Skip to main content
SpringerLink
Log in

Wave Evolution of Heated Falling Films. Numerical Analysis Using Finite-Difference Method

  • Conference paper
  • First Online:
Large-Scale Scientific Computing (LSSC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2179))

Included in the following conference series:

Abstract

Surface wave and thermocapillary instabilities in a thin layer of viscous liquid falling down a non-uniformly heated inclined plate are studied by a numerical simulation of long-wave evolution equation. An efficient computational scheme adapted to this problem based on finite difference method is applied. Free-surface shapes as a function of the Reynolds and Marangoni numbers as well as the disturbance wavenumber are calculated. The numerical results for the isothermal problem are in good agreement with the full-scale numerical calculations performed by other authors and predict the free-surface configurations that are observed in experiments for thin-film flows. The present numerical procedure allows to obtain traveling waves for liquids with relatively small surface tension. The nonlinear interactions in non-uniformly heated falling films exhibit a tendency towards permanent two-dimensional waves for weak heating.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  1. H.-C. Chang. Annu. Rev. Fluid Mech., 26, 103–136, 1994.

    Article  Google Scholar 

  2. S. V. Alekseenko, V. Ye. Nakoryakov, and B. G. Pokusaev. Wave Flow of Liquid Films, NY, Begell House, 1994.

    MATH  Google Scholar 

  3. A. Oron, S. H. Davis, and S. G. Bankoff. Review Modern Phys., 69, 931–980, 1997.

    Article  Google Scholar 

  4. S. W. Joo, S. H. Davis, and S. G. Bankoff. J. Fluid Mech., 230, 117–146, 1991.

    Article  Google Scholar 

  5. S. Slavtchev, S. Miladinova, G. Lebon, and J.-C. Legros. in Proc. of 1st Intern. Symp. on Microgravity Research & Applications in Physical Sciences & Biotechnology, Sorrento, Italy, (SP-454, v. I), 33–41, 2001.

    Google Scholar 

  6. B. Ramaswamy, S. Chippada, and S. W. Joo. J. Fluid Mech., 325, 163–194, 1996.

    Article  Google Scholar 

  7. T. S. Salamon, R. C. Armstrong, and R. A. Brown. Phys. Fluids,6, 2202–2220, 1994.

    Article  Google Scholar 

  8. D. J. Benney. J. Maths. Phys., 45, 150–155, 1966.

    Article  MathSciNet  Google Scholar 

  9. A. Pumir, P. Manneville, and Y. Pomeau. J. Fluid Mech., 135, 27–50, 1983.

    Article  Google Scholar 

  10. B. Gjevik. Phys. Fluids, 13, 1918–1925, 1970.

    Article  Google Scholar 

  11. S. W. Joo and S. H. Davis. J. Fluid Mech., 242, 529–547, 1992.

    Article  Google Scholar 

  12. J. Liu, J. D. Paul, and J. P. Gollub. J. Fluid Mech., 250, 69–101, 1993.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanics, Acad. G. Bontchev Street, Block 4, Sofia, 1113, Bulgaria

    Svetla Miladinova

Authors
  1. Svetla Miladinova
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad G. Bontchev, 1113, Sofia, Bulgaria

    Svetozar Margenov

  2. DTU, UNI•C, Danish IT Centre for Education and Research, Bldg. 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

  3. University of Rousse, Studentska 8, 7017, Rousse, Bulgaria

    Plamen Yalamov

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Miladinova, S. (2001). Wave Evolution of Heated Falling Films. Numerical Analysis Using Finite-Difference Method. In: Margenov, S., Waśniewski, J., Yalamov, P. (eds) Large-Scale Scientific Computing. LSSC 2001. Lecture Notes in Computer Science, vol 2179. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45346-6_45

Download citation

  • DOI: https://doi.org/10.1007/3-540-45346-6_45

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43043-8

  • Online ISBN: 978-3-540-45346-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation