Authors: Manuel Ehrlich, James Hamilton, Chang Jiang, Antonio Marques, Benjamin McMillan. \ Supervisor: Dr. Prasun Ray.
Abstract: Non-Newtonian fluids are hugely important in our lives; from the blood in our veins to the ketchup in our kitchen cupboards, we come into contact with them every day. They are essential in a wide range of subjects, such as chemical engineering and pharmaceutics, so it is useful to develop and understand the mathematics behind these fluids. In this project, we aim to compare properties of Newtonian and non- Newtonian fluids both analytically and numerically. Starting with Newtonian fluids, we explore problems such as the Couette Plane Problem and the Stokes Second Problem. We introduce the idea of modelling non-Newtonian fluids, in particular we explore the Oldroyd-B model in order to differentiate between viscoelastic fluids and Newtonian fluids in similar problems. We go on to numerically investigate solutions for non-Newtonian fluids based on more complex models, such as the power-law and Carreau-Yasuda models.