Skip to main content
Log in

Steady-state conditions of a nonisothermal film with a heat-insulated free boundary

Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

The equilibrium shapes of a nonisothermal liquid film with a heat-insulated free surface for large Marangoni numbers are investigated in the long-wave approximation using a combination of analytical and numerical methods. It is proved that the two-dimensional problem of the equilibrium of a strip-shaped film has a steady-state solution for an arbitrary large temperature gradient on the boundaries of the strip. An increase in this gradient leads to an abrupt thinning of the film near the heated boundary, which can result in instability and rupture of the film. In the equilibrium problem for a film fixed on a circular contour, the nonuniform distribution of the heat flux on the contour was found to have a significant influence on the free-surface shape.

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.

Institutional subscriptions

References

  1. S. V. Alekseenko, V. E. Nakoryakov, and B. G. Pokusaev, Wave Flow of Liquid Films [in Russian], Nauka, Novosibirsk (1992).

    Google Scholar 

  2. O. A. Kabov, “Formation of regular structures in a falling liquid film under local heating,” Teplofiz. Aéromekh., 5, No. 4, 547–552 (1998).

    Google Scholar 

  3. O. A. Kabov, V. V. Kuznetsov, I. V. Marchuk, et al., “Regular structures in thermocapillary convection in a moving thin liquid layer,” Poverkh. Rentgen., Sinkhr. Neitron. Issled., No. 9, 84–90 (2001).

  4. A. M. Frank, “3D numerical simulation of regular structure formation in a locally heated falling film,” Eur. J. Mech., Ser. B: Liquids, 22, No. 3, 445–471 (2003).

    Article  MATH  Google Scholar 

  5. E. A. Chinnov and O. A. Kabov, “Influence of three-dimensional deformations on local heat transfer to a nonuniformly heated falling liquid film,” Teplofis. Vysok. Temp., 42, No. 2, 269–278 (2004).

    Google Scholar 

  6. V. V. Pukhnachov, “Model of a viscous layer deformation by thermocapillary forces,” Eur. J. Appl. Math., 13, No. 2, 205–224 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  7. V. M. Pukhnachev and S. B. Dubinkina, “Model of deformation and rupture of a film under the action of thermocapillary forces,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 89–107 (2006).

  8. O. V. Voinov, “Equations of motion of free liquid films and a model of their plane-parallel thinning,” Dokl. Akad. Nauk SSSR, 216, No. 2, 285–288 (1974).

    Google Scholar 

  9. L. Caratenuto and L. K. Antanovskii, “Influence of surfactants on the thinning of a free liquid film with rims fixed at a frame,” Microgravity Quart., 5, No. 4, 199–209 (1995).

    Google Scholar 

  10. O. V. Voinov, “Motion of liquid films in a gas,” Prikl. Mat. Mekh., 72, No. 1, 70–80 (2008).

    Google Scholar 

  11. V. M. Pukhnachev, “Equilibrium of a free nonisothermal liquid film,” J. Appl. Mech. Tech. Phys., 48, No. 3, 310–321 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  12. E. Ya. Gatapova, O. A. Kabov, V. V. Kuznetsov, and J.-C. Legros, “Evaporating shear-driven liquid film flow in minichannel with local heat source,” J. Eng. Thermophys., 13, No. 2, 17–46 (2005).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. A. Karabut.

Additional information

__________

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 59–73, July–August, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karabut, E.A., Pukhnachev, V.V. Steady-state conditions of a nonisothermal film with a heat-insulated free boundary. J Appl Mech Tech Phy 49, 568–579 (2008). https://doi.org/10.1007/s10808-008-0074-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10808-008-0074-7

Key words

Navigation