Stability and break-up of thin liquid films on patterned and structured surfaces

Solid surfaces with chemical patterning or topographical structure have attracted attention due to many potential applications such as manufacture of flexible electronics, microfluidic devices, microscale cooling systems, as well as development of self-cleaning, antifogging, and antimicrobial surfaces. In many configurations involving patterned or structured surfaces, liquid films are in contact with such solid surfaces and the issue of film stability becomes important. Studies of stability in this context have been largely focused on specific applications and often not connected to each other. The purpose of the present review is to provide a unified view of the topic of stability and rupture of liquid films on patterned and structured surfaces, with particular focus on common mathematical methods, such as lubrication approximation for the liquid flow, bifurcation analysis, and Floquet theory, which can be used for a wide variety of problems. The physical mechanisms of the instability discussed include disjoining pressure, thermocapillarity, and classical hydrodynamic instability of gravity-driven flows. Motion of a contact line formed after the film rupture is also discussed, with emphasis on how the receding contact angle is expected to depend on the small-scale properties of the substrate.