Purely elastic instabilities in viscometric flows

Annual Review of Fluid Mechanics

Volumn 28, Issue , 1996, Pages 129-185

  Shaqfeh, Eric S G ^a  

^a Stanford University ^*  (United States)

Author keywords

Bifurcation; Normal stresses; Polymer; Rheology

Indexed keywords

EID: 0344936448     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.fl.28.010196.001021     Document Type: Article

References (81)

1. Avgousti M, Beris AN. 1993a. Non-axi symmetric modes in viscoelastic Taylor-Couette flow. J. Non-Newtonian Fluid Mech. 50:2252
2. Avgousti M, Beris AN. 1993b. Viscoelastic Taylor-Couette flow: bifurcation analysis in the presence of symmetries, Proc. R. Soc. London Ser. A 443:17-37
3. Avgousti M, Liu B, Beris A. 1993. Spectral methods for the viscoelastic time-dependent flow equations with applications to Taylor-Couette flow. Int. J. Numer. Methods Fluids 17:49-74
4. Beard DW, Davies MH, Walters K. 1966. The stability of elastic-viscous flow between rotating cylinders. Part 3. Overstability in viscous and Maxwell Fluids. J. Fluid Mech. 24:321
5. Bennett MJ, Brown RA. 1989. Cellular dynamics during directional solidification: interaction of multiple cells. Phys. Rev. B 39(6):39
6. Beris AN, Avgousti M, Souvliotis A. 1992. Spectral calculations of viscoelastic flows: Evaluation of the Giesekus constitutive equation in model flow problems. J. Non-Newtonian Fluid Mech. 44:197-228
7. Binnington B, Boger DV. 1986. Remarks on non-shear thinning elastic liquids. Polymer Eng. Sci. 26:133-38
8. Bird RB, Curtiss CF, Hassager O. 1987a. Dynamics of Polymeric Liquids, Vol. 1, Fluid Mechanics. New York: Wiley. 649 pp. 2nd ed
9. Bird RB, Curtiss CF, Armstrong RC, Hassager O. 1987b. Dynamics of Polymeric Liquids, Vol. 2, Kinetic Theory. New York: Wiley. 439 pp, 2nd ed.
10. Bixler NE, Kraynik AM. 1987. The onset of Taylor vortices in flows with a circumferential pressure gradient: application to the helical screw rheometer. Proc. XIth Can. Congr, Appl. Mech., Univ. Alberta, Edmonton
11. Boger DV. 1977/78. A highly elastic constant viscosity fluid. J. Non-Newtonian Fluid Mech. 3:87-91
12. Braumert BM, Muller SJ. 1995. Flow visualization of the elastic Taylor-Couette instability in Boger fluids. Rheol. Acta 34: In press
13. Byars JA, Oztekin A, Brown RA, McKinley GH. 1994. Spiral instabilities in the flow of highly elastic fluids between rotating parallel disks. J. Fluid Mech. 271:173
14. Cathey CA, Fuller GG. 1990. The optical and mechanical response of the flexible polymer solutions to extensional flow. J. Non-Newtonian Fluid Mech. 34:63
15. Chandrasekhar S. 1961. Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon
16. Chiba K, Sakatani T, Nakamura K. 1990. Anomalous flow patterns in the viscoelastic entry flow through a planar contraction. J. Non-Newtonian Fluid Mech. 36:193-203
17. Chiba K, Tanaka S, Nakamura K. 1992. The structure of anomalous entry flow patterns through a planar contraction. J. Non-Newtonian Fluid Mech. 42:315-22
18. Chilcott MD, Rallison JM. 1988. Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newtonian Fluid Mech. 29:381
19. Coleman BD, Noll W. 1960. An approximation theorem for functionals, with applications in continuum mechanics. Arch. Rat. Mech. Anal. 6:355
20. Conte SD. 1966. The numerical solution of linear boundary value problems. SIAM Rev. 8:309-21
21. Crawford JD, Knobloch E. 1991. Symmetry and symmetry-breaking bifurcations in fluid dynamics. Annu. Rev. Fluid. Mech. 23:341-87
22. Dean WR. 1928. Fluid motion in a curved channel. Proc. R. Soc. London Ser. A 121:402-20
23. DiPrima RC. 1959. The stability of viscous flow between rotating concentric cylinders with a pressure gradient acting around the cylinders. J. Fluid Mech. 6:462-68
24. Drazin PG, Reid WH. 1981. Hydrodynamic Stability. Cambridge: Cambridge Univ. Press
