Mathematical modelling of cereal extrusion

Thesis

In this thesis we analyse a mathematical model for an industrial process known as extrusion, and develop techniques for finding solutions to this model. The model for extrusion describes the evolution of a viscous liq- uid containing small vapour bubbles. The lengthscales corresponding to different features in this model can differ by orders of magnitude; so, we first distinguish a macroscale and a microscale. The parameters govern- ing the dynamics of the system also vary over orders of magnitude. We exploit the asymptotic structure of the model to develop reduced systems of equations that are easier to solve, and give physical insight more readily.

In Chapter 1 we describe extrusion, and existing models for extrusion. In Chapter 2 we describe the model for extrusion used throughout this thesis. This model is decomposed into a macroscale model, describing the flow of a viscous, compressible fluid on lengthscales comparable to the extruder; and a microscale model, describing the evolution of vapour bubbles in the mixture. In Chapter 3 we consider the microscale model. We develop reduced models in different parameter regimes and estimate a macroscopic lengthscale for bubble growth, from which we predict param- eter regimes for which the extruded product is long and thin. In Chapter 4 we exploit the slenderness of the product to construct reduced macroscale models, similar to the Trouton model for incompressible flows. In Chapter 5 we develop a numerical scheme capable of solving the full system de- scribed in Chapter 2, and compare these solutions to those of the reduced models developed in Chapters 3 and 4. Finally, in Chapter 6 we provide some concluding remarks on the model for extrusion we have considered, and on the key findings of Chapters 3, 4, and 5.

Authors: McPhail, M

• DOI: 10.5287/ora-dea9jw6ew
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Asymptotics; Industrial mathematics; Fluid mechanics; Extrusion; Cereal
• Subjects: Applied mathematics