Skip to main content
Log in

Change of the types of instability of a steady two-layer flow in an inclined channel

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

A plane steady-state two-layer fluid flow under the coupled action of the buoyancy and Marangoni forces is considered. The system is oriented at an arbitrary angle with respect to the gravity force. Exact solutions generalizing the Ostroumov-Birikh solution are obtained and their stability is studied in the framework of a linear theory. On the basis of numerical calculations, the influence of the inclination angle, the thickness of the layers, and the wall heating conditions on the instability mechanisms is investigated.

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. R.Kh. Zeitunyan, “Problem of Bénard-Marangoni Thermocapillary Instability,” Usp. Fiz. Nauk 168(3), 259–286 (1998).

    Article  Google Scholar 

  2. G.Z. Gershuni and E.M. Zhukhovitskii, Convective Instability in Incompressible Fluid [in Russian] (Nauka, Moscow, 1972).

    Google Scholar 

  3. V.K. Andreev, V.E. Zakhvataev, and E.A. Ryabitskii, Thermocapillary Instability [in Russian] (Nauka, Novosibirsk, 2000).

    Google Scholar 

  4. L.G. Napolitano, “Plane Marangoni-Poiseuille Flow of Two Immiscible Fluids,” Acta Astronaut. 7(4), 461–478 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  5. Ph. Georis, M. Hennenberg, I.B. Simanovskii, et al., “Thermocapillary Convection in Multilayer System,” Phys. Fluids A 5(7), 1575–1582 (1993).

    Article  ADS  MATH  Google Scholar 

  6. N.I. Lobov, D.V. Luibimov, and T.P. Lyubimova, “Convective Instability in a System of Horizontal Layers of Immiscible Liquids with a Deformable Interface,” Fluid Dynamics 31(2), 186–192 (1996).

    Article  ADS  MATH  Google Scholar 

  7. A.A. Nepomnyashchii and I.B. Simanovskii, “Thermocapillary Convection in a Two-Layer System,” Fluid Dynamics 18(4), 629–633 (1983).

    Article  ADS  Google Scholar 

  8. R.V. Birikh and S.V. Bushueva, “Thermocapillary Instability in a Two-Layer System with a Deformable Interface,” Fluid Dynamics 36(3), 349–355 (2001).

    Article  MATH  Google Scholar 

  9. D. Joseph, Stability of Fluid Motions. V. 1–2 (Springer-Verlag, Berlin, 1976).

    Google Scholar 

  10. G.A. Ostroumov, Free Convection in the Internal-Problem Conditions [in Russian] (Gos. Izd. Tekh. Teoret. Liter., Moscow, 1952).

    Google Scholar 

Download references

Authors

Additional information

Original Russian Text © V.B. Bekezhanova, 2011, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2011, Vol. 46, No. 4, pp. 24–35.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bekezhanova, V.B. Change of the types of instability of a steady two-layer flow in an inclined channel. Fluid Dyn 46, 525–535 (2011). https://doi.org/10.1134/S001546281104003X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S001546281104003X

Keywords

Navigation