Interfacial dynamics of a bi-layer system with a small viscosity ratio: a simple mathematical model

Abstract Stability properties of thin liquid films on solid substrates are relevant in industrial applications such as coating and drying processes. The study of such systems helps researchers develop methods to stabilize thin films or to break them into droplets in a controlled manner. While the dynamics of film rupture of single-fluid systems have been thoroughly investigated, the stability properties of systems comprising two immiscible fluid layers have received less attention, being more complex due to the coupled interactions between the liquid–liquid and liquid–gas interfaces. This work focuses on developing a simplified, asymptotically-consistent mathematical model that describes the evolution of two immiscible liquid layers, of very 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 interface in the case where the viscosity ratio of the two liquid layers is asymptotically small. Analytical and numerical methods are used to gain insight into the conditions under which dewetting/rupture of the film occurs. Our model results are also compared to those arising from existing models in the literature.