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No description available.

The primary objective of this research is to develop a mathematical framework that could be used to model or predict the rate of fluid absorption and release in fibrous sheets made up of solid or porous fibers. In the first step, a two-scale two-phase modeling methodology is developed for studying fluid release from saturated/unsaturated thin fibrous media made up of solid fibers when brought in contact with a moving solid surface. Our macroscale model is based on the Richards’ equation for two-phase fluid transport in porous media. The required constitutive relationships, capillary pressure and relative permeability as functions of the medium’s saturation, are obtained through microscale modeling. Here, a mass convection boundary condition is considered to model the fluid transport at the boundary in contact with the target surface. The mass convection coefficient plays a significant role in determining the release rate of fluid. Moreover the release rate depends on the properties of the fluid, fibrous sheet, the target surface as well as the speed of the relative motion, and remains to be determined experimentally. Obtaining functional relationships for relative permeability and capillary pressure is only possible through experimentation or expensive microscale simulations, and needs to be repeated for different media having different fiber diameters, thicknesses, or porosities. In this concern, we conducted series of 3-D microscale simulations in order to investigate the effect of the aforementioned parameters on the relative permeability and capillary pressure of fibrous porous sheets. The results of our parameter study are utilized to develop general expressions for kr(S) and Pc(S). Furthermore, these general expressions can be easily included in macroscale fluid transport equations to predict the rate of fluid release from partially saturated fibrous sheets in a time and cost-effective manner. Moreover, the ability of the model has been extended to simulate the radial spreading of liquids in thin fibrous sheets. By simulating different fibrous sheets with identical parameters but different in-plane fiber orientations has revealed that the rate of fluid spread increases with increasing the in-plane alignment of the fibers. Additionally, we have developed a semi-analytical modeling approach that can be used to predict the fluid absorption and release characteristics of multi-layered composite fabric made up of porous (swelling) and soild (non-swelling) fibrous sheets. The sheets capillary pressure and relative permeability are obtained via a combination of numerical simulations and experiment. In particular, the capillary pressure for swelling media is obtained via height rise experiments. The relative permeability expressions are obtained from the analytical expressions previously developed with the 3-D microscale simulations, which are also in agreement with experimental correlations from the literature. To extend the ability of the model, we have developed a diffusion-controlled boundary treatment to simulate fluid release from partially-saturated fabrics onto surfaces with different hydrophilicy. Using a custom made test rig, experimental data is obtained for the release of liquid from partially saturated PET and Rayon nonwoven sheets at different speeds, and on two different surfaces. It is demonstrated that the new semi-empirical model redeveloped in this work can predict the rate of fluid release from wet nonwoven sheets as a function of time.