Torsional flow: Elastic instability in a finite domain

Journal of Fluid Mechanics

Volumn 312, Issue , 1996, Pages 279-298

  Avagliano, Aaron ^a   Phan Thien, Nhan ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

DEBORAH NUMBER; ELASTIC INSTABILITY; FINITE RADIAL DOMAIN; OLDROYD-B FLUID; PARALLEL PLATE GEOMETRY; ROTATIONAL SHEAR FLOW; SECONDARY FLOW; STOKES SOLUTION;

ASPECT RATIO; BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; FLUIDS; GEOMETRY; MATHEMATICAL MODELS; SHEAR FLOW; STABILITY; VISCOELASTICITY;

ROTATIONAL FLOW;

ELASTICS; INSTABILITY; ROTATIONAL; SHEAR FLOW;

EID: 0030128427     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096002005     Document Type: Article

References (19)

1. 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.
2. 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.
3. 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.
4. GOTTLEIB, D. & ORSZAG, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Application. SIAM.
5. IOOSS, G. & JOSEPH, D. D. 1980 Elementary Stability and Bifurcation Theory. Springer.
6. JACKSON, K. P., WALTERS, K. & WILLIAMS, R. W. 1984 A rheometrical study of Boger fluids. J. Non-Newtonian Fluid Mech. 14, 173-188.
7. KÁRMÁN, T. VON 1921 Laminare und turbulente Reibung. Z. Angew. Math. Mech. 1, 233-252.
8. LADYZHENSKAYA, O. A. 1969 The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach.
9. LARSON, R. G. 1992 Instabilities in viscoelastic flows. Rheol. Acta 31, 213-263.
10. 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.
11. 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.
12. 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.
13. OLAGUNJU, D. O. 1994 Effect of free surface and inertia on viscoelastic parallel plate flow. J. Rheol. 38, 151-168.
14. 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.
15. 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. Canuto & A.Quarteroni).
16. PHAN-THIEN, N. 1983 Coaxial-disc flow of an Oldroyd-B fluid: exact solution and stability. J. Non-Newtonian Fluid Mech. 13, 325-340.
17. SAAD, Y. 1992 Numerical Methods for Large Eigenvalue problems. Manchester University Press.
18. WALSH, W. P. 1987 On the flow of a Non-Newtonian fluid between rotating coaxial discs. Z. Angew. Math. Phys. 38, 495-511.
19. ZEBIB, A. 1984 A Chebyshev method for the solution of boundary value problems. J. Comput. Phys. 53, 443-455.