Exploding solutions for three-dimensional rimming flows

We examine the linear stability of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. Unlike previous models, both axial and azimuthal components of the hydrostatic pressure gradient are taken into account, which yields solutions which collapse in both dimensions. Two types of such solutions are found: disturbances with zero and non-zero net mass (the former have greater explosion rates, that is, their amplitudes grow faster than those of the latter). It is also shown that, despite the existence of exploding disturbances, all solutions with harmonic dependence on time (eigenmodes) are neutrally stable.