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 solutio(l by (di-)electrophoresis effects or induce the movement of the solution itself, through electro-hydrodynamic effects. Finding theoretical models for those phenomena requires a multiiphysic 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.
