화학공학소재연구정보센터
홈 로그인 로그아웃 연락처 사이트맵
Korea-Australia Rheology Journal, Vol.12, No.1, 1-25, March, 2000
Export Citation
Non-Newtonian fluid mechanics for polymeric liquids: A status report
L. Gary Leal†, and James P. Oberhauser1
  • Materials Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, USA
  • 1Departments of Chemical and Materials Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, USA
E-mail:
In this paper, we review recent progress in the development of constitutive models for both dilute and entangled polymeric liquids, The status of recent applications of these models for fluid dynamics predictions is then discussed, as well as possible future research directions.
  1. Baaijens HP, Peters GW, Baaijens FP, Meijer HE, J. Rheol., 39(6), 1243 (1995) 
  2. Berman NS, Phys. Fluids, 20, 715 (1977) 
  3. Bird RB, Curtiss CF, Armstrong RC, Hassager O, Dynamics of Polymeric Liquids: Vol II Kinetic Theory. John Wiley and Sons, New York (1987)
  4. Bishko G, McLeish TCB, Harlen OG, Larson RG, Phys. Rev. Lett., 79, 2352 (1997) 
  5. Bishko GB, Harlen OG, McLeish TCB, Nicholson TM, J. Non-Newton. Fluid Mech., 82(2), 255 (1999) 
  6. Boger DV, J. Non-Newton. Fluid Mech., 3, 87 (1977) 
  7. Britton MM, Callaghan PT, Eur. Phys. J. B, 7, 237 (1999) 
  8. Britton MM, Mair RW, Lambert RK, Callaghan PT, J. Rheol., 43(4), 897 (1999) 
  9. Brown EF, Burghardt WR, J. Rheol., 40(1), 37 (1996) 
  10. Brown EF, Burghardt WR, Kahvand H, Venerus DC, Rheol. Acta, 34(3), 221 (1995) 
  11. Callaghan PT, Cates ME, Rofe CJ, Smeulders JBAF, A Study of the "Spurt Effect," in Wormlike Micelles Using Nuclear Magnetic Resonance Microscopy, Journal de Physique II Atomic, Molecular and Cluster Physics, Chemical Physics, Mechanics and Hydrodynamics, 6, 375 (1996)
  12. Carrington SP, Odell JA, J. Non-Newton. Fluid Mech., 67, 269 (1996)
  13. Carrington SP, Tatham JP, Odell JA, Saez AE, Polymer, 38(18), 4595 (1997) 
  14. Chaubal CV, Leal LG, J. Non-Newton. Fluid Mech., 82(1), 25 (1999) 
  15. Chaubal CV, Leal LG, Fredrickson GH, J. Rheol., 39(1), 73 (1995) 
  16. Chaubal CV, Srinivasan A, Egecioglu O, Leal LG, J. Non-Newton. Fluid Mech., 70(1), 125 (1997) 
  17. Chilcott M, Rallison J, J. Non-Newton. Fluid Mech., 29, 381 (1988) 
  18. Chin S, Hoagland DA, Muri JJ, Parkhe AD, Rheol. Acta, 28, 202 (1989) 
  19. Chmielewski C, Nichols KL, Jayaraman K, J. Non-Newton. Fluid Mech., 35, 37 (1990) 
  20. Phys. Fluids, Conference Proceedings, Structure of Turbulence and Drag Reduction, 20 (1977)
  21. Cressely R, Hocquart H, Scrivener O, Optica Acta, 26, 1173 (1979)
  22. Cressely R, Hocquart R, Optica Acta, 27, 699 (1980)
  23. Cressely R, Hocquart R, Scrivener O, Optica Acta, 25, 559 (1978)
  24. de Gennes PG, J. Chem. Phys., 55, 572 (1971) 
  25. de Gennes PG, J. Chem. Phys., 60, 5030 (1974) 
  26. Den Toonder JMJ, Hulsen MA, Kuiken GDC, Nieuwstadt FTM, J. Fluid Mech., 337, 193 (1997) 
  27. des Cloizeaux J, Europhys. Lett., 5, 437 (1988)
  28. des Cloizeaux J, Macromolecules, 23, 4678 (1990) 
  29. des Cloizeaux J, Macromolecules, 23, 3992 (1990) 
  30. Dimitropoulos CD, Sureshkumar R, Beris AN, J. Non-Newton. Fluid Mech., 79(2), 433 (1998) 
