In our pilot study, we perform pore-scale simulations of two-phase flows in a reconstructed fibrous porous microstructure. We provide a quantitative analysis of the multiphase pore-scale dynamics and we identify the dominant fluid structures governing mass transport. We observe that the fibrous porous material presents significant variations in its microscopic morphology, which have an important effect on the pore invasion dynamics. Liquid transport is affected by the presence of a microstructure-induced capillary pressure acting adversely to the flow, leading to capillary fingering transport mechanisms even in the absence of hydrophobic treatments of the porous material. We underline the significance of the results for the optimal design of fuel cells electrodes and face masks in an effort to mitigate the current COVID-19 pandemic. The design of a layered porous structure with a increasing/decreasing size of the pore diameters along the flow direction can reduce/augment the filtration mechanism of liquids, such as water within fuel cells or large respiratory droplets within face masks, without necessarily increasing the thickness of the filter layer.