Multiphase modelling of coffee bean roasting

The coffee industry relies on fundamental research to improve the techniques and processes related to its products. However, the exploitation of mathematical models that provide insight into improving the roasting of coffee beans has been largely unexplored. In this thesis, we develop mathematical models to understand specific processes in a roasting coffee bean that are crucial in flavour development and consistency. We explore these processes using several models in a multiphase framework to highlight how phase changes, gas pressures, and various chemical reactions occur in different parts of the bean. These new models are then compared to new and existing experimental data, where the merits and pitfalls of each model are then discussed. One main phenomenon that is crucial to the roasting process is the evaporation of water. Various models of evaporation rates are proposed and incorporated into the multiphase models, where the resulting qualitative features of the behaviour are discussed. The behaviour of these multiphase models is studied using asymptotic analysis and the leading-order water and vapour transport predicted from this analysis faithfully reproduce the salient features of the model. We also examine how deformations and material stresses occur during the roasting process. We model the cellulose structure of a coffee bean as a poroviscoelastic material and couple the resulting constitutive equations with aforementioned multiphase models. The qualitative behaviour of this coupled model is discussed for various parameter regimes and used to explain various physical phenomena observed during the roasting process. A summary of key findings is then presented.