Non-linear stability characterization of the thin micropolar liquid film flowing down the inner surface of a rotating vertical cylinder

Linear and non-linear stability analysis for characterization of micropolar film flowing down the inner surface of a rotating infinite vertical 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 the following procedure. First, the normal mode method is used to characterize the linear behaviors. Then, an elaborated non-linear film flow model is solved by using the method of multiple scales to characterize flow behaviors at various states of sub-critical stability, sub-critical instability, supercritical stability, and supercritical explosion. The modeling results indicate that by increasing the rotation speed, Ω, and the radius of cylinder, R, the film flow will generally stabilize the flow system.