Constitutive equations for viscoelastic liquids: Formulation, analysis and comparison with data

Rheology Series

Volumn 8, Issue C, 1999, Pages 519-575

  Leonov, A I ^a  

^a The University of Akron   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957068573     PISSN: 01693107     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0169-3107(99)80040-9     Document Type: Article

References (127)

1. Odroyd. Proc. Roy. Soc. A200 (1950) 1063
2. Oldroyd. Proc. Roy. Soc. A245 (1958) 278
3. Rivlin. Research Frontiers in fluid Dynamics 144 (1965), Interscience, New York
4. Truesdell, and Noll W. The Non-Linear Field Theories of Mechanics (1992), Springer, New York
5. Coleman. Arch. Rat. Mech. Anal. 17 (1964) 1
6. Coleman. Arch. Rat. Mech. Anal. 17 (1964) 230
7. Coleman, and Mizel V.J. Arch. Rat. Mech. Anal. 29 (1968) 105
8. de Gennes. Scaling Concepts in Polymer Physics (1979), Cornell University, Ithaka, New York
9. Green, and Tobolsky A.V. J. Chem. Phys. 14 (1946) 80
10. Lodge. Trans. Faraday Soc. 52 (1956) 120
11. Yamamoto. J. Phys. Soc. Japan 11 (1956) 413
12. Yamamoto. J. Phys. Soc. Japan 12 (1957) 1148
13. Yamamoto. J. Phys. Soc. Japan 13 (1958) 1200
14. Treloar. Physics of Rubber Elasticity. 3rd ed. (1975), Oxford University Press, Oxford
15. Edwards. Proc. Phys. Soc. 92 (1967) 9
16. Doi, and Edwards S.F. J. Chem. Soc., Faraday Trans. II 74 (1978) 560
17. Doi, and Edwards S.F. J. Chem. Soc., Faraday Trans. II 74 (1978) 918
18. Doi, and Edwards S.F. J. Chem. Soc., Faraday Trans. II 74 (1978) 1818
19. Doi, and Edwards S.F. J. Chem. Soc., Faraday Trans. II 75 (1978) 38
20. Curtiss, and Bird R.B. J. Chem. Phys. 74 (1981) 2016
21. Bird, and Deaguiar J.R. J. Non-Newton. Fluid Mech. 13 (1983) 149
22. Bird, and Deaguiar J.R. J. Non-Newton. Fluid Mech. 13 (1983) 161
23. Curtiss, Bird R.B., and Hassager O. Adv. Chem. Phys. 35 (1976) 31
24. Bird, Armstrong R.C., and Hassager O. Dynamics of Polymeric Liquids. 2nd Ed. Vol. I & II (1987), John Wiley and Sons, New York
25. Pokrovsky, and Volkov V.S. Visokomolekularnie Soed. (Russian) A20 (1978) 2700
26. Volkov. Int. J. Polym. Mater. 9 (1982) 115
27. Schweizer. J. Chem. Phys. 91 (1989) 5802
28. Schweizer. J. Chem. Phys. 91 (1989) 5822
29. Schweizer. J. Non-Cryst. Solids 131-133 (1991) 643
30. Leonov. Rheol. Acta 15 (1976) 85
31. Leonov. J. Non-Newton. Fluid Mech. 25 (1987) 1
32. Dashner, and Vanarsdale W.E. J. Non-Newton. Fluid Mech. 8 (1981) 59
33. Dashner, and Vanarsdale W.E. J. Non-Newton. Fluid Mech. 8 (1981) 69
34. Larson. Constitutive Equations for Polymer Melts and Solutions (1988), Butterworth, Boston
35. Hunter, and Slemrod M. Phys. Fluids 26 (1983) 2345
36. Ramamurthy. J. Rheol. 30 (1986) 337
37. Tanner. Engineering Rheology (1992), Clarendon Press, Oxford
38. Janeschitz-Kriegl. Polymer Melt Rheology and Flow Birefringence (1983), Springer, New York
39. Pearson. Mechanics of Polymer Processing (Part I: Polymers, Mechanics and Rheology) (1985), Elsevier, New York
