Abstract
Face masks are important in respiratory disease control, yet their effectiveness varies widely depending on the mask material and its fit on the wearer's face. In this study, a new semi-analytical flow network model based on the Kármán-Pohlhausen technique is introduced and utilized to efficiently assess mask performance across diverse facial features that represent the observed variations inside a large population. The reduced-order model enables the evaluation of the role of different facial geometrical features with significantly lower computational costs compared to traditional computational fluid dynamics simulations. This research reveals that the area around the nose, particularly without a nose clip, is most susceptible to peripheral leakage and high-velocity jets due to larger gaps. It is argued that subtle variations in facial features, especially the zygomatic arch, significantly influence leakage patterns, emphasizing the importance of customized mask designs. The study also elucidates the complex role of nose clips in improving sealing efficacy for tightly fitted masks and redirecting leaked flow in typical imperfect facemasks. This dual function of nose clips significantly influences overall mask performance, though the exact impact varies depending on individual facial features and mask fit. The reduced-order fluid model presented here has the potential to quantify the effectiveness of face masks for a large population and influence the design of future face masks, with a focus on minimizing or redirecting leakage jets to mitigate the dispersion of respiratory aerosols thus enhancing public health strategies for respiratory disease control.