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.
Similar content being viewed by others
References
MiDi, G.D.R.: On dense granular flows. Eur. Phys. J. E 14, 341 (2004)
Jop, P., Forterre, Y., Pouliquen, O.: A constitutive law for dense granular flows. Nature 441, 727 (2006)
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)
Heyman, J., Delannay, R., Tabuteau, H., Valance, A.: Compressibility regularizes the μ(I)-rheology for dense granular flows. J. Fluid Mech. 830, 553 (2017)
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)
Goddard, J., Lee, J.: On the stability of the μ(I) rheology for granular flow. J. Fluid Mech. 833, 302 (2017)
Goddard, J., Lee, J.: Regularization by compressibility of the μ(I) model of dense granular flow. Phys. Fluids 30, 073302 (2018)
Jenkins, J.T., Berzi, D.: Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory. Granular Matter 12, 151 (2010)
Larcher, M., Jenkins, J.T.: The evolution of segregation in dense inclined flows of binary mixtures of spheres. J. Fluid Mech. 782, 405 (2015)
Larcher, M., Jenkins, J.T.: Segregation and mixture profiles in dense, inclined flows of two types of spheres. Phys. Fluids 25, 113301 (2013)
Bridgwater, J., Foo, W., Stephens, D.: Particle mixing and segregation in failure zones—theory and experiment. Powder Technol. 41, 147 (1985)
Dolgunin, V.N., Ukolov, A.A.: Segregation modelling of particle rapid gravity flow. Powder Technol. 83, 95 (1995)
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)
Gray, J.M.N.T., Chugunov, V.A.: Particle-size segregation and diffusive remixing in shallow granular avalanches. J. Fluid Mech. 569, 365 (2006)
Fan, Y., Hill, K.M.: Theory for shear-induced segregation of dense granular mixtures. New J. Phys. 13, 095009 (2011)
Hill, K.M., Fan, Y.: Granular temperature and segregation in dense sheared particulate mixtures. KONA Powder Part. J. 33, 150 (2016)
Lueptow, R.M., Deng, Z., Xiao, H., Umbanhowar, P.B.: Modeling segregation in modulated granular flow. EJP Web Conf. 140, 03018 (2017)
Grey, J.M.N.T.: Particle segregation in dense granular flows. Annu. Rev. Fluid Mech. 50, 407 (2018)
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
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)
Hajra, S.K., Khakhar, D.V.: Sensitivity of granular segregation of mixtures in quasi-two-dimensional fluidized layers. Phys. Rev. E 69, 031304 (2004)
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)
Arnarson, B.O., Jenkins, J.T.: Binary mixtures of inelastic spheres: simplified constitutive theory. Phys. Fluids 16, 4543 (2004)
Jenkins, J.T., Larcher, M.: Dense, layered, inclined flows of spheres. Phys. Rev. Fluids 2, 124301 (2017)
Jenkins, J.T.: Dense inclined flows of inelastic spheres. Granular Matter 10, 47 (2007)
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)
Gray, J.M.N.T., Ancey, C.: Particle-size and particle-density segregation in granular avalanches. J. Fluid Mech. 779, 622 (2015)
Berzi, D., Jenkins, J.T.: Inertial shear bands in granular materials. Phys. Fluids 27, 033303 (2015)
Berzi, D., Jenkins, J.T.: Dense, inhomogeneous shearing flows of spheres. EPJ Web Conf. 140, 11006 (2017)
Larcher, M., Jenkins, J.T.: Segregation in binary mixtures of spheres in dense, inclined lows over particle beds (2020) (in preparation)
Funding
This study was financially supported by Libera Università di Bolzano (I52F17001340005).
Author information
Authors and Affiliations
Corresponding author
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
About this article
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
Received:
Published:
DOI: https://doi.org/10.1007/s10035-020-0996-1