Oscillatory long-wave Marangoni convection in a heated liquid layer covered by insoluble surfactant: Bifurcation analysis

A bifurcation analysis of the deformational mode of three-dimensional long-wave oscillatory Marangoni convection, which occurs in a heated layer of liquid covered by insoluble surfactant, is performed. The analysis is carried out in the framework of a set of nonlinear evolution equations derived in our previous work. The bifurcation analysis of monotonic mode has been done formerly. Here we consider the oscillatory instability mode. The weakly nonlinear expansions are applied near the instability threshold. We find stability regions for a variety of convective patterns including single traveling and standing waves, superpositions of two traveling and two standing waves, and superpositions of three traveling waves. It is found that stability of convective patterns strongly depends on the parameters related to the surfactant adsorbed on the free deformable surface of the layer.