We present experimental, numerical, and theoretical studies of droplet flows in hydrodynamic networks. Using both millifluidic and microfluidic devices, we study the partitioning of monodisperse droplets in an asymmetric loop. In both cases, we show that droplet traffic results from the hydrodynamic feedback due to the presence of droplets in the outlet channels. We develop a recently-introduced phenomenological model [W. Engl, Phys. Rev. Lett. 95, 208304 (2005)] and successfully confront its predictions to our experimental results. This approach offers a simple way to measure the excess hydrodynamic resistance of a channel filled with droplets. We discuss the traffic behavior and the variations in the corresponding hydrodynamic resistance length L_{d} and of the droplet mobility beta , as a function of droplet interdistance and confinement for channels having circular or rectangular cross sections.

By studying the repartition of monodisperse droplets at a simple T junction, we show that the traffic of discrete fluid systems in microfluidic networks results from two competing mechanisms, whose significance is driven by confinement. Traffic is dominated by collisions occurring at the junction for small droplets and by collective hydrodynamic feedback for large ones. For each mechanism, we present simple models in terms of the pertinent dimensionless parameters of the problem.

We investigate two different textures of smectic A liquid crystals. These textures are particularly symmetric when they are observed at crossed polars optical microscopy. For both textures, a model has been made in order to examine the link between the defective macroscopic texture and the microscopic disposition of the layers. We present in particular in the case of some hexagonal tiling of circles (similar to the Apollonius tiling) some numeric simulation in order to visualize the smectic layers. We discuss of the nature of the smectic layers, which permit to assure their continuity from one focal conic domain to another adjacent one.