  31. Doi M, J. Polym. Sci. B: Polym. Phys., 21, 667 (1983)
  32. Doi M, Edwards SF, J. Chem. Soc.-Faraday Trans., 74, 1789 (1978) 
  33. Doi M, Edwards SF, J. Chem. Soc.-Faraday Trans., 74, 1802 (1978) 
  34. Doi M, Edwards SF, J. Chem. Soc.-Faraday Trans., 74, 1818 (1978) 
  35. Doi M, Edwards SF, J. Chem. Soc.-Faraday Trans., 75, 38 (1979) 
  36. Doi M, Edwards SF, The Theory of Polymer Dynamics. Oxford University Press, Oxford (1986)
  37. Doi M, Graessley WW, Helfand E, Pearson DS, Macromolecules, 20 (1987)
  38. Doyle PS, Shaqfeh ESG, J. Non-Newton. Fluid Mech., 76(1), 43 (1998) 
  39. Dressler M, Edwards BJ, Ottinger HC, Rheol. Acta, 38(2), 117 (1999) 
  40. Dunlap PN, Leal LG, J. Non-Newton. Fluid Mech., 23, 5 (1986) 
  41. Dunlap PN, Wang CH, Leal LG, J. Polym. Sci. B: Polym. Phys., 25, 2211 (1987) 
  42. Durst F, Haas R, Kaczmar BU, J. Appl. Polym. Sci., 26, 3125 (1981) 
  43. Elata C, Burger J, Michlin J, Takserman U, Phys. Fluids, 20, S49 (1977) 
  44. El-Kareh AW, Leal LG, J. Non-Newton. Fluid Mech., 33, 257 (1989) 
  45. Feng J, Leal LG, J. Non-Newton. Fluid Mech., 72(2), 187 (1997) 
  46. Ferry JD, Viscoelastic Properties of Polymers, John Wiley & Sons, New York (1980)
  47. Fuller GG, Leal LG, Rheol. Acta, 19, 580 (1980) 
  48. Fuller GG, Leal LG, J. Non-Newton. Fluid Mech., 8, 271 (1981) 
  49. Gallez X, Halin P, Lielens G, Keunings R, Legat V, Comput. Methods Appl. Mechanics Eng., to appear (1999)
  50. Grillet AM, Shaqfeh ESG, J. Non-Newton. Fluid Mech., 64(2), 141 (1996) 
  51. Grmela M, Ottinger HC, Phys. Rev. E, 56, 6620 (1997) 
  52. Haas R, Durst F, Rheol. Acta, 21, 566 (1982) 
  53. Halin P, Lielens G, Keunings R, Legat V, J. Non-Newton. Fluid Mech., 79(2), 387 (1998) 
  54. Harlen OG, Hinch EJ, Rallison JM, J. Non-Newton. Fluid Mech., 44, 229 (1991) 
  55. Harrison G, An Experimental and Theoretical Study of the Dynamics of Polymeric Liquids in Strong Flows. Chemical Engineering. University of California at Santa Barbara, Santa Barbara (1997)
  56. Harrison GM, Remmelgas J, Leal LG, J. Rheol., 42(5), 1039 (1998) 
  57. Harrison GM, Remmelgas J, Leal LG, J. Rheol., 43(1), 197 (1999) 
  58. Hinch EJ, Phys. Fluids, 20, S22 (1976)
  59. Hinch EJ, J. Non-Newton. Fluid Mech., 54, 209 (1994) 
  60. Hinch EJ, Leal LG, J. Fluid Mech., 52(4), 683 (1972) 
  61. Hinch EJ, Leal LG, J. Fluid Mech., 71(3), 481 (1975) 
  62. Hinch EJ, Leal LG, J. Fluid Mech., 76(1), 187 (1976) 
  63. Hua CC, Schieber JD, Venerus DC, J. Rheol., 43(3), 701 (1999) 
  64. Hulsen MA, vanHeel APG, vandenBrule BHAA, J. Non-Newton. Fluid Mech., 70(1), 79 (1997) 
  65. Ianniruberto G, Marrucci G, J. Non-Newton. Fluid Mech., 65(2), 241 (1996) 
  66. Ianniruberto G, Marrucci G, J. Non-Newton. Fluid Mech., 79(2), 225 (1998) 
  67. Inkson NJ, McLeish TCB, Harlen OG, Groves DJ, J. Rheol., 43(4), 873 (1999) 
  68. James DF, McLaren DR, J. Fluid Mech., 70, 733 (1975) 
  69. Larson RG, J. Rheol., 28, 545 (1984) 
  70. Larson RG, Constitutive Equations for Polymer Melts and Solutions, Butterworth, Boston (1988)
  71. Larson RG, Rheol. Acta, 29, 371 (1990) 
  72. Larson RG, The Structure and Rheology of Complex Fluids, Oxford University Press, New York, Oxford (1999)
