A study of the time independent grade two model in a 2D contraction rheometer

Non-Newtonian fluids are found in many fields of science: food, medicine, engineering, etc, properties of these fluids are studied with rheometers. Not all rheometers can properly describe each model and we aim to evaluate if a contraction rheometer can distinguish the model parameters of the Grade two model.

This is first done in 2D with a simplified well studied algorithm and then with a general method proposed in [1]. Both methods are based on transforming the problem into a coupling between a Stokes-like system and a transport equation.

Incompressibility is enforced by penalty iteration and Scott–Vogelius elements since it is hypothesised that divergence free elements are advantageous when solving the coupled transport equation. The transport is solved with linear polynomials with different stabilizations investigated. We discuss preliminary results and limitations.

This non-Newtonian modeling is part of a larger predictive Real Unified Continuum framework for modeling full systems of eg swallowing (part of the Swallow project), plant-based food production, blood flow, gastrointestinal modeling, etc.

References

• [1] Nadir Arada, Paulo Correia, and Adélia Sequeira. Analysis and finite element simulations of a second-order fluid model in a bounded domain, Numerical Methods for Partial Differential Equations: An International Journal 23, 1468–1500, 2007. [DOI: 10.1002/num.20236]