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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.

Information

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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References

Avgousti, M. & Beris, A. N. 1993 Viscoelastic Taylor-Couette flow: bifurcation analysis in the presence of symmetries. Proc. R. Soc. Lond. A 443, 17–37.Google Scholar
Byars J. A., Öztekin, A., Brown, R. A. & McKinley, G. H. 1994 Spiral instabilities in the flow of highly elastic fluids between rotating parallel discs. J. Fluid Mech. 271, 173–218.Google Scholar
Crewthers, I., Huilgol, R. R. & Josza, R. J. 1991 Axisymmetric and nonaxisymmetric flows of a non-Newtonian fluid between coaxial rotating discs. Phil. Trans. R. Soc. Lond. A 337, 467–495.Google Scholar
Gottleib, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Application. SIAM.
Iooss, G. & Joseph, D. D. 1980 Elementary Stability and Bifurcation Theory. Springer.
Jackson, K. P. Walters, K & Williams, R. W 1984 A rheometrical study of Boger fluids. J. Non-Newtonian Fluid Mech. 14, 173–188.Google Scholar
Kármán, T. von 1921 Laminare und turbulente Reibung. Z. Angew. Math. Mech. 1, 233–252.Google Scholar
Ladyzhenskaya, O. A. 1969 The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach.
Larson, R. G. 1992 Instabilities in viscoelastic flows. Rheol. Acta 31, 213–263.Google Scholar
Larson, R. G., Shaqfeh, E. S. G. & Muller, S. J. 1990 A purely elastic instability in Taylor-Couette flow. J. Fluid Mech. 218, 573–600.Google Scholar
Magda, J. J. & Larson, R. G. 1988 A transition occurring in ideal elastic liquids during shear flow. J. Non-Newtonian Fluid Mech. 30, 1–19.Google Scholar
McKinley, G. H., Byars, J. A., Brown, R. A. & Armstrong, R. C. 1991 Observations on the elastic instability in cone-and-plate and plate-and-plate flow of a non-Newtonian fluid. J. Non-Newtonian Fluid Mech. 40, 201–229.Google Scholar
Olagunju, D. O. 1994 Effect of free surface and inertia on viscoelastic parallel plate flow. J. Rheol. 38, 151–168.Google Scholar
Öztekin, A. & Brown, R. A. 1993 Instability of a viscoelastic fluid between rotating parallel discs: analysis for the Oldroyd-B fluid. J. Fluid Mech. 255, 473–502.Google Scholar
Peyret, R. 1989 The Chebyshev multidomain approach to stiff problems in fluid Mechanics. In Proc. ICOSAHOM 1989 Conf. on Spectral and Higher Order Methods for Partial Differential Equations (ed. C. Canute & A. Quarteroni).
Phan-thien, N. 1983 Coaxial-disc flow of an Oldroyd-B fluid: exact solution and stability. J. Non-Newtonian Fluid Mech. 13, 325–340.Google Scholar
Saad, Y. 1992 Numerical Methods for Large Eigenvalue problems Manchester University Press.
Walsh, W. P. 1987 On the flow of a Non-Newtonian fluid between rotating coaxial discs. Z. Angew. Math. Phys. 38, 495–511.Google Scholar
Zebib, A. 1984 A Chebyshev method for the solution of boundary value problems. J. Comput. Phys. 53, 443–455.Google Scholar