A new mechanism of film thinning: Enhancement of reynolds' velocity by surface waves

Abstract

The celebrated Reynolds' law of film thinning is based on the assumptions of tangential immobility and plane-parallel configuration of film interfaces. It is, however, well established that even the tangentially immobile thin films are neither plane-parallel, nor do they follow Reynolds' law (both qualitatively and quantitatively) for film radii larger than a certain small value (typically 5 × 10 −3 cm). Further, departures from both the plane-parallel configuration and Reynolds' law increase as the film radius increases. The present theory obtains the frequency of temporal oscillations and the propagation speeds of the experimentally observed thickness nonhomogeneities from the equations of motion. For large radii (typically larger than 10 −2 cm), the pumping of the fluid that is generated by the thickness fluctuations gives the dominant contribution to the velocity of film thinning. In these circumstances, the velocity of thinning is orders of magnitude larger than Reynolds' velocity and it varies inversely with three-fourth power of the film radius. This is to be contrasted with Reynolds' velocity that is inversely proportional to the second power of the film radius. Finally, the drainage times and the thinning velocities calculated from the present theory are in both qualitative and quantitative agreement with the experimental data.