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A reduced-order model of face mask aerodynamics and aerosol filtration is introduced. This model incorporates existing empirical data on filtration efficiency for different types of face masks, as well as the size distribution of exhaled aerosol particles. By considering realistic peripheral gap profiles, our model estimates both the extent of peripheral leakage and the fitted filtration efficiency of face masks in terms of outward protection. Simulations employing realistic peripheral gap profiles reveal that, for surgical masks, 80% or more of the total exhaled airflow could leak through the mask periphery, even when the average peripheral gap measures only 0.65 mm. However, the majority of exhaled aerosol particles do not follow the flow path through the peripheral gaps but, instead, impact directly on the mask fabric. As a result, these face masks can filter out approximately 70% of the exhaled particles despite the significant peripheral leakage. To validate our model, we compare its predictions with experimental data, and we find a reasonable agreement in estimating the outward protection provided by surgical masks. This validation underscores the reliability of our model in assessing the efficacy of surgical masks. Moreover, leveraging the insights gained from our model, we explore the impact of mask usage on the transmission of respiratory viruses within communities. By considering various scenarios, we can assess the potential reduction in viral spread achieved through widespread mask adoption. 

Recent studies have shown that the effectiveness of the face masks depends not only on the mask material but also on their fit on faces. The mask porosity and fit dictate the amount of filtered flow and perimeter leakage. Lower porosity is usually associated with better filtration; however, lower porosity results in higher perimeter leakage. The resulting leakage jets generated from different types of faces and different mask porosities are of particular interest. Direct numerical simulations of the flow dynamics of respiratory events while wearing a face mask can be used to quantify the distribution of the perimeter leaks. Here, we present a novel model for porous membranes (i.e., masks) and use it to study the leakage pattern of a fabric face mask on a realistic face obtained from a population study. The reduction in perimeter leakage with higher porosities indicates that there would be an optimal porosity such that the total leakage and maximum leakage velocities are reduced. The current model can be used to inform the quantification of face mask effectiveness and guide future mask designs that reduce or redirect the leakage jets to limit the dispersion of respiratory aerosols.