Finite-Amplitude Elastic Instability of Plane-Poiseuille Flow of Viscoelastic Fluids

[+] Author and Article Information
R. E. Khayat, N. Ashrafi

Department of Mechanical and Materials Engineering, University of Western Ontario, London, Ontario N6A 5B9, Canada

J. Appl. Mech 67(4), 834-837 (Jul 27, 1999) (4 pages) doi:10.1115/1.1308580 History: Received April 28, 1999; Revised July 27, 1999
Copyright © 2000 by ASME
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Bird, R. B., Armstrong, R. C., and Hassager, O., 1987, Dynamics of Polymeric Liquids, Vol. 1, 2nd Ed., John Wiley and Sons, New York.
Vinogradov,  G. V., Malkin,  A. Ya., Vanovskii,  Yu G., Borisenkova,  E. K., Yarlykov,  B. V., and Berezheneya,  G. V., 1972, J. Polym. Sci., Part A: Gen. Pap., 10, p. 1061.
Joseph,  D. D., Renardy,  M., and Saut,  J. C., 1985, “Hyperbolicity and Change of Type in the Flow of Viscoelastic Fluids,” Arch. Ration. Mech. Anal., 87, p. 213.
Denn,  M. M., 1990, “Issues in Viscoelastic Fluid Mechanics,” Annu. Rev. Fluid Mech., 22, p. 13.
Larson,  R. G., 1992, “Instabilities in Viscoelastic Flows,” Rheol. Acta, 31, p. 213.
Kolkka,  R. W., Malkus,  D. S., Hansen,  M. G., and Ierley,  G. R., 1988, “Spurt Phenomena of the Johnson-Segalman Fluid and Related Models,” J. Non-Newtonian Fluid Mech., 29, p. 303.
Malkus,  D. S., Nohel,  J. A., and Plohr,  B. J., 1990, “Dynamics of Shear Flow of a Non-Newtonian Fluid,” J. Comput. Phys., 87, p. 464.
Georgiou,  G. C., and Vlassopoulos,  D., 1998, “On the Stability of the Simple Shear Flow of a Johnson-Segalman Fluid,” J. Non-Newtonian Fluid Mech., 75, p. 77.
Sell, G. R., Foias, C., and Temam, R., 1993, Turbulence in Fluid Flows: A Dynamical Systems Approach, Springer-Verlag, New York.
Khayat,  R. E., 1994, “Chaos and Overstability in the Thermal Convection of Viscoelastic Fluids,” J. Non-Newtonian Fluid Mech., 53, p. 227.
Khayat,  R. E., 1995, “Nonlinear Overstability in the Thermal Convection of Viscoelastic Fluids,” J. Non-Newtonian Fluid Mech., 58, p. 331.
Khayat,  R. E., 1995, “Fluid Elasticity and Transition of Chaos in Thermal Convection,” Phys. Rev. E, 51, p. 380.
Avgousti,  M., and Beris,  A. N., 1993, “Non-Axisymmetric Subcritical Bifurcations in Viscoelastic Taylor-Couette Flow,” Proc. R. Soc. London, Ser. A, A443, p. 17.
Khayat,  R. E., 1995, “Onset of Taylor Vortices and Chaos in Viscoelastic Fluids,” Phys. Fluids A, 7, p. 2191.
Khayat,  R. E., 1997, “Low-Dimensional Approach to Nonlinear Overstability of Purely Elastic Taylor-Vortex Flow,” Phys. Rev. Lett., 78, p. 4918.
Graham,  M. D., 1998, “Effect of Axial Flow on Viscoelastic Taylor-Couette Instability,” J. Fluid Mech., 360, p. 341.
Ashrafi,  N., and Khayat,  R. E., 2000, “Finite Amplitude Taylor-Vortex Flow of Weakly Shear-Thinning Fluids,” Phys. Rev. E, 61, p. 1455.
Muller,  S. J., Shaqfeh,  E. S. J., and Larson,  R. G., 1993, “Experimental Study of the Onset of Oscillatory Instability in Viscoelastic Taylor-Couette Flow,” J. Non-Newtonian Fluid Mech., 46, p. 315.
Johnson,  M. W., and Segalman,  D., 1977, “A Model for Viscoelastic Fluid Behavior Which Allows Non-Affine Deformation,” J. Non-Newtonian Fluid Mech., 2, p. 278.
Khayat,  R. E., and Derdouri,  A., 1994, “Inflation of Hyperelastic Cylindrical Membranes as Applied to Blow Moulding, Part I. Axisymmetric Case,” Int. J. Numer. Methods Eng., 37, p. 3773.


Grahic Jump Location
Steady-state shear stress versus shear-rate curves for ζ=0.2 and ε∊[0,1]. The loci of the two extrema are also shown, which join into one curve denoted here by γ̇c. The curves in the figure resemble the pressure/stretch-ratio related to the inflation of a Mooney-Rivlin material (see Fig. 2 in 20).
Grahic Jump Location
Bifurcation diagrams for the normal stress difference, N(0,∞), at the center of the channel as function of We for ζ=0.2 and ε∊[0.06,0.08]. The smallest diagram corresponds to the highest viscosity ratio, ε. As ε exceeds a critical level (in this case 1/8), the (closed) diagram reduces to zero, as the base flow is always stable. The branches AB, CD, EF, and GH of diagram ε=0.06 are unstable, whereas the branches BC, DE, EF, FG, and HA are stable.



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