Abstract
We report on a new effect observed in horizontally shaken granular material in a rectangular box. Within a certain region of parameters of the oscillation the granular material swells recurrently with a characteristic frequency (see http://summa.physik.hu-berlin.de/GranMat/). This frequency is significantly smaller than the frequency of forcing. We claim that this new effect is caused by the the interplay between Reynolds dilatancy due to convective motion and mechanical stability of the diluted granular material in the box. Measurements of the dissipated energy per time supports this explanation.
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Ayer, J. E. and Soppet, F. E. (1965/1966): Vibratory Compaction, Part I: Compaction of Spherical Shapes and Part II: Compaction of Angular Shapes. J. Am. Ceramic Soc. 48, 180–183 and 49, 207–210.
Behringer, R. P. and Jenkins, J. T. (eds.) (1997): Powders and Grains'97, Balkema, Rotterdam.
Bourzutschky, M. and Miller, J. (1995): “Granular” Convection in a Vibrated Fluid. Phys. Rev. Lett. 74, 2216–2219.
Clément, E., Vanel, L., Rajchenbach, J. and Duran, J. (1996): Pattern formation in a vibrated 2d granular layer. Phys. Rev. E, 53, 2972–2975.
Ehrichs, E. E., Jaeger, H. M., Karczmar, G. S., Knight, J. B., Kuperman, V. Yu. and Nagel, S. R. (1995): Granular Convection Observed by Magnetic Resonance Imaging, Science 267, 1632–1634.
Esipov, S. E., Salueña, C. and Pöschel, T. (1996): Glassy Behavior of Granular Media and Fluctuational Hydrodynamics. subm. Phys. Rev. E (1996).
Evesque, P. (1990): Comment on (Laroche et al. (1989)), J. Phys. France 51, 697–699 and reply by Laroche, C., Douady, S. and Fauve, S.. J. Phys. France 51, 700.
Evesque, P. and Rajchenbach, J. (1989): Instability in a Sand Heap. Phys. Rev. Lett. 62, 44–46.
Fauve, S., Douady, S. and Laroche, C. (1989): Collective behaviours of granular masses under vertical vibrations. J. Physique C3, 187–191.
Gallas, J. A. C., Herrmann, H. J. and Sokołowski, S. (1992): Convection Cells in Vibrating Granular Media. Phys. Rev. Lett. 69, 1371–1374.
Gallas, J. A. C., Herrmann, H. J., Pöschel, T. and Sokolowski, S. (1994): Molecular dynamics simulation of size segregation in three dimensions. J. Stat. Phys. 82, 443–450.
Hayakawa, H., Yue, S. and Hong, D. C. (1995): Hydrodynamic description of granular convection. Phys. Rev. Lett. 75, 2328–2331.
Horikawa, S., Nakahara, A., Nakayama, T., and Matsushita, M. (1995): Self-Organized Critical Density Waves of Granular Material Flowing through a Pipe. J. Phys. Soc. Jpn. 64, 1870–1873.
Iwashita, K., Tarumi, Y., Casaverde, L., Uemura, D., Meguro, K. and Hakuno, M. (1988): Granular assembly simulation for ground collapse. in: Satake, M. and Jenkins, J. T. (eds) Micromechanics of Granular Material, Elsevier, Amsterdam, 125–132.
Jaeger, H. M. and Nagel, S. R. (1992): Physics of the Granular State. Science 255, 1523–1531.
Jaeger, H. M., Nagel, S. R. and Behringer, R. P. (1996): Granular Solids, Liquids and Gases. Rev. Mod. Phys. 68, 1259–1273.
Knight, J. B., Jaeger H. M., and Nagel S. R. (1993): Vibration-Induced Size Separation in Granular Media: The Convection Connection. Phys. Rev. Lett. 70, 3728–3731.
Laroche, C., Douady, S. and Fauve, S. (1989): Convective Flow of Granular Masses under Vertical Vibration. J. Physique 50, 699–706.
