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A Nonequilibrium Approach for Self-Diffusion in Unbounded Rapid Granular Flows

Published online by Cambridge University Press:  01 February 2011

Payman Jalali ,
Piroz Zamankhan  and
William Polashenski Jr
Payman Jalali
Affiliation:
Department of Energy Technology, Lappeenranta University of Technology, Lappeenranta, Finland
Piroz Zamankhan
Affiliation:
Department of Energy Technology, Lappeenranta University of Technology, Lappeenranta, Finland
William Polashenski Jr
Affiliation:
Lomic, Inc., PA 16803, U.S.A
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Abstract

A nonequilibrium simulation scheme is introduced to investigate the transverse diffusive motion in unbounded shear flows of smooth, monodisperse, inelastic spherical particles. A certain labeling algorithm is used in this scheme to extract a one-way particle mass flux which results a concentration gradient for the labeled particles. The self-diffusion coefficient can then be obtained from Fick's law. Using this scheme, one may find that the self-diffusion phenomenon across any layer inside the granular shear flow is analogous to the classic diffusion problem across a membrane. Under steady conditions, the current simulation results revealed that the particle diffusivity can be described by a linear law. This finding justifies the assumption of a linear law relationship in the kinetic theory type derivation of an expression for self-diffusivity. Moreover, it is shown that the results of self-diffusion coefficient obtained from the computer simulations are in agreement with the predictions of kinetic theory formulations in the range of solid volume fractions less than 0.5.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 627: Symposium BB – The Granular State , 2000 , BB4.7
Copyright
Copyright © Materials Research Society 2000

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References

REFERENCES

1. Natarajan, V.V.R., Hunt, M.L., and Taylor, E.D., J. Fluid Mech., 304, 1–25 (1995).Google Scholar
2. Menon, N., and Durian, D.J., Science, 275, 1920–1922 (1997).Google Scholar
3. Savage, S.B., and Dai, R., Mechanics of Materials, 16, 225–238 (1993).Google Scholar
4. Campbell, C.S., J. Fluid Mech., 348, 85–102 (1997).Google Scholar
5. Lees, A.W., and Edwards, S.F., J. Phys., C5, 1921–1929 (1972).Google Scholar
6. Boon, J.P., and Yip, S., Molecular Hydrodynamics, p. 48. New York: Dover Publications, Inc., 1980.Google Scholar
7. Jenkins, J.T., and Richman, M.W., Arch. Rat. Mech. Anal., 87, 355–377 (1985).Google Scholar
8. Erpenbeck, J.J., and Wood, W.W., “Molecular Dynamics Techniques for Hard-Core Systems” in Statistical Mechanics, Part B: Time-dependent Processes, Chapter 1. Berne, B. J., Ed., New York: Plenum 1977.Google Scholar
9. Allen, M.P., and Tildesley, D.J., Computer Simulation of Liquids, p. 24, 246. Oxford: Clarendon Press, 1997.Google Scholar
10. Lun, C.K.K., and Bent, A.A., J. Fluid Mech., 258, 335–353 (1994).Google Scholar
11. Schwager, T., and Pöschel, T., Phys. Rev. E, 57, 650–654 (1998).Google Scholar
12. Goldshtein, A., Shapiro, M., and Gutfinger, C., J. Fluid Mech. 316, 29–51 (1996).Google Scholar