Two-layer film flow on a rough rotating disk in the presence of air shear

Abstract

The development of a two-layer thin film over a rough non-uniformly rotating disk with constant air shear is analyzed under the consideration of planar interface and free surface. von Karman’s similarity variables are applied to transform the guiding Navier–Stokes equations into a set of coupled unsteady nonlinear partial differential equations. These equations with moving boundary conditions are solved using the finite difference method. Here, it is found that the azimuthal roughness slows down the film thinning rate and the radial roughness enhances the thinning rate slightly. Also, the effect of air shear on film thinning is discussed. For different types of rotation, effects on the flow due to azimuthal roughness, radial roughness, and air shear remain the same.