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Origin of the long-ranged attraction or repulsion between intruders in a confined granular medium

Published online by Cambridge University Press:  15 January 2020

Manish Dhiman ,
Sonu Kumar Open the ORCID record for Sonu Kumar [Opens in a new window] ,
K. Anki Reddy Open the ORCID record for K. Anki Reddy [Opens in a new window]  and
Raghvendra Gupta
Manish Dhiman
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Guwahati, Assam,781039, India
Sonu Kumar
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Guwahati, Assam,781039, India
K. Anki Reddy*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Guwahati, Assam,781039, India
Raghvendra Gupta
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Guwahati, Assam,781039, India
*
†Email address for correspondence: anki.reddy@iitg.ac.in
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Abstract

Zuriguel et al. (Phys. Rev. Lett., vol. 95, 2005a, 258002) and Pacheco-Vázquez and Ruiz-Suárez (Nat. Commun., vol. 1, 2010, p. 123) demonstrated that there exists a long-ranged force between intruders placed at a certain distance from each other in granular flow. The origin of these long-ranged forces, induced collectively by the grains, has not been fully understood. In our work, we provide a unified explanation for the origin of both attraction and repulsion between two intruders in terms of the building up of force chains and their subsequent buckling. The surface and shear zone of the other intruder makes a significant contribution to the strength or buckling of the force chains. Bernoulli’s effect used in earlier studies predicts the nature of these forces, viz., attraction or repulsion, correctly but is not well supported as observed in our study. The time-averaged flow fields around the intruders also support our explanation for the origin as evidenced by the burst in kinetic energy and granular temperature. The model proposed in this work predicts the qualitative trend of the sideways force with the separation between the intruders by combining Bernoulli’s equation with a minimum contact criterion of force chains. There exists an equilibrium at which the intruders neither attract nor repel each other and a certain separation distance where maximum attraction occurs between the two intruders. The effects of the static pressure, the velocity of the moving intruders and the friction coefficient on the attraction or repulsion force between the intruders have also been explored in our system.

