In this study, the transport of virus-laden aerosols in real human airways is investigated through numerical simulations. Three different breathing modes (nasal, oral, and nasal–oral) are studied to analyze the behavior of the particle deposition in the respiratory airways of humans through realistic anatomical models. Increasing the flow rate typically leads to the augmentation of velocity profiles, turbulence, and pressure changes, specifically expanding the high velocity regions in the pharynx, larynx, and trachea. As a result, the deposition fractions of the total number of aerosols deposited in these regions increase, while a decrease in aerosol deposition is observed in the nasal and oral cavities. For the effects of increasing particle sizes, 2–10 μm particles exhibit a higher degree of clustering in the trachea for the nasal mode, in the larynx for the oral mode, and in the trachea for the nasal–oral mode, compared to the clustering of 1–10 μm particles. Considering the high deposition fraction in the upper airway regions, which are the primary factors contributing to the easy transmission of the virus through casual talking and coughing, the results demonstrate that the highest deposition fraction, exceeding 85%, is observed in the nasal mode with small aerosols ranging from 1 to 2 μm in diameter, and at the lowest flow rate of 15 LPM. In the lower airway regions, targeted drug delivery with the highest deposition fraction in the bronchial regions can be a solution for reducing respiratory diseases, such as asthma and chronic obstructive pulmonary disease, which are caused by inflammatory conditions in the bronchi.

Ever since the advent of Coronavirus Disease 2019 (COVID-19) and the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the transmission of diseases has become a major concern in everyone's life. It is well known that most diseases occur through respiratory aerosols (  10 μm) as well as direct (in-person) and indirect (fomite) contacts.1–4 Exhaled airborne aerosols from breathing are one of the main pathways for the spread of viruses, such as SARS-CoV-2.4–9 Given the nosocomial outbreaks and rapid spread of the virus, there is a growing need to investigate aerodynamic mechanisms, such as aerosol dispersion and deposition, as well as the effects of molecular interactions between viruses and humans' breathing system.10–15 

Many experimental observations on dispersed aerosols inside human airways have been performed. Traditionally, the efficiencies of aerosols deposition have been studied using simple tube models of human lungs.16–22 With the development of electro-medical and monitoring equipment, more precise diagnoses of flow quantities and particle disposition in a real human lung are now possible.21–25 For example, Mylavarapu et al.26 used an anatomically accurate human upper airway model constructed from multiple magnetic resonance imaging (MRI) axial scans for investigating flow quantities and pressure changes in human airways. Zeman et al.27 investigated the regional deposition of radio-labeled particles with the higher spatial resolution provided by gamma camera scanning. However, there is still a great challenge in measuring instantaneous flow and particle statistics due to limited access to specific lung regions.28,29

Aerosol dynamics in human airways, as well as flow characteristics in specific regions, have been a main interest for numerical simulations.30–55 Recently, various numerical simulations have been conducted in human airways. Corley et al.56 and Tian et al.57 compared differences in flow quantities in airways between humans and animals. Prinz et al.58 investigated aerosol-laden flows in children's respiratory tracts using the lattice Boltzmann method (LBM). Wedel et al.59 compared particle disposition in human lungs of different age groups. Even though meaningful conclusions have been obtained during these numerical simulations, most studies examine simplified human lung models. Therefore, it is important to consider real human lung models with respiratory process, which contains both inhalation and exhalation.

In this paper, three breathing modes (nasal, oral, and nasal–oral modes) based on a real human respiratory system (lungs and airways) are used to investigate aerosol dynamics under different breathing rates (15, 30, and 60 LPM) and two particle diameter ranges (1–2 and 2–10 μm). The primary focus of this study is to analyze the flow fields and particle deposition in each lung region. Particularly, the most important aspect is to observe the trends in the deposition fraction of the total number of aerosols deposited in the upper airway regions, including the nasal and oral cavities, pharynx, and larynx regions. This paper is organized as follows: Sec. II introduces the methodology for modeling the fluid and particles, including the description of the lung geometry and the boundary conditions. In Sec. III, the trends of flow structures and deposition of virus-laden aerosols are described in specific lung regions based on the two cycles of the complete respiratory process, which includes both inhalation and exhalation. Additionally, the effects of different sizes of the particles are also examined to observe the dispersion of the particles in human airways. Finally, we summarize the notable findings of our study and future work in Sec. IV.

For the simulations in this study, we use the CONVERGE CFD platform ver. 3.0.60 Our simulations are based on the Eulerian–Lagrangian framework, in which the aerosols are tracked as Lagrangian particles, and fluid is computed as an Eulerian field. To interpolate flow information for the Lagrangian particles, we utilize a Taylor series expansion, which reduces the grid effects on the Lagrangian particles. At the computational nodes (i.e., cell centers) for the Eulerian field, we compute and store other flow quantities driven from summed fluxes through cell faces and internal source terms at cell centers. We solve the conservation equations of mass and momentum for an incompressible flow using a collocated finite volume approach. The conservation equations are represented as follows:
ρ u i x i = S ,
(1)
ρ ( u i t + u i u j x j ) = P x i + σ i j x j + ρ g i + S F , i ,
(2)
where ρ is the fluid density, ui (or uj) and gi are the fluid velocity and gravitational force in the ith (or jth) direction, respectively. t is the time, P is the pressure, σij is the viscous stress tensor, and S and SF are source terms incurred by Lagrangian particles. The terms σij, S, and SF can be defined as follows:
σ i j = μ ρ ( u i x j + u j x i ) + ( μ 2 3 μ ) ( ρ u k x k δ i j ) ,
(3)
S = 1 V cell ( q m ̇ q ) = 0 ,
(4)
S F = 1 V cell ( q F q , drag ) ,
(5)
where μ is the fluid viscosity, μ is the dilatational viscosity (which is set to zero42), δij is the Kronecker delta function, Vcell is the cell volume, and m ̇ q and F q , drag are the rate of change in mass and the drag force acting on the qth Lagrangian particle, respectively.

The Lagrangian particles (i.e., aerosols) are assumed to have spherical shapes with diameters in the range of 1–2 and 2–10 μm, which are considered the most significant sizes for airborne transmission of diseases in bio-aerosols.28,61 To better simulate realistic breathing conditions for particles, a Rosin–Rammler diameter distribution is employed for the particle-size distribution (PSD).60,62–64 The particle density ρp is set to 1050 kg/m3 at 310 K, considering water aerosols with human body temperature.65–67 

The equation of motion for the particles can be solved by considering the drag F q , drag and gravity F q , g acting on the qth particle, as follows:
m q d v q d t = F q , drag + F q , g ,
(6)
F q , drag , i = C D A f ρ | U i | 2 U i ,
(7)
F q , g , i = ρ p V p g i ,
(8)
where mq and v q are the mass and velocity of the qth particle and CD is the drag coefficient, respectively. Note that CD is determined by the particle Reynolds number R e r ( = U i d p / ν ), where C D = 0.424 for R e r > 1000 and C D = 24 ( 1 + R e r 2 / 3 / 6 ) / R e r for R e r 1000.59,68 A f ( = π d p 2 / 4) is the cross-sectional area of the particle, Vp is the particle volume, and Ui is the particle–air relative velocity, which is given by
U i = u i v i + u i ,
(9)
where u i and vi are the turbulent fluctuating air velocity and particle velocity in the ith direction. Equation (6) can be rewritten as
d v i d t = 3 4 C D ρ ρ p | U i | d p U i + g i .
(10)
Equation (10) incorporates the simultaneous effects of turbulent fluctuation and particle dispersion. For the turbulence model, the Reynolds-averaged Navier–Stokes (RANS) equation is employed with the RNG (renormalization group) k ε model,69–71 and the O'Rourke turbulent dispersion model is adopted for Lagrangian particles.72 Note that the particles in our simulations are diluted, with a volume fraction smaller than 10 4, as suggested by the literature.73 Therefore, interactions between the particles are ignored.

The geometries considered for real human airways are nasal, oral, and nasal–oral modes. Each case includes a cylinder (inlet), respiratory tract (nose and/or mouth), pharynx, larynx, trachea, bronchi, and alveoli (outlet) as shown in Fig. 1, which displays the geometry of a nasal–oral mode and its enlarged view of right bronchi and alveoli (outlet). Air flows in and out through the cylinder, and virus-laden aerosols are injected at the respiratory tract (nose or/and mouth). At the alveoli, there is an exchange of oxygen and carbon dioxide in the blood due to pressure changes. The complex geometry of bronchi and alveoli can be accounted for using CONVERGE CFD, which provides mesh refinement and unique cut-cell approaches for underlying geometries, such as STL, CAD, and NASTRAN files.

FIG. 1.

The geometry of a nasal–oral model in human lung airways: (a) the total view and (b) enlarged views of right bronchi and alveoli (outlet).

FIG. 1.

