The surface tension effect on the flow of liquid down vertical or inclined surfaces

Abstract

The flow studied is that of a liquid film draining down a vertical or inclined plane surface, with the upper edge of the film at an edge of the solid surface. Similarity laws are derived governing the film profiles, with the effect of surface tension included, both for the vertical plate and for a case involving time-varying inclination. The vertical plate case has a practical application in viscometry, and an improved estimate of the surface tension correction for the gravitational viscometer is given. The theoretical analysis is confirmed by experimental measurement of time variation of the upper edge slope of the film.