Infectious respiratory diseases have long been a serious public health issue, with airborne transmission via close person-to-person contact being the main infection route. Coughing episodes are an eruptive source of virus-laden droplets that increase the infection risk of susceptible individuals. In this study, the droplet generation process during a coughing event was reproduced using the Eulerian wall film (EWF) model, and the absorption/expulsion of droplets was tracked using the discrete phase model (DPM). A realistic numerical model that included the oral cavity with teeth features and the respiratory system from the throat to the first bifurcation was developed. A coughing flow profile simulated the flow patterns of a single coughing episode. The EWF and DPM models were coupled to predict the droplet formation, generation, absorption, and exhalation processes. The results showed that a large droplet number concentration was generated at the beginning of the coughing event, with the peak concentration coinciding with the peak cough rate. Analysis of the droplet site of origin showed that large amounts of droplets were generated in the oral cavity and teeth surface, followed by the caudal region of the respiratory system. The size of the expelled droplets was 0.25–24 μm, with the peak concentration at 4–8 μm. This study significantly contributes to the realm on the site of origin and localized number concentration of droplets after a coughing episode. It can facilitate studies on infection risk assessment, droplet dispersion, and droplet generation mechanisms from other sneezing or phonation activities.

Infectious respiratory diseases have long been a significant public health concern. This includes instances of plagues, measles, tuberculosis, influenza, severe acute respiratory syndrome coronavirus (SARS-CoV), Middle East respiratory syndrome coronavirus (MERS-CoV), and the most recent SARS-CoV-2 (Churchyard , 2017; Piret and Boivin, 2021). Person-to-person airborne transmission of respiratory viruses can occur via direct or indirect contact, respiratory droplets, and droplet nuclei transmission (Dhand and Li, 2020; Wang , 2021). Infected patients can expel pathogen carriers into the ambient environment via respiratory activities such as breathing, talking, phonating, singing, sneezing, or coughing (Wei and Li, 2016; Stadnytskyi , 2021). Once in the surrounding environment, viral-laden droplets can remain airborne for an extended period and be transported by indoor airflow to the effective breathing zone of residents and subsequently be inhaled at various exposure levels, as reported by previous studies that were comprehensively reviewed by Inthavong (Inthavong, 2020). During the expiratory phase, the infection risks are associated with (1) droplet number concentration, (2) size distribution, (3) content of infectious agents, and (4) performance frequency (Morawska, 2006). In addition, more recent studies underscore the dependence of disease transmission on infective dose threshold of the virus (SeyedAlinaghi , 2022) and the viral shedding rate (Widders , 2020). Thus, quantitative studies are required to determine the pathogen susceptibility targeting each activity.

The threat of coughing-related infections has gained public attention, being extensively studied over the past decades owing to its possibility for the eruptive release of many pathogens in a short period (Stadnytskyi , 2021). When coughing, the sequent build-up of expiratory flow velocity, reaching a Reynolds number of 104 (Bourouiba , 2014), expulses compressed air through the open mouth. Due to the high speed, droplets are produced in the oral cavity due to shear-induced surface-wave instabilities (Wei and Li, 2016; Pöhlker , 2021). The stripped droplet parcels follow the air stream and escape to the environment through the open mouth or are re-absorbed into the mucus layer. Virus-laden droplets are generally deposited in the respiratory tract after inhalation (Li , 2022; Wang , 2021). The mucus clearance process (i.e., coughing) can trigger the re-emittance of deposited virions or the local transmission of progeny viruses shed by infected cells (Schaefer and Lai, 2022). Therefore, the number concentration and size distribution of droplets from coughing have gained significant attention from the scientific community. A review of studies over the past 20 years has indicated significant scatter (Yang , 2007; Chao , 2009; Morawska , 2009; Johnson , 2011; Lindsley , 2012; and Zayas , 2012), which can be attributed to the heterogeneity of measurement techniques, sampling methods, or intersubject variability. More recently, facilitated by advanced techniques, the realm of measuring ejected cloud characteristics and generated droplet properties from oral activities in an indoor environment has been embarked upon to deliver a comprehensive understanding during the pandemic epoch (Wang , 2020a, 2020b; Archer , 2022; Harrison , 2023; and Bahramian and Ahmadi, 2023). Drawing upon the properties of generated droplets from experimental studies, computer-aided approaches have been expanded to explore further the deleterious effects of these droplets in the context of disease transmission. Among them, computational fluid dynamics (CFD) has been universally adopted for the numerical investigation of the contagion risk of coughing. Most studies have investigated the cough-jet stream characteristics and fate of expiratory droplets in an enclosed environment (Li , 2021; Payri , 2021; Nie , 2022; Aljabair , 2023; and Nishandar , 2023), or the distance-based exposure risks between residents (Calmet , 2021; Mariam , 2021; Hossain , 2023; and Li , 2023). As can be seen, to date, both experimental and numerical endeavors have extensively advanced our understanding of droplet size distribution and their behavior under varying microclimatic conditions within an enclosed environment. Nonetheless, the site origin and generation mechanism of these droplets in the respiratory tract have yet to be discussed in the listed studies.

Against this background, further numerical studies have been conducted on the interactions between high-speed, chaotic exhaled air and the liquid-layer lining the inner surface of the airway (i.e., the mucus layer) during the coughing episode. The two most common methods adopted are the volume of fluid (Paz , 2019; Rajendran and Banerjee, 2019; Pairetti , 2021; and Yi , 2021) and Eulerian wall film (EWF) models (Paz , 2017a; Paz , 2017b; Ren , 2018, 2020, 2022; and Anzai , 2022). These studies provide an understanding of the respiratory droplet generation process, the effects of mucus properties on cough clearance efficiency, and the impact of airway deformation. To facilitate the assessment of the infection risks of virus-laden droplets, it is crucial to qualitatively and quantitatively investigate the origin of respiratory droplets during expiratory events (i.e., coughing). Furthermore, the realistic and comprehensive characteristics of the target respiratory airway model should be considered to ensure the accuracy of the cough-jet stream and expelled droplet features.

