Asymptotic solution for film flow on a rotating disk

Unsteady liquid film flow of nonuniform thickness on a rotating disk is analyzed. Assuming small aspect ratio of the initial film thickness to the disk radius and applying Higgins’ asymptotic method [Phys. Fluids 29, 3522 (1986)], the long and short-time scale solutions for transient film thickness were obtained and these two solutions were matched to give a composite solution. The results reveal the effects of gravitational and surface tension forces as well as the effect of inertial force on the film thinning and planarization.