The lattice Boltzmann (LB) method is a versatile way to model complex fluids with hydrodynamic interactions through solving the Navier-Stokes equations. It is well-known that the role of hydrodynamic interactions is ignorable in studying the Boltzmann equilibrium of colloidal (Brownian) particles. However, full hydrodynamic interactions play an important role in their dynamics. In the LB framework for moving colloids, the “bounce-back on links” method is used to calculate the hydrodynamic forces. In this thesis, three kinds of colloidal complex fluids with full hydrodynamic interactions are simulated by lattice Boltzmann methods: colloids in a binary fluid, magnetic colloids in a single fluid and magnetic colloids in a binary fluid. First, we have done extensive simulations of nanoparticles in a binary fluid, following up previous work[1] which predicted formation of a “bijel” (bicontinuous interfacially jammed emulsion gel) in symmetric fluid quenches. Our work in this thesis focuses on the analysis of the dynamics after nanoparticles become arrested on the fluid-fluid interfaces under conditions varying from a symmetric quench to a strongly asymmetric quench. Although these new simulations extend the time window studied by a factor of two, slow domain growth is still observed. Our new analyses address the mechanics of the slow residual dynamics which involves cooperative motion of the nanoparticles at the fluid-fluid interfaces. The second topic is the LB simulation of colloidal ferrofluids to see the effect of full hydrodynamic interactions among magnetic colloids. The main focus is on how the hydrodynamic interaction affects both the equilibrium dynamics of these dipolar systems and also their transient dynamics to form clusters. Numerically, magnetic colloids are implemented with the long-range dipolar interactions described by Ewald summation. To check the effect of full hydrodynamic interactions, Brownian dynamics without any hydrodynamic interaction has been done for comparison: Monte Carlo results are also reported. We confirm that our LB generates the Boltzmann distribution for static equilibrium properties, by comparison with these methods. However, the equilibrium dynamics is altered: hydrodynamic interactions make the structural relaxations slower in both the short-time and the long-time regime. This slow relaxation rate is also found for transient motions. The third topic addresses magnetic colloids in a binary fluid. In contrast with the preceding two systems which correspond directly to laboratory experiments, this last system is so far only predicted by the LB results in this thesis. To explore this hypothetical new material by the LB method, the basic structures are investigated in terms of both domain growth morphology and the arrangement of magnetic colloids. Under conditions varying from a symmetric quench to an asymmetric quench, a chainlike arrangement is observed for dipoles jammed on the surfaces, but the basic morphology of domains is still maintained regardless of the dipolar strength. In addition, applying external field affects the morphology of domains and the stability of domain structures.

Cette thèse porte sur le développement d’une nouvelle technique de modélisation des problèmes IFS utilisant les méthodes particulaires. Ce travail s’inscrit dans la continuité des travaux de recherche de l’équipe biomécanique du LAMIH, concernant la compréhension du comportement de l’os humain dans son environnement de moelle osseuse. La méthode SPH a été utilisée pour la modélisation des travées osseuses, supposées dans une première approche comme des solides élastiques. La méthode LB a été développée pour la modélisation des écoulements de moelle considérée comme un fluide visqueux incompressible. L’efficacité et la performance de ces deux méthodes ont été démontrées grâce aux benchmarks académiques évalués et les résultats comparés à ceux de la littérature ou ceux obtenus par des logiciels commerciaux. A l’issue d’une revue de l’état de l’art des techniques de couplage fluide-structure, une approche partitionnée en temps a été choisie, permettant d’utiliser deux codes distincts basés sur des algorithmes de résolution de type dynamique explicite. La discrétisation spatiale est faite par une technique spécifique basée sur les domaines fictifs, cette technique est très efficace car elle ne nécessite pas de rediscrétisation des domaines. L’approche de couplage développée a été appliquée à des benchmarks académiques ainsi qu’à une application en biomécanique, ayant permis d’aboutir à des résultats numériques satisfaisants. Plusieurs pistes d’amélioration sont maintenant nécessaires afin d’aller vers des modélisations plus biofidèles telles que la prise en compte du contact et de l’endommagement. / The objective of this thesis is the development of a new technique for the FSI problems modelling using particulars methods. This work is in the continuity of the LAMIH biomechanics team research works, regarding the comprehension of behavior of bone in its environment of marrow. The SPH method was used for the trabeculae modelling, supposed in a first attempt as an elastic solid. The LB method was developed for the marrow flow modelling considered as a viscous incompressible liquid. The efficacy and performance of these two methods were demonstrated using academics benchmarks which were evaluated and the results were compared of those of literature and of those obtained from commercials softwares. Following a bibliographic review of FSI coupling techniques, a partitioned approach in time was chosen, allowing the use of two separates codes, both based on a dynamic explicit algorithm resolution scheme. The special discretization was done based on a specific technique of fictional domain, this technique is very efficient because it doesn’t require an additional domain discretization. The coupling approach developed was applied on academic benchmarks and on a biomechanical application, leading to satisfactory numerical results. Many Improvement track are now necessary to go towards more biofidelic modeling as taking into account the contact and the damage.