Suspension flows in varied settings and at different concentrations of particles are studied theoretically using various modeling techniques. Particulate suspension flows are dispersion of particles in a continuous medium and their properties are a consequence of the interplay among hydrodynamic, buoyancy, interparticle and Brownian forces. The applicability of continuum modeling techniques to suspension flows at different particle concentration was assessed by studying systems at different time and length scales. The first two studies involve the use of modeling techniques that are valid in systems where the forces between particles are negligible, which is the case in dilute suspension flows. In the first study, the growth and progradation of deltaic geologic bodies from the sedimentation of particles from dilute turbidity currents is modeled using the shallow water equations or vertically averaged equations of motions coupled with a particle conservation equation. The shallow water model provides a basis for extracting grain size and depositional history information from seismic data. Next, the Navier-Stokes equations of motion and the convection-diffusion equation are used to model suspension flow in a biomedical application involving the flow and reaction of drug laden nanovectors in arteries. Results from this study are then used prescribe the best design parameters for optimal nanovector uptake at the desired sites within an artery. The third study involves the use of macroscopic two phase models to describe concentrated suspension flows where interparticle hydrodynamic forces cannot be neglected. The isotropic form of both the diffusion-flux and the suspension balance models are solved for a buoyant bidisperse pressure-driven flow system. The model predictions are found to compare fairly well with experimental results obtained previously in our laboratory. Finally, the power of discrete type models in connecting macroscopic observations to structural details is demonstrated by studying a system of aggregating colloidal particles via Brownian dynamics. The results from the simulations match experimental shear rheology and also provide a structural explanation for the observed macroscopic behavior of aging. / text

Cette thèse s'intéresse à une étude variée des EDSRs. Une grande partie des résultats sont obtenus sous l'hypothèse d'une croissance de type quadratique du générateur en sa dernière variable. Un premier lien entre EDSRs quadratiques unidimensionnelles et théorie des jeux nous amène à développer des résultats avec générateurs convexes. La théorie du contrôle optimal nécessite quant à elle de traiter du cas multidimensionnel, dans lequel existence et unicité globales ne sont obtenues que pour des générateurs diagonalement quadratiques. Les résultats majeurs sur les EDSRs réfléchies (dont la solution est contrainte à rester dans un domaine) concernent des générateurs Lipschitziens. C'est dans ce cadre que nous développons un résultat de propagation du chaos, avec une contrainte portant sur la loi de la solution plutôt que sur sa trajectoire. Nous dressons enfin un pont entre EDSRs quadratiques et EDSRs réfléchies grâce aux EDSRs quadratiques de type champ moyen. Nous donnons plusieurs nouveaux résultats sur la possibilité de résoudre une équation quadratique dont le générateur dépend également de la moyenne des deux variables. / In this thesis, we are interested in studying variously Backward Stochastic Differential Equations. A large proportion of the results are obtained under the assumption that the driver is of quadratic growth in its last variable. A first link between one-dimensional quadratic BSDEs and game theory leads us to develop results with convex drivers. Optimal control theory requires as for it to deal with the multidimensional case, in which global existence and uniqueness are obtained only for diagonaly quadratic drivers. Major achievements in reflected BSDEs (whose solution is constrained to remain in a domain) are reached for Lipschitz drivers. We develop a result of chaos propagation in this setting, with a constraint on the law of the solution rather than on its path. We finaly build bridge between quadratic BSDEs and reflected BSDEs thanks to mean field quadratic BSDEs. We give several new results on solvability of a quadratic BSDE whose driver depends also on the mean of both variables.