Nonlinear stability analysis of thin condensate falling film inside a rotating vertical cylinder

This paper investigates the stability of thin condensate film flowing down on the inner surface of a rotating vertical cylinder by means of long wave perturbation method in a two-step procedure. In the first step, the normal mode method is used to characterize the linear behavior. In the second step, an elaborated nonlinear film flow model is solved by using the method of multiple scales to characterize flow behavior at various states of sub-critical stability, sub-critical instability, supercritical stability, and supercritical explosion. The procedure follows the previous research [C.I. Chen, C.K. Chen, Y.T. Yang, Int. J. Heat Mass Transfer 47 (2004) 1937–1951] which concerns with the thin condensate falling film on the outer surface of a rotating vertical cylinder. The modeling results indicate that by increasing the rotation speed, Ω, and the radius of cylinder, R, the condensate film becomes more stable, which is totally opposite to the previous study.