Unsteady coating flow on a rotating cylinder in the presence of an irrotational airflow with circulation

Unsteady two-dimensional coating flow of a thin film of a viscous fluid on the outside of a uniformly rotating horizontal circular cylinder in the presence of a steady two-dimensional irrotational airflow with circulation is considered. The analysis of this problem by Newell and Viljoen [Phys. Fluids 31(3), 034106 (2019)], who sought to generalize the work of Hinch and Kelmanson [Proc. R. Soc. London, Ser. A 459(2033), 1193–1213 (2003)] to include the effect of the airflow, is revisited. In contrast with the claim of Newell and Viljoen that the flow is conditionally unstable (in the sense that the solution for the film thickness grows without bound for certain values of the physical parameters), it is shown that, in fact, the film remains unconditionally stable in the presence of the airflow.