The COVID-19 pandemic highlighted the important role face coverings can play in protecting the wearer and others from aerosolised pathogens. Public health organisations and regulatory agencies worldwide set standards for the performance of face coverings. Although there may be minor differences in the details, all these regulations focus on two key metrics: the filtration efficiency (FE) and the breathability. The FE is defined as the proportion of aerosol particles passing through the mask material that are captured, while the breathability is assessed by measuring the permeability of the mask material. However, it has been recognised that both of these metrics describe the properties of the material the mask is made from and not their real-world performance.
To quantify performance in real-world conditions it has been proposed to consider two alternative metrics: the leakage ratio, defined as the proportion of the total volume flux of air exhaled that does not pass through the mask, and the face-fitted filtration efficiency (FFE), defined as the proportion of the total flux of aerosols exhaled which are filtered by the mask. Oxford mathematicians Ian Griffiths, Chris Breward, and Matthew Shirley recently collaborated with Lucy Hope, Paul Hope and Joseph Houghton from Virustatic SHIELD®, through the Innovate UK Analysis for Innovators scheme, to develop mathematical models to show how these real-world measures depend on the material properties.
Previous studies of the effect of face coverings on the airflow during breathing have relied either on computational fluid dynamics (CFD) simulations, which are costly in terms of time and computing power, or on empirical models that treat the face covering and the gap as parallel resistances to flow. By exploiting the thinness of the face covering, and the gap that it forms between the mask and the wearer’s face, the Oxford team used asymptotic analysis to derive a much simpler mathematical model from physical laws, which captures the spatial distribution of leakage and flow throughout the mask, whilst still being extremely simple to solve. This reduced model depends on only a single dimensionless parameter that describes the relative size of the resistance to flow through the mask and through the gap, along with geometric information about the size of the gap at each point, and the position of the mouth. This model can be solved for realistic geometries, in less than 10 seconds on a standard laptop. The resulting flux of air out of the mask and sides for an example simulation is shown in Figure 1. Using this reduced model, we can simulate both traditional face coverings and bioactive snoods, such as the Virustatic SHIELD® (see Figure 2).
The results of this work will help build mechanistic insight into what additional tests should be added to regulatory standards to reliably quantify real-world mask performance. In addition, it will provide a tool to help optimise new mask designs, particularly of bioactive face coverings, such as the Virustatic SHIELD®, to maximise the wearer’s protection and comfort and improve aerosol infection inhibition.
