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Dense, Inhomogeneous, Granular Shearing

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Views on Microstructures in Granular Materials

Part of the book series: Advances in Mechanics and Mathematics ((ACM,volume 44))

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Abstract

We make use of recent extensions of kinetic theory for dense, dissipative shearing flows to phrase and solve boundary-value problems for steady flows of a dense aggregate of identical frictional spheres sheared in a gravitational field between horizontal, rigid, bumpy boundaries by the upper boundary or in the absence of gravity between two coaxial, bumpy cylinders by the inner cylinder. In both scenarios, the resulting flow consists of a region of rapid, collisional flow and a denser region of slower flow in which more enduring particle contacts play a role. In the denser region, or bed, we assume that the collisional production of energy is negligible and the anisotropy of the contact forces influences the shear stress and the pressure in the same way. We show profiles of average velocity and provide relationships between the thickness of the fast flow, the gravitational acceleration (if present), the velocity of the moving boundary, the shear stress and the confining pressure.

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References

  1. Jenkins, J.T., Savage, S.B.: A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202 (1983). https://doi.org/10.1017/S0022112083001044

    Article  Google Scholar 

  2. Garzó, V., Dufty, J.W.: Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59, 5895–5911 (1999). https://doi.org/10.1103/PhysRevE.59.5895

    Article  Google Scholar 

  3. Goldhirsch, I.: Introduction to granular temperature. Powd. Tech. 182, 130–136 (2008). https://doi.org/10.1016/j.powtec.2007.12.002

    Article  Google Scholar 

  4. GDR MiDi: On dense granular flows. Eur. Phys. J. E 14, 341–365 (2004). https://doi.org/10.1140/epje/i2003-10153-0

  5. da Cruz, F., Emam, S., Prochnow, M., Roux, J.-N., Chevoir, F.: Rheophysics of dense granular materials: Discrete simulation of plane shear flows. Phys. Rev. E 72, 021309 (2005). https://doi.org/10.1103/PhysRevE.72.021309

    Article  Google Scholar 

  6. Jop, P., Forterre, Y., Pouliquen, O.: Crucial role of side walls for granular surface flows: consequences for the rheology. J. Fluid Mech. 541, 167–192 (2005). https://doi.org/10.1017/S0022112005005987

    Article  Google Scholar 

  7. Kamrin, K., Henann, D.L.: Nonlocal modeling of granular flows down inclines. Soft Matt. 11, 179–185 (2014). https://doi.org/10.1039/c4sm01838a

    Article  Google Scholar 

  8. Koval, G., Roux, J.-N., Corfdir, A., Chevoir, F.: Rheology of Confined Granular Flows: Annular shear of cohesionless granular materials: From the inertial to quasistatic regime. Phys. Rev. E 79, 021306 (2009). https://doi.org/10.1103/PhysRevE.79.021306

    Article  Google Scholar 

  9. Kamrin, K., Koval, G.: Nonlocal Constitutive Relation for Steady Granular Flow. Phys. Rev. Lett. 108, 178301 (2012). https://doi.org/10.1103/PhysRevLett.108.178301

    Article  Google Scholar 

  10. Zhang, Q., Kamrin, K.: Microscopic Description of the Granular Fluidity Field in Nonlocal Flow Modeling. Phys. Rev. Lett. 118, 058001 (2017). https://doi.org/10.1103/PhysRevLett.118.058001

    Article  Google Scholar 

  11. Jenkins, J.T.: Dense shearing flows of inelastic disks. Phys. Fluids 18, 103307 (2006). https://doi.org/10.1063/1.2364168

    Article  Google Scholar 

  12. Jenkins, J.T.: Dense inclined flows of inelastic spheres. Granul. Matt. 10, 47–52 (2007). https://doi.org/10.1007/s10035-007-0057-z

    Article  Google Scholar 

  13. Berzi, D.: Extended kinetic theory applied to dense, granular, simple shear flows. Acta Mech. 225, 2191–2198 (2014). https://doi.org/10.1007/s00707-014-1125-1

    Article  MathSciNet  Google Scholar 

  14. Mitarai, N., Nakanishi, H.: Bagnold Scaling, Density Plateau, and Kinetic Theory Analysis of Dense Granular Flow. Phys. Rev. Lett. 94, 128001 (2005). https://doi.org/10.1103/PhysRevLett.94.128001

    Article  Google Scholar 

  15. Mitarai, N., Nakanishi, H.: Velocity correlations in dense granular shear flows: Effects on energy dissipation and normal stress. Phys. Rev. E 75, 031305 (2007). https://doi.org/10.1103/PhysRevE.75.031305

