A two-scale modeling of motion-induced fluid release from thin fibrous porous media

In this work, a two-scale two-phase modeling methodology is presented for studying fluid release from saturated/unsaturated thin fibrous media 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 medium's saturation, are obtained through microscale modeling. At microscales, a 3-D model based on fiber diameter, fiber orientation, and medium's solid volume fraction (SVF), is generated to resemble the internal structure of the fibrous sheets and be used in full-morphology analysis as well as microscale permeability simulation. A mass convection boundary condition is considered here to model the fluid transport at the boundary in contact with the target surface. It was shown that the mass convection coefficient, k_f, plays a significant role in determining the release rate and is expected to be in the range of 10^-6<k_f<10^-9, depending 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.