The dynamics of a thin liquid film on the underside of a curved cylindrical
substrate is studied. The evolution of the liquid layer is investigated as the
film thickness and the radius of curvature of the substrate are varied. A
dimensionless parameter (a modified Bond number) that incorporates both
geometric parameters, gravity, and surface tension is identified, and allows
the observations to be classified according to three different flow regimes:
stable films, films with transient growth of perturbations followed by decay,
and unstable films. Experiments and theory confirm that, below a critical value
of the Bond number, curvature of the substrate suppresses the Rayleigh-Taylor
instability