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Segregation of large particles in dense granular flows suggests a granular Saffman effect

K. van der Vaart1,2, M. P. van Schrojenstein Lantman2, T. Weinhart2, S. Luding2, C. Ancey1, and A. R. Thornton2

  • 1Environmental Hydraulics Laboratory, École Polytechnique Fédérale de Lausanne, Écublens, 1015 Lausanne, Switzerland
  • 2Multi-Scale Mechanics, ET and MESA+, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands

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Phys. Rev. Fluids 3, 074303 – Published 13 July, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.074303

Abstract

We report on the scaling between the lift force and the velocity lag experienced by a single particle of different size in a monodisperse dense granular chute flow. The similarity of this scaling to the Saffman lift force in (micro-) fluids, suggests an inertial origin for the lift force responsible for segregation of (isolated, large) intruders in dense granular flows. We also observe an anisotropic pressure field surrounding the particle, which potentially lies at the origin of the velocity lag. These findings are relevant for modeling and theoretical predictions of particle-size segregation. At the same time, the suggested interplay between polydispersity and inertial effects in dense granular flows with stress and strain gradients, implies striking new parallels between fluids, suspensions, and granular flows with wide application perspectives.

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References (56)

  1. I. S. Aranson and L. S. Tsimring, Patterns and collective behavior in granular media: Theoretical concepts, Rev. Mod. Phys. 78, 641 (2006).
  2. J. C. Williams, The segregation of particulate materials. A review, Powder Technol. 15, 245 (1976).
  3. A. Rosato, K. J. Strandburg, F. Prinz, and R. H. Swendsen, Why the Brazil Nuts are on Top: Size Segregation of Particulate Matter by Shaking, Phys. Rev. Lett. 58, 1038 (1987).
  4. J. M. Ottino and D. V. Khakhar, Mixing and segregation of granular materials, Annu. Rev. Fluid. Mech. 32, 55 (2000).
  5. J. Duran, J. Rajchenbach, and E. Clément, Arching Effect Model for Particle Size Segregation, Phys. Rev. Lett. 70, 2431 (1993).
  6. S. Dippel and S. Luding, Simulation on size segregation: Geometrical effects in the absence of convection, J. Phys. I 5, 1527 (1995).
  7. J. B. Knight, H. M. Jaeger, and S. R. Nagel, Vibration-Induced Size Separation in Granular Media: The Convection Connection, Phys. Rev. Lett. 70, 3728 (1993).
  8. GDR-MiDi, On dense granular flows, Eur. Phys. J. E 14, 341 (2004).
  9. P. Jop, Y. Forterre, and O. Pouliquen, A constitutive law for dense granular flows, Nature (London) 441, 727 (2006).
  10. L. A. Golick and K. E. Daniels, Mixing and segregation rates in sheared granular materials, Phys. Rev. E 80, 042301 (2009).
  11. Yi Fan and K. M. Hill, Shear-driven segregation of dense granular mixtures in a split-bottom cell, Phys. Rev. E 81, 041303 (2010).
  12. Yi Fan and K. M. Hill, Theory for shear-induced segregation of dense granular mixtures, New J. Phys. 13, 095009 (2011).
  13. J. A. Drahun and J. Bridgwater, The mechanisms of free surface segregation, Powder Technol. 36, 39 (1983).
  14. S. B. Savage and C. K. K. Lun, Particle size segregation in inclined chute flow of dry cohesionless granular solids, J. Fluid Mech. 189, 311 (1988).
  15. C. R. K. Windows-Yule, B. J. Scheper, A. J. van der Horn, N. Hainsworth, J. Saunders, D. J. Parker, and A. R. Thornton, Understanding and exploiting competing segregation mechanisms in horizontally rotated granular media, New J. Phys. 18, 023013 (2016).
  16. K. M. Hill and D. S. Tan, Segregation in dense sheared flows: Gravity, temperature gradients, and stress partitioning, J. Fluid Mech. 756, 54 (2014).
  17. T. Weinhart, S. Luding, and A. R. Thornton, From discrete particles to continuum fields in mixtures, AIP Conf. Proc. 1542, 1202 (2013).
  18. L. Staron and J. C. Phillips, Stress partition and microstructure in size-segregating granular flows, Phys. Rev. E 92, 022210 (2015).
  19. D. R. Tunuguntla, T. Weinhart, and A. R. Thornton, Comparing and contrasting size-based particle segregation models, Computat. Part. Mech. 4, 387 (2017).
  20. S. Wiederseiner, N. Andreini, G. Épely-Chauvin, G. Moser, M. Monnereau, J. M. N. T. Gray, and C. Ancey, Experimental investigation into segregating granular flows down chutes, Phys. Fluids 23, 013301 (2011).
  21. L. Staron and J. C. Phillips, Segregation time-scale in bi-disperse granular flows, Phys. Fluids 26, 033302 (2014).
  22. M. Harrington, J. H. Weijs, and W. Losert, Suppression and Emergence of Granular Segregation Under Cyclic Shear, Phys. Rev. Lett. 111, 078001 (2013).
  23. L. Staron and J. C. Phillips, How large grains increase bulk friction in bi-disperse granular chute flows, Computat. Part. Mech. 3, 367 (2016).
  24. A. N. Edwards and N. M. Vriend, Size segregation in a granular bore, Phys. Rev. Fluids 1, 064201 (2016).
  25. L. Jing, C. Y. Kwok, and Y. F. Leung, Micromechanical Origin of Particle Size Segregation, Phys. Rev. Lett. 118, 118001 (2017).
