Capillarity driven motion of solid film wedges

Abstract

A solid film freshly deposited on a substrate may form a non-equilibrium contact angle with the substrate, and will evolve. This morphological evolution near the contact line is investigated by studying the motion of a solid wedge on a substrate. The contact angle of the wedge changes at time t = 0 from the wedge angle α to the equilibrium contact angle β, and its effects spread into the wedge via capillarity-driven surface diffusion. The film profiles at different times are found to be self-similar, with the length scale increasing at t 1 4 . The self-similar film profile is determined numerically by a shooting method for α and β between 0 and 180°. In general, we find that the film remains a wedge when α = β. For α < β, the film retracts, whereas for α > β, the film extends. For α = 90°, the results describe the growth of grain-boundary grooves for arbitrary dihedral angles. For β = 90°, the solution also applies to a free-standing wedge, and the thin-wedge profiles agree qualitatively with those observed in transmission electron microscope specimens.