The geometry of a nasal–oral model in human lung airways: (a) the total view and (b) enlarged views of right bronchi and alveoli (outlet).

Close modal

Table I presents the geometry information for the nasal, oral, and nasal–oral modes. The lung geometries of each mode are based on multi-slice CT imaging of the head and torso of an adult female.56 The size (i.e., width and height of the entire geometry) of each mode is the same and designed to be similar to that of human lungs, enabling to observe the effects of nasal-only, oral-only, and nasal–oral modes separately. A base grid size of 1 mm is used for the lung model to accurately calculate flow quantities and Lagrangian particles.74–79 Adaptive mesh refinement (AMR) with a two-level embedding is employed in all regions to enhance the accuracy of the solution.75 A minimum sub-grid scale velocity (above which AMR will be triggered) of 0.001 m/s (i.e., a very low value) was used to ensure that AMR would be triggered with complete certainty in these regions, if it was necessary. These regions require higher resolution than other parts due to their complex geometry. Based on the uniform base grid size of 1 mm, the total number of initial cells was 1.5 × 106 for the nasal mode, 770 000 for the oral mode, and 1.6 × 106 for the nasal–oral mode. With AMR activated, it is found that the number of cells increases to more than twice the initial amount (exceeding over 2 × 106 cells in the nasal and nasal–oral cases, and over 1.5 × 106 cells in the oral case) before even 0.2 s of simulation time was reached. Hence, AMR proved to be a vital tool in improving the numerical accuracy of the simulations by refining and increasing the number of cells at important regions. These numbers of cells (post AMR refinement) were concluded to be sufficient for numerical accuracy, as even fewer than 1 × 106 cells can still be expected to achieve good numerical accuracy and results for a whole lung model without AMR.56,80 It is assumed that 25 000 particles per opening are injected, specifically two openings in the nose and one opening in the mouth, which is a similar rate used in the literature.81,82 Particles are injected over an inhalation cycle of 2 s per breathing cycle. It is also known that increasing the number of particles to 50 000 by a factor of 2 results in less than a 2% difference in the total and regional deposition results.30 Each CFD simulation was run on a single high performance computing (HPC) node containing 128 AMD third-Gen EPYC Milan processors with 512 GB of RAM. The computational time of running a single simulation case varied between 3 and 4 days (72 to 96 h).

TABLE I.

The geometry information of nasal, oral, and nasal–oral modes.

Object Nasal Oral Nasal–oral
Number of grid cells  2 × 106  1 × 106  2 × 106 
Width (m × m)  0.306 × 0.347  0.306 × 0.347  0.306 × 0.347 
Height (m)  0.625  0.625  0.625 
Breathing method  Nose only  Mouth only  Nose and mouth 
Number of injected particles ( # / s 50 000  25 000  75 000 
Object Nasal Oral Nasal–oral
Number of grid cells  2 × 106  1 × 106  2 × 106 
Width (m × m)  0.306 × 0.347  0.306 × 0.347  0.306 × 0.347 
Height (m)  0.625  0.625  0.625 
Breathing method  Nose only  Mouth only  Nose and mouth 
Number of injected particles ( # / s 50 000  25 000  75 000 

Figure 2 shows a comparison of the differences among each human airway in a right-side view. The nasal mode comprises only the nasal cavity through which virus-laden aerosols (blue particles) pass. The oral mode, on the other hand, has only the oral cavity for breathing through the mouth, meaning that particles can only enter through the mouth. The nasal–oral mode includes both the nasal and oral cavities, allowing particles to pass through both the nose and mouth.

FIG. 2.

The right side views of each lung model with virus-laden aerosols (blue particles): (a) nasal, (b) oral, and (c) nasal–oral models.

FIG. 2.

The right side views of each lung model with virus-laden aerosols (blue particles): (a) nasal, (b) oral, and (c) nasal–oral models.

Close modal

Table II shows the boundary conditions for the inlet, outlet, and walls. At the inlet, where the air passes through the cylinder head, constant mass flow rates are applied while maintaining zero gauge pressure. At the outlets (i.e., the alveoli), a zero normal gradient condition is applied for velocity, and different pressure conditions are employed during breathing. Specifically, the pressure at alveoli is 1 cmH2O lower than the zero gauge pressure for inhalation and 1 cmH2O higher than the zero gauge pressure for exhalation.83 The temperature is specified to have a uniform value of 310 K throughout the human lung.65–67 A no-slip boundary condition is applied to all surfaces except the outlets, which allows particles to attach to the walls in the lung.

TABLE II.

Boundary conditions for the inlet, outlet, and walls.

B.C. Inlet Outlet Surface (wall)
Pressure (atm)  1 ± 1 cmH2 ⋯ 
Velocity (LPM)  Mass flows  Zero normal gradient  No-slip 
Temperature (K)  310  310  310 
B.C. Inlet Outlet Surface (wall)
Pressure (atm)  1 ± 1 cmH2 ⋯ 
Velocity (LPM)  Mass flows  Zero normal gradient  No-slip 
Temperature (K)  310  310  310 

This section discusses flows and particle deposition under different geometries, breathing rates, and particle diameters. Table III lists the various breathing rates used in the simulations, which are slow (15 LPM), moderate (30 LPM), and fast (60 LPM).33,35,36,59,80,84–86 Two particle size ranges, 1–2 μm and 2–10 μm, based on a Rosin–Rammler diameter distribution particle-size distribution (PSD),60,62–64 are used separately for each mode and breathing rate.36,59,80 Different injection rates of particles per second are applied for each lung mode: 50 000 particles/s for the nasal mode, 25 000 particles/s for the oral mode, and 75 000 particles/s for the nasal–oral mode. The simulations cover a total time of 8 s (two cycles of 4 s each), which includes 2 s for inhaling and 2 s for exhaling per cycle,30,36 and are continuously simulated over time. A time step of dt = 10−5 s is employed for each lung mode, which is finer than many of the similar studies in the literature.26,30,31,38,85 In this section, flow quantities and particle (aerosol) deposition are analyzed separately for each mode.

TABLE III.

Initial conditions of different breathing rates.

Breathing rate Slow Moderate Fast
Volume flow rate (l/min)  15 LPM  30 LPM  60 LPM 
Mass flow rate (m3/s)  0.00285  0.00570  0.01140 
Particle size (μm)  1–2, 2–10  1–2, 2–10  1–2, 2–10 
Inhaling timestamps (s)  0–2, 4–6  0–2, 4–6  0–2, 4–6 
Exhaling timestamps (s)  2–4, 6–8  2–4, 6–8  2–4, 6–8 
Breathing rate Slow Moderate Fast
Volume flow rate (l/min)  15 LPM  30 LPM  60 LPM 
Mass flow rate (m3/s)  0.00285  0.00570  0.01140 
Particle size (μm)  1–2, 2–10  1–2, 2–10  1–2, 2–10 
Inhaling timestamps (s)  0–2, 4–6  0–2, 4–6  0–2, 4–6 
Exhaling timestamps (s)  2–4, 6–8  2–4, 6–8  2–4, 6–8 

Breathing conditions in our study depend on the rates of mass flows and pressure changes. During inhalation, mass flows are injected at the cylinder head (inlet) at atmospheric pressure (1 atm). At the alveoli (outlet), pressure is maintained 1 cmH2O lower than the atmospheric pressure to enable air to flow from the respiratory tract to the outlet. During exhalation, the mass flow at the cylinder head (inlet) is extracted based on the breathing rate, and the pressure is kept at atmospheric pressure (1 atm). At the alveoli (outlet), the pressure is maintained 1 cmH2O higher than atmospheric pressure, allowing air to flow from the alveoli to the lung branches. In this section, the effects of different flow rates (15, 30, and 60 LPM) on the velocity magnitude and turbulent kinetic energy (TKE) are investigated in each lung mode. High velocity regions (exceeding 10 m/s) are predominantly formed in the pharynx, larynx, and trachea regions, ultimately resulting in increased deposition fractions of aerosols in these areas. Additionally, an increase in the flow rate leads to decreased deposition fractions in the nasal and oral cavities across all modes, subsequently resulting in increased deposition fractions in other regions.

1. Nasal mode

Figure 3 depicts 2D instantaneous contours of velocity magnitude and turbulent kinetic energy (TKE) for the nasal mode at different breathing rates (30 and 60 LPM) at t = 1 s (inhalation) and 3 s (exhalation). It is evident that the velocity magnitude increases in the pharynx, larynx, and bottom trachea regions as the airways become narrower, and this effect becomes more pronounced with increasing breathing rates. Velocity profiles exceeding 10 m/s are observed in the pharynx and larynx regions. Investigating TKE is crucial because turbulence plays a significant role in determining the deposition of particles in the respiratory system. Turbulent flows can cause particles to collide with and deposit on the walls of the airways, thereby affecting their distribution and potential health effects. In Fig. 3, an increase in the breathing rate results in the occurrence of high TKE around the pharynx, larynx, and sometimes bottom trachea. This trend is similar to that observed in the velocity contours, but it is more localized.

