On the stability of rimming flows to two-dimensional disturbances

It is well known that a variety of qualitatively different flows is realisable when a horizontal cylinder containing a small amount of highly viscous liquid is rotated about its axis at constant speed. A mathematical model first proposed by Moffatt and based on lubrication analysis has proved very fertile ground for basing the study of these flows. In this study we develop, using kinetic-wave theory, the two-dimensional stability results of Benjamin et al. reported in an unpublished paper and bring new insights into this now-classical problem. Moreover, we find fascinating new results by extending the class of flows to incorporate the effects of constant traction at the free surface of the liquid film. In particular, we describe a novel weak solution where the stable surface profile contains a shock at any location around the cylinder.