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Torsional flow: elastic instability in a finite domain

Published online by Cambridge University Press:  26 April 2006

Aaron Avagliano  and
Nhan Phan-Thien
Aaron Avagliano
Affiliation:
Department of Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
Nhan Phan-Thien
Affiliation:
Department of Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
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Abstract

A rotational shear flow is examined in the parallel plate geometry for the Oldroyd-B fluid. The Stokes solution is found to have eigenfunctions in an unbounded radial domain while it is unique for general boundary conditions in a finite radial domain. Critical conditions for the onset of an axisymmetric secondary flow are determined for the viscoelastic fluid, and we show that there is an almost linear relationship between the aspect ratio of the plates and the critical Deborah number for this model, especially at small values of the aspect ratio. The form of the initial secondary flow is also in agreement with experimental results obtained for a Boger fluid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 312 , 10 April 1996 , pp. 279 - 298
Copyright
© 1996 Cambridge University Press

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