Skip to main content
  • 1041 Accesses

Abstract

Pressure driven flow through tubes, slits and other types of channels is of central importance in experimental rheology and in polymer processing. Not only is this flow used as the basis for the most popular type of melt rheometer, but it is also a flow that occurs often in melt processing, for example in an extrusion die or in the runner feeding an injection mold. We will derive the basic equations for flow in tubes and slits and show how these can be used to interpret rheometer data and to design flow systems. The irregular flows that can occur at the entrance and exit of a die are described, and methods for estimating the pressure drop in dies are reviewed.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. Walters, Rheometry, Chapman and Hall, London, 1975.

    Google Scholar 

  2. R. W. Whorlow, Rheological Techniques, Ellis Norwood, distributed by John Wiley & Sons, New York, 1979.

    Google Scholar 

  3. P. Schlimmer and R. H. Worthoff, Chem. Eng. Sci. 33: 759 (1978).

    Google Scholar 

  4. H. Chmiel and P. Schlimmer, Chemie-Ing.-Techn. 43: 1257 (1971).

    Google Scholar 

  5. A. V. Ramamurthy, J. Rheol. 30: 337 (1986).

    ADS  Google Scholar 

  6. D. S. Kalika and M. M. Denn, J. Rheol. 31: 815 (1987).

    ADS  Google Scholar 

  7. H. M. Laun, Rheol. Acta 22: 171 (1983).

    Google Scholar 

  8. A. S. Lodge, “Normal stress differences from hole pressure measurements,” Chapter 11 of Rheological Measurement, edited by A. A. Collyer and D. W. Clegg, Elsevier Applied Science, London & NY, 1988.

    Google Scholar 

  9. R. I. Tanner and A. C. Pipkin, Trans. Soc. Rheol. 13: 471 (1979).

    Google Scholar 

  10. K. Higashitani and W. G. Pritchard, Trans. Soc. Rheol. 16: 687 (1972).

    Google Scholar 

  11. R. D. Pike and D. G. Baird, J. Non-Newt. Fl. Mech. 16: 211 (1984).

    Google Scholar 

  12. D. G. Baird, M. D. Read and R. D. Pike, Polym. Eng. Sci. 26: 225 (1986).

    Google Scholar 

  13. D. G. Baird, Trans. Soc. Rheol. 19: 147 (1975).

    Google Scholar 

  14. D. G. Baird, J. Polym. Sci. 20: 3155 (1976).

    Google Scholar 

  15. F. Sugeng, N. Phan-Thien and R. I. Tanner, J. Rheol. 32: 215 (1988).

    ADS  Google Scholar 

  16. D. G. Baird, M. D. Read and J. N. Reddy, J. Rheol. 32: 621 (1988).

    ADS  MATH  Google Scholar 

  17. A. S. Lodge and L. de Vargas, Rheol. Acta 22: 151 (1983).

    Google Scholar 

  18. R. Srinivasan and B. A. Finlayson, J. Non-Newt. Fl. Mech. 27: 1 (1988).

    Google Scholar 

  19. C. D. Han, Trans. Soc. Rheol. 22: 171 (1983).

    Google Scholar 

  20. J. M. Davis, J. F. Hutton and K. Walters, J. Phys. (D) 6: 2259 (1973).

    ADS  Google Scholar 

  21. C. D. Han, Trans. Soc. Rheol. 18: 163 (1974).

    Google Scholar 

  22. M. Gottlieb and R. B. Bird, Ind. Eng. Chem. Fund. 18: 357 (1979).

    Google Scholar 

  23. C. D. Han and L. H. Drexler, Trans. Soc. Rheol. 17: 659 (1973).

    Google Scholar 

  24. K. R. Reddy and R. I. Tanner, J. Rheol. 22: 66 (1978).

    Google Scholar 

  25. N. Y. Tuna and B. A. Finlayson, J. Rheol. 28: 79 (1984).

    ADS  Google Scholar 

  26. J. Vlachopoulos and E. Mitsoulis, J. Polym. Eng. 5: 173 (1985).

    Google Scholar 

  27. D. V. Boger and M. M. Denn, J. Non-Newt. FI. Mech. 6: 163 (1980).

    Google Scholar 

  28. C. D. Han, “Slit Rheometry,” Chapter 2 of Rheological Measurement, edited by A. A. Collyer and D. W. Clegg, Elsevier Applied Science, London & NY, 1988.

    Google Scholar 

  29. C. Rauwendaal and F. Fernandez, Polym. Eng. Sci. 25: 765 (1985).

    Google Scholar 

  30. N. Y. Tuna and B. A. Finlayson, J. Rheol. 32: 285 (1988).

    ADS  Google Scholar 

  31. W. Kozicki, C. H. Chou and C. Tiu, Chem. Eng. Sci. 21: 665 (1966).

    Google Scholar 

  32. C. Miller, Ind. Eng. Chem. Fundam. 11: 524 (1972).

    Google Scholar 

  33. T.-J. Liu and C.-N. Hong, Polym. Eng. Sci. 28: 1559 (1988).

    Google Scholar 

  34. J. L. White and A. Kondo, J. Non-Newt. Fl. Mech. 3: 41 (1977).

    Google Scholar 

  35. J. M. Piau, N. El Kissi and B. Tremblay, J. Non-Newt. Fl. Mech. 30: 197 (1988).

    Google Scholar 

  36. J. M. Piau, N. El Kissi and B. Tremblay, “Influence of upstream instabilities and wall slip on melt fracture and sharkskin phenomena during silicone extrusion through orifice dies,” to be published, 1990.

