Axisymmetric dynamics and equilibria of annular liquid films coating a fiber

This paper presents a theoretical and numerical analysis of the influence of adhesion forces on the instability of an initially uniform annular liquid film coating a cylindrical solid fiber. Wetting films are stable when the initial thickness is smaller than a critical value given by the balance of surface tension and van der Waals forces and are unstable otherwise reaching an equilibrium configuration, where the film exhibits a periodic arrangement of drops and macroscopic films. In the non-wetting case, films are always unstable and equilibrate into a periodic sequence of drops separated by molecularly thin precursor films. The apparent contact angle has a strong influence on the relaxation time toward the equilibrium state, with larger angles leading to longer relaxation times. The lobes between collars described in previous studies performed without adhesion forces are shown to appear only transiently. Thus, a key contribution of this work is the detailed description of the transient regime in the presence of adhesion forces, which has not been addressed in previous studies, such as those by Roe [J. Colloid Interface Sci. 50(1), 70–79 (1975)] and Neimark [J. Adhes. Sci. Technol. 13(10), 1137–1154 (1999)], and which we show to be crucial for predicting the temporal evolution and relaxation time of the film.