Skip to main content
Log in

Segregation in a dense, inclined, granular flow with basal layering

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

We consider an inclined flow of two different types of spheres in which there is a dense collisional flow above a layered flow that involves force-chains that extend through its depth. In the latter, the granular temperature increases linearly from its base, in the former the granular temperature increases linearly from its top. Consequently, for spheres of the same material, the larger spheres segregate away from the point of transition between the flows and towards the bottom of the layered flow and the top of the collisional flow. The concentration profiles for spheres made of different materials exhibit more complicated behaviour, depending on the ratios of mass and size.

Graphical abstract

Theoretical predictions of the segregation measure, X, and of the relative concentration of large (A) and small (B) particles. The parameters are given in the caption of Fig. 3.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. MiDi, G.D.R.: On dense granular flows. Eur. Phys. J. E 14, 341 (2004)

    Article  Google Scholar 

  2. Jop, P., Forterre, Y., Pouliquen, O.: A constitutive law for dense granular flows. Nature 441, 727 (2006)

    Article  ADS  Google Scholar 

  3. Barker, T., Schaeffer, D.G., Bohorquez, P., Gray, J.M.N.T.: Well-posed and ill-posed behaviour of the μ(I)-rheology for granular flow. J. Fluid Mech. 779, 794–818 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  4. Heyman, J., Delannay, R., Tabuteau, H., Valance, A.: Compressibility regularizes the μ(I)-rheology for dense granular flows. J. Fluid Mech. 830, 553 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  5. Barker, T., Schaeffer, D.G., Shearer, M., Gray, J.M.N.T.: Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology. Proc. R. Soc. A 473, 20160846 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  6. Goddard, J., Lee, J.: On the stability of the μ(I) rheology for granular flow. J. Fluid Mech. 833, 302 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  7. Goddard, J., Lee, J.: Regularization by compressibility of the μ(I) model of dense granular flow. Phys. Fluids 30, 073302 (2018)

    Article  ADS  Google Scholar 

  8. Jenkins, J.T., Berzi, D.: Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory. Granular Matter 12, 151 (2010)

    Article  Google Scholar 

  9. Larcher, M., Jenkins, J.T.: The evolution of segregation in dense inclined flows of binary mixtures of spheres. J. Fluid Mech. 782, 405 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  10. Larcher, M., Jenkins, J.T.: Segregation and mixture profiles in dense, inclined flows of two types of spheres. Phys. Fluids 25, 113301 (2013)

    Article  ADS  Google Scholar 

  11. Bridgwater, J., Foo, W., Stephens, D.: Particle mixing and segregation in failure zones—theory and experiment. Powder Technol. 41, 147 (1985)

    Article  Google Scholar 

  12. Dolgunin, V.N., Ukolov, A.A.: Segregation modelling of particle rapid gravity flow. Powder Technol. 83, 95 (1995)

    Article  Google Scholar 

  13. Thornton, A.R., Gray, J.M.N.T., Hogg, A.J.: A three-phase mixture theory for particle size segregation in shallow granular free-surface flows. J. Fluid Mech. 550, 1 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  14. Gray, J.M.N.T., Chugunov, V.A.: Particle-size segregation and diffusive remixing in shallow granular avalanches. J. Fluid Mech. 569, 365 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  15. Fan, Y., Hill, K.M.: Theory for shear-induced segregation of dense granular mixtures. New J. Phys. 13, 095009 (2011)

    Article  ADS  Google Scholar 

  16. Hill, K.M., Fan, Y.: Granular temperature and segregation in dense sheared particulate mixtures. KONA Powder Part. J. 33, 150 (2016)

    Article  Google Scholar 

  17. Lueptow, R.M., Deng, Z., Xiao, H., Umbanhowar, P.B.: Modeling segregation in modulated granular flow. EJP Web Conf. 140, 03018 (2017)

    Article  Google Scholar 

  18. Grey, J.M.N.T.: Particle segregation in dense granular flows. Annu. Rev. Fluid Mech. 50, 407 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  19. Berzi, D., Jenkins, J.T., Richard, P.: Extended kinetic theory for collisional shearing over and within an inclined, erodible bed. J. Fluid Mech. 885, A27 (2020). https://doi.org/10.1017/jfm.2019.1017

    Article  ADS  MATH  Google Scholar 

  20. Meninno, S., Armanini, A., Larcher, M.: Gravity-driven, dry granular flows over a loose bed in stationary and homogeneous conditions. Phys. Rev. E 3, 024301 (2018)

    Google Scholar 

  21. Hajra, S.K., Khakhar, D.V.: Sensitivity of granular segregation of mixtures in quasi-two-dimensional fluidized layers. Phys. Rev. E 69, 031304 (2004)

    Article  ADS  Google Scholar 

  22. Berzi, D., Vescovi, D.: Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows. Phys. Fluids 27, 013302 (2015)

    Article  ADS  Google Scholar 

  23. Arnarson, B.O., Jenkins, J.T.: Binary mixtures of inelastic spheres: simplified constitutive theory. Phys. Fluids 16, 4543 (2004)

    Article  ADS  Google Scholar 

  24. Jenkins, J.T., Larcher, M.: Dense, layered, inclined flows of spheres. Phys. Rev. Fluids 2, 124301 (2017)

    Article  ADS  Google Scholar 

  25. Jenkins, J.T.: Dense inclined flows of inelastic spheres. Granular Matter 10, 47 (2007)

    Article  Google Scholar 

  26. Tunuguntla, D.R., Bokhove, O., Thornton, A.R.: A mixture theory for size and density segregation in shallow granular free-surface flows. J. Fluid Mech. 749, 99 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  27. Gray, J.M.N.T., Ancey, C.: Particle-size and particle-density segregation in granular avalanches. J. Fluid Mech. 779, 622 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  28. Berzi, D., Jenkins, J.T.: Inertial shear bands in granular materials. Phys. Fluids 27, 033303 (2015)

    Article  ADS  Google Scholar 

  29. Berzi, D., Jenkins, J.T.: Dense, inhomogeneous shearing flows of spheres. EPJ Web Conf. 140, 11006 (2017)

    Article  Google Scholar 

  30. Larcher, M., Jenkins, J.T.: Segregation in binary mixtures of spheres in dense, inclined lows over particle beds (2020) (in preparation)

Download references

Funding

This study was financially supported by Libera Università di Bolzano (I52F17001340005).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michele Larcher.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the Topical Collection: In Memoriam of Robert P. Behringer.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jenkins, J.T., Larcher, M. Segregation in a dense, inclined, granular flow with basal layering. Granular Matter 22, 35 (2020). https://doi.org/10.1007/s10035-020-0996-1

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1007/s10035-020-0996-1

Keywords

Navigation