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A mixture theory for size and density segregation in shallow granular free-surface flows

Published online by Cambridge University Press:  14 May 2014

D. R. Tunuguntla ,
O. Bokhove  and
A. R. Thornton
D. R. Tunuguntla*
Affiliation:
Mathematics of Computational Science group, University of Twente, The Netherlands Multi-Scale Mechanics group, MESA+, University of Twente, The Netherlands
O. Bokhove
Affiliation:
Mathematics of Computational Science group, University of Twente, The Netherlands School of Mathematics, University of Leeds, UK
A. R. Thornton
Affiliation:
Mathematics of Computational Science group, University of Twente, The Netherlands Multi-Scale Mechanics group, MESA+, University of Twente, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

In the past ten years much work has been undertaken on developing mixture theory continuum models to describe kinetic sieving-driven size segregation. We propose an extension to these models that allows their application to bidisperse flows over inclined channels, with particles varying in density and size. Our model incorporates both a recently proposed explicit formula for how the total pressure is distributed among different species of particles, which is one of the key elements of mixture theory-based kinetic sieving models, and a shear rate-dependent drag. The resulting model is used to predict the range of particle sizes and densities for which the mixture segregates. The prediction of no segregation in the model is benchmarked by using discrete particle simulations, and good agreement is found when a single fitting parameter is used which determines whether the pressure scales with the diameter, surface area or volume of the particle.

JFM classification

Granular media: Granular media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 749 , 25 June 2014 , pp. 99 - 112
Copyright
© 2014 Cambridge University Press 

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References

Bokhove, O. & Thornton, A. R. 2012 Shallow granular flows. In Handbook of Environmental Fluid Dynamics (ed. Fernando, H. J.), pp. 545–556. CRC Press.Google Scholar
Bridgwater, J. 1976 Fundamental powder mixing mechanisms. Powder Technol. 15, 215–236.CrossRefGoogle Scholar
Brito, R. & Soto, R. 2009 Competition of Brazil nut effect, buoyancy, and inelasticity induced segregation in a granular mixture. Eur. Phys. J. Spec. Top. 179, 207–219.Google Scholar
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Geotechnique 29 (1), 47–65.Google Scholar
Drahun, J. A. & Bridgwater, J. 1983 The mechanisms of free surface segregation. Powder Technol. 36, 39–53.Google Scholar
Duran, J. 2000 Sands, Powders, and Grains. Springer.CrossRefGoogle Scholar
Felix, G. & Thomas, N. 2004 Evidence of two effects in the size segregation process in dry granular media. Phys. Rev. E 70, 051307.Google 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.Google 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, 1447–1473.Google Scholar
Grigorian, S. S., Eglit, M. E. & Iakimov, I. L. 1967 New statement and solution of the problem of the motion of snow avalanche. In Snow, Avalanches & Glaciers, Tr. Vysokogornogo Geofizich Inst., vol. 12, pp. 104–113. Vysokogornogo Geofizich Institute.Google Scholar
Jain, N., Ottino, J. M. & Lueptow, R. M. 2005 Regimes of segregation and mixing in combined size and density granular systems: an experimental study. Granul. Matt. 7, 69–81.CrossRefGoogle Scholar
Jenkins, J. T. & Yoon, D. K. 2002 Segregation in binary mixtures under gravity. Phys. Rev. Lett. 88, 194301.Google Scholar
Khakhar, D. V., McCarthy, J. J. & Ottino, J. M. 1999 Mixing and segregation of granular materials in chute flows. Chaos 9, 594–610.Google Scholar
Luding, S. 2008 Introduction to discrete element methods: basic of contact force models and how to perform the micro-macro transition to continuum theory. Eur. J. Environ. Civ. Engng 12 (7–8), 785–826.Google Scholar
Marks, B. & Einav, I. 2011 A cellular automaton for segregation during granular avalanches. Granul. Matt. 13, 211–214.Google Scholar
Marks, B., Rognon, P. & Einav, I. 2012 Grainsize dynamics of polydisperse granular segregation down inclined planes. J. Fluid Mech. 690, 499–511.Google Scholar
Morland, L. W. 1992 Flow of viscous fluids through a porous deformable matrix. Surv. Geophys. 13, 209–268.CrossRefGoogle Scholar
Pesch, L., Bell, A., Sollie, H., Ambati, V. R., Bokhove, O. & Van Der Vegt, J. J. W. 2007 hpGEM – a software framework for discontinuous Galerkin finite element methods. ACM Trans. Math. Softw. 33, 23.Google Scholar
Pollard, B. L. & Henein, H. 1989 Kinetics of radial segregation of different sized irregular particles in rotary cylinders. Can. Metall. Q. 28, 29–40.Google Scholar
Savage, S. B. & Hutter, K. 1991 The dynamics of avalanches of granular materials from initiation to runout. Part I: analysis. Acta Mechanica 86, 201–223.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, 311–335.Google Scholar
Shinbrot, T., Alexander, A. & Muzzio, F. J. 1999 Spontaneous chaotic granular mixing. Nature 397, 675–678.Google Scholar
Tassi, P. A., Bokhove, O. & Vionnet, C. A. 2007 Space discontinuous Galerkin method for shallow water flows – kinetic and HLLC flux, and potential vorticity generation. Adv. Water Resour. 30, 998–1015.Google Scholar
Thornton, A. R., Gray, J. M. N. T. & Hogg, A. J. 2006 A three-phase mixture theory for particle size segregation in shallow granular free-surface flows. J. Fluid Mech. 550, 1–26.Google Scholar
Thornton, A. R., Weinhart, T., Luding, S. & Bokhove, O. 2012 Modeling of particle size segregation: calibration using the discrete particle method. Intl J. Mod. Phys. C 23, 1240014.Google Scholar
Tripathi, A. & Khakhar, D. V. 2013 Density difference-driven segregation in a dense granular flow. J. Fluid Mech. 717, 643–669.Google Scholar
Ulrich, S., Schröter, M. & Swinney, H. L. 2007 Influence of friction on granular segregation. Phys. Rev. E 76, 042301.CrossRefGoogle ScholarPubMed
Voortwis Te, A.2013 Closure laws for granular, shallow-layer, bi-dispersed flows down an inclined chute. Master thesis, Multi Scale Mechanics Group, Mechanical Engineering Faculty of Engineering Technology, Universiteit Twente (§ 3.2.4).Google Scholar
Weinhart, T., Luding, S. & Thornton, A. R. 2013 From discrete particles to continuum fields in mixtures. AIP Conf. Proc. 1542, 1202–1205.CrossRefGoogle Scholar
Weinhart, T., Thornton, A. R., Luding, S. & Bokhove, O. 2012 Closure relations for shallow granular flows from particle simulations. Granul. Matt. 14 (4), 531–552.CrossRefGoogle Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. John Wiley & Sons.Google 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
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, 543–580.Google Scholar