40. Leonov, and Prokunin A.N. Nonlinear Phenomena in Flows of Viscoelastic Polymer Fluids (1994), Chapman & Hall, London
41. Grmela. Physica D21 (1986) 179
42. Grmela. Phys. Lett. A130 (1988) 81
43. Beris, and Edwards B.J. J. Rheol. 34 (1990) 55
44. Beris, and Edwards B.J. J. Rheol. 34 (1990) 503
45. Leonov. J. Non-Newton. Fluid Mech. 42 (1992) 323
46. Jongschaap. Physica A94 (1978) 531
47. Jongschaap, de Haas K.H., and Damen C.A.J. J. Rheol. 38 (1994) 769
48. Kwon, and Shen S. Rheol. Acta 23 (1984) 217
49. Kwon, and Shen S. Rheol. Acta 24 (1985) 175
50. Simhambhatla, and Leonov A.I. Rheol. Acta 34 (1995) 259
51. Leonov. Polym. Internat. 36 (1995) 187
52. De Groot, and Mazur P. Non-Equilibrium Thermodynamics (1962), North-Holland, Amsterdam
53. Gyarmati. Non-Equilibrium Thermodynamics. Field Theory and Variational Principles (1970), Springer, New York
54. Hulsen. J. Non-Newton Fluid Mech. 38 (1990) 93
55. Murnaghan. Amer. J. Math. 59 (1937) 235
56. Leonov. Ann. N.-Y. Acad. Sci. 410 (1983) 23
57. Stickforth. Rheol. Acta 25 (1986) 447
58. accepted for publication in. Leonov. On the constitutive equations for non-isothermal bulk relaxation. Macromolecules (1997)
59. Gordon, and Schowalter W.R. Trans. Soc. Rheol. 16 (1972) 79
60. Johnson Jr., and Segalman D. J. Non-Newton. Fluid Mech. 2 (1977) 255
61. Phan Thien, and Tanner R.I. J. Non-Newton. Fluid Mech. 2 (1977) 353
62. Phan Thien. J. Rheol. 22 (1978) 259
63. Larson, and Monroe K. Rheol. Acta 23 (1984) 10
64. White, and Metzner A.B. J. Appl Polym. Sci. 7 (1963) 1867
65. Giesekus. Rheol. Acta 21 (1982) 366
66. Larson. J. Rheol. 28 (1984) 545
67. Simhambhatla, and Leonov A.I. Rheol. Acta 32 (1993) 259
68. Rivlin, and Sawyers K.N. Ann. Rev. Fluid. Mech. 8 (1971) 17
69. Kaye. College of Aeronautics, Cranford, U. K., Note No. 134 (1962)
70. Bernstein, Kearsley E.A., and Zapas L.J. Trans. Soc. Rheol. 7 (1963) 391
71. Kwon, and Leonov A.I. Rheol. Acta 33 (1994) 398
72. Wagner, Raible T., and Meissner J. Rheol. Acta 18 (1979) 427
73. Wagner, and Demarmels A. J. Rheol. 34 (1990) 943
74. Luo, and Tanner R.I. Int. J. Num. Meth. Eng. 25 (1988) 9
75. Papanastasiou, Scriven L.E., and Macosko C.W. J. Rheol. 27 (1983) 387
76. Larson, and Monroe K. Rheol. Acta 26 (1987) 208
77. Currie, Astarita G., Marrucci G., and Nicolais L. Rheology Vol. 1 (1980), Plenum, New York
78. Yen, and McIntire L.V. Trans. Soc. Rheol. 16 (1972) 711
79. Zapas. J. Res. Natl. Bur. Std. 70A (1966) 565
80. Ogden. Proc. Roy. Soc. A326 (1972) 565
81. Mooney. J. Appl. Phys. 11 (1940) 582
82. Valanis, and Landel R.F. J. Appl. Phys. 38 (1967) 2997
83. Blatz, Sharda S.C., and Tschoegl N.W. Trans. Soc. Rheol. 18 (1974) 145
84. Crochet, Davies A.R., and Walters K. Numerical Simulation of Non-Newtonian Flow (1984), Elsevier, Amsterdam
85. Dupret, and Marchal J.M. J. Non-Newton. Fluid Mech. 20 (1986) 143
86. Joseph. Fluid Mechanics of Viscoelastic Liquids (1990), Springer, New York
87. Rutkevich. J. Appl. Math. Mech. 33 (1969) 30
