Inertia effects in thin film flow with a corrugated boundary

An analytical solution is presented for two-dimensional, incompressible film flow between a sinusoidally grooved (or rough) surface and a flat-surface. The upper grooved surface is stationary whereas the lower, smooth surface moves with a constant speed. The Navier-Stokes equations were solved employing both mapping techniques and perturbation expansions. Due to the inclusion of the inertia effects, a different pressure distribution is obtained than predicted by the classical lubrication theory. In particular, the amplitude of the pressure distribution of the classical lubrication theory is found to be in error by over 100 perent (for modified Reynolds number of 3-4).