Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-09T06:04:36.435Z Has data issue: false hasContentIssue false
  • English
  • Français

Segregation in dense sheared flows: gravity, temperature gradients, and stress partitioning

Published online by Cambridge University Press:  01 September 2014

K. M. Hill  and
Danielle S. Tan Open the ORCID record for Danielle S. Tan [Opens in a new window]
K. M. Hill*
Affiliation:
St Anthony Falls Laboratory, University of Minnesota, 2 Third Avenue SE, Minneapolis, MN 55414, USA Department of Civil Engineering, University of Minnesota, 500 Pillsbury Drive SE, Minneapolis, MN 55455, USA
Danielle S. Tan
Affiliation:
St Anthony Falls Laboratory, University of Minnesota, 2 Third Avenue SE, Minneapolis, MN 55414, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

It is well-known that in a dense, gravity-driven flow, large particles typically rise to the top relative to smaller equal-density particles. In dense flows, this has historically been attributed to gravity alone. However, recently kinetic stress gradients have been shown to segregate large particles to regions with higher granular temperature, in contrast to sparse energetic granular mixtures where the large particles segregate to regions with lower granular temperature. We present a segregation theory for dense gravity-driven granular flows that explicitly accounts for the effects of both gravity and kinetic stress gradients involving a separate partitioning of contact and kinetic stresses among the mixture constituents. We use discrete-element-method (DEM) simulations of different-sized particles in a rotated drum to validate the model and determine diffusion, drag, and stress partition coefficients. The model and simulations together indicate, surprisingly, that gravity-driven kinetic sieving is not active in these flows. Rather, a gradient in kinetic stress is the key segregation driving mechanism, while gravity plays primarily an implicit role through the kinetic stress gradients. Finally, we demonstrate that this framework captures the experimentally observed segregation reversal of larger particles downward in particle mixtures where the larger particles are sufficiently denser than their smaller counterparts.

JFM classification

Granular media: Granular media Mixing: Mixing Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 54 - 88
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

Present address: Department of Mechanical Engineering, National University of Singapore, 9 Engineering Dr. 1, Singapore 117575, Republic of Singapore.

