Skip to main content
Log in

Bénard-Marangoni Instability of a Two-Layer System with Allowance for Variations in the Interfacial Internal Energy

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The effect of variations of the internal surface energy due to local increments in the interfacial area on the conditions of onset of thermocapillary Marangoni instability in a two-layer system of reduced-viscosity fluids is studied. It is shown that in the linear approximation the effect considered leads to stabilization of the development of the monotonic instability mode.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. S. H. Davis, “Thermocapillary instabilities,” Annu. Rev. Fluid Mech., 19, 403 (1987).

    Google Scholar 

  2. J. F. Harper, D. W. Moore, and J. R. A. Pearson, “The effect of the variation of surface tension with temperature on the motion of bubbles and drops,” J. Fluid Mech., 27, 361 (1967).

    Google Scholar 

  3. F. E. Torres and E. Helborzheimer, “Temperature gradients and drag effects produced by convection of interfacial internal energy around bubbles,” Phys. Fluids. A, 5, 537 (1993).

    Google Scholar 

  4. V. E. Zakhvataev, “Effect of variations in the interfacial internal energy on the stability of a two-layer Poiseuille flow,” Izv. Ross. Acad. Nauk, Mekh. Zhidk. Gaza, No. 6, (2000).

  5. L. D. Landau and E. M. Lifshitz, Theoretical Physics, Vol. 5. Statistical Physics, [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  6. A. W. Adamson, Physical Chemistry of Surfaces, Wiley, New York (1976).

    Google Scholar 

  7. N. B. Vargaftik, Handbook of Thermophysical Properties of Gases and Liquids, [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  8. V. E. Zakhvataev, “Certain weakly nonlinear amplitude equations describing the behavior of a thin layer in a two-phase viscous heat-conducting fluid flow along a cylinder,” Zh. Prikl. Mekh. Tekh. Fiz., 38, No. 1, 178 (1997).

    Google Scholar 

  9. V. E. Zakhvataev, “Possible effect of the variation of the internal energy of the free surface of a thin fluid layer on its wave flow,” Zh. Prikl. Mekh. Tekh. Fiz., 40, No. 1, 10 (1999).

    Google Scholar 

  10. L. D. Landau and E. M. Lifshitz, Theoretical Physics, Vol. 6. Hydrodynamics, [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  11. D. Bedeaux, A. M. Albano, and P. Mazur, “Boundary conditions and nonequilibrium thermodynamics,” Physica. A, 82, 438 (1976).

    Google Scholar 

  12. V. V. Pukhnachev, Motion of a Viscous Fluid with Free Boundaries [in Russian], Novosibirsk University Press, Novosibirsk (1989).

    Google Scholar 

  13. H. A. Stone, “A simple derivation of the time-dependent convective-diffusion equation for surfactant transport along a deforming interface,” Phys. Fluids. A, 2, 111 (1990).

    Google Scholar 

  14. K. A. Smith, “On convective instability induced by surface-tension gradients,” J. Fluid Mech., 24, 401 (1966).

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zakhvataev, V.E. Bénard-Marangoni Instability of a Two-Layer System with Allowance for Variations in the Interfacial Internal Energy. Fluid Dynamics 36, 984–988 (2001). https://doi.org/10.1023/A:1017979029814

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1017979029814

Keywords

Navigation