    Google Scholar 

  37. S. A. White and D. G. Baird, J. Non-Newt. FI. Mech. 29: 245 (1988).

    Google Scholar 

  38. S. A. White, A. D. Gotsis and D. G. Baird, J. Non-Newt. FI. Mech. 24: 121 (1987).

    Google Scholar 

  39. C. D. Han and L. H. Drexler, J. Appl. Polym. Sci. 17: 2369 (1973).

    Google Scholar 

  40. S. T. E. Aldhouse, M. R. Mackley and I. P. T. Moore, J. Non-Newt. Fl. Mech. 21: 359 (1986).

    Google Scholar 

  41. M. R. Mackley and I. P. T. Moore, J. Non-Newt. Fl. Mech. 21: 337 (1986).

    Google Scholar 

  42. C. D. Han, Rheology in Polymer Processing, Academic Press, New York, 1976.

    Google Scholar 

  43. E. B. Bagley, J. Appl. Phys. 28: 624 (1957).

    ADS  Google Scholar 

  44. H. L. Weissberg, Phys. Fl. 5: 1033 (1962).

    MathSciNet  ADS  MATH  Google Scholar 

  45. F. N. Cogswell, Polymer Melt Rheology, John Wiley & Sons, New York, 1981.

    Google Scholar 

  46. H. M. Laun and H. Schuch, J. Rheol. 33: 119 (1989).

    ADS  Google Scholar 

  47. W. Philippoff and F. H. Gaskins, Trans. Soc. Rheol. 2: 263 (1958).

    Google Scholar 

  48. F. N. Cogswell, Trans. Soc. Rheol 16: 383 (1972).

    Google Scholar 

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

    Google Scholar 

  50. D. M. Binding, J. Non-Newt. Fl. Mech. 27: 173 (1988).

    MATH  Google Scholar 

  51. R. Ramanathan, D. G. Baird and L. G. Krauskoff, SPE Tech. Papers 3: 773 (1989).

    Google Scholar 

  52. J. M. Dealy, Rheometers for Molten Plastics, Van Nostrand Reinhold, New York, 1982.

    Google Scholar 

  53. R. C. Penwell, R. S. Porter and S. Middleman, J. Polym Sci. A-2 9: 731 (1971).

    Google Scholar 

  54. G. H. France, Chapter 7 of Rheological Measurement, edited by A. A. Collyer and D. W. Clegg, Elsevier Applied Science, London and New York, 1988.

    Google Scholar 

  55. A. V. Shenoy, S. Chattopadhyay, and V. M. Nadkarni, Rheol. Acta 22: 90 (1983).

    Google Scholar 

  56. D. R. Saini and A. V. Shenoy, Eur. Polym J. 19: 811 (1983).

    Google Scholar 

  57. A. V. Shenoy, D. R. Saini and V. M. Nadkarni, Rheol. Acta 22: 209 (1983).

    Google Scholar 

  58. D. R. Saini and A. V. Shenoy, J. Elastomers Plastics 17: 189 (1985).

    Google Scholar 

  59. J. P. Villemaire and J. F. Agassant, Polym. Proc. Eng. 1:223 (1983–4).

    Google Scholar 

  60. J. R. A. Pearson, Mechanics of Polymer Processing, Elsevier Applied Science Publishers, New York, 1985.

    Google Scholar 

  61. A. G. Gibson, Chapter 3 of Rheological Measurement, edited by A. A. Collyer and D. W. Clegg, Elsevier Applied Science, London and New York, 1988.

