Advertisement

Particle-laden two-dimensional elastic turbulence

  • Himani GargEmail author
  • Enrico Calzavarini
  • Gilmar Mompean
  • Stefano Berti
Regular Article
Part of the following topical collections:
  1. Flowing Matter, Problems and Applications

Abstract.

The aggregation properties of heavy inertial particles in the elastic turbulence regime of an Oldroyd-B fluid with periodic Kolmogorov mean flow are investigated by means of extensive numerical simulations in two dimensions. Both the small- and large-scale features of the resulting inhomogeneous particle distribution are examined, focusing on their connection with the properties of the advecting viscoelastic flow. We find that particles preferentially accumulate on thin highly elastic propagating structures and that this effect is the largest for intermediate values of particle inertia. We provide a quantitative characterization of this phenomenon that allows to relate it to the accumulation of particles in filamentary highly strained flow regions producing clusters of correlation dimension close to 1. At larger scales, particles are found to undergo turbophoretic-like segregation. Indeed, our results indicate a close relationship between the profiles of particle density and fluid velocity fluctuations. The large-scale inhomogeneity of the particle distribution is interpreted in the framework of a model derived in the limit of small, but finite, particle inertia. The qualitative characteristics of different observables are, to a good extent, independent of the flow elasticity. When increased, the latter is found, however, to slightly reduce the globally averaged degree of turbophoretic unmixing.

