Wavy film flows down an inclined plane. Part I: Perturbation theory and general evolution equation for the film thickness

Abstract

Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be approximately reduced for all time to a single evolution equation for the film thickness. An unconventional perturbation approach yields the most general evolution equation and least restrictive conditions on its validity. The advantages of this equation for analytical and numerical studies of 3D waves in inclined films are pointed out.