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Lift on side-by-side intruders within a granular flow

Published online by Cambridge University Press:  01 July 2016

R. A. López de la Cruz  and
G. A. Caballero-Robledo
R. A. López de la Cruz
Affiliation:
CINVESTAV-Monterrey, PIIT, Nuevo León, 66600, México
G. A. Caballero-Robledo*
Affiliation:
CINVESTAV-Monterrey, PIIT, Nuevo León, 66600, México
*
†Email address for correspondence: g.a.caballero.robledo@gmail.com
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Abstract

For the first time, we used computer simulations to study lift forces on two static disks placed side-by-side within a two-dimensional granular flow and found them to be either repulsive or attractive depending on the flow velocity and separation between the disks. Our simulations results reveal that differences in the flow velocity between the disks and outside of that region are closely correlated with the lift force. We propose an empirical function for the lift force based on this correlation and our dimensional analysis. The specific region where the measured velocity exhibits this correlation suggests that attractive lift is not a Bernoulli-like effect. Instead, we speculate that it might be explained by a force balance based on Coulomb’s theory of passive failure in a Mohr–Coulomb material. Our results confirm that repulsive lift is due to the jamming of particles flowing between the disks.

JFM classification

Complex Fluids: Complex Fluids Granular media: Granular media Mixing: Granular mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 800 , 10 August 2016 , pp. 248 - 263
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Copyright
© 2016 Cambridge University Press 

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References

Albert, R., Pfeifer, M. A., Barbasi, A. L. & Schiffer, P. 1999 Slow drag in a granular medium. Phys. Rev. Lett. 82, 205–208.Google Scholar
Andreotti, B., Forterre, Y. & Pouliquen, O. 2013 Granular Media: Between Fluid and Solid. Cambridge University Press.Google Scholar
Aumaître, S., Kruelle, C. A. & Rehberg, I. 2001 Segregation in granular matter under horizontal swirling excitation. Phys. Rev. E 64, 041305.Google Scholar
Caballero-Robledo, G. & Clément, E. 2009 Rheology of a sonofluidized granular packing. Eur. Phys. J. E 30, 395–401.CrossRefGoogle ScholarPubMed
Cattuto, C., Brito, R., Marconi, U. M. B., Nori, F. & Soto, R. 2006 Fluctuation-induced casimir forces in granular fluids. Phys. Rev. Lett. 96, 178001.Google Scholar
Chehata, D., Zenit, R. & Wassgren, C. R. 2003 Dense granular flow around an immersed cylinder. Phys. Fluids 15, 1622.Google Scholar
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Géotechnique 29 (1), 47–65.CrossRefGoogle Scholar
Ding, Y., Gravish, N. & Goldman, D. I. 2011 Drag induced lift in granular media. Phys. Rev. Lett. 106, 028001.Google Scholar
Faug, T. 2015 Macroscopic force experienced by extended objects in granular flows over a very broad froude-number range. Eur. Phys. J. E 38 (5), 1–10.Google Scholar
Geng, J. & Behringer, R. P. 2005 Slow drag in two-dimensional granular media. Phys. Rev. E 71, 011302.Google Scholar
Goldman, D. I. 2014 Colloquium: biophysical principles of undulatory self-propulsion in granular media. Rev. Mod. Phys. 86, 943–958.CrossRefGoogle Scholar
Guillard, F., Forterre, Y. & Pouliquen, O. 2014 Lift forces in granular media. Phys. Fluids 26 (4), 043301.CrossRefGoogle Scholar
Guillard, F., Forterre, Y. & Pouliquen, O. 2013 Depth-independent drag force induced by stirring in granular media. Phys. Rev. Lett. 110, 138303.Google Scholar
Kim, I., Elghobashi, S. & Sirignano, W. A. 1993 Three-dimensional flow over two spheres placed side by side. J. Fluid Mech. 246, 465–488.CrossRefGoogle Scholar
Kneib, F., Faug, T., Dufour, F. & Naaim, M. 2016 Numerical investigations of the force experienced by a wall subject to granular lid-driven flows: regimes and scaling of the mean force. Comput. Particle Mech. 3 (3), 293–302.Google Scholar
Legendre, D., Magnaudet, J. & Mougin, G. 2003 Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid. J. Fluid Mech. 497, 133–166.Google Scholar
Moro, F., Faug, T., Bellot, H. & Ousset, F. 2010 Large mobility of dry snow avalanches: insights from small-scale laboratory tests on granular avalanches of bidisperse materials. Cold Reg. Sci. Technol. 62 (1), 55–66.CrossRefGoogle Scholar
Nelson, E. L., Katsuragi, H., Mayor, P. & Durian, D. J. 2008 Projectile interactions in granular impact cratering. Phys. Rev. Lett. 101 (6), 068001.CrossRefGoogle ScholarPubMed
Ottino, J. M. & Khakhar, D. V. 2000 Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32 (1), 55–91.Google Scholar
Pacheco-Vázquez, F., Caballero-Robledo, G. A., Solano-Altamirano, J. M., Altshuler, E., Batista-Leyva, A. J. & Ruiz-Suárez, J. C. 2011 Infinite penetration of a projectile into a granular medium. Phys. Rev. Lett. 106, 218001.Google Scholar
Pacheco-Vazquez, F. & Ruiz-Suarez, J. C. 2010 Cooperative dynamics in the penetration of a group of intruders in a granular medium. Nat. Commun. 1, 123.Google Scholar
Sanders, D. A., Swift, M. R., Bowley, R. M. & King, P. J. 2004 Are brazil nuts attractive? Phys. Rev. Lett. 93, 208002.Google Scholar
Seguin, A., Bertho, Y., Gondret, P. & Crassous, J. 2011 Dense granular flow around a penetrating object: experiment and hydrodynamic model. Phys. Rev. Lett. 107, 048001.CrossRefGoogle ScholarPubMed
Shaebani, M. R., Sarabadani, J. & Wolf, D. E. 2012 Nonadditivity of fluctuation-induced forces in fluidized granular media. Phys. Rev. Lett. 108, 198001.Google Scholar
Solano-Altamirano, J. M., Caballero-Robledo, G. A., Pacheco-Vázquez, F., Kamphorst, V. & Ruiz-Suárez, J. C. 2013 Flow-mediated coupling on projectiles falling within a superlight granular medium. Phys. Rev. E 88, 032206.Google Scholar
Vélez-Cordero, J. R., Sámano, D., Yue, P., Feng, J. J. & Zenit, R. 2011 Hydrodynamic interaction between a pair of bubbles ascending in shear-thinning inelastic fluids. J. Non-Newtonian Fluid Mech. 166 (1–2), 118–132.CrossRefGoogle Scholar
Walton, O. R. & Braun, R. L. 1986 Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. J. Rheol. 30 (5), 949–980.Google Scholar
Wassgren, C. R.1996 Vibration of granular materials. PhD thesis, California Institute of Technology.Google Scholar
Wieghardt, K. 1975 Experiments in granular flow. Annu. Rev. Fluid Mech. 7 (1), 89–114.CrossRefGoogle Scholar
Wijngaarden, L. V. & Jeffrey, D. J. 1976 Hydrodynamic interaction between gas bubbles in liquid. J. Fluid Mech. 77, 27–44.Google Scholar
Wu, J. & Manasseh, R. 1998 Dynamics of dual-particles settling under gravity. Intl J. Multiphase Flow 24 (8), 1343–1358.Google Scholar
Zuriguel, I., Boudet, J. F., Amarouchene, Y. & Kellay, H. 2005 Role of fluctuation-induced interactions in the axial segregation of granular materials. Phys. Rev. Lett. 95, 258002.Google Scholar

