Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-17T07:24:17.415Z Has data issue: false hasContentIssue false
  • English
  • Français

Shear-induced diffusion in cohesive granular flows: effect of enduring clusters

Published online by Cambridge University Press:  08 November 2018

Matthew Macaulay  and
Pierre Rognon Open the ORCID record for Pierre Rognon [Opens in a new window]
Matthew Macaulay*
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
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the effect of intergranular cohesive forces on the properties of self-diffusion in dense granular flows. The study is based on a series of simulated plane shear flows at different inertial and cohesion numbers, in which transverse diffusivities are measured. Results evidence an increase in diffusivity by up to two orders of magnitude when introducing cohesion. This strong effect is analysed using the Green–Kubo framework, expressing the diffusivity in terms of instantaneous grain velocity fluctuations and their time correlation. This analysis shows that cohesion, by forming enduring clusters in the flow, enhances the velocity fluctuations and their time persistence, which both contribute to enhancing grain mixing and self-diffusion.

JFM classification

Granular media: Granular media Mixing: Granular mixing Non-Newtonian Flows: Rheology
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 858 , 10 January 2019 , R2
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Campbell, C. S. 1997 Self-diffusion in granular shear flows. J. Fluid Mech. 348, 85–101.Google Scholar
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 (2), 021309.Google Scholar
DeGiuli, E., McElwaine, J. N. & Wyart, M. 2016 Phase diagram for inertial granular flows. Phys. Rev. E 94 (1), 012904.Google Scholar
Dufty, J. W., Brey, J. J. & Lutsko, J. 2002 Diffusion in a granular fluid. I. Theory. Phys. Rev. E 65 (5), 051303.Google Scholar
Gilabert, F. A., Roux, J.-N. & Castellanos, A. 2007 Computer simulation of model cohesive powders: influence of assembling procedure and contact laws on low consolidation states. Phys. Rev. E 75 (1), 011303.Google Scholar
Griffani, D., Rognon, P., Metzger, B. & Einav, I. 2013 How rotational vortices enhance transfers. Phys. Fluids 25 (9), 093301.Google Scholar
Gross, M., Krüger, T. & Varnik, F. 2015 Fluctuations and diffusion in sheared athermal suspensions of deformable particles. Europhys. Lett. 108 (6), 68006.Google Scholar
Hsiau, S.-S., Lu, L.-S., Chou, C.-Y. & Yang, W.-L. 2008 Mixing of cohesive particles in a shear cell. Intl J. Multiphase Flow 34 (4), 352–362.Google Scholar
Hsiau, S.-S. & Shieh, Y.-M. 2000 Effect of solid fraction on fluctuations and self-diffusion of sheared granular flows. Chem. Engng Sci. 55 (11), 1969–1979.Google Scholar
Khamseh, S., Roux, J.-N. & Chevoir, F. 2015 Flow of wet granular materials: a numerical study. Phys. Rev. E 92 (2), 022201.Google Scholar
Kharel, P. & Rognon, P. 2017 Vortices enhance diffusion in dense granular flows. Phys. Rev. Lett. 119 (17), 178001.Google Scholar
Losert, W., Bocquet, L., Lubensky, T. C. & Gollub, J. P. 2000 Particle dynamics in sheared granular matter. Phys. Rev. Lett. 85 (7), 1428.Google Scholar
Luding, S. 2008 Cohesive, frictional powders: contact models for tension. Granul. Matt. 10 (4), 235.Google Scholar
MiDi, G. D. R. 2004 On dense granular flows. Eur. Phys. J. E 14 (4), 341–365.Google Scholar
Mueth, D. M. 2003 Measurements of particle dynamics in slow, dense granular Couette flow. Phys. Rev. E 67 (1), 011304.Google Scholar
Natarajan, V. V. R., Hunt, M. L. & Taylor, E. D. 1995 Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow. J. Fluid Mech. 304, 1–25.Google Scholar
Pouliquen, O. & Chevoir, F. 2002 Dense flows of dry granular material. C. R. Phys. 3 (2), 163–175.Google Scholar
Richefeu, V., El Youssoufi, M. S., Peyroux, R. & Bohatier, C. 2005 Frictional contact and cohesion laws for casagrandes shear test on granular materials by 3d dem – comparison with experiments. Powders and Grains 5, 1–4.Google Scholar
Rognon, P. G., Roux, J.-N., Wolf, D., Naaïm, M. & Chevoir, F. 2006 Rheophysics of cohesive granular materials. Europhys. Lett. 74 (4), 644.Google Scholar
Rognon, P. G., Roux, J.-N., Naaim, M. & Chevoir, F. 2008 Dense flows of cohesive granular materials. J. Fluid Mech. 596, 21–47.Google Scholar
Sierou, A. & Brady, J. F. 2004 Shear-induced self-diffusion in non-colloidal suspensions. J. Fluid Mech. 506, 285–314.Google Scholar
Utter, B. & Behringer, R. P. 2004 Self-diffusion in dense granular shear flows. Phys. Rev. E 69 (3), 031308.Google Scholar
Zik, O. & Stavans, J. 1991 Self-diffusion in granular flows. Europhys. Lett. 16 (3), 255.Google Scholar

Macaulay and Rognon supplementary movie 1

Shear induced diffusion at high inertial number and without cohesion (I = 0.3 and C=0) . Grains initially at the centre of the shear cell are coloured in red, while other grains are coloured in blue. All grains keep their colour during shear.

Download Macaulay and Rognon supplementary movie 1(Video)
Video 9.8 MB

Macaulay and Rognon supplementary movie 2

Shear induced diffusion at high inertial number and with cohesion (I = 0.3 and C=25) . Grains initially at the centre of the shear cell are coloured in red, while other grains are coloured in blue. All grains keep their colour during shear.

Download Macaulay and Rognon supplementary movie 2(Video)
Video 9.8 MB

Macaulay and Rognon supplementary movie 3

Shear induced diffusion at low inertial number and without cohesion (I = 0.01 and C=0) . Grains initially at the centre of the shear cell are coloured in red, while other grains are coloured in blue. All grains keep their colour during shear.

Download Macaulay and Rognon supplementary movie 3(Video)
Video 9.8 MB

Macaulay and Rognon supplementary movie 4

Shear induced diffusion at low inertial number and with cohesion (I = 0.01 and C=25) . Grains initially at the centre of the shear cell are coloured in red, while other grains are coloured in blue. All grains keep their colour during shear.

Download Macaulay and Rognon supplementary movie 4(Video)
Video 9.6 MB