Interfacial instability in bilayer films due to solvent evaporation

We perform a linear analysis of the Marangoni instability of a deformable interface between two fluid layers of finite depths, submitted to a gradient of solvent concentration induced by evaporation at the top layer, in the presence of convective as well as diffusive solvent transport. We discuss, in turn, the influence on the onset of the instability of the solvent evaporation rate, of the ratios of viscosity and diffusivity, of the rate of convection and of the layer depths. Qualitative comparison with experimental observations of spin-coating processes of solution of two immiscible polymers are then performed, yielding satisfactory agreement.