The dynamical equations governing a lubricating film consisting of a gas film overlying a liquid film

The dynamical equations governing a two-phase lubricating configuration are derived. It is assumed that a gas film overlies a liquid film, both thin enough that the lubrication approximation may be used. The analysis leads to coupled Reynolds equations governing the pressure and the relative thickness of the two films. The coupling, which is determined by continuity of tangential stress across the gas-liquid interface, is considerably simplified if the shear viscosity of the liquid greatly exceeds that of the gas.