Christian graduated from the University of Bath in 2020. During his MMath degree, he focused on applied mathematics, developing interests in fluid dynamics and quantum mechanics. His final year project concerned rheology, in which he classified and appraised a range of models for viscoelastic fluids. In his spare time, Christian enjoys reading, video games, and playing tuba as part of a brass band.

Research project title:
Viscoelastic Flows of White-Metzner Type Fluids

Supervisor(s):
Jonathan Evans

Project description:
Polymer melts and solutions are highly important materials in industry, and display characteristics of both viscous fluids and elastic solids. Due to this, these viscoelastic fluids can be quite complicated to model, and require a constitutive relation in order to relate any material deformation to the internal stresses. Moreover, in many polymer processing applications, geometries are encountered in which singularities arise in the stress, such as re-entrant corners, and flow out of a die. Understanding these singularities; therefore, is a crucial task, as failure to do so can have negative implications on the quality of the processed product.

However, it is only fairly recently that asymptotic analysis has been utilised to quantify these stress singularities for a range of models, largely based on the upper convected Maxwell (UCM) model. This is usually combined with formulating the problem in a natural stress basis, where the stress variables are aligned with the flow direction. In many geometries, this is vital for producing a full description of the fluid flow. Thus, the main goal of this PhD project is to continue and expand the use of these techniques through application to other viscoelastic models.