Linearized analysis of the deformation of ultra-thin lubricant films under gas pressures by the long wave equation

Long wave theory was employed to examine the deformations of ultra-thin but continuum liquid films produced by applied pressures and shearing stresses. Long wave theory is based on the time-evolution equation for the shape and deformation of thin liquid films and includes surface tension and surface forces such as van der Waals forces. As the deformations caused by gas pressures are usually very small, the linearized long wave equation, which is applicable to infinitesimal deformations, was derived and employed to predict the steady-state liquid surface. deformations of a non-polar lubricant produced by concentrated or distributed gas pressures. It was found that the results obtained using the linearized equation agree well with those obtained using the nonlinear long wave equation.