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Theoretical models for the electrokinetics of weakly permeable porous colloidal particles are absent from the literature. The understanding of this topic will be advanced through a systematic analysis of the standard electrokinetic equations, resulting in a theory for the electrophoretic mobility of weakly permeable porous colloidal particles. / The standard electrokinetic equations are employed to model the flux of solvent and ions outside the porous particle. To be consistent with this approach, the flux of solvent and ions in the pores must also be governed by the standard electrokinetic equations. However, in practice, only transport phenomena on the particle scale are observed and it is sufficient for information regarding pore-scale behaviour to be retained purely in the form of averaged quantities. To complete the theoretical description, the standard electrokinetic equations outside the particle must be coupled to particle-scale transport equations inside the particle via boundary conditions at the porous/free-fluid interface. / It has been shown experimentally and theoretically for coupled Stokes and Darcy flows, that the correct interfacial boundary condition for the tangential external flow is given by the Beavers-Joseph-Saffman (BJS) condition. The effect of the BJS boundary condition on the hydrodynamic drag on an oscillating porous particle is investigated. It is found that the particle may be regarded as impermeable with a slip length independent of frequency, and the resulting drag is significantly reduced in comparison with an equivalent impermeable particle that does not exhibit a slip length. / The transport of a general electrolyte solution through a rigid porous body subjected to a static (d.c.) electric field is studied. The pore-scale description is given by the standard electrokinetic equations, including the effects of ion diffusion, electromigration and convection. Homogenization theory is used to derive transport equations that capture the particle-scale behaviour. It is proven that the transport coefficient tensors obey Onsager’s reciprocal relations and the diagonal coefficient tensors are positive definite. / New interfacial boundary conditions are derived using conservation arguments supplemented by Stern-layer theory. When combined with the particle-scale transport equations, these boundary conditions incorporate four principal effects into the standard electrokinetic model: solvent slip and Stern-layer ionic conduction at the interface, and macroscopic ionic conduction together with the electroosmotic flow of solvent through the particle. / The method of matched asymptotic expansions is then used to construct an approximate solution to the aforementioned system, in the thin double-layer limit. An expression for the electrophoretic mobility of a weakly permeable colloidal sphere is produced that consists of a generalization of Smoluchowski’s formula to encompass porous particles, and a next order correction. For the first time, the effects of solvent slip and Stern-layer ionic conduction within the porous/free-fluid interface, in conjunction with macroscopic ionic conduction and electroosmosis through the particle, are exhibited. It is shown that solvent slip at the porous interface is overwhelmingly the dominant effect on the mobility of weakly permeable porous colloidal particles.

L'utilisation de systèmes électromécaniques microstructurés pour analyser et manipuler des solutions biologiques ou des cellules vivantes (bio-MEMS) a pris un essor considérable ces dernières années. Dans ce genre de dispositifs, l'utilisation de champs électriques est fréquente, que ce soit pour percer les membranes des cellules et effectuer une transfection de gènes par exemple (électroporation), pour les déplacer ((di )électrophorèse) ou agir sur le milieu dans lequel elles baignent (électro-hydrodynamique). La modélisation des phénomènes induits par ces champs électriques dans les solutions aqueuses est un problème multi-physique et multi-échelle. Au déplacement des électrons s'ajoute en effet la migration des ions présents dans la solution. Ceux-ci se concentrent en particulier aux abords des électrodes formant des couches minces dont les paramètres évoluent de façon encore mal connue en fonction notamment des conditions d'alimentation. La thèse se concentre sur les applications électro-hydrodynamiques dans lesquelles une solution saline est mise en mouvement par des forces électriques agissant sur ses ions, concentrés dans des couches de charges minces, au voisinage des électrodes. Sont d'abord présentés les résultats expérimentaux et des modèles simples du problème électromécanique dans le cas de structures 2D à électrodes coplanaires. Devant l’importance des écarts entre les résultats théoriques et expérimentaux, des modèles plus complets sont alors proposés et évalués. Malgré les améliorations fournies par ces modèles, des écarts importants subsistent entre théorie et expérimentation, et une étude totalement découplée des aspects électriques et mécaniques est alors réalisée sur une structure 1D. Cette étude permet de mieux cerner les dépendances de certains paramètres physiques vis-à-vis des conditions d’alimentation avec une comparaison systématique des résultats expérimentaux et des résultats de modèles circuits linéaires et non linéaires, au travers d’une approche fréquentielle par diagrammes de Bode et d’une approche temporelle par figures de Lissajous. Il a ainsi pu être mis en évidence l’importance pratique potentielle de certains phénomènes rarement pris en compte dans des modèles globaux : saturation des couches minces, permittivité non constante, effets de bords,… Des applications pratiques ont pu être dégagées et testées expérimentalement, dans le domaine des micro-mélangeurs. Outre ces développements, une brève étude est décrite, portant sur la modélisation des cellules et de leurs membranes extrêmement fines en regard des autres dimensions caractéristiques du système, dans la perspective par exemple d'applications en électroporation. Une autre étude est faite portant sur l’utilisation potentielle de méthodes numériques dites « sans maillage » pour ce type d’applications, l’accent étant mis sur la résolution du problème de Poisson dans des systèmes 2D. / Analysis and manipulation of biological solutions or cells in micro-electromechanical systems has considerably improved during last years. In such systems, it is common to use electric fields, in order e.g. to increase cells membrane porosity, which is known as electroporation, and thus allow for gene transfection. Electric fields can also generate the motion of cells in a solution by (di-)electrophoresis effects or induce the movement of the solution itself, through electro-hydrodynamic effects. Finding theoretical models for those phenomena requires a multi-physic and multi-scale approach. The ions present in the saline solution react mechanically to the electrical excitation of the system. They migrate to the regions close to the electrodes, in very thin layers whose parameters vary in non-obvious ways, depending namely on the power supply conditions. The text focuses on electro-hydrodynamic applications in which a flow is generated by electric forces acting on the ions present in the solution, mostly in thin charge layers near the electrodes. Experimental results and simple existing models are first presented for 2D coplanar electrodes systems. Regarding the important differences between models and experimentation, more complete models are then proposed and tested. In spite of the improvements of those new models, some important differences remain, so that a fully decoupled approach of electrical and mechanical aspects is needed, which is pursued on a 1D structure. This new study allows for a better understanding of the dependences of some physical parameters with regard to supply conditions, with a systematic comparison of experimental results and non-linear circuit models results. A frequency approach with Bode diagrams is used, as well as a time approach with Lissajous figures. It has been shown that some phenomena are of practical and fundamental importance, which are not always taken into account in more general and global models : saturation phenomena, non constant physical parameters, border effects,… Practical applications have been deduced and tested experimentally, in the case of micro-mixing. A brief study is also mentioned, concerning the modeling of cells with extremely thin membranes compared to the other characteristic dimensions of the system, in the perspective e.g. of electroporation applications. Another short study is performed about the potential use of « meshless » numerical methods for the solving of this kind of applications, focusing more specifically on the solving of a Poisson problem in 2D.