Transport Out of a Gravitationally Stable Layer with the Help of a Faster Diffusing Substance: PDE Simulations and Scaling Laws

  • Karsten Koetter
  • Malte Schmick
  • Mario Markus
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 32)


Hydrodynamic equations of an incompressible fluid with two dissolved substances are integrated to simulate previously reported observations of double diffusive convection. These observations had been performed in a setup that is extremely easy to implement and to observe: a layer consisting of a mixture of a surfactant, glycerine and water is placed below water; fingers arising at the interface transport the surfactant upwards. The calculated mean distance between fingers, as well as their emergence time, both as functions of the initial concentration of glycerine, are described by power laws. These results are in agreement with analytical approximations and with the experimental observations.


Lower Layer Incompressible Fluid Stable Layer Double Diffusive Convection Step Profile 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chen, C. F., Johnson, D. H.: J. Fluid Mech. 138 (1984) 405–416CrossRefGoogle Scholar
  2. 2.
    Huppert, H. E., Turner, J. S.: J. Fluid Mech. 106 (1981) 299–329MATHCrossRefGoogle Scholar
  3. 3.
    Turner, J. S.: Ann. Rev. Fluid Mech. 6 (1974) 37–56CrossRefGoogle Scholar
  4. 4.
    Schmitt, R. W.: Phys. Fluids 26 (1983) 2373–2377MATHCrossRefGoogle Scholar
  5. 5.
    Koetter, K., Markus, M.: Europhys. Lett. 55 (2001) 807–813CrossRefGoogle Scholar
  6. 6.
    Williams, A. J.: Science 185 (1974) 941–943CrossRefGoogle Scholar
  7. 7.
    Tait, R. I., Howe, M. R.: Nature 231 (1971) 178–179CrossRefGoogle Scholar
  8. 8.
    Fisher, H.: Water Res. 5 (1971) 909–915CrossRefGoogle Scholar
  9. 9.
    Coriell, S. R., Cordes, M. R., Boettinger, W.J., Sekerka, R.F.: J. Crystal Growth 49 (1980) 13–28CrossRefGoogle Scholar
  10. 10.
    McBirney, A. R., Noyes, R. M.: J. Pet. 20 (1979) 487–554CrossRefGoogle Scholar
  11. 11.
    McBirney, A. R.: J. Volcanol. Geotherm. Res. 7 (1980) 357–371CrossRefGoogle Scholar
  12. 12.
    Schmitt, J., Rossner, R.: Astrophys. J. 265 (1983) 901–924CrossRefGoogle Scholar
  13. 13.
    Goldreich, P., Schubert, G.: Astrophys. J. 150 (1967) 571–587CrossRefGoogle Scholar
  14. 14.
    Spiegel, E. A.: Ann. Rev. Astron. Astrophys. 10 (1972) 261–304CrossRefGoogle Scholar
  15. 15.
    Laurent, T. C., Preston, B. N., Sundelof, L.O.: Nature 279 (1979) 60–62CrossRefGoogle Scholar
  16. 16.
    Harper, G. S., Comper, W. D., Preston, B. N.: J. Biol. Chem. 259 (1984) 582–589Google Scholar
  17. 17.
    Linden, P. F.: Deep-Sea Res. 20 (1973) 325–340Google Scholar
  18. 18.
    Turner, J. S.: Deep-Sea Res. 14 (1973) 599–611Google Scholar
  19. 19.
    Huppert, H. E., Manins, P. C.: Deep-Sea Res. 20 (1973) 315–323Google Scholar
  20. 20.
    Shirtcliffe, T. G. L.: J. Fluid. Mech. 57 (1973) 27–43CrossRefGoogle Scholar
  21. 21.
    Taylor, J. R., Veronis, G.: Fluid Mech. 321 (1996) 315–333CrossRefGoogle Scholar
  22. 22.
    Stern, M. E.: Tellus 12 (1960) 172–175CrossRefGoogle Scholar
  23. 23.
    Ferziger, J. H., Peric, M.: Computational methods for fluid dynamics ( Springer, New York, 1997 )Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Karsten Koetter
    • 1
  • Malte Schmick
    • 1
  • Mario Markus
    • 1
  1. 1.Max-Planck-Institut fuer molekulare PhysiologieDortmundGermany

Personalised recommendations