Continuum-scale modeling of water infiltration into a stack of two thin fibrous layers and their inter-layer space

Unsaturated water flow through thin porous layers plays an important role in many applications such as water management in hydrogen fuel cells and hygiene products. It is well known that void spaces between adjacent thin layers (i.e., layer-layer interfaces) considerably impact through-plane water infiltration. Therefore, it is essential to account for this fact in the model development. Recently, we reported Nuclear Magnetic Resonance (NMR) measurements of water infiltration into a stack of two thin porous layers of 43-gsm polyester and showed crucial effect of the inter-layer space on the transfer of liquid from one layer to the other. In this work, we aim to test two numerical models of water infiltration into two (partially dry) thin porous layers. One is the standard Richards model for unsaturated flow and the other is Reduced Continua Model (RCM). The latter model is based on thickness-averaged properties and does not provide through-plane distribution of saturation in the layers. Layer-scale material properties are experimentally measured. Sub-layer material properties, which are used in the Richards model, are obtained by pore-morphology modeling of micro-CT images. Our results show that the RCM is superior to the Richards model. It can predict NMR measurements of temporal evolutions of water contents in the two layers quite well. Moreover, it is computationally much more efficient.