Multi-scale modelling of fibre suspensions : particle inertia, confined flows and data-driven approach

Suspensions of fibres and non-spherical particles are encountered in many fields ranging from engineering to biology, e.g. papermaking, composite manufacturing, pharmaceutical applications, red blood cells, food-processing and cosmetics industries, etc. Predicting the evolution of the orientation state of the particles is crucial to estimate the rheology of the suspension, that is its flow behaviour, as well as the final properties of the material. Jeffery's theory, describing the kinematics of a single particle immersed in an homogeneous flow of Newtonian fluid, lays the foundation for almost every models used today. Coarser representations, built upon this theory, have been introduced later to describe statistically the orientation state of the particles, either using a probability density function, or even moments of this function (Advani-Tucker orientation tensors). The assumptions underlying Jeffery's model are however quite restrictive to predict reliably what happens in fibre suspensions flows encountered in industrial processes. In this thesis, we first revisit this model, studying the impact of particle inertia and of confinement (wall effects) on the particle kinematics. In each case, we propose a multi-scale approach, but given the challenges to upscale the microscopic description to the macroscopic scale, we then came up with an innovative approach based on data-driven simulations to circumvent upscaling issues and inaccuracies introduced by macroscopic closure approximations. Finally, we developed efficient numerical methods to simulate fluid flows in thin geometries, considering, within the Proper Generalized Decomposition (PGD) framework, an in-plane/out-of-plane separated representation of the solutions of the incompressible Navier-Stokes equations.(FSA - Sciences de l'ingénieur) -- UCL, 201