Dynamics of liquid interfaces, from thin films to ship wakes.

Summary We present results on the dynamics of liquid interfaces at different scales. In the first part, we study confined liquid systems in the framework of the lubrication approximation. We obtain interesting analytical and numerical results on the thin film equation that governs the dynamics of such systems. The theoretical results are successfully confronted with atomic force microscopy experiments on polymer thin films in different geometries. We explore the physics resulting from the inherent effects of the nature of polymeric materials such as viscoelasticity, wall sliding and dynamics near the glass transition temperature. In the second part, we focus on the wake generated by the motion of a perturbation at the liquid-air interface. Motivated by experimental results that seem to challenge Kelvin's theory of the wake, we show that two angles can be distinguished in the wake. The angle formed by the edges of the domain is indeed constant, in accordance with Kelvin's theory, while the angle described by the waves of higher amplitude decreases with the Froude number. We also look at gravitocapillary waves and are particularly interested in the effects of finite size on the wave resistance. The two parts can be approached independently.