Navigating the Nano-Labyrinth: Reduced-Order Modeling of Porous Media for Next-Gen Filtration

This study presents a comprehensive multiphysics investigation of flow patterns, heat transfer, and species transport within an oxygen mask during the respiratory cycle. A coupled numerical model incorporating turbulent flow, conjugate heat transfer, and diluted species transport was developed to simulate cyclic breathing through time-varying boundary conditions. The model, validated against experimental measurements of gap flow velocities with a relative discrepancy of only 2.8%, captures the complex interactions between fluid dynamics, thermal response, and gas exchange throughout inspiration and expiration phases. Key findings reveal the formation of counter-rotating recirculation zones during expiration that significantly increase gas residence times and promote mixing between fresh oxygen and exhaled carbon dioxide. The thermal analysis demonstrates that mask walls require approximately 600 seconds (150 breathing cycles) to reach cyclic steady-state, highlighting the importance of material properties for patient comfort. Species transport calculations show incomplete flushing of carbon dioxide during inspiration, with residual CO₂ persisting in recirculation zone cores, leading to rebreathing and reduced oxygen delivery efficiency. Additionally, a reduced-order model based on lumped-element representation enables rapid parametric analysis of mask performance across varying fabric resistances and fit conditions. This model predicts that peripheral leakage ratios reach 85-95% for surgical and N95 masks, yet outward fitted filtration efficiency exceeds 70% for medical-grade masks due to particle inertia effects. The complementary approaches provide quantitative insights for optimizing mask geometry and material selection to improve gas delivery efficiency, minimize CO₂ rebreathing, and enhance patient comfort while maintaining effective filtration.