FIG. 3.

2D slice view of velocity magnitude | u | (m/s) and turbulent kinetic energy (TKE) k (m2/s2) of the nasal mode with different breathing rate at t = 1 s (inhalation) and 3 s (exhalation). | u |, inhalation (a) 30 LPM, (b) 60 LPM, exhalation, (c) 30 LPM, (d) 60 LPM; k inhalation, (e) 30 LPM, (f) 60 LPM, exhalation, (g) 30 LPM, and (h) 60 LPM.

FIG. 3.

2D slice view of velocity magnitude | u | (m/s) and turbulent kinetic energy (TKE) k (m2/s2) of the nasal mode with different breathing rate at t = 1 s (inhalation) and 3 s (exhalation). | u |, inhalation (a) 30 LPM, (b) 60 LPM, exhalation, (c) 30 LPM, (d) 60 LPM; k inhalation, (e) 30 LPM, (f) 60 LPM, exhalation, (g) 30 LPM, and (h) 60 LPM.

Close modal

A more detailed analysis of the velocity field and TKE is conducted for the nasal mode, with a focus on the pharynx, larynx, and bottom trachea regions, which have higher velocity and TKE levels. Figure 4 represents contours of velocity magnitude for the nasal mode and four cross-sectional areas where the higher velocity and TKE appear (in pharynx, larynx, bottom trachea, and bronchi, respectively). In the cross-sectional areas, the velocity vectors and streamlines reveal the presence of secondary flows, which are relatively weaker flow patterns superimposed on the stronger primary flows. These secondary flows exhibit different patterns during inhalation and exhalation. In Fig. 4(b), vortex structures can be observed at slice B due to the separation of the flows after passing through the narrow regions in the larynx, as shown in Fig. 3. Furthermore, this trend becomes more pronounced with a decrease in the flow rate, which is associated with a narrowing of high velocity magnitude regions. Figure 5 illustrates the specific velocity and TKE along the lines from each slice presented in Fig. 4(b), demonstrating the proportionality between the velocity profile and flow rates. The velocity profiles exhibit similar asymptotic shapes regardless of changes in the flow rate. However, there is a clear distinction in the shapes of velocity profiles between inhalation and exhalation stages, caused by the different topology of the preceding regions. The exception to this distinction is observed in slice DD′ due to the very similar preceding topology of the bronchus. In the TKE graphs from Figs. 5(e)–5(h), the TKE values also exhibit the consistent asymptotic profiles regardless of flow rates.

FIG. 4.

The overall and local velocity contours of the nasal mode, along with streamlines at four cross-sectional areas, are shown at t = 1 and 3 s for different flow rates: (a) contours of velocity magnitude at 60 LPM; local velocities at (b) t = 1 s (inhalation) and (c) t = 3 s (exhalation).

FIG. 4.

The overall and local velocity contours of the nasal mode, along with streamlines at four cross-sectional areas, are shown at t = 1 and 3 s for different flow rates: (a) contours of velocity magnitude at 60 LPM; local velocities at (b) t = 1 s (inhalation) and (c) t = 3 s (exhalation).

Close modal
FIG. 5.

The local velocity and TKE profiles of the nasal mode for each line along slices in Fig. 4. At t = 1 s (inhalation) for 15 LPM (black, solid), 30 LPM (red, solid), and 60 LPM (blue, solid). At t = 3 s (exhalation) for 15 LPM (black, dashed), 30 LPM (red, dashed), and 60 LPM (blue, dashed). Velocity profiles are shown for (a) AA′, (b) BB′, (c) CC′, and (d) DD′; and TKE profiles (log scales) are depicted on (e) AA′, (f) BB′, (g) CC′, and (h) DD′.

FIG. 5.

The local velocity and TKE profiles of the nasal mode for each line along slices in Fig. 4. At t = 1 s (inhalation) for 15 LPM (black, solid), 30 LPM (red, solid), and 60 LPM (blue, solid). At t = 3 s (exhalation) for 15 LPM (black, dashed), 30 LPM (red, dashed), and 60 LPM (blue, dashed). Velocity profiles are shown for (a) AA′, (b) BB′, (c) CC′, and (d) DD′; and TKE profiles (log scales) are depicted on (e) AA′, (f) BB′, (g) CC′, and (h) DD′.

Close modal

2. Oral mode

Figure 6 illustrates contours of 2D instantaneous velocity and TKE for the oral mode at different breathing rates (30 and 60 LPM) at t = 1 s (inhalation) and 3 s (exhalation). With increasing flow rate, high-velocity regions exceeding 10 m/s are observed in the pharynx and larynx regions during inhalation, and the bottom trachea region additionally shows a high velocity region during exhalation. At 60 LPM during exhalation in Fig. 6(d), a wide range of high velocities is observed, which is attributed to the small area between the oral cavity and pharynx. During inhalation, the oral cavity and larynx regions present increasing TKE as flow rates increase. The high TKE regions during exhalation are observed in the narrow high velocity flow regions of the pharynx, larynx, and bottom trachea walls.

FIG. 6.

2D slice view of velocity | u | (m/s) and turbulent kinetic energy (TKE) k ( m 2 / s 2) of the oral mode with different breathing rate at t = 1 s (inhalation) and 3 s (exhalation). | u |, inhalation (a) 30 LPM, (b) 60 LPM, exhalation, (c) 30 LPM, (d) 60 LPM; k inhalation, (e) 30 LPM, (f) 60 LPM, exhalation, (g) 30 LPM, and (h) 60 LPM.

FIG. 6.

2D slice view of velocity | u | (m/s) and turbulent kinetic energy (TKE) k ( m 2 / s 2) of the oral mode with different breathing rate at t = 1 s (inhalation) and 3 s (exhalation). | u |, inhalation (a) 30 LPM, (b) 60 LPM, exhalation, (c) 30 LPM, (d) 60 LPM; k inhalation, (e) 30 LPM, (f) 60 LPM, exhalation, (g) 30 LPM, and (h) 60 LPM.

Close modal

Figure 7 displays the velocity contours and cross sections for the oral mode. Due to the high velocity profile in Fig. 6, separation of flows is hardly observed at slice B. Nevertheless, different shapes of velocity and TKE can still be observed between inhalation and exhalation in Fig. 8, except in slice D. It should be noted that the velocity magnitude during exhalation is consistently higher than that during inhalation at the same flow rate, which is comparable to the nasal mode.

FIG. 7.

The overall and local velocity contours of the oral mode, along with streamlines at four cross-sectional areas, are shown at t = 1 and 3 s for different flow rates: (a) contours of velocity magnitude at 60 LPM; local velocities at (b) t = 1 s (inhalation) and (c) t = 3 s (exhalation).

FIG. 7.

The overall and local velocity contours of the oral mode, along with streamlines at four cross-sectional areas, are shown at t = 1 and 3 s for different flow rates: (a) contours of velocity magnitude at 60 LPM; local velocities at (b) t = 1 s (inhalation) and (c) t = 3 s (exhalation).

Close modal
FIG. 8.

The local velocity and TKE profiles of the oral mode for each line along slices in Fig. 7. At t = 1 s (inhalation) for 15 LPM (black, solid), 30 LPM (red, solid), and 60 LPM (blue, solid). At t = 3 s (exhalation) for 15 LPM (black, dashed), 30 LPM (red, dashed), and 60 LPM (blue, dashed). Velocity profiles are shown for (a) AA′, (b) BB′, (c) CC′, (d) DD′, and TKE profiles (log scales) are depicted on (e) AA′, (f) BB′, (g) CC′, and (h) DD′.

FIG. 8.

The local velocity and TKE profiles of the oral mode for each line along slices in Fig. 7. At t = 1 s (inhalation) for 15 LPM (black, solid), 30 LPM (red, solid), and 60 LPM (blue, solid). At t = 3 s (exhalation) for 15 LPM (black, dashed), 30 LPM (red, dashed), and 60 LPM (blue, dashed). Velocity profiles are shown for (a) AA′, (b) BB′, (c) CC′, (d) DD′, and TKE profiles (log scales) are depicted on (e) AA′, (f) BB′, (g) CC′, and (h) DD′.

Close modal

3. Nasal–Oral mode

Figure 9 shows 2D contours for the instantaneous velocity and TKE for the nasal–oral mode, representing real human lung airways, at different breathing rates (30 LPM and 60 LPM) at t = 1 s (inhalation) and 3 s (exhalation). The main difference in the velocity contour, compared to the nasal and oral modes, is the presence of a high velocity region exceeding 10 m/s exclusively in the larynx. This is attributed to the integration of air flows from both cavities, which leads to a slower velocity in the pharynx region. The trend of TKE in the larynx region in the nasal–oral mode shows a higher region exceeding 5 m2/s2 in the larynx, similar to that observed in the nasal mode, primarily due to the similar magnitude of velocity in this region.