In this study, the EWF model and Lagrangian discrete phase model (DPM) were coupled to characterize the following: (1) fluid flow profiles of coughing; (2) number concentration, size distribution, and locality of generated and expelled droplet particles during coughing; and (3) absorption efficiency of stripped droplets. The results establish a link between the high viral load of the infected respiratory tract and the possibility of such viral pathogens being released into the environment by coughing. Subsequently, the infection risk can be determined for different respiratory viruses.

The realistic airway model comprised a computed tomography (CT)-based trachea-bronchus model and oral cavity produced by the open-source DAZ Studio software (DAZ Productions, Inc.) shown in Fig. 1. During coughing, various oral shapes and sizes were observed (Dbouk and Drikakis, 2020). In this study, the newly developed oral cavity model mimicked the configuration of a slightly open mouth with dimensions of L = 4.7 and H = 0.85 cm (Fig. 1) to similarly match the data provided by experimental measurements from high-speed imaging (Dbouk and Drikakis, 2020). The total area of the open mouth of 3.76 cm2 was within the range of 4 ± 0.95 cm2, as stated in a previous study (Seminara , 2020). In addition, the teeth attributes were integrated to provide the most realistic traits of the oral cavity (Fig. 1). The realistic trachea-bronchus model was created from CT scans, and details on the process are available in the previous study by Ito (2016). This trachea-bronchus model, in combination with the nasal cavity, has been validated by our research group, providing reliable results in diverse research themes (Wang , 2020a, 2020b; Yoo and Ito, 2022; Kuga , 2021, 2022, 2023; Murga , 2023; and Khoa , 2023).

FIG. 1.

Outline of the simulation model.

FIG. 1.

Outline of the simulation model.

Close modal

The discretization process was executed using the poly-hex core elements, which proposed the CFD simulation with higher accuracy at a reduced computational cost (Zore , 2019). The accuracy in the vicinity of the wall was enhanced by applying ten prism layers. This hybrid mesh has been successfully used to predict airflow and particle transportation/deposition simulation of the respiratory tract (Khoa , 2023a; Khoa , 2023b). According to the mesh independence test, the mesh size of 15.5 × 106 cells was selected for subsequent simulation in this study, more detailed information can be found in Fig. S1 (supplementary material). This analysis strikes a balance between the computational burden and prediction accuracy.

The unsteady, incompressible, and isothermal fluid flow in the human respiratory tract was obtained by solving the Reynolds-averaged Navier–Stokes equations,
U ¯ i x i = 0 ,
(1)
U i ¯ t + U i ¯ U j ¯ x j = 1 ρ g p g ¯ x i + x j [ ( ν + ν T ) ( U i ¯ x j + U j ¯ x i ) ] ,
(2)
where U ¯ is the mean velocity; u′ is the fluctuating components; and pg, ρg, ν, and νΤ are the pressure, density, kinematic viscosity of the fluid, and turbulent viscosity, respectively.

This study selected the turbulent model of the shear stress transport (SST) kω. This model has been used to predict adverse pressure gradient flow, strong curvature, and swirling flow in airway systems, as shown in previous experiments (Phuong and Ito, 2015; Elcner , 2016). The coughing flow profile was obtained from field measurements of Gupta for male subjects, as shown in Fig. 2(a) (Gupta , 2009). From the empirical equation, the coughing flow rate was allocated to four inlets according to the flow weighting of each lobe of the lung proposed in the study by Shelley (2014) and reasonably applied in our study (Khoa , 2023a; 2023b), as shown in Fig. 2(b). This procedure was implemented via a user-defined function (UDF) macro in ANSYS Fluent. The numerical boundary conditions for the coughing airflow simulation are listed in Table I.

FIG. 2.

(a) Coughing flow rate following the previous field measurement and (b) the description of inlet boundary conditions.

FIG. 2.

(a) Coughing flow rate following the previous field measurement and (b) the description of inlet boundary conditions.

Close modal
TABLE I.

Numerical boundary conditions for the coughing airflow simulation.

Parameter Information
Algorithm  SIMPLE (Semi-Implicit Method for Pressured Linked Equations 
Convection scheme  Second-order upwind 
Density (kg/m3 1.185 
Viscosity (kg/m s)  1.81 × 10–5 
Averaged cough peak flow rate (L/s)  5.75 
Averaged cough exhaled volume (cm3 1000 
Total simulation time (s)  0.5 
Time step size (s)  0.001 
Parameter Information
Algorithm  SIMPLE (Semi-Implicit Method for Pressured Linked Equations 
Convection scheme  Second-order upwind 
Density (kg/m3 1.185 
Viscosity (kg/m s)  1.81 × 10–5 
Averaged cough peak flow rate (L/s)  5.75 
Averaged cough exhaled volume (cm3 1000 
Total simulation time (s)  0.5 
Time step size (s)  0.001 

In a coughing episode, an excessive fluid flow velocity is rapidly produced and subjected to turbulence and high shear stress at the interface between the airstream and thin liquid film (mucus/saliva). Under such conditions, Kelvin–Helmholtz instabilities occur, which cause waves with an escalating amplitude on the surface of a thin liquid film (Pöhlker , 2021). Droplets form from the crest of these waves in a multimodal mode and are carried by the flow.

The droplet generation mechanism can be predicted using the EWF model, in which thin liquid mucus layers were hypothesized to be aligned on the inner surface of the oral-tracheal model. The governing equation of the EWF model is as follows (ANSYS, Inc., 2022):
ρ l h t + s · ( ρ l h V l ) = m ̇ s ,
(3)
ρ l h V l t + s · ( ρ l h V l V l + D V ) = h s P L + ρ l h g τ + 3 2 τ f s 3 μ l h V l + q s . ,
(4)
D V = s 0 h v l 2 d y ,
(5)
P L = P gas + P h + P σ ,
(6)
P h = ρ h ( n · g ) ,
(7)
P σ = σ s · ( s h ) ,
(8)
where ρl is the film density, h is the film height, Vl is the mean film velocity, and ms is the mass source per unit wall area owing to droplet collection, film separation, film stripping, and phase change. In Eq. (4), DV is the differential advection term computed based on the quadratic film velocity with fluctuating velocity vl(s,y,t), in which s is the horizontal flow direction, and y is the vertical direction (Kakimpa , 2015). The term PL is the mucus film pressure, gτ is the gravity component, τfs is the shear force at the film–liquid interface, μl is the viscosity, qs is the momentum source, σ is the surface tension, Pσ is the pressure exerted by the surface tension, Ph is the gravity component normal to the wall, and n is the normal vector.

