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Interfacial shapes between two superimposed rotating simple fluids

Published online by Cambridge University Press:  20 April 2006

H. A. Tieu ,
D. D. Joseph  and
G. S. Beavers
H. A. Tieu
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455 Present address: Goodyear Tire and Rubber Company, Akron, Ohio.
D. D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455
G. S. Beavers
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455
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Abstract

The interfacial shape of two immiscible simple fluids in a vertical cylinder which oscillates about its axis is investigated using the theory of domain perturbations. The perturbation stresses are expressed by integrals over the history of the deformation. At first order the azimuthal velocity field satisfies the requirements of continuity in velocity and shear stresses across the interface. At second order the solution consists of a mean part and a time-periodic part varying at twice the frequency of the cylinder. The mean problem is inverted for the mean secondary flow, pressure and interfacial shape. Experimental data for two polymeric oils (TLA227 and STP) show qualitative agreement with theoretical predictions for the mean interfacial shapes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 145 , August 1984 , pp. 11 - 70
Copyright
© 1984 Cambridge University Press

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