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The bulk stress in a suspension of spherical particles of condensed phase in its slightly rarefied vapour gas

Published online by Cambridge University Press:  20 April 2006

Yoshimoto Onishi
Yoshimoto Onishi
Affiliation:
Department of Mechanical Engineering, University of Osaka Prefecture, Sakai 591, Japan
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Abstract

The rheological behaviour of a dilute suspension of spherical particles of condensed phase dispersed in its own slightly rarefied vapour gas is investigated on the basis of suspension theory (Batchelor 1970) and generalized slip-flow theory for a two-phase system of a gas and its condensed phase derived from the Boltzmann equation. The rarefaction of the gas and the phase-change process at the interfaces of the particles have the effect of reducing the Einstein coefficient of ϕ, volume fraction, in the expression for the effective viscosity in the suspension. In the case in which the pure rarefaction effect alone enters the problem, the coefficient is $\frac{5}{2}(1-2.702\,K)$, where K is the Knudsen number, a rarefaction parameter defined by K = l/L, l and L being respectively the mean free path of gas molecules and the radius of a spherical particle. When both the rarefaction and the phase-change process are taken into account, this becomes $\frac{5}{2} (1-3.533\,K)$. These modifications are not small, even at ordinary pressures, when the size of the particles is of the order of microns.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 175 - 186
Copyright
© 1972 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Batchelor, G. K. 1970 J. Fluid Mech. 41, 545.
Batchelor, G. K. & Green, J. T. 1972 J. Fluid Mech. 56, 401.
Bhatnager, P. L., Gross, E. P. & Krook, M. 1954 Phys. Rev. 94, 511.
Einstein, A. 1906 Ann. Phys. 19, 289.
Einstein, A. 1911 Ann. Phys. 34, 591.
Kennard, E. H. 1938 Kinetic Theory of Gases. McGraw-Hill.
Kogan, M. N. 1958 J. Appl. Math. Mech. 22, 597.
Landau, L. D. & Lifshitz, E. M. 1958 Statistical Physics. Pergamon.
Landau, L. D. & Lifshitz, E. M. 1966 Fluid Mechanics. Pergamon.
Onishi, Y. 1977a J. Phys. Soc. Japan 42, 2023.
Onishi, Y. 1977b J. Phys. Soc. Japan 43, 1434.
Pao, Y. P. 1971 Phys. Fluids 14, 306.
Sone, Y. 1966 J. Phys. Soc. Japan 21, 1836.
Sone, Y. 1972 Phys. Fluids 15, 1418.
Sone, Y. & Onishi, Y. 1978 J. Phys. Soc. Japan 44, 1981.
Taylor, G. I. 1932 Proc. R. Soc. Lond. A 138, 41.
Vincenti, W. G. & Kruger, C. H. 1965 Introduction to Physical Gas Dynamics. Wiley.
Welander, P. 1954 Arkiv Fysik 7, 507.