FIG. 9.

2D slice view of velocity | u | (m/s) and turbulent kinetic energy (TKE) k (m2/s2) of the nasal–oral mode with different breathing rate at t = 1 s (inhalation) and 3 s (exhalation). | u |, inhalation (a) 30 LPM, (b) 60 LPM, exhalation, (c) 30 LPM, (d) 60 LPM; k inhalation, (e) 30 LPM, (f) 60 LPM, exhalation, (g) 30 LPM, and (h) 60 LPM.

FIG. 9.

2D slice view of velocity | u | (m/s) and turbulent kinetic energy (TKE) k (m2/s2) of the nasal–oral mode with different breathing rate at t = 1 s (inhalation) and 3 s (exhalation). | u |, inhalation (a) 30 LPM, (b) 60 LPM, exhalation, (c) 30 LPM, (d) 60 LPM; k inhalation, (e) 30 LPM, (f) 60 LPM, exhalation, (g) 30 LPM, and (h) 60 LPM.

Close modal

Figure 10 presents the velocity contours and cross-sectional areas of the nasal–oral mode. Due to the similarity in velocity magnitude in the nasal mode, the velocity magnitude and TKE at slices AA′, BB′, and CC′ in the nasal–oral mode exhibit a comparable trend to those in the nasal mode. This similarity can be quantitatively demonstrated by examining the local velocities and TKE along the cross-sectional areas shown in Fig. 11. The increase in the velocity magnitude in the nasal–oral mode from point A is lower than that in the nasal mode.

FIG. 10.

The overall and local velocity contours of the nasal–oral mode, along with streamlines at four cross-sectional areas, are shown at t = 1 and 3 s for different flow rates: (a) 3D contour for a velocity magnitude at 60 LPM; local velocities at (b) t = 1 s (inhalation) and (c) t = 3 s (exhalation).

FIG. 10.

The overall and local velocity contours of the nasal–oral mode, along with streamlines at four cross-sectional areas, are shown at t = 1 and 3 s for different flow rates: (a) 3D contour for a velocity magnitude at 60 LPM; local velocities at (b) t = 1 s (inhalation) and (c) t = 3 s (exhalation).

Close modal
FIG. 11.

The local velocity and TKE profiles of the nasal–oral mode for each line along slices in Fig. 10. At t = 1 s (inhalation) for 15 LPM (black, solid), 30 LPM (red, solid), and 60 LPM (blue, solid). At t = 3 s (exhalation) for 15 LPM (black, dashed), 30 LPM (red, dashed), and 60 LPM (blue, dashed). Velocity profiles are shown for (a) AA′, (b) BB′, (c) CC′, (d) DD′, and TKE profiles (log scales) are depicted on (e) AA′, (f) BB′, (g) CC′, and (h) DD′.

FIG. 11.

The local velocity and TKE profiles of the nasal–oral mode for each line along slices in Fig. 10. At t = 1 s (inhalation) for 15 LPM (black, solid), 30 LPM (red, solid), and 60 LPM (blue, solid). At t = 3 s (exhalation) for 15 LPM (black, dashed), 30 LPM (red, dashed), and 60 LPM (blue, dashed). Velocity profiles are shown for (a) AA′, (b) BB′, (c) CC′, (d) DD′, and TKE profiles (log scales) are depicted on (e) AA′, (f) BB′, (g) CC′, and (h) DD′.

Close modal

4. Effects of pressure on each mode

The pressure difference at various locations is of significant importance in the human respiratory system. Figure 12 illustrates the pressure change from the outlet to the cross-sectional areas for each mode. In the nasal and nasal–oral modes in Figs. 12(a) and 12(c), an increase in pressure is observed during inhalation, while a pressure drop is shown during exhalation. As the flow rate increases, the magnitudes of pressure changes become larger in the same areas. The pressure changes increase from slice D to A, and this trend is more pronounced at higher flow rates. In Fig. 12(b), the oral mode also shows an increase in the pressure change from slice D to A during inhalation. However, during exhalation, very large pressure increases are observed at all slices. The pressure changes become larger as the flow moves toward the upper side of the airways. Additionally, the pressure change at 30 LPM is higher than that at 60 LPM. This is due to the wider high-velocity regions observed at 60 LPM, which result in a lower decrease in velocity. As a result, the increase in pressure change is relatively low compared to that at 30 LPM, similar to a previous study.80 

FIG. 12.

Pressure change from outlet to the cross-sectional areas in the (a) nasal, (b) oral, and (c) nasal–oral mode. In the oral mode, a different scale is used during exhalation due to a significant increase in the pressure change.

FIG. 12.

Pressure change from outlet to the cross-sectional areas in the (a) nasal, (b) oral, and (c) nasal–oral mode. In the oral mode, a different scale is used during exhalation due to a significant increase in the pressure change.

Close modal

High shear stress plays an important role in vasodilation and anti-coagulation. It promotes endothelial cell survival and quiescence, alignment in the direction of flow, and secretion of substances.87,88 Figure 13 shows the maximum shear stress of the cross-sectional areas using a logarithmic scale. It is evident that the wall shear stress at the same slice increases for all modes with an increase in the flow rate. However, at the same flow rate, the wall shear stress does not have a proportional relationship among slices due to variations in the velocity profile across different cross-sectional areas. Moreover, it also varies at the same slice during inhalation and exhalation.

FIG. 13.

Maximum wall shear stress for the cross-sectional areas in the (a) nasal, (b) oral, and (c) nasal–oral mode.

FIG. 13.

Maximum wall shear stress for the cross-sectional areas in the (a) nasal, (b) oral, and (c) nasal–oral mode.

Close modal

The analysis of regional particle deposition is highly desirable for the study of pulmonary illnesses, drug delivery in the lung airways, and respiratory patterns.89,90 As virions and aerosols tend to bind together, the deposition of virus-laden aerosols during breathing processes should be investigated for assessing its consequences in human airways and optimizing drug delivery using pharmaceutical aerosols.90–93 The deposition of two particle size ranges, dp = 1–2 and 2–10 μm for transmission of bio-aerosols, is investigated under different breathing rates in the three breathing modes in this section. Figure 14 illustrates the cumulative particle deposition in each lung mode at different time sets. In the figure, dp = 1–2 μm and a breathing rate of 30 LPM are used with extended snapshots of some cavity, larynx, and bronchi regions. Note that the cylinder part is excluded in the cavity snapshots for a better visualization, but the particles in the cylinder are included in the figures. It is evident that the number of particles increases in the regions over time and exhibits varying deposition fractions of the total number of aerosols deposited in lung airways for each mode. To further investigate the effects of flow rates and aerosol sizes on particle deposition, the three breathing modes (i.e., nasal, oral, and nasal-oral modes) are divided into Secs. III B 1–III B 3.

FIG. 14.

Cumulative particle distributions (1–2 μm, 30 LPM) along human airways during inhalation (t = 1 s) and exhalation (t = 3 s): (a) nasal mode, inhalation, (b) nasal mode, exhalation, (c) oral mode, inhalation, (d) oral mode, exhalation, (e) nasal–oral mode, inhalation, and (f) nasal–oral mode, exhalation.

FIG. 14.

Cumulative particle distributions (1–2 μm, 30 LPM) along human airways during inhalation (t = 1 s) and exhalation (t = 3 s): (a) nasal mode, inhalation, (b) nasal mode, exhalation, (c) oral mode, inhalation, (d) oral mode, exhalation, (e) nasal–oral mode, inhalation, and (f) nasal–oral mode, exhalation.

Close modal

1. Nasal mode

Figure 15 depicts the deposition fraction of 1–2 μm aerosols under different breathing rates in the nasal mode. To consider more realistic conditions in observing aerosol deposition, two breathing cycles, ranging from 0 to 4 s and 4 to 8 s, are employed. Note that four time intervals are chosen in the middle of inhalation and exhalation to observe the effects of flow rates and aerosol sizes on particle deposition. The majority of particles are observed in the nasal cavity, which accounts for over 70% of the injected particles. As the flow rate increases, the deposition fraction in the nasal cavity decreases at the same time frames, while the fractions in the other regions increase. Figure 16 illustrates the deposition fraction of 2–10 μm particles in the nasal mode. A very similar trend in deposition is observed when comparing it to that of 1–2 μm aerosols, except for the pharynx region, which instead decreases with increasing flow rate.

FIG. 15.

The deposition of aerosol particles (dp = 1–2 μm) in the nasal mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

FIG. 15.

The deposition of aerosol particles (dp = 1–2 μm) in the nasal mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

Close modal
FIG. 16.

The deposition of aerosol particles (dp = 2–10 μm) in the nasal mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

FIG. 16.

The deposition of aerosol particles (dp = 2–10 μm) in the nasal mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

Close modal

Tables IV and V list the deposition fractions in the nasal mode for two breathing cycles, comparing the results of two particle sizes and their differences. In the first breathing cycle of Table IV at t = 1 s (inhalation), the difference in deposition fractions of 2–10 μm particles in the nasal cavity and pharynx decreases sharply compared to those of 1–2 μm aerosols as the flow rate increases, resulting in a difference of −9.7% and −6.5% of total aerosols within the lungs, respectively, at 60 LPM. In contrast, the difference in deposition fractions of 2–10 μm particles in the larynx and trachea shows a gradual increase compared to those of 1–2 μm aerosols in the same regions. During exhalation at t = 3 s, the trend in the difference is actually the same as that during inhalation. In the second breathing cycle of Table V, the difference in deposition fractions exhibits the same trend for both inhalation and exhalation, similar to the first cycle. Consequently, the cumulative behaviors of particle deposition in each regions are mostly determined by the first breathing cycle.

TABLE IV.

The deposition fractions of 1–2 and 2–10 μm particles in the nasal mode at the first breathing cycle.

15 LPM 30 LPM 60 LPM
t = 1 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Nasal cavity  82.6%  83.1%  +0.5%  76.6%  73.6%  −3.0%  72.5%  62.8%  −9.7% 
Pharynx  8.7%  6.9%  −1.8%  11.0%  7.1%  −3.9%  13.2%  6.7%  −6.5% 
Larynx  3.3%  3.3%  0%  4.5%  5.9%  +1.4%  5.0%  12.4%  +7.4% 
Trachea  4.2%  5.3%  +1.3%  4.6%  8.4%  +3.8%  4.9%  11.5%  +6.6% 
Right bronchi  0.1%  0.1%  0%  0.5%  0.6%  +0.1%  0.7%  0.8%  +0.1% 
Left bronchi  0.8%  1.0%  +0.2%  2.5%  3.9%  +1.4%  3.3%  5.2%  +1.9% 
t = 3 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Nasal cavity  74.9%  75.4%  +0.5%  72.5%  69.4%  −3.1%  70.4%  60.0%  −10.4% 
Pharynx  10.2%  7.9%  −2.3%  11.8%  7.2%  −4.6%  13.8%  6.7%  −7.1% 
Larynx  4.4%  4.4%  0%  5.3%  7.0%  +1.7%  5.6%  13.8%  +8.2% 
Trachea  3.2%  4.4%  +1.2%  4.2%  7.8%  +3.6%  4.5%  11.3%  +6.8% 
Right bronchi  0.4%  0.4%  0%  0.7%  0.8%  +0.1%  0.9%  0.9%  +0% 
Left bronchi  2.2%  2.8%  +0.6%  3.3%  5.1%  +1.8%  3.8%  5.7%  +1.9% 
15 LPM 30 LPM 60 LPM
t = 1 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Nasal cavity  82.6%  83.1%  +0.5%  76.6%  73.6%  −3.0%  72.5%  62.8%  −9.7% 
Pharynx  8.7%  6.9%  −1.8%  11.0%  7.1%  −3.9%  13.2%  6.7%  −6.5% 
Larynx  3.3%  3.3%  0%  4.5%  5.9%  +1.4%  5.0%  12.4%  +7.4% 
Trachea  4.2%  5.3%  +1.3%  4.6%  8.4%  +3.8%  4.9%  11.5%  +6.6% 
Right bronchi  0.1%  0.1%  0%  0.5%  0.6%  +0.1%  0.7%  0.8%  +0.1% 
Left bronchi  0.8%  1.0%  +0.2%  2.5%  3.9%  +1.4%  3.3%  5.2%  +1.9% 
t = 3 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Nasal cavity  74.9%  75.4%  +0.5%  72.5%  69.4%  −3.1%  70.4%  60.0%  −10.4% 
Pharynx  10.2%  7.9%  −2.3%  11.8%  7.2%  −4.6%  13.8%  6.7%  −7.1% 
Larynx  4.4%  4.4%  0%  5.3%  7.0%  +1.7%  5.6%  13.8%  +8.2% 
Trachea  3.2%  4.4%  +1.2%  4.2%  7.8%  +3.6%  4.5%  11.3%  +6.8% 
Right bronchi  0.4%  0.4%  0%  0.7%  0.8%  +0.1%  0.9%  0.9%  +0% 
Left bronchi  2.2%  2.8%  +0.6%  3.3%  5.1%  +1.8%  3.8%  5.7%  +1.9% 
TABLE V.

The deposition fractions of 1–2 and 2–10 μm particles in the nasal mode at the second breathing cycle.

15 LPM 30 LPM 60 LPM
t= 5 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Nasal cavity  77.5%  77.8%  +0.3%  74.1%  71.1%  −3.0%  71.3%  60.9%  −10.4% 
Pharynx  10.2%  8.1%  −2.1%  11.6%  7.2%  −4.4%  13.6%  6.8%  −6.8% 
Larynx  4.3%  4.3%  0%  5.2%  6.7%  +1.5%  5.5%  13.5%  +8.0% 
Trachea  3.9%  5.2%  +1.3%  4.5%  8.2%  +3.7%  4.5%  11.5%  +7.0% 
Right bronchi  0.4%  0.4%  0%  0.7%  0.8%  +0.1%  0.8%  0.9%  +0.1% 
Left bronchi  1.9%  2.3%  +0.4%  3.1%  4.9%  +1.8%  3.6%  5.6%  +2.0% 
t= 7 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Nasal cavity  74.3%  74.6%  +0.3%  72.3%  69.2%  −3.1%  70.2%  59.6%  −10.6% 
Pharynx  10.9%  8.7%  −2.2%  12.1%  7.5%  −4.6%  14.0%  6.8%  −7.2% 
Larynx  4.8%  4.7%  −0.1%  5.5%  7.1%  +1.6%  5.7%  14.0%  +8.3% 
Trachea  3.6%  4.9%  +1.3%  4.3%  8.2%  +3.9%  4.6%  11.5%  +6.9% 
Right bronchi  0.5%  0.5%  0%  0.8%  0.8%  0%  0.9%  1.0%  +0.1% 
Left bronchi  2.5%  3.1%  +0.6%  3.4%  5.1%  +1.7%  3.8%  5.9%  +2.1% 
15 LPM 30 LPM 60 LPM
t= 5 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Nasal cavity  77.5%  77.8%  +0.3%  74.1%  71.1%  −3.0%  71.3%  60.9%  −10.4% 
Pharynx  10.2%  8.1%  −2.1%  11.6%  7.2%  −4.4%  13.6%  6.8%  −6.8% 
Larynx  4.3%  4.3%  0%  5.2%  6.7%  +1.5%  5.5%  13.5%  +8.0% 
Trachea  3.9%  5.2%  +1.3%  4.5%  8.2%  +3.7%  4.5%  11.5%  +7.0% 
Right bronchi  0.4%  0.4%  0%  0.7%  0.8%  +0.1%  0.8%  0.9%  +0.1% 
Left bronchi  1.9%  2.3%  +0.4%  3.1%  4.9%  +1.8%  3.6%  5.6%  +2.0% 
t= 7 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Nasal cavity  74.3%  74.6%  +0.3%  72.3%  69.2%  −3.1%  70.2%  59.6%  −10.6% 
Pharynx  10.9%  8.7%  −2.2%  12.1%  7.5%  −4.6%  14.0%  6.8%  −7.2% 
Larynx  4.8%  4.7%  −0.1%  5.5%  7.1%  +1.6%  5.7%  14.0%  +8.3% 
Trachea  3.6%  4.9%  +1.3%  4.3%  8.2%  +3.9%  4.6%  11.5%  +6.9% 
Right bronchi  0.5%  0.5%  0%  0.8%  0.8%  0%  0.9%  1.0%  +0.1% 
Left bronchi  2.5%  3.1%  +0.6%  3.4%  5.1%  +1.7%  3.8%  5.9%  +2.1% 

2. Oral mode

Figure 17 illustrates the deposition fractions of 1–2 μm aerosols in the oral mode. It is clear that the majority of particles are deposited in the oral cavity, pharynx, and trachea regions. With an increase in the flow rate, the deposition in the oral cavity and pharynx gradually decreases, while the other regions show increased deposition. Figure 18 shows the aerosol deposition for a particle size of 2–10 μm, which demonstrates a similar trend to that of 1–2 μm aerosols, except for fluctuations in deposition observed in the pharynx region as the flow rate increases.

FIG. 17.

The deposition of aerosol particles (dp = 1–2 μm) in the oral mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

FIG. 17.

The deposition of aerosol particles (dp = 1–2 μm) in the oral mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

Close modal
FIG. 18.

The deposition of aerosol particles (dp = 2–10 μm) in the oral mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

FIG. 18.

