Interfacial dynamics of a two-layer thin film

Stability properties of thin films on solid substrates are relevant in industrial applications such as coating and drying processes. They help researchers develop methods to stabilize thin films or to break thin films in a controlled manner. While the dynamics of film rupture of one layer systems have been thoroughly investigated, the stability properties of two layer systems are more complex as a result of the coupled interactions between the liquid-liquid and liquid-gas interfaces. This work focuses on developing a mathematical model that describes the evolution of two liquid layers of different viscosities on a solid substrate. We use the long-wave approximation scalings to obtain the evolution equations for the liquid-liquid and liquid-gas interfaces where the viscosity ratio of the two liquid layers is $O(\epsilon^2)$. Analytical methods such as linear stability analysis are used to gain insight into the stability of each layer.