Dynamic analysis of free-surface thin film flows driven by gravity over undulated substrate

This paper studies thin film flows with free surfaces driven by gravity through two types of undulated planes: periodically sinusoidal plane and triangle. The substrate plane is fixed and inclined to a certain angle and the flow with a free surface. Through finite element method (FEM), commenced from Navier-Stokes equations and continuity equation, the exact numerical results of free-surface film flows are obtained through discretization solution to finite equations in flowing areas. Based on the numerical calculations, the streamlines and wall shearing stress during the flowing process are visualized via post-proceeding, and the streamlines separation, the onset and evolution of vortex near the substrate boundary during the flow are also analyzed. The influences from the waviness of the substrate planes profile, height of the triangle plane, and change of the film height on film flow dynamics properties are shown.