Stability analysis of a thin film on a rotating cylinder with low airflow

Abstract

This paper studies the operating conditions of a novel pesticide applicator, by analyzing the stability of a thin film on a rotating horizontal cylinder in the presence of low airflow. The analysis shows that the film is destabilized by the airflow, with a few notable further findings. First, when the airflow coincides with the angular velocity at the underside of the cylinder, the film becomes unstable at smaller wind speeds compared to airflow anti-parallel to the angular velocity. Second, in the absence of surface tension, the thin film model does not have a stable stationary state. The solution settles into an oscillatory state instead. Finally, an analytical solution is presented for the special case where the initial condition is a uniform film thickness. When surface tension is included in this analysis, the temporal terms decay when the stability condition is satisfied. Some of the modes decay very slowly, as confirmed by the multiple time scale analysis.