88. Rutkevich. J. Appl. Math. Mech. 33 (1969) 573
89. Rutkevich. J. Appl. Math. Mech. 34 (1970) 35
90. Godunov. Elements of Continuum Mechanics (1978), Nauka, Moscow
91. Joseph, Renardy M., and Saut J.C. Arch. Rat. Mech. Anal. 87 (1985) 213
92. Joseph, and Saut J.C. J. Non-Newton. Fluid Mech. 20 (1986) 117
93. Verdier, and Joseph D.D. J. Non-Newton. Fluid Mech. 31 (1989) 325
94. Kreiss. Numerical Methods for Solving Time-Dependent Problems for Partial Differential Equations (1978), Les presses de l'Universite de Montreal, Montreal
95. Strang. J. Diff. Eq. 2 (1966) 107
96. Baker, and Ericksen J.L. J. Wash. Acad. Sci. 44 (1954) 33
97. Zee, and Sternberg E. Arch. Rat. Mech. Anal. 83 (1983) 53
98. Knowles, and Sternberg E. Arch. Rat. Mech. Anal. 63 (1977) 321
99. Kwon, and Leonov A.I. J. Non-Newton. Fluid Mech. 47 (1993) 77
100. Kwon, and Leonov A.I. J. Non-Newton. Fluid Mech. 58 (1995) 25
101. Kwon. J. Non-Newton. Fluid Mech. 65 (1996) 151
102. Kwon, and Leonov A.I. Rheol. Acta 33 (1994) 398
103. Kwon, and Leonov A.I. J. Rheol. 36 (1992) 1515
104. Hulsen. J. Non-Newton. Fluid Mech. 38 (1990) 93
105. Renardy. Arch. Rat. Mech. Anal. 88 (1985) 83
106. Simhambhatla. The Rheological Modeling of Simple Flows of Unfilled and Filled Polymers. Ph.D. Dissertation (1994), The University of Akron
107. Kwon. Studies of Viscoelastic Constitutive Equations and Some Flow Effects for Concentrated Polymeric Fluids. Ph.D. Dissertation (1994), The University of Akron
108. Einaga, Osaki K., Kurata M., Kimura S., and Tamura M. Polym. J. 2 (1971) 550
109. Laun. Rheol. Acta 17 (1978) 1
110. Khan, Prud'homme R.K., and Larson R.G. Rheol. Acta 26 (1987) 144
111. Soskey, and Winter H.H. J. Rheol. 28 (1984) 625
112. Takahashi, Taku K., and Masuda T. J. Soc. Rheol., Japan 18 (1990) 18
113. Laun. J. Rheol. 30 (1986) 459
114. Leonov, and Prokunin A.N. Rheol. Acta 19 (1983) 137
115. Laun. Stress and recoverable strains of stretched polymer melts and their prediction by means of a single integral constitutive equation. Rheology vol. 2 (1980), Plenum Press, New York
116. Munstedt, and Laun H.M. Rheol. Acta 20 (1981) 211
117. Vinogradov, and Malkin A.Ya. J. Polym. Sci. A-2 2 (1964) 2357
118. Vinogradov, and Malkin A.Ya. J. Polym. Sci. A-2 4 (1966) 135
119. Leonov, and Prokunin A.N. Rheol. Acta 19 (1980) 393
120. Laun, and Schuch H. J. Rheol. 33 (1989) 119
121. Wagner. J. Non-Newton. Fluid Mech. 4 (1978) 39
122. Laun. Rheol. Acta 21 (1982) 464
123. Wagner, and Laun H.M. Rheol. Acta 17 (1978) 138
124. Giacomin, Jeyaseelan R.S., Samurkas T., and Dealy J.M. J. Rheol. 37 (1993) 811
125. Meissner. Trans. Soc. Rheol. 16 (1972) 405
126. Takahashi, Isaki T., Takigava T., and Masuda T. J. Rheol. 37 (1993) 827
127. Kompani, Venerus D.C., and Bernstein B. Development and evaluation of lubricated squeezing flow technique. In: Ait-Kadi A., Dealy J.M., James D.F., and Williams M.C. (Eds). Proc. XIIth Int. Congr. on Rheology. Quebec City, Canada (August 18-23, 1996) 754