Equations for the interpretation of normal stress differences in polymer solutions and melts

  • M. Soylu
  • R. A. Mashelkar
  • J. Ulbrecht


Polymer solutions and melts are known to exhibit two types of anomalies, viz. viscous (resulting in shear dependent viscosity under steady flow conditions) and elastic (manifesting in normal stresses under steady flow conditions). An industrial rheologist is faced with the pressing problem of describing such experimentally observed viscous and elastic anomalies in mathematical terms of general utility or specifying in turn explicit constitutive equations with a small number of constants so as to be able to correlate the phenomena satisfactorily. Once such equations are found one hopes to apply these equations directly to the problem of interest. If the problems under consideration are too complicated then one may be able to at least suggest relevant dimensionless groups based on these equations.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    Coleman, B. D., H. Markowitz, and W. Noll, Viscometric flows of non-Newtonian fluids. (New York 1966).Google Scholar
  2. 2).
    Bueche, F., J. Chem. Phys. 22, 1570 (1954).ADSCrossRefGoogle Scholar
  3. 3).
    Yamamoto, M., J. Phys. Soc. Japan 11, 413 (1956).ADSCrossRefMathSciNetGoogle Scholar
  4. Yamamoto, M., J. Phys. Soc. Japan 12, 1148 (1957).ADSCrossRefMathSciNetGoogle Scholar
  5. Yamamoto, M., J. Phys. Soc. Japan 13, 1200 (1958).ADSCrossRefMathSciNetGoogle Scholar
  6. 4).
    Pao, Y H., J. Appl. Phys. 28, 591 (1957).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  7. 5).
    Bogue, D. C. and J. O. Doughty, Ind. Eng. Chem. Fundls. 2, 243 (1966).CrossRefGoogle Scholar
  8. 6).
    Williams, M. C. and R. B. Bird, Ind. Eng. Chem. Fundls. 3, 42 (1964).CrossRefGoogle Scholar
  9. 7).
    Mashelkar, R. A., D. D. Kale, J. V. Kelkar, and J. Ulbrecht, Chem. Eng. Sci. 27, 973 (1972).CrossRefGoogle Scholar
  10. 8).
    Bird, R. B., W. E. Stewart, and E. W. Lightfoot, Transport Phenomena. (New York 1960).Google Scholar
  11. 9).
    Middleman, S., The flow of high polymers. (New York 1968).Google Scholar
  12. 10).
    Pao, Y. H., J. Polymer Sci. 61, 413 (1962).ADSCrossRefGoogle Scholar
  13. 11).
    Oliver, D. R., Can. Jl. Chem. Engg. 44, 100 (1966).CrossRefGoogle Scholar
  14. 12).
    Darby, R., Trans. Soc. Rheol. 14, 185 (1970).CrossRefGoogle Scholar
  15. 13).
    Williams, M. C., Ph. D. Thesis (University of Wisconsin, 1964).Google Scholar
  16. 14).
    Huppler, J. D., Ph. D. Thesis (University of Wisconsin, 1965).Google Scholar
  17. 15).
    Bruce, C. and W. H. Schwarz, J. Polymer Sci. 7, 909 (1969).Google Scholar
  18. 16).
    Kale, D. D., Ph. D. Thesis (University of Salford, 1973).Google Scholar
  19. 17).
    Soylu, M., M. Sc. Thesis (University of Salford, 1971).Google Scholar
  20. 18).
    Marsh, B. D. and J. R. A. Pearson, Rheol. Acta 7, 326 (1968).CrossRefGoogle Scholar
  21. 19).
    Kotaka, T., M. Kurata, and M. Tamura, Jl. Appl. Phys. 30, 1705 (1959).ADSCrossRefGoogle Scholar
  22. 20).
    Ginn, R. F. and A. B. Metzner, Proc. 4th International Rheological Congress, Part 2, 1965, p. 583.Google Scholar
  23. 21).
    Ginn, R. F. and A. B. Metzner, Trans. Soc. Rheol. 13, 429 (1969).CrossRefGoogle Scholar
  24. 22).
    Brodnyan, J. G., F. H. Gaskins, and W. Philippoff, Trans. Soc. Rheol. 1, 109 (1957).CrossRefGoogle Scholar
  25. 23).
    Markowitz, H. and D. R. Brown, Trans. Soc. Rheol. 7, 137 (1963).CrossRefGoogle Scholar
  26. 24).
    Kotaka, T., M. Kurata, and M. Tamura, Rheol. Acta 2, 179 (1962).CrossRefGoogle Scholar
  27. 25).
    Tamura, M., M. Kurata, K. Osaki, and K. Tanaka, J. Phys. Chem 70, 516 (1966).CrossRefGoogle Scholar
  28. 26).
    Osaki, K., K. Tanaka, M. Kurata, and M. Tamura, J. Phys. Chem. 70, 2271 (1966).CrossRefGoogle Scholar
  29. 27).
    Kelkar, J. V, R. A. Mashelkar, and J. Ulbrecht, Trans. Inst. Chem. Engrs. 50, 343 (1972).Google Scholar
  30. 28).
    Blyler, L. L., Trans. Soc. Rheol. 13, 39 (1969).CrossRefGoogle Scholar
  31. 29).
    Sakamoto, K., N. Ishida, and Y. Fukasawa, J. Polymer Sci. 6, 1999 (1968).Google Scholar
  32. 30).
    Rouse, P. E., J. Chem. Phys. 21, 1272 (1953).ADSCrossRefGoogle Scholar
  33. 31).
    Zimm, B. H., J. Chem. Phys. 24, 269 (1956).ADSCrossRefMathSciNetGoogle Scholar
  34. 32).
    Subbaraman, V., R. A. Mashelkar, and J. Ulbrecht, Rheol. Acta 10, 429 (1970).CrossRefGoogle Scholar
  35. 33).
    Spriggs, T. W., Chem. Eng. Sci. 20, 931 (1965).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • M. Soylu
    • 1
  • R. A. Mashelkar
    • 1
  • J. Ulbrecht
    • 1
  1. 1.Department of Chemical EngineeringUniversity of SalfordSalford 5, LancsEngland

Personalised recommendations