The reliability of applying the EWF model in anticipating the interaction between the coughing stream jet and lining fluid is emphasized through supplementary simulations conducted using a simplified airway model. The simulation results were subsequently compared with experimental data, and additional information on this validation process is elaborated upon in Fig. S2 (supplementary material).

In the context of our primary simulation, the EWF model was included with the fluid flow at the beginning of the coughing episode. The simulation was applied to the total inner surface of the numerical domain, including the teeth surface. In general, the mucus thickness varies along the airway system. However, to simplify the simulation, a constant thickness of 30 μm was used to represent the mucus layer in the throat, larynx, trachea, and bifurcation, based on previous studies (Paz , 2017a; Paz , 2017b; Ren , 2022; and Anzai , 2022). For the oral cavity, the saliva thickness ranged from 11.3 to 68.9 μm, as proposed by the research of Assy (2022). For the teeth surface, the saliva thickness was assigned based on early experimental data (Collins and Dawes, 1987), which ranged from 2.59 to 4.44 μm following the mandibular, maxillary, left, or right position of teeth. The saliva and mucus layers were assumed to be water with a density of 998.2 kg/m3 and viscosity of 0.001 kg/m s.

Shear-induced droplet generation was considered through the high velocity and turbulent flow, causing the instability of the lining mucus/saliva layers and leading to droplets peeling from the crests of the formed waves. This process was defined by the initial parameters given in Table II. Among them, the critical shear stress is the main factor that governs the number concentration of generated droplets. A parametric analysis was required prior to the main simulation to determine an appropriate value for the simulation, which is delivered in Fig. S3 (supplementary material). Notably, this analysis was significantly influenced by the individual morphological characteristics considered in this study. Then, a value of 5 Pa was specified for the critical shear stress, which imposed the limit that any region subjected to shear stress greater than 5 Pa would trigger the shedding of mucus/saliva layers into droplets. In addition, a diameter coefficient, which specifies the droplet size range (ANSYS, Inc., 2022), was also determined by experiencing the parametric analysis with a value of 0.0003 (Fig. S4, supplementary material). Finally, the film time step size was automatically assigned by ANSYS Fluent using adaptive time-stepping functions, which controlled the time step size to be small enough to ensure that the maximum Courant number during the simulation was less than 1. The continuous generation of mucus/saliva layers beneath the epithelial cells was neglected, which indicated no refill of mucus/saliva layers after being dispossessed.

TABLE II.

Initial parameter for Eulerian wall film model.

Parameter Value
Critical shear stress—CSS (Pa) 
Diameter coefficient  0.0003 
Mass coefficient  0.25 
Surface tension (N/m)  0.0589 
Parameter Value
Critical shear stress—CSS (Pa) 
Diameter coefficient  0.0003 
Mass coefficient  0.25 
Surface tension (N/m)  0.0589 
The EWF model was coupled with the DPM to track the trajectories of droplets stripped from the liquid film. Forces acting on the body were used to predict the droplet transportation, absorption, and exhalation characteristics of the oral-tracheal model. The Lagrangian discrete phase of the particle trajectories was computed by the following equation:
d u p d t = F D + F G + F S ,
(9)
where the subscript p is the droplet phase, and F D is the drag force per unit particle mass derived from Stokes' drag law, expressed in the following equation:
F D = 18 μ ρ p d a 2 C D Re p 24 ( U u p ) ,
(10)
where μ is the air viscosity, U is the fluid flow velocity, u p is the droplet velocity, da is the aerodynamic droplet diameter, ρp is the droplet density, CD is the drag coefficient, and Rep is the particle Reynolds number.
The second term, F G, denotes the gravitational settling. The third term, F s, is Saffman's lift force due to shear on a unit mass basis. The lift force was adapted from a previous study by Li and Ahmadi (1992) and is a generalization of the expression provided by Saffman (1965), expressed as the following equation:
F S = 5.188 v 1 2 ρ d i j ρ p d a ( d l k d k l ) 1 4 ( U u p ) ,
(11)
where dij, dlk, and dkl are deformation rate tensors.

The aerodynamic diameter and number of tracked droplets were determined based on the EWF simulation. The droplets were defined with a unit density (1000 kg/m3), equal to that of pure water. The fate of the droplets was considered as exhaled via the mouth opening or was re-absorbed into the mucus layer; hence, the “escape” boundary condition was assigned to the mouth opening, and the “perfect trap” condition was applied as the wall boundary conditions. The evaporation and breakup of the droplets were negligible. The droplets were continuously generated during the simulation; therefore, the velocity, size, and spatial and temporal information of the droplets stripped from the mucus layer were recorded using the UDF macro for each time step.

The generated, exhaled, and absorbed percentages, denoted as ηG-i, ηE-i, and ηA-i, can be expressed by Eqs. (12)–(14), respectively,
η G i = N G i N G × 100 % ,
(12)
η E i = N E i N E × 100 % ,
(13)
η A i = N A i N A × 100 % ,
(14)
where NG-i, NA-i, and NE-i are the number of droplets generated, absorbed, and exhaled that belong to region i, which corresponds to the regions defined in Fig. 1. NG, NA, and NE are the total stripped, absorbed, and exhaled droplets after a single coughing episode (duration of 0.5 s), respectively. The size distribution of the coughed droplets was multimodal; accordingly, the droplet size bin was identified to establish the size distribution percentage of the generated, exhaled, and absorbed droplets (ηG-s, ηE-s, and ηA-s), given in Eqs. (15)–(17), respectively,
η G s = N G s N G × 100 % ,
(15)
η E s = N E s N E × 100 % ,
(16)
η A s = N A s N A × 100 % ,
(17)
where NG-s, NA-s, and NE-s are the number of droplets generated, absorbed, and exhaled, respectively, which decreases in the size bin, as listed in Table III.
TABLE III.

