Instabilities of Thin Films Flowing Down Flat and Smoothly Deformed Walls

Results are presented of the numerical analysis of an evolution equation obtained by Davalos-Orozco (Phys Fluids 19(074103):1-8, 2007) which describes the perturbations on the free surface of thin films flowing down walls with smooth deformations. The main goal is to investigate the possibility of stabilizing free surface time dependent perturbations by means of wall deformations distributed in a small space interval. The effects of three smooth functions representing wall deformations are investigated. It is shown that, for some Reynolds numbers and frequencies of the perturbation, those wall functions are in fact able to stabilize. In some cases, they are only able to decrease, in a considerable way, the amplitude of the perturbations in a long distance before they start to grow again.