A new Direct Simulation fibre model was developed which allowed flexibility in the fibre during the simulation of fibre suspension flow.This new model was called the �Chain-of-Spheres �model.It was hypothesised that particle shape and deformation could signi ficantly a ffect partic e dynamics,and also suspension bulk properties such as viscosity.Data collected from the simulation showed that flexible fibres in shear flow resulted in an order of 7 −10% bulk relative viscosity increase over the �rigid �fibre result.Results also es- tablished the existence of a relationship between bulk viscosity and particle sti ffness.In comparison with experimental results,other more conventional rigid fibre based methods appeared to underpredict relative viscosity.The flexible fibre method thus markedly improved the ability to estimate relative viscosity.The curved rigid fibre suspension also exhibited increased viscosity of the order twice that of the equivalent straight rigid fibre suspension.With such sensitivity to fibre shape,this result has some important implications for the quality of fibre inclusions used.For consistent viscosity,the shape quality of the fibres was shown to be important. The �Chain of Spheres �simulation was substantially extended to create a new simulation method with the ability to model the dynamics of arbitrarily shaped particles in the Newtonian flow field.This new �3D Particle �simulation method accounted for the inertial force on the particles,and also allowed particles to be embedded in complex flow fields.This method was used to reproduce known dynamics for common particle shapes,and then to predict the unknown dynamics of various other particle shapes in shear flow. In later sections, the simulation demonstrated inertia-induced particle migration inthe non-linear shear gradient Couette cylinder flow,and was used to predict the fibre orientation within a diverging channel flow.The performance of the method was verified against known experimental measurements,observations and theoretical and numerical results where available.The comparisons revealed that the current method reproduced single particle dynamics with great fidelity. The broad aim of this research was to better understand the microstruc- tural dynamics within the fibre-filled suspension and from it,derive useful engineering information on the bulk flow of these fluids.This thesis represents a move forward to meet this broad aim.It is hoped that future researchers may bene fit from the new approaches and algorithms developed here.

A new Direct Simulation fibre model was developed which allowed flexibility in the fibre during the simulation of fibre suspension flow.This new model was called the �Chain-of-Spheres �model.It was hypothesised that particle shape and deformation could signi ficantly a ffect partic e dynamics,and also suspension bulk properties such as viscosity.Data collected from the simulation showed that flexible fibres in shear flow resulted in an order of 7 −10% bulk relative viscosity increase over the �rigid �fibre result.Results also es- tablished the existence of a relationship between bulk viscosity and particle sti ffness.In comparison with experimental results,other more conventional rigid fibre based methods appeared to underpredict relative viscosity.The flexible fibre method thus markedly improved the ability to estimate relative viscosity.The curved rigid fibre suspension also exhibited increased viscosity of the order twice that of the equivalent straight rigid fibre suspension.With such sensitivity to fibre shape,this result has some important implications for the quality of fibre inclusions used.For consistent viscosity,the shape quality of the fibres was shown to be important. The �Chain of Spheres �simulation was substantially extended to create a new simulation method with the ability to model the dynamics of arbitrarily shaped particles in the Newtonian flow field.This new �3D Particle �simulation method accounted for the inertial force on the particles,and also allowed particles to be embedded in complex flow fields.This method was used to reproduce known dynamics for common particle shapes,and then to predict the unknown dynamics of various other particle shapes in shear flow. In later sections, the simulation demonstrated inertia-induced particle migration inthe non-linear shear gradient Couette cylinder flow,and was used to predict the fibre orientation within a diverging channel flow.The performance of the method was verified against known experimental measurements,observations and theoretical and numerical results where available.The comparisons revealed that the current method reproduced single particle dynamics with great fidelity. The broad aim of this research was to better understand the microstruc- tural dynamics within the fibre-filled suspension and from it,derive useful engineering information on the bulk flow of these fluids.This thesis represents a move forward to meet this broad aim.It is hoped that future researchers may bene fit from the new approaches and algorithms developed here.

Cette thèse étudie la possibilité de simuler des écoulements complexes (polymères chargés, suspensions de fibres courtes, polymères) en prenant en compte la structure à l'échelle microscopique dans le cadre de la théorie cinétique. Il y a un couplage fort entre la structure microscopique et la cinématique à l'échelle macroscopique. Le caractère multidimensionnel de l'équation de Fokker-Planck décrivant la microstructure du fluide rend la simulation difficile avec des approches déterministes classiques. Pour palier ce problème, plusieurs méthodes visant à réduire les dimensions sont développées et testées. <br /><br />Ces méthodes sont appliquées en particulier dans le cas des écoulements recirculants. Le cas d'une recirculation ajoute une difficulté supplémentaire car nous ne connaissons ni les conditions initiales, ni les conditions aux limites. Or les recirculations se trouvent dans beaucoup d'écoulements industriels, lors de la mise en forme des matériaux. Pour cette raison nous avons développé des méthodes numériques spécifiques à ce type d'écoulement.<br /><br />Finalement, une partie de la thèse est dédiée à une étude expérimentale permettant de valider les résultats numériques obtenus et d'étudier les phénomènes physiques entrant en jeu dans la mise en forme des polymères chargés.