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            <title xml:lang="en">Charge dynamics at the interface separating two dielectric media.</title>
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                <term xml:lang="en">Rayleigh</term>
                <term xml:lang="en">Ion transport</term>
                <term xml:lang="en">insulating capillaries</term>
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              <p>Charged droplets at the Rayleigh limit: We model and simulate the shape evolution of critically charged droplets, from the initial spherical shape to the charge emission and back to the spherical shape. The shape deformation is described using the viscous correction for viscous potential flow model, which is a potential flow approximation of the Navier-Stokes equation for incompressible Newtonian fluids. The simulated shapes are compared to snapshots of experimentally observed drop deformations. We highlight the influence of the viscosity and charge carrier mobility of the liquid on the shape evolution of droplets and discuss the observed trends. We give an explanation as to why the observed deformation pathways of positively and negatively charged pure water droplets differ.Ion transport through insulating capillaries: Self-organized charged particle guiding by insulating capillaries is modeled and simulated by our code InCa4D. Additionally, an original experimental setup is presented that allows us to monitor the accumulated total charge in the capillary and to link the charge to the transmitted fraction of the beam. In a combined theoretical and experimental study, we give evidence that the self-organized electricpotential in tapered glass capillaries has the strength to focus a low energy ion beam, similar to Einzel lenses. The experimental data are corroborated by our simulations, which allows a valuable and comprehensive insight into the dynamics of the self-organized Coulomb potential in irradiated insulating capillaries.</p>
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              <p>Gouttelettes à la limite de Rayleigh: Lorsqu'une gouttelette chargée atteint une charge critique, elle devient instable et se déforme spontanément. Initialement sphérique, la gouttelette  s'allonge, puis émet  2 jets de matières chargés. Ici, nous modélisons  et simulons l'évolution de la forme d'une  gouttelette chargées  et comparons  nos simulations aux résultats  expérimentaux.   La déformation de la gouttelette est décrite en utilisant  le modèle d'écoulement potentiel visqueux avec correction visqueuse (VCVPF), qui est une approximation de l'équation de Navier-Stokes pour les fluides newtoniens incompressibles et faiblement visqueux. Nos simulations mettent  en évidence l'influence de la viscosité et  mobilité des charges du liquide sur l'évolution de la forme des gouttelettes. Nous explications ainsi pourquoi la déformation observée pour des gouttelettes d'eau pure chargée positivement et négativement, est différente.Transport d'ions à travers les capillaires isolants: Le guidage auto-organisé des particules chargées  par des capillaires isolants est modélisé, puis simulé par notre code InCa4D. Un dispositif expérimentale original, qui permet de mesurer  la charge totale dans le capillaire et de relier cette dernière à la fraction transmise du faisceau, est présenté. Dans une étude théorique et expérimentale combinée, nous montrons que le potentiel électrique auto-organisédans les capillaires coniques peuvent  focaliser un faisceau d'ions de basse énergie, semblable à une lentille d'Einzel. Les données expérimentales sont corroborées par nos simulations, permettant ainsi une compréhension  complète de la dynamique de charge à l'interface des isolants.</p>
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