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Streaming motions in a bed of vibrationally fluidized dry granular material

Published online by Cambridge University Press:  21 April 2006

Stuart B. Savage
Stuart B. Savage
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada.
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Abstract

Experimental and theoretical studies of vibration-induced flow and mixing of dry granular materials are described. Tests were performed on rounded polystyrene beads contained in a rectangular box having transparent front and back walls and a flexible, nominally horizontal bottom which could be driven at various frequencies and amplitudes. The amplitude of the bottom vibrations was a maximum at the centre and decreased towards the vertical sidewalls. Slow recirculating flows were observed; they had the form of two vortices in which the velocity was upwards at the vertical centreline and downwards along the vertical sidewalls. The streaming velocities were measured as a function of bed vibration frequency and displacement amplitude. An explanation proposed for the recirculating flows is that the vibrating base sends ‘acoustic’ waves upwards through the bed. These waves ‘fluidize’ the granular material but are in turn attenuated because of the dissipative nature of the collisions between the ‘fluidized’ particles. Thus the slow recirculating flows in the granular material are analogous to the more familiar ‘acoustic streaming’ in air. An approximate analysis of these streaming motions is developed by making use of a modification of the constitutive theory of Jenkins & Savage (1983). A number of simplifying assumptions are introduced to make the analysis tractable. The general flow patterns of the streaming motions are predicted, but the velocities are overestimated as a result of the simplifying assumptions. The analysis is restricted to a rather narrow range of conditions.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 194 , September 1988 , pp. 457 - 478
Copyright
© 1988 Cambridge University Press

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References

Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 49–63.Google Scholar
Campbell, C. S. & Brennen, C. E. 1983 Computer simulation of shear flows of granular material. In Mechanics of Granular Materials: New Models and Constitutive Relations (ed. J. T. Jenkins & M. Satake), pp. 313–326. Elsevier.
Campbell, C. S. & Brennen, C. E. 1985 Chute flows of granular material: some computer simulations. Trans. ASME E: J. Appl. Mech. 52, 172–178.Google Scholar
Carnahan, N. F. & Starling, K. E. 1969 Equations of state for non-attracting rigid spheres. J. Chem. Phys. 51, 635–636.Google Scholar
Cebeci, T. & Smith, A. M. O. 1974 Analysis of Turbulent Boundary Layers. Academic.
Chapman, S. & Cowling, T. G. 1960 The Mathematical Theory of Non-Uniform Gases, 2nd edn. Cambridge University Press.
Faraday, M. 1831 On a peculiar class of acoustical figures assumed by groups of particles upon vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 299–340 (see also Faraday's Diary, vol. 1 (ed. T. Martin), pp. 324–359. G. Bell & Sons Ltd., London.)
Gutman, R. G. 1976 Vibrated beds of powders. Part 1. A theoretical model for the vibrated bed. Trans. Inst. Chem. Engrs 54, 174–183.Google Scholar
Haff, P. K. 1983 Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134, 401–430.Google Scholar
Jenkins, J. T. & Richman, M. W. 1985 Grad's 13-moment system for a dense gas of inelastic spheres. Arch. Rat. Mech. Anal. 87, 355–377.Google Scholar
Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202.Google Scholar
Kroll, W. 1955 Fliesserscheinungen an Haufwerken in schwingenden Gafassen. Chem. Ingr.- Tech. 27, 33.Google Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.
Lun, C. K. K. & Savage, S. B. 1986 The effects of an impact velocity dependent coefficient of restitution on stresses developed by sheared granular materials. Acta Mech. 63, 15–44.Google Scholar
Lun, C. K. K., Savage, S. B., Jeffrey, D. J. & Chepurniy, N. 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140, 223–256.Google Scholar
Ogawa, S., Umemura, A. & Oshima, N. 1980 On the equations of fully fluidized granular materials. Z. Angew. Math. Phys. 31, 483–493.Google Scholar
Rátkai, G. 1976 Particle flow and mixing in vertically vibrated beds. Powder Technol. 15, 187–192.Google Scholar
Savage, S. B. 1983a Granular flows at high shear rates. In Theory of Dispersed Multiphase Flow (ed. R. E. Meyer), pp. 339–358. Academic.
Savage, S. B. 1983b Granular flows down rough inclines: Review and extension. In Mechanics of Granular Materials: New Models and Constitutive Relations (ed. J. T. Jenkins & M. Satake), pp. 261–282. Elsevier.
Savage, S. B. 1984 The mechanics of rapid granular flows. In Advances in Applied Mechanics, vol. 24 (ed. J. Hutchinson & T. Y. Wu), pp. 289–366. Academic.
Savage, S. B. & Jeffrey, D. J. 1981 The stress tensor in a granular flow at high shear rates. J. Fluid Mech. 110, 225–272.Google Scholar
Savage, S. B. & Sayed, M. 1984 Stresses developed by dry cohesionless granular materials sheared in an annular shear cell. J. Fluid Mech. 142, 391–430.Google Scholar
Shen, H. & Ackermann, N. L. 1982 Constitutive relationships for fluid-solid mixtures. J. Engng Mech. Div. ASCE 108, 748–763.Google Scholar
Suzuki, A., Takahashi, H. & Tanaka, T. 1968/9 Behaviour of a particle bed in a field of vibration. III. Mixing of particles in a vibrating bed. Powder Technol. 2, 78–81.Google Scholar
Takahashi, H., Suzuki, A. & Tanaka, T. 1968/9 Behaviour of a particle bed in a field of vibration. I. Analysis of particle motion in a vibrating vessel. Powder Technol. 2, 65–71.Google Scholar
Walker, J. 1982 The amateur scientist. Scient. Am. 247, 206–216.Google Scholar