Nonlinear Stability Analysis of the Thin Micropolar Film Falling Exterior to a Rotating Vertical Cylinder

C.-I. Chen and C.-K. Chen (Taiwan)

Keywords

Mathematical Modelling, micropolar liquid, Rotation number, Ginzburg-Landau equation

Abstract

In the paper, linear and nonlinear stability analysis of the thin micropolar film falling exterior to a rotating cylinder is studied. A generalized nonlinear kinematic model is solved by the long wave perturbation method, the normal mode method is used to characterize the linear behaviors, and the elaborated nonlinear film flow model is solved by using the method of multiple scales to characterize flow behaviors at various stability states. The modeling results indicate that by increasing the rotation speed, Ω , and decreasing the radius of cylinder, R, the film flow will generally make the flow system less stable. In this study, the interaction of the rotation and the radius of cylinder are taken into consideration. Generally, Reynolds number is divided into three regions, which are Re<3, 3

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