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Time-reversed flows

Published online by Cambridge University Press:  28 March 2006

John C. Slattery
John C. Slattery
Affiliation:
Department of Chemical Engineering, Northwestern University, Evanston, Illinois
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Abstract

Under the assumption that the local acceleration and inertial terms are to be neglected in the equation of motion, a comparison is made between the unsteadystate movement of a suspension of particles and the same problem in reversed (or negative) time. The formalized discussion confirms Bretherton's (1962) conclusion that, if in a steady unidirectional shear flow at small Reynolds number a rotationally symmetric particle twice assumes a position with its axis of rotation in the plane perpendicular to the flow, its orbit must be periodic. The reversibility phenomena observed by S. G. Mason (1963) in dilute and concentrated suspensions are explained as well.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 19 , Issue 4 , August 1964 , pp. 625 - 630
Copyright
© 1964 Cambridge University Press

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References

Bretherton, F. P. 1962 J. Fluid Mech. 14, 284.
Coleman, B. D. & Noll, W. 1961 Ann. N.Y. Acad. Sci. 89, 672.
Markovitz, H. & Brown, D. R. 1963 Trans. Soc. Rheol. 7, 137.
Mason, S. G. 1963 The Microrheology of Suspensions. Invited Paper, 4th Int. Congr. Rheol., Brown University, Providence, R.I.
Noll, W. 1958 Arch. Rat. Mech. Anal. 2, 197.
Reiner, M. 1945 Amer. J. Math. 67, 350.
Rivlin, R. S. 1947 Nature, Lond., 160, 611.
Truesdell, C. & Toupin, R. A. 1960 Handbuch der Physik, Vol. III/1, p. 531. Berlin: Springer-Verlag.