Rheologica Acta

, Volume 14, Issue 5, pp 397–401 | Cite as

A note on co-current laminar flows of two immiscible elastico-viscous liquids

  • J. R. Jones
Article
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Summary

An analysis is presented of steady (isothermal) co-current laminar flows of two immiscible elasticoviscous liquids in cylindrical channels to include (i) unidirectional stratified flow with ripple-free, plane liquid interface, and (ii) concentric-layered swirling flow with ripple-free cylindrical liquid interface. The general conditions are derived for such two-phase channel flows to be physically realizable. It is shown that, whereas (under certain circumstances)single-phase laminar flows are physically possible,two-phase flows, on the other hand, of liquids of the same class may not be. But liquids of theRoberts type (Roberts 1953), with a normal stress difference equivalent to an extra simple tension along the streamlines in simple shearing, are capable of steady unidirectional flowin all circumstances (whether in single or two-phase flow), though they are not in a privileged position so far astwo-phase swirling flows are concerned.

Keywords

Polymer General Condition Normal Stress Laminar Flow Liquid Interface 
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References

  1. 1).
    Roberts, J. E., Proc. II Int. Congr. Rheology, Oxford 1953.Google Scholar
  2. 2).
    Charles, M. E. andP. J. Redburger Canad. J. Chem. Eng.40, 70 (1962).Google Scholar
  3. 3).
    Gemmell, A. R. andN. Epstein Canad. J. Chem. Eng.40, 215 (1962).Google Scholar
  4. 4).
    Yu, H. S. andE. M. Sparrow, Amer. Inst. Chem. Eng. J.13, 10 (1967).Google Scholar
  5. 5).
    Packham, B. A. andR. Shail, Proc. Cambridge Philos. Soc.69, 443 (1971).Google Scholar
  6. 6).
    Isaacs, J. D. andJ. B. Speed U.S. Patent 2, 533, 878 (1950).Google Scholar
  7. 7).
    Chernikin, V. I. Trudy Moskov. Neft. in-ta17, 101 (1956).Google Scholar
  8. 8).
    Charles, M. E. andL. U. Lilleleht, Canad. J. Chem. Eng.43, 110 (1965).Google Scholar
  9. 9).
    Oldroyd, J. G. Proc. Roy. Soc. Ser. A.283, 115 (1965).Google Scholar
  10. 10).
    Oldroyd, J. G. Proc. Roy. Soc. Ser. A200, 523 (1950).Google Scholar
  11. 11).
    Oldroyd, J. G. Proc. Roy. Soc. Ser. A.245, 278 (1958).Google Scholar
  12. 12).
    Walters, K. Quart. J. Mech. Appl. Math.15, 63 (1962).Google Scholar
  13. 13).
    Tanner, R. I. Rheol. Acta3, 21, 26 (1963).Google Scholar
  14. 14).
    Reiner, M. Amer. J. Math.70, 433 (1948).Google Scholar
  15. 15).
    Rivlin, R. S. Proc. Roy. Soc. Ser. A.193, 260 (1948).Google Scholar

Copyright information

© Dr. Dietrich Steinkopff Verlag 1975

Authors and Affiliations

  • J. R. Jones
    • 1
  1. 1.Dept. of Applied MathematicsUniversity of WalesSwanseaU.K.

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