A computational fluid dynamics-Population balance equation approach for evaporating cough droplets transport

Airborne diseases, including COVID-19, are transmitted by respiratory droplets, which makes the study of the evolution of these droplets important to control the transmission. However, the evolution of the droplets is complex, being a multiphase, polydisperse, multicomponent system undergoing evaporation. To numerically investigate such multiphase flows, there are mainly two approaches. One is the Eulerian-Lagrangian (E-L) approach, which is widely used due to its ability to trace the dispersion and evaporation of individual droplets. However, this approach generally has high costs and difficulty in post-processing. The other one is the Eulerian- Eulerian (E-E) approach, which, though having lower costs, is less adopted because of its failure to treat the features of polydispersity and evaporation. In order to take advantage of the low-costs of E-E approach, the population balance equation (PBE) is combined with the E-E approach to trace the polydisperse evaporating droplets. Two PBE solving methods, sectional method (SM) and quadrature based moment method (QBMM), are used and compared. The codes are developed based on the OpenFOAM library and their abilities to predict size changes of evaporating droplets, evolution of expelled airflow front, and aerosols concentration are assessed by using the experimental and numerical results in literature. Good agreements with the reported results are found, indicating the reliability of the CFD-PBE approaches. The SM and QBMM are finally applied in the transport of cough droplets in a 3D chamber. The suspending trends of small droplets and the falling trends of the large droplets are obtained by both methods. The droplets are found to be able to travel a distance longer than 2 m, which is valuable for the guidelines of social distancing. Additionally, the advantages and disadvantages of SM and QBMM are discussed.