Abstract
We study a variety of granular flows and some models by means of a combination of simulations, experiments and analytic considerations. The models as well as the physical systems are governed by the presence of an interstitial gas. Through experimental comparison and validation of the models their applicability is determined. In particular we study bubbles of air in tubes (by experiment and simulation) the formation of stagnant zones in grain flow from a hopper (by experiment and simulation), fluidized beds (by simulation) and the intermittent flow in an hourglass (by experiment and simulation).
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References
J. T. Jenkins and S. B. Savage. A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech., Vol. 130, pp. 187, 1983.
I. Goldhirsch and G. Zanetti. Clustering instability in dissipative gases. Phys. Rev. Lett., Vol. 70, pp. 1619, 1993.
G. Pengand H. J. Herrmann. Density waves of granular flow using lattice gas automata. Phys. Rev. E, Vol. 47, pp. 1796, 1994.
S. Mc Namara, E. G. FlekkOy, and K. J. Máloy. Grains and gas flow. Molecular dynamics with hydrodynamic interactions. preprint, 1999.
E. G. Flekkoy and K. J. Mley .A continuum description of dry granular flows: Experiment and simulation.Phys. Rev. E,Vol. 57, pp. 6962, 1998.
X.I. Wu, K. J. Måløy, A. Hansen, M. Ammi, and D. Bideau.Why hourglasses tick. Phys. Rev. Lett., Vol. 71, pp. 1363, 1993.
T. Le Pennec, K. J. Má10y, A. Hansen, M. Ammi, D. Bideau, and X 1. Wu. Ticking hour glasses: Experimental analysis of intermittent flow. Phys. Rev. E, Vol. 53, pp. 2257–2264, 1996.
C. T. Veje and P. Dimon. Power spectra of flow in an hourglass. Phys. Rev. E, Vol. 56, pp. 4376, 1997.
H. Hayakawa, S. Yue, and D. C. Hong. Hydrodynamic description of granular convection. Phys. Rev. Lett., Vol. 75, pp. 2328, 1995.
M-L. Tan, Y. H. Qian, I. Goldhirsch, and S. A. Orzaag. Lattice bgk approach to simulating granular flows. J. Stat. Phys., Vol. 81, 1995.
E. Manger, T. Solberg, and B. H. Hjertager. Numerical simulation of the ticking hourglass. preprint, 1994.
W. A. Beverloo, H. A. Leniger, and J. van de Velde. The flow of granular solids through orifices. Chem. Eng. Science, Vol. 15, pp. 260, 1961.
J. F. Davidson. Bubbles in fluidized beds. In E. Guazzelli and L. Oger, editors, Mobile Particulate Systems, page 197, New York, 1995. Kluwer Academic Publisher.
J. F. Davidson and D. Harrison. Fluidization. Academic Press, New York, 1971.
D. Gidaspau. Multiphase flow and fluidization. Academic Press, San Diego California, 1994.
G. W. Baxter and R. P. Behringer. Pattern formation in flowing sand. Phys. Rev Lett., Vol. 62, pp. 2825, 1989.
D. Frenkel M. A. van der Hoef and A. J. C. Ladd. Self-diffusion in colloidal particles in a two-dimensional suspension: Are deviations from Fick’s law experimentally observable? Phys. Rev Lett., Vol. 67, pp. 3459, 1991.
A. J. C. Ladd. Numerical simulations of particulate suspensions via a discretized boltzmann equation. part 1. J. Fluid Mech., Vol. 271, pp. 285–309, 1994.
A. J. C. Ladd. Numerical simulations of particulate suspensions via a discretized boltzmaim equation. part 2. J. Fluid Mech., Vol. 271, pp. 309–339, 1994.
W. Kalthoff, S. Schwarzer, and H. J. Herrmann. Simulations of particle suspensions with inertial effects. Phys. Rev. E, Vol. 56, pp. 2234, 1997.
O. Reynolds. On the dilatancy of media composed of rigid particles in contact. Phil. Mag., Vol. 20, pp. 469–482, 1885.
K. S. Lim, J. X. Zhu, and J. R. Grace. Hydrodynamics of gas-solid fluidization. Int. J. Multiphase Flow, Vol. 21, pp. 141–193, 1995.
G. D. Scott Packing of equal spheres. Nature, Vol. 188, pp. 908–909, 1960.
P. Carman. Fluid flow through granular beds. Trans. Inst. Chem. Eng. Lond., Vol. 15, pp. 150–160, 1937.
L. D. Landau and E. M. Lifshitz. Fluid Mechanics. Pergamon Press, New York, 1959. G. M. Homsy. Aspects of flow and mixing in fluidized beds. In Disorder and Mixing, pages 185–201, Dordrecht, 1988. Kluwer academic publisher.
A. Zick and G. Homsy. Stokes flow through periodic arrays of spheres. J. Fluid Mech., Vol. 115, pp. 13–26, 1982.
E. G. Flekkpy. Lattice bgk models for miscible fluids. Phys. Rev. E, Vol. 47, pp. 4247, 1993.
G. McNamara and G. Zanetti. Use of the Boltzmann equation to simulate lattice-gas automata. Phys. Rev. Lett., Vol. 61, pp. 2332, 1988.
U. Frisch, D. d’Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivet. Lattice gas hydrodynamics in two and three dimensions. Complex Systems, Vol. 1, pp. 648, 1987.
T. Le Pennec, K. J. Máloy, E. G. Flekkoy, J. C. Messager, and M. Ammi. Silo hiccups. dynamic effects of dilatancy in granular flows. Phys. of Fluids, Vol. 10, pp. 3072, 1998.
R. M. Davies and G. I. Taylor. Bubbles in fluidized bed. Proc. Roy. Soc., Vol. A200, pp. 375, 1950.
T. Raafat, H. J. Herrmann, and J. P. Hulin. The pneumatic instability of granular materials. preprint, 1995.
J. J. Alonso and H. J. Herrmann. Shape of the tail of a two-dimensional sandpile. Phys. Rev. Lett., Vol. 76, pp. 4911–4915, 1996.
T. Kawaguchi, T. Tanaka, and Y. Tsuji. Numerical simulation of two-dimensional fluidized beds using the discrete element method (comparision between two-and three dimensional models). Powder technology, Vol. 96, pp. 129–138, 1998.
S. Luding and S. McNamara. Tcmodel. cond-mat/9810009, Vol. 1, pp. 111, 1998.
L. Brendel and S. Dippel. Physics of dry granular media. In H. J. Herrmann, J.-P. Hovi,and S. Luding, editors, Physics of Dry Granular Media, page 313, Dordrecht, 1998.Kluwer Academic Publishers.
F. Radjai and D. Wolf. Contact dynamics. Granular Matter, Vol. 1, pp. 3, 1998. S. Foerster, M. Louge, H. Chang, and K. Allia. Measurements of the collision properties of small spheres. Phys. Fluids, Vol. 6, pp. 1108, 1994.
S. Luding. Granular materials under vibration—simulations of rotating spheres. Phys. Rev. E, Vol. 52, pp. 4442, 1995.
P. N. Rowe. Fluidization, chapter 4, page 121. Academic Press, London and New York, 1971.
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Flekkøy, E., Mcnamara, S., Måløy, K.J. (2000). Modeling Granular Flows. In: Skjeltorp, A.T., Edwards, S.F. (eds) Soft Condensed Matter: Configurations, Dynamics and Functionality. NATO Science Series, vol 552. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4189-5_12
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DOI: https://doi.org/10.1007/978-94-011-4189-5_12
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