Deformation and Stability Analysis of Ultra-Thin Lubricant Films by the Long Wave Equation: Analysis Considering the van der Waals Force and Gas Pressure at the Liquid Surface

To examine deformations of ultra-thin but continuum liquid film, the long wave theory was employed, which is the time-evolution equation for the shape and deformation of the thin liquid film and includes the surface tension and surface forces such as the van der Waals (vdW) force. By solving the linearized long wave equation considering the vdW pressure and gas pressures at the lubricant surface, deformations of the ultra-thin lubricant film caused by air pressure were obtained. Stability/instability of the liquid surface was analyzed as the growth and decay problem of the infinitesimal deformation of the liquid surface.