Comparison between uniaxial and biaxial elongational flow behavior of viscoelastic fluids as predicted by differential constitutive equations |
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| Authors: | T Isaki M Takahashi T Takigawa T Masuda |
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| Institution: | (1) Research Center for Biomedical Engineering, Kyoto University, 606 Kyoto, Japan;(2) Present address: Nagoya Laboratory, Mitsui Toatsu Chemicals, 457 Nagoya, Japan;(3) Department of Polymer Chemistry, Kyoto University, 606 Kyoto, Japan |
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| Abstract: | Behavior of polymer melts in biaxial as well as uniaxial elongational flow is studied based on the predictions of three constitutive models (Leonov, Giesekus, and Larson) with single relaxation mode. Transient elongational viscosities in both flows are calculated for three constitutive models, and steady-state elongational viscosities are obtained as functions of strain rates for the Giesekus and the Larson models.Change of elongational flow behavior with adjustable parameter is investigated in each model. Steady-state viscosities 
E
and
B
are obtained for the Leonov model only when the strain-hardening parameter  is smaller than the critical value
cr
determined in each flow. In this model, uniaxial elongational viscosity
E
increases with increasing strain rate
, while biaxial elongational viscosity
B
decreases with increasing biaxial strain rate
B
. The Giesekus model predictions depend on the anisotropy parameter  .
E
and
B
increase with strain rates for small
B
while they decrease for large . When is 0.5,
E
in increasing, but
B
is decreasing. The Larson model predicts strain-softening behavior for both flows when the chain-contraction parameter   > 0.5. On the other hand, when is small, the steady-state viscosities of this model show distinct maximum around
 =
B
= 1.0 with relaxation time . The maximum is more prominent in
E
than in
B
. |
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| Keywords: | Constitutive equation biaxial extension Leonov model Giesekus model Larson model |
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