Advertisement

Abstract

Extensional viscosity measurements are being made at increasingly high strain rates. The behaviour of semi-solid materials and molten polymers was generally studied at extensional strain rates well below one reciprocal second (1–4); some tests on polymer solutions were also carried out at low strain rates (5). These experiments showed that the Trouton ratio (extensional viscosity divided by shear viscosity) sometimes rose above the value 3 predicted by Newtonian theory. At higher rates of strain, for polymer solutions, the Trouton ratio rises rapidly and novel experimental methods are required (6). The orifice jet thrust technique of Metzner and Metzner (7) has been used independently by the present authors (8), confirming that the Trouton ratio for dilute polyacrylamide solutions is in excess of 103 for extensional strain rates of 103–104 sec−1. Precise knowledge of the flow pattern upstream of the orifice is essential for the accurate use of this method.

Nomenclature

C

Constant defining extensional strain rate (see Appendix)

d11

Extensional strain rate in axial direction

L

Effective length of central jet, covering region of constant extensional strain rate

R0

Initial radius of central jet just outside orifice, corresponding to velocity R 0

R1

Final radius of central jet, corresponding to velocity V 1

Rx

Radius of central jet at point distant x from tube exit

R

Radius of orifice in orifice jet thrust experiment

t

Time for which fluid has been subjected to extensional flow

ΔT

Reduction of thrust on central capillary following jet attachment

V0

Mean velocity of fluid in central jet before extensional flow commences

V1

Mean velocity of fluid in central jet at point distant “L” from tube exit

Vx

Mean velocity of fluid in central jet at point distant “x” from tube exit

V

Mean velocity of fluid through orifice (in orifice jet thrust experiment)

x

Axial distance from central tube exit

δ11

Axial stress in fluid

11)0

Initial axial stress in fluid in central jet

11)av

Time-average axial stress in fluid in central jet

μE

Extensional viscosity i.e. (τ11) av /d 11

μS

Shear viscosity

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1).
    Reiner, M., Deformation, Strain and Flow. Second Edition, p. 78 (New York 1960).Google Scholar
  2. 2).
    Ballman, R. L., Rheol. Acta 4, 137 (1965).CrossRefGoogle Scholar
  3. 3).
    Cogswell, F. N., Plastics Polymers 109 (1968).Google Scholar
  4. 4).
    Stevenson, J. F., Amer. Inst. Ch. Eng. J. 18, 540 (1972).CrossRefGoogle Scholar
  5. 5).
    Acierno, D., R. Greco, and G. Titemanlio, Elongational Flow of Dilute and Concentrated Polymer Solutions. Euromech 37 (Naples 1972).Google Scholar
  6. 6).
    Astarita, G., Ind. Eng. Chem. Fund. 7, 171 (1968).CrossRefGoogle Scholar
  7. 7).
    Metzner, A. B. and A. P. Metzner, Rheol. Acta 9, 174 (1970).CrossRefGoogle Scholar
  8. 8).
    Oliver, D. R. and R. Bragg, Chem. Eng. J. 5, 1 (1973).CrossRefGoogle Scholar
  9. 9).
    Oliver, D. R. and W. C. Macsporran, Rheol. Acta 8, 176 (1969).CrossRefGoogle Scholar
  10. 10).
    Oliver, D. R. and R. Bragg, Canad. J. Chem. Eng. 51, 287 (1973).CrossRefGoogle Scholar
  11. 11).
    Oliver, D. R., Canad. J. Chem. Eng. 44, 100 (1966).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • D. R. Oliver
    • 1
  • R. Bragg
    • 1
  1. 1.Chemical Engineering DepartmentUniversity of BirminghamEngland

Personalised recommendations