Non-Linear Stability Analysis of a Thin Newtonian Film Flowing Down an Infinite Vertical Rotating Cylinder

Abstract

Non-linear stability theories for the characterization of Newtonian film flow down an infinite vertical rotating cylinder is given. A generalized non-linear kinematic model is derived to represent the physical system and is solved by the long-wave perturbation method in a two-step procedure. In the first step, the normal mode method is used to characterize the linear behaviours. In the second step, an elaborated non-linear film flow model is solved by using the method of multiple scales to characterize flow behaviours at various states of subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The modelling results indicate that by increasing the rotation speed, ω, and decreasing the radius of cylinder, R, the film flow becomes less stable, generally.