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

TL;DR

This paper investigates the simulation of the grade-two fluid model in a contraction rheometer setup, focusing on parameter identification and the potential to determine viscosity and model parameters from experimental data.

Contribution

It provides a computational framework for simulating the grade-two fluid model and analyzes the conditions under which model parameters can be identified from rheometer data.

Findings

Simulation approach for grade-two fluid in contraction rheometer

Conditions for parameter identifiability from experimental data

Potential to determine viscosity from force measurements

Abstract

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.