Applied Scientific Research

, Volume 52, Issue 4, pp 295–308 | Cite as

Bénard-Marangoni convection in a rotating fluid with and without surface deformation

  • A. Kaddame
  • G. Lebon
Article

Abstract

This paper deals with Bénard-Marangoni convection in a thin horizontal layer heated from below and rotating uniformly about a vertical axis. The analysis is linear and its objective is to determine the critical temperature drop and the critical wavenumber at the onset of convection. The lower surface of the layer is in contact with an uniformly heated rigid plate and the upper face is deformed and subjected to a temperature-dependent surface tension. Exchange of stability and Boussinesq's approximation are taken for granted. It is shown that rotation has a stabilizing effect while surface deflection plays a stabilizing role at large angular velocity and has an opposite influence at low angular velocity. By increasing the angular velocity, one reinforces the stability, whatever the surface deformation.

Keywords

Convection Surface Tension Angular Velocity Critical Temperature Vertical Axis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nield, D. A., Surface tension and buoyancy effect in cellular convection.J. Fluid Mech. 19 (1964) 341–352.Google Scholar
  2. 2.
    Lebon, G. and Perez-Garcia, C., Study of surface tension effects in thermal convection by variational methods.Bull. Cl. Sc. Acad. Roy. Belgique 66 (1980) 520–542.Google Scholar
  3. 3.
    Davis, S. H., Buoyancy-surface tension instability by the method of energy.J. Fluid Mech. 39 (1969) 347–359.Google Scholar
  4. 4.
    Koschmieder, E. and Biggerstaff, M. I., Onset of surface-tension-driven Bénard convection.J. Fluid Mech. 167 (1986) 49–64.Google Scholar
  5. 5.
    Pantaloni, J., Bailleux, R., Salan, J. and Velarde, M., Rayleigh-Bénard instability: new experimental results.J. Non-Equilib. Thermodyn. 4 (1979) 201–218.Google Scholar
  6. 6.
    Velarde, M. and Normand, G., Convection.Scientific American 243 (1980) 92–108.Google Scholar
  7. 7.
    Scriven, L. and Sternling, C., On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity.J. Fluid Mech. 19 (1964) 321–340.Google Scholar
  8. 8.
    Perez-Garcia, C. and Carneiro, G., Linear stability analysis of Bénard-Marangoni convection in fluids with a deformable free surface.Phys. Fluids 3 (1991) 292–298.Google Scholar
  9. 9.
    Lebon, G. and Cloot, A., Marangoni instability in a fluid layer with variable viscosity and free interface in microgravity.Physico-Chemical Hydrod. 6 (1985) 453–462.Google Scholar
  10. 10.
    Smith, K. A., On convective instability induced by surface-tension gradients.J. Fluid Mech. 24 (1966) 401–414.Google Scholar
  11. 11.
    Chandrasekhar, S.,Hydrodynamic and Hydromagnetic Stability Chapter, Oxford University Press (1961).Google Scholar
  12. 12.
    Veronis, G., Motions at subcritical values of the Rayleigh number in a rotating fluid.J. Fluid Mech. 24 (1966) 545–554.Google Scholar
  13. 13.
    Veronis, G., Large-amplitude Bénard convection in a rotating fluid.J. Fluid Mech. 31 (1968) 113–139.Google Scholar
  14. 14.
    Rossby, H. T., A study of Bénard convection with and without rotation.J. Fluid Mech. 36 (1969) 309–335.Google Scholar
  15. 15.
    Finlayson, B. A., The Galerkin method applied to convective instability problems.J. Fluid Mech. 33 (1968) 201–208.Google Scholar
  16. 16.
    Busse, F. H. and Carrigan, C. R., Convection induced by centrifugal buoyancy.J. Fluid Mech. 62 (1974) 579–592.Google Scholar
  17. 17.
    Vidal, A. and Acrivos, A., The influence of Coriolis force on surface-tension-driven convection.J. Fluid Mech. 26 (1966) 807–818.Google Scholar
  18. 18.
    McConaghy, G. A. and Finlayson, B. A., Surface tension driven oscillatory instability in a rotating fluid layer.J. Fluid Mech. 39 (1969) 49–55.Google Scholar
  19. 19.
    Sarma, G. S. R., On oscillatory modes of thermocapillary instability in a liquid layer rotating about a transverse axis.Physico-Chemical Hydro 2 (1981) 143–151.Google Scholar
  20. 20.
    Sarma, G. S. R., Interfacial effects on the onset of convection in horizontal liquid layers. In: Velarde (ed.),Physico-Chemical Hydrodynamics, Plenum (1988) 271–289.Google Scholar
  21. 21.
    Velarde, M. and Hennenberg, M., Private communication, 1993.Google Scholar
  22. 22.
    Kaddame, A. and Lebon, G., Overstability in Marangoni convection of an electrically conducting fluid in presence of an external magnetic field.Microgravity Quat. 3 (1993) 1–6.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • A. Kaddame
    • 1
  • G. Lebon
    • 1
  1. 1.Institute of Physics B5Liège UniversityLiègeBelgium

Personalised recommendations