key: cord-306861-qcctchsk authors: Chen, Xiaole; Zhou, Xianguang; Xia, Xueying; Xie, Xiaojian; Lu, Ping; Feng, Yu title: Modeling of the transport, hygroscopic growth, and deposition of multi-component droplets in a simplified airway with realistic thermal boundary conditions date: 2020-07-24 journal: J Aerosol Sci DOI: 10.1016/j.jaerosci.2020.105626 sha: doc_id: 306861 cord_uid: qcctchsk Accurate predictions of the droplet transport, evolution, and deposition in human airways are critical for the quantitative analysis of the health risks due to the exposure to the airborne pollutant or virus transmission. The droplet/particle-vapor interaction, i.e., the evaporation or condensation of the multi-component droplet/particle, is one of the key mechanisms that need to be precisely modeled. Using a validated computational model, the transport, evaporation, hygroscopic growth, and deposition of multi-component droplets were simulated in a simplified airway geometry. A mucus-tissue layer is explicitly modeled in the airway geometry to describe mucus evaporation and heat transfer. Pulmonary flow and aerosol dynamics patterns associated with different inhalation flow rates are visualized and compared. Investigated variables include temperature distributions, relative humidity (RH) distributions, deposition efficiencies, droplet/particle distributions, and droplet growth ratio distributions. Numerical results indicate that the droplet/particle-vapor interaction and the heat and mass transfer of the mucus-tissue layer must be considered in the computational lung aerosol dynamics study, since they can significantly influence the precise predictions of the aerosol transport and deposition. Furthermore, the modeling framework in this study is ready to be expanded to predict transport dynamics of cough/sneeze droplets starting from their generation and transmission in the indoor environment to the deposition in the human respiratory system. The interaction between the bio-aerosol and water vapor also has been investigated. Zhang et al., 2006) , we developed and validated a multi-component 18 droplet/particle-vapor interaction model (Chen et al., 2017) . The difference between our 19 predictions and the experimental results (W. Li et al., 1992) for the hygroscopic growth 20 of NaCl particle is only ± 0.2 % RH (or ± 0.4 in growth ratio) (Chen, et al., 2017) . 21 airway wall boundary conditions (Chen, et al., 2017) . Asgari et al. (2019) developed 1 experiment, which can maintain the airway surface temperature at 37°C using 3D 2 printed casing with a circulated water bath, for exposure studies of hygroscopic 3 particulate matters. However, the system mentioned above still cannot represent the 4 physiologically realistic non-uniform temperature distributions in airways (McFadden 5 Jr et al., 1985) . The inhalation flow rate affects the deposition of the hygroscopic 6 droplet/particle. More specifically, higher inhalation flow rate increases the deposition 7 of the hygroscopic droplets/particles due to inertial impaction. However, higher 8 inhalation flow rate decreases the average RH-value in the airway when using a 9 boundary condition with constant temperature and RH (Chen, et al., 2017) , which 10 enhances the evaporation of the droplet. If the more realistic thermal boundary (Chen, 11 al., 2018; Wu, et al., 2014) and indoor air conditions (McFadden Jr, et al., 1985) are 12 considered, higher inhalation flow rate also has a stronger cooling effect on the 13 mucus-tissue layer, which further affects the mucus evaporation. Therefore, the 14 transport, hygroscopic growth, and deposition of multi-component droplets have not 15 been investigated under different inhalation flow rate conditions, when employing the 16 more realistic thermal boundary conditions. 