Classification of droplet size bin.

Droplet size bin (μm) Averaged size (μm)
0.1–0.25  0.175 
0.25–0.5  0.375 
0.5–0.75  0.625 
0.75–1.0  0.875 
1.0–2.0  1.5 
2.0–4.0  3.0 
4.0–8.0  6.0 
8.0–16.0  12.0 
16.0–24.0  20.0 
24.0–32.0  28.0 
Droplet size bin (μm) Averaged size (μm)
0.1–0.25  0.175 
0.25–0.5  0.375 
0.5–0.75  0.625 
0.75–1.0  0.875 
1.0–2.0  1.5 
2.0–4.0  3.0 
4.0–8.0  6.0 
8.0–16.0  12.0 
16.0–24.0  20.0 
24.0–32.0  28.0 

The size distribution of exhaled droplets can be calculated by dividing the number of droplets within the specific size bin by the logarithm of the droplet size class interval (dNE-s/dLogD). Finally, the exhaled droplet size distribution was normalized with the total cough exhaled volume (1000 cm3) to obtain the number concentration divided by the logarithm of the droplet size class interval (dCNE-s/dLogD).

The results of the coughing fluid flow features are depicted in Fig. 3 at the start of the coughing episode at 0.01 s, cough peak flow rate (CPFR) at 0.077 s, and near the end of the coughing event at 0.4 s. Notably, the velocity magnitude and distribution herein are described at the instantaneous times. At the onset of coughing [Fig. 3(a)], the culminated velocity occurred at the bifurcation, trachea, glottis, and throat regions with a value of 3 m/s. At CPFR, the spatial distribution of the jet stream remained, but the magnitude increased by almost 13-fold up to 40 m/s. In the final coughing stage, the coughing velocity rapidly decreased to less than 3 m/s in identical acceleration regions.

FIG. 3.

(a) Instantaneous streamline velocity distribution at the specific time during coughing, (b) instantaneous 2D flow features in the oral cavity and the mouth opening, and (c) in the vicinity of the maxillary teeth surface at the CPFR (0.077 s).

FIG. 3.

(a) Instantaneous streamline velocity distribution at the specific time during coughing, (b) instantaneous 2D flow features in the oral cavity and the mouth opening, and (c) in the vicinity of the maxillary teeth surface at the CPFR (0.077 s).

Close modal

In the oral cavity [Fig. 3(b)], the airstream accelerated in the throat region and impacted the palate and bends following the curvilinear shape of the oral ceiling. The expulsive flow that escaped the oral region was primarily distributed at the bottom of the mouth opening. Reserve flow also formed in the basal region near the mouth opening, which contributed to the swirling flow at the mouth opening [Fig. 3(b)]. Due to the flow features toward the ceiling of the oral cavity, the maxillary teeth are expected to endure the high-velocity flow during the cough. Figure 3(c) shows the two-dimensional flow distribution for the maxillary teeth, which revealed that the high-velocity fluid flow attacked the inner surface of the molars, premolars, canines, and incisors.

The rapid increase in the flow rate due to coughing induces substantial shear stress on the airway wall, closely linked to the droplet production criteria in the EWF model simulation. The relationship between shear stress, mucus thickness, and stripped droplets is presented in Fig. 4, which describes the instantaneous value of each variable. At 0.01 s [Fig. 4(a)], the low coughing velocity resulted in a modest shear stress of less than 5 Pa on the airway wall, which failed to meet the minimum threshold to produce droplets; hence, the droplets were not observed and the mucus/saliva thickness remained in its original state. At CPFR [Fig. 4(b)], the cough ejection velocity increased to 40 m/s, which induced significant shear stress on the wall surfaces. Multiple airway surfaces experienced shear stress levels greater than 5 Pa, which fulfilled the criterion for droplet generation off the thin liquid film on the oral-airway surfaces. Accordingly, the mucus/saliva thickness decreased to almost 0 μm and droplets simultaneously emerged in the corresponding regions [Fig. 4(b)]. The complex and uneven surface of the oral-airway model produced an uneven distribution of the peak shear stresses. This completely removed the mucus/saliva layers in several specific regions, while the remaining areas preserved their initial liquid film thickness. Droplet production decreased significantly at 0.15 s [Fig. 4(c)] due to the mucus/saliva layers dissipating, following the former intense erosion process during CPFR.

FIG. 4.

Immediate distribution of wall shear stress (left), mucus/saliva thickness (middle), and initial position of stripped droplets (right) at (a) 0.01, (b) 0.077, and (c) 0.15 s.

FIG. 4.

Immediate distribution of wall shear stress (left), mucus/saliva thickness (middle), and initial position of stripped droplets (right) at (a) 0.01, (b) 0.077, and (c) 0.15 s.

Close modal
FIG. 5.

(a) Instantaneous number of generated droplets during the cough event associated with the coughing flow rate, (b) instantaneous positions of droplets at different times during the cough, (c) the percentage of droplets produced from their origin, and (d) the surface area of each airway region that experienced wall shear stresses greater than 5 Pa.

FIG. 5.

(a) Instantaneous number of generated droplets during the cough event associated with the coughing flow rate, (b) instantaneous positions of droplets at different times during the cough, (c) the percentage of droplets produced from their origin, and (d) the surface area of each airway region that experienced wall shear stresses greater than 5 Pa.

