A semi-analytical model for simulating fluid transport in multi-layered fibrous sheets made up of solid and porous fibers

Direct simulation of fluid transport in fibrous media consisting of swelling (i.e., fluid-absorbing) and non-swelling (i.e., solid) fibers is a challenge. In this work, we have developed a semi-analytical modeling approach that can be used to predict the fluid absorption and release characteristics of multi-layered composite fabrics made up of swelling and non-swelling fibrous sheets. The simulations presented here are based on a numerical solution of Richards’ equation. Two different fibrous sheets composed of non-swelling (PET) and swelling (Rayon) fibers with different Solid Volume Fractions (SVFs) and thicknesses were arbitrarily chosen in this study for demonstration purposes. The sheets’ capillary pressure and relative permeability are obtained via a combination of numerical simulations and experiment. In particular, the capillary pressure expression for non-swelling media is obtained from the analytical expressions that we previously developed via 3-D microscale simulations, while the capillary pressure for swelling media is obtained via height rise experiments. The relative permeability expressions for both swelling and non-swelling media are obtained from the analytical expressions previously developed via 3-D microscale simulations, which are also in agreement with experimental correlations from the literature. On the macroscale, simulation results are reported for fluid transport in bi-layered composite fabrics, and comparison is made between the performances of these fabrics in terms of the order in which the layers are stacked on top of one another. A higher rate of absorption was observed when the layer in contact with the fluid is that comprised of swelling fibers. A similar study was conducted for motion-induced fluid release from the composite fabrics when partially-saturated with a fluid. It was shown that less fluid release is expected when the swelling sheet is placed in contact with the surface.