Skip to main content
Log in

Flow instability in polymer solutions and melts

  • Published:
Polymer Science Series C Aims and scope Submit manuscript

Abstract

The existing experimental data concerning the problem of flow instability in polymer solutions and melts is considered and critically discussed. The instability is understood as both regular distortions of the jet surface shape and turbulence of the flow as such. The visual manifestations and physical mechanisms determining the development of flow instability are analyzed and classified. The following principal forms of instability are distinguished: small-scale regular surface defects, periodic oscillations with the scale of the jet diameter, the slip—stick periodic transition phenomenon, self-oscillations of the stream, jet spurt, and large-scale distortions passing into stream discontinuities. In all cases, the instability of the jet is due to rubber elasticity of polymer fluids, a property which causes storage of elastic energy during deformation with its subsequent release in the form of stream distortions. Therefore, the general criterion for the onset of instability is a certain critical value of the Weissenberg number. The key factors determining the loss of the flow stability are concentration of stresses at the channel outlet, transition from laminar flow to slip along a solid wall (adhesive ruptures) under certain critical conditions, and mechanical fracture (cohesive ruptures) of a material. In the appearance of hysteresis oscillations, bulk elasticity and compressibility of the melt also play a certain role. Alternative mechanisms proposed in the literature are also discussed. Examples illustrating the possibility of suppressing jet distortions are given; this suppression is important for many industrial applications in polymer processing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. O. Reynolds, Philos. Trans. R. Soc. London 174, 935 (1883).

    Google Scholar 

  2. G. Lamb, Treatise on High Mathematical Theory of the Motion of Liquids (Oxford Univ. Press, Oxford, 1932; Gostekhizdat, Moscow, 1947).

