Advertisement

Macroscopic force experienced by extended objects in granular flows over a very broad Froude-number range

Macroscopic granular force on extended object
  • Thierry Faug
Regular Article

Abstract

This paper revisits a great number of data from previous studies about the macroscopic force experienced by either objects moving at constant speed and depth inside static granular materials or motionless objects subject to steady granular flows. It focuses on extended objects whose immersed height is equal or close to the thickness of the surrounding granular medium. A simple scaling argument allows demarcating quasi-static from speed-squared force contributions for all the data from different geometries over a very broad range of Froude number. However, a wide scatter of the data is observed in the quasi-static regime. In the first step, a mean-field model is proposed to describe the average force. Mass and momentum balances are applied to a control volume, namely the expected volume of grains disturbed by the object, which is assumed to extend across the whole width and the entire height of the granular system. This allows defining an equivalent length scale which is computed by fitting the force predicted by the model to the available force data. In the second step, a circular shape is assumed for the effective mobilized domain and the associated diameter can be directly extracted from the computed equivalent length scale. This effective diameter is found to vary linearly with both the object width and the thickness of the granular layer moving around the extended object or the immersed depth of the object. The scaling highlights the key role played by the geometry which may enhance the force in the quasi-static regime.

Graphical abstract

Keywords

Flowing Matter: Granular Matter 

References

  1. 1.
    K. Wieghardt, Annu. Rev. Fluid. Mech. 7, 89 (1975).CrossRefADSGoogle Scholar
  2. 2.
    H. Katsuragi, D.J. Durian, Nat. Phys. 3, 420 (2007).CrossRefGoogle Scholar
  3. 3.
    T. Faug, R. Beguin, B. Chanut, Phys. Rev. E 80, 021305 (2009).CrossRefADSGoogle Scholar
  4. 4.
    J. Geng, R.P. Behringer, Phys. Rev. E 71, 011302 (2005).CrossRefADSGoogle Scholar
  5. 5.
    V. Buchholtz, T. Poschel, Granular Matter 1, 33 (1998).CrossRefzbMATHGoogle Scholar
  6. 6.
    C.R. Wassgren, J.A. Cordova, R. Zenit, A. Karion, Phys. Fluids 15, 3318 (2003).CrossRefADSGoogle Scholar
  7. 7.
    J.F. Boudet, H. Kellay, Phys. Rev. Lett. 105, 104501 (2010).CrossRefADSGoogle Scholar
  8. 8.
    R. Albert, M.A. Pfeifer, A.-L. Barabasi, P. Schiffer, Phys. Rev. Lett. 82, 205 (1999).CrossRefADSGoogle Scholar
  9. 9.
    I. Albert, J.G. Sample, A.J. Morss, S. Rajagolapan, A.-L. Barabasi, P. Schiffer, Phys. Rev. E 64, 061303 (2001).CrossRefADSGoogle Scholar
  10. 10.
    D. Chehata, R. Zenit, C.R. Wassgren, Phys. Fluids 15, 1622 (2003).CrossRefADSGoogle Scholar
  11. 11.
    T.A. Brzinski, P. Mayor, D.J. Durian, Phys. Rev. Lett. 111, 168002 (2013).CrossRefADSGoogle Scholar
  12. 12.
    A.H. Clark, R.P. Behringer, EPL 101, 64001 (2013).CrossRefADSGoogle Scholar
  13. 13.
    L. Favier, PhD Thesis, University of Grenoble, France (2009).Google Scholar
  14. 14.
    Y. Takehara, S. Fujimoto, K. Okumura, EPL 92, 44003 (2010).CrossRefADSGoogle Scholar
  15. 15.
    P. Caccamo, PhD Thesis, University of Grenoble, France (2012).Google Scholar
  16. 16.
    L. Favier, D. Daudon, F.-V. Donzé, Cold Reg. Sci. Tech. 85, 232 (2013).CrossRefGoogle Scholar
  17. 17.
    A. Tordesillas, J.E. Hilton, S.T. Tobin, Phys. Rev. E 89, 042207.Google Scholar
  18. 18.
    M. Sperl, Granular Matter 8, 59 (2006).CrossRefzbMATHGoogle Scholar
  19. 19.
    J.E. Hilton, A. Tordesillas, Phys. Rev. E 88, 062203 (2013).CrossRefADSGoogle Scholar
  20. 20.
    D.J. Costantino, J. Bartell, K. Scheidler, P. Schiffer, Phys. Rev. E 83, 011305 (2011).CrossRefADSGoogle Scholar
  21. 21.
    P. Caccamo, B. Chanut, T. Faug, H. Bellot, F. Naaim-Bouvet, Granular Matter 14, 577 (2012).CrossRefGoogle Scholar
  22. 22.
    I. Albert, P. Tegzes, B. Kahng, R. Albert, J.G. Sample, M. Pfeifer, A.-L. Barabasi, T. Vicsek, P. Schiffer, Phys. Rev. Lett. 84, 5122 (2000).CrossRefADSGoogle Scholar
  23. 23.
    N. Taberlet, P. Richard, A. Valance, W. Losert, J.M. Pasini, J.-T. Jenkins, R. Delannay, Phys. Rev. Lett. 91, 264301 (2003).CrossRefADSGoogle Scholar
  24. 24.
    L.E. Silbert, D. Ertas, G.S. Grest, T.C. Halsey, D. Levine, S.J. Plimpton, Phys. Rev. E 64, 051302 (2001).CrossRefADSGoogle Scholar
  25. 25.
    C.A. de Coulomb, Mem. Sav. Etr. Acad. Sci. Paris (1776).Google Scholar
  26. 26.
    W.J.W. Rankine, Philos. Trans. R. Soc. London 147, 9 (1857).CrossRefGoogle Scholar
  27. 27.
    O. Pouliquen, Phys. Fluids 11, 542 (1999).CrossRefADSzbMATHMathSciNetGoogle Scholar
  28. 28.
    F. Guillard, Y. Forterre, O. Pouliquen, Phys. Fluids 26, 043301 (2014).CrossRefADSGoogle Scholar
  29. 29.
    A. Seguin, Y. Bertho, F. Martinez, J. Crassous, P. Gondret, Phys. Rev. E 87, 012201 (2013).CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Irstea, Grenoble, UR ETGRSt Martin d’HeresFrance
  2. 2.Univ. Grenoble AlpesGrenobleFrance
  3. 3.School of Civil EngineeringThe University of SydneySydneyAustralia

Personalised recommendations