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Shear-induced particle diffusion and longitudinal velocity fluctuations in a granular-flow mixing layer

Published online by Cambridge University Press:  26 April 2006

S. S. Hsiau  and
M. L. Hunt
S. S. Hsiau
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
M. L. Hunt
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

In flows of granular material, collisions between individual particles result in the movement of particles in directions transverse to the bulk motion. If the particles were distinguishable, a macroscopic overview of the transverse motions of the particles would resemble a self-diffusion of molecules as occurs in a gas. The present granular- flow study includes measurements of the self-diffusion process, and of the corresponding profiles of the average velocity and of the streamwise component of the fluctuating velocity. The experimental facility consists of a vertical channel fed by an entrance hopper that is divided by a splitter plate. Using differently-coloured but otherwise identical glass spheres to visualize the diffusion process, the flow resembles a classic mixing-layer experiment. Unlike molecular motions, the local particle movements result from shearing of the flow; hence, the diffusion experiments were performed for different shear rates by changing the sidewall conditions of the test section, and by varying the flow rate and the channel width. In addition, experiments were also conducted using different sizes of glass beads to examine the scaling of the diffusion process. A simple analysis based on the diffusion equation shows that the thickness of the mixing layer increases with the square-root of downstream distance and depends on the magnitude of the velocity fluctuations relative to the mean velocity. The results are also consistent with other studies that suggest that the diffusion coefficient is proportional to the particle diameter and the square-root of the granular temperature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 251 , June 1993 , pp. 299 - 313
Copyright
© 1993 Cambridge University Press

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References

Ahn, H. 1989 Experimental and analytical investigations of granular materials: shear flow and convective heat transfer. PhD thesis, California Institute of Technology; Rep. E200.28.
Ahn, H., Brennen, C. E. & Sabersky, R. H. 1991 Measurements of velocity, velocity fluctuation, density, and stresses in chute flows of granular materials. Trans. ASME E: J. Appl. Mech. 58, 792–803.Google Scholar
Bridgwater, J. 1980 Self-diffusion coefficients in deforming powders. Powder Tech. 25, 129–131.Google Scholar
Buggisch, H. & Loffelmann, G. 1989 Theoretical and experimental investigations into local granulate mixing mechanisms. Chem. Engng Process. 26, 193–200.Google Scholar
Campbell, C. S. 1989 The stress tensor for simple shear flows of a granular material. J. Fluid Mech. 203, 449–473.Google Scholar
Campbell, C. S. 1990 Rapid granular flows. Ann. Rev. Fluid Mech. 22, 57–92.Google Scholar
Campbell, C. S. & Brennen, C. E. 1985 Computer simulations of granular shear flows. J. Fluid Mech. 52, 167–188.Google Scholar
Chapman, S. & Cowling, T. G. 1971 The Mathematical Theory of Non-uniform Gases, 3rd edn. Cambridge University Press.
Hsiau, S. S. & Hunt, M. L. 1992 Kinetic theory analysis of flow-induced particle diffusion and thermal conduction in granular material flows. J. Heat Transfer (in press); also in General Papers in Heat Transfer, HTD 204 (ed. R. Jensen et al.), pp. 41–48. ASME, New York.
Hunt, M. L. & Hsiau, S. S. 1992 Experimental measurements of particle diffusion and velocity profiles in a granular-flow mixing layer. In Advances in Micromechanics of Granular Materials (ed. H. H. Shen et al.) pp. 141–150. Elsevier.
Hwang, C. L. & Hogg, R. 1980 Diffusive mixing in flowing powders. Powder Tech. 26, 93–101.Google Scholar
Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic, particles. J. Fluid Mech. 130, 187–202.Google Scholar
Johnson, P. C., Nott, P. & Jackson, R. 1990 Frictional-collisional equations of motion for particulate flows and their application to chutes. J. Fluid Mech. 210, 501–535.Google Scholar
Kennard, E. H. 1938 Kinetic Theory of Gases. McGraw-Hill.
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 flowfield. J.Fluid Mech. 140, 223–256.CrossRefGoogle Scholar
Savage, S. B. 1979 Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech. 92, 53–96.Google Scholar
Savage, S. B. 1992 Disorder, diffusion and structure formation in granular flows. In Disorder and Granular Media (ed. D. Bideau). Elsevier.
Savage, S. B. & Jeffrey, D. J. 1981 The stress tensor in a granular flow at high shear rates. J. Fluid Mech. 110, 255–272.Google Scholar
Walton, O. R. & Braun, R. L. 1986 Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. J. Rheol. 30, 949–980.Google Scholar
Wang, D. G. & Campbell, C. S. 1992 Reynolds’ analogy for a shearing granular material. J. Fluid Mech. 244, 527–546.Google Scholar