    Google Scholar 

  3. G. I. Taylor, Philos. Trans. R. Soc. London, A 223, 289 (1923).

    Google Scholar 

  4. G. I. Taylor, Proc. R. Soc. London, A 151, 494 (1935).

    Google Scholar 

  5. H. K. Nason, J. Appl. Phys. 16, 338 (1945).

    CAS  Google Scholar 

  6. M. Mooney, J. Colloid Sci. 2, 69 (1947).

    CAS  Google Scholar 

  7. R. S. Spenser and R. E. Dillon, 4, 241 (1949).

  8. J. P. Tordella, J. Appl. Phys. 27, 454 (1956).

    CAS  Google Scholar 

  9. P. L. Clegg, Rheology of Elastomeys, Ed. by P. Mason and N. Wookey (Pergamon, New York, 1957).

    Google Scholar 

  10. J. P. Tordella, SPE J. 12(2), 36 (1957).

    Google Scholar 

  11. P. L. Clegg, Plast. Inst. Trans. J. 26, 151 (1958).

    Google Scholar 

  12. E. B. Bagley and A. M. Birks, J. Appl. Phys. 31, 556 (1960).

    Google Scholar 

  13. E. B. Bagley and H. P. Schreiber, Trans. Soc. Rheol. 5, 341 (1961).

    Google Scholar 

  14. J. P. Tordella, J. Appl. Polym. Sci. 7, 215 (1963).

    CAS  Google Scholar 

  15. J. J. Banbow and P. Lamb, SPE Trans. 3, 7 (1963).

    Google Scholar 

  16. J. P. Tordella, J. Polym. Sci., Part C 15, 495 (1966).

    Google Scholar 

  17. G. V. Vinogradov and V. N. Manin, Kolloidn. Zh. 27, 784 (1965).

    Google Scholar 

  18. G. V. Vinogradov and V. N. Manin, Kolloid Z.Z. Polym. 201, 93 (1965).

    CAS  Google Scholar 

  19. J. P. Tordella, Rheology. Theory and Applications, Ed. by F. R. Eirich (Academic, New York, 1969), Vol. 5.

    Google Scholar 

  20. E. Miller and J. F. Rothstein, Rheol. Acta 44, 160 (2004).

    CAS  Google Scholar 

  21. M. Fernández, A. Santamaria, A. Muños-Escalona, and L. Mendez, J. Rheol. (N. Y.) 45, 595 (2001).

    Google Scholar 

  22. C. J. S. Petrie and M. M. Denn, AIChE J. 22, 209 (1976).

    CAS  Google Scholar 

  23. M. M. Denn, Annu. Rev. Fluid Mech. 22, 13 (1990).

    Google Scholar 

  24. J.-M. Piau, N. El Kissi, F. Toussaint, and A. Mezghani, Rheol. Acta 34, 40 (1995).

    CAS  Google Scholar 

  25. S.-Q. Wang and P. P. Drda, Macromolecules 29, 2627 (1996).

    CAS  Google Scholar 

  26. S.-Q. Wang and P. P. Drda, Macromol. Chem. Phys. 198, 673 (1997).

    CAS  Google Scholar 

  27. L. Robert, Y. Demay, and B. Vergnes, Rheol. Acta 43, 89 (2004).

    CAS  Google Scholar 

  28. E. B. Bagley, I. M. Cabott, and D. C. West, J. Appl. Phys. 29, 109 (1958).

    Google Scholar 

  29. A. P. Metzger, C. W. Hamilton, and E. H. Merz, SPE Trans. 3, 21 (1963).

    CAS  Google Scholar 

  30. A. P. Metzger and C. W. Hamilton, SPE Trans. 4, 107 (1964).

    CAS  Google Scholar 

  31. I. M. Lupton, Chem. Eng. Prog., Symp. Ser. 60, 17 (1964).

    Google Scholar 

  32. I. M. Lupton and J. W. Regester, Polym. Eng. Sci. 5, 235 (1965).

    CAS  Google Scholar 

  33. R. W. Myerholtz, J. Appl. Polym. Sci. 11, 687 (1967).

    CAS  Google Scholar 

  34. J. Molenaar and R. J. Koopmans, J. Rheol. (N. Y.) 38, 99 (1994).

    CAS  Google Scholar 

