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Grainsize dynamics of polydisperse granular segregation down inclined planes

Published online by Cambridge University Press:  14 November 2011

Benjy Marks ,
Pierre Rognon  and
Itai Einav
Benjy Marks
Affiliation:
Particles and Grains Laboratory, School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
Pierre Rognon
Affiliation:
Particles and Grains Laboratory, School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
Itai Einav*
Affiliation:
Particles and Grains Laboratory, School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
*
†Email address for correspondence: itai.einav@sydney.edu.au
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Abstract

Granular materials segregate by size when sheared, which increases the destructive power in avalanches and causes demixing in industrial flows. Here we present a concise theory to describe this phenomenon for systems that for the first time include particles of arbitrary size. The evolution of the grainsize distribution during flow is described based on mass and momentum conservation. The theory is derived in a five-dimensional space, which besides position and time, includes a grainsize coordinate. By coupling the theory with a simple constitutive law we predict the kinematics of the flow, which depends on the grainsize dynamics. We show that the underpinning mechanism controlling segregation is a stress variation with grainsize. The theory, solved by a finite difference scheme, is found to predict the dynamics of segregation consistent with results obtained from discrete element simulations of polydisperse granular flow down inclined planes. Moreover, when applied to bimixtures, the general polydisperse theory reveals the role of grainsize contrast.

JFM classification

Granular media: Granular media Nonlinear Dynamical Systems: Pattern formation Mixing: Granular mixing

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 690 , 10 January 2012 , pp. 499 - 511
Copyright
Copyright © Cambridge University Press 2011

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References

1. Bridgwater, J. 1976 Fundamental powder mixing mechanisms. Powder Technol. 15 (2), 215–236.CrossRefGoogle Scholar
2. Bridgwater, J. & Ingram, N. D. 1971 Rate of spontaneous inter-particle percolation. Chem. Engng Res. Des. 49a, 163–169.Google Scholar
3. Campbell, C. S. 1997 Self-diffusion in granular shear flows. J. Fluid Mech. 348, 85–101.CrossRefGoogle Scholar
4. da Cruz, F., Emam, S., Prochnow, M., Roux, J-N. & Chevoir, F. 2005 Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72, 021309.CrossRefGoogle ScholarPubMed
5. Dolgunin, V. N. & Ukolov, A. A. 1995 Segregation modelling of particle rapid gravity flow. Powder Technol. 83 (2), 95–104.CrossRefGoogle Scholar
6. Dolgunin, V. N., Kudy, A. N. & Ukolov, A. A. 1998 Development of the model of segregation of particles undergoing granular flow down an inclined chute. Powder Technol. 96 (3), 211–218.CrossRefGoogle Scholar
7. Einav, I. 2007 Breakage mechanics – part 1: theory. J. Mech. Phys. Solids 55 (6), 1274–1297.CrossRefGoogle Scholar
8. 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
9. 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
10. 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
11. LeVeque, R. J. 2002 Finite Volume Methods for Hyperbolic Problems. Cambridge University Press.CrossRefGoogle Scholar
12. Lorincz, J., Imre, E., Glos, M., Trang, Q. P., Rajkai, K., Fityus, S. & Telekes, G. 2005 Grading entropy variation due to soil crushing. Intl J. Geomech. 5 (4), 311–319.CrossRefGoogle Scholar
13. Marks, B. & Einav, I. 2011 A cellular automaton for segregation during granular avalanches. Granul. Matt. 13, 211–214.CrossRefGoogle Scholar
14. May, L. B. H., Shearer, M. & Daniels, K. E. 2010 Scalar conservation laws with non-constant coefficients with application to particle size segregation in granular flow. J. Nonlinear Sci. 1–19.Google Scholar
15. MiDi, G. D. R. 2004 On dense granular flows. Eur. Phys. J. E 14 (4), 341–365.CrossRefGoogle Scholar
16. Morland, L. 1992 Flow of viscous fluids through a porous deformable matrix. Surv. Geophys. 13 (3), 209–268.CrossRefGoogle Scholar
17. Ottino, J. M. & Khakhar, D. V. 2000 Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32 (1), 55–91.CrossRefGoogle Scholar
18. Quarteroni, A. & Valli, A. 1997 Numerical Approximation of Partial Differential Equations. Springer.Google Scholar
19. Ramkrishna, D. 2000 Population Balances: Theory and Applications to Particulate Systems in Engineering. Academic.Google Scholar
20. Ricard, Y. & Bercovici, D. 2009 A continuum theory of grain size evolution and damage. J. Geophys. Res. (Solid Earth) 114 (13), 01204.CrossRefGoogle Scholar
21. Rognon, P., Einav, I., Bonivin, J. & Miller, T. 2010 A scaling law for heat conductivity in sheared granular materials. EPL 89 (5), 58006.CrossRefGoogle Scholar
22. Rognon, P. G., Roux, J. N., Naaïm, M. & Chevoir, F. 2007 Dense flows of bidisperse assemblies of disks down an inclined plane. Phys. Fluids 19, 058101.CrossRefGoogle Scholar
23. 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
24. Shinbrot, T., Alexander, A. & Muzzio, F. J. 1999 Spontaneous chaotic granular mixing. Nature 397, 675–678.CrossRefGoogle Scholar
25. Utter, B. & Behringer, R. P. 2004 Self-diffusion in dense granular shear flows. Phys. Rev. E 69 (3), 031308.CrossRefGoogle ScholarPubMed
26. 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
27. Yohannes, B. & Hill, K. M. 2010 Rheology of dense granular mixtures: particle-size distributions, boundary conditions, and collisional time scales. Phys. Rev. E 82 (6), 061301.CrossRefGoogle ScholarPubMed