Skip to main content
Log in

Nonlinear Waves in Two-Layer Systems with a Temperature-Dependent Interfacial Heat Release

  • ORIGINAL ARTICLE
  • Published:
Microgravity Science and Technology Aims and scope Submit manuscript

Abstract

Nonlinear convective flows developed under the joint action of buoyant and thermocapillary effects in a two-layer system with periodic boundary conditions on the lateral walls, have been investigated. The influence of a temperature-dependent interfacial heat release/consumption on oscillatory regimes, has been studied. It is shown that sufficiently strong temperature dependence of interfacial heat sources and heat sinks can lead to the change of the sequence of bifurcations and the development of new nonlinear regimes.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  • Colinet, P., Legros, J.C.: On the Hopf bifurcation occuring in the two-layer Rayleigh-Bénard convective instability. Phys. Fluids 6, 2631 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Danov, K.D., Paunov, V.N., Alleborn, N., Raszillier, H., Durst, F.: Stability of evaporating two-layered liquid film in the presence of surfactant. I. The equations of lubrication approximation. Chem. Eng. Sci. 53, 2809 (1998)

    Article  MATH  Google Scholar 

  • Degen, M.M., Colovas, P.W., Andereck, C.D.: Time-dependent patterns in the two-layer Rayleigh-Bénard system. Phys. Rev. E 57, 6647 (1998)

    Article  Google Scholar 

  • Eckert, K., Grahn, A.: Plume and finger regimes driven by an exothermic interfacial reaction. Phys. Rev. Lett. 82, 4436 (1999)

    Article  Google Scholar 

  • Gershuni, G.Z., Zhukhovitsky, E.M.: Convective stability of incompressible fluid. Keter, Jerusalem (1976)

    MATH  Google Scholar 

  • Gershuni, G.Z., Zhukhovitsky, E.M.: On monotonic and oscillatoty instability of a two-layer immiscible fluids system heated from below. Sov. Phys. Dokl. 27, 531 (1982)

    Google Scholar 

  • Gilev, A.Y.U., Nepomnyashchy, A.A., Simanovskii, I.B.: Onset of the oscillatory thermogravitational convection in a two-layer system when heating from below, Dynamics of Viscous Fluids. Sverdlovsk, 36 (1987). (in Russian)

  • Juel, A., Burgess, J.M., McCormick, W.D., Swift, J.B., Swinney, H.L.: Surface-tension-driven convection patterns in two liquid layers. Physica D 143, 169 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • Levich, V.G., Krylov, V.S.: Surface - tension - driven phenomena. Annu. Rev. Fluid. Mech. 1, 293 (1969)

    Article  Google Scholar 

  • Nepomnyashchy, A.A., Simanovskii, I.B.: Thermocapillary and thermogravitational convection in a two-layer system with a distorted interface. Fluid Dyn. 19, 494 (1984)

    Article  Google Scholar 

  • Nepomnyashchy, A.A., Simanovskii, I.B.: Influence of thermocapillary effect and interfacial heat release on convective oscillations in a two-layer system. Phys. Fluids 16, 1127 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Nepomnyashchy, A.A., Simanovskii, I.B., Legros, J.C.: Interfacial Convection in Multilayer Systems, Second Edition. Springer, New York (2012)

    Book  MATH  Google Scholar 

  • Rao, C.N.R.: Chemical Applications of Infrared Spectroscopy. Academic, New York (1963)

    Google Scholar 

  • Renardy, Y.Y.: Pattern formation for oscillatory bulk-mode competition in a two-layer Bénard problem. Z. Angew. Math. Phys. 47, 567 (1996)

    Article  MATH  Google Scholar 

  • Renardy, Y., Renardy, M., Fujimura, K.: Takens - Bogdanov bifurcation on the hexagonal lattice for double-layer convection. Physica D 129, 171 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Simanovskii, I.B.: The influence of the interfacial heat release on nonlinear convective oscillations in two-layer systems. Phys. Fluids 25, 072106 (2013)

    Article  MATH  Google Scholar 

  • Simanovskii, I.B., Nepomnyashchy, A.A.: Convective Instabilities in Systems with Interface. Gordon and Breach, London (1993)

    MATH  Google Scholar 

  • Simanovskii, I.B., Viviani, A., Dubois, F., Legros, J.C.: Nonlinear buoyant-thermocapillary waves in two-layer systems with an interfacial heat release. Microgravity Sci. Technol. 27, 11 (2015)

    Article  Google Scholar 

  • Szekely, J.: Fluid Flow Phenomena in Metals Processing. Academic, New York (1979)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ilya Simanovskii.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Simanovskii, I., Nepomnyashchy, A., Viviani, A. et al. Nonlinear Waves in Two-Layer Systems with a Temperature-Dependent Interfacial Heat Release. Microgravity Sci. Technol. 28, 381–393 (2016). https://doi.org/10.1007/s12217-016-9491-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12217-016-9491-z

Keywords

Navigation