Analytic characterization of the permeability of dual-scale fibrous porous media

It has been known for some time now that fabrics that contain fiber tows, which are bundles of thousands of aligned fiber filaments, can be represented as dual-scale porous media; these tows are woven or stitched together and the flow through the resulting fabrics can be modeled to account for the delayed impregnation of tows, which draw fluid away from the advancing flow front. From such flow simulations, one can predict not only the macroflow front, but also the saturation of the fiber tows, as well as determine the partially-saturated region. The simulations require one to input two material parameters to quantify the two distinct length scales of the porous media: the bulk permeability, which characterizes the overall resistance to the flow, and the tow permeability, which is the resistance to the flow within the tow and is related to the saturation of the fiber tows. Techniques to characterize the bulk permeability are well established and can be performed in one, two, and three dimensions; however, methods to measure tow permeability are sparse. Hence, an analytical model is developed to characterize both permeability values: the bulk permeability (K) and the fiber tow permeability (Kt) from a one-dimensional constant flow rate experiment in which the inlet pressure profile during the filling is recorded. These two permeability values determine the time scales of resin impregnation in between the fiber tows and within the fiber tows thus playing an important role in the decision process of how long to leave the resin injection gate open to ensure filling of the fiber tows. For dual-scale preforms, the inlet pressure profile for a constant rate injection is not only dependant on the structure of the preform and fluid viscosity, but also on the mold length. If the mold is sufficiently long, it can be mathematically proven that the partially-saturated region is constant. Examination of the solution also reveals that the partially-saturated length increases as the bulk permeability increases and as the tow permeability decreases. The analytical methodology is demonstrated by characterizing four different fabrics.