Modeling permeability of fibrous filters combining submicron and micron fibers in slip flow regime

Fibrous media are essential in aerosol filtration due to their ability to balance filtration efficiency, pressure drop, and dust holding capacity. Their performance depends on structural parameters such as fiber diameter, packing density, and thickness and the most efficient filters often include submicron or nanofibers. However, predicting pressure drop remains challenging, particularly due to slip flow effects at small scales. Existing models rarely account for both slip effects and fiber size distribution. This study extends a model originally developed for micronic fibers to submicron fibers, incorporating both the influence of slip effects and fiber size distribution. In order to overcome uncertainties in determining the structural parameters of fibrous media, the model was initially validated on numerically generated fibrous structures. This broader-scope model, when compared with other models from the literature, exhibits an improved predictive accuracy (within ± 10 %) for permeability values obtained from numerical simulations on both monomodal (219 cases) and polymodal (183 cases) fibrous structures, covering a packing density range from 0.1 % to 50 % and a fiber diameter range from 0.03 to 20 µm, leading to fiber Knudsen numbers between 0.007 and 4. An experimental validation was also performed on five commercial fibrous media and on data from the literature.