Mathematical modeling and stability criteria for ultra-thin layered gas-liquid interface

To examine behaviors of ultra-thin but continuum liquid film, the long wave theory was employed, which is the time-evolution equation for the shape of the thin liquid film and includes the surface tension and surface forces at boundaries such as the van der Waals force. Stability/ instability of the liquid surface can be analyzed as growth and decay problem of infinitesimal deformations of the liquid surface. The van der Waals force from neighboring slider may cause instabilities of the liquid surface, whereas the van der Waals force from the disk and the surface tension of the gas-liquid interface stabilize the disturbances.