Viscoelastic Flows of White-Metzner Type Fluids

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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 materials can be quite hard to model effectively, and require a constitutive relation in order to relate any material deformation to the internal stresses. This is particularly the case in many polymer processing applications, where these materials are encountered in situations such as flow round a re-entrant corner, and flow out of a die. These geometries are linked by the existence of stress singularities, and failure to understand the mathematics of these singularities can ultimately lead to negative implications on the quality of any processed products.Most of the early work on understanding this viscoelastic flow was completed by chemical engineers, who took a largely data-driven approach to proposing and testing models for these materials; analytical approaches were rarely attempted. However, in the last thirty years, this has begun to change via the usage of asymptotic analysis, which can produce a simpler 'leading order' description of the flow whilst retaining the key underlying physics.The main aim of this project is to build on the success of these techniques by applying them to classes of viscoelastic fluids governed by White-Metzner type constitutive relations. In particular, flow around a re-entrant corner will be studied, in which leading order governing equations will be constructed via the use of boundary layer theory, and by utilising a natural stress formulation to describe the stresses within the fluid. These equations will then be analysed numerically, and their suitability for describing the re-entrant corner flow will be assessed via comparisons with simulations from computational fluid dynamics (CFD) software such as OpenFOAM.