Skip to main content
Log in

Nonlinear Buoyant-Thermocapillary Waves in Two-Layer Systems with an 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 an interfacial heat release on oscillatory regimes, has been studied. It is shown that the development of oscillatory instability can lead to the appearance of different non-steady flows. Specifically, regimes of standing symmetric oscillations, traveling waves and modulated traveling waves, have been found.

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
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  • Nepomnyashchy, A.A., Simanovskii, I.B., Legros, J.C. Interfacial Convection in Multilayer Systems, 2nd Edn. Springer, New York (2012)

    Book  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • Doi, T., Koster, J.N.: Thermocapillary convection in two immiscible layers with free surface. Phys. Fluids A5, 1914 (1993)

    Article  Google Scholar 

  • Groothuis, H., Zuiderweg, F.G.: Influence of mass transfer on coalescence of drops. Chem. Eng. Sci. 12, 288 (1960)

    Article  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 

  • 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)

    MATH  Google Scholar 

  • Gilev, A.Yu., 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)

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

    Article  MATH  MathSciNet  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  MATH  MathSciNet  Google Scholar 

  • Diwakar, S.V., Tiwari, S., Das, S.K., Sundararajan, T.: Stability and resonant wave interactions of confined two-layer Rayleigh? Bénard systems. J. Fluid Mech. 754, 415 (2014)

    Article  MathSciNet  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 

  • 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  MATH  MathSciNet  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 

  • 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  Google Scholar 

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

    Google Scholar 

  • Esplugas, S., Gimienez, J., Contreras, S., Pascual, E., Rodriguez, M.: Comparison of different advanced oxidation processes for phenol degradation. Water Res. 36, 1034 (2002)

    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  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • Simanovskii, I.B.: Standing symmetric oscillations and traveling waves in two-layer systems with periodic boundary conditions. Interfacial Phenomena and Heat Transfer 1(1), 1 (2013b)

    Article  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., Viviani, A., Dubois, F. et al. Nonlinear Buoyant-Thermocapillary Waves in Two-Layer Systems with an Interfacial Heat Release. Microgravity Sci. Technol. 27, 11–26 (2015). https://doi.org/10.1007/s12217-014-9406-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12217-014-9406-9

Keywords

Navigation