25. Dris I, Shaqfeh ESG. 1995. On purely elastic instabilities in eccentric cylinder flow. J. Non-Newtonian Fluid Mech. 56:349-60
26. Evans AR, Shaqfeh ESG, Frattini PL. 1994. Observations of polmyer conformation during flow through a fixed fiber bed. J. Fluid Mech. 281:319-56
27. Flory PJ. 1969. Statistical Mechanics of Chain Molecules. New York: Wiley
28. Giesekus H. 1966. Zur Stabilität von Strömungen viskoelastischen Flüssigkeiten. Rheol. Acta 5:239-52
29. Ginn RF, Denn MM. 1969. Rotational stbility in viscoelastic liquids: theory. AIChE J. 15:450
30. Golubitsky M, Schaeffer DG, Stewart IN. 1988. Singularities and Groups in Bifurcation Theory. New York: Springer-Verlag
31. Gorodtsov VA, Leonov AI. 1967. On a linear instability of a plane parallel Couette flow of viscoelastic fluid. J. Appl. Math. Mech. 31:310
32. Griffiths DF, Jones DT, Walters K. 1969. A flow reversal due to edge effects. J. Fluid Mech. 36:161-75
33. Hill CT. 1972. Nearly viscometric flow in the disk and cylinder system II. Exp. Trans. Soc. Rheol. 16(2):213-45
34. Ho TC, Denn MM, 1977/78, Stability of plane Poiseuille flow of a highly elastic fluid. J. Non-Newtonian Fluid Mech. 3:179
35. Ioos G, Joseph DD. 1980. Elementary Stability and Bifurcation Theory. New York: Springer-Verlag
36. Jackson KP, Walters K, William RW. 1984. A rheometrical study of Boger fluids. J. Non-Newtonian Fluid Mech. 14:173
37. Joo YL, Shaqfeh ESG. 1991. Viscoelastic Poiseuille flow through a curved channel: a new elastic instability. Phys. Fluids A 3:1691-94
38. Joo YL, Shaqfeh ESG. 1992b. The effects of inertia on the viscoelastic Dean and Taylor-Couette flow instabilities with application to coating flows. Phys. Fluids A 4(1):2415
39. Joo YL, Shaqfeh ESG. 1992a. A purely elastic instability in Dean and Taylor-Dean flow. Phys. Fluids A 4(3):524-42
40. Joo YL, Shaqfeh ESG. 1994. Observations of purely elastic instabilities in the Taylor-Dean flow of a Boger fluid. J. Fluid Mech. 262:27-73
41. Kemblowski Z, Sek J, Budzynski P. 1988. The concept of a rotational rheometer with helical screw impeller. Rheol. Acta 27:82-91
42. Kraynik A, Aubert JH, Chapman RN. 1984. The helical screw rheometer. Proc. IX Int. Congr. on Rheology, Mexico
43. Larson RG. 1988. Constitutive Equations for Polymer Melts and Solutions. London: Butterworth
44. Larson RG. 1992. Instabilities in viscoelastic flows. Rheol. Acta. 31:213
45. Larson RG, Muller SJ, Shaqfeh ESG. 1994. The effect of fluid rheology on the elastic Taylor-Couette instability. J. Non-Newtonian Fluid Mech. 51:195-225
46. Larson RG, Shaqfeh ESG, Muller SJ. 1990. A purely viscoelastic instability in Taylor-Couette flow. J. Fluid Mech. 218:573-600
47. Laun H, Hingmann R. 1990. Rheological characterization of the fluid M1 and of its components. J. Non-Newtonian Fluid Mech. 35:137-57
48. Lawler JV, Muller SJ, Brown RA, Armstrong RC. 1986-92. Laser Doppler velocimetry measurements of velocity fields and transitions in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 20:51
49. Mackay ME, Boger DV. 1987. An explanation of the rheological properties of Boger fluids. J. Non-Newtonian Fluid Mech. 22:235-43
50. Magda JJ, Larson RG. 1988. A transition occurring in ideal elastic liquids during shear flow. J. Non-Newtonian Fluid Mech. 30:1-19
51. Magda JJ, Lou J, Bark SG. 1991. Second normal stress difference of a Boger fluid. Polymer 32:2000-9
52. Malik MR, Wilkinson SP, Orszag SA. 1981. Instability and transition in rotating disk flow. AIAA J. 19:1131-38
53. McKinley GH, Byars JA, Brown RA, Armstrong RC. 1991b. Observations on the elastic instability in cone-and-plate and parallel-plate flows of a polyisobutylene Boger fluid. J. Non-Newtonian Fluid Mech. 40:201-29
54. McKinley GH, Oztekin A, Byars JA, Brown RA. 1995. Self-similar spiral instabilities in the elastic flows between a cone and a plate. J. Fluid Mech. 285:123-64
