The guidelines for analyzing the problem that were presented in Choosing the Differential Viscoelastic Model for differential viscoelastic flow are also valid for integral viscoelastic flow. Specific guidelines for integral viscoelastic model selection are provided below. The Ansys Polymat module of Ansys Polyflow can be used to compare experimental data with model predictions, in order to help you determine appropriate viscoelastic models. See the Ansys Polymat User’s Guide for details.
Both the Doi-Edwards model and the KBKZ model provide realistic simulations of viscoelastic flow behavior, although the KBKZ model provides more flexibility in the choice of the damping function.
Theoretically, the Doi-Edwards model has an infinite number of relaxation
times (represented by the 
summation in Equation 11–47)
determined by two parameters: the main relaxation time and the zero-shear-rate
viscosity. This model is characterized by shear thinning and a non-quadratic
first normal-stress difference at high shear rates. It also predicts a nonzero
second normal-stress difference and a finite steady extensional viscosity.
For simple shear flows, however, a purely viscous component must be added to
the extra-stress tensor for stability purposes. The viscosity associated with
the purely viscous stress leads to a plateau zone at high shear rates. Thus, the
slope of the curve 
as a function of 
is greater than –1.
The KBKZ model adds another level of complexity compared to the Doi-Edwards
model. In addition to the spectrum that describes the linear viscoelastic
behavior of the material, you can also define a damping function. Both the PSM
and the Wagner damping functions involve two material constants that mainly
control the shear and elongational behavior, respectively: 
and 
for the PSM model, and 
and 
for the Wagner model. Another parameter, 
, controls the normal-stress-difference ratio. See KBKZ Model for
details about the equations used for the damping function.
For the PSM model, high values of 
lead to a large zone of the zero-shear-rate plateau.
corresponds to a constant damping function. In the latter
case, the constitutive equation for the Maxwell-B model (Equation 11–11) is
recovered. If the value of 
is decreased, the zero-shear-rate plateau moves toward lower
shear rates. In the case of the Wagner model, high values of 
lead to a short plateau of zero shear rate, while a small
value of 
gives a plateau for a large range of shear rates.
For small values of 
(defined by Equation 11–54), both the PSM and the Wagner damping functions are
very similar. For high values of 
, however, the exponential function of the Wagner model
decreases more rapidly than the rational function of the PSM model. High values
of 
occur in the case of large deformations.
The 
parameter has no effect on shear viscosity, nor on the first
and second normal-stress differences. It affects only the extensional viscosity.
A value of zero for 
leads to an unbounded steady extensional viscosity. Increasing
decreases the maximum value of the steady extensional
viscosity curve.
For both the PSM and the Wagner models, it is possible to introduce the concept of irreversibility originally mentioned by Wagner [38]. The idea is that the damping function must never be allowed to increase along the past trajectory of a fluid particle. According to Wagner, this is a realistic assumption when intermolecular association occurs, as in an entanglement, for example. For a material moving at a high flow rate through a contraction followed by an expansion, it is reasonable not to allow the damping function to increase again after the entanglement.
The KBKZ model also makes use of the normal-stress-difference ratio. This ratio does not affect the shear viscosity or the normal-stress differences, but it does have an impact on the extensional viscosity.
Like the Doi-Edwards model, the KBKZ model requires a purely viscous component of the extra-stress tensor in order to avoid instability in simple shear flows at high shear rates. For further information, see [16].