Enhanced spread of expiratory droplets by turbulence in a cough jet

Coughing has been confirmed as a significant vector for transmitting respiratory diseases. It can be modelled physically as a turbulent jet to study the dispersion of expiratory droplets. The discrete random walk model for particle tracking is employed to study the effect of turbulence fluctuation on dispersion of particles and/or droplets. The concept of reach probability is proposed to characterise the streamwise spread distance. Our study shows that jet-like cough airflow turbulence prompts the wide spread of particles and expiratory droplets, and that the effect of evaporation on medium droplets (50 μm) is most significant. When turbulence fluctuations are considered for the 100 μm particles, there is a four-fold increase in the dispersion range in the streamwise direction, and a thirteen-fold increase in the transverse direction compared to that without fluctuation. Small particles are found to follow the airflow closely, dispersing in the whole jet region, while only 1% of large particles exceed 2 m in the streamwise direction; nearly 10% of medium particles travel 4.0 m (initial u0 = 10 m/s, mouth diameter D = 2 cm). Droplets evaporate after being exhaled, but fates of small droplets with initial diameter dp0 = 30μm as well as large droplets with dp0 = 100μm are little affected by relative humidity (RH). The 30 μm droplets evaporate in seconds and behave similarly to the 10 μm particles. The spread distance of large droplets is mainly determined by the jet outlet diameter and velocity. In contrast, the medium droplets are found to be very sensitive to RH under humid conditions (RH≥80%).