JFM classification

Granular media: Granular media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A23
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Acevedo-Escalante, M. F. & Caballero-Robledo, G. A. 2017 Lift on side by side intruders of various geometries within a granular flow. Eur. Phys. J. Web Conf. 140, 03048.CrossRefGoogle Scholar
Albert, R., Pfeifer, M. A., Barabási, A.-L. & Schiffer, P. 1999 Slow drag in a granular medium. Phys. Rev. Lett. 82, 205–208.CrossRefGoogle Scholar
Aumaître, S., Kruelle, C. A. & Rehberg, I. 2001 Segregation in granular matter under horizontal swirling excitation. Phys. Rev. E 64, 041305.Google ScholarPubMed
Brilliantov, N. V., Spahn, F., Hertzsch, J.-M. & Pöschel, T. 1996 Model for collisions in granular gases. Phys. Rev. E 53, 5382.Google ScholarPubMed
Butlanska, J., Arroyo, M., Gens, A. & OSullivan, C. 2014 Multi-scale analysis of cone penetration test (CPT) in a virtual calibration chamber. Can. Geotech. J. 51 (1), 51–66.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
de la Cruz, R. A. L. & Caballero-Robledo, G. A. 2016 Lift on side-by-side intruders within a granular flow. J. Fluid Mech. 800, 248–263.Google Scholar
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Géotechnique 29 (1), 47–65.CrossRefGoogle Scholar
Drescher, A. & de Josselin de Jong, G. 1972 Photoelastic verification of a mechanical model for the flow of a granular material. J. Mech. Phys. Solids 20 (5), 337–340.CrossRefGoogle Scholar
Forterre, Y. & Pouliquen, O. 2008 Flows of dense granular media. Annu. Rev. Fluid Mech. 40 (1), 1–24.CrossRefGoogle Scholar
Geng, J. & Behringer, R. P. 2004 Diffusion and mobility in a stirred dense granular material. Phys. Rev. Lett. 93, 238002.CrossRefGoogle Scholar
Geng, J. & Behringer, R. P. 2005 Slow drag in two-dimensional granular media. Phys. Rev. E 71, 011302.Google ScholarPubMed
Guillard, F., Forterre, Y. & Pouliquen, O. 2014 Lift forces in granular media. Phys. Fluids 26 (4), 043301.CrossRefGoogle Scholar
Hilton, J. E. & Tordesillas, A. 2013 Drag force on a spherical intruder in a granular bed at low Froude number. Phys. Rev. E 88, 062203.Google Scholar
Hutter, K., Koch, T., Pluüss, C. & Savage, S. B. 1995 The dynamics of avalanches of granular materials from initiation to runout. Part II. Experiments. Acta Mech. 109 (1), 127–165.CrossRefGoogle Scholar
Jaeger, H. M., Nagel, S. R. & Behringer, R. P. 1996 Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 1259–1273.CrossRefGoogle Scholar
Jenkins, J. T. & Yoon, D. K. 2002 Segregation in binary mixtures under gravity. Phys. Rev. Lett. 88, 194301.CrossRefGoogle ScholarPubMed
Kamrin, K. & Henann, D. L. 2015 Nonlocal modeling of granular flows down inclines. Soft Matt. 11, 179–185.CrossRefGoogle ScholarPubMed
Kumar, S., Anki Reddy, K., Takada, S. & Hayakawa, H.2017 Scaling law of the drag force in dense granular media. arXiv:1712.09057.Google Scholar
Liu, D. & Henann, D. L. 2018 Size-dependence of the flow threshold in dense granular materials. Soft Matt. 14, 5294–5305.CrossRefGoogle ScholarPubMed
Lozano, C., Zuriguel, I., Garcimartín, A. & Mullin, T. 2015 Granular segregation driven by particle interactions. Phys. Rev. Lett. 114, 178002.CrossRefGoogle ScholarPubMed
Lu, K., Hou, M., Jiang, Z., Wang, Q., Sun, G. & Liu, J. 2018 Understanding earthquake from the granular physics point of view causes of earthquake, earthquake precursors and predictions. Intl J. Model. Phys. B 32 (07), 1850081.Google Scholar
Lucy, L. B. 1977 A numerical approach to the testing of the fission hypothesis. Astron. J. 82, 1013–1024.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.CrossRefGoogle Scholar
Pacheco-Vázquez, F. & Ruiz-Suárez, J. C. 2010 Cooperative dynamics in the penetration of a group of intruders in a granular medium. Nat. Commun. 1, 123.CrossRefGoogle Scholar
Peters, J. F., Muthuswamy, M., Wibowo, J. & Tordesillas, A. 2005 Characterization of force chains in granular material. Phys. Rev. E 72, 041307.Google ScholarPubMed
Plimpton, S., Crozier, P. & Thompson, A.2007 LAMMPS: large-scale atomic/molecular massively parallel simulator. Sandia National Laboratories. Available at: https://lammps.sandia.gov/.Google Scholar
Reddy, A. V. K., Kumar, S., Anki Reddy, K. & Talbot, J. 2018 Granular silo flow of inelastic dumbbells: clogging and its reduction. Phys. Rev. E 98, 022904.Google Scholar
Reddy, K. A., Forterre, Y. & Pouliquen, O. 2011 Evidence of mechanically activated processes in slow granular flows. Phys. Rev. Lett. 106, 108301.CrossRefGoogle ScholarPubMed
Sanders, D. A., Swift, M. R., Bowley, R. M. & King, P. J. 2004 Are brazil nuts attractive? Phys. Rev. Lett. 93, 208002.CrossRefGoogle ScholarPubMed
Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177–215.CrossRefGoogle Scholar
Seguin, A., Coulais, C., Martinez, F., Bertho, Y. & Gondret, P. 2016 Local rheological measurements in the granular flow around an intruder. Phys. Rev. E 93, 012904.Google ScholarPubMed
Shaebani, M. R., Sarabadani, J. & Wolf, D. E. 2012 Nonadditivity of fluctuation-induced forces in fluidized granular media. Phys. Rev. Lett. 108, 198001.CrossRefGoogle ScholarPubMed
Silbert, L. E., Ertaş, D., Grest, G. S., Halsey, T. C., Levine, D. & Plimpton, S. J. 2001 Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64, 051302.Google ScholarPubMed
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 ScholarPubMed
Stukowski, A. 2009 Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool. Model. Simul. Mater. Sci. Engng 18 (1), 015012.Google Scholar
Tordesillas, A., Hilton, J. E. & Tobin, S. T. 2014 Stick-slip and force chain evolution in a granular bed in response to a grain intruder. Phys. Rev. E 89, 042207.Google Scholar
Trujillo, L., Alam, M. & Herrmann, H. J. 2003 Segregation in a fluidized binary granular mixture: competition between buoyancy and geometric forces. Eur. Phys. Lett. 64 (2), 190–196.CrossRefGoogle Scholar
Trujillo, L. & Herrmann, H. J. 2003 Hydrodynamic model for particle size segregation in granular media. Physica A 330 (3), 519–542.CrossRefGoogle Scholar
Walker, D. M., Tordesillas, A. & Froyland, G. 2014 Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution. Phys. Rev. E 89, 032205.Google ScholarPubMed
Weinhart, T., Hartkamp, R., Thornton, A. R. & Luding, S. 2013 Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface. Phys. Fluids 25 (7), 070605.CrossRefGoogle Scholar
Wieghardt, K. 1975 Experiments in granular flow. Annu. Rev. Fluid Mech. 7 (1), 89–114.CrossRefGoogle Scholar
Williams, J. C. 1976 The segregation of particulate materials. A review. Powder Technol. 15 (2), 245–251.CrossRefGoogle Scholar
Zhang, Q. & Kamrin, K. 2017 Microscopic description of the granular fluidity field in nonlocal flow modeling. Phys. Rev. Lett. 118, 058001.Google ScholarPubMed
Zuriguel, I., Boudet, J. F., Amarouchene, Y. & Kellay, H. 2005a Role of fluctuation-induced interactions in the axial segregation of granular materials. Phys. Rev. Lett. 95, 258002.CrossRefGoogle Scholar
Zuriguel, I., Garcimartín, A., Maza, D., Pugnaloni, L. A. & Pastor, J. M. 2005b Jamming during the discharge of granular matter from a silo. Phys. Rev. E 71, 051303.Google Scholar
Zuriguel, I., Janda, A., Garcimartín, A., Lozano, C., Arévalo, R. & Maza, D. 2011 Silo clogging reduction by the presence of an obstacle. Phys. Rev. Lett. 107, 278001.CrossRefGoogle ScholarPubMed