References

Abbott, J. R., Tetlow, N., Graham, A. L., Altobelli, S. A., Fukushima, E., Mondy, L. A. & Stephens, T. S. 1991 Experimental observations of particle migration in concentrated suspensions: Couette flow. J. Rheol. 35, 773–795.CrossRefGoogle Scholar
Alam, M. & Luding, S. 2003 Rheology of bidisperse granular mixtures via event-driven simulations. J. Fluid Mech. 276, 69–103.CrossRefGoogle Scholar
Alonso, M., Satoh, M. & Miyanami, K. 1991 Optimum combination of size ratio, density ratio and concentration to minimize free surface segregation. Powder Technol. 68 (3), 145–152.CrossRefGoogle Scholar
Arnarson, B. Ö. & Jenkins, J. T. 2000 Particle segregation in the context of the species momentum balances. In Traffic and Granular Flow ‘99: Social, Traffic and Granular Dynamics (ed. Helbing, D., Herrmann, H. J., Schreckenberg, M. & Wolf, D. E.), pp. 481–487. Springer.CrossRefGoogle Scholar
Arnarson, B. Ö. & Jenkins, J. T. 2004 Binary mixtures of inelastic spheres: simplified constitutive theory. Phys. Fluids 16, 4543–4550.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bonamy, D., Daviaud, F. & Laurent, L. 2002 Experimental study of granular surface flows via a fast camera: a continuous description. Phys. Fluids 15, 1666–1674.CrossRefGoogle Scholar
Bridgwater, J. 1976 Fundamental powder mixing mechanisms. Powder Technol. 15, 215–231.CrossRefGoogle Scholar
Campbell, C. S. 2002 Granular shear flows at the elastic limit. J. Fluid Mech. 465, 261–291.CrossRefGoogle Scholar
Chikkadi, V. & Alam, M. 2009 Slip velocity and stresses in granular poiseuille flow via event-driven simulation. Phys. Rev. E 80, 021303.CrossRefGoogle ScholarPubMed
Conway, S. L., Liu, X. & Glasser, B. J. 2006 Instability-induced clustering and segregation in high-shear couette flows of model granular materials. Chem. Engng Sci. 61, 6404–6423.CrossRefGoogle Scholar
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Geotechnique 29, 47–65.CrossRefGoogle Scholar
Dietrich, W. E., Kirchner, J. W., Ikeda, H. & Iseya, F. 1989 Sediment supply and the development of the coarse surface layer in gravel-bedded rivers. Nature 340, 215–217.CrossRefGoogle Scholar
Dolgunin, V. N. & Ukolov, A. A. 1995 Segregation modeling of particle rapid gravity flow. Powder Technol. 83 (3), 95–103.CrossRefGoogle Scholar
Donald, M. B. & Roseman, B. 1962 Mixing and de-mixing of solid particles: Part i. mechanisms in a horizontal drum mixer. Brit. Chem. Engng 7, 749–752.Google Scholar
Fan, Y. & Hill, K. M. 2011a Phase transitions in shear-induced segregation of granular materials. Phys. Rev. Lett. 106, 218301.CrossRefGoogle ScholarPubMed
Fan, Y. & Hill, K. M. 2011b Theory for shear-induced segregation of dense granular mixtures. New J. Phys. 13, 095009.CrossRefGoogle Scholar
Fan, Y. & Hill, K. M.2014 Shear-induced segregation of mixtures of particles differing in density. Under review.CrossRefGoogle Scholar
Félix, G. & Thomas, N. 2004 Evidence of two effects in the size segregation process in dry granular media. Phys. Rev. E 70 (5), 051307.CrossRefGoogle ScholarPubMed
Foo, W. S. & Bridgwater, J. 1983 Particle migration. Powder Technol. 36, 271–273.CrossRefGoogle Scholar
Forterre, Y. & Pouliquen, O. 2008 Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1–24.CrossRefGoogle Scholar
Galvin, J. E., Dahl, S. R. & Hrenya, C. M. 2005 On the role of non-equipartition in the dynamics of rapidly flowing, granular mixtures. J. Fluid Mech. 528, 207–232.CrossRefGoogle Scholar
Gioia, G., Ott-Monsivais, S. E. & Hill, K. M. 2006 Fluctuating velocity and momentum transfer in dense granular flows. Phys. Rev. Lett. 96, 138001.CrossRefGoogle ScholarPubMed
Gray, J. M. N. T. & Ancey, C. 2011 Multi-component particle-size segregation in shallow granular avalanches. J. Fluid Mech. 678, 535–588.CrossRefGoogle Scholar
Gray, J. M. N. T. & Chugunov, V. A. 2006 Particle-size segregation and diffusive remixing in shallow granular avalanches. J. Fluid Mech. 569, 365–398.CrossRefGoogle Scholar
Gray, J. M. N. T. & Thornton, A. R. 2005 A theory for particle size segregation in shallow granular free-surface flows. Proc. R. Soc. Lond. A 461, 1447–1473.Google Scholar
Hill, K. M., Caprihan, A. & Kakalios, J. 1997 Bulk segregation in rotated granular material measured by magnetic resonance imaging. Phys. Rev. Lett. 78, 50–53.CrossRefGoogle Scholar
Hill, K. M., DellAngelo, L. & Meerschaert, M. M. 2010a Heavy-tailed travel distance in gravel bed transport: an exploratory enquiry. J. Geophys. Res. 115, F00A14.Google Scholar
