KAPITZAS METHOD OF FILM FLOW DESCRIPTION

Kapitza's third-order equation for the surface wave motion associated with pseudo-laminar film flow has been rederived by consistently applying the boundary layer approximation to the Navier-Stokes equations and free surface conditions. In Kapitza's original treatment, the equilibrium wave amplitude was estimated by invoking a plausible argument which involves minimizing energy dissipation by viscosity. Here we have deduced the wave amplitude entirely from the dynamic equations by investigating the nonlinear effect on an isolated class of periodic wave motions pertaining to the linear system. The first-order equilibrium wave amplitude is h0ω0, where h0 and ω0 are respectively the average film thickness and wave number for the linear problem. Our predicted wave amplitude and wave speed compare very well with experiment. © 1969.