Asymptotic study of film thinning process on a spinning annular disk

TLDR: In this paper, an axisymmetric flow of a thin liquid film on a rotating annular disk is considered, and an asymptotic solution for the free surface of the thin film is found using an expansion for the film thickness in powers of a small parameter characterizing the thickness in comparison to the inner disk radius.

Abstract: We consider an axisymmetric flow of a thin liquid film on a rotating annular disk. The effects of surface tension and gravity terms are included. An asymptotic solution for the free surface of the thin film is found using an expansion for the film thickness in powers of a small parameter characterizing the film thickness in comparison to the inner disk radius, and then applying the method of matched asymptotic expansion. The asymptotic solution is capable of predicting several features of spin-coating processes. For example, we find that the surface tension enhances film thinning at the central region whereas the gravity does not. The results show that the final film thickness does not depend on the initial distribution of the film thickness (be it uniform or nonuniform) and on the initial amount of liquid deposited. We find that most of the liquid initially deposited on the disk flows out of the disk in a very short time at the initial stages of spinning, regardless of the type of initial distribution of the film thickness. The retention of fluid for nonuniform initial distribution is more than that for uniform distribution at the early stages of the spreading of the thin film.