  35. K. P. Adewale and A. I. Leonov, Rheol. Acta 36, 110 (1997).

    CAS  Google Scholar 

  36. M. Ranganathan, M. R. Mackley, and P. H. J. Spitteler, J. Rheol. (N.Y.) 43, 443 (1999).

    CAS  Google Scholar 

  37. L. Robert, B. Vergnes, and Y. Demay, J. Rheol. (N. Y.) 44, 1183 (2000).

    CAS  Google Scholar 

  38. S.-Q. Wang and N. Plucktaveesak, J. Rheol. (N. Y.) 43, 453 (1999).

    CAS  Google Scholar 

  39. G. V. Vinogradov, Vysokomol. Soedin., Ser. A 13, 294 (1971).

    CAS  Google Scholar 

  40. G. V. Vinogradov, A. Ya. Malkin, Yu. G. Yanovskii, et al., Vysokomol. Soedin., Ser. A 14, 2425 (1972).

    CAS  Google Scholar 

  41. G. W. Winogradow, A. Ja. Malkin, B. W. Jarlykow, et al., Plast. Kautsch. 19, 907 (1972).

    Google Scholar 

  42. G. V. Vinogradov, A. Ya. Malkin, Yu. G. Yanovski, et al., J. Polym. Sci., Part A-2 10, 1061 (1972).

    CAS  Google Scholar 

  43. G. V. Vinogradov, A. Ya. Malkin, N. K. Blinova, et al., Eur. Polym. J. 9, 1231 (1973).

    CAS  Google Scholar 

  44. G. V. Vinogradov, Pure Appl. Chem. 39, 115 (1974).

    CAS  Google Scholar 

  45. G. V. Vinogradov, V. P. Protasov, and V. E. Dreval, Rheol. Acta 23, 46 (1984).

    CAS  Google Scholar 

  46. X. Yang, S.-Q. Wang, A. Halasa, and H. Ishida, Rheol. Acta 37, 415 (1998).

    CAS  Google Scholar 

  47. P. Taradia and S.-Q. Wang, Phys. Rev. Lett. 91, 198301 (2003).

    Google Scholar 

  48. P. Taradia and S.-Q. Wang, in Proceedings of Annual European Rheological Conference, Grenoble, 2005, p. 35.

  49. R. E. Westover and B. Maxwell, SPE J. 13(8), 27 (1957).

    CAS  Google Scholar 

  50. R. E. Westover and B. Maxwell, SPE J. 13(8), 62 (1957).

    Google Scholar 

  51. F. B. Metzner, Ind. Eng. Chem. 50, 1577 (1958).

    CAS  Google Scholar 

  52. J. P. Tordella, Trans. Soc. Rheol. 1, 203 (1957).

    CAS  Google Scholar 

  53. F. Ram and F. Tamir, J. Appl. Polym. Sci. 8, 2751 (1964).

    CAS  Google Scholar 

  54. E. B. Bagley, Trans Soc. Rheol. 5, 355 (1961).

    CAS  Google Scholar 

  55. H. Schott, J. Polym. Sci., Part A 2, 3791 (1964).

    CAS  Google Scholar 

  56. S. M. Barnett, Polym. Eng. Sci. 7, 168 (1967).

    CAS  Google Scholar 

  57. J. L. White, J. Appl. Polym. Sci. 8, 1129 (1964).

    Google Scholar 

  58. J. L. White, J. Appl. Polym. Sci. 8, 2339 (1964).

    CAS  Google Scholar 

  59. A. Ya. Malkin and A. I. Leonov, Dokl. Akad. Nauk SSSR 151, 380 (1963).

    CAS  Google Scholar 

  60. G. V. Vinogradov, A. Ya. Malkin, and A. I. Leonov, Kolloid Z. Z. Polym. 191, 25 (1963).

    CAS  Google Scholar 

  61. J. R. A. Pearson and C. J. S. Petrie, in Proceedings of the Fourth International Rheological Congress, 1964, Vol. 3, p. 265.

  62. N. Tokita and J. L. White, J. Appl. Polym. Sci. 10, 1011 (1966).

    CAS  Google Scholar 

  63. A. Ya. Malkin and A. I. Leonov, in Progress in Rheology of Polymers, Ed. by G. V. Vinogradov (Khimiya, Moscow, 1970) [in Russian].

