Curvature Suppresses the Rayleigh-Taylor Instability

Thin films on curved surfaces are widely observed in coating and painting processes and wetting problems. We consider a thin film on a curved substrate under the effect of gravitational, viscous, and surface tension forces. When the film is on the underside of the substrate, gravity works as a destabilizing force, and a Rayleigh-Taylor type instability is expected (i.e. dripping). We consider the stability of a uniform thin film coating the inside of a horizontal circular cylinder. Using asymptotic techniques, we find that "instabilities" are only transient in nature, thus showing that curvature helps stabilize the film. We also show that experimental results agree very well with our asymptotic theory.