Close modal

The relationship between the coughing flow profile and droplet production was correlated to understand the droplet generation process better. The instantaneous number of droplets stripped from the mucus/saliva layers due to the coughing flow rate during the single coughing episode (∼0.5 s) is shown in Fig. 5(a). The results demonstrate that the coughing flow rate rapidly increased in the early stage of coughing. In contrast, droplet generation lagged and did not start until 0.04 s with an initial rapid rise. The number of droplets produced increased rapidly in parallel with the coughing flow rate and formed a sharp slope, with the peak almost coinciding with the CPFR (at approximately 0.077 s). After reaching their peaks, the cough flow rate and number of stripped droplets exhibited a downward trend. The number of droplets produced rapidly dropped to almost 0 at 0.25 s, in contrast to the cough flow that gradually decreased to 0 taking 0.5 s. After the single coughing episode, 11 594 566 droplets were generated (Table IV). The instantaneous position of the droplets during different times during the cough are shown in Fig. 5(b) for time, t = 0.025, 0.04, 0.077, and 0.2 s, where the droplets are colored by diameter. The results indicate an early appearance of droplets in the bifurcation and throat regions (at 0.025 s). At 0.04 s, a dense population of droplets was observed in the bifurcation and oral cavity, which corresponds to the airway curvature of the palate region in line with the flow distribution in the oral cavity. At CPFR at t = 0.077 s, the oral-airway model is filled with a very high density of droplets due to the rapid droplet production [shown in Fig. 5(a)]. At t = 0.2 s, most of the droplets were re-absorbed into the mucus/saliva layers or transported by the coughing flow toward the oral region and released into the external environment via the mouth opening. Hence, fewer droplets are found in the airway compared to the oral cavity. Furthermore, the droplet size was less than 10 μm for the entire coughing episode.

TABLE IV.

Generated, exhaled, and absorbed efficiency of droplets during the coughing event following the droplet size bin.

Droplet size bin (μm) Generated percentage-ηG-s a (%) Exhaled percentage-ηΕ-sa (%) Absorbed percentage-ηA-sa(%)
0.1–0.25  0.078  0.49  0.044 
0.25–0.5  0.133  0.79  0.078 
0.5–0.75  0.149  0.65  0.108 
0.75–1.0  0.181  0.50  0.157 
1.0–2.0  1.94  2.60  1.94 
2.0–4.0  11.81  12.82  11.58 
4.0–8.0  78.01  73.06  78.47 
8.0–16.0  7.53  8.93  7.47 
16.0–24.0  0.15  0.15  0.15 
24.0–32.0  0.019  0.01  0.003 
Total percentage  100  100  100 
Total number count  11 594 566 (NG 938 206 (NE 10 128 559 (NA
Droplet size bin (μm) Generated percentage-ηG-s a (%) Exhaled percentage-ηΕ-sa (%) Absorbed percentage-ηA-sa(%)
0.1–0.25  0.078  0.49  0.044 
0.25–0.5  0.133  0.79  0.078 
0.5–0.75  0.149  0.65  0.108 
0.75–1.0  0.181  0.50  0.157 
1.0–2.0  1.94  2.60  1.94 
2.0–4.0  11.81  12.82  11.58 
4.0–8.0  78.01  73.06  78.47 
8.0–16.0  7.53  8.93  7.47 
16.0–24.0  0.15  0.15  0.15 
24.0–32.0  0.019  0.01  0.003 
Total percentage  100  100  100 
Total number count  11 594 566 (NG 938 206 (NE 10 128 559 (NA
a

The percentage was calculated using Eqs. (15)–(17).

One advantage of this study is that it provides details on the origin of the stripped droplet during the coughing event, illustrated in Fig. 5(c). The oral region was identified as the primary source of droplets (up to 46.8%) during the cough. In the remaining regions, the droplet production levels were similar (approximately 11.9%–14.3%), slightly reducing toward the bifurcation region. The large amount of stripped droplets in the oral cavity is attributed to higher shear stresses (exceeding 5 Pa) than in other regions. Figure 5(d) shows the total surface area (cm2) of each region subjected to shear stress of >5 Pa, where the oral cavity exhibited the highest surface area. Therefore, more droplets were produced from the saliva film in the oral airway region.

The percentage of droplets generated per droplet diameter size bin can be estimated using Eq. (15), as shown in Table IV. Most droplets produced were in the size interval of 4–8 μm (approximately 78.01%), followed by 2–4 and 8–16 μm, respectively. The droplets in the size bin of <1 μm had a low percentage of 0.078%–0.181%, while for the larger size bins (>16 μm), the rate was only 0.169%.

An analysis of the expelled droplet concentration for different droplet diameters was performed and compared with experimental measurements of Yang (2007). In the experimental work, 54 volunteers of varying ages and genders coughed into a sampling bag with a well-controlled relative humidity; thus, the coughed droplets retained their original size. Figure 6(a) shows the number concentration of droplets at the mouth opening plotted against the average droplet size and compared with the study by Yang (2007). The EWF model closely matched the profile with the measured exhaled number concentration. There was a sharp increase in the number concentration for droplet sizes approximately at 2 μm before reaching a peak concentration (approximately 2500/cm3) at 4–8 μm. After the peak, a downward trend was observed, and the cutoff diameter where no droplets were expelled was >10 μm.

FIG. 6.

(a) Validation of total concentration of exhaled droplets after one single cough event, (b) the percentage of exhaled droplets following their site origin, and (c) spatial distribution of exhaled droplets on the mouth opening after a single coughing episode.

FIG. 6.

(a) Validation of total concentration of exhaled droplets after one single cough event, (b) the percentage of exhaled droplets following their site origin, and (c) spatial distribution of exhaled droplets on the mouth opening after a single coughing episode.

Close modal

The source of droplets expelled to the environment is shown in Fig. 6(b), where the oral cavity (including the teeth surface) was responsible for the largest amount of droplets exhaled into the environment (up to 75%). The amount gradually reduced for the geometry moving posteriorly toward the caudal airway; specifically, 12.3% originated from the throat, followed by the larynx (approximately 8.3%), trachea, and bifurcation (approximately 2.2%), respectively.

Most exhaled droplets, 73.1%, were between 4 and 8 μm due to the highest percentage of droplets produced in this range (Table IV). For smaller droplets, the exhalation rates were 12.8% and 8.9% for size bins of 2–4 and 8–16 μm, respectively. Despite the low production rate of droplets in the size bin of <1 μm, the appearance of these small droplets in the exhaled breath was 0.49%–0.79%.