17 To address the knowledge gap mentioned above, this study investigates the 18 evaporation, hygroscopic growth, and transport of a representative multi-component 19 stands for the sea salt and other soluble compositions. Fluorescein represents the 1 non-evaporable and non-soluble composition, e.g., crustal matter. The validated 2 transition shear stress transport (SST) model and discrete phase model (DPM) were 3 employed for the prediction of the airflow and inhaled droplet/particle transport, 4 respectively. Temperature and RH distributions in the MT airway, as well as the 5 deposition of the hygroscopic multi-component droplets are visualized and analyzed. The simplified mouth-throat (MT) airway geometry (see Figure 1 ) consists of two 9 parts, i.e., an MT cavity and a mucus-tissue layer surrounding the cavity. The concluded that the simplified MT models with outlet diameters of 7.5 and 8.5 mm 12 were better in accordance to in vivo experimental data comparing to the models with 13 other outlet diameters and the USP model. Therefore, the simplified MT cavity with a 14 diameter of 8.5 mm was used as the fluid region in our study. Furthermore, the fluid 15 region was covered by a 1.0 mm thick mucus-tissue layer. The mucus-tissue layer (the blue cells shown in Figure 1 ) contains two sublayers, 3 i.e., a mucus layer with a thickness of 10 μm and a tissue layer with a thickness of 990 4 μm. This setup ensures an accurate prediction of the temperature distribution in the 5 mucus-tissue layer (Chen, et al., 2018; Wu, et al., 2014) . The structured hexahedral 6 mesh was generated for both the fluid region and the mucus-tissue layer. The mesh 7 was refined in the fluid region and the mucus-tissue layer near the air-mucus interface. The mesh refinement ensured that the non-dimensional distance y + was smaller than 9 1.0 for the first layer of the fluid mesh cells. Mesh independence test was carried out 10 following the same procedure that is documented in our previous study (Chen, et al., 11 2017). The final mesh contained 2,287,197 cells for the fluid region, and 605,880 cells 12 for the mucus-tissue region. 13 Figure 2 visualizes the coupling mechanisms of the heat and mass transfer 14 between air and mucus. Specifically, the airflow over the air-mucus interface affects 15 the convective heat transfer, and the resultant water vapor flux evaporated from the 1 mucus layer. Assuming RH = 99.5% at the air-mucus interface (Finlay, 2001), the 2 latent heat loss due to evaporation contribute to the variations of mucus temperature. The temperature at the air-mucus interface was calculated by the iterations 4 between the MT cavity and the mucus-tissue layer. If the temperature of a given mucus 5 cell t m1 is known, the airflow simulation determines the heat flux due to convection and 6 and the mass flux of the water vapor, which determines the latent heat loss of the 7 mucus layer. Note that the calculations for the airflow and the heat transfer in the 8 mucus-tissue layer are separated. t m1 is used as the boundary surface temperature for 9 the airflow calculation. In the mucus-tissue layer, the temperature of the same cell t m2 is 10 is obtained by solving the energy balance equation based on the conduction in the 11 mucus-tissue layer, as well as the convection and latent heat loss due to the evaporation 12 evaporation effect. The latter two are obtained from the calculation in the domain of 13 the MT domain. The iteration continues until t m1 is equal to t m2 . To predict the RH distribution in the airway, the transport both the dry air and 2 water vapor were simulated. The transition SST model was employed to simulate the 3 laminar-to-turbulent airflow (Chen, et al., 2017; Chen, et al., 2018) Equations (1) and (2), i.e., the k and ω equations, are modified based on the SST model 12 (Menter, 1994) using the production term k P % and destruction term k D % of turbulence 13 kinetic energy (TKE). k P % and k D % are determined by the intermittency γ (see Eq. (3)) and the transition momentum thickness in terms of the Reynolds number Re t θ % , 15 (see Eq. (4)). The scalar transport equation for both the dry air and water vapor is given by (Z. where s Y and , s m D are the mass fraction and mass diffusion coefficient for species s. where H is the enthalpy of the mixture, c k and tc k are the thermal conductivity and 8 turbulent thermal conductivity, respectively. A Lagrangian method was employed in this study to predict the transport, size 11 change, and deposition of the droplets. All governing equations listed in this section 12 were solved using in-house C codes, implemented as user-defined functions (UDFs). 13 The droplets and particles are assumed to be spherical in our simulations. The primary 14 deposition mechanisms are