Three mechanisms of respiratory droplet generation associated with exhalation have been described in the literature: in the oral cavity, trachea–bronchi, and bronchioles . However, almost no reports have quantified the number, mass, and particle size distribution of droplets generated by each mechanism. This study focused on reproducing the stripping of the airway wall mucosa due to airflow shear stress in the tracheal–bronchial region. The coupled DPM-EWF model was used to simulate droplet generation in the airway wall mucosa during coughing, and the effects of the mucous viscosity and cough flow rate on the number, mass, and particle size distribution of generated droplets were evaluated.
Various approaches have been used to measure the particle size distributions of respiratory droplets [8–26]. However, obtaining a comprehensive distribution experimentally is impossible because of differences in measurement methods and conditions. In addition, because particles emitted from the oral cavity are measured, studying the generation mechanisms separately is impossible. In this study, the coupled DPM-EWF model was applied to CFD analysis of droplet generation by the stripping of the mucous membrane in the airway by the coughing airflow, and the droplet generation and distribution were quantified.
The simulation results showed that a wide range of droplet sizes from 100 nm to 400 µm was generated. Because this method does not require a superfine mesh to resolve small droplets, it is applicable to large-scale geometries such as the entire airway. Furthermore, by applying this method to obtain the droplet distribution for various airway shapes, individual differences in droplet distributions can be considered for a more detailed simulation of droplet dispersion in the air.
Considering the algorithm of DPM-EWF coupling, WSS on airway wall is the dominant factor to control the droplet generation. And WSS is highly affected by the amount of airflow. Increasing the CFPR from 2 L/s to 8 L/s increased the velocity of the internal airflow. In our ideal geometry, the maximum velocities were (Fig. 3) are close to the values reported by Kou et al.  using patient specific airway geometry. Increasing the velocity also increased WSS (Fig. 4). Increasing WSS increased the stripped droplet mass of the droplets. A comparison between the stripped droplet mass distribution (Fig. 5) and WSS distribution (Fig. 4) indicates that more droplets tended to be generated in high-WSS regions.
Coupled DPM-EWF simulation can be applied for whole airway model and can exhibit the certain location of droplet generation. At CPFR = 2 L/s, droplet generation was only observed on the G1 surface. This may be because CSS was set to 1 Pa, and WSS was less than CSS for most airway walls other than that at G1. Increasing CPFR increased the stripped droplet mass over time (Fig. 6), which suggests that a higher CPFR resulted in a larger area where WSS > CSS. The droplet stripping started earlier with increasing CPFR (Fig. 7-(a)). In this study, CSS was fixed at 1 Pa. Lowering CSS should increase the droplet number because the region where CSS < WSS would increase.
In addition to the airflow, airway mucous condition also affects on droplet generation. Total mass of generated droplet has a linear correlation, but the total number and the maximum diameter do not have a linear correlation. The maximum number of stripped droplets and maximum droplet size were obtained at 8.25 mPa·s (Fig. 8-(b)), which suggest that the droplet number and maximum droplet size do not have a linear correlation with the viscosity, unlike the total mass of droplets. The droplets larger than 100 µm were generated only at 8.25 mPa·s. These large droplets may affect the total mass of generated droplets.
The maximum droplet diameter had a range of 70–400 µm depending on the CPFRs considered in this study. Pairetti et al. used the VOF method to reproduce droplet generation with a uniform profile of a 30 m/s airflow on a flat liquid film, which resulted in a maximum droplet size of about 400 µm . In the present study, the maximum flow velocity was 47.9 m/s at CPFR = 8 L/s, which resulted in a maximum droplet size at about 400 µm and agrees with Pairetti et al.’s results. Pairetti et al.  tracked a minimum droplet size of 100 µm. The VOF requires an extremely fine mesh to track droplet behavior at the microscale or nanoscale because the droplet size depends on mesh resolution. Therefore, for airway tree geometries with complex 3D structures, simulating the generation of droplets with a wide particle size distribution requires a fully resolved mesh and is very computationally expensive. In the present study, droplets were generated with a minimum droplet size of 0.1 nm, but only droplets larger than 0.1 µm were counted because coronaviruses are generally around that size.
The droplet size distribution in the present study showed that smaller droplets were generated in larger numbers. Because only shear-induced droplets in the lower airway were considered and the droplets generated were counted rather than the droplets released from oral cavity, the obtained droplet size distributions were significantly different from those obtained experimentally in previous studies [8–26]. For many of these studies, the droplet size distributions peaked at the microscale. Guo et al.  simulated the droplet deposition during expiration by using the geometry of the entire respiratory system, including the vocal cords and oral cavity. Their results showed that the arrival rate of droplets in the oral cavity was affected by the expiratory flow rate and droplet size, and very small droplets were deposited in the pharyngeal region. Therefore, modeling from the pharynx to the oral cavity may significantly reduce the number of droplets that reach the oral cavity, especially small droplets.
The presence or absence of relative humidity outside the oral cavity should greatly affect the results of both numerical simulations and experimental measurements. The relative humidity in the human respiratory tract is usually 100% owing to its high humidity compared with the surrounding environment. Therefore, when droplets are released from the respiratory tract into the atmosphere, the water in the droplets evaporates, which reduces their diameter. Because the evaporation rate is generally faster with a smaller droplet size , in the actual environment, nanoscale droplets may evaporate completely before reaching the measurement device or become smaller than the measurement resolution. Thus, they are unlikely to be captured by the particle size distribution measured outside the oral cavity.
In this study, Weibel’s model was used to represent the ideal airway shape, in which the airway cross-section is a circle and symmetric branches form with smooth airway walls. However, the actual human body has a more complex and asymmetric airway shape. The wall surface was simplified to be a rigid wall that does not move. When a fast airflow is expelled such as by coughing, the cross-sections of the trachea and bronchi may be deformed without the support of cartilage. By creating an airway model considering left–right asymmetry and a patient-specific model of expiration constructed from dynamic computed tomography, the methods used in this study can obtain droplet distributions for complex airway shapes.
Although various protein components are dissolved in body fluids, a single-phase liquid film comprising a Newtonian fluid with uniform viscosity was applied to the airway walls in this study. Because the fluid film moves during coughing and results in a nonuniform shear rate, applying a non-Newtonian model to the mucous membrane viscosity may reproduce more complex fluid film behavior by showing localized changes in viscosity.