Filtering efficiency model that includes the statistical randomness of non-woven fiber layers in facemasks

Facemasks have become important tools to fight virus spread during the recent COVID-19 pandemic, but their effectiveness is still under debate. We present a computational model to predict the filtering efficiency of an N95-facemask, consisting of three non-woven fiber layers with different particle capturing mechanisms. Parameters such as fiber layer thickness, diameter distribution, and packing density are used to construct two-dimensional cross-sectional geometries. An essential and novel element is that the polydisperse fibers are positioned randomly within a simulation domain, and that the simulation is repeated with different random configurations. This strategy is thought to give a more realistic view of practical facemasks compared to existing analytical models that mostly assume homogeneous fiber beds of monodisperse fibers. The incompressible Navier-Stokes and continuity equations are used to solve the velocity field for various droplet-laden air inflow velocities. Droplet diameters are ranging from 10 nm to 1.0 µm, which covers the size range from the SARS-CoV-2 virus to the large virus-laden airborne droplets. Air inflow velocities varying between 0.1 m·s^-1 to 10 m·s^-1 are considered, which are typically encountered during expiratory events like breathing, talking, and coughing. The presented model elucidates the different capturing efficiencies (i.e., mechanical and electrostatic filtering) of droplets as a function of their diameter and air inflow velocity. Simulation results are compared to analytical models and particularly compare well with experimental results from literature. Our numerical approach will be helpful in finding new directions for anti-viral facemask optimization.