The whirling helical structure obtained when pouring honey onto toast may seem like an easy enough problem to solve at breakfast. Specifically, one would hope that a quick back-of-the-envelope scaling argument would help rationalize the observed behaviour and predict the coiling frequency. Not quite: multiple forces come into play, both in the part of the flow stretched by gravity and in the coil itself, which buckles and bends like a rope. In fact, the resulting abundance of regimes requires the careful numerical continuation method reported by Ribe (J. Fluid Mech., vol. 812, 2017, R2) to build a complete phase diagram of the problem and untangle this sticky situation.

We investigate the Rayleigh–Taylor instability of a thin liquid film coated on the inside of a cylinder whose axis is orthogonal to gravity. We are interested in the effects of geometry on the instability, and contrast our results with the classical case of a thin film coated under a flat substrate. In our problem, gravity is the destabilizing force at the origin of the instability, but also yields the progressive drainage and stretching of the coating along the cylinder’s wall. We find that this flow stabilizes the film, which is asymptotically stable to infinitesimal perturbations. However, the short-time algebraic growth that these perturbations can achieve promotes the formation of different patterns, whose nature depends on the Bond number that prescribes the relative magnitude of gravity and capillary forces. Our experiments indicate that a transverse instability arises and persists over time for moderate Bond numbers. The liquid accumulates in equally spaced rivulets whose dominant wavelength corresponds to the most amplified mode of the classical Rayleigh–Taylor instability. The formation of rivulets allows for a faster drainage of the liquid from top to bottom when compared to a uniform drainage. For higher Bond numbers, a two-dimensional stretched lattice of droplets is found to form on the top part of the cylinder. Rivulets and the lattice of droplets are inherently three-dimensional phenomena and therefore require a careful three-dimensional analysis. We found that the transition between the two types of pattern may be rationalized by a linear optimal transient growth analysis and nonlinear numerical simulations.