Nonlinear Stability Analysis of the Thin Micropolar Liquid Film Flowing Down on a Vertical Cylinder

This paper investigates the weakly nonlinear stability theory of a thin micropolar liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. The modeling results indicate that both subcritical instability and supercritical stability conditions are possible to occur in a micropolar film flow system. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The modeling results also indicate that by increasing the micropolar parameter $K=κ/μ$ and increasing the radius of the cylinder the film flow can become relatively more stable traveling down along the vertical cylinder.