Simulations and Experiments on Low-Pressure Permeation of Fabrics: Part II The Variable Gap Model and Prediction of Permeability

Abstract

Use of the creeping flow assumption provides a computationally efficient and accurate means of predicting flow fronts in reinforcement media in many technologically important polymer processes. In the case of fabrics, this creeping flow is shown to proceed primarily through the gaps in fabrics, with capillarity playing little if any role for commonly used materials. This finding has important implications for selection of strategy in modeling manufacturing processes of such materials. Namely, in the presence of fabric deformation which induces local shear, changes in the gap architecture greatly affect the flow patterns, and are not well predicted by tensor transformation of Darcy-type permeabilities. A simple, classic flow model is adapted to the case of fabrics penetrated by low-pressure viscous liquids after careful analysis of fabric architecture. An applicability range of this creeping flow model, the variable gap model, is developed. The present paper gives the model assumptions, and confirmation of its agreement with more sophisticated calculations. A demonstration of the approach for an unbalanced fabric (Knytex 24 5×4 unbalanced plain-woven glass fabric) shows excellent prediction of the bounds on flow behavior, and supports our earlier experimental findings on flow front orientation. This approach also shows clear superiority to semi-empirical, geometry-based models, since no fitting parameters at all are used in the modeling: only the constituent materials' geometry and properties are needed. This methodology is better able to predict trends in flow fronts, both qualitatively and quantitatively, than semi-empirical fitting. Extension of this work to realistic production processes is planned.