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We present a statistical framework to account for effects of recycling and filtration in ventilation systems for the estimation of airborne droplet nuclei concentration in indoor spaces. We demonstrate the framework in a canonical room with a four-way cassette air-conditioning system. The flow field within the room is computed using large eddy simulations for varying values of air changes per hour, and statistical overloading is used for droplet nuclei, which are tracked with a Langevin model accounting for sub-grid turbulence. A key element is to break up the path that a virus-laden droplet nucleus can take from the time it is ejected by the sick individual to the time it reaches the potential host into four separate elementary processes. This approach makes it possible to provide turbulence-informed and statistically relevant pathogen concentration at any location in the room from a source that can be located anywhere else in the room. Furthermore, the approach can handle any type of filtration and provides a correction function to be used in conjunction with the well-mixed model. The easy-to-implement correction function accounts for the separation distance between the sick and the susceptible individuals, an important feature that is inherently absent in the well-mixed model. The analysis shows that using proper filtration can increase the cumulative exposure time in typical classroom settings by up to four times and could allow visitations to nursing homes for up to 45 min.


© 2023 Author(s). Original published version available at

Publication Title

Physics of Fluids



Available for download on Tuesday, January 30, 2024