The spatial distribution of the droplets that escaped through the mouth during the coughing is illustrated in Fig. 6(c), where the different droplet colors denote the source location. The results show that the oral cavity is the primary location of the expelled droplets, and the droplets exit through the entire space of the mouth opening. For the other airway regions (throat, larynx, trachea, and bifurcation), the expelled droplets mainly dispersed through the lower half of the mouth opening. There was a small scattering of droplets in the upper half of the mouth opening. Despite the significant variation in the vertical distribution of droplets expelled, the horizontal distribution in the lower half was consistent. This distribution was due to the oral cavity shape and the exhaled jet stream found in the lower half of the mouth opening (shown in Fig. 3).

The total number of droplets absorbed onto the mucus/saliva layers was 10 128 559 (Table IV), accounting for approximately 87.3% of the total droplets produced by the cough. The primary absorption region was the oral cavity (including the teeth surface), with 47.8% [Fig. 7(a)]. In contrast, in the remaining regions, the absorption efficiency significantly decreased by approximately fourfold in the 11.2%–14.1% range. Most of the generated droplets re-absorbed into the oral region's saliva layer can be associated with the complex morphology of this region, which prevented the smooth movement of the droplets.

Figure 7(b) shows the droplet absorption efficiency categorized by the region where the droplets originated from (e.g., slice color indicates the droplet source location). In general, droplets were immediately re-absorbed back into its own region where they were generated. For example, 87.5% of droplets produced in the oral cavity re-absorbed in its region, and that of the throat, larynx, trachea, and bifurcation, the re-absorption rate was 88.2%, 91.9%, 93.1%, and 100%, respectively.

FIG. 7.

(a) Total absorbed efficiency of the generated droplets on the inner surface of the airway region and (b) the absorption efficiency rate for different droplet source locations.

FIG. 7.

(a) Total absorbed efficiency of the generated droplets on the inner surface of the airway region and (b) the absorption efficiency rate for different droplet source locations.

Close modal

The cough-jet stream began from the tracheal bifurcation, and the oral region had the greatest exposure to all droplets originating from lower regions, including the throat (5.3%), larynx (4.2%), trachea (1.8%), and bifurcation (1.3%). This geometry and flow feature explains the lack of absorbed droplets from geometrically lower regions (e.g., upstream flow) than the region itself since the jet flow transports the droplets from the bifurcation to the oral cavity. Droplets with sizes of 4–8 μm (Table IV) were the most re-absorbed due to the greater number of generated droplets in this size bin. For the other size bins, the absorption rate was similar to its generation rate.

Figure 8 shows the deposition pattern on specific airway regions based on where the droplets were produced. Deposition in the oral cavity showed that the focal absorption region occurred in the palate regardless of the droplet origin. Most droplets in the throat tended to accumulate in the upper and branching regions. In the larynx and trachea, there was a high rate of re-absorption from itself. Only the droplets produced by itself were re-absorbed for the bifurcation, and most were observed in the left bifurcation.

FIG. 8.

Visualization of the absorbed droplets in local regions of the oral-tracheal model (column) derived from a specific location (row).

FIG. 8.

Visualization of the absorbed droplets in local regions of the oral-tracheal model (column) derived from a specific location (row).

Close modal

Generally, the cough-jet stream influenced droplet deposition in the oral airway, and the droplet absorption patterns coincided with the high-velocity regions, as discussed in Sec. III A.

The results reveal the critical role of the oral cavity in droplet generation, emission, and absorption. This raises the question of the contribution of the teeth surface to the areas of interest in this study. In this section, the droplet generation, absorption, and exhalation from the oral cavity were divided into the teeth surface and the remaining portion of the oral airway surface [shown in Fig. 9(a)]. The total of 46.8% of droplets that were produced from the oral cavity [from Fig. 5(c)], were found to originate evenly between the teeth surface and the remaining portion (approximately 23%), as exhibited in Fig. 9(b).

FIG. 9.

(a) Outline of the oral cavity, including teeth surface and the remaining regions. (b) Total percentage of generation, exhalation, and absorption of droplets collapsed for the teeth surface and the remaining portion.

FIG. 9.

(a) Outline of the oral cavity, including teeth surface and the remaining regions. (b) Total percentage of generation, exhalation, and absorption of droplets collapsed for the teeth surface and the remaining portion.

Close modal

The instantaneous shear stress at 0.04 and 0.077 s is given in Fig. 10(a). Shear stress >5 Pa was observed on the maxillary incisor surface in the early stage of the coughing event (0.04 s). A high shear rate was found on the inner surface of the maxillary teeth, including the incisors, canines, and molars, at the CPFR (0.077 s). Consequently, many droplets were stripped from the saliva layers along the inner side of the maxillary teeth surface [Fig. 10(b)]. This phenomenon is closely associated with the cough-jet stream, which impacted the upper jaw, as discussed in Sec. III A.

FIG. 10.

(a) Instantaneous wall shear stress distribution on the teeth surface at 0.04 s (left) and 0.077 s (right). (b) Generated location and distribution of droplets on the teeth surface during coughing.

FIG. 10.

(a) Instantaneous wall shear stress distribution on the teeth surface at 0.04 s (left) and 0.077 s (right). (b) Generated location and distribution of droplets on the teeth surface during coughing.

Close modal

For the expelled droplets [Fig. 9(b)], approximately 40% was derived from the teeth's surface. This was attributed to the droplets that formed on the teeth surface, especially on the incisors, which traveled a short distance without any obstacles to the mouth opening. For the re-absorption capacity, the larger surface area of the remaining portion of the oral region caused a larger number of droplets to re-absorb (approximately 27%). In comparison, 21% of droplets re-absorbed onto the teeth surface.

