Abstract
We performed a series of experiments to investigate the flow of an assembly of non-cohesive spherical grains in both high and low gravity conditions (i.e. above and under the Earth’s gravity). In high gravity conditions, we studied the flow of glass beads out of a cylindrical silo and the flow of metallic beads out of a vertical Hele-Shaw rectangular silo. Both silos were loaded in one of the gondolas of the large diameter centrifuge facility (located at ESTEC) in which an apparent gravity up to 20 times the Earth’s gravity can be established. To simulate low gravity conditions, we submitted a horizontal monolayer of metallic beads to the centrifuge force of a small rotation device (located at University of Liege). The influences of both gravity and aperture size on the mass flow were analysed in these various conditions. For the three systems (cylindrical silo, the Hele-shaw silo and the monolayer of beads), we demonstrated that (i) the square root scaling of the gravity found by Beverloo is relevant and (ii) the critical aperture size below which the flow is jammed does not significantly increase with the apparent gravity. Moreover, we studied in more details the Hele-Shaw silo in high gravity because this configuration allowed to determine local properties of the flow at the level of the aperture. We measured the velocity profiles and the packing fraction profiles for the various aperture sizes and apparent high gravities. We demonstrate the existence of a slip length for the flow at the level of the aperture. This later fact seems to result from the geometrical configuration of the silo.
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Notes
François Huber-Burnand (1750–1831) was blind since he was 15. He was helped by his domestic François Burnens during his experiments in Yverdon-les-Bains (Switzerland).
References
Scheeres, D.J., Hartzell, C.M., Sánchez, P., Swift, M.: Scaling forces to asteroid surfaces: the role of cohesion. Icarus 210, 968–984 (2010)
Arndt, T., Brucks, A., Ottino, J.M., Lueptow, R.M.: Creeping granular motion under variable gravity levels. Phys. Rev. E 74, 031307 (2006)
Brucks, A., Arndt, T., Ottino, J.M., Lueptow, R.M.: Behavior of flowing granular materials under variable g. Phys. Rev. E 75, 032301 (2007)
Kleinhans, M.G., Markies, H., de In’t Vet, S.J., Postema, F.N.: Postema, static and dynamic angles of repose in loose granular materials under reduced gravity. J. Geophys. Res. 116, E11004 (2011)
Dorbolo, S., Scheller, T., Ludewig, F., Lumay, G., Vandewalle, N.: Influence of a reduced gravity on the volume fraction of a monolayer of spherical grains. Phys. Rev. E 84, 041305 (2011)
Huber-Burnand, F.: Sur l’ écoulement et la pression du sable. Ann. de Chimie et de Physique 50, 159–173 (1829); Lieut. T.S. Brown, Experiments on the resistance of sand to motion through tubes, with especial reference to its use in the blasting of rocks, made at Fort Adams, Newport harbour, under the direction of Col. Totten, translated in English, F. Huber-Burnand, J. Franklin Inst. 22, 1–8 (1836)
Beverloo, W.A., Leninger, H.A., van de Valde, J.: The flow of granular solids through orifices. Chem. Eng. Sci. 15, 260–269 (1961)
Vanel, L., Claudin, Ph, Bouchaud, J.-P., Cates, M.E., Clément, E., Wittmer, J.P.: Stresses in silos: comparison between theoretical models and new experiments. Phys. Rev. Lett. 84, 1439–1442 (2000)
Bertho, Y., Giorgiutti-Dauphiné, F., Hulin, J.P.: Dynamical Janssen effect on granular packing with moving walls. Phys. Rev. Lett. 90, 144301 (2003)
Pacheco-Martinez, H., van Gerner, H.J., Ruiz-Suárez, J.C.: Storage and discharge of a granular fluid. Phys. Rev. E 77, 021303 (2008)
De-Song, B., Xun-Sheng, Z., Guang-Lei, X., Zheng-Quan, P., Xiao-Wei, T., Kun-Quan, L.: Critical phenomenon of granular flow on a conveyor belt. Phys. Rev. E 67, 062301 (2003)
