On the effects of fiber orientation in permeability of fibrous media to power-law fluids

In this note, for the first time, the flow of power-law fluids is numerically simulated in 3-D fibrous structures resembling the internal microstructure of fibrous hygiene products to study the effects of fibers’ in-plane and through-plane orientations on the media’s permeability. It was found that while the permeability of a fibrous material to a power-law fluid hardly depends on the in-plane orientation of the fibers, it increases with increasing the fibers’ through-plane orientation. Moreover, we developed a simple analytical expression that can be used together with the empirical correlation of Davies (1973) [16], modified with an equation derived by Banks (1987) [17], to predict the permeability of anisotropic fibrous media to power-law non-Newtonian fluids. The predictions of our formulation are compared with our numerical simulations and good agreement is observed.