Advertisement

Abstract

During recent years the unsteady flow of elastico-viscous liquids in various geometries has attracted much attention. Ting (1963) considered a number of unsteady flow problems for the “second order” fluid of Coleman and Noll (1960) but found that bounded solutions could not be obtained for the cases of physical interest. Waters and King (1970, 1971) found that bounded solutions could be obtained to these problems for liquids with equations of state of the type proposed by Oldroyd(1950). The problems considered by these authors all involved the generation or decay of steady flow in fairly simple geometries. Waters and King found that the flows were strongly affected by the presence of elasticity and that, for quite realistic values of the elastic parameters, the velocity profiles oscillated about their final steady form before tending to it. Of course it has been known for some time that the presence of elasticity has a considerable effect in unsteady flow situations. Often experimentalists try to eliminate such effects from their experiments. Sometimes unsteady behaviour is actually used to determine rheological parameters, for example, in oscillatory experiments and Balance Rheometers (Walters, 1970).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bateman, H., Tables of Integral Transforms, Vol. 1 (New York 1954).Google Scholar
  2. Bullivant, S., M. Sci. Dissertation University of Liverpool (1971).Google Scholar
  3. Coleman, B. D. and W. Noll, Arch. Rat. Mech. Anal. 6, 355 (1960).CrossRefzbMATHMathSciNetGoogle Scholar
  4. Fielder, R. and R. H. Thomas, Rheol. Acta 6, 306 (1967).CrossRefGoogle Scholar
  5. Hunter, S. C., Proc. Edin. Math. Soc. 16, 56 (1968).CrossRefGoogle Scholar
  6. Hwang, S. H., M. Litt, and W. C. Forsman, Rheol. Acta 8, 438 (1969).CrossRefGoogle Scholar
  7. Jones, J. R., and T. S. Walters, Mathematika 13, 83 (1966).CrossRefzbMATHMathSciNetGoogle Scholar
  8. King, M. J., Ph. D. Thesis University of Liverpool (1970).Google Scholar
  9. King, M. J. and N. D. Waters, J. of Phys. D. 5, 141 (1972).ADSCrossRefGoogle Scholar
  10. Oldroyd, J. G., Proc. Roy. Soc. A200, 235 (1950).MathSciNetGoogle Scholar
  11. Oliver, D. R. and W. C. MacSporran, Can. J. Chem. Eng. 48, 243 (1970).CrossRefGoogle Scholar
  12. Tsian Wu Ting, Arch. Rat. Mech. Anal. 14, 1 (1963).Google Scholar
  13. Walters, K., Proc. I.U.M.T.A.M. Conference III, 507 (Israel 1962).Google Scholar
  14. Walters, K. J. Fluid Mech. 40, 191 (1970).ADSCrossRefzbMATHGoogle Scholar
  15. Waters, N. D. and M. J. King, Rheol. Acta 9, 345 (1970).CrossRefzbMATHGoogle Scholar
  16. Waters, N. D. and M. J. King, J. Phys. D. 4, 204 (1971).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • N. D. Dr. Waters
    • 1
  • M. J. Dr. King
    • 2
  1. 1.Dept. of Applied Mathematics, The UniversityLiverpoolEngland
  2. 2.Dept. of MathematicsLiverpool PolytechnicLiverpoolEngland

Personalised recommendations