The geometric moisture diffusivity model developed by this research indicates that fiber volume fraction and shape coefficient are the most important structural parameters affecting water vapor diffusivity through nonhydrophilic nonwoven fabrics. Water vapor diffusivity decreases with increasing fiber volume fraction and decreases as the flatness of the fiber cross section increases. Although structural properties such as fiber fineness and fabric thickness affect optical porosity, their effect on water vapor diffusivity through nonhygroscopic nonwoven materials is small. Part II of this series describes an analytical model that we developed to describe water vapor diffusion through nonwoven fabrics composed of nonhydrophilic fibers. This model is used to gain a deeper understanding of the role played by the size and shape of component fibers, and the effect of web constructional variables, especially fabric thickness and density, on moisture diffusion through these nonwovens.
Water Vapor Diffusivity ModelUsing an analogy with our thermal conductivity model (Equation 1, Part I of this series [ 3 ] ), assuming a vapor pressure gradient across the fabric thickness, and allowing for vapor diffusion through fibers and air interstices, we write a, water vapor diffusion model as follows:where In this model, D, is the diffusion coefficient of water vapor in air and Djll and Dil represent the diffusion I coefficient along the fiber axis and perpendicular to it, Xj is the fiber volume fraction, a is the anisotropy factor (ratio of the number of filaments in the machine and cross machine directions), 4 is the polar orientation angle ( Figure 10 [ 3 ] ), L is the fabric thickness, and d is the fiber diameter. A detailed derivation of this model and the underlying assumptions are given in Appendix A of Part I [3].Since Da is generally much larger than Df( DJ/ Do = 10-6 ^-10-8), Djl D,, can be neglected and Equation