The deposition of aerosol particles (dp = 2–10 μm) in the oral mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

Close modal

Tables VI and VII list comparison of the deposition fractions of different aerosol diameters during two breathing cycles. The difference in deposition fractions between 2 and 10 μm and 1–2 μm in the oral cavity significantly decreases with increasing flow rate. In contrast, the difference in decomposition fractions in the pharynx and larynx regions increases. Note that the overall trend of the difference for different aerosol sizes remains largely unchanged over time.

TABLE VI.

The deposition fractions of 1–2 and 2–10 μm particles in the oral mode at the first breathing cycle.

15 LPM 30 LPM 60 LPM
t = 1 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Oral cavity  38.0%  32.2%  −5.8%  37.5%  28.3%  −9.2%  32.4%  21.7%  −10.7% 
Pharynx  23.3%  13.1%  −10.2%  15.9%  6.2%  −9.7%  11.7%  11.9%  +0.2% 
Larynx  1.6%  2.7%  +1.1%  2.0%  6.6%  +4.6%  3.8%  21.1%  +17.3% 
Trachea  22.5%  35.1%  +12.6%  26.1%  40.2%  +14.1%  31.2%  32.1%  +0.9% 
Right bronchi  1.8%  2.0%  +0.2%  3.4%  2.7%  −0.7%  4.6%  1.9%  −2.7% 
Left bronchi  10.8%  12.8%  +2.0%  13.3%  13.7%  +0.4%  14.1%  9.4%  −4.7% 
t = 3 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Oral cavity  39.8%  33.6%  −6.2%  39.2%  29.4%  −9.8%  33.2%  22.1%  −11.1% 
Pharynx  24.0%  13.9%  −10.1%  16.8%  6.3%  −10.5%  11.7%  11.9%  +0.2% 
Larynx  1.3%  2.5%  +1.2%  1.7%  6.1%  +4.4%  3.9%  21.0%  +17.1% 
Trachea  17.3%  28.9%  +11.6%  22.9%  37.6%  +14.7%  29.3%  31.0%  +1.7% 
Right bronchi  2.3%  2.7%  +0.4%  3.6%  2.9%  −0.7%  4.7%  2.0%  −2.7% 
Left bronchi  12.4%  15.2%  −2.8%  13.7%  14.7%  +1.0%  14.4%  9.8%  −4.6% 
15 LPM 30 LPM 60 LPM
t = 1 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Oral cavity  38.0%  32.2%  −5.8%  37.5%  28.3%  −9.2%  32.4%  21.7%  −10.7% 
Pharynx  23.3%  13.1%  −10.2%  15.9%  6.2%  −9.7%  11.7%  11.9%  +0.2% 
Larynx  1.6%  2.7%  +1.1%  2.0%  6.6%  +4.6%  3.8%  21.1%  +17.3% 
Trachea  22.5%  35.1%  +12.6%  26.1%  40.2%  +14.1%  31.2%  32.1%  +0.9% 
Right bronchi  1.8%  2.0%  +0.2%  3.4%  2.7%  −0.7%  4.6%  1.9%  −2.7% 
Left bronchi  10.8%  12.8%  +2.0%  13.3%  13.7%  +0.4%  14.1%  9.4%  −4.7% 
t = 3 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Oral cavity  39.8%  33.6%  −6.2%  39.2%  29.4%  −9.8%  33.2%  22.1%  −11.1% 
Pharynx  24.0%  13.9%  −10.1%  16.8%  6.3%  −10.5%  11.7%  11.9%  +0.2% 
Larynx  1.3%  2.5%  +1.2%  1.7%  6.1%  +4.4%  3.9%  21.0%  +17.1% 
Trachea  17.3%  28.9%  +11.6%  22.9%  37.6%  +14.7%  29.3%  31.0%  +1.7% 
Right bronchi  2.3%  2.7%  +0.4%  3.6%  2.9%  −0.7%  4.7%  2.0%  −2.7% 
Left bronchi  12.4%  15.2%  −2.8%  13.7%  14.7%  +1.0%  14.4%  9.8%  −4.6% 
TABLE VII.

The deposition fractions of 1–2 and 2–10 μm particles in the oral mode at the second breathing cycle.

15 LPM 30 LPM 60 LPM
t = 5 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Oral cavity  41.1%  35.7%  −5.4%  40.4%  29.3%  −11.1%  31.7%  19.7%  −12.0% 
Pharynx  20.2%  11.2%  −9.0%  13.4%  5.2%  −8.2%  9.5%  12.2%  +2.7% 
Larynx  1.6%  2.6%  +1.0%  2.0%  6.3%  +4.3%  3.7%  21.5%  +17.8% 
Trachea  20.4%  31.0%  +10.6%  24.7%  38.9%  +14.2%  31.5%  32.0%  +0.5% 
Right bronchi  2.2%  2.3%  +0.1%  3.6%  2.9%  −0.7%  4.8%  2.0%  −2.8% 
Left bronchi  12.1%  14.3%  +2.1%  13.9%  14.8%  +0.9%  16.0%  10.1%  −5.9% 
t = 7 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Oral cavity  41.4%  36.7%  −4.7%  42.6%  30.0%  −12.6%  31.6%  18.5%  −13.1% 
Pharynx  18.2%  10.0%  −8.2%  11.9%  4.5%  −7.4%  8.4%  12.1%  +3.7% 
Larynx  1.7%  2.7%  +1.0%  1.8%  6.2%  +4.4%  3.3%  22.1%  +18.8% 
Trachea  19.8%  29.7%  +9.9%  23.6%  38.1%  +14.5%  31.4%  31.9%  +0.5% 
Right bronchi  2.6%  2.6%  0%  3.7%  3.0%  −0.7%  4.8%  2.0%  −2.8% 
Left bronchi  13.3%  15.2%  −2.0%  14.2%  15.1%  +0.9%  17.2%  10.7%  −6.5% 
15 LPM 30 LPM 60 LPM
t = 5 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Oral cavity  41.1%  35.7%  −5.4%  40.4%  29.3%  −11.1%  31.7%  19.7%  −12.0% 
Pharynx  20.2%  11.2%  −9.0%  13.4%  5.2%  −8.2%  9.5%  12.2%  +2.7% 
Larynx  1.6%  2.6%  +1.0%  2.0%  6.3%  +4.3%  3.7%  21.5%  +17.8% 
Trachea  20.4%  31.0%  +10.6%  24.7%  38.9%  +14.2%  31.5%  32.0%  +0.5% 
Right bronchi  2.2%  2.3%  +0.1%  3.6%  2.9%  −0.7%  4.8%  2.0%  −2.8% 
Left bronchi  12.1%  14.3%  +2.1%  13.9%  14.8%  +0.9%  16.0%  10.1%  −5.9% 
t = 7 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Oral cavity  41.4%  36.7%  −4.7%  42.6%  30.0%  −12.6%  31.6%  18.5%  −13.1% 
Pharynx  18.2%  10.0%  −8.2%  11.9%  4.5%  −7.4%  8.4%  12.1%  +3.7% 
Larynx  1.7%  2.7%  +1.0%  1.8%  6.2%  +4.4%  3.3%  22.1%  +18.8% 
Trachea  19.8%  29.7%  +9.9%  23.6%  38.1%  +14.5%  31.4%  31.9%  +0.5% 
Right bronchi  2.6%  2.6%  0%  3.7%  3.0%  −0.7%  4.8%  2.0%  −2.8% 
Left bronchi  13.3%  15.2%  −2.0%  14.2%  15.1%  +0.9%  17.2%  10.7%  −6.5% 

3. Nasal–Oral mode

Figures 19 and 20 display the deposition fraction of 1–2 and 2–10 μm particles, respectively, in the nasal–oral mode, which represents the real human airways. The same trend of particle deposition is observed with an increase in the flow rate, similar to the nasal mode, where the deposition fraction in the nasal cavity decreases, while it increases in other regions. Notably, the deposition fraction in the oral cavity regions remains relatively unchanged for particles with a diameter of 1–2 μm.

FIG. 19.

The deposition of aerosol particles (dp = 1–2 μm) in the nasal–oral mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

FIG. 19.

The deposition of aerosol particles (dp = 1–2 μm) in the nasal–oral mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

Close modal
FIG. 20.

The deposition of aerosol particles (dp = 2–10 μm) in the nasal–oral mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

FIG. 20.

The deposition of aerosol particles (dp = 2–10 μm) in the nasal–oral mode. Here, black bar (15 LPM), red bar (30 LPM), and blue bar (60 LPM), respectively. (a) t = 1 s (inhalation), (b) t = 3 s (exhalation), (c) t = 5 s (inhalation), and (d) t = 7 s (exhalation).

