The European Physical Journal Special Topics

, Volume 179, Issue 1, pp 69–90 | Cite as

Density waves and the effect of wall roughness in granular Poiseuille flow: Simulationand linear stability

Regular Article

Abstract

The formation of density waves and the effect of wall roughness on them are studied using molecular dynamics simulations of gravity-driven granular Poiseuille flow. Three basic types of structures are found in moderately dense flows: a plug, a sinuous wave and a slug; a new varicose wave mode has been identified in dense flows with channels of large widths at moderate dissipations; only clump-like structures appear in dilute flows. The simulation results are contrasted with the predictions of a linear stability analysis of the kinetic-theory continuum equations for granular Poiseuille flow. The theoretical predictions on the form of density waves are in qualitative agreement with simulations in denser flows, however, there are discrepancies between simulation and theory in dilute flows.

Keywords

European Physical Journal Special Topic Density Wave Linear Stability Analysis Particle Volume Fraction Symmetric Mode 

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References

  1. 1.
    I. Goldhirsch, Ann. Rev. Fluid Mech. 35, 267 (2003)CrossRefMathSciNetADSGoogle Scholar
  2. 2.
    T. Pöschel, S. Luding, eds., Granular Gases, Lecture Notes in Physics, Vol. 564 (Springer, Berlin, 2001)Google Scholar
  3. 3.
    T. Pöschel, N.V. Brilliantov (eds.), Granular Gas Dynsmics, Lecture Notes in Physics, Vol. 624 (Springer, Berlin, 2003)Google Scholar
  4. 4.
    N.V. Brilliantov, T. Pöschel, Kinetic Theory of Granular Gases (Oxford University Press, Oxford, 2004)Google Scholar
  5. 5.
    I. Aranson, L.S. Tsimring, Rev. Mod. Phys. 78, 1641 (2006)CrossRefADSGoogle Scholar
  6. 6.
    P.K. Haff, J. Fluid Mech. 134, 401 (1983)MATHCrossRefADSGoogle Scholar
  7. 7.
    C.K.K. Lun, S.B. Savage, D.J. Jeffrey, N. Chepurniy, J. Fluid Mech. 140, 223 (1984)MATHCrossRefADSGoogle Scholar
  8. 8.
    J.T. Jenkins, R.W. Richman, J. Fluid Mech. 192, 313 (1986)CrossRefADSGoogle Scholar
  9. 9.
    A. Goldshtein, M. Shapiro, J. Fluid Mech. 282, 75 (1995)MATHCrossRefMathSciNetADSGoogle Scholar
  10. 10.
    N. Sela, I. Goldhirsch, J. Fluid Mech. 361, 41 (1998)MATHCrossRefMathSciNetADSGoogle Scholar
  11. 11.
    J.J. Brey, J.W. Dufty, C.S. Kim, A. Santos, Phys. Rev. E 58, 4638 (1998)CrossRefADSGoogle Scholar
  12. 12.
    J.J. Brey, D. Cubero, M.J. Ruiz-Montero, Phys. Rev. E 59, 1256 (1999)CrossRefADSGoogle Scholar
  13. 13.
    V. Garzo, J.W. Dufty, Phys. Rev. E 59, 5895 (1999)CrossRefADSGoogle Scholar
  14. 14.
    R. Ramirez, D. Risso, R. Soto, P. Cordero, Phys. Rev. E 62, 2521 (2000)CrossRefADSGoogle Scholar
  15. 15.
    N. Mitarai, H. Hayakawa, H. Nakanashi, Phys. Rev. Lett. 88, 174301 (2002)CrossRefADSGoogle Scholar
  16. 16.
