Instability of Inelastic Shear-Thinning Liquids in a Couette Flow Between Concentric Cylinders

[+] Author and Article Information
O. Coronado-Matutti, P. R. Souza Mendes, M. S. Carvalho

Department of Mechanical Engineering, Pontifı́cia Universidade Católica do Rio de Janeiro, Rua Marque⁁s de São Vicente 225, Gávea, Rio de Janeiro, RJ, 22453-900, Brazile-mail: msc@mec.puc-rio.br

J. Fluids Eng 126(3), 385-390 (Jul 12, 2004) (6 pages) doi:10.1115/1.1760537 History: Received April 11, 2003; Revised January 05, 2004; Online July 12, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Taylor,  G. I., 1923, “Stability of a viscous liquid contained between two rotating cylinders,” Philos. Trans. R. Soc. London, Ser. A, 289–343.
Gravas,  N., and Martin,  B. W., 1978, “Instability of viscous axial flow in annuli having a rotating inner cylinder,” J. Fluid Mech., 86(2), 385–394.
Andereck,  C. D., Liu,  S. S., and Swinney,  H. L., 1986, “Flow regimes in a circular Couette system with independently rotating cilinders,” J. Fluid Mech., 164, 155–183.
Lueptow,  R. M., Docter,  A., and Min,  K., 1992, “Stability of axial flow in an annulus with a rotating inner cylinder,” Phys. Fluids A, 4(11), 2446–2455.
Chandrasekhar, S., “Hydrodynamic and hydromagnetic stability,” Dover Publications, Inc. New York (1961).
Diprima,  R. C., 1960, “The stability of a viscous fluid between rotating cylinders with an axial flow,” J. Fluid Mech., 9(4), 621–631.
Lee,  M. H., 2001, “The stability of spiral flow between coaxial cylinders,” Comp. Math. Appl., 41, 289–300.
Muller,  S. J., Larson,  R. G., and Shaqfeh,  E. S. G., 1989, “A purely elastic transition in Taylor-Couette flow,” Rheol. Acta, 28, 499–503.
Shaqfeh,  E. S. G., 1996, “Purely Elastic Instability in Viscometric Flows,” Annu. Rev. Fluid Mech., 28, 129–185.
Larson,  R. G., 1989, “Taylor-Couette stability analysis for Doi-Edwards Fluid,” Rheol. Acta, 28, 504–510.
Al-Mubaiyedh,  U. A., Sureshkumar,  R., and Khomami,  B., 2002, “The effect of viscous heating on the stability of Taylor-Couette flow,” J. Fluid Mech., 462, 111–132.
White,  J. M., and Muller,  S. J., 2003, “Experimental studies on the effect of viscous heating on the hydrodynamic stability of viscoelastic Taylor-Couette flow,” J. Rheol., 47(6), 1467–1492.
Miller, C., “A Study of Taylor-Couette Stability of Viscoelastic Fluids,” Ph.D. Thesis, University of Michigan (1967).
Lockett,  T. J., Richardson,  S. M., and Worraker,  W. J., 1992, “The stability of inelastic non-Newtonian fluids in Couette flow between concentric cylinders: a finite-element study,” J. Non-Newtonian Fluid Mech., 43, 165–177.
Bolstad,  J. H., and Keller,  H. B., 1986, “A multi-grid continuation method for elliptic problems with folds,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput., 7(4), 1081.
Recktenwald,  A., Lucke,  M., and Muller,  H. W., 1993, “Taylor vortex formation in axial through-flow: Linear and weakly non-linear analysis,” Phys. Rev. E, 48, 4444.
Ali,  M. E., Mitra,  D., Schwille,  J. A., and Lueptow,  R. M., 2002, “Hydrodynamic stability of a suspension in cylindrical Couette flow,” Phys. Fluids, 14(3), 1236–1243.


Grahic Jump Location
Geometrical configuration of flow between concentric rotating cylinders
Grahic Jump Location
Sketch of the phase diagram of the flow between concentric rotating cylinders. Continuous lines represent stable branches.
Grahic Jump Location
Solution path computed with both meshes tested. The results are virtually insensitive to the level of discretization.
Grahic Jump Location
(a) Solution path for Newtonian liquid as Taylor number rises. The radius ratio is Π=0.6. The flow states are characterized by the intensity of the flow in the axial direction. (b) Derivative of the flow intensity in the axial direction with respect to Taylor number. The critical condition is defined as the value at which the derivative is maximum.
Grahic Jump Location
Evolution of the vortex pattern as the Taylor number rises above the critical value. The radius ratio is Π=0.6.
Grahic Jump Location
Critical Taylor number for Newtonian liquids as a function of the radius ratio Π≡ri/ro
Grahic Jump Location
Comparison of Lockett’s critical Taylor number for inelastic shear-thinning liquids obtained in this work with those predicted by linear stability analysis
Grahic Jump Location
Critical conditions at the onset of the instability as a function of the power-law index n and high-shear viscosity η. λ=0.1 s and Π=0.95. The results are also presented in terms of a modified Taylor Number Tamod.
Grahic Jump Location
Critical Taylor number as a function of the radius ratio Π and power-law index n. λ=0.1 s. (a) η=0.01 Pa.s and (b) η=0.0001 Pa.s.
Grahic Jump Location
Results presented in Fig. 9 in terms of the modified Taylor number, that takes into account the shear-thinning effect on the definition of the Taylor number
Grahic Jump Location
Critical Taylor number as a function of the time constant of the Carreau viscosity function. η=0.0001 Pa.s,n=0.8 and Π=0.95.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In