A mechanism of Marangoni instability in evaporating thin liquid films due to soluble surfactant

In film coating and other applications involving thin liquid films, surfactants are typically employed to suppress the usually undesirable instabilities driven by surface phenomena. Yet, in the present study a mechanism of Marangoni instability in evaporating thin films is presented and analyzed, which has its origin on the effects of a soluble surfactant. As the film thins due to evaporation, thickness perturbations lead to surfactant concentration perturbations, which in turn drive film motion and tend to enhance uneven drying. A thin-film analysis is applied and evolution equations for the film thickness and the surfactant concentration are derived and analyzed by the techniques of linear stability and numerical simulation. In the linear analysis a nonautonomous system is obtained for the film thickness and surfactant concentration perturbations, which shows that the instability will manifest itself provided that an appropriate Marangoni number is relatively large and the surfactant solubility in the bulk is large as well. On the other hand, low solubility in the bulk, diffusion, and the effect of surfactant on interfacial mobility through the surface viscosity are found to suppress disturbance growth. Direct numerical simulations of the full nonlinear evolution equations confirm those results and add to the picture obtained for the physical system behavior. Estimates of the relevant dimensionless parameters suggest that the conditions for instability may be met in relatively thick films, on the order of tens of microns, for which the effects of molecular forces and disjoining pressure are not dominant. Moreover, the stabilizing effects of diffusion and interfacial mobility are not likely to become significant unless the films are much thinner, i.e., on the order of 1 mu m or below. (C) 2010 American Institute of Physics. [doi:10.1063/1.3316785]