    N.V. Brilliantov, T. Pöschel, Phys. Rev. E 67, 061304 (2003)CrossRefADSGoogle Scholar
  17. 17.
    V. Kumaran, J. Fluid Mech. 561, 43 (2006)MATHCrossRefMathSciNetADSGoogle Scholar
  18. 18.
    M.A. Hopkins, M.Y. Louge, Phys. Fluids A 3, 47 (1991)CrossRefADSGoogle Scholar
  19. 19.
    I. Goldhirsch, G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993)CrossRefADSGoogle Scholar
  20. 20.
    S. McNamara, W.R. Young, Phys. Rev. E 50, R28 (1994)CrossRefADSGoogle Scholar
  21. 21.
    M.-L. Tan, I. Goldhirsch, Phys. Fluid 9, 856 (1997)CrossRefADSGoogle Scholar
  22. 22.
    J.S. Olafsen, J.S. Urbach, Phys. Rev. Lett. 81, 4369 (1998)CrossRefADSGoogle Scholar
  23. 23.
    S. Luding, H.J. Herrmann, Chaos 9, 673 (1999)MATHCrossRefADSGoogle Scholar
  24. 24.
    D. van der Meer, K. van der Welle, D. Lohse, Phys. Rev. Lett. 88, 174302 (2002)CrossRefADSGoogle Scholar
  25. 25.
    N.V. Brilliantov, C. Saluena, T. Schwager, T. Pöschel, Phys. Rev. Lett. 90, 1619 (2004)Google Scholar
  26. 26.
    M. Alam, S. Luding, Phys. Fluids 17, 063303 (2005)CrossRefMathSciNetADSGoogle Scholar
  27. 27.
    G. Peng, H.J. Herrmann, Phys. Rev. E 49, 1796 (1994)CrossRefADSGoogle Scholar
  28. 28.
    T. Pöschel, J. Phys. 4, 499 (1994)Google Scholar
  29. 29.
    T. Raafat, J.P. Hulin, H.J. Herrmann, Phys. Rev. E 53, 4345 (1996)CrossRefADSGoogle Scholar
  30. 30.
    T. Riethmüller, L. Schimanky-Geier, D. Rosenkranz, T. Pöschel, J. Stat. Phys. 86, 421 (1997)MATHCrossRefADSGoogle Scholar
  31. 31.
    C.-H. Wang, R. Jackson, S. Sundaresan, J. Fluid Mech. 342, 179 (1997)MATHCrossRefMathSciNetADSGoogle Scholar
  32. 32.
    G. Reydellet, F. Rioual, E. Clement, Europhys. Lett. 51, 27 (2000)CrossRefADSGoogle Scholar
  33. 33.
    E. Liss, S.L. Conway, B.J. Glasser, Phys. Fluids 14, 3309 (2002)CrossRefMathSciNetADSGoogle Scholar
  34. 34.
    K.C. Vijayakumar, M. Alam, Phys. Rev. E 75, 051306 (2007)CrossRefADSGoogle Scholar
  35. 35.
    V. Chikkadi, M. Alam, Phys. Rev. E 80, 021303 (2009)CrossRefADSGoogle Scholar
  36. 36.
    M. Alam, V. Chikkadi, J. Fluid Mech.(2010) (in press)Google Scholar
  37. 37.
    M. Alam, P.R. Nott, J. Fluid Mech. 377, 99 (1998)MATHCrossRefMathSciNetADSGoogle Scholar
  38. 38.
    M. Alam, P. Shukla, S. Luding, J. Fluid Mech. 615, 293 (2008)MATHCrossRefMathSciNetADSGoogle Scholar
  39. 39.
    K. Hui, P.K. Haff, J.E. Ungar, R. Jackson, J. Fluid Mech. 145, 223 (1984)MATHCrossRefADSGoogle Scholar
  40. 40.
    I. Goldhirsch, N. Sela, Phys. Rev. E 54, 4458 (1996)CrossRefADSGoogle Scholar
  41. 41.
    M. Alam, S. Luding, Phys. Fluids 15, 2298 (2003)CrossRefADSGoogle Scholar
  42. 42.
    P. Shukla, M. Alam, Phys. Rev. Lett. 103, 068001 (2009)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences and Springer 2009

Authors and Affiliations

  1. 1.Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific ResearchBangaloreIndia

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