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2014 Nous avons suivi l'évolution de la forme de gouttes magnétiques de ferrofluide plongées dans un champ magnétique. La forme ellipsoidale allongée de la goutte devient instable pour un certain champ magnétique seuil : la goutte passe d'une forme peu allongée à une forme beaucoup plus allongée. En baissant le champ magnétique, le même phénomène se produit mais pour une valeur de seuil plus faible. Cette instabilité est interprétée à partir des énergies magnétique et interfaciale de la goutte. Abstract. 2014 We have followed the evolution of the shape of ferrofluid magnetic drops in presence of a magnetic field. The prolate ellipsoid shape of the drop becomes unstable for a certain magnetic field threshold : the drop jumps from a slightly elongated shape to a much more elongated shape. When decreasing the magnetic field the same feature occurs for a smaller threshold. This instability is simply understood from a balance between magnetic energy and interfacial tension energy.

We study experimentally and theoretically the downward vertical displacement of one miscible fluid by another lighter one in the gap of a Hele-Shaw cell at sufficiently high velocities for diffusive effects to be negligible. Under certain conditions on the viscosity ratio, M, and the normalized flow rate, U, this results in the formation of a two-dimensional tongue of the injected fluid, which is symmetric with respect to the midplane. Thresholds in flow rate and viscosity ratio exist above which the two- dimensional flow destabilizes, giving rise to a three-dimensional pattern. We describe in detail the two-dimensional regime using a kinematic wave theory similar to Yang & Yortsos (1997) and we delineate in the (M, U)-plane three different domains, characterized respectively by the absence of a shock, the presence of an internal shock and the presence of a frontal shock. Theoretical and experimental results are compared and found to be in good agreement for the first two domains, but not for the third domain, where the frontal shock is not of the contact type. An analogous treatment is also applied to the case of axisymmetric displacement in a cylindrical tube.