Nonlinear large-scale Marangoni convection in a heated liquid layer with insoluble surfactant

The nonlinear development of monotonic and oscillatory long-wave Marangoni instabilities in a heated horizontal layer of a liquid, containing an insoluble surfactant on its surface, is investigated. By means of asymptotic expansions, weakly nonlinear amplitude equations, which govern the evolution of disturbances near the instability threshold, are derived. It turns out that both kinds of instabilities are subcritical; therefore, the asymptotic analysis does not allow us to find any stable supercritical regimes. In the case of sufficiently small concentration of the surfactant, where only monotonic instability is possible, the preferred kind of hexagons is predicted.