    Google Scholar 

  64. G. V. Vinogradov, N. I. Insarova, V. V. Boiko, and E. K. Borisenkova, Polym. Eng. Sci. 12, 323 (1972).

    CAS  Google Scholar 

  65. G. V. Vinogradov, Rheol. Acta 12, 357 (1973).

    CAS  Google Scholar 

  66. G. V. Vinogradov and A. Ya. Malkin, Rheology of Polymers (Khimiya, Moscow, 1977; Springer, Berlin, 1980).

    Google Scholar 

  67. A. V. Ramamurthy, J. Rheol. (N. Y.) 30, 337 (1986).

    CAS  Google Scholar 

  68. V. G. Ghanta, B. L. Ruse, and M. M. Denn, J. Rheol. (N. Y.) 43, 435 (1999).

    CAS  Google Scholar 

  69. D. R. Arda and M. R. Mackley, J. Non-Newtonian Fluid Mech. 126, 47 (2005).

    CAS  Google Scholar 

  70. S. B. Kharchenko, P. M. McGuiggan, and K. B. Migler, J. Rheol. (N. Y.) 47, 1523 (2003).

    CAS  Google Scholar 

  71. R. Yip, S. G. Hatzikiriakos, and T. M. Clere, J. Vinyl Additive Technol. 6, 113 (2000).

    CAS  Google Scholar 

  72. E. E. Rosenbaum, S. K. Randa, S. G. Hatzikiriakos, et al., Polym. Eng. Sci. 40, 179 (2000).

    CAS  Google Scholar 

  73. G. R. Smoluk, Plast. Eng., 115 (1964).

  74. L. L. Blyler and A. C. Hart, Polym. Eng. Sci. 10, 193 (1970).

    CAS  Google Scholar 

  75. D. S. Kalika and M. M. Denn, J. Rheol. (N. Y.) 31, 815 (1987).

    CAS  Google Scholar 

  76. S. G. Hatzikiriakos and J. M. Dealy, J. Rheol. (N. Y.) 36, 703 (1992).

    CAS  Google Scholar 

  77. S. G. Hatzikiriakos, Int. Polym. Process. 8, 135 (1993).

    CAS  Google Scholar 

  78. H. Mizunuma and H. Takagi, J. Rheol. (N. Y.) 47, 737 (2003).

    CAS  Google Scholar 

  79. S. H. Anastasiadis and S. G. Hatzikiriakos, J. Vinyl Additive Technol. 8, 7 (1998).

    Google Scholar 

  80. N. El Kissi and J.-M. Piau, J. Rheol. (N. Y.) 38, 1447 (1994).

    Google Scholar 

  81. S.-Q. Wang, P. A. Drda, and Y. W. Inn, J. Rheol. (N. Y.) 40, 875 (1996).

    CAS  Google Scholar 

  82. F. Legrand and J.-M. Piau, J. Non-Newtonian Fluid Mech. 77, 123 (1998).

    CAS  Google Scholar 

  83. Y. W. Inn, S.-Q. Wang, and M. T. Shaw, Macromol. Symp. 148, 65 (2000).

    Google Scholar 

  84. K. B. Migler, C. Lavallée, and M. P. Dillon, J. Rheol. (N. Y.) 45, 565 (2001).

    CAS  Google Scholar 

  85. F. N. Cogswell, Polym. Eng. Sci. 12, 64 (1972).

    CAS  Google Scholar 

  86. E. B. Howells and J. J. Benbow, Plast. Trans. J. 30, 240 (1962).

    CAS  Google Scholar 

  87. F. N. Cogswell, J. Non-Newtonian Fluid Mech. 2, 37 (1977).

    CAS  Google Scholar 

  88. C. Venet and B. Vergnes, J. Non-Newtonian Fluid Mech. 93, 117 (2000).

    CAS  Google Scholar 

  89. R. Rurgers and M. Mackley, J. Rheol. (N. Y.) 44, 1319 (2000).

    Google Scholar 

  90. V. I. Brizitsky, G. V. Vinogradov, A. I. Isayev, and Yu. Ya. Podolsky, J. Appl. Polym. Sci. 20, 25 (1976).

    Google Scholar 

  91. J.-M. Piau, N. El Kissi, and F. Mezghani, J. Non-Newtonian Fluid Mech. 59, 11 (1995).

    CAS  Google Scholar 

  92. N. El Kissi, J.-M. Piau, and F. Toussaint, J. Non-Newtonian Fluid Mech. 68, 271 (1997).

    Google Scholar 

  93. Yu. G. Yanovskii, L. I. Ivanova, and E. I. Frenkin, Mekh. Polim., No. 3, 530 (1970).

  94. R. H. Moynihan, D. G. Baird, and R. Ramanathan, J. Non-Newtonian Fluid Mech. 36, 255 (1990).

    CAS  Google Scholar 

  95. C. I. Chung, Extrusion of Polymers. Theory and Practice (Hanser, Munich, 2000).

    Google Scholar 

  96. A. Santamaria, M. Fernández, E. Sanz, et al., Polymer 44, 2473 (2003).

    CAS  Google Scholar 

  97. A. S. Kechek’yan, G. P. Andrianova, and V. A. Kargin, Vysokomol. Soedin., Ser. A 12, 2424 (1970).

    CAS  Google Scholar 

  98. G. P. Andrianova, Yu. V. Popov, and B. A. Arutyunov, Vysokomol. Soedin., Ser. A 18, 2311 (1976).

    CAS  Google Scholar 

  99. G. P. Andrianova, B. A. Arutyunov, and Yu. V. Popov, J. Polym. Sci., Part B: Polym. Phys. 16, 1139 (1978).

    CAS  Google Scholar 

  100. S. L. Bazhenov, Yu. A. Rodionova, A. S. Kechek’yan, and A. K. Rogozinskii, Vysokomol. Soedin., Ser. A 47, 1131 (2005) [Polymer Science, Ser. A 47, 692 (2005)].