  73. Larson RG, Hu H, Smith DE, Chu S, J. Rheol., 43(2), 267 (1999) 
  74. Larson RG, Magda JJ, Macromolecules, 22, 3004 (1989) 
  75. Larson RG, Perkins TT, Smith DE, Chu S, Hydrodynamics of a DNA Molecule in a Flow Field, Physical Review E Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 55, 1794 (1997)
  76. Laso M, Ottinger HC, J. Non-Newton. Fluid Mech., 47, 1 (1993) 
  77. Leal LG, AIP Conference Proceedings, 137, 5 (1985)
  78. Lielens G, Halin P, Jaumain I, Keunings R, Legat V, J. Non-Newton. Fluid Mech., 76(1), 249 (1998) 
  79. Lielens G, Keunings R, Legat V, J. Non-Newton. Fluid Mech., 87(2), 179 (1999) 
  80. Magueur A, Moan M, Chauveteau, Chem. Eng. Commun., 36, 351 (1985)
  81. Mair RW, Callaghan PT, Europhys. Lett., 36, 719 (1996) 
  82. Mair RW, Callaghan PT, J. Rheol., 41(4), 901 (1997) 
  83. Makhloufi R, Decruppe JP, Ait-Ali A, Cressely R, Europhys. Lett., 32, 253 (1995)
  84. Marrucci G, J. Non-Newton. Fluid Mech., 62(2), 279 (1996) 
  85. Marrucci G, de Cindio B, Rheol. Acta, 19, 68 (1980) 
  86. Marrucci G, Grizzuti N, Gazz. Chim. Ital., 118, 179 (1988)
  87. Marrucci G, Ianniruberto G, J. Non-Newton. Fluid Mech., 82(2), 275 (1999) 
  88. McKinley GH, Byars JA, Brown RA, Armstrong RC, J. Non-Newton. Fluid Mech., 40, 201 (1991) 
  89. McLeish TCB, Larson RG, J. Rheol., 42(1), 81 (1998) 
  90. Mead DW, J. Rheol., 38(6), 1797 (1994) 
  91. Mead DW, J. Rheol., 40(4), 633 (1996) 
  92. Mead DW, Larson RG, Doi M, Macromolecules, 31(22), 7895 (1998) 
  93. Mead DW, Leal LG, Rheol. Acta, 34(4), 339 (1995) 
  94. Mead DW, Yavich D, Leal LG, Rheol. Acta, 34(4), 360 (1995) 
  95. Mhetar V, Archer LA, J. Non-Newton. Fluid Mech., 81(1), 71 (1999) 
  96. Miles MJ, Keller A, Polymer, 21, 1295 (1980) 
  97. Milner ST, J. Rheol., 40(2), 303 (1996) 
  98. Milner ST, Mcleish TC, Macromolecules, 30(7), 2159 (1997) 
  99. Milner ST, McLeish TCB, Macromolecules, 31(21), 7479 (1998) 
  100. Milner ST, McLeish TCB, Phys. Rev. Lett., 81, 725 (1998) 
  101. Nollert MU, Olbricht WL, Rheol. Acta, 24, 3 (1985) 
  102. Oberhauser J, Experimental and Theoretical Studies of Entangled Polymer Solutions in Steady and Transient Flows, Chemical Engineering University of California at Santa Barbara, Santa Barbara (2000)
  103. Oberhauser JP, Leal LG, Mead DW, J. Polym. Sci. B: Polym. Phys., 36(2), 265 (1998) 
  104. Oberhauser JP, Milner ST, Leal LG, J. Rheol., preprint (2000)
  105. Oberhauser JP, Pham KQ, Leal LG, J. Polym. Sci. B: Polym. Phys., submitted (2000)
  106. Odell JA, Keller A, AIP Conference Proceedings, 33 (1985)
  107. Oliver DR, Bakhtiyarov SI, J. Non-Newton. Fluid Mech., 12, 113 (1983) 
  108. Ottinger HC, ARTICLE Theoretical Mathematical, 43, 1461 (1999)
  109. Ottinger HC, Grmela M, Phys. Rev. E, 56, 6633 (1997) 
  110. Ottinger HC, vandenBrule BHAA, Hulsen MA, J. Non-Newton. Fluid Mech., 70(3), 255 (1997) 
  111. Oztekin A, Brown RA, McKinley GH, J. Non-Newton. Fluid Mech., 54, 351 (1994) 
  112. Pearson D, Herbolzheimer E, Grizzuti N, Marrucci G, J. Polym. Sci. B: Polym. Phys., 29, 1589 (1991) 
  113. Pearson DS, Helfand E, Macromolecules, 17, 888 (1984) 
  114. Pearson DS, Kiss AD, Fetters LJ, J. Rheol., 33, 517 (1989) 
