This doctoral thesis deals with the study of electro-hydrodynamics in the area of numerical modelling of biomechanical systems, concretely in the method of bioimpedance plethysmography. Solving tasks of pulsatile blood flow in the elastic vessel wall is currently one of the most complicated problem in mechanics and biomechanics due to the interaction of two continua on the common boundary. The whole system is additionally loaded by diagnostic electric current. This doctoral thesis was created in cooperation with the Institute of Scientific Instruments of the CAS, v. v. i. Brno with the team engaged in medical signals (the leader Ing. Pavel Jurák, CSc.). Experimental measurements were made independently in the St. Anne's University Hospital Brno in the International Clinical Research Center ICRC and in the Mayo Clinic USA.

The realm of the nano-world begins when things start getting smaller in size than one thousandth of the thickness of the human hair. Surface patterning at the nanoscale has started to find applications in information storage, self-cleaning of surfaces due to the "lotus effect", biocompatible materials based on surface roughness and many more. Several methods such as particle-beam writing, optical lithography, stamping and various kinds of self-assembly are widely used to serve the purpose of patterning smaller surface structures. However, globally much research is going into developing more efficient, reproducible and simple methods of patterning surfaces and in better controlling the order of these nanostructures. Researchers have always looked upon Nature to get inspiration and to mimic its model in engineering novel architectures. One of the methods used by this greatest artist (Nature) to make beautiful patterns around is through reaction diffusion based non-linear processes. Non-linear systems driven away from equilibrium sustain pattern only during the continuous dissipation of a regular flow of energy and are different from equilibrium processes that are converging towards a minimum in free energy (a. k. a. self-assembly). Dissipative pattern formation from micrometer to kilometers scale has been known but ordered patterns at nanoscale have never been achieved. In the process of thoroughly characterizing suitable substrates for nanoelectronics applications, we came across a remarkable process leading to the formation of highly ordered arrays of dimples on tantalum. The pattern formation happens in a narrow electrochemical windows which are functions of many parameters such as concentration, external applied voltage, temperature etc. After investigating the formation of dimples by performing spatio-temporal studies, we found that the underlying principles behind this unique way of engineering nano-structures have their roots in nonlinear interaction/reaction electro-hydrodynamics. We then have demonstrated the generality of this process by extending it to titanium, tungsten and zirconium surfaces. The pattern similar to Rayleigh-Bernard convection cells originates inside the electrochemical solution due to coupling among electrolyte ions during their migration across the electrochemical double layer (Helmholtz layer) and simultaneously imprints on the surface due to dissolution of metal oxide via etching. Based on these results we further postulate that, given appropriate electropolishing chemistry; these patterns can be formed on virtually any metal or semiconductor surface. The application of these nanostructures as nanobeakers for placing metal nanoparticles is also elucidated Highly porous materials such as mesoporous oxides are of technological interest for catalytic, sensing, optical and filtration applications: the mesoporous materials (with pores of size 2-50 nm) in the form of thin films can be used as membranes due large surface area. In the second part of this thesis, a new technique of making detachable ultrathin membranes of transition metal oxides is presented. The underlying concepts behind the detachment of membranes from the underlying substrate surface are discussed. The control on the size of the pores by modulating the voltage and concentration is also elucidated. The method is generalized by showing the similar detachment behavior on other metal oxide membranes.Thus, the results of this work introduces new techniques of engineering nanostructures on surfaces based on reaction-diffusion adaptive systems and contribute to the better understanding of electrochemical self-organization phenomena due to migration coupling induced electro-hydrodynamics. / Thesis / Doctor of Philosophy (PhD)

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.