Figure 11 presents both the quantitative analysis and spatial distribution of droplets absorbed on the teeth surface. Primarily, the quantitative analysis serves to delineate the proportion of total absorbed droplets on the teeth surface, which was generated from distinct regions within the model. The findings revealed that out of the total number of droplets absorbed on the teeth surface, 81.02% of absorbed droplets originated from this area. Subsequently, droplets emanating from the oral cavity constituted 14.79% of the total absorbed droplets on the teeth surface. The percentage gradually reduced for the posterior regions and reached 0.45% for the bifurcation, which implies a limited quantity of droplets stemmed from this region absorbed onto the teeth surface. In addition, the spatial distribution of the droplet deposition on the teeth surface indicates that most droplets tended to settle on the inner surface of the maxillary teeth or partially in the mandibular molars and canines, regardless of their origin.

FIG. 11.

3D visualization of deposited droplets on the teeth surface colored by where the droplet was produced.

FIG. 11.

3D visualization of deposited droplets on the teeth surface colored by where the droplet was produced.

Close modal

The coupled EWF-DPM model was applied to explore droplet generation and flow behavior during a single coughing event, where the origin and local number concentration of the generated, absorbed, and expelled droplets were determined. This study first analyzed the coughing flow rate, which provides insight into the droplet generation process during coughing. The rapid development of airflow velocity along the airway and oral cavity subjected the surface walls to high shear stress, which caused the stripping of mucus/saliva layers into droplets. The airstream accelerated through the narrow airway lumen (e.g., trachea, glottis, and throat regions), consistent with a previous study (Kou , 2018). Thus, the predicted fluid flow is recognized as a constant feature of coughing in terms of the velocity distribution but would vary in magnitude depending on the lumen diameter of individual airway structures. In the oral cavity, this study included the teeth geometry, which has been lacking in reported simulation studies of the fluid flow characteristics during coughing. Our results indicate a strong interaction between the cough-jet stream and maxillary teeth surface, which could influence droplet generation and absorption/exhalation.

The shear-induced droplet generation due to the high-speed velocity is one of the four generation mechanisms that mainly occurs in the main bronchus, trachea, and larynx regions (Pöhlker , 2021). The results revealed an essential connection between the shear stress and the number concentration of generated droplets, summarized as follows. The higher the coughing flow rate, the greater the shear stress, and the larger the number of droplets generated. This relationship indicates the uncertainty of the generated droplet number concentration owing to the coughing flow profile, particularly at the CPFR. For instance, the significant diversity between individuals and genders has been recorded for coughing parameters, such as the peak velocity, peak velocity time, and coughing duration by field measurements (Han , 2021). These variations are expected to affect droplet generation. In addition, the fidelity of the numerical domain needs to be considered. Earlier simulation studies used an idealized model that proposed a smooth shear stress distribution on the wall surface (Anzai , 2022). The study by Ren (2022) reported a nonuniform distribution of shear stress on a realistic lower airway wall. The results showed heterogeneities in spatial distribution and magnitude of shear stress compared with ours; consequently, the droplet generation differed. Nevertheless, the coughing flow profile, realistic attributes, and intersubject variability presented challenges, and the simulation results need to be benchmarked against the experimental results.

For infection risk assessment, it is crucial to understand the origins of droplets during expiratory activities within a specific area and to quantify the droplets generated from each source (Morawska, 2006). For coughing, droplet-released sources are well established and consist of the lungs, trachea, nasopharynx-larynx, and nasal and oral passages (Stadnytskyi , 2021; Zhou and Zou, 2021). However, the exact location of droplet generation/exhalation and their localized number concentration remain uncertain. Our droplet generation analysis indicates that the most likely sources of droplets produced during coughing were the oral cavity and teeth surface. Although common respiratory viruses primarily occur in the epithelial cells of the respiratory system (Alexander-Brett and Holtzman, 2015), evidence suggests high viral loads of SARS-CoV-2 in saliva samples from an asymptomatic cohort and the active replication of infected cells in the oral cavity (Huang , 2021). In addition, previous clinical studies have detected SARS-CoV-2 in patient saliva (To , 2020; Wölfel , 2020; and Wyllie , 2020). Thus, from our results, the high infection risk of SARS-CoV-2 may be associated with a high droplet concentration in the oral cavity. Apart from the oral cavity, the deposition site can be determined in the airway system of the potential host (Wang , 2021), but this depends on the aerosols or virus-laden droplet size. Droplets from the deposition regions may cause the re-emission of progeny viruses shed by infected cells (Schaefer and Lai, 2022). Therefore, the possibility of transmission droplets originating from the respiratory system was indicated by our analytical data, where considerable quantities of exhaled droplets were recorded from the throat, larynx, trachea, and bifurcation. The results showed that the generation sites of droplets tended to be in a particular position rather than evenly distributed.

The site of origin affected the potential direction of the droplet cloud during a cough. Our results showed that exhaled droplets from the oral cavity escaped to the surroundings at all locations and angles from the mouth opening; hence, the droplets traveled further and dispersed widely. Meanwhile, exhaled droplets stripped from the respiratory airway exhibited a downward direction as they exited the mouth into the ambient environment. This phenomenon is expected to direct the droplets to the ground outside. Thus, our location-specific results can inform studies on the threat of coughing-related infections in indoor environments.

In addition to identifying the origin site, the local number concentration and size distribution of droplets exhaled during coughing were determined. Based on the literature review, these two parameters were estimated for a varied population and measurement techniques. As summarized in Fig. S5 (supplemental material), the field measurement data were scattered broadly regarding the size distribution and number concentration. In particular, the peak number concentration was recorded in the 4–8 μm range proposed by Yang (2007) and Chao (2009). This peak shifted to 0.75–2 μm in the experiment by Morawska (2009) and Johnson (2011). The highest number concentration was recorded at a much smaller size, at 0.3 μm measured by Lindsley (2012) and Zayas (2012). In addition, the number concentration among the references indicated significant variations. Therefore, our analysis was validated by recruiting one specific experimental data from Yang (2007). Both experimental and simulated data showed that a 4–8 μm droplet size was formed and exhaled at a high number concentration during coughing. Within this size range, the expelled droplets would travel further into the environment and suspend for longer, enhancing the exposure risk of residents in a confined space (Jones and Brosseau, 2015; Dhand and Li, 2020; and Bourouiba, 2021). Nevertheless, the lifetime and size of droplets have a complex relationship with many environmental factors, including temperature, humidity, and ventilation mechanisms (Jayaweera , 2020; Bahramian, 2023). Once inhaled by a susceptible person, fine aerosols (<5 μm) have a high possibility of escaping the defense mechanism of the upper airway and penetrating the lower airway, which is often associated with higher severity, morbidity, and fatality (Zuo , 2020; Sosnowski, 2021). A more significant amount of viral genomes of common respiratory viruses have been revealed in fine aerosols (<5 μm) compared with larger ones (Gralton , 2013; Yan , 2018). Information regarding the site origin and local number concentration was revealed by our analysis, which may not be possible in field measurements with volunteers owing to ethical and technical barriers.

