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Kinetic theory and rheology of dilute polymer solutions

  • R. Byron Bird
  • Ole Hassager
  • Robert C. Armstrong
Chapter

Abstract

Treatises on transport phenomena and kinetic theory have given the molecular theory for the transport properties of simple gases and liquids, but have ignored the extensive literature on polymer solutions. Much of this literature is based on the configuration-space theory developed through the years and summarized and exploited by Kirkwood and his collaborators (1). Most of the kinetic theory workers, however, have not been interested in obtaining the expression for the stress tensor for use in solving flow problems, nor in obtaining relations among the results of various rheological experiments. It is to these topics that this short note is addressed.

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References

  1. 1).
    Kirkwood, J. G., Macromolecules (New York 1967).Google Scholar
  2. 2).
    Giesekus, H., Kolloid-Z. 147, 29–45 (1956).CrossRefGoogle Scholar
  3. 3).
    Prager, S., Trans. Soc. Rheol. 1, 53–62 (1957).CrossRefzbMATHGoogle Scholar
  4. 4).
    Bird, R. B. and R. C. Armstrong, J. Chem. Phys. 56, 3680–3682 (1972).ADSCrossRefGoogle Scholar
  5. 5).
    Bird, R. B., Z. angew. Math. Phys. 23, 157–159 (1972).CrossRefGoogle Scholar
  6. 6).
    Armstrong, R. C. and R. B. Bird, J. Chem. Phys. 58, 2715–2723 (1973).ADSCrossRefGoogle Scholar
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    Armstrong, R. C., Doctoral Dissertation, University of Wisconsin (1973); J. Chem. Phys. 60, 724–733 (1974).ADSCrossRefGoogle Scholar
  8. 8).
    Bird, R. B., H. R. Warner Jr. and D. C. Evans, Adv. Polymer Science 8, 1–90 (1971). In Eq. [10.6] on page 44, 15/14 should read 4/7, and in Eq. [12.9] on page 49, 1/120 should be replaced by 1/280. Finally, it should be noted that H. Giesekus (see Rheol. Acta 2, 50, 1962) has developed expressions equivalent to Eqs. [25.20]-[25.22] on page 83.CrossRefGoogle Scholar
  9. 9).
    Stevenson, J. F. and R. B. Bird, Trans. Soc. Rheol. 15, 135–145 (1971).CrossRefGoogle Scholar
  10. 10).
    Warner, H. R. Jr., Ind. Eng. Chem. Fund. 11, 379–387 (1972).CrossRefMathSciNetGoogle Scholar
  11. 11).
    Hassager, O. and R. B. Bird, J. Chem. Phys. 56, 2498–2501 (1972).ADSCrossRefGoogle Scholar
  12. 12).
    Hassager, O., J. Chem. Phys. 60, 2111–2124, 4001-4008 (1974).ADSCrossRefGoogle Scholar
  13. 13).
    Hassager, O., Doctoral Dissertation, University of Wisconson (1973).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • R. Byron Bird
    • 1
  • Ole Hassager
    • 1
  • Robert C. Armstrong
    • 1
  1. 1.Chemical Engineering Dept.University of WisconsinMadisonUSA

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