    Google Scholar 

  62. R. L. Boles, H. L. Davis and D. C. Bogue, Polym. Eng. Sci. 10: 24 (1970).

    Google Scholar 

  63. T. H. Kwon, S. F. Shen and K. K. Wang, Polym. Eng. Sci. 26: 214 (1986).

    Google Scholar 

  64. W. Michaeli, Extrusion Dies, Hanser, Munich and New York, 1984.

    Google Scholar 

  65. Z. Tadmor and C. G. Gogos, Principles of Polymer Processing, John Wiley & Sons, New York, 1979 (Chapter 13).

    Google Scholar 

  66. T.-J. Liu, C.-N. Hong and K.-C. Chen, Polym. Eng. Sci. 28: 1517 (1988).

    Google Scholar 

  67. J. Gavins and M. Modan, Phys. Fl. 10: 487 (1967).

    ADS  Google Scholar 

  68. R. I. Tanner, Appl. Polym. Symp. 20: 201 (1973).

    Google Scholar 

  69. K. Reddy and R. I. Tanner, J. Rheol. 22: 661 (1978).

    ADS  Google Scholar 

  70. V. I. Brizitsky, G. V. Vinogradov, A. I. Isayev and Y. Y. Podolsky, J. Appl. Polym. Sci. 27: 751 (1978).

    Google Scholar 

  71. C. D. Han, M. Charles and W. Philippoff, Trans. Soc. Rheol. 14: 393 (1970).

    Google Scholar 

  72. W. W. Graessley, S. D. Glasscock and R. L. Crawley, Trans. Soc. Rheol. 14: 19 (1970).

    Google Scholar 

  73. J. L. White and J. F. Roman, J. Appl. Polym. Sci. 20: 1005 (1976).

    Google Scholar 

  74. L. A. Utracki, Z. Bakerdjian and M. R. Kamal, J. Appl. Polym. Sci. 19: 481 (1975).

    Google Scholar 

  75. S. J. Kurtz, T. A. De Rossett and M. T. Shaw, U.S. Patent 4,449, 395, (1984).

    Google Scholar 

  76. A. Garcia-Rejon and J. M. Dealy, Polym. Eng. Sci. 22: 158 (1982).

    Google Scholar 

  77. N. Orbey and J. M. Dealy, Polym. Eng. Sci. 24: 511 (1984).

    Google Scholar 

  78. R. I. Tanner, “Recoverable Elastic Strain and Swelling Ratio,” Chapter 4 of Rheological Measurement, edited by A. A. Collyer and D. W. Clegg, Elsevier Applied Science, London and New York, 1988.

    Google Scholar 

  79. M. J. Crochet, A. R. Davies and K. Walters, Numerical Simulation of Non-Newtonian Flow, Elsevier, Amsterdam 1984.

    MATH  Google Scholar 

  80. R. I. Tanner, J. Rheol. 32: 673 (1988).

    ADS  Google Scholar 

  81. A. M. Henderson and A. Rudin, J. Appl. Polym. Sci. 31: 353 (1986).

    Google Scholar 

  82. B. Yang and L. J. Lee, Polym. Eng. Sci. 27: 1079 (1987).

    Google Scholar 

  83. J. L. White and D. Huang, Polym. Eng. Sci. 21: 1101 (1981).

    Google Scholar 

  84. D. C. Huang and J. L. White, Polym. Eng. Sci. 19: 609 (1979).

    Google Scholar 

  85. J. F. Stevenson, L. J. Lee and R. M. Griffith, Polym. Eng. Sci. 26: 233 (1986).

    Google Scholar 

  86. M. G. Rogers, J. Appl. Polym. Sci. 14: 1679 (1970).

    Google Scholar 

  87. R. A. Mendelson and F. L. Finger, J. Appl. Polym. Sci. 19: 1061 (1975).

    Google Scholar 

  88. R. J. Koopmans, J. Polym. Sci. A 26: 1157 (1988).

    Google Scholar 

  89. T. F. Ballenger, I.-Jen Chen, J. W. Crowder, G. E. Hagler, D. C. Bogue and J. L. White, Trans. Soc. Rheol. 15: 195 (1971).

    Google Scholar 

  90. Y. Oyanagi, Appl. Polym. Symp. 20: 123 (1973).

    Google Scholar 

  91. J. L. White, Appl. Polym. Symp. 20: 155 (1973).

    Google Scholar 

  92. C. J. S. Petrie and M. M. Denn, A. I. Ch.E. J. 22: 209 (1976).

    Google Scholar 

  93. N. Bergem, Proc. VIIIth Int. Congr. Rheol., Gothenberg, 1976, p. 50.

    Google Scholar 

  94. N. F. Cogswell, Polymer Melt Rheology, John Wiley & Sons, New York, 1981, p. 101.

    Google Scholar 

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

    Google Scholar 

  96. G. V. Vinogradov, Polymer 18: 1275 (1977).

    Google Scholar 

  97. J. M. Lupton and R. W. Regester, Polym. Eng. Sci. 5: 235 (1965).

    Google Scholar 

  98. R. S. Spencer and R. E. Dillon, J. Colloid Sci. 4: 241 (1949).

    Google Scholar 

  99. M. Fujiyama and H. Awaya, J. Appl. Polym. Sci. 16: 275 (1972).

    Google Scholar 

  100. A. V. Ramamurthy, U.S. Patent 4,552, 712 (1985).

    Google Scholar 

  101. A. V. Ramamurthy, U.S. Patent 4, 554, 120 (1985).

    Google Scholar 

  102. A. V. Ramamurthy, U.S. Patent 4,522, 776 (1985).

    Google Scholar 

  103. H. Yamane and J. L. White, J. Rheol. Japan 15: 131 (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Kluwer Academic Publishers

About this chapter

Cite this chapter

Dealy, J.M., Wissbrun, K.F. (1999). Flow in Capillaries, Slits and Dies. In: Melt Rheology and Its Role in Plastics Processing. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2163-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-2163-4_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5886-2

  • Online ISBN: 978-94-009-2163-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics