Advertisement

The European Physical Journal Special Topics

, Volume 146, Issue 1, pp 291–300 | Cite as

Thermal convection in a rotating binary viscoelastic liquid mixture

  • D. Laroze
  • J. Martínez-Mardones
  • J. BragardEmail author
Article

Abstract.

In this work we report theoretical and numerical results on convection in a viscoelastic binary mixture under rotation. In particular, we focus in the Maxwelian case of viscoelastic fluid. We obtain explicit expressions for the convective thresholds in terms of the mixture parameters of the system in the case of idealized boundary conditions. We also calculate numerically the convective thresholds for the case of realistic rigid–rigid boundary conditions.

Keywords

Binary Mixture Rayleigh Number European Physical Journal Special Topic Thermal Convection Linear Stability Analysis 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G.J. Nuovo, PCR in situ Hybridization: Protocols and Applications (Lippincott-Raven, Philadelphia, 1997) Google Scholar
  2. M. Krishna, V.M. Ugaz, M.A. Burns, Science 298, 793 (2002) Google Scholar
  3. D. Braun, A. Libchaber, Phys. Rev. Lett. 89, 188103 (2002) Google Scholar
  4. D. Braun, N.L. Goddard, A. Libchaber, Phys. Rev. Lett. 91, 158103 (2003) Google Scholar
  5. M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993) Google Scholar
  6. P.R. Kolodner, H. Williams, C. Moe, J. Chem. Phys. 88, 6512 (1988) Google Scholar
  7. P.R. Kolodner, J. Non Newtonian Fluid Mech. 75, 167 (1998) Google Scholar
  8. R.B. Bird, O. Hassager, Dynamics of Polymeric Liquids, Fluid Mechanics, Vol. I (Wiley-Interscience, New York, 1987) Google Scholar
  9. S.R. Quake, H. Babcock, S. Chu, Nature 388, 151 (1997) Google Scholar
  10. Perkins, T.T., Smith, D.E. Chu, Science 276, (1997) 2016 Google Scholar
  11. D.E. Smith, H. Babcock, S. Chu, Science 283, 1724 (1999) Google Scholar
  12. H. Babcock, D.E. Smith, J.S. Hur, E.S.G. Shaqfeh, S. Chu, Phys. Rev. Lett. 85, 2018 (2000) Google Scholar
  13. J. Martínez-Mardones, R. Tiemann, D. Walgraef, W. Zeller, Phys. Rev. E 54, 1478 (1996) Google Scholar
  14. J. Martínez-Mardones, R. Tiemann, D. Walgraef, J. Non Newtonian Fluid Mech. 93, 1 (2000) Google Scholar
  15. S. Chandrasekhar, Hydrodynamics and Hydromagnetic Stability (Oxford University Press, Oxford, 1961) Google Scholar
  16. E. Bodenschatz, G. Ahlers, W. Pesch, Ann. Rev. Fluid Mech 32, 709 (2000) Google Scholar
  17. J.K. Bhattacharjee, Phys. Fluids 31, 2456 (1988) Google Scholar
  18. J.K. Bhattacharjee, Phys. Rev. A 37, 1368 (1988) Google Scholar
  19. K. Kumar, Phys. Rev. A 41, 3134 (1990) Google Scholar
  20. P.K. Bhatia, J.M. Steiner, ZAMM 52, 321 (1972) Google Scholar
  21. G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1990) Google Scholar
  22. P. Parmentier, G. Lebon, V. Regnier, J. Non Newtonian Fluid Mech. 89, 63 (2000) Google Scholar
  23. R. Cerbino, A. Vailati, M. Giglio, Phys. Rev. E 66, 5301 (2002) Google Scholar
  24. A. Ryskin, H.W. Müller, H. Pleiner, Phys. Rev. E 67, 6302 (2003) Google Scholar
  25. I.A. Eltayeb, ZAMM 55, 599 (1975) Google Scholar
  26. S.D. Fisher, Complex Variables (Brooks and Cole, Pacific Grove, 1990) Google Scholar
  27. see: http://en.wikipedia.org/wiki/Deborah_number Google Scholar
  28. L.N. Trefethen, Spectral Methods in Matlab (SIAM, Philadelphia, 2000) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Instituto de Física, Pontificia Universidad Católica de ValparaísoValparaísoChile
  2. 2.Departamento de Física y Matemática AplicadaUniversidad de NavarraPamplonaSpain

Personalised recommendations