    CAS  Google Scholar 

  101. L. Robert, Y. Demay, and B. Vergnes, Rheol. Acta 43, 89 (2004).

    CAS  Google Scholar 

  102. J. R. A. Pearson, Mechanical Principles of Polymer Melt Processing (Pergamon, Oxford, 1966).

    Google Scholar 

  103. A. V. Karakin and A. I. Leonov, Zh. Prikl. Mekh. Tekh. Fiz., No. 3, 110 (1968).

  104. V. Durand, B. Vergnes, J. F. Agassant, et al., J. Rheol. (N. Y.) 40, 383 (1996).

    CAS  Google Scholar 

  105. J. Van Doelder, R. Koopmans, M. Dees, and M. Mangnus, J. Rheol. (N. Y.) 49, 113 (2005).

    Google Scholar 

  106. H. Münstedt, M. Schmidt, and E. Wassner, J. Rheol. (N. Y.) 44, 413 (2000).

    Google Scholar 

  107. S.-O. Wang and P. A. Drda, Rheol. Acta 36, 128 (1997).

    CAS  Google Scholar 

  108. J. D. Ferry, Viscoelastic Properties of Polymers, 3rd ed. (Wiley, New York, 1981; Inostrannaya Literatura, Moscow, 1963).

    Google Scholar 

  109. G. V. Vinogradov, A. Ya. Malkin, Yu. G. Yanovsky, et al., Rheol. Acta 8, 490 (1969).

    Google Scholar 

  110. Yu. G. Yanovskii and A. Ya. Malkin, in Progress in Rheology of Polymers, Ed. by G. V. Vinogradov (Khimiya, Moscow, 1970) [in Russian].

    Google Scholar 

  111. A. I. Leonov, Rheol. Acta 15, 85 (1976).

    Google Scholar 

  112. A. I. Leonov, J. Non-Newtonian Fluid Mech. 25, 1 (1987).

    CAS  Google Scholar 

  113. A. I. Leonov and A. Srinivasan, Rheol. Acta 30, 14 (1991).

    CAS  Google Scholar 

  114. E. K. Borisenkova, G. V. Vasil’ev, V. G. Kulichikhin, et al., Vysokomol. Soedin., Ser. A 40, 1823 (1998) [Polymer Science, Ser. A 40, 1124 (1998)].

    Google Scholar 

  115. K. P. Adewale and A. I. Leonov, Rheol. Acta 36, 110 (1997).

    CAS  Google Scholar 

  116. P. Taradia and S.-Q. Wang, Macromolecules 37, 9083 (2004).

    Google Scholar 

  117. T. C. B. McLeish and R. C. Ball, J. Polym. Sci., Part B: Polym. Phys. 24, 1735 (1986).

    CAS  Google Scholar 

  118. M. E. Cates, T. C. B. McLeish, and G. Marrucci, Europhys. Lett. 21, 451 (1993).

    CAS  Google Scholar 

  119. A. Ya. Malkin and B. V. Yarlykov, Mekh. Polim., No. 5, 930 (1978).

  120. J. Lyngaae-Jorgensen and B. Marcher, Chem. Eng. Commun. 32, 117 (1985).

    Google Scholar 

  121. V. E. Dreval, G. V. Vinogradov, and V. P. Protasov, in Proceedings of IX International Congress on Rheology, Ed. by B. Mena, A. Garcia-Rejón, and C. Rangel-Nafaile (Univ. Nacional, México, 1984), Vol. 3, p. 185.

    Google Scholar 

  122. J. Pérez-González, J. Rheol. (N. Y.) 45, 845 (2001).

    Google Scholar 

  123. L. Pérez-Trejo, J. Pérez-González, L. De Vargas, and E. Moreno, Wear 257, 329 (2004).

    Google Scholar 

  124. J. Pérez-González, J. Rheol. (N. Y.) (in press) (2005).

  125. S. Tonon, A. Levernhe-Gerbier, F. Flores, et al., J. Non-Newtonian Fluid Mech. 126, 63 (2005).

    CAS  Google Scholar 

  126. J. P. Tordella, Trans. Soc. Rheol. 7, 231 (1963).

    CAS  Google Scholar 

  127. G. V. Vinogradov, N. I. Insarova, B. B. Boiko, and E. K. Borisenkova, Polym. Eng. Sci. 12, 323 (1972).

    CAS  Google Scholar 

  128. C. D. Han and L. H. Drexler, J. Polym. Sci. 17, 2329 (1973).

    CAS  Google Scholar 

  129. A. B. Metzner, E. L. Carley, and I. K. Park, Mod. Plast. 37(11), 133 (1960).

    Google Scholar 

  130. C. Combeaud, Y. Demay, R. Valette, and B. Vergnes, in Proceedings of Annual European Rheological Conference, Grenoble, 2005, p. 179.

  131. S. Kim and J. M. Dealy, Polym. Eng. Sci. 42, 482 (2002).

    CAS  Google Scholar 

  132. M. Sentmanat, E. B. Multiawan, and S. G. Hatzikiriakos, Rheol. Acta 44, 1 (2004).

    CAS  Google Scholar 

  133. M. Sentmanat and S. G. Hatzikiriakos, Rheol. Acta 43, 624 (2004).

    CAS  Google Scholar 

  134. S. G. Hatzikiriakos and J. M. Dealy, J. Rheol. (N. Y.) 36, 845 (1992).

    CAS  Google Scholar 

  135. S. G. Hatzikiriakos and J. M. Dealy, J. Rheol. (N. Y.) 35, 497 (1991).

    CAS  Google Scholar 

  136. K. M. Awati, Y. Park, E. Weisser, and M. E. Mackay, J. Non-Newtonian Fluid Mech. 89, 117 (2000).

    CAS  Google Scholar 

  137. K. B. Migler, H. Hervet, and I. Legér, Phys. Rev. Lett. 70, 287 (1993).

    CAS  Google Scholar 

  138. D. M. Kalyon and H. Gevgilili, J. Rheol. (N. Y.) 47, 683 (2003).

    CAS  Google Scholar 

  139. N. El Kissi and J.-M. Piau, J. Non-Newtonian Fluid Mech. 37, 55 (1990).

    Google Scholar 

  140. F. Brochard-Wyart, C. Gay, and P. G. De Gennes, Macromolecules 29, 377 (1996).

    CAS  Google Scholar 

  141. J. C. Baudez, S. Rodts, X. Chateau, and P. Coussot, J. Rheol. (N. Y.) 48, 49 (2004).

    Google Scholar 

  142. H. Gevgilili and D. M. Kalyon, J. Rheol. (N. Y.) 45, 1 (2001).

    Google Scholar 

  143. M. Mooney, J. Rheol. (N. Y.) 2, 210 (1931).

    CAS  Google Scholar 

  144. D. F. Moore, The Friction and Lubrication of Elastomers (Pergamon, New York, 1972).

    Google Scholar 

  145. A. Ya. Malkin, A. V. Baranov, and N. E. Vickulenkova, Rheol. Acta 32, 150 (1993).

    CAS  Google Scholar 

  146. J.-M. Piau and N. El Kissi, J. Non-Newtonian Fluid Mech. 54, 121 (1994).

    CAS  Google Scholar 

  147. J.-M. Piau and N. El Kissi, in Proceedings of XI International Congress on Rheology (Elsevier, Brussels, 1992), p. 70.

