Oscillatory Marangoni convection in a liquid-gas system heated from below

We investigate a longwave Marangoni convection in a two-layer system which consists of a liquid layer and a poorly conductive gas layer. The system is heated from below and confined between two rigid walls: the upper wall is ideally conductive, the lower one is thermally insulated. We aim at finding the analogue of the novel oscillatory mode that was detected analytically within the one-layer approach in [S. Shklyaev, M. Khenner, and A. A. Alabuzhev, "Oscillatory and monotonic modes of long-wave Marangoni convection in a thin film," Phys. Rev. E 82, 025302 (2010)]. To properly account for the influence of processes in gas on deformation of the interface we apply the two-layer approach. Considering only the heat transfer in gas phase we derive nonlinear amplitude equations that describe the coupled evolution of the layer thickness and temperature perturbation. Linear stability analysis of these equations yields the results similar to those obtained for a single layer whereas nonlinear equations reveal certain differences. The new oscillatory mode is found to be critical in a certain range of parameters, which allows us to provide the recommendations for a possible experiment.