Perturbation analysis to the nonlinear stability characterization of thin condensate falling film on the outer surface of a rotating vertical cylinder

Abstract

The linear and nonlinear stability theories for characterization of condensate film flow down on the outer surface of a rotating infinite vertical cylinder is investigated analytically. A generalized nonlinear 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 behaviors. The amplitude growth rates and the threshold conditions are characterized subsequently and summarized as the by-products of the linear solutions. In the second step, an elaborated nonlinear 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 decreasing the radius of cylinder, R, the film flow becomes less stable, generally.