  We consider the unsteady thin-film dynamics of a long bubble of negligible
viscosity that advances at a uniform speed in a cylindrical capillary tube. The
bubble displaces a viscous, nonwetting fluid, creating a thin film between its
interface and the tube walls. The film is considered thin enough that
intermolecular forces in the form of van der Waals attractions are significant
and thin-film rupture is possible. In the case of negligible intermolecular
forces, a steady-state solution exits where a film of uniform thickness is
deposited in the annular region between the bubble interface and the tube
walls. However, once intermolecular interactions are important, the interface
is perturbed out of its steady state and either (i) the perturbation grows
sufficiently before reaching the rear meniscus of the bubble such that rupture
occurs; or (ii) the perturbation remains small due to weak intermolecular
forces until it leaves the bubble interface through the rear meniscus. We
obtain, both numerically and asymptotically, the time-scale over which rupture
occurs, and thus, we find a critical capillary number, depending on the bubble
length and the strength of the intermolecular forces, below which the film is
predicted to rupture.