  115. Perkins TT, Quake SR, Smith DE, Chu S, Science, 264(5160), 822 (1994) 
  116. Perkins TT, Smith DE, Chu S, Science, 276(5321), 2016 (1997) 
  117. Perkins TT, Smith DE, Larson RG, Chu S, Science, 268(5207), 83 (1995) 
  118. Phan-Thien N, Manero O, Leal LG, Rheol. Acta, 23, 151 (1984) 
  119. Phan-Thien N, Tanner RI, Phys. Fluids, 21, 311 (1978) 
  120. Purnode B, Crochet MJ, J. Non-Newton. Fluid Mech., 65(2), 269 (1996) 
  121. Purnode B, Crochet MJ, J. Non-Newton. Fluid Mech., 77(1), 1 (1998) 
  122. Quake SR, Babcock H, Chu S, Nature, 388(6638), 151 (1997) 
  123. Remmelgas J, Harrison G, Leal LG, J. Non-Newton. Fluid Mech., 80(2), 115 (1999) 
  124. Remmelgas J, Leal LG, J. Non-Newton. Fluid Mech., sumitted for publication (1999)
  125. Remmelgas J, Leal LG, J. Non-Newton. Fluid Mech., to appear (1999)
  126. Remmelgas J, Singh P, Leal LG, J. Non-Newton. Fluid Mech., 88(1), 31 (1999) 
  127. Rodriguez S, Romero C, Sargenti ML, Muller AJ, Saez AE, Odell JA, J. Non-Newton. Fluid Mech., 49, 63 (1993) 
  128. Rubinstein M, Colby RH, J. Chem. Phys., 89, 5291 (1988) 
  129. Satrape JV, Crochet MJ, J. Non-Newton. Fluid Mech., 55(1), 91 (1994) 
  130. Singh P, Leal LG, J. Rheol., 38(3), 485 (1994) 
  131. Singh P, Leal LG, J. Non-Newton. Fluid Mech., 67, 137 (1996) 
  132. Sizaire R, Lielens G, Jaumain I, Keunings R, Legat V, J. Non-Newton. Fluid Mech., 82(2), 233 (1999) 
  133. Smith DE, Chu S, Science, 281(5381), 1335 (1998) 
  134. Solomon MJ, Muller SJ, J. Non-Newton. Fluid Mech., 62(1), 81 (1996) 
  135. Solomon MJ, Muller SJ, J. Rheol., 40(5), 837 (1996) 
  136. Suen JK, Brown RA, Armstrong RC, J. Non-Newton. Fluid Mech., to appear (1999)
  137. Sureshkumar R, Beris AN, Handler RA, Phys. Fluids, 9, 743 (1997) 
  138. Szabo P, Rallison JM, Hinch EJ, J. Non-Newton. Fluid Mech., 72(1), 73 (1997) 
  139. Szeri AJ, Leal LG, Nonlinear Dynamics of Polymers with Conformation Dependent Anisotropic Friction in Periodic Extensional Flows (Preprint) (1996)
  140. Tatham JP, Carrington S, Odell JA, Gamboa AC, Muller AJ, Saez AE, J. Rheol., 39(5), 961 (1995) 
  141. Toms BA, Phys. Fluids, 20, S3 (1977) 
  142. van Heel APG, Hulsen MA, van den Brule BHAA, J. Rheol., 43(5), 1239 (1999) 
  143. Verhoef MRJ, van den Brule BHAA, Hulsen MA, J. Non-Newton. Fluid Mech., 80(2), 155 (1999) 
  144. Viovy JL, Rubinstein M, Colby RH, Macromolecules, 36, 3587 (1991) 
  145. Wagner MH, Rheol. Acta, 29, 594 (1990) 
  146. Wagner MH, J. Rheol., 38(3), 655 (1994) 
  147. Wagner MH, J. Non-Newton. Fluid Mech., 68(2), 169 (1997) 
  148. Wagner MH, Schaeffer J, J. Rheol., 36, 1 (1992) 
  149. Wagner MH, Schaeffer J, Rheol. Acta, 33(6), 506 (1994) 
  150. Wang JJ, Yavich D, Leal LG, Phys. Fluids, 6, 3519 (1994) 
  151. Yang B, Khomami B, J. Non-Newton. Fluid Mech., 82(2), 429 (1999) 
  152. Yavich D, Experimental and Theoretical Studies of Strong Flow Effects in Semi-Dilute Solutions. Chemical Engineering, University of California at Santa Barbara, Santa Barbara (1995)
  153. Yavich D, Mead DW, Oberhauser JP, Leal LG, J. Rheol., 42(3), 671 (1998) 
  154. Yong LJ, Shaqfeh ESG, J. Fluid Mech., 262, 27 (1994) 
  155. Zebrowski BE, Fuller GG, J. Polym. Sci. B: Polym. Phys., 23, 575 (1985)