Hill, K. M. & Fan, Y. 2008 Isolating segregation mechanisms in a split-bottom cell. Phys. Rev. Lett. 101, 088001.CrossRefGoogle Scholar
Hill, K. M., Fan, Y., Zhang, J., Van Niekerk, C., Zastrow, E., Hagness, S. C. & Bernhard, J. T. 2010b Granular segregation studies for the development of a radar-based three-dimensional sensing system. Granul. Matt. 12, 201–207.CrossRefGoogle Scholar
Hill, K. M., Gioia, G. & Amaravadi, D. 2004 Radial segregation patterns in rotating granular mixtures: waviness selection. Phys. Rev. Lett. 93, 224301.CrossRefGoogle ScholarPubMed
Hill, K. M., Gioia, G. & Tota, T. 2003 Structure and kinematics in dense free-surface granular flow. Phys. Rev. Lett. 91, 064302.CrossRefGoogle ScholarPubMed
Hill, K. M., Khakhar, D. V., Gilchrist, J. F., McCarthy, J. J. & Ottino, J. M. 1999 Segregation-driven organization in chaotic granular flows. Proc. Natl Acad. Sci. USA 96, 11701–11706.CrossRefGoogle ScholarPubMed
Hill, K. M. & Yohannes, B. 2011 Rheology of dense granular mixtures: boundary pressures. Phys. Rev. Lett. 106, 058302.CrossRefGoogle ScholarPubMed
Hill, K. M. & Zhang, J. 2008 Kinematics of densely flowing granular mixtures. Phys. Rev. E 77, 061303.CrossRefGoogle ScholarPubMed
Hsu, L., Dietrich, W. E. & Sklar, L. S. 2008 Experimental study of bedrock erosion by granular flows. J. Geophys. Res. 113, F02001.Google Scholar
Ide, J. M. 1935 Comparison of statically and dynamically determined youngś modulus of rocks. Proc. Natl Acad. Sci. USA 22, 81–92.CrossRefGoogle Scholar
Jain, N., Ottino, J. M. & Lueptow, R. M. 2002 An experimental study of the flowing granular layer in a rotating tumbler. Phys. Fluids 14, 572–582.CrossRefGoogle Scholar
Jain, N., Ottino, J. M. & Lueptow, R. M. 2005 Combined size and density segregation and mixing in non-circular tumblers. Phys. Rev. E 71, 051301.CrossRefGoogle Scholar
Jenkins, J. T. & Mancini, F. 1987 Balance laws and constitutive relations for plane flows of a dense, binary mixture of smooth, nearly elastic, circular disks. Trans. ASME: J. Appl. Mech. 54, 27–34.CrossRefGoogle Scholar
Khakhar, D. V., McCarthy, J. J. & Ottino, J. M. 1997 Radial segregation of granular mixtures in rotating cylinders. Phys. Fluids 9, 3600–3614.CrossRefGoogle Scholar
Krishnan, G. P., Beimfohr, S. & Leighton, D. T. 1996 Shear-induced radial segregation in bidisperse suspensions. J. Fluid Mech. 321, 371–393.CrossRefGoogle Scholar
Kuhl, E., D’Addetta, G. A., Herrmann, H. J. & Ramm, E. 2000 A comparison of discrete granular material models with continuous microplane formulations. Granul. Matt. 2 (5), 113–121.CrossRefGoogle Scholar
Larcher, M. & Jenkins, J. T. 2009a The influence of size segregation in particle-fluid flows. In Powders and Grains 2009 (ed. Nakagawa, M. & Luding, S.), vol. 1145, pp. 1055–1058. American Institute of Physics.Google Scholar
Larcher, M. & Jenkins, J. T. 2009b Size segregation in dry granular flows of binary mixtures. In IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows (ed. Goddard, J. D., Jenkins, J. T. & Giovine, P.), vol. 1227, pp. 363–370. American Institute of Physics.Google Scholar
Larcher, M. & Jenkins, J. T.2010 Particle size and density segregation in dense, dry granular flows. In Proceedings of the First IAHR European Meeting, Edinburgh, UK.CrossRefGoogle Scholar
Larcher, M. & Jenkins, J. T. 2013 Segregation and mixture profiles in dense, inclined flows of two types of spheres. Phys. Fluids 25, 113301.CrossRefGoogle Scholar
Leighton, D. & Acrivos, A. 1987a Measurement of shear-induced self-diffusion in concentrated suspensions of spheres. J. Fluid Mech. 177, 109–131.CrossRefGoogle Scholar
Leighton, D. & Acrivos, A. 1987b Shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.CrossRefGoogle Scholar
Marks, B. & Einav, I. 2011 A cellular automaton for segregation during granular avalanches. Granul. Matt. 13, 211–214.CrossRefGoogle Scholar
Marks, B., Rognon, P. & Einav, I. 2012 Grainsize dynamics of polydisperse granular segregation down inclined planes. J. Fluid Mech. 690, 499–511.CrossRefGoogle Scholar
May, L. B. H., Golick, L. A., Phillips, K. C., Shearer, M. & Daniels, K. E. 2010a Shear-driven size segregation of granular materials: modeling and experiment. Phys. Rev. E 81, 051301.CrossRefGoogle ScholarPubMed
May, L. B. H., Shearer, M. & Daniels, K. E. 2010b Scalar conservation laws with nonconstant coefficients with application to particle size segregation in granular flows. J. Nonlinear Sci. 20, 689–707.CrossRefGoogle Scholar
