A three-parameter model describing the behaviour of a viscoelastic liquid in a tangential annular flow |
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Authors: | P J Hamersma J Ellenberger J M H Fortuin |
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Institution: | (1) Laboratory of Chemical Engineering, University of Amsterdam, Plantage Muidergracht 30, NL-1018 TV Amsterdam, The Netherlands |
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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 <
< 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.
a
physical quantity defined by:a = {1 – (
/
0)}/
0 (Pa–1)
-
C
constant of integration (1)
-
r
distancer from the center (m)
-
r
1,r
2
radius of the inner and outer cylinder (m)
-
v
r
local tangential velocity at a distancer from the center (v
r
=
r
r) (m s–1)
-
v
2
local tangential velocity at a distancer
2 from the center (m s–1)
-
shear rate (s–1)
-
local shear rate
(s–1)
-
1
wall shear rate at the inner cylinder (s–1)
-
dynamic viscosity (Pa s)
-
a
apparent viscosity (a = /
) (Pa s)
-
a1
apparent viscosity at the inner cylinder (Pa s)
-
0
zero-shear viscosity (Pa s)
-
infinite-shear viscosity (Pa s)
-
shear stress (Pa)
-
r
local shear stress at a distancer from the center (Pa)
-
0
yield stress (Pa)
-
1,
2
wall shear-stress at the inner and outer cylinder (Pa)
-
r
local angular velocity (s–1)
-
2
angular velocity of the outer cylinder (s–1) |
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Keywords: | Couette flow polymer solution shear stress shear rate three-parameter model |
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