Transverse permeability determination of dual-scale fibrous materials

Transverse flow through aligned yarns with two length scales is theoretically studied. Darcy's law and Stokes equation are employed to describe flow behaviors inside the porous yarns and in the open channels between yarns, respectively. Beavers and Joseph's semi-empirical model and Brinkman's extension of Darcy's law are used to characterize the jump-velocity and continuum-stress boundary condition at the interface layer between the clear fluid and the porous yarn. The analytical model for predicting permeability is developed as a function of porosity, fiber radius, fiber cross-sectional shape, and fiber packing pattern, which would help improve the physical understandings of dual-scale flows in fibrous media. Additionally, a simple but effective semi-analytical model is provided for easy use. Permeability predictions calculated from our model agree fairly well with experimental and numerical results in literature.