Graphical abstract

Keywords

Topical issue: Flowing Matter, Problems and Applications 

References

  1. 1.
    A. Groisman, V. Steinberg, Nature 405, 53 (2000)CrossRefGoogle Scholar
  2. 2.
    A. Groisman, V. Steinberg, Nature 410, 905 (2001)CrossRefGoogle Scholar
  3. 3.
    L. Pan, A. Morozov, C. Wagner, P. Arratia, Phys. Rev. Lett. 110, 174502 (2013)CrossRefGoogle Scholar
  4. 4.
    A. Souliès, J. Aubril, C. Castelain, T. Burghelea, Phys. Fluids 29, 083102 (2017)CrossRefGoogle Scholar
  5. 5.
    P.C. Sousa, F.T. Pinho, M.A. Alves, Soft Matter 14, 1344 (2018)CrossRefGoogle Scholar
  6. 6.
    B. Traore, C. Castelain, T. Burghelea, J. Non-Newton. Fluid Mech. 223, 62 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    W.M. Abed, R.D. Whalley, D.J.C. Dennis, R.J. Poole, J. Non-Newton. Fluid Mech. 231, 68 (2016)CrossRefGoogle Scholar
  8. 8.
    R.J. Poole, B. Budhiraja, A.R. Cain, P.A. Scott, J. Non-Newton. Fluid Mech. 177, 15 (2012)CrossRefGoogle Scholar
  9. 9.
    J. Mitchell, K. Lyons, A.M. Howe, A. Clarke, Soft Matter 12, 460 (2016)CrossRefGoogle Scholar
  10. 10.
    K.D. Squires, J.K. Eaton, Phys. Fluids A 3, 1169 (1991)CrossRefGoogle Scholar
  11. 11.
    F. Picano, G. Sardina, C.M. Casciola, Phys. Fluids 21, 093305 (2009)CrossRefGoogle Scholar
  12. 12.
    G. Sardina, P. Schlatter, L. Brandt, F. Picano, C.M. Casciola, J. Fluid Mech. 699, 50 (2012)MathSciNetCrossRefGoogle Scholar
  13. 13.
    F. De Lillo, M. Cencini, S. Musacchio, G. Boffetta, Phys. Fluids 28, 035104 (2016)CrossRefGoogle Scholar
  14. 14.
    D. Mitra, N.E.L. Haugen, I. Rogachevskii, Eur. Phys. J. Plus 133, 35 (2018)CrossRefGoogle Scholar
  15. 15.
    J. Bec, Phys. Fluids 15, L81 (2003)MathSciNetCrossRefGoogle Scholar
  16. 16.
    E. Calzavarini, M. Kerscher, D. Lohse, F. Toschi, J. Fluid Mech. 607, 13 (2008)CrossRefGoogle Scholar
  17. 17.
    F. Toschi, E. Bodenschatz, Annu. Rev. Fluid Mech. 41, 375 (2009)CrossRefGoogle Scholar
  18. 18.
    F. De Lillo, G. Boffetta, S. Musacchio, Phys. Rev. E 85, 036308 (2012)CrossRefGoogle Scholar
  19. 19.
    A. Nowbahar, G. Sardina, F. Picano, L. Brandt, J. Fluid Mech. 732, 706 (2013)MathSciNetCrossRefGoogle Scholar
  20. 20.
    E. Afik, V. Steinberg, Nat. Commun. 8, 468 (2017)CrossRefGoogle Scholar
  21. 21.
    B. Bird, C.F. Curtiss, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Fluids (Wiley, New York, 1987)Google Scholar
  22. 22.
    S. Berti, A. Bistagnino, G. Boffetta, A. Celani, S. Musacchio, Phys. Rev. E 77, 055306(R) (2008)CrossRefGoogle Scholar
  23. 23.
    S. Berti, G. Boffetta, Phys. Rev. E 82, 036314 (2010)CrossRefGoogle Scholar
  24. 24.
    E.L.C. VI, M. Plan, A. Gupta, D. Vincenzi, J.D. Gibbon, J. Fluid Mech. 822, R4 (2017)CrossRefGoogle Scholar
  25. 25.
    G. Boffetta, A. Celani, A. Mazzino, A. Puliafito, M. Vergassola, J. Fluid Mech. 523, 161 (2005)MathSciNetCrossRefGoogle Scholar
  26. 26.
    M.R. Maxey, J.J. Riley, Phys. Fluids 26, 883 (1983)CrossRefGoogle Scholar
  27. 27.
    R. Sureshkumar, A.N. Beris, J. Non-Newton. Fluid Mech. 60, 53 (1995)CrossRefGoogle Scholar
  28. 28.
    T. Vaithianathan, L.R. Collins, J. Comput. Phys. 187, 1 (2003)CrossRefGoogle Scholar
  29. 29.
    A. Fouxon, V. Lebedev, Phys. Fluids 15, 2060 (2003)CrossRefGoogle Scholar
  30. 30.
    E. De Angelis, C.M. Casciola, R. Piva, Physica D 241, 297 (2012)MathSciNetCrossRefGoogle Scholar
  31. 31.
    M.Q. Nguyen, A. Delache, S. Simoëns, W.J.T. Bos, M. El Hajem, Phys. Rev. Fluids 1, 083301 (2016)CrossRefGoogle Scholar
  32. 32.
    Y. Jun, V. Steinberg, Phys. Rev. Fluids 2, 103301 (2017)CrossRefGoogle Scholar
  33. 33.
    A. Gupta, R. Pandit, Phys. Rev. E 95, 033119 (2017)CrossRefGoogle Scholar
  34. 34.
    M.R. Maxey, J. Fluid Mech. 174, 441 (1987)CrossRefGoogle Scholar
  35. 35.
    J. Bec, L. Biferale, G. Boffetta, A. Celani, M. Cencini, A. Lanotte, S. Musacchio, F. Toschi, J. Fluid Mech. 550, 349 (2006)CrossRefGoogle Scholar
  36. 36.
    A. Okubo, Deep-Sea Res. 17, 445 (1970)Google Scholar
  37. 37.
    J. Weiss, Physica D 48, 273 (1991)MathSciNetCrossRefGoogle Scholar
  38. 38.
    K. Gustavvson, B. Mehlig, Adv. Phys. 65, 1 (2016)CrossRefGoogle Scholar
  39. 39.
    P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50, 346 (1983)MathSciNetCrossRefGoogle Scholar
  40. 40.
    G. Falkovich, A. Fouxon, M.G. Stepanov, Nature 419, 151 (2002)CrossRefGoogle Scholar
  41. 41.
    J. Bec, J. Fluid Mech. 528, 255 (2005)MathSciNetCrossRefGoogle Scholar
  42. 42.
    M. Caporaloni, F. Tampieri, F. Trombetti, O. Vittori, J. Atmos. Sci. 32, 565 (1975)CrossRefGoogle Scholar
  43. 43.
    J.W. Brooke, K. Kontomaris, T. Hanratty, J.B. McLaughlin, Phys. Fluids A 4, 825 (1992)CrossRefGoogle Scholar
  44. 44.
    S. Belan, I. Fouxon, G. Falkovich, Phys. Rev. Lett. 112, 234502 (2014)CrossRefGoogle Scholar
  45. 45.
    A. Guha, J. Aerosol Sci. 28, 1517 (1997)CrossRefGoogle Scholar
  46. 46.
    J.O. Hinze, Turbulence: An Introduction to its Mechanism and Theory (McGraw-Hill, New York, 1959)Google Scholar
  47. 47.
    Y. Liu, V. Steinberg, EPL 90, 44002 (2010)CrossRefGoogle Scholar
  48. 48.
    A. Nowbahar, G. Sardina, F. Picano, L. Brandt, J. Fluid Mech. 732, 706 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Himani Garg
    • 1
    Email author
  • Enrico Calzavarini
    • 1
  • Gilmar Mompean
    • 1
  • Stefano Berti
    • 1
  1. 1.Université de Lille, Unité de Mécanique de Lille, UML EA 7512LilleFrance

Personalised recommendations