Middleton, G. V. & Hampton, M. A. 1976 Subaqueous sediment transport and deposition by sediment gravity flows. In Marine Sediment Transport and Environmental Management (ed. Stanley, D. J. & Swift, D. J. P.), pp. 197–218. John Wiley & Sons.Google Scholar
Morland, L. W. 1972 A simple constitutive theory for a fluid-saturated porous solid. J. Geophys. Res. 77, 890–900.CrossRefGoogle Scholar
Morland, L. W. 1978 A theory of slow fluid flow through a porous thermoelastic matrix. Geophys. J. R. Astron. Soc. 55, 393–410.CrossRefGoogle Scholar
Morland, L. W. 1992 Flow of viscous fluids through a porous deformable matrix. Surv. Geophys. 13, 209–268.CrossRefGoogle Scholar
Naylor, M. A. 1980 The origin of inverse grading in muddy debris flow deposits—a review. J. Sedim. Petrol. 50, 1111–1116.Google Scholar
Paola, C. & Seal, R. 1995 Grain size patchiness as a cause of selective deposition and downstream fining. Water Resour. Res. 31, 1395–1407.CrossRefGoogle Scholar
Pierre, J., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature 441, 727–730.Google Scholar
Reddy, K. A. & Kumaran, V. 2010 Dense granular flow down an inclined plane: a comparison between the hard particle model and soft particle simulations. Phys. Fluids 22, 113302.CrossRefGoogle Scholar
Savage, S. B. & Lun, C. K. K. 1988 Particle size segregation in inclined chute flow of dry cohesionless granular solids. J. Fluid Mech. 189, 311–335.CrossRefGoogle Scholar
Schlichting, H. 1979 Boundary-Layer Theory. McGraw-Hill.Google Scholar
Shinbrot, T. & Muzzio, F. 2000 Nonequilibrium patterns in granular mixing and segregation. Phys. Today 53 (3), 25–30.CrossRefGoogle Scholar
Simmons, G. & Brace, B. F. 1965 Comparison of static and dynamic measurements of compressibility of rocks. J. Geophys. Res. 70 (22), 5649–5656.CrossRefGoogle Scholar
Stephens, D. J. & Bridgwater, J. 1978 The mixing and segregation of cohesionless particulate materials, part II. Microscopic mechanisms for particles differing in size. Powder Technol. 21, 29–44.CrossRefGoogle Scholar
Stock, J. D. & Dietrich, W. E. 2006 Erosion of steepland valleys by debris flows. Geol. Soc. Am. Bull. 118, 1125–1148.CrossRefGoogle Scholar
Taberlet, N., Losert, W. & Richard, P. 2004 Understanding the dynamics of segregation bands of simulated granular material in a rotating drum. Europhys. Lett. 68, 522–528.CrossRefGoogle Scholar
Thornton, A., Weinhart, T., Luding, S. & Bokhove, O. 2012 Modeling of particle size segregation: calibration using the discrete particle method. Intl J. Mod. Phys. C 23 (8), 1240014.CrossRefGoogle Scholar
Tripathi, A. & Khakhar, D. V. 2011 Numerical simulation of the sedimentation of a sphere in a sheared granular fluid: a granular Stokes experiment. Phys. Rev. Lett. 107, 108001.CrossRefGoogle Scholar
Tripathi, A. & Khakhar, D. V. 2013 Density difference-driven segregation in a dense granular flow. J. Fluid Mech. 717, 643–669.CrossRefGoogle Scholar
Tsuji, Y., Tanaka, T. & Ishida, T. 1992 Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol. 71, 239–250.CrossRefGoogle Scholar
Weinhart, T., Luding, S. & Thornton, A. R. 2013 From discrete particles to continuum fields in mixtures. In Powders and Grains 2011, vol. 1542, pp. 1202–1205. American Institute of Physics.Google Scholar
Weinhart, T., Thornton, A. R., Luding, S. & Bokhove, O. 2012 From discrete particles to continuum fields near a boundary. Granul. Matt. 14 (2), 289–294.CrossRefGoogle Scholar
Wiederseiner, S., Andreini, N., Épely-Chauvin, G., Moser, G., Monnereau, M., Gray, J. M. N. T. & Ancey, C. 2011 Experimental investigation into segregating granular flows down chutes. Phys. Fluids 23, 013301.CrossRefGoogle Scholar
Williams, J. C. 1963 The segregation of powders and granular materials. Powder Technol. 14, 29–34.Google Scholar
Williams, J. C. 1976 The segregation of particulate materials. Powder Technol. 15, 245–256.CrossRefGoogle Scholar
Xu, H., Louge, M. & Reeves, A. 2003 Solutions of the kinetic theory for bounded collisional granular flows. Contin. Mech. Thermodyn. 15, 321–349.CrossRefGoogle Scholar
Yohannes, B. & Hill, K. M. 2010 Rheology of dense granular mixtures: particle-size distributions, boundary conditions, and collisional time scales. Phys. Rev. E 82, 061301.CrossRefGoogle ScholarPubMed
Yohannes, B., Hsu, L., Dietrich, W. E. & Hill, K. M. 2010 Boundary stresses due to impacts from dry granular flows. J. Geophys. Res. 117, F02027.Google Scholar