Surface instability of an annular thin film

We apply a linear stability analysis to examine the effect of lattice diffusion on the surface stability of an annular thin film subjected to longitudinal and circumferential surface disturbances, respectively, in which the film is coated and supported by a rigid substrate. No surface instability is found for circumferential surface perturbations. For longitudinal surface disturbances, the critical spatial frequency of surface perturbation for zero growth rate is inversely proportional to the radius of free surface. The maximum growth rate at which the instability develops increases with increasing the ratio |Δr/r₀|, where Δr is the radius difference and r₀ is the radius of the free surface. For a thin film coating, surface perturbations will rapidly lead to the break up of the coating with the spatial wavelength of maximum growth rate being 8.89r₀.