Spectral methods applied to axisymmetric thin film flows

Abstract

We employ numerical techniques to investigate the influence of slot injec- tion/suction on the thin film axisymmetric flow of a Newtonian fluid subject to centrifugal and Coriolis forces, gravity and rotation. Surface tension ef- fects are neglected. We obtain a nonlinear diffusion equation when modeling the spreading of the free surface of a thin film under gravity with blowing or suction at the base. When we model the spreading of the free surface of a thin film under both gravity and rotation with blowing or suction we obtain a nonlinear second order partial differential equation. A first order quasi-linear partial differential equation is obtained when modeling the thickness of the thin film under the effects of rotation only with blowing or suction at the base. We compare and contrast spectral methods with MATLAB built-in functions as well as finite differences. We also examine the effect that the slot has on the wave breaking process.