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Torsional flow: effect of second normal stress difference on elastic instability in a finite domain

Published online by Cambridge University Press:  25 March 1998

AARON AVAGLIANO  and
NHAN PHAN-THIEN
AARON AVAGLIANO
Affiliation:
Department of Mechanical & Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
NHAN PHAN-THIEN
Affiliation:
Department of Mechanical & Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
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Abstract

A rotational shear flow is examined in the bounded parallel-plate geometry for a four-constant Oldroyd-type fluid which has a constant viscosity, and constant first and second normal stress coefficients. A new type of Galerkin spectral technique is introduced to solve the resulting two-dimensional stiff boundary value problem. We show that even a small second normal stress difference can lead to a significant increase (nearly 100%) in the stability of the base torsional flow. Beyond a critical Deborah number the secondary flow, in the form of travelling waves, appears to be confined between two critical radii, in qualitative agreement with the experimental results of Byars et al. (1994). The mechanism behind this instability is investigated for dilute polymer solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 359 , 25 March 1998 , pp. 217 - 237
Copyright
© 1998 Cambridge University Press

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