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The drag on a cloud of spherical particles in low Reynolds number flow

Published online by Cambridge University Press:  29 March 2006

Christopher K. W. Tam
Christopher K. W. Tam
Affiliation:
Department of Aeronautics and Astronautics Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

A formula for the drag exerted on a cloud of spherical particles of a given particle size distribution in low Reynolds number flow is derived. It is found that the drag experienced by a particle depends only on the first three moments of the distribution function. A treatment of viscous interaction between N particles to the lowest order is carried out systematically. By appealing to the concept of ‘randomness’ of the particle cloud, equations describing the averaged properties of the fluid motion are derived. The averages are formed over a statistical ensemble of particle configurations. These mean flow equations so obtained are in a form resembling a generalized version of Darcy's empirical equation for the motion of fluid in a porous medium. The physical meaning of these equations is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 3 , 18 September 1969 , pp. 537 - 546
Copyright
© 1969 Cambridge University Press

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References

Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles Appl. Scientific Research, A1, 27.Google Scholar
Foldy, F. L. 1945 The multiple scattering of waves Phys. Rev. 67, 107.Google Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. New York: Prentice Hall.
Happel, J. & Epstein, N. 1954 Cubical assemblages of uniform spheres Ind. and Engng Chem. 46, 1187.Google Scholar
Keller, J. B. 1964 Stochastic equations and wave propagation in random media. Proc. of Symposia in Appl. Math. vol. XVI. Amer. Math. Soc.
Lamb, H. 1945 Hydrodynamics. 6th ed. New York: Dover.
Lax, M. 1951 Multiple scattering of waves Rev. Modern Phys. 23, 287.Google Scholar
Stimson, M. & Jeffery, G. B. 1926 The motion of two spheres in a viscous fluid Proc. Roy. Soc. Lond. 111, 110.Google Scholar
Twerksy, V. 1964 On propagation in random media of discrete scatters. Proc. of Symposia in Appl. Math. vol. xvi. Amer. Math. Soc.