A closed form solution for flow in dual scale fibrous porous media under constant injection pressure conditions

In liquid composite molding (LCM), the resin is infused into stationary fiber reinforcements to impregnate all the empty spaces between the fibers. Most fabric reinforcements used in such processes consist of fiber tows or bundles that are woven, stitched, or braided to create a mat. The fiber tows and the spaces between the fiber tows saturate with resin at different rates and hence the use of a single permeability parameter to describe the flow using Darcy’s law is insufficient. An analytic solution for resin flow through such dual scale porous media is presented. It introduces the use of two distinctly different permeability values that describe the resin flow in these types of fabrics. The first permeability parameter is the bulk permeability (K), which characterizes the overall resistance to flow. The second is the tow permeability (Kt), which represents the resistance to flow inside each individual fiber tow. A closed form solution is developed to characterize the bulk and the tow permeability for a one-dimensional constant injection pressure experiment in which the flow front position during the filling is recorded. It is also mathematically proven that the partially saturated region remains constant if the mold is sufficiently long. The analytical methodology is validated by using a numerical simulation technique that allows one to predict the motion of the fully and partially saturated flow fronts by assigning bulk and tow permeabilities.