Dynamical Analysis On Thin Film Flow Over Wavyplate

Under creeping flow conditions, the steady state of thin film flow over strongly undulated bottom profiles is numerically analyzed in this paper. As the boundary of the domain is different, there are two kinds of thin film flow, one of them is creeping Couette flow, and the other one is free-surface flow. For free-surface flow model, fluid flow over fixed undulated profile; for Couette flow model, fluid flow between two plates, one of them is a moving plane, the other one with a undulated profile. Sinusoidal profile and triangular profile are chosen as the bottom profile, and the undulated profile varies periodically. Newtonian fluid and non-Newtonian fluid are considered in each flow model.The streamlines of the flow are obtained from an exact analytical treatment of the Stokes equations by making use of finite element methods and complex function theory. Based on the calculations, the formation and evolution of vortices in the flow are visualized. For Newtonian fluid, the influence of the plate undulations, the Reynolds number and the thickness of the film are shown by parameter studies; for non-Newtonian fluid, the shear-thinning coefficient on the film flow is shown by parameter studies.For both Newtonian flow and non-Newtonian flow, the vortices are generated when the waviness of the bottom profile is beyond a critical number. By increasing the waviness, a second vortex can be generated. With the increasing of Reynolds number, the symmetry of the streamlines at Re = 0 is destroyed and the vortices are sloped and become larger. In addition, for the non-Newtonian flow, the streamlines are symmetrical and the vortices become smaller with the decreasing of shear-thinning rate n.The Visual Fortran code Wavyplate and Wavyfilm are applied in numerical simulation, and Matlab mathematical library is used in post-processing.