    Article  Google Scholar 

  16. Kumaran, V.: Dynamics of dense sheared granular flows. Part II. The relative velocity distributions. J. Fluid Mech. 632, 145–198 (2009). https://doi.org/10.1017/S0022112009006958

    MathSciNet  MATH  Google Scholar 

  17. Jenkins, J.T., Zhang, C.: Kinetic theory for identical, frictional, nearly elastic spheres. Phys. Fluids 14, 1228–1235 (2002). https://doi.org/10.1063/1.1449466

    Article  Google Scholar 

  18. Larcher, M., Jenkins, J.T.: Segregation and mixture profiles in dense, inclined flows of two types of spheres. Phys. Fluids 25, 113301 (2013). https://doi.org/10.1063/1.4830115

    Article  Google Scholar 

  19. 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). https://doi.org/10.1063/1.4905461

    Article  Google Scholar 

  20. Berzi, D., Jenkins, J.T.: Steady shearing flows of deformable, inelastic spheres. Soft Matt. 11, 4799–4808 (2015). https://doi.org/10.1039/c5sm00337g

    Article  Google Scholar 

  21. Komatsu, T.S., Inagaki, S., Nakagawa, N., Nasuno, S.: Creep Motion in a Granular Pile Exhibiting Steady Surface Flow. Phys. Rev. Lett. 86, 1757–1760 (2001). https://doi.org/10.1103/PhysRevLett.86.1757

    Article  Google Scholar 

  22. Richard, P., Valance, A., Met́ayer, J.-F., Sanchez, P., Crassous, J., Louge, M., Delannay, R.: Rheology of Confined Granular Flows: Scale Invariance, Glass Transition, and Friction Weakening. Phys. Rev. Lett. 101, 248002 (2008). https://doi.org/10.1103/PhysRevLett.101.248002

  23. Jenkins, J.T., Askari, E.: Boundary conditions for rapid granular flows: phase interfaces. J. Fluid Mech. 223, 497–508 (1991). https://doi.org/10.1017/S0022112091001519

    Article  Google Scholar 

  24. Berzi, D., Jenkins, J.T.: Dense, inhomogeneous shearing flows of spheres. EPJ Web of Conferences 140, 11006 (2017). https://doi.org/10.1051/epjconf/201714011006

    Article  Google Scholar 

  25. Siavoshi, S., Orpe, A.V., Kudrolli, A.: Friction of a slider on a granular layer: Nonmonotonic thickness dependence and effect of boundary conditions. Phys. Rev. E 73, 010301 (2006). https://doi.org/10.1103/PhysRevE.73.010301

    Article  Google Scholar 

  26. Richman, M.W.: Boundary conditions based upon a modified Maxwellian velocity distribution for flows of identical, smooth, nearly elastic spheres. Acta Mech. 75, 227–240 (1988). https://doi.org/10.1007/BF01174637

    Article  Google Scholar 

  27. Chialvo, S., Sun, J., Sundaresan, S.: Bridging the rheology of granular flows in three regimes. Phys. Rev. E 85, 021305 (2012). https://doi.org/10.1103/PhysRevE.85.021305

    Article  Google Scholar 

  28. Jenkins, J.T., Berzi, D.: Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory. Granul. Matt. 12, 151–158 (2010). https://doi.org/10.1007/s10035-010-0169-8

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Politecnico di Milano, Milano, Italy

    Diego Berzi

  2. Cornell University, Ithaca, NY, USA

    James T. Jenkins

Authors
  1. Diego Berzi
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  2. James T. Jenkins
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Corresponding author

Correspondence to Diego Berzi .

Editor information

Editors and Affiliations

  1. Department of Civil, Energy, Environment, and Materials Engineering (DICEAM), University ‘Mediterranea’ of Reggio Calabria, Reggio Calabria, Italy

    Pasquale Giovine

  2. Department of Civil and Environmental Engineering, University of Florence, Firenze, Italy

    Paolo Maria Mariano

  3. Department of Civil, Energy, Environment, and Materials Engineering (DICEAM), University of Reggio Calabria, Reggio Calabria, Italy

    Giuseppe Mortara

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Berzi, D., Jenkins, J.T. (2020). Dense, Inhomogeneous, Granular Shearing. In: Giovine, P., Mariano, P.M., Mortara, G. (eds) Views on Microstructures in Granular Materials. Advances in Mechanics and Mathematics(), vol 44. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-49267-0_2

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