Weakly nonlinear study of Marangoni instabilities in an evaporating liquid layer

We propose a theoretical study of Marangoni driven convection in an evaporating liquid layer surmounted by an inert gas-vapor mixture. After reduction of the full two-layer problem to a one-sided model we use a Galerkin-Eckhaus method leading to a finite set of amplitude equations for the weakly nonlinear analysis of the problem. We analyze the stability of the roll, square, and hexagonal patterns emerging above the linear stability threshold for a water-air and for an ethanol-air system.