STEADY STATE FLOW IN THIN FILMS,

A steady motion of a thin layer of viscous fluid bounded by the surface of rigid body from one side and by moving gas from the other side is considered. The free surface of the layer is assumed in a wave form. Navier-Stokes equations, after introducing a stream function and linearization, are reduced to an ordinary fourth-order differential equation, which is solved. In the linear case, the velocity of propagation of longitudinal waves is independent of the wavelength. The nonlinear case is treated with the small parameter method and the solution gives the relations between the wavelength and the velocity of propagation and the amplitude. Author