Liffman, K. and Metcalfe, G. (1997): Convection due to horizontal shaking. in: (Behringer and Jenkins (1997)), 405–408.
Melo, F., Umbanhowar, P. and Swinney, H. L. (1995): Hexagons, kinks, and disorder in oscillated granular layers. Phys. Rev. Lett. 75 3838–3841.
Metcalfe, T., Knight, J. B., and Jaeger, H. M. (1997): Surface Patterns in Shallow Beds of Vibrated Granular Material. Physica A 236, 202–210.
Pöschel, T. and Herrmann, H. J. (1995): Size Segregation and Convection. Europhys. Lett. 29, 123–128.
Raafat, T., Hulin, J. P. and Herrmann, H. J. (1996): Density Waves in Dry Granular Media Falling through a Vertical Pipe. Phys. Rev. E 53, 4345–4350.
Rátkai, G. (1976): Particle Flow and Mixing in Vertically Vibrated Beds. Powder Technol. 15, 187–192.
Reynolds, O. (1885): On the dilatancy of media composed of rigid particles in contact. Phil. Mag. Soc. 20 469.
Ristow, G., Strassburger, G. and Rehberg, I. (1997): Phase Diagram and Scaling of Granular Material under Horizontal Vibrations. preprint.
Rosenkranz, D. (1997): Dynamic Phenomena in Granular Materials, PhD Thesis, Humboldt-Universität zu Berlin (in preparation).
Rosenkranz, D. and Pöschel, T. (1997): Recurrent swelling of horizontally shaken granular material. subm. Phys. Rev. Lett. (1997).
Rosenkranz, D. and Pöschel, T. (1997): Convective motion in three dimensional horizontally shaken granular material. (in preparation).
Salueña, C., Esipov, S. E. and Pöschel, T. (1997): Hydrodynamic fluctuations and averaging problems in dense granular flows. in: (Behringer and Jenkins (1997)), 341–344.
Savage, S. B. (1988): Streaming motions in a bed of vibrationally fluidized dry granular material. J. Fluid Mech. 194, 457–478.
Spahn, F., Schwarz, U. and Kurths, J. (1997): Clustering of granular Assemblies with temperature dependent restitution under Keplerian differential rotation. Phys. Rev. Lett. 78, 1596–1599.
Strassburger, G., Betat, A., Scherer, M. A. and Rehberg, I. (1996) in: Wolf, D. E. and Schreckenberg, M. and Bachem, A. (eds.) Traffic and Granular Flow, World Scientific (Singapore), 329–333.
Taguchi, Y-h. (1992): New Origin of a Convective Motion: Elastically Induced Convection in Granular Materials. Phys. Rev. Lett. 69, 1367–1370.
Tennakoon, S. G. K. and Behringer, R. P. (1997): Liquefaction of a horizontally vibrated granular bed. preprint.
Umbanhowar, P. B., Melo, F. and Swinney, H. L. (1996): Localized excitations in a vertically vibrated granular layer. Nature 382, 793–796. Nature 382 793 (1996).
Wang, D. G. and Campbell, C. S. (1992): Reynolds’ Analogy for a Shearing Granular Material. J. Fluid Mech. 224, 527–546.
Warr, S., Huntley, J. M., and Jacques, G. T. H. (1995): Fluidization of a two-dimensional granular system: Experimental study and scaling behavior. Phys. Rev. E, 52, 5583–5595.
Williams, J. C. (1976): The Segregation of Particulate Materials. A Review. Powder Technology 15, 245–251.
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© 1998 Springer-Verlag
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Pöschel, T., Rosenkranz, D.E. (1998). Experimental study of horizontally shaken granular matter — The swelling effect. In: Parisi, J., Müller, S.C., Zimmermann, W. (eds) A Perspective Look at Nonlinear Media. Lecture Notes in Physics, vol 503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104957
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DOI: https://doi.org/10.1007/BFb0104957
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