López de la Cruz Supplementary Movie 1

Movie showing the whole simulation cell during the first two seconds of simulation with the following parameters: v = 0.44 m/s, Xsep = 2.5 cm, D = 2.54 cm, d = 0.52 cm, # of particles = 8300. In this case, the average lift force is attractive.

Download López de la Cruz Supplementary Movie 1(Video)
Video 16.9 MB

López de la Cruz Supplementary Movie 2

Movie showing the whole simulation cell during the first two seconds of simulation with the following parameters: v = 0.6 m/s, Xsep = 2.5 cm, D = 2.54 cm, d = 0.52 cm, # of particles = 8300. In this case, the average lift force is almost zero.

Download López de la Cruz Supplementary Movie 2(Video)
Video 7.4 MB

López de la Cruz Supplementary Movie 3

Movie showing the whole simulation cell during the first two seconds of simulation with the following parameters: v = 1.1 m/s, Xsep = 2.5 cm, D = 2.54 cm, d = 0.52 cm, # of particles = 8300. In this case, the average lift force is repulsive.

Download López de la Cruz Supplementary Movie 3(Video)
Video 18.8 MB

López de la Cruz Supplementary Movie 4

Movie showing the region around the intruders during the first two seconds of simulation with the following parameters: v = 0.44 m/s, Xsep = 2.5 cm, D = 2.54 cm, d = 0.52 cm, # of particles = 8300. In this case, the average lift force is attractive.

Download López de la Cruz Supplementary Movie 4(Video)
Video 15.2 MB

López de la Cruz Supplementary Movie 5

Movie showing the region around the intruders during the first two seconds of simulation with the following parameters: v = 0.6 m/s, Xsep = 2.5 cm, D = 2.54 cm, d = 0.52 cm, # of particles = 8300. In this case, the average lift force is almost zero.

Download López de la Cruz Supplementary Movie 5(Video)
Video 15.4 MB

López de la Cruz Supplementary Movie 6

Movie showing the region around the intruders during the first two seconds of simulation with the following parameters: v = 1.1 m/s, Xsep = 2.5 cm, D = 2.54 cm, d = 0.52 cm, # of particles = 8300. In this case, the average lift force is repulsive.

Download López de la Cruz Supplementary Movie 6(Video)
Video 16.1 MB
Supplementary material: PDF

Lopez de la Cruz supplementary material

Supplementary figures

Download Lopez de la Cruz supplementary material(PDF)
PDF 564.6 KB