Aguirre, M.A., Grande, J.G., Calvo, A., Pugnaloni, L.A., Géminard, J.C.: Pressure independence of granular flow through an aperture. Phys. Rev. Lett. 104, 238002 (2010)
Aguirre, M.A., Grande, J.G., Calvo, A., Pugnaloni, L.A., Géminard, J.C.: Granular flow through an aperture: pressure and flow rate are independent. Phys. Rev. E 83, 061305 (2011)
Perge, C., Aguirre, M.A., Gago, P.A., Pugnaloni, L.A., Le Tourneau, D., Géminard, J.C.: Evolution of pressure profiles during the discharge of a silo. Phys. Rev. E 85, 021303 (2012)
Zuriguel, I., Pugnaloni, L.A., Garcimartín, A., Maza, D.: Jamming during the discharge of grains from a silo described as a percolating transition. Phys. Rev. E 68, 030301 (R) (2003)
Mankoc, C., Janda, A., Arévalo, R., Pastor, J.M., Zuriguel, I., Garcimartín, A., Maza, D.: The flow rate of granular materials through an orifice. Granul. Matter 9, 407–414 (2007)
Janda, A., Zuriguel, I., Garcimartín, A., Pugnaloni, L.A., Maza, D.: Jamming and critical outlet size in the discharge of a two-dimensional silo. Europhys. Lett. 84, 44002 (2008)
Lumay, G., Vandewalle, N.: Controlled flow of smart powders. Phys. Rev. E 78, 061302 (2008)
Mersch, E., Lumay, G., Boschini, F., Vandewalle, N.: Effect of an electric field on an intermittent granular flow. Phys. Rev. E 81, 041309 (2010)
Bertho, Y., Becco, C., Vandewalle, N.: Dense bubble flow in a silo: an unusual flow of a dispersed medium. Phys. Rev. E 73, 056309 (2006)
Janda, A., Maza, D., Garcimartín, A., Kolb, E., Lanuza, J., Clément, E.: Unjamming a granular hopper by vibration. Europhys. Lett. 87, 24002 (2009)
Zuriguel, I., Janda, A., Garcimartín, A., Lozano, C., Arévalo, R.: Silo clogging reduction by the presence of an obstacle. Phys. Rev. Lett. 107, 278001 (2011)
Janda, A., Zuriguel, I., Maza, D.: Flow rate of particles through apertures obtained from self-similar ensity and velocity profiles. Phys. Rev. Lett. 108, 248001 (2012)
Garcimartín, A., Zuriguel, I., Pugnaloni, L.A., Janda, A.: Shape of jamming arches in two-dimensional deposits of granular materials. Phys. Rev. E 82, 031306 (2010)
Lozano, C., Lumay, G., Zuriguel, I., Hidalgo, R.C., Garcimartín, A.: Breaking arches with vibrations: the role of defects. Phys. Rev. Lett. 109, 068001 (2012)
SiLibeads, Sigmund-Lindner, Type S, roundness > 0.89 %
ZEUGMA, Tecnologia de Sistemas Inudstriais, Lda, large Diameter Centrifuge vibrations measurement and analysis (97278001B1), August 2011
Janda, A., Harich, R., Zuriguel, I., Maza, D., Cixous, P., Garcimartín, A.: Flow-rate fluctuations in the outpouring of grains from a two-dimensional silo. Phys. Rev. E 79, 031302 (2009)
Midi, G.D.R.: On dense granular flows. Europhys. J. E 14, 341–365 (2004)
Sakaie, K., Fenistein, D., Carroll, T.J., Van Hecke, M., Umbanhowar, P.: MR imaging of Reynolds dilatancy in the bulk of smooth granular flows. Europhys. Lett. 84, 49902 (2008)
Bazant, M.Z.: The spot model for random-packing dynamics. Mech. Mater. 38, 717–731 (2006)
Rycroft, C.H., Bazant, M.Z., Landry, J., Grest, G.S.: Dynamics of random packings in granular flow. Phys. Rev. E 73, 051306 (2006)
Acknowledgments
S.D. and G.L. thanks FNRS for financial support. Part of this work was supported by Université de Liège (Credit voyage etudiant and Bourse Post-Doc). The authors would like to thank the European Space Agency for the access to the Large Diameter Centrifuge in ESTEC.
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Dorbolo, S., Maquet, L., Brandenbourger, M. et al. Influence of the gravity on the discharge of a silo. Granular Matter 15, 263–273 (2013). https://doi.org/10.1007/s10035-013-0403-2
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DOI: https://doi.org/10.1007/s10035-013-0403-2