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Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations

Published online by Cambridge University Press:  11 April 2006

E. J. Hinch  and
L. G. Leal
E. J. Hinch
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
L. G. Leal
Affiliation:
Chemical Engineering, California Institute of Technology, Pasadena
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Abstract

Approximate constitutive equations are derived for a dilute suspension of rigid spheroidal particles with Brownian rotations, and the behaviour of the approximations is explored in various flows. Following the suggestion made in the general formulation in part 1, the approximations take the form of Hand's (1962) fluid model, in which the anisotropic microstructure is described by a single second-order tensor. Limiting forms of the exact constitutive equations are derived for weak flows and for a class of strong flows. In both limits the microstructure is shown to be entirely described by a second-order tensor. The proposed approximations are simple interpolations between the limiting forms of the exact equations. Predictions from the exact and approximate constitutive equations are compared for a variety of flows, including some which are not in the class of strong flows analysed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 1 , 14 July 1976 , pp. 187 - 208
Copyright
© 1976 Cambridge University Press

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References

Barthès-Biesel, D. & Acrivos, A. 1973 Int. J. Multiphase Flow, 1, 1.
Bretherton, F. P. 1962 J. Fluid Mech. 14, 284.
Hand, G. L. 1962 J. Fluid Mech. 54, 423.
Hinch, E. J. & Leal, L. G. 1972 J. Fluid Mech. 52, 683.
Hinch, E. J. & Leal, L. G. 1973 J. Fluid Mech. 57, 753.
Hinch, E. J. & Leal, L. G. 1975 J. Fluid Mech. 71, 481.
Jeffery, G. B. 1922 Proc. Roy. Soc. A 102, 161.
Kramers, M. A. 1945 J. Chem. Phys. 14, 415.
Leal, L. G. & Hinch, E. J. 1971 J. Fluid Mech. 46, 685.
Leal, L. G. & Hinch, E. J. 1973 Rheologica Acta, 12, 127.
Prager, S. 1957 Trans. Soc. Rheol. 1, 53.
Scheraga, H. A. 1955 J. Chem. Phys. 23, 1526.
Scheraga, H. A., Edsall, J. T. & Gadd, J. O. 1951 J. Chem. Phys. 19, 110.