Computational analysis of a contraction rheometer for the grade-two fluid model

We explore the possibility of simulating the grade-two fluid model in a geometry related to a contraction rheometer, and we provide details on several key aspects of the computation. We show how the results can be used to determine the viscosity $\nu$ from experimental data. We also explore the identifiability of the grade-two parameters ${\alpha }_1$ and ${\alpha }_2$ from experimental data. In particular, as the flow rate varies, force data appears to be nearly the same for certain distinct pairs of values ${\alpha }_1$ and ${\alpha }_2$; however we determine a regime for ${\alpha }_1$ and ${\alpha }_2$ for which the parameters may be identifiable with a contraction rheometer.