  26. J. M. N. T Gray and A. R. Thornton, A theory for particle size segregation in shallow granular free-surface flows, Proc. R. Soc. A. 461, 1447 (2005).
  27. A. R. Thornton, J. M. N. T. Gray, and A. J. Hogg, A three-phase mixture theory for particle size segregation in shallow granular free-surface flows, J. Fluid Mech. 550, 1 (2006).
  28. B. Marks, P. Rognon, and I. Einav, Grainsize dynamics of polydisperse granular segregation down inclined planes, J. Fluid Mech. 690, 499 (2012).
  29. D. R. Tunuguntla, O. Bokhove, and A. R. Thornton, A mixture theory for size and density segregation in shallow granular free-surface flows, J. Fluid Mech. 749, 99 (2014).
  30. K. van der Vaart, P. Gajjar, G. Epely-Chauvin, N. Andreini, J. M. N. T. Gray, and C. Ancey, Underlying Asymmetry within Particle Size Segregation, Phys. Rev. Lett. 114, 238001 (2015).
  31. P. Gajjar and J. M. N. T. Gray, Asymmetric flux models for particle-size segregation in granular avalanches, J. Fluid Mech. 757, 297 (2014).
  32. K. Kamrin and G. Koval, Nonlocal Constitutive Relation for Steady Granular Flow, Phys. Rev. Lett. 108, 178301 (2012).
  33. D. L. Henann and K. Kamrin, A predictive, size-dependent continuum model for dense granular flows, Proc. R. Soc. A 110, 6730 (2013).
  34. R. J. Phillips, R. C. Armstrong, R. A. Brown, A. L. Graham, and J. R. Abbott, A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration, Phys. Fluids 4, 30 (1992).
  35. F. Boyer, O. Pouliquen, and É. Guazzelli, Dense suspensions in rotating-rod flows: Normal stresses and particle migration, J. Fluid Mech. 686, 5 (2011).
  36. F. Guillard, Y. Forterre, and O. Pouliquen, Scaling laws for segregation forces in dense sheared granular flows, J. Fluid Mech. 807, R1 (2016).
  37. MercuryDPM.org.
  38. A. R. Thornton, D. Krijgsman, A. Voortwis, V. Ogarko, S. Luding, R. Fransen, S. Gonzalez, O. Bokhove, O. Imole, and T. Weinhart, A review of recent work on the discrete particle method at the University of Twente: An introduction to the open-source package mercurydpm, in DEM6 International Conference DEMs, edited by G. Mustoe (Colorado School of Mines, Golden, CO, 2013), pp. 50–56.
  39. T. Weinhart, D. R. Tunuguntla, M. P. van Schrojenstein-Lantman, A. J. van der Horn, I. F. C. Denissen, C. R. Windows-Yule, A. C. de Jong, and A. R. Thornton, Mercurydpm: A fast and flexible particle solver part A: Technical advances, in Proceedings of the 7th International Conference DEM, edited by X. Li, Y. Feng, and G. Mustoe (Springer, Singapore, 2017), pp. 1353–1360.
  40. P. A. Cundall and O. D. L. Strack, A discrete numerical model for granular assemblies, Geotechnique 29, 47 (1979).
  41. T. Weinhart, R. Hartkamp, A. R. Thornton, and S. Luding, Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface, Phys. Fluids 25, 070605 (2013).
  42. D. R. Tunuguntla, A. R. Thornton, and T. Weinhart, From discrete elements to continuum fields: Extension to bidisperse systems, Computat. Part. Mech. 3, 349 (2016).
  43. I. Goldhirsch, Stress, stress asymmetry and couple stress: From discrete particles to continuous fields, Granular Matter 12, 239 (2010).
  44. C. H. Rycroft, VORO++: A three-dimensional Voronoi cell library in C++, Chaos 19, 041111 (2009). Obtainable via: math.lbl.gov/voro++
  45. C. Rycroft, Voro++: A three-dimensional Voronoi cell library in C++, Lawrence Berkeley National Laboratory (2009).
  46. T. Weinhart, A. R. Thornton, S. Luding, and O. Bokhove, Closure relations for shallow granular flows from particle simulations, Granular Matter 14, 531 (2012).
  47. F. Guillard, Y. Forterre, and O. Pouliquen, Lift forces in granular media, Phys. Fluids 26, 043301 (2014).
  48. F. Guillard, Y. Forterre, and O. Pouliquen, Origin of a depth-independent drag force induced by stirring in granular media, Phys. Rev. E 91, 022201 (2015).
  49. A. Tripathi and D. V. Khakhar, Numerical Simulation of the Sedimentation of a Sphere in a Sheared Granular Fluid: A Granular Stokes Experiment, Phys. Rev. Lett. 107, 108001 (2011).
  50. A. Thornton, T. Weinhart, S. Luding, and O. Bokhove, Modeling of particle size segregation: Calibration using the discrete particle method, Int. J. Mod. Phys. C 23, 1240014 (2012).
  51. J. M. N. T. Gray and C. Ancey, Multi-component particle-size segregation in shallow granular avalanches, J. Fluid Mech. 678, 535 (2011).
  52. P. G. T. Saffman, The lift on a small sphere in a slow shear flow, J. Fluid Mech. 22, 385 (1965).
  53. H. A. Stone, Philip Saffman and viscous flow theory, J. Fluid Mech. 409, 165 (2000).
  54. K. A. Gillemot, E. Somfai, and T. Börzsönyi, Shear-driven segregation of dry granular materials with different friction coefficients, Soft Matter 13, 415 (2017).
  55. N. Thomas, Reverse and intermediate segregation of large beads in dry granular media, Phys. Rev. E 62, 961 (2000).
  56. G. Félix and N. Thomas, Evidence of two effects in the size segregation process in dry granular media, Phys. Rev. E 70, 051307 (2004).

Outline

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Phys. Rev. Fluids 3, 074303– Published 13 July, 2018
  • Received 12 April 2017
  • Revised 15 September 2017
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