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Modelling segregation of bidisperse granular mixtures varying simultaneously in size and density for free surface flows

Published online by Cambridge University Press:  11 May 2021

Yifei Duan Open the ORCID record for Yifei Duan [Opens in a new window] ,
Paul B. Umbanhowar Open the ORCID record for Paul B. Umbanhowar [Opens in a new window] ,
Julio M. Ottino Open the ORCID record for Julio M. Ottino [Opens in a new window]  and
Richard M. Lueptow Open the ORCID record for Richard M. Lueptow [Opens in a new window]
Yifei Duan
Affiliation:
Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL60208, USA
Paul B. Umbanhowar
Affiliation:
Department of Mechanical Engineering, Northwestern University, Evanston, IL60208, USA
Julio M. Ottino
Affiliation:
Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL60208, USA Department of Mechanical Engineering, Northwestern University, Evanston, IL60208, USA Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, IL60208, USA
Richard M. Lueptow*
Affiliation:
Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL60208, USA Department of Mechanical Engineering, Northwestern University, Evanston, IL60208, USA Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, IL60208, USA
*
†Email address for correspondence: [email protected]
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Abstract

Flowing granular materials segregate due to differences in particle size (driven by percolation) and density (driven by buoyancy). Modelling the segregation of mixtures of large/heavy particles and small/light particles is challenging due to the opposing effects of the two segregation mechanisms. Using discrete element method (DEM) simulations of combined size and density segregation we show that the segregation velocity is well described by a model that depends linearly on the local shear rate and quadratically on the species concentration for free surface flows. Concentration profiles predicted by incorporating this segregation velocity model into a continuum advection–diffusion–segregation transport model match DEM simulation results well for a wide range of particle size and density ratios. Most surprisingly, the DEM simulations and the segregation velocity model both show that the segregation direction for a range of size and density ratios depends on the local species concentration. This leads to a methodology to determine the combination of particle size ratio, density ratio and particle concentration for which a bidisperse mixture will not segregate.

JFM classification

Granular media: Granular media Mixing: Granular mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 918 , 10 July 2021 , A20
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Alonso, M., Satoh, M. & Miyanami, K. 1991 Optimum combination of size ratio, density ratio and concentration to minimize free surface segregation. Powder Technol. 68 (2), 145–152.CrossRefGoogle Scholar
Arnarson, B. & Jenkins, J.T. 2004 Binary mixtures of inelastic spheres: simplified constitutive theory. Phys. Fluids 16 (12), 4543–4550.CrossRefGoogle Scholar
Atkin, R.J. & Craine, R.E. 1976 Continuum theories of mixtures: basic theory and historical development. Q. J. Mech. Appl. Maths 29 (2), 209–244.CrossRefGoogle Scholar
Barker, T., Rauter, M., Maguire, E.S.F., Johnson, C.G. & Gray, J.M.N.T. 2021 Coupling rheology and segregation in granular flows. J. Fluid Mech. 909, A22.CrossRefGoogle Scholar
Breu, A.P.J., Ensner, H.M., Kruelle, C.A. & Rehberg, I. 2003 Reversing the brazil-nut effect: competition between percolation and condensation. Phys. Rev. Lett. 90 (1), 014302.CrossRefGoogle ScholarPubMed
Bridgwater, J. 1980 Self-diffusion coefficients in deforming powders. Powder Technol. 25 (1), 129–131.CrossRefGoogle Scholar
Bridgwater, J., Foo, W.S. & Stephens, D.J. 1985 Particle mixing and segregation in failure zones–theory and experiment. Powder Technol. 41 (2), 147–158.CrossRefGoogle Scholar
Cai, R., Xiao, H., Zheng, J. & Zhao, Y. 2019 Diffusion of size bidisperse spheres in dense granular shear flow. Phys. Rev. E 99 (3), 032902.CrossRefGoogle ScholarPubMed
Ciamarra, M.P., De Vizia, M.D., Fierro, A., Tarzia, M., Coniglio, A. & Nicodemi, M. 2006 Granular species segregation under vertical tapping: effects of size, density, friction, and shaking amplitude. Phys. Rev. Lett. 96 (5), 058001.CrossRefGoogle ScholarPubMed
Combarros, M, Feise, H.J., Zetzener, H. & Kwade, A. 2014 Segregation of particulate solids: experiments and DEM simulations. Particuology 12, 25–32.CrossRefGoogle Scholar
Cundall, P.A. & Strack, O.D.L. 1979 A discrete numerical model for granular assemblies. Géotechnique 29 (1), 47–65.CrossRefGoogle Scholar
Deng, Z., Fan, Y., Theuerkauf, J., Jacob, K.V., Umbanhowar, P.B. & Lueptow, R.M. 2020 Modeling segregation of polydisperse granular materials in hopper discharge. Powder Technol. 374, 389–398.CrossRefGoogle Scholar
Deng, Z., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2018 Continuum modelling of segregating tridisperse granular chute flow. Proc. R. Soc. A 474 (2211), 20170384.CrossRefGoogle ScholarPubMed
Deng, Z., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2019 Modeling segregation of polydisperse granular materials in developing and transient free-surface flows. AIChE J. 65 (3), 882–893.CrossRefGoogle Scholar
Dolgunin, V.N. & Ukolov, A.A. 1995 Segregation modeling of particle rapid gravity flow. Powder Technol. 83 (2), 95–103.CrossRefGoogle Scholar
Drahun, J.A. & Bridgwater, J. 1983 The mechanisms of free surface segregation. Powder Technol. 36 (1), 39–53.CrossRefGoogle Scholar
Duan, Y. & Feng, Z.G. 2017 Incorporation of velocity-dependent restitution coefficient and particle surface friction into kinetic theory for modeling granular flow cooling. Phys. Rev. E 96 (6), 062907.CrossRefGoogle ScholarPubMed
Duan, Y. & Feng, Z.G. 2019 A new kinetic theory model of granular flows that incorporates particle stiffness. Phys. Fluids 31 (1), 013301.CrossRefGoogle Scholar
Duan, Y., Umbanhowar, P.B. & Lueptow, R.M. 2021 Designing non-segregating granular mixtures. arXiv:2103.00725. Also to appear in Powders & Grains, 2021.Google Scholar
Duan, Y., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2020 Segregation models for density-bidisperse granular flows. Phys. Rev. Fluids 5, 044301.CrossRefGoogle Scholar
Fan, Y., Boukerkour, Y., Blanc, T., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2012 Stratification, segregation, and mixing of granular materials in quasi-two-dimensional bounded heaps. Phys. Rev. E 86 (5), 051305.CrossRefGoogle ScholarPubMed
Fan, Y. & Hill, K.M. 2011 Theory for shear-induced segregation of dense granular mixtures. New J. Phys. 13 (9), 095009.CrossRefGoogle Scholar
Fan, Y., Jacob, K.V., Freireich, B. & Lueptow, R.M. 2017 Segregation of granular materials in bounded heap flow: a review. Powder Technol. 312, 67–88.CrossRefGoogle Scholar
Fan, Y., Schlick, C.P., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2013 Kinematics of monodisperse and bidisperse granular flows in quasi-two-dimensional bounded heaps. Proc. R. Soc. A 469 (2157), 20130235.CrossRefGoogle Scholar
Fan, Y., Schlick, C.P., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2014 Modelling size segregation of granular materials: the roles of segregation, advection and diffusion. J. Fluid Mech. 741, 252–279.CrossRefGoogle Scholar
Fan, Y., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2015 Shear-rate-independent diffusion in granular flows. Phys. Rev. Lett. 115 (8), 088001.CrossRefGoogle ScholarPubMed
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
Fry, A.M., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2019 Diffusion, mixing, and segregation in confined granular flows. AIChE J. 65 (3), 875–881.CrossRefGoogle Scholar
Gajjar, P. & Gray, J.M.N.T. 2014 Asymmetric flux models for particle-size segregation in granular avalanches. J. Fluid Mech. 757, 297–329.CrossRefGoogle Scholar
Gao, S., Ottino, J.M., Umbanhowar, P.B. & Lueptow, R.M. 2021 Modeling granular segregation for overlapping species distributions. Chem. Engng Sci. 231, 116259.CrossRefGoogle Scholar
Garcia, M.C., Feise, H.J., Strege, S. & Kwade, A. 2016 Segregation in heaps and silos: comparison between experiment, simulation and continuum model. Powder Technol. 293, 26–36.CrossRefGoogle Scholar
GDR-MiDi 2004 On dense granular flows. Eur. Phys. J. E 14 (4), 341–365.CrossRefGoogle Scholar
Golick, L.A. & Daniels, K.E. 2009 Mixing and segregation rates in sheared granular materials. Phys. Rev. E 80, 042301.CrossRefGoogle ScholarPubMed
Gray, J.M.N.T. 2018 Particle segregation in dense granular flows. Annu. Rev. Fluid Mech. 50, 407–433.CrossRefGoogle Scholar
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. & Ancey, C. 2015 Particle-size and-density segregation in granular free-surface flows. J. Fluid Mech. 779, 622–668.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. & Kokelaar, B.P. 2010 Large particle segregation, transport and accumulation in granular free-surface flows. J. Fluid Mech. 652, 105–137.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. A 461 (2057), 1447–1473.CrossRefGoogle Scholar
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. 96 (21), 11701–11706.CrossRefGoogle ScholarPubMed
Hong, D.C., Quinn, P.V. & Luding, S. 2001 Reverse brazil nut problem: competition between percolation and condensation. Phys. Rev. Lett. 86 (15), 3423.CrossRefGoogle ScholarPubMed
Hsiau, S.S. & Shieh, Y.M. 1999 Fluctuations and self-diffusion of sheared granular material flows. J. Rheol. 43 (5), 1049–1066.CrossRefGoogle Scholar
Isner, A.B., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2020 a Axisymmetric granular flow on a bounded conical heap: kinematics and size segregation. Chem. Engng Sci. 217, 115505.CrossRefGoogle Scholar
Isner, A.B., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2020 b Granular flow in a wedge-shaped heap: velocity field, kinematic scalings, and segregation. AIChE J. 66 (5), e16912.CrossRefGoogle Scholar
Jain, N., Ottino, J.M. & Lueptow, R.M. 2005 a Combined size and density segregation and mixing in noncircular tumblers. Phys. Rev. E 71 (5), 051301.CrossRefGoogle ScholarPubMed
Jain, N., Ottino, J.M. & Lueptow, R.M. 2005 b Regimes of segregation and mixing in combined size and density granular systems: an experimental study. Granul. Matt. 7 (2–3), 69–81.CrossRefGoogle Scholar
Jenkins, J.T. & Yoon, D.K. 2002 Segregation in binary mixtures under gravity. Phys. Rev. Lett. 88 (19), 194301.CrossRefGoogle ScholarPubMed
Jing, L., Kwok, C.Y. & Leung, Y.F. 2017 Micromechanical origin of particle size segregation. Phys. Rev. Lett. 118 (11), 118001.CrossRefGoogle ScholarPubMed
Jing, L., Ottino, J.M., Lueptow, R.M. & Umbanhowar, P.B. 2020 Rising and sinking intruders in dense granular flows. Phys. Rev. Res. 2, 022069.CrossRefGoogle Scholar
Johnson, C.G., Kokelaar, B.P., Iverson, R.M., Logan, M., LaHusen, R.G. & Gray, J.M.N.T. 2012 Grain-size segregation and levee formation in geophysical mass flows. J. Geophys. Res. Earth Surf. 117, F01032.CrossRefGoogle Scholar
Jones, R.P., Isner, A.B., Xiao, H., Ottino, J.M., Umbanhowar, P.B. & Lueptow, R.M. 2018 Asymmetric concentration dependence of segregation fluxes in granular flows. Phys. Rev. Fluids 3, 094304.CrossRefGoogle Scholar
Jones, R.P., Ottino, J.M., Umbanhowar, P.B. & Lueptow, R.M. 2020 Remarkable simplicity in the prediction of non-spherical particle segregation. Phys. Rev. Res. 2 (4), 042021.CrossRefGoogle Scholar
Khakhar, D.V., McCarthy, J.J. & Ottino, J.M. 1997 Radial segregation of granular mixtures in rotating cylinders. Phys. Fluids 9 (12), 3600–3614.CrossRefGoogle Scholar
Khakhar, D.V., McCarthy, J.J. & Ottino, J.M. 1999 Mixing and segregation of granular materials in chute flows. Chaos 9 (3), 594–610.CrossRefGoogle ScholarPubMed
Larcher, M. & Jenkins, J.T. 2013 Segregation and mixture profiles in dense, inclined flows of two types of spheres. Phys. Fluids 25 (11), 113301.CrossRefGoogle Scholar
Larcher, M. & Jenkins, J.T. 2015 The evolution of segregation in dense inclined flows of binary mixtures of spheres. J. Fluid Mech. 782, 405–429.CrossRefGoogle Scholar
Liu, P.Y., Yang, R.Y. & Yu, A.B. 2013 The effect of liquids on radial segregation of granular mixtures in rotating drums. Granul. Matt. 15 (4), 427–436.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
Ottino, J.M. & Khakhar, D.V. 2000 Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32 (1), 55–91.CrossRefGoogle Scholar
Ottino, J.M. & Lueptow, R.M. 2008 On mixing and demixing. Science 319 (5865), 912–913.CrossRefGoogle ScholarPubMed
Pereira, G.G., Sinnott, M.D., Cleary, P.W., Liffman, K., Metcalfe, G. & Šutalo, I.D. 2011 Insights from simulations into mechanisms for density segregation of granular mixtures in rotating cylinders. Granul. Matt. 13 (1), 53–74.CrossRefGoogle Scholar
Pouliquen, O. 1999 Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11 (3), 542–548.CrossRefGoogle Scholar
Ristow, G.H. 1994 Particle mass segregation in a two-dimensional rotating drum. Europhys. Lett. 28 (2), 97.CrossRefGoogle Scholar
Savage, S.B. & Dai, R. 1993 Studies of granular shear flows wall slip velocities, ‘layering’ and self-diffusion. Mech. Mater. 16 (1-2), 225–238.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
Schlick, C.P., Fan, Y., Isner, A.B., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2015 a Modeling segregation of bidisperse granular materials using physical control parameters in the quasi-2d bounded heap. AIChE J. 61 (5), 1524–1534.CrossRefGoogle Scholar
Schlick, C.P., Fan, Y., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2015 b Granular segregation in circular tumblers: theoretical model and scaling laws. J. Fluid Mech. 765, 632–652.CrossRefGoogle Scholar
Schlick, C.P., Isner, A.B., Freireich, B.J., Fan, Y., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2016 A continuum approach for predicting segregation in flowing polydisperse granular materials. J. Fluid Mech. 797, 95–109.CrossRefGoogle Scholar
Shäfer, J., Dippel, S. & Wolf, D.E. 1996 Force schemes in simulations of granular materials. J. Phys. I 6 (1), 5–20.Google Scholar
Silbert, L.E., Ertaş, D., Grest, G.S., Halsey, T.C., Levine, D. & Plimpton, S.J. 2001 Granular flow down an inclined plane: bagnold scaling and rheology. Phys. Rev. E 64 (5), 051302.CrossRefGoogle ScholarPubMed
Tripathi, A. & Khakhar, D.V. 2013 Density difference-driven segregation in a dense granular flow. J. Fluid Mech. 717, 643–669.CrossRefGoogle Scholar
Tunuguntla, D.R., Bokhove, O. & Thornton, A.R. 2014 A mixture theory for size and density segregation in shallow granular free-surface flows. J. Fluid Mech. 749, 99–112.CrossRefGoogle Scholar
Tunuguntla, D.R., Weinhart, T. & Thornton, A.R. 2017 Comparing and contrasting size-based particle segregation models. Comput. Part. Mech. 4 (4), 387–405.CrossRefGoogle Scholar
Umbanhowar, P.B., Lueptow, R.M. & Ottino, J.M. 2019 Modeling segregation in granular flows. Annu. Rev. Chem. Biomol. Engng 10, 129–153.CrossRefGoogle ScholarPubMed
Utter, B. & Behringer, R.P. 2004 Self-diffusion in dense granular shear flows. Phys. Rev. E 69 (3), 031308.CrossRefGoogle ScholarPubMed
van der Vaart, K., Gajjar, P., Epely-Chauvin, G., Andreini, N., Gray, J.M.N.T. & Ancey, C. 2015 Underlying asymmetry within particle size segregation. Phys. Rev. Lett. 114 (23), 238001.CrossRefGoogle ScholarPubMed
Wandersman, E., Dijksman, J.A. & Van Hecke, M. 2012 Particle diffusion in slow granular bulk flows. Europhys. Lett. 100 (3), 38006.CrossRefGoogle Scholar
Weinhart, T., Luding, S. & Thornton, A.R. 2013 From discrete particles to continuum fields in mixtures. AIP Conf. Proc. 1542 (1), 1202–1205.CrossRefGoogle Scholar
Weinhart, T., et al. 2020 Fast, flexible particle simulations–an introduction to MercuryDPM. Comput. Phys. Commun. 249, 107129.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 (1), 013301.CrossRefGoogle Scholar
Williams, J.C. 1968 The mixing of dry powders. Powder Technol. 2 (1), 13–20.CrossRefGoogle Scholar
Xiao, H., Fan, Y., Jacob, K.V., Umbanhowar, P.B., Kodam, M., Koch, J.F. & Lueptow, R.M. 2019 Continuum modeling of granular segregation during hopper discharge. Chem. Engng Sci. 193, 188–204.CrossRefGoogle Scholar
Xiao, H., Umbanhowar, P.B., Ottino, J.M. & Lueptow, R.M. 2016 Modelling density segregation in flowing bidisperse granular materials. Proc. R. Soc. A 472 (2191), 20150856.CrossRefGoogle Scholar
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