  We study numerically and theoretically the gravity-driven flow of a viscous
liquid film coating the inner side of a horizontal cylindrical tube and
surrounding a shear-free dynamically inert gaseous core. The liquid-gas
interface is prone to the Rayleigh-Plateau and Rayleigh-Taylor instabilities.
Here, we focus on the limit of low and intermediate Bond numbers, Bo, where the
capillary and gravitational forces are comparable and the Rayleigh-Taylor
instability is known to be suppressed. We first study the evolution of the
axially invariant draining flow, initiating from a uniform film thickness until
reaching a quasi-static regime as the bubble approaches the upper tube wall. We
then investigate the flow linear stability within two frameworks: frozen
time-frame (quasi-steady) stability analysis and transient growth analysis. We
explore the effect of the surface tension (Bo) and inertia (measured by the
Ohnesorge number, Oh) on the flow and its stability. The linear stability
analysis suggests that the interface deformation at large Bo results in the
suppression of the Rayleigh-Plateau instability in the asymptotic long-time
limit. Furthermore, the transient growth analysis suggests that the initial
flow evolution does not lead to any considerable additional amplification of
initial interface perturbations, a posteriori rationalising the quasi-steady
assumption. The present study yields a satisfactory prediction of the
stabilisation threshold found experimentally by Duclaux et al. [15].