55. McKinley GH, Raiford WP, Brown RA, Armstrong RC. 1991a. Non-linear dynamics of viscoelastic flow in axisymmetric abrupt contractions. J. Fluid Mech. 223:411
56. Muller SJ. 1986. Experimental analysis of flow through an axisymmetric sudden contraction: rheological characterization and LDV measurements. PhD thesis. Dept. Chem. Eng., MIT, Cambridge, MA
57. Muller SJ, Larson RG, Shaqfeh ESG. 1989. A purely elastic transition in Taylor-Couette flow. Rheol. Acta 28:499-503
58. Muller SJ, Shaqfeh ESG, Larson RG. 1993. Experimental studies of the onset of oscillatory instability in viscoelastic Taylor-Couette flow. J. Non-Newtonian Fluid Mech. 46:315-30
59. Mutubazi I, Normand C, Peerhossaini H, Wesfried JE. 1989. Oscillatory modes in the flow between two horizontally corotating cylinders with a partially filled gap. Phys. Rev. A 39:763-71
60. Mutabazi I, Hegseth JJ, Andereck CD. 1990. Spatiotemporal pattern modulations in the Taylor-Dean system. Phys. Rev. Lett. 64:1729-32
61. Newell AC, Passat T, Lega J. 1993. Order parameter equations for patterns. Annu. Rev. Fluid Mech. 25:399-453
62. Nguyen QD, Boger DV. 1979. The kinematics and stability of die entry flows. J. Non-Newtonian Fluid Mech. 5:353
63. Northey PJ, Armstrong RC, Brown RA. 1992. Finite-amplitude time-periodic states in viscoelastic Taylor-Couette flow described by the UCM model. J. Non-Newtonian Fluid Mech. 42:117-39
64. Oztekin A, Brown RA. 1993. Instability of a viscoelastic fluid between rotating parallel disks: analysis for the Oldroyd-B fluid. J. Fluid Mech. 255:473-502
65. Oztekin A, Brown RA, McKinley GH. 1994. Quantitative prediction of the viscoelastic instability in cone-and-plate flow of a Boger fluid using a multi-mode Giesekus model. J. Non-Newtonian Fluid Mech 54:351-77
66. Phan-Thien N. 1983. Coaxial-disk flow of an Oldroyd-B fluid: exact solution and stability. J. Non-Newtonian Fluid Mech. 13:325-40
67. Phan-Thien N. 1985. Cone and plate flow of the Oldroyd-B fluid is unstable. J. Non-Newtonian Fluid Mech. 17:37-44
68. Quinzani LM, McKinley GH, Brown RA, Armstrong RC. 1991. Modelling the rheology of polyisobutylene solutions. J. Rheol. 34:705-48
69. Rayleigh L. 1880. On the stability, or instability, of certain fluid motions. Proc. London Math. Soc. 11:57-70
70. Renardy M, Renardy Y. 1986. Linear stability of plane Couette flow of an upper convected Maxwell fluid. J. Non-Newtonian Fluid Mech. 22:23-33
71. Rhee HS, Koseff JL, Street RL. 1984. Flow visualization of a recirculating flow by rheoscopic liquid and liquid crystal techniques. Exp. Fluids 2:57-64
72. Shaqfeh ESG, Larson RG, Fredrickson GH. 1989. The stability of gravity driven viscoelastic film-flow at low to moderate Reynolds number. J. Non-Newtonian Fluid Mech. 31:87
73. Shaqfeh ESG, Muller SJ, Larson RG. 1992. The effects of gap width and dilute solutions properties on the viscoelastic instability. J. Fluid Mech. 235:285-317
74. Sridhar T. 1990. An overview of the project M1. J. Non-Newtonian Fluid Mech. 35:85-92
75. Sridhar T, Gupta RK, Boger DV, Binnington B. 1986. Steady spinning of the Oldroyd fluid B. II: Experimental results. J. Non-Newtonian Fluid Mech. 21:115-26
76. Steiert P, Wolff C. 1990. Rheological properties of a polyisobutylene in a kerosene/polybutene mixture in simple shear flow. J. Non-Newtonian Fluid Mech. 35:189-96
77. Sun Z-S, Denn MM. 1972. Stability of rotational Couette flow of polymer solutions. AIChE J. 18:1010
78. Sureshkumar R, Beris AN, Avgousti M. 1994. Non-axisymmetric subcritical bifurcations in viscoelastic Taylor-Couette flow. Proc. R. Soc. London Ser. A 447:135-53
79. Tanner RI. 1985. Engineering Rheology. New York: Oxford Univ. Press
80. Taylor GI. 1923. Stability of a viscous liquid contained between rotating cylinders. Phil. Trans. R. Soc. London Ser. A 223:289-343
81. Zebib A. 1987. Removal of spurious modes encountered in solving stability problems by spectral methods. J. Comput. Phys. 70:521-25