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

  • D. R. Tunuguntla (a1) (a2), O. Bokhove (a1) (a3) and A. R. Thornton (a1) (a2)

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.

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Corresponding author

Email address for correspondence: d.r.tunuguntla@utwente.nl

References

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Bokhove, O. & Thornton, A. R. 2012 Shallow granular flows. In Handbook of Environmental Fluid Dynamics (ed. Fernando, H. J.), pp. 545556. CRC Press.
Bridgwater, J. 1976 Fundamental powder mixing mechanisms. Powder Technol. 15, 215236.
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, 207219.
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Geotechnique 29 (1), 4765.
Drahun, J. A. & Bridgwater, J. 1983 The mechanisms of free surface segregation. Powder Technol. 36, 3953.
Duran, J. 2000 Sands, Powders, and Grains. Springer.
Felix, G. & Thomas, N. 2004 Evidence of two effects in the size segregation process in dry granular media. Phys. Rev. E 70, 051307.
Gray, J. M. N. T. & Chugunov, V. A. 2006 Particle-size segregation and diffusive remixing in shallow granular avalanches. J. Fluid Mech. 569, 365398.
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, 14471473.
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. 104113. Vysokogornogo Geofizich Institute.
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, 6981.
Jenkins, J. T. & Yoon, D. K. 2002 Segregation in binary mixtures under gravity. Phys. Rev. Lett. 88, 194301.
Khakhar, D. V., McCarthy, J. J. & Ottino, J. M. 1999 Mixing and segregation of granular materials in chute flows. Chaos 9, 594610.
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), 785826.
Marks, B. & Einav, I. 2011 A cellular automaton for segregation during granular avalanches. Granul. Matt. 13, 211214.
Marks, B., Rognon, P. & Einav, I. 2012 Grainsize dynamics of polydisperse granular segregation down inclined planes. J. Fluid Mech. 690, 499511.
Morland, L. W. 1992 Flow of viscous fluids through a porous deformable matrix. Surv. Geophys. 13, 209268.
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.
Pollard, B. L. & Henein, H. 1989 Kinetics of radial segregation of different sized irregular particles in rotary cylinders. Can. Metall. Q. 28, 2940.
Savage, S. B. & Hutter, K. 1991 The dynamics of avalanches of granular materials from initiation to runout. Part I: analysis. Acta Mechanica 86, 201223.
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.
Shinbrot, T., Alexander, A. & Muzzio, F. J. 1999 Spontaneous chaotic granular mixing. Nature 397, 675678.
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, 9981015.
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, 126.
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.
Tripathi, A. & Khakhar, D. V. 2013 Density difference-driven segregation in a dense granular flow. J. Fluid Mech. 717, 643669.
Ulrich, S., Schröter, M. & Swinney, H. L. 2007 Influence of friction on granular segregation. Phys. Rev. E 76, 042301.
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).
Weinhart, T., Luding, S. & Thornton, A. R. 2013 From discrete particles to continuum fields in mixtures. AIP Conf. Proc. 1542, 12021205.
Weinhart, T., Thornton, A. R., Luding, S. & Bokhove, O. 2012 Closure relations for shallow granular flows from particle simulations. Granul. Matt. 14 (4), 531552.
Whitham, G. B. 1974 Linear and Nonlinear Waves. John Wiley & Sons.
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.
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.
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A mixture theory for size and density segregation in shallow granular free-surface flows

  • D. R. Tunuguntla (a1) (a2), O. Bokhove (a1) (a3) and A. R. Thornton (a1) (a2)

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