Instability of a two-layer thin liquid film with surfactants: Dewetting waves

Dewetting dynamics of a liquid film composed of two superposed ultra-thin layers of immiscible liquids resting on a solid substrate is investigated in the case when surfactants are present at the liquid-liquid interface. Two cases are considered: insoluble surfactant and surfactant soluble in the lower liquid. The dependence of Hamaker constants on the surfactant concentration is taken into account. A system of three strongly nonlinear evolution equations describing large (comparable to the layer thicknesses), long-wave perturbations of the liquid-liquid and liquid-gas interfaces, as well as the surfactant concentration, is derived for each case in the lubrication approximation. The linear stability analysis shows that in the presence of surfactants, oscillatory dewetting instability can occur. Numerical simulations of this system of nonlinear evolution equations are performed. It is found that in the case of oscillatory instabilities, the system exhibits either standing or traveling "dewetting waves." The weakly nonlinear analysis explains this phenomenon.