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Rheologica Acta

, Volume 21, Issue 6, pp 705–712 | Cite as

A three-parameter model describing the behaviour of a viscoelastic liquid in a tangential annular flow

  • P. J. Hamersma
  • J. Ellenberger
  • J. M. H. Fortuin
Original Contributions

Abstract

A three-parameter model describing the shear rate-shear stress relation of viscoelastic liquids and in which each parameter has a physical significance, is applied to a tangential annular flow in order to calculate the velocity profile and the shear rate distribution. Experiments were carried out with a 5000 wppm aqueous solution of polyacrylamide and different types of rheometers. In a shear-rate range of seven decades (5 ⋅ 10−3 s−1 <\(\dot \gamma\) < 1.2 ⋅ 105 s−1) a good agreement is obtained between apparent viscosities calculated with our model and those measured with three different types of rheometers, i.e. Couette rheometers, a cone-and-plate rheogoniometer and a capillary tube rheometer.

Key words

Couette flow polymer solution shear stress shear rate three-parameter model 
a

physical quantity defined by:a = {1 − (η/η0)}/τ0 (Pa−1)

C

constant of integration (1)

r

distancer from the center (m)

r1,r2

radius of the inner and outer cylinder (m)

v

local tangential velocity at a distancer from the center (v =ω r) (m s−1)

v2

local tangential velocity at a distancer2 from the center (m s−1)

\(\dot \gamma\)

shear rate (s−1)

\(\dot \gamma _{r\theta }\)

local shear rate\(\left\{ {r\frac{d}{{dr}}\left( {\frac{{\upsilon _{r\theta } }}{r}} \right)} \right\}\) (s−1)

\(\dot \gamma\)1

wall shear rate at the inner cylinder (s−1)

η

dynamic viscosity (Pa s)

ηa

apparent viscosity (ηa = τ/\(\dot \gamma\)) (Pa s)

ηa1

apparent viscosity at the inner cylinder (Pa s)

η0

zero-shear viscosity (Pa s)

η

infinite-shear viscosity (Pa s)

τ

shear stress (Pa)

τ

local shear stress at a distancer from the center (Pa)

τ0

yield stress (Pa)

τ1,τ2

wall shear-stress at the inner and outer cylinder (Pa)

ω

local angular velocity (s−1)

ω2

angular velocity of the outer cylinder (s−1)

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References

  1. 1.
    Hamersma, P. J., J. Ellenberger, J. M. H. Fortuin, Rheol. Acta20, 270–279 (1981).Google Scholar
  2. 2.
    Abramowitz, M., I. A. Stegun, Handbook of Mathematical Functions, Dover Publications (New York 1965).Google Scholar
  3. 3.
    Weast, R. C., S. M. Selby, Handbook of Tables for Mathematics, The Chemical Rubber Co. (Ohio 1967).Google Scholar
  4. 4.
    Int. Math. and Stat. Library (IMSL), IMSL Co. (Houston, Texas, 1980).Google Scholar
  5. 5.
    Friebe, H. W., Rheol. Acta15, 329–355 (1976).Google Scholar
  6. 6.
    Schlegel, D., Rheol. Acta19, 375–380 (1980).Google Scholar

Copyright information

© Dr. Dietrich Steinkopff Verlag 1982

Authors and Affiliations

  • P. J. Hamersma
    • 1
  • J. Ellenberger
    • 1
  • J. M. H. Fortuin
    • 1
  1. 1.Laboratory of Chemical EngineeringUniversity of AmsterdamAmsterdamThe Netherlands

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