Large-scale nonlinear evolution of parametrically excited Marangoni convection in a liquid layer covered by insoluble surfactant

Abstract

Horizontally infinite liquid layer with a deformable free upper surface covered by insoluble surfactant is considered. The heat flux at the bottom is periodically modulated with a zero mean value. A set of nonlinear evolution equations describing the dynamics of large-scale Marangoni instability is obtained. The linear analysis gives two modes of instability—monotonic and oscillatory ones. A bifurcation analysis near the threshold of the convection shows the existence of the subcritical as well as supercritical bifurcations. In the former case, corresponding to the rupture of the layer, the problem is governed by the Sivashinsky equation. In the latter case, the problem is governed by the Cahn–Hilliard equation, which describes a separation of the liquid film into domains of different thickness.