Hostname: page-component-7dd5485656-wlg5v Total loading time: 0 Render date: 2025-10-31T04:42:41.250Z Has data issue: false hasContentIssue false
  • English
  • Français

On a nonlinear thermocapillary effect in thin liquid layers

Published online by Cambridge University Press:  26 April 2006

Alexander Oron  and
Philip Rosenau
Alexander Oron
Affiliation:
Faculty of Mechanical Engineering and Center for Research in Nonlinear Phenomena, Technion–Israel Institute of Technology, Haifa 32000, Israel
Philip Rosenau
Affiliation:
Faculty of Mechanical Engineering and Center for Research in Nonlinear Phenomena, Technion–Israel Institute of Technology, Haifa 32000, Israel Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Dilute aqueous solutions of long alcohol chains were recently found to cause a quadratic dependence of surface tension on the temperature without affecting other bulk properties of the liquid: σ = σ0 + αQ(T − T0)2, αQ > 0. The impact of such Marangoni instability on the behaviour of a thin liquid layer is studied in this work. We derive an equation describing a nonlinear spatiotemporal evolution of a thin film. The behaviour of the perturbed film in the absence of gravity, critically depends on whether the temperature T0, yielding a minimal surface tension, is attained on the surface of the film. When this is the case, a qualitatively new behaviour is observed: perturbations of the film interface may evolve into continuous steady patterns that do not rupture. Otherwise, the observed patterns due to the linear and quadratic Marangoni effects are qualitatively similar and result in the rupture of the film into separate drops.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 273 , 25 August 1994 , pp. 361 - 374
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Nonlinear stability of evaporating/ condensing liquid films. J. Fluid Mech. 195, 463–494.Google Scholar
Cloot, A. & Lebon, G. 1986 Marangoni convection induced by a nonlinear temperature-dependent surface tension. J. Phys. Paris 47, 23–29.Google Scholar
Davis, S. H. 1987 Thermocapillary instabilities. Ann. Rev. Fluid Mech. 19, 403–435 and references therein.Google Scholar
Deissler, R. J. & Oron, A. 1992 Stable localized patterns in thin liquid films. Phys. Rev. Lett. 68, 2948–2951.Google Scholar
Gupalo, Yu. P. & Ryazantsev, Yu. S. 1989 Thermocapillary motion of a liquid with a free surface with nonlinear dependence of the surface tension on the temperature. Fluid Dyn. 23, 752–757.Google Scholar
Gupalo, Yu. P., Ryazantsev, Yu. S. & Skvortsova, A. V. 1990 Effect of thermocapillary forces on free-surface fluid motion. Fluid Dyn. 24, 657–661.Google Scholar
Guyon, E. & Pantaloni, J. 1980 Effet de tension superficielle sur la convection de Rayleigh–Bénard. CR Acad. Sci. Paris B 290, 301–304.Google Scholar
Hocherman, T. & Rosenau, P. 1993 On KS-type equations describing the evolution and rupture of a liquid interface. Physica, D 67, 113–125.Google Scholar
Legros, J. C. 1986 Problems related to non-linear variations of surface tension. Acta Astr. 13, 697–703.Google Scholar
Legros, J. C., Limbourg-Fontaine, M. C. & Petre, G. 1984 Influence of a surface tension minimum as a function of temperature on the Marangoni convection. Acta Astr. 11, 143–147.Google Scholar
Limbourg, M. C. & Georis, Ph. 1989 Preliminary results of Texus 19 (Temo6–8) experiment: Marangoni convection around a surface tension minimum. Proc. VIIth Eur. Symp. on Materials and Fluid Sci. in Microgravity (Oxford, UK), ESA SP-295, pp. 347–351.
Oron, A. & Rosenau, P. 1992 Formation of patterns induced by thermocapillarity and gravity. J. Phys. France II 2, 131–148.Google Scholar
Pearson, J. R. A. 1958 On convection cells induced by surface tension. J. Fluid Mech. 4, 489–500.Google Scholar
Tan, M. J., Bankoff, S. G. & Davis, S. H. 1990 Steady thermocapillary flows of thin liquid layers. I. Theory. Phys. Fluids A 2, 313–321.Google Scholar