    Google Scholar 

  148. Y. Chen, D. A. Kalyon, and E. Bayramli, J. Appl. Polym. Sci. 50, 1169 (1993).

    CAS  Google Scholar 

  149. M. M. Denn, Annu. Rev. Fluid Mech. 33, 265 (2001).

    Google Scholar 

  150. U. Yilmazer and D. A. Kalyon, J. Rheol. (N. Y.) 33, 1197 (1989).

    CAS  Google Scholar 

  151. B. K. Aral and D. A. Kalyon, J. Rheol. (N. Y.) 38, 957 (1994).

    CAS  Google Scholar 

  152. L. Legér, B. Paphael, and H. Hervet, Adv. Polym. Sci. 138, 185 (1999).

    Google Scholar 

  153. M. M. Britton and P. T. Callaghan, J. Rheol. (N. Y.) 41, 1365 (1997).

    CAS  Google Scholar 

  154. M. M. Britton, R. V. Mair, R. K. Lambert, and P. T. Callaghan, J. Rheol. (N. Y.) 43, 897 (1999).

    CAS  Google Scholar 

  155. Y. N. Joshi, A. K. Lele, and A. K. Mashelkar, J. Non-Newtonian Fluid Mech. 89, 303 (2000).

    CAS  Google Scholar 

  156. G. M. Wise, M. M. Denn, and A. T. Bell, AIChE J. 44, 701 (1998).

    CAS  Google Scholar 

  157. G. M. Wise, M. M. Denn, A. T. Bell, et al., J. Rheol. (N. Y.) 44, 549 (2000).

    CAS  Google Scholar 

  158. F. Brochard and P. G. De Gennes, Langmuir 8, 3033 (1992).

    CAS  Google Scholar 

  159. D. F. Hill, J. Rheol. (N. Y.) 42, 581 (1998).

    CAS  Google Scholar 

  160. Y. Cohen and A. B. Metzner, AIChE Symp. 78, Ser. 212, 77 (1982).

    CAS  Google Scholar 

  161. M. Tirrel and M. P. Malone, J. Polym. Sci., Part B: Polym. Phys. 15, 1569 (1977).

    Google Scholar 

  162. H. Muller-Mohnssen, H. P. Lobl, and W. Schauerte, J. Rheol. (N. Y.) 31, 323 (1987).

    Google Scholar 

  163. G. M. Bartenev and Yu. S. Zuev, Strength and Fracture of Rubberlike Materials (Khimiya, Moscow, 1964) [in Russian].

    Google Scholar 

  164. T. L. Smith, J. Polym. Sci., Part A 1, 3597 (1963).

    Google Scholar 

  165. G. V. Vinogradov, A. Ya. Malkin, V. V. Volosevitch, et al., J. Polym. Sci., Part B: Polym. Phys. 13, 1721 (1975).

    CAS  Google Scholar 

  166. G. V. Vinogradov, A. Ya. Malkin, and V. V. Volosevitch, Appl. Polym. Symp., No. 27, 47 (1975).

  167. M. K. Kurbanaliev, E. K. Borisenkova, G. V. Vinogradov, and A. Ya. Malkin, Vysokomol. Soedin., Ser. B 23, 912 (1981).

    CAS  Google Scholar 

  168. A. Ya. Malkin and G. V. Vinogradov, Vysokomol. Soedin., Ser. A 27, 227 (1985).

    CAS  Google Scholar 

  169. A. Ya. Malkin and C. J. S. Petrie, J. Rheol. (N. Y.) 41, 1 (1997).

    CAS  Google Scholar 

  170. A. Ya. Malkin, Rheology—Fundamentals (ChemTech, Toronto, 1994).

    Google Scholar 

  171. R. G. Larson, Rheol. Acta 31, 213 (1992).

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © A.Ya. Malkin, 2006, published in Vysokomolekulyarnye Soedineniya, Ser. C, 2006, Vol. 48, No. 7, pp. 1241–1262.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Malkin, A.Y. Flow instability in polymer solutions and melts. Polym. Sci. Ser. C 48, 21–37 (2006). https://doi.org/10.1134/S1811238206010024

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1811238206010024

Keywords

Navigation