Modeling motion-induced fluid release from partially saturated fibrous media onto surfaces with different hydrophilicity

Modeling the rate of fluid release from moving partially saturated nonwoven sheets in contact with a solid surface is a challenge, as the release rate depends on many parameters, some of which are difficult to quantify. In this paper, we report on a diffusion-controlled boundary treatment which we have developed to simulate fluid release from partially saturated porous materials onto surfaces with different hydrophilicy. The new boundary treatment considers the solid impermeable surface as a fictitious porous layer with a known fluid diffusive coefficient. Motion of the porous sheet on the surface is incorporated in the simulations by periodically resetting the saturation of the fictitious layer equal to zero, with a period obtained from the sheet’s speed of motion. Fluid transport inside the fibrous sheets is calculated by solving Richards’ equation of two-phase flows in porous media. Our numerical simulations are accompanied with experimental data obtained using a custom-made test rig for the release of liquid from partially saturated media at different speeds. It is demonstrated that the novel mathematical formulations presented here can correctly predict the rate of fluid release from moving fibrous sheets onto solid surfaces with different hydrophilicity as a function of time.