Linear Surface Waves in Roll Coating Flows of Thin Viscoelastic Polymer Liquid Films Using Power-Series Approximation Approach Techniques

The linear stability of a thin viscoelastic polymer fluid film flowing down the surface of a rotating vertical roller is studied. In contrast to most previous studies, the solutions of governing equations are obtained in this study based on a numerical approximation approach rather than an analytical method. The normal mode method is then used to establish the conditions required to ensure the stability of the film. Stability behavior of the valid solutions for the rotational speed of roller, the viscoelastic effect and the roller radius is analyzed to gain some physical insight into flow pattern. The result displays the flow becomes relatively more unstable as both the viscoelastic parameter and the Ross by number are increased.