Skip to main content
SpringerLink
Log in

Influence of the Marangoni Effect on the Emergence of Fluid Rotation in a Thermogravitational Boundary Layer

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

Steady axisymmetric regimes of the fluid flow in a thermogravitational boundary layer near the free surface with a nonuniform temperature distribution on this boundary are calculated for equations of fluid motion in the Oberbeck-Boussinesq approximation, where the viscosity and thermal diffusivity are small. With due allowance for the thermocapillary effect, it is demonstrated that nonhomogeneous fluid flow regimes with rotation can arise in the boundary layer owing to a bifurcation in the case of local cooling of the free surface, whereas rotation outside this layer is absent.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. G. Napolitano, “Marangoni Boundary Layers,” in Proc. of the 3rd Europ. Symp. on Material Science in Space, Grenoble, France, April 24–27, 1979 (Europ. Space Agency, 1979), pp. 313–315.

  2. V. V. Pukhnachev, “Group Analysis of Equations of the Unsteady Marangoni Boundary Layer,” Dokl. Akad. Nauk SSSR 279 (5), 1061–1064 (1984).

    ADS  MathSciNet  Google Scholar 

  3. V. A. Batishchev, V. V. Kuznetsov, and V. V. Pukhnachev, “Marangoni Boundary Layers,” Progr. Aerospace Sci. 26, 353–370 (1984).

    Article  ADS  Google Scholar 

  4. V. A. Batishchev and E. V. Khoroshunova, “Emergence of Rotational Regimes in a Thermocapillary Flow of a Nonhomogeneous Fluid in the Layer,” Prikl. Mat. Mekh. 64 (5), 560–568 (2000).

    MATH  Google Scholar 

  5. V. Kh. Izakson and V. I. Yudovich, “On the Emergence of Convection in a Fluid Layer with a Free Boundary,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 23–28 (1968).

    MATH  Google Scholar 

  6. M. A. Vishik and L. A. Lyusternik, “Regular Degeneration and Boundary Layer for Linear Differential Equations with a Small Parameter,” Usp. Mat. Nauk 12 (5), 3–102 (1957).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. South Federal University, Rostov-on-Don, 344090, Russia

    V. A. Batishchev

Authors
  1. V. A. Batishchev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. A. Batishchev.

Additional information

Original Russian Text © V.A. Batishchev.

__________

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 61, No. 3, pp. 120–128, May–June, 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Batishchev, V.A. Influence of the Marangoni Effect on the Emergence of Fluid Rotation in a Thermogravitational Boundary Layer. J Appl Mech Tech Phy 61, 417–425 (2020). https://doi.org/10.1134/S002189442003013X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S002189442003013X

Keywords

Search

Navigation