Macroscopic Effects of Surface Roughness in Confined Air-Flow

The general framework deals with the winding of thin plastic films. It is well known by the man-of-the art that the “windability” of plastic films is mainly governed by their surface topography. One key issue is then to optimize their surface topography so that to improve the quality of the wound roll. In a previous work, we proposed a simple model which considers the flow of an air layer squeezed between a solid 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? To answer this question, we assimilate the confined air flow to a flow through a periodic array of cylinders. A mathematical model based on homogenization techniques was proposed, where the heights of the cylinders, their diameter and their spatial distribution are the governing parameters. In the present paper, we propose pertinent parameters which describes the real surface roughness of plastic films fairly well. The measurements were carried out by using a 3D roughness measurement device. The first observation is that the films roughness distribution is not uniform, but forms “packages” (agglomerates) giving place to large packs of roughness. We made a sampling at different levels expressed by the percentage of peaks exceeding some given height. The heights of the peaks over a threshold value are averaged and the corresponding averaged value will be regarded as the initial gap in the squeeze flow model. Now, the networks of cylinders is built as follows : • The cylinder diameters is the averaged width of the large peaks, • The distance between the cylinder axes is the mean value of the spatial distribution of the peaks. Thus, for each type of film, the threshold value will be the only adjustable parameter. Introducing these parameters into the mathematical model which predicts the evolution of the squeezed air layer and comparing to the experimental data, the following results are obtained: (1) It is possible to adjust one single parameter so that to obtain a very good agreement between the experimental data and the theoretical results. (2) The smoother the film, the more important the highest peaks are in terms of air leakage.