Simulating through-plane permeability of fibrous materials with different fiber lengths

Assuming that fibers can be represented as straight cylinders, an algorithm for generating virtual 3D layered fibrous media made up of fibers having identical diameters but different lengths is presented. It is shown that for a given basis weight and computational box (sample size), reducing the fiber length causes the solid volume fraction (SVF) to increase as the fibers pack next to one another more efficiently. The air permeability of these media is numerically simulated and discussed in detail with respect to the available 2D and 3D studies in the literature. Our permeability calculations show an excellent agreement with the predictions of the empirical equation of Davies [1] as well as the analytical model of Spielman and Goren [2]. Such an agreement indicates that, within the range of dimensions considered, the fiber length has no significant influence on the materials' through-plane permeability as long as the SVF remains constant. While this concept has been empirically observed in the past, our work is the first numerical simulation devised to confirm it.