Close modal

Tables VIII and IX present the variations in deposition fractions for both 1–2 and 2–10 μm particles across different flow rates. As the flow rate increases, the differences in deposition fractions decrease in the oral cavity and pharynx regions. This pattern is different from the nasal mode, where the deposition fractions decrease in the nasal cavity and pharynx regions. Moreover, in the nasal–oral mode, the deposition fractions fluctuate in the nasal and larynx regions with an increase in the flow rate. On the other hand, in the nasal mode, the deposition fractions increase in the larynx and trachea regions.

TABLE VIII.

The deposition fractions of 1–2 and 2–10 μm particles in the nasal–oral mode at the first breathing cycle.

15 LPM 30 LPM 60 LPM
t = 1 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Nasal cavity  65.1%  65.2%  +0.1%  60.6%  61.0%  +0.4%  54.8%  55.0%  +0.2% 
Oral cavity  17.1%  17.2%  +0.1%  16.5%  15.3%  −1.2%  15.9%  12.4%  −3.5% 
Pharynx  5.3%  4.6%  −0.7%  9.0%  6.9%  −2.1%  12.5%  7.9%  −4.6% 
Larynx  3.7%  2.7%  −1.0%  4.6%  3.3%  −1.3%  6.1%  6.3%  +0.2% 
Trachea  4.6%  5.8%  +1.2%  5.2%  7.9%  +2.7%  5.7%  11.5%  +5.8% 
Right bronchi  0.3%  0.3%  0%  0.6%  0.7%  +0.1%  0.9%  1.0%  +0.1% 
Left bronchi  1.5%  2.1%  +0.6%  2.7%  4.1%  +1.4%  3.6%  5.5%  +1.9% 
t = 3 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Nasal cavity  54.0%  54.4%  +0.4%  53.2%  54.1%  +0.9%  50.6%  50.5%  −0.1% 
Oral cavity  15.7%  15.8%  +0.1%  16.0%  14.7%  −1.3%  15.7%  12.0%  −3.7% 
Pharynx  7.8%  6.9%  −0.9%  11.3%  8.8%  −2.5%  14.3%  8.9%  −5.4% 
Larynx  4.7%  3.5%  −1.2%  5.6%  4.2%  −1.4%  6.9%  7.7%  +0.8% 
Trachea  4.0%  5.1%  +1.1%  5.0%  8.0%  +3.0%  5.8%  11.8%  +6.0% 
Right bronchi  0.6%  0.6%  0%  0.8%  0.9%  +0.1%  1.0%  1.2%  +0.2% 
Left bronchi  2.7%  3.5%  +0.8%  3.5%  5.4%  +1.9%  4.1%  6.2%  +2.1% 
15 LPM 30 LPM 60 LPM
t = 1 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Nasal cavity  65.1%  65.2%  +0.1%  60.6%  61.0%  +0.4%  54.8%  55.0%  +0.2% 
Oral cavity  17.1%  17.2%  +0.1%  16.5%  15.3%  −1.2%  15.9%  12.4%  −3.5% 
Pharynx  5.3%  4.6%  −0.7%  9.0%  6.9%  −2.1%  12.5%  7.9%  −4.6% 
Larynx  3.7%  2.7%  −1.0%  4.6%  3.3%  −1.3%  6.1%  6.3%  +0.2% 
Trachea  4.6%  5.8%  +1.2%  5.2%  7.9%  +2.7%  5.7%  11.5%  +5.8% 
Right bronchi  0.3%  0.3%  0%  0.6%  0.7%  +0.1%  0.9%  1.0%  +0.1% 
Left bronchi  1.5%  2.1%  +0.6%  2.7%  4.1%  +1.4%  3.6%  5.5%  +1.9% 
t = 3 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Nasal cavity  54.0%  54.4%  +0.4%  53.2%  54.1%  +0.9%  50.6%  50.5%  −0.1% 
Oral cavity  15.7%  15.8%  +0.1%  16.0%  14.7%  −1.3%  15.7%  12.0%  −3.7% 
Pharynx  7.8%  6.9%  −0.9%  11.3%  8.8%  −2.5%  14.3%  8.9%  −5.4% 
Larynx  4.7%  3.5%  −1.2%  5.6%  4.2%  −1.4%  6.9%  7.7%  +0.8% 
Trachea  4.0%  5.1%  +1.1%  5.0%  8.0%  +3.0%  5.8%  11.8%  +6.0% 
Right bronchi  0.6%  0.6%  0%  0.8%  0.9%  +0.1%  1.0%  1.2%  +0.2% 
Left bronchi  2.7%  3.5%  +0.8%  3.5%  5.4%  +1.9%  4.1%  6.2%  +2.1% 
TABLE IX.

The deposition fractions of 1–2 and 2–10 μm particles in the nasal–oral mode at the second breathing cycle.

15 LPM 30 LPM 60 LPM
t = 5 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Nasal cavity  58.8%  59.2%  +0.4%  56.4%  56.9%  +0.5%  52.3%  52.3%  0% 
Oral cavity  18.0%  18.0%  0%  17.7%  16.3%  −1.4%  17.3%  13.8%  −3.5% 
Pharynx  7.4%  6.6%  −0.8%  10.5%  8.2%  −2.3%  13.4%  8.5%  −4.9% 
Larynx  4.0%  3.0%  −1.0%  5.1%  3.8%  −1.3%  6.4%  7.0%  +0.6% 
Trachea  4.0%  5.1%  +1.1%  4.8%  7.6%  +2.8%  5.5%  11.0%  +5.5% 
Right bronchi  0.5%  0.5%  0%  0.7%  0.8%  +0.1%  0.9%  1.1%  +0.2% 
Left bronchi  2.1%  2.9%  +0.8%  3.0%  4.8%  +1.8%  3.6%  5.6%  +2.0% 
t = 7 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Nasal cavity  54.9%  55.4%  +0.5%  54.1%  54.7%  +0.6%  50.8%  50.9%  +0.1% 
Oral cavity  16.5%  16.5%  0%  16.4%  15.1%  −1.3%  16.8%  13.3%  −3.5% 
Pharynx  8.5%  7.6%  −0.9%  11.6%  9.0%  −2.6%  14.1%  8.9%  −5.2% 
Larynx  5.0%  3.7%  −1.3%  5.6%  4.2%  −1.4%  6.7%  7.3%  −0.6% 
Trachea  4.2%  5.3%  +1.1%  5.0%  8.0%  +3.0%  5.6%  11.3%  +5.7% 
Right bronchi  0.6%  0.6%  0%  0.8%  0.9%  +0.1%  0.9%  1.1%  +0.2% 
Left bronchi  2.7%  3.6%  +0.6%  3.5%  5.4%  +1.9%  3.8%  5.9%  +2.1% 
15 LPM 30 LPM 60 LPM
t = 5 s (inhalation) 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference 1–2 μm 2–10 μm Difference
Nasal cavity  58.8%  59.2%  +0.4%  56.4%  56.9%  +0.5%  52.3%  52.3%  0% 
Oral cavity  18.0%  18.0%  0%  17.7%  16.3%  −1.4%  17.3%  13.8%  −3.5% 
Pharynx  7.4%  6.6%  −0.8%  10.5%  8.2%  −2.3%  13.4%  8.5%  −4.9% 
Larynx  4.0%  3.0%  −1.0%  5.1%  3.8%  −1.3%  6.4%  7.0%  +0.6% 
Trachea  4.0%  5.1%  +1.1%  4.8%  7.6%  +2.8%  5.5%  11.0%  +5.5% 
Right bronchi  0.5%  0.5%  0%  0.7%  0.8%  +0.1%  0.9%  1.1%  +0.2% 
Left bronchi  2.1%  2.9%  +0.8%  3.0%  4.8%  +1.8%  3.6%  5.6%  +2.0% 
t = 7 s (exhalation)  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference  1–2 μ 2–10 μ Difference 
Nasal cavity  54.9%  55.4%  +0.5%  54.1%  54.7%  +0.6%  50.8%  50.9%  +0.1% 
Oral cavity  16.5%  16.5%  0%  16.4%  15.1%  −1.3%  16.8%  13.3%  −3.5% 
Pharynx  8.5%  7.6%  −0.9%  11.6%  9.0%  −2.6%  14.1%  8.9%  −5.2% 
Larynx  5.0%  3.7%  −1.3%  5.6%  4.2%  −1.4%  6.7%  7.3%  −0.6% 
Trachea  4.2%  5.3%  +1.1%  5.0%  8.0%  +3.0%  5.6%  11.3%  +5.7% 
Right bronchi  0.6%  0.6%  0%  0.8%  0.9%  +0.1%  0.9%  1.1%  +0.2% 
Left bronchi  2.7%  3.6%  +0.6%  3.5%  5.4%  +1.9%  3.8%  5.9%  +2.1% 

Investigating the flow field and deposition fractions of particles in lung mode is highly beneficial for analyzing viral transmission. As discussed in this study, three independent factors, namely different breathing modes (nasal, oral, and nasal–oral modes), flow rates (15, 30, and 60 LPM), and particle diameter ranges (1–2 and 2–10 μm) directly influence the deposition of particles, resulting in varying deposition fractions in each lung region. In the flow field analysis, high velocity profiles (exceeding 10 m/s) are predominantly formed in the pharynx, larynx, and trachea regions, and the velocity profiles also increase in these regions with higher flow rates. As a result, the deposition fractions of aerosols increase in the pharynx, larynx, and trachea regions, while a decrease in the deposition fractions is observed in the nasal and oral cavities. Here is our summary regarding the effects of breathing modes, flow rates, and particle sizes on flow fields and particle deposition:

  • The presence of the nasal cavity contributes to relatively narrower regions of low velocity due to its more complex structure compared to the oral cavity. As a result, in the nasal mode, high velocity regions (exceeding 10 m/s) are observed in the pharynx and larynx regions, while in the nasal–oral mode, only the larynx region shows the high velocity region. The oral mode exhibits a wider range of high velocity regions, including the pharynx, larynx, and bottom trachea.

