Skip to main content

Influence of the Surface Deformability on Concentration-Dependent, Oscillatory and Stationary Convection in a Liquid Layer

  • Chapter
Instabilities in Multiphase Flows
  • 197 Accesses

Abstract

The main goal of the present paper is to lay stress on the influence of the free surface deformability on the Marangoni instability in a horizontal liquid layer. Here, by means of the small disturbance analysis, the conditions for presence of stationary and oscillatory convection due to physical absorption are discussed.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Benguria, R. D., and Depassier, M. C., 1989, On the linear stability theory of Benard-Marangoni convection, Phys. Fluids A. 1:1127.

    Article  Google Scholar 

  • Brian, P. L. T., 1971, Effect of Gibbs adsorption on Marangoni instability, A. I. Ch. E. J. 17:765.

    Article  CAS  Google Scholar 

  • Brian, P. L. T., and Smith, K. A., 1972, Influence of Gibbs adsorption on oscillatory Marangoni instability, A. I. Ch. E. J. 18:231.

    Article  Google Scholar 

  • Chandrasekhar, S., 1961, “Hydrodynamic and Hydromagnetic Stability, Oxford Univ. Press, Oxford.

    Google Scholar 

  • Chu, X.-L., and Chen, L.-Y., 1986, Stability of two-component Benard fluid with surface adsorption, Commun. Theor. Phys. (Beijing) 6:237.

    CAS  Google Scholar 

  • Chu, X.-L., and Velarde, M. G., 1989, Benard-Marangoni convection in liquid layers with a deformable open surface: note on the role of solute accumulation at the air-liquid interface, J. Coll. Int. Sci. 127:205.

    Article  CAS  Google Scholar 

  • Elenin, G. G., Kalachinskaya, I. S., and Rabinovich, L. M., 1987, Numerical modelling of interface instability in a two-dimensional layer of reacting liquid, Fluid Dynamics, Consults Bureau. 22:927 (translated from Russian).

    Google Scholar 

  • Gouesbet. G., Maquet, J., Roze, C, and Darrigo R., 1990, Surface tension-and coupled buoyancy-driven instability in a horizontal liquid layer. Overstability and exchange of stability, Phys. Fluids A. 2:903.

    Article  CAS  Google Scholar 

  • Kozhoukharova, Zh., 1991, Influence of the surface deformability on the instability in an insulating layer, J. Teor. Apll. Mech. 22, No. 4:50.

    Google Scholar 

  • Kozhoukharova, Zh., and Slavchev, S., 1991, Influence of the surface deformability in a liquid layer with surface chemical reaction. I. Stationary convection, J. Coll. Int. Sci. 148:42.

    Article  Google Scholar 

  • Kozhoukharova, Zh., and Slavchev, S., 1992, Influence of the surface deformability in a liquid layer with surface chemical reaction. II. Overstability, J. Coll. Int. Sci. 152:473.

    Article  CAS  Google Scholar 

  • Linde, H., and Schwarz, E., 1963, Unterschungen zur Charakteristik der freien Grenzflachankonvektion beim Stoffubergang an fluiden Grenzen, Z. Phys. Chem. 224:331.

    Google Scholar 

  • Orell, A., and Westwater, J. W., 1961, Natural convection cells accompanying liquid-liquid extraction, Chem. Eng Sei. 16:127.

    Article  Google Scholar 

  • Palmer, H. J., and Berg, J. C., 1972, Hydrodynamic stability of surfactant solution heated from below, J. Fluid Mech. 51:385.

    Article  CAS  Google Scholar 

  • Pearson, J. R. A., 1958, On convection cells induced by surface tension, J. Fluid Mech. 4:489.

    Article  Google Scholar 

  • Perez-Garcia, C., and Carneiro, G., 1991, Linear stability analysis of Benard-Marangoni convection in fluids with a deformable free surface, Phys. Fluids A, 3:292.

    Article  CAS  Google Scholar 

  • Smith, K. A., 1966, On convective instability induced by surface-tension gradients, J. Fluid. Mech. 24:401.

    Article  Google Scholar 

  • Sterling, C. V., and Scriven, L. E., 1959, Interfacial turbulence: hydrodynamic instability and the Marangoni effect, A. I. Ch. E. J. 5:514.

    Article  Google Scholar 

  • Takashima, M., 1981a, Surface tension driven instability in a horizontal liquid layer with a deformable free surface. I. Stationary convection, J. Phys. Soc. Japan 50:2745.

    Article  CAS  Google Scholar 

  • Takashima, M., 1981b, Surface tension driven instability in a horizontal liquid layer with a deformable free surface. II. Overstability, J. Phys. Soc. Japan 50:2751.

    Article  CAS  Google Scholar 

  • Vidal, A., and Acrivos, A., 1966, Nature of the neutral state in surface-tension driven convection, Phys. Fluids 9:615.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media New York

About this chapter

Cite this chapter

Kozhoukharova, Z.D. (1993). Influence of the Surface Deformability on Concentration-Dependent, Oscillatory and Stationary Convection in a Liquid Layer. In: Gouesbet, G., Berlemont, A. (eds) Instabilities in Multiphase Flows. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1594-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-1594-8_13

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1596-2

  • Online ISBN: 978-1-4899-1594-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics