Macroscopic effects of surface roughness in confined air flow

The general framework deals with the winding of thin plastic films, in order to obtain good-quality rolls. This issue is tightly connected to the thickness of the residual air layer entrapped between the film layers. It is then of importance to optimize the surface topography of the films so that to improve the quality of the wound rolls. In a previous work, we proposed a simple model for the flow of an air layer squeezed between a valid smooth substrate and a plastic film sample: it was shown experimentally that the macroscopic characteristics of the flow are connected to the film roughness, but how? In order to answer this question, we assimilated the confined air flow to a flow through a periodic array of cylinders and it mathematical model based on homogenization techniques was developed. In the present paper, we search for pertinent parameters which describe the real surface roughness of plastic films. The experiments were carried out by using a 3-D roughness measurement device and the first observation is that the roughness distribution is not uniform. We made a sampling expressed by the percentage of peaks exceeding some given height threshold. The corresponding experimental parameters are used to define the network of cylinders. For each type of film, the threshold value is the only adjustable parameter and the following results are obtained: It is possible to adjust this parameter so that to obtain a very good agreement between the experimental data and the theoretical predictions. In addition, the smoother the film, the more important the highest peaks tire in terms of air leakage.