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

Macroscopic granular force on extended object

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.

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References

  1. 1.

    K. Wieghardt, Annu. Rev. Fluid. Mech. 7, 89 (1975).

    Article  ADS  Google Scholar 

  2. 2.

    H. Katsuragi, D.J. Durian, Nat. Phys. 3, 420 (2007).

    Article  Google Scholar 

  3. 3.

    T. Faug, R. Beguin, B. Chanut, Phys. Rev. E 80, 021305 (2009).

    Article  ADS  Google Scholar 

  4. 4.

    J. Geng, R.P. Behringer, Phys. Rev. E 71, 011302 (2005).

    Article  ADS  Google Scholar 

  5. 5.

    V. Buchholtz, T. Poschel, Granular Matter 1, 33 (1998).

    Article  MATH  Google Scholar 

  6. 6.

    C.R. Wassgren, J.A. Cordova, R. Zenit, A. Karion, Phys. Fluids 15, 3318 (2003).

    Article  ADS  Google Scholar 

  7. 7.

    J.F. Boudet, H. Kellay, Phys. Rev. Lett. 105, 104501 (2010).

    Article  ADS  Google Scholar 

  8. 8.

    R. Albert, M.A. Pfeifer, A.-L. Barabasi, P. Schiffer, Phys. Rev. Lett. 82, 205 (1999).

    Article  ADS  Google Scholar 

  9. 9.

    I. Albert, J.G. Sample, A.J. Morss, S. Rajagolapan, A.-L. Barabasi, P. Schiffer, Phys. Rev. E 64, 061303 (2001).

    Article  ADS  Google Scholar 

  10. 10.

    D. Chehata, R. Zenit, C.R. Wassgren, Phys. Fluids 15, 1622 (2003).

    Article  ADS  Google Scholar 

  11. 11.

    T.A. Brzinski, P. Mayor, D.J. Durian, Phys. Rev. Lett. 111, 168002 (2013).

    Article  ADS  Google Scholar 

  12. 12.

    A.H. Clark, R.P. Behringer, EPL 101, 64001 (2013).

    Article  ADS  Google Scholar 

  13. 13.

    L. Favier, PhD Thesis, University of Grenoble, France (2009).

  14. 14.

    Y. Takehara, S. Fujimoto, K. Okumura, EPL 92, 44003 (2010).

    Article  ADS  Google Scholar 

  15. 15.

    P. Caccamo, PhD Thesis, University of Grenoble, France (2012).

  16. 16.

    L. Favier, D. Daudon, F.-V. Donzé, Cold Reg. Sci. Tech. 85, 232 (2013).

    Article  Google Scholar 

  17. 17.

    A. Tordesillas, J.E. Hilton, S.T. Tobin, Phys. Rev. E 89, 042207.

  18. 18.

    M. Sperl, Granular Matter 8, 59 (2006).

    Article  MATH  Google Scholar 

  19. 19.

    J.E. Hilton, A. Tordesillas, Phys. Rev. E 88, 062203 (2013).

    Article  ADS  Google Scholar 

  20. 20.

    D.J. Costantino, J. Bartell, K. Scheidler, P. Schiffer, Phys. Rev. E 83, 011305 (2011).

    Article  ADS  Google Scholar 

  21. 21.

    P. Caccamo, B. Chanut, T. Faug, H. Bellot, F. Naaim-Bouvet, Granular Matter 14, 577 (2012).

    Article  Google 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).

    Article  ADS  Google 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).

    Article  ADS  Google 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).

    Article  ADS  Google Scholar 

  25. 25.

    C.A. de Coulomb, Mem. Sav. Etr. Acad. Sci. Paris (1776).

  26. 26.

    W.J.W. Rankine, Philos. Trans. R. Soc. London 147, 9 (1857).

    Article  Google Scholar 

  27. 27.

    O. Pouliquen, Phys. Fluids 11, 542 (1999).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  28. 28.

    F. Guillard, Y. Forterre, O. Pouliquen, Phys. Fluids 26, 043301 (2014).

    Article  ADS  Google Scholar 

  29. 29.

    A. Seguin, Y. Bertho, F. Martinez, J. Crassous, P. Gondret, Phys. Rev. E 87, 012201 (2013).

    Article  ADS  Google Scholar 

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Correspondence to Thierry Faug.

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Faug, T. Macroscopic force experienced by extended objects in granular flows over a very broad Froude-number range. Eur. Phys. J. E 38, 34 (2015). https://doi.org/10.1140/epje/i2015-15034-3

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Keywords

  • Flowing Matter: Granular Matter