Viscoelastic Fluid: Extended Pom-Pom Model

In this section of the tutorial, modify the set of models and select the input data for the simulation of a viscoelastic fluid with the eXtended Pom-Pom (XPP) model, then use the Fitting Tool from the Material Calibration model to obtain a fitted curve.

The eXtended Pom-Pom model as given by Eqn. (720) and Eqn. (721) uses a set of six model parameters. The polymer viscosity ${\mu }_0$ and the relaxation time $\lambda$ are the linear (or Maxwell) model parameters. The anisotropy parameter $\alpha$, the number of arms on the polymer molecule $Q$, and $1/ϵ$ are the non-linear parameters of the model.

For viscoelastic models, you are generally advised to fit the linear model parameters first by using the experimental $G\prime$ and $G"$ versus frequency curves. Then, in a second step, freezing the linear parameters, you fit the non-linear model parameters by using one of various rheological data curves. For this tutorial, you use the uniaxial elongational viscosity measured against time at a constant elongation rate of 1000 1/s to curve-fit the non-linear model parameters.

This section of the tutorial proceeds in three stages:

1. Fit the $G\prime \left(\omega \right)$, $G"\left(\omega \right)$ curves to obtain the linear model parameters using one viscoelastic mode.
2. Fit the $G\prime \left(\omega \right)$, $G"\left(\omega \right)$ curves again to obtain an improved fit for the linear model parameters using three viscoelastic modes.
3. Fit the ${\eta }_{E\left(t\right)}$ curve to obtain the non-linear model parameters using three viscoelastic modes.