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A continuum approach for predicting segregation in flowing polydisperse granular materials

Published online by Cambridge University Press:  16 May 2016

Conor P. Schlick ,
Austin B. Isner ,
Ben J. Freireich ,
Yi Fan ,
Paul B. Umbanhowar ,
Julio M. Ottino  and
Richard M. Lueptow
Conor P. Schlick
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
Austin B. Isner
Affiliation:
Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA
Ben J. Freireich
Affiliation:
The Dow Chemical Company, Midland, MI 48667, USA
Yi Fan
Affiliation:
The Dow Chemical Company, Midland, MI 48667, USA
Paul B. Umbanhowar
Affiliation:
Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
Julio M. Ottino
Affiliation:
Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA The Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, IL 60208, USA
Richard M. Lueptow*
Affiliation:
Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA The Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, IL 60208, USA
*
†Email address for correspondence: r-lueptow@northwestern.edu
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Abstract

Segregation of polydisperse granular materials occurs in many natural and industrial settings, but general theoretical modelling approaches with predictive power have been lacking. Here we describe a model capable of accurately predicting segregation for both discrete and continuous particle size distributions based on a generalized expression for the percolation velocity. The predictions of the model depend on the kinematics of the flow and other physical parameters such as the diffusion coefficient and the percolation length scale, quantities that can be determined directly from experiment, simulation or theory and that are not arbitrarily adjustable. The model is applied to heap and chute flow, and the resulting predictions are consistent with experimentally validated discrete element method (DEM) simulations. Several different continuous particle size distributions are considered to demonstrate the broad applicability of the approach.

JFM classification

Complex Fluids: Complex Fluids Granular media: Granular media Mixing: Mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 797 , 25 June 2016 , pp. 95 - 109
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Copyright
© 2016 Cambridge University Press 