  • The cumulative deposition fractions of aerosols exhibit different trends in each lung mode and region depending the particle sizes and flow rate. To be specific, for 1–2 μm aerosols, all three modes show decreasing particle deposition in the nasal or oral cavity with an increase in flow rates, while other regions exhibit increasing deposition fractions. The higher velocity of the airflow tends to carry away the smaller aerosol particles, resulting in reduced deposition in these regions.

  • The large particle sizes of 2–10 μm are less affected by the increased airflow velocity and are more likely to deposit in other regions due to their inertia. As the flow rate increases, in the nasal mode, particles are more likely to cluster in the larynx and trachea regions compared to those of 1–2 μm. In the oral mode, there is a noticeable increase in the deposition fraction in the larynx for 2–10 μm particles. Lastly, the particle deposition in the trachea significantly increases in the nasal–oral mode. A notable point is that the deposition fractions in each region are not affected by the breathing cycles over time.

It is well known that the primary cause of viral transmission originates from the high deposition fraction in the upper airways, including the larynx region.33 In our study, the specific condition most susceptible to infection is characterized by the highest deposition fractions in the upper airways, particularly at the lowest flow rate of 15 LPM, with smaller particle diameters of 1–2 μm in the nasal mode. Our research findings can also contribute to targeted drug delivery in the lower airways. Respiratory diseases, such as asthma and chronic obstructive pulmonary disease (COPD), are affected by particle deposition.94–96 Specifically, asthma and COPD are inflammatory conditions of the lungs predominantly caused by the inhalation of noxious gases in the bronchial region.97 Therefore, the highest deposition fraction for drug delivery is achieved in the bronchi, reducing airway inflammation and bronchoconstriction (narrowing of the airways). This can be attained at the highest flow rate of 60 LPM with smaller particle sizes of 1–2 μm in the oral mode.

This research was partially supported by the University of Minnesota (UMN) Medical School and the UMN Physicians and Fairview Health Services's CO:VID (Collaborative Outcomes: Visionary Innovation & Discovery) grants program, which supported UMN faculty to catalyze and energize small-scale research projects designed to address and mitigate the COVID-19 virus and its associated risks. The project was also partially supported by the UMN Interdisciplinary Doctoral Fellowship (IDF). The authors would like to thank Dr. Susan Arnold, Dr. David Odde, and the Institute for Engineering in Medicine (IEM) for their helpful discussions. The authors would like to thank Dr. Richard A. Corley and Dr. Andrew P. Kuprat from the Pacific Northwest National Laboratory (PNNL) for their valuable inputs and for providing the lung geometries for this study. The authors would like to thank Ismail Guler from Boston Scientific and Kerrim Genc from Synopsis Inc. for their helpful discussions. The authors would like to thank the Minnesota Supercomputing Institute (MSI) for providing the HPC resources to conduct the simulations for this project. Finally, the authors would like to thank Convergent Science for providing CONVERGE licenses and technical support for this work.

The authors have no conflicts to disclose.

Gihun Shim: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead). Sai Ranjeet Narayanan: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Suo Yang: Conceptualization (lead); Formal analysis (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (lead); Resources (supporting); Software (supporting); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

A conventional grid convergence study requires that the base grid size be fixed throughout the domain and then varied from coarse to fine. However, due to computational restrictions on time and resources, adaptive mesh refinement (AMR) was used along with an initial fixed base grid size (which was carefully chosen through existing literature on similar numerical modeling of respiratory aerosols76–79). The cylinder in front of the mouth/nose region has a large number of cells on its own, which will further increase the computational cost if the base grid size is reduced further.

In an attempt at a rudimentary grid convergence study for this non-conventional non-uniform mesh, the total number of cells in the domain was varied from 2 M cells to 9 M cells, by adding fixed embedding (manual mesh refinement) near the walls, and allowing more cells to be added by AMR. Figure 21 illustrates velocity and turbulent kinetic energy (TKE) contours based on the different total cell counts of 2, 4, and 9 M. The images show that AMR is effective for all three mesh count cases in resolving the high velocity regions, such as in the narrow larynx regions and near the walls. The trends in observed results of velocity [Figs. 21(a), 21(b), and 21(c)] and TKE [Figs. 21(d), 21(e), and 21(f)] remain largely unchanged, despite the change in computational cells.

FIG. 21.

2D contours of velocity and turbulent kinetic energy (TKE) in the nasal mode with a breathing rate of 60 LPM at t = 0.6 s: (a) velocity with 2 × 106 cells, (b) velocity with 4 × 106 cells, (c) velocity with 9 × 106 cells, (d) TKE with 2 × 106 cells, (e) TKE with 4 × 106 cells, and (f) TKE with 9 × 106 cells.

FIG. 21.

2D contours of velocity and turbulent kinetic energy (TKE) in the nasal mode with a breathing rate of 60 LPM at t = 0.6 s: (a) velocity with 2 × 106 cells, (b) velocity with 4 × 106 cells, (c) velocity with 9 × 106 cells, (d) TKE with 2 × 106 cells, (e) TKE with 4 × 106 cells, and (f) TKE with 9 × 106 cells.

Close modal

The challenge of restricted computational time/resources in such a broad parametric study is, thus, tackled by literature-guided choosing of a non-conventional mesh with an initial base grid size, AMR, and fixed embedding. The figures provided here can hopefully convince the reader that the results do not change much when varying the cell count in this study, and the cited references adequately support the selection of the base grid size for this study.

Similar to k–ω shear stress transport (SST) and large eddy simulation (LES) models, the RNG (renormalization group) k–ε model is frequently employed in numerical modeling of human respiratory airways.69–71 The RNG k–ε turbulence model effectively captures the essential transition from laminar to turbulent flow in the pharyngeal airway, based on the literature.69–71 Additionally, an LES simulation also requires a very refined mesh, which is computationally expensive to simulate for a broad parametric study such as this.

Figure 22 presents the velocity and turbulent kinetic energy (TKE) contours for both RANS and LES models with 2 × 106 cells each. As evident, the velocity and TKE profiles exhibit remarkable similarity for both the RANS and LES cases.

FIG. 22.

2D contours of velocity and turbulent kinetic energy (TKE) in the nasal mode with 30 LPM at t = 1 s. (a) Velocity with a RANS model, (b) velocity with a LES model, (c) TKE with a RANS model, and (d) TKE with a LES model.

FIG. 22.

2D contours of velocity and turbulent kinetic energy (TKE) in the nasal mode with 30 LPM at t = 1 s. (a) Velocity with a RANS model, (b) velocity with a LES model, (c) TKE with a RANS model, and (d) TKE with a LES model.

Close modal

Figure 23 illustrates the volume fraction contours of large 2–10 μm particles in the nasal–oral mode, at flow rates 15 LPM during the middle of the second inhalation phase (t = 5 s). The range of volume fractions observed is usually between 10 7 and 10 9, as seen in the contour images. Since we observe a volume fraction of less than 10−4, a significant particle-flow interaction is not seen in our study, according to the literature.73 

FIG. 23.

2D contours of volume fraction for large 2–10 μm particles in the nasal–oral mode with 15 LPM at t = 5 s. Front views (a) volume fraction from 10−8 to 10−7, (b) volume fraction from 10−7 to 10−6; top views (c) volume fraction from 10−8 to 10−7, and (d) volume fraction from 10−7 to 10−6.

FIG. 23.

2D contours of volume fraction for large 2–10 μm particles in the nasal–oral mode with 15 LPM at t = 5 s. Front views (a) volume fraction from 10−8 to 10−7, (b) volume fraction from 10−7 to 10−6; top views (c) volume fraction from 10−8 to 10−7, and (d) volume fraction from 10−7 to 10−6.

Close modal

Converge 3.0 considers two-way coupling between the Eulerian and Lagrangian phases, as evident from the momentum source term and particle drag force being coupled by Eqs. (2), (5), and (7).

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