Abstract
The gravity-driven flow of granular material through a rough, narrow vertical pipe is described using the Langevin equation formalism. Above a critical particle density the homogeneous flow becomes unstable with respect to short-wave length perturbations. In correspondence with experimental observations, we find clogging and density waves in the flowing material.
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References
S. R. Nagel,Rev. Mod. Phys. 64:321 (1992).
M. Jaeger and S. R. Nagel,Science 255:1523 (1992).
G. Ristow, InAnnual Reviews of Computational Physics I D. Stauffer, ed. (World Scientific, Singapore, 1995).
K. L. Schick and A. A. Verveen,Nature 251:599 (1974).
T. Pöschel,J. Phys. France 4:499 (1994).
T. Raafat, J. P. Hulin, and H. J. Herrmann, Density waves in dry granular media falling through a vertical pipe, Preprint (1995).
G. Ristow and H. J. Herrmann,Phys. Rev. E 50:R5 (1994).
G. W. Baxter, R. P. Behringer, T. Fagert, and G. A. Johnson,Phys. Rev. Lett. 62: 2825 (1989); J. O. Cutress and R. F. Pulfer,Powder Technol. 1:213 (1967).
G. Baxter and R. P. Behringer,Phys. Rev. A 42:1017 (1990);Physica D 51:465 (1991).
G. Peng and H. J. Herrmann,Phys. Rev. E 49:R1796 (1994);Phys. Rev. E 51:1745 (1995).
U. Frisch, B. Hasslacher, and Y. Pomeau,Phys. Rev. Lett. 56:1505 (1986).
J. Lee and M. Leibig,J. Phys. France 4:507 (1994).
M. J. Lighthill and G. B. Whitham,Proc. Roy. Soc. A 229: 281, 317 (1955).
A. Mehta, R. J. Needs, and S. Dattagupta,J. Stat. Phys. 68:1131 (1992).
I. Prigogine and R. Herman,Kinetic Theory of Vehicular Traffic (Elsevier, New York, 1971).
G. B. Whitham,Linear and Nonlinear Waves (Wiley, New York, 1974).
I. Goldhirsch and G. Zanetti,Phys. Rev. Lett. 70:1619 (1993).
T. Riethmüller, Theoretische Modellierung granularer Strome in dünnen Röhren mit Langevin-Gleichungen, Diploma Thesis, Humboldt Universität zu Berlin (1995).
B. S. Kerner and P. Konhäuser,Phys. Rev. E 48:R2335 (1994); D. Helbing,Phys. Rev. E 51:1745 (1995).
D. A. Kurtze and D. C. Hong,Phys. Rev. E 52:218 (1995).
S. Savage,J. Fluid Mech. 241:109 (1992).
L. Schimansky-Geier, M. Mieth, H. Rosé, and H. Malchow,Phys. Lett. A 207: 140 (1995).
J. Duran, T. Mazozi, S. Luding, E. C'ément, and J. Rajchenbach, Preprint (1995).
P. A. Cundall and O. D. L. Strack,Géotechnique 29:47 (1979).
P. K. Haff and B. T. Werner,Powder Technol. 48:239 (1986).
J. Lee,Phys. Rev. E 49:281 (1994).
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Communicated by D. Stauffer
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Riethmüller, T., Schimansky-Geier, L., Rosenkranz, D. et al. Langevin equation approach to granular flow in a narrow pipe. J Stat Phys 86, 421–430 (1997). https://doi.org/10.1007/BF02180213
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DOI: https://doi.org/10.1007/BF02180213