Macroscopic effects of surface roughness in confined air-flow

Abstract

One challenge when processing flexible media such as plastic films is to obtain rolls without any aspect defect : if one considers that a "defect" (i.e. wrinkling or buckling) is due to the fact that the stress generated within the roll is greater than some "plasticity yield", then it is crucial to predict the internal stress state.

Several process parameters must be carefully mastered (winding tension, velocity, etc.) as well as the material pertinent properties. One key issue is to optimize the surface topography of the flexible medium so that to improve the quality of the wound roll.

We propose here new parameters which describe the surface roughness of plastic films fairly well. The measurements were carried out by using a 3D roughness measurement device.

A mathematical model based on homogenization techniques is proposed, where the heights of the roughness peaks, their diameter and their spatial distribution are the governing parameters.

Sampling at different levels is carried out by expressing the percentage of peaks which exceed some given threshold value.

For each tested 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 :

- It is possible to adjust one single parameter so that to obtain a very good agreement between the experimental data and the theoretical results.

- The smoother the film, the more important the highest peaks are in terms of air leakage.