, N. Logan, M. Lucia, D. Lundberg, R. Majeski, D. Mansfield, J. Menard, J. Spaleta, T. Strickler, J. Timberlake, J. Yoo, L. Zakharov, R. Maingi, V. Soukhanovskii, K. Tritz, and S. Gershman, “Experiments with liquid metal walls: Status of the lithium tokamak experiment,” Fus. Eng. Des. 85, 874881 (2010).
12. L. W. Schwartz and D. E. Weidner, “Modeling of coating flows on curved surfaces,” J. Eng. Math. 29, 91103 (1995).
13. O. E. Jensen, “The thin liquid lining of a weakly curved cylindrical tube,” J. Fluid Mech. 331, 373403 (1997).
14. H. K. Moffatt, “Behaviour of a viscous film on the outer surface of a rotating cylinder,” J. Mech. 16, 651673 (1977).
15. J. Ashmore, A. E. Hosoi, and H. A. Stone, “The effect of surface tension on rimming flows in a partially filled rotating cylinder,” J. Fluid Mech. 479, 6598 (2003).
16. E. S. Benilov, N. Kopteva, and S. B. G. O’Brien, “Does surface tension stabilize liquid films inside a rotating horizontal cylinder?Q. J. Mech. Appl. Math. 58, 185200 (2005).
17. R. V. Roy, A. J. Roberts, and M. E. Simpson, “A lubrication model of coating flows over a curved substrate in space,” J. Fluid Mech. 454, 235261 (2002).
18. P. D. Howell, “Surface-tension-driven flow on a moving curved surface,” J. Eng. Math. 45, 283308 (2003).
19. T. G. Myers, J. P. F. Charpin, and S. J. Chapman, “The flow and solidification of a thin fluid film on an arbitrary three-dimensional surface,” Phys. Fluids 14, 27882803 (2002).
20. H. Ockendon and J. R. Ockendon, Viscous Flow (Cambridge University Press, Cambridge, 1995).
21. P.-G. De Gennes, F. Brochard-Wyart, and D. Quéré, Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves (Springer-Verlag, New York, 2004).
22. J. M. Burgess, A. Juel, W. D. McCormick, J. B. Swift, and H. L. Swinney, “Suppression of dripping from a ceiling,” Phys. Rev. Lett. 86, 1203 (2001).
23. N. A. Bezdenezhnykh, V. A. Briskman, A. A. Cherepanov, and M. T. Sharov, “Control of the stability of liquid surfaces by means of variable fields,” Fluid Mech. Sov. Res. 15, 1132 (1986).
24. G. H. Wolf, “Dynamic stabilization of the interchange instability of a liquid-gas interface,” Phys. Rev. Lett. 24, 444 (1970).

Data & Media loading...


Article metrics loading...



The dynamics of a thin liquid film on the underside of a curved cylindrical substrate is studied. The evolution of the liquid layer is investigated as the film thickness and the radius of curvature of the substrate are varied. A dimensionless parameter (a modified Bond number) that incorporates both geometric parameters, gravity, and surface tension is identified, and allows the observations to be classified according to three different flow regimes: stable films, films with transient growth of perturbations followed by decay, and unstable films. Experiments and linear stability theory confirm that below a critical value of the Bond number curvature of the substrate suppresses the Rayleigh-Taylor instability.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd