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Size segregation of intruders in perpetual granular avalanches

Published online by Cambridge University Press:  21 July 2017

Benjy Marks*
Affiliation:
Particles and Grains Laboratory, School of Civil Engineering, The University of Sydney, 2006, Sydney, Australia Condensed Matter Physics, Department of Physics, University of Oslo, PO Box 1048, Blindern, N-0316, Oslo, Norway
Jon Alm Eriksen
Affiliation:
Condensed Matter Physics, Department of Physics, University of Oslo, PO Box 1048, Blindern, N-0316, Oslo, Norway
Guillaume Dumazer
Affiliation:
PoreLab, Department of Physics, University of Oslo, PO Box 1048, Blindern, N-0316, Oslo, Norway
Bjørnar Sandnes
Affiliation:
College of Engineering, Swansea University, Swansea, SA1 8EN, UK
Knut Jørgen Måløy
Affiliation:
PoreLab, Department of Physics, University of Oslo, PO Box 1048, Blindern, N-0316, Oslo, Norway
*
Email address for correspondence: benjy.marks@sydney.edu.au

Abstract

Granular flows such as landslides, debris flows and avalanches are systems of particles with a large range of particle sizes that typically segregate while flowing. The physical mechanisms responsible for this process, however, are still poorly understood, and there is no predictive framework for ascertaining the segregation behaviour of a given system of particles. Here, we provide experimental evidence of individual large intruder particles being attracted to a fixed point in a dry two-dimensional flow of particles of otherwise uniform size. A continuum theory is proposed which captures this effect using only a single fitting parameter that describes the rate of segregation, given knowledge of the bulk flow field. Predictions of the continuum theory are compared with the experimental findings, both for the typical location and velocity field of a range of intruder sizes. For large intruder particle sizes, the continuum model successfully predicts that a fixed point attractor will form, where intruders are drawn to a single location.

Type
Papers
Copyright
© 2017 Cambridge University Press 

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References

Baker, J. L., Johnson, C. G. & Gray, J. M. N. T. 2016 Segregation-induced finger formation in granular free-surface flows. J. Fluid Mech. 809, 168212.CrossRefGoogle Scholar
Bartelt, P. & McArdell, B. W. 2009 Granulometric investigations of snow avalanches. J. Glaciol. 55 (193), 829833.CrossRefGoogle Scholar
Bedford, A. & Drumheller, D. S. 1983 Theories of immiscible and structured mixtures. Intl J. Engng Sci. 21 (8), 863960.CrossRefGoogle Scholar
Branney, M. J. & Kokelaar, P. 1992 A reappraisal of ignimbrite emplacement: progressive aggradation and changes from particulate to non-particulate flow during emplacement of high-grade ignimbrite. Bull. Volcanol. 54 (6), 504520.CrossRefGoogle Scholar
Brown, R. L. 1939 The fundamental principles of segregation. Inst. Fuel 13, 1519.Google Scholar
Dolgunin, V. N. & Ukolov, A. A. 1995 Segregation modeling of particle rapid gravity flow. Powder Technol. 83 (2), 95103.CrossRefGoogle Scholar
Fan, Y. & Hill, K. M. 2011 Theory for shear-induced segregation of dense granular mixtures. New J. Phys. 13 (9), 095009.CrossRefGoogle Scholar
Gajjar, P., van der Vaart, K., Thornton, A. R., Johnson, C. G., Ancey, C. & Gray, J. M. N. T. 2016 Asymmetric breaking size-segregation waves in dense granular free-surface flows. J. Fluid Mech. 794, 460505.CrossRefGoogle Scholar
Gray, J. M. N. T. & Ancey, C. 2009 Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts. J. Fluid Mech. 629, 387423.CrossRefGoogle Scholar
Gray, J. M. N. T. & Ancey, C. 2011 Multi-component particle-size segregation in shallow granular avalanches. J. Fluid Mech. 678, 535588.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, 105137.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 (2057), 14471473.CrossRefGoogle Scholar
Guillard, F., Forterre, Y. & Pouliquen, O. 2016 Scaling laws for segregation forces in dense sheared granular flows. J. Fluid Mech. 807, R1R11.CrossRefGoogle Scholar
Hill, K. M., Gilchrist, J. F., Ottino, J. M., Khakhar, D. V. & McCarthy, J. J. 1999a Mixing of granular materials: a test-bed dynamical system for pattern formation. Intl J. Bifurcation Chaos 9 (08), 14671484.CrossRefGoogle Scholar
Hill, K. M., Khakhar, D. V., Gilchrist, J. F., McCarthy, J. J. & Ottino, J. M. 1999b Segregation-driven organization in chaotic granular flows. Proc. Natl Acad. Sci. USA 96 (21), 1170111706.CrossRefGoogle ScholarPubMed
Hill, K. M. & Tan, D. S. 2014 Segregation in dense sheared flows: gravity, temperature gradients, and stress partitioning. J. Fluid Mech. 756, 5488.CrossRefGoogle Scholar
Hill, K. M. & Zhang, J. 2008 Kinematics of densely flowing granular mixtures. Phys. Rev. E 77, 061303.Google ScholarPubMed
Hong, D. C., Quinn, P. V. & Luding, S. 2001 Reverse Brazil nut problem: competition between percolation and condensation. Phys. Rev. Lett. 86, 34233426.CrossRefGoogle ScholarPubMed
Huerta, D. A. & Ruiz-Suárez, J. C. 2004 Vibration-induced granular segregation: a phenomenon driven by three mechanisms. Phys. Rev. Lett. 92 (11), 114301.CrossRefGoogle Scholar
Iverson, R. M. 2003 The debris-flow rheology myth. Debris-flow Hazards Mitigation: Mechanics, Prediction, and Assessment 1, 303314.Google 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 (1), 2734.CrossRefGoogle Scholar
Jenkins, J. T. & Mancini, F. 1989 Kinetic theory for binary mixtures of smooth, nearly elastic spheres. Phys. Fluids A 1 (12), 20502057.CrossRefGoogle Scholar
Jenkins, J. T. & Yoon, D. K. 2002 Segregation in binary mixtures under gravity. Phys. Rev. Lett. 88 (19), 194301.CrossRefGoogle ScholarPubMed
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. 117, F01032.CrossRefGoogle Scholar
Khakhar, D. V., McCarthy, J. J. & Ottino, J. M. 1997 Radial segregation of granular mixtures in rotating cylinders. Phys. Fluids 9 (12), 36003614.CrossRefGoogle Scholar
Knight, J. B., Jaeger, H. M. & Nagel, S. R. 1993 Vibration-induced size separation in granular media: the convection connection. Phys. Rev. Lett. 70, 37283731.CrossRefGoogle ScholarPubMed
Marks, B. & Einav, I. 2015 A mixture of crushing and segregation: the complexity of grainsize in natural granular flows. Geophys. Res. Lett. 42 (2), 274281.CrossRefGoogle Scholar
Marks, B., Rognon, P. & Einav, I. 2012 Grainsize dynamics of polydisperse granular segregation down inclined planes. J. Fluid Mech. 690, 499511.CrossRefGoogle Scholar
Möbius, M. E., Lauderdale, B. E., Nagel, S. R. & Jaeger, H. M. 2001 Brazil-nut effect: size separation of granular particles. Nature 414 (6861), 270270.CrossRefGoogle Scholar
Morland, L. W. 1992 Flow of viscous fluids through a porous deformable matrix. Surv. Geophys. 13 (3), 209268.CrossRefGoogle Scholar
Perng, A. T. H., Capart, H. & Chou, H. T. 2006 Granular configurations, motions, and correlations in slow uniform flows driven by an inclined conveyor belt. Granul. Matt. 8 (1), 517.CrossRefGoogle Scholar
Ramkrishna, D. 2000 Population Balances: Theory and Applications to Particulate Systems in Engineering. Academic.Google 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, 311335.CrossRefGoogle Scholar
Shadden, S. C., Lekien, F. & Marsden, J. E. 2005 Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212 (3), 271304.CrossRefGoogle Scholar
Staron, L. & Phillips, J. C. 2015 Stress partition and microstructure in size-segregating granular flows. Phys. Rev. E 92 (2), 022210.Google ScholarPubMed
Thielicke, W. & Stamhuis, E. J. 2014 Pivlab–towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB. J. Open Res. Softw. 2 (1), e30.CrossRefGoogle Scholar
Thomas, N. 2000 Reverse and intermediate segregation of large beads in dry granular media. Phys. Rev. E 62 (1), 961974.Google ScholarPubMed
Thornton, A. R. & Gray, J. M. N. T. 2008 Breaking size segregation waves and particle recirculation in granular avalanches. J. Fluid Mech. 596, 261284.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, 99112.CrossRefGoogle Scholar
Tunuguntla, D. R., Weinhart, T. & Thornton, A. R. 2016 Comparing and contrasting size-based particle segregation models. Comput. Part. Mech. 119.Google Scholar
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 Scholar
Voivret, C. 2013 Cushioning effect in highly polydisperse granular media. In Powders and Grains 2013: Proceedings of the 7th International Conference on Micromechanics of Granular Media, vol. 1542, pp. 405408. AIP Publishing.Google Scholar
Weinhart, T., Luding, S., Thornton, A. R., Yu, A., Dong, K., Yang, R. & Luding, S. 2013 From discrete particles to continuum fields in mixtures. In AIP Conference Proceedings, vol. 1542, pp. 12021205. AIP Publishing.Google Scholar
Williams, J.-C. 1976 The segregation of particulate materials. A review. Powder Technol. 15 (2), 245251.CrossRefGoogle Scholar
Woodhouse, M. J., Thornton, A. R., Johnson, C. G., Kokelaar, B. P. & Gray, J. M. N. T. 2012 Segregation-induced fingering instabilities in granular free-surface flows. J. Fluid Mech. 709, 543580.CrossRefGoogle Scholar
Zhang, L. M., Xu, Y., Huang, R. Q. & Chang, D. S. 2011 Particle flow and segregation in a giant landslide event triggered by the 2008 Wenchuan earthquake, Sichuan, China. Nat. Hazards Earth Syst. Sci. 11 (4), 11531162.CrossRefGoogle Scholar

Marks et al. supplementary movie

Video of two intruder particles flowing in a perpetual avalanche. Note that the large red particle tends to stay towards the right hand side, while the small blue particle explores the whole system.

Download Marks et al. supplementary movie(Video)
Video 523 MB
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