Our simulation data showed that one issue that should be addressed in droplet generation, absorption, and exhalation studies is the inclusion of detailed oral cavity and teeth features. The oral cavity was a significant source of droplet expulsion; however, due to its complex anatomy with the existence of the teeth, the region provided a source for droplet absorption, thereby contributing to the mitigation of droplet emissions from caudal respiratory areas. By eliminating realistic features or simplifying the oral cavity, the high local concentrated absorption regions may shift to the larynx-throat region, according to our data and a previous simulation (Guo , 2020), allowing more droplets to be expelled. Thus, the realistic anatomy of the oral cavity alters the number concentration and spread angle of ejected droplets, thereby changing the dispersion and migration characteristics of the expelled droplets.

Throughout the discussion points, it is noteworthy that the data were obtained upon the assumption of one single cough event. Concerns may arise regarding whether introducing a successive coughing process would impact the results. In this context, the previous experimental research revealed the second cough characteristics with a homogeneous profile but weakened mechanical effectiveness, such as cough peak flow rate and expired volume (Gupta , 2009; Hegland , 2013). This weakening was prolonged until the end of the cough epoch. Upon these conditions, outcome variation can be anticipated as following points:

  • Within the coughing flow patterns, continuous accelerations are expected to occur during each coughing episode, with the highest magnitude in the first cough and a precipitous decline in the subsequent cough events.

  • Regarding the generated droplet number concentration, although a number concentration increase is conceivable, it would not be anticipated to yield a significant deviation from the current results. This expectation is rooted in the observation that the mucous membrane almost diminished after the initial coughing event, as indicated in Fig. 4. Additionally, the WSS exerted on the respiratory wall may fall below the given CSS and be insufficient to trigger the droplet stripping.

  • In terms of droplet behaviors (absorbed or expelled), consecutive acceleration of fluid flow can result in the variation of the absorption rate due to the inertia, subsequently leading to the corresponding alternations in the escaped rate.

Henceforth, subjecting the current research to successive cough simulations while maintaining consistent initial conditions is expected to yield modest variations. Hence, it may be reasoned that the applicability of the results may be regarded as akin to the current findings under the assumption of a single cough process.

Detailed information on the droplet generation, exhalation, and absorption behavior in a realistic oral-tracheal model was elucidated using the coupled EWF-DPM model. The main points of the analysis are summarized as follows:

  • The EWF model reliably predicted the interaction between the free stream and liquid film lining by validating it against measured data. Coupled with the DPM model, the concentration profile of exhaled droplets from the mouth opening after a coughing episode could represent experimental data.

  • The morphometry fidelity of the oral-tracheal model and the coughing flow rate affect the cough-jet stream and are expected to alter droplet generation, transportation/absorption, and exhalation.

  • Shear stress at the liquid film-air interface is a critical factor governing the droplet generation properties. Therefore, appropriate values as the input criteria for the EWF and benchmarking against experimental data are required.

  • The oral and teeth surface were primary locations for droplet generation. While other regions of the respiratory system showed a much lower droplet production rate. The rates gradually decreased toward the posterior regions.

  • Most exhaled droplets were 4–8 μm in diameter. Droplet sizes of <1 μm and >10 μm were also detected but were much fewer upon exhalation through the mouth opening.

  • Including the teeth surface provided a more realistic simulation, directly influencing the droplet number concentration that could be expelled through the mouth opening.

Our simulation can be a foundation for further studies on droplet cloud generation and the transmission of viral genomes in the environment from sneezing, speaking, singing, or phonation activities. It also provides quantitative and qualitative assessments of infection risk based on the site of origin, size distribution, and localized number concentration.

This study focused on a specific oral-tracheal model, which did not cover the individual-related variability. In addition, it is notable that the initial parameters for the EWF model, including critical shear stress, CSS, and diameter coefficient, F, were emphasized by the individual structure and numerical boundary conditions of this study. In addition, a rigid airway model was assumed, which is the opposite of the elastic nature of the respiratory tract and ignores glottis deformation during coughing.

See the supplementary material for details and discussions regarding the optimization processes for the total mesh counts and the initial parameters for the EWF model, such as critical shear stress, CSS, and diameter coefficient, F. In addition, detailed boundary conditions and results, which serve to reinforce the reliability of employing the EWF model to simulate the interaction between the free-stream flow and the lining fluid on the surface, are provided.

This study was partially funded by the Japan Science and Technology (JST), CREST Japan (No. JP 20356547), FOREST program from JST, Japan (No. JPMJFR225R) and JSPS KAKENHI (Nos. JP 22H00237, JP 22K18300, JP 20KK0099, and JP 22K14371), and MEXT as “Program for Promoting Researches on the Supercomputer Fugaku” (No. JPMXP1020210316).

The authors have no conflicts to disclose.

Nguyen Dang Khoa: Data curation (lead); Formal analysis (lead); Methodology (equal); Software (lead); Visualization (lead); Writing – original draft (lead). Kazuki Kuga: Funding acquisition (equal); Methodology (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Kiao Inthavong: Supervision (equal); Validation (equal); Writing – review & editing (lead). Kazuhide Ito: Conceptualization (lead); Funding acquisition (lead); Project administration (lead); Resources (lead); Validation (lead); Writing – review & editing (equal).

The data supporting this study's findings are available from the corresponding author upon reasonable request.

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Supplementary Material