| Hydrodynamic systems with interacting interfaces are relevant in many applications. In the present thesis three such systems are investigated.; In Chapter 1, we preform the nonlinear analysis and numerical simulations of a liquid film composed of two superposed thin layers of immiscible liquids resting on a solid substrate. We show that the coupling of van der Waals interactions in the two layers can lead to an autophobic behavior in the form of morphological phase separation of two planar liquid layers into a system of localized drops divided by almost planar wetting layers. The kinetics of the drop coarsening at late stages is studied. It is also shown that gravity effects can become significant even for very thin two-layer films.; In Chapter 2, we investigate the dewetting dynamics of a two-layer liquid film in the case when surfactants are present at the liquid-liquid interface. A system of three strongly nonlinear evolution equations is derived in the lubrication approximation that describes the evolution of the liquid-liquid and liquid-gas interfaces as well as the surfactant concentration. The linear stability analysis shows that, if the Hamaker constants depend on the surfactant concentration, oscillatory dewetting instability can occur. Numerical simulations of this system show that standing or traveling "dewetting waves," can occur, which is explained by the weakly nonlinear analysis.; In Chapter 3, we consider the motion of a droplet placed in a gas phase near an evaporating planar liquid-gas interface. We show that the interplay between thermocapillary and gravity forces can result in the drop levitation above the evaporating interface. We also show that the thermocapillary flow generated at the evaporating interface can capture the drop leading to its attachment to the interface. |