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References

Ames, W. F. 1977 Numerical Methods for Partial Differential Equations, 2nd edn. Academic.Google Scholar
Ancey, C. 2001 Dry granular flows down an inclined channel: experimental investigations on the frictional-collisional regime. Phys. Rev. E 65, 011304.CrossRefGoogle ScholarPubMed
Bartelt, P. & McArdell, B. 2009 Granulometric investigation of snow avalanches. J. Glaciol. 55, 829–833.CrossRefGoogle Scholar
Bertin, D., Cotabarren, I., Bucula, V. & Pina, J. 2011 Analysis of the product granulometry, temperature and mass flow of an industrial multichamber fluidized bed urea granulator. Powder Technol. 206, 122–131.CrossRefGoogle Scholar
Bhattacharya, T. & McCarthy, J. 2014 Chute flow as a means of segregation characterization. Powder Technol. 256, 126–139.CrossRefGoogle Scholar
Conway, S., Lekhal, A., Khinast, J. & Glasser, B. 2005 Granular flow and segregation in a four-bladed mixer. Chem. Engng Sci. 60, 7091–7107.CrossRefGoogle Scholar
Dolgunin, V., Kudy, A. & Ukolov, A. 1998 Development of the model of segregation of particles undergoing granular flow down an inclined chute. Powder Technol. 96, 211–218.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, 051305.Google Scholar
Fan, Y. & Hill, K. 2011 Theory for shear-induced segregation of dense granular mixtures. New J. Phys. 13, 095009.CrossRefGoogle Scholar
Fan, Y., Schlick, C. P., Umbanhowar, P. B., Ottino, J. M. & Lueptow, R. M. 2014 Modeling segregation of bidisperse 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. 2013 Kinematics of monodisperse and bidisperse granular flows in quasi-two-dimensional bounded heaps. Proc. R. Soc. Lond. A 469, 20130235.Google Scholar
Fan, Y., Umbanhowar, P. B., Ottino, J. M. & Lueptow, R. M. 2015 Shear-rate-independent diffusion in granular flows. Phys. Rev. Lett. 115, 088001.CrossRefGoogle ScholarPubMed
Gray, J. & Ancey, C. 2011 Multi-component particle-size segregation in shallow granular avalanches. J. Fluid Mech. 678, 535–588.Google Scholar
Gray, J. & Chugunov, V. 2006 Particle size segregation and diffusive remixing in shallow granular avalanches. J. Fluid Mech. 569, 365–398.CrossRefGoogle Scholar
Gray, J. & Thornton, A. 2005 A theory for particle size segregation in shallow granular free-surface flows. Proc. R Soc. Lond. A 461, 1447–1473.Google Scholar
Hutter, K., Svendsen, B. & Rickenmann, D. 1996 Debris flow modeling: a review. Contin. Mech. Thermodyn. 8, 1–35.CrossRefGoogle Scholar
Iverson, R. 1997 The physics of debris flows. Rev. Geophys. 35, 245–296.CrossRefGoogle Scholar
Jain, A., Metzger, M. J. & Glasser, B. 2013 Effect of particle size distribution on segregation in vibrated systems. Powder Technol. 237, 543–553.CrossRefGoogle Scholar
Khakhar, D. V., McCarthy, J. J. & Ottino, J. M. 1997 Radial segregation of granular mixtures in rotating cylinders. Phys. Fluids 9, 3600–3614.CrossRefGoogle Scholar
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
Limpert, E., Stahel, W. & Abbt, M. 2001 Log-normal distributions across the sciences: keys and clues. Bioscience 51, 341–352.CrossRefGoogle Scholar
Makse, H. A., Havlin, S., King, P. & Stanley, H. E. 1997 Spontaneous stratification in granular mixtures. Nature 386, 379–382.CrossRefGoogle Scholar
Marks, B. & Einav, I. 2015 A mixture of crushing and segregation: the complexity of grainsize in natural granular flows. Geophys. Res. Lett. 42, 274–281.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
May, L., Golick, L., Phillips, K., Shearer, M. & Daniels, K. 2010 Shear-driven size segregation of granular materials: modeling and experiment. Phys. Rev. E 81, 051301.CrossRefGoogle ScholarPubMed
Midi, G. D. R. 2004 On dense granular flow. Eur. Phys. J. E 14, 341–365.CrossRefGoogle Scholar
Montgomery, D. & Buffington, J. 1997 Channel-reach morphology in mountain drainage basins. Geol. Soc. Am. Bull. 109, 596–611.2.3.CO;2>CrossRefGoogle Scholar
Mulder, T. & Alexander, J. 2001 The physical character of subaqueous sedimentary density flows and their deposits. Sedimentology 48, 269–299.CrossRefGoogle Scholar
Newey, M., Ozik, J., Van der Meer, S., Ott, E. & Losert, W. 2004 Band-in-band segregation of multidisperse mixtures. Europhys. Lett. 66, 205–211.CrossRefGoogle Scholar
Peng, C. & Dai, D. 1994 Magnetic properties and magnetoresistance in granular fe-cu alloys. J. Appl. Phys. 76, 2986–2990.Google Scholar
Pereira, G. & Cleary, P. 2013 Radial segregation of multi-component granular media in a rotating tumbler. Granul. Matt. 15, 705–724.CrossRefGoogle Scholar
Rognon, P. G., Roux, J. N., Naaim, M. & Chevoir, F. 2007 Dense flows of bidisperse assemblies of disks down an inclined plane. Phys. Fluids 19, 058101.CrossRefGoogle Scholar
Savage, S. & Lun, C. 1988 Particle size segregation in inclined chute flow of dry cohesionless granular solids. J. Fluid Mech. 189, 311–335.CrossRefGoogle Scholar
Schlick, C. P.2014 Applications of advection-diffusion based methodologies to fluid and granular flows. PhD thesis Northwestern University.Google Scholar
Schlick, C. P., Fan, Y., Isner, A. B., Umbanhowar, P. B., Ottino, J. M. & Lueptow, R. M. 2015a Segregation of bidisperse granular material in quasi-two-dimensional bounded heaps: model application to physical systems. AIChE J. 61, 1524–1534.CrossRefGoogle Scholar
Schlick, C. P., Fan, Y., Umbanhowar, P. B., Ottino, J. M. & Lueptow, R. M. 2015b Granular segregation in circular tumblers: theoretical modeling and scaling laws. J. Fluid Mech. 765, 632–652.CrossRefGoogle Scholar
Silbert, L., Ertas, D., Grest, G., Halsey, T., Levine, D. & Plimpton, S. 2001 Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64, 051302.CrossRefGoogle ScholarPubMed
Su, K. & Yu, H. 2005 Formation and characterization of aerobic granules in a sequencing batch reactor treating soybean-processing wastewater. Environ. Sci. Technol. 39, 2818–2827.CrossRefGoogle Scholar
Thornton, A., 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.CrossRefGoogle Scholar
Tripathi, A. & Khakhar, D. V. 2013 Density difference-driven segregation in a dense granular flow. J. Fluid Mech. 717, 643–669.Google Scholar
Tunuguntla, D., Bokhove, O. & Thornton, A. 2014 A mixture theory for size and density segregation in shallow granular free-surface flows. J. Fluid Mech. 749, 99–112.CrossRefGoogle Scholar
Utter, B. & Behringer, R. 2004 Self-diffusion in dense granular shear flows. Phys. Rev. E 69, 031308.CrossRefGoogle ScholarPubMed
Wiederseiner, S., Andreini, N., Epely-Chauvin, G., Moser, G., Monnereau, M., Gray, J. & Ancey, C. 2011 Expeirmental investigation into segregating granular flows down chutes. Phys. Fluids 23, 013301.CrossRefGoogle Scholar