Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-21T01:16:34.328Z Has data issue: false hasContentIssue false
  • English
  • Français

Surface wave and thermocapillary instabilities in a liquid film flow

Published online by Cambridge University Press:  26 April 2006

D. A. Goussis  and
R. E. Kelly
D. A. Goussis
Affiliation:
Mechanical, Aerospace, and Nuclear Engineering Department, University of California, Los Angeles, Los Angeles, CA 90024, USA Present address: Mechanical and Aerospace Engineering Department, Princeton University, Princeton, NJ 08544, USA.
R. E. Kelly
Affiliation:
Mechanical, Aerospace, and Nuclear Engineering Department, University of California, Los Angeles, Los Angeles, CA 90024, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A liquid film flowing down an inclined heated plane subject to surface wave and thermocapillary instabilities is studied. Three mechanisms exist by which energy can be transferred to the disturbance. Two of these mechanisms are associated with the thermocapillary forces and one with the shear stress of the basic flow at the deformed free surface. Depending on which mechanism is dominant, the instability can assume the form of either long transverse waves or short longitudinal rolls.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 25 - 45
Copyright
© 1991 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.)

References

Benjamin, T. B.: 1957 Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2, 554.Google Scholar
De Bruin, G. J. 1974 Stability of a layer of liquid flowing down an inclined plane. J. Engng Maths 8, 259.Google Scholar
Floryan, J. M., Davis, S. H. & Kelly, R. E., 1987 Instabilities of a liquid film flowing down a slightly inclined plane. Phys. Fluids 30, 983.Google Scholar
Gage, K. S. & Reid, W. H., 1968 The stability of thermally stratified plane Poiseuille flow. J. Fluid Mech. 33, 21.Google Scholar
Gallagher, A. P. & Mercer, A., 1965 On the behavior of small disturbances in plane Couette flow with a temperature gradient. Proc. R. Soc. Lond. A 286, 117.Google Scholar
Gottlieb, D. & Orszag, S. A., 1977 Numerical Analysis of Spectral Methods: Theory and Applications. Philadelphia: SIAM.
Goussis, D. A.: 1986 Instabilities of stratified film flows. Ph.D. thesis, University of California, Los Angeles.
Goussis, D. A. & Kelly, R. E., 1990 On the thermocapillary instabilities in a liquid layer heated from below. Intl J. of Heat Mass Transfer (in press).Google Scholar
Goussis, D. A. & Pearlstein, A. J., 1989 Removal of infinite eigenvalues in the generalized eigenvalue problem. J. Comput. Phys. 84, 242.Google Scholar
Kelly, R. E., Davis, S. H. & Goussis, D. A., 1986 On the instability of heated film flow with variable surface tension. In Heat Transfer 1986. Proc. 9th Intl Heat Transfer Conference, San Francisco, vol. 4, p. 1936.Google Scholar
Kelly, R. E. & Goussis, D. A., 1982 Instability of a liquid film flowing down a heated inclined plane. In Heat Transfer 1982. Proc. 8th Intl Heat Transfer Conference, Munich, vol. 5, p. 319.Google Scholar
Kelly, R. E., Goussis, D. A., Lin, S. P. & Hsu, F. K., 1989 The mechanism for surface wave instability in liquid film flow. Phys. Fluids A 1, 819.Google Scholar
Lin, S. P.: 1967 Instability of a liquid film flowing down an inclined plane. Phys. Fluids 10, 308.Google Scholar
Lin, S. P.: 1975 Stability of liquid flow down a heated inclined plane. Lett. Heat Mass Transfer 2, 361.Google Scholar
Moler, G. B. & Stewart, G. W., 1973 An algorithm for the generalized eigenvalue problem. SIAM J. Numer. Anal. 10, 241.Google Scholar
Pearlstein, A. J. & Goussis, D. A., 1988 Efficient transformation of singular polynomial matrix eigenvalue problems. J. Comput. Phys. 78, 305.Google Scholar
Pearson, J. R. A.: 1958 On convection cells induced by surface tension. J. Fluid Mech. 4, 489.Google Scholar
Smith, K. A.: 1966 On convective instability induced by surface tension gradients. J. Fluid Mech. 24, 401.Google Scholar
Smith, M. K.: 1990a The mechanism for the long-wave instability in thin liquid films. J. Fluid Mech. 217, 469.Google Scholar
Smith, M. K.: 1990b The long-wave instability in heated or cooled inclined liquid layers. J. Fluid Mech. 219, 337.Google Scholar
Sreenivasan, S. & Lin, S. P., 1978 Surface tension driven instability of a liquid film down a heated incline. Intl J. Heat Mass Transfer 21, 1517.Google Scholar
Takashima, M.: 1981 Surface tension driven instability in a liquid layer with a deformable free surface. J. Phys. Soc. Japan 50, 2745.Google Scholar
Yih, C.-S.: 1955 Stability of laminar parallel flow with a free surface. In Proc. 2nd US Nail Congr. Applied Mechanics, p. 623. ASME.
Yth, C.-S.: 1963 Stability of liquid flow down an inclined plane. Phys. Fluids 6, 321.Google Scholar