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The development of instabilities under the joint action of the van der Waals forces and Marangoni stresses in a two-layer film on a heated or cooled substrate, is considered. The problem is solved by means of a linear stability theory and nonlinear simulations. Nontrivial change of the droplet shape in the presence of the Marangoni effect, which manifests itself as the deformation of a “plateau” into an “inkpot,” is observed. The appearance of the threshold oscillations predicted by the linear stability theory is confirmed by nonlinear simulations.

The decomposition of a laterally heated two-layer film caused by intermolecular forces is considered. Long-wave nonlinear equations, which incorporate thermocapillary flows and the influence of the van der Waals forces, are derived. The main stages of the three-dimensional evolution of films are presented. The influence of the thermocapillary flow on the morphology and the evolution of unstable two-layer films is investigated. It is shown that the film instability leads typically to formation of droplets driven by the thermocapillary flow. Anisotropic coalescence of droplets and formation of rivulets are observed.

The nonlinear stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient, is investigated. Two types of boundary conditions, periodic boundary conditions and heat-insulated lateral walls, are considered. The nonlinear simulations of the wavy convective regimes for a particular set of fluids, are performed. The dependence of the direction of the wave propagation depends on two factors, which are studied, the ratio of the layers thicknesses and the Marangoni number.

The oscillatory convection for a real system of fluids under the joint action of buoyancy and thermocapillary effect or in the presence of the interfacial heat release is investigated. The nonlinear development of the oscillatory instability is studied. In the case of periodic boundary conditions, regimes of traveling waves and pulsating traveling waves are predicted. For different types of boundary conditions, the period doubling bifurcation is obtained. It is shown that the region of the Grashof number values, where nonlinear oscillations take place, is bounded both from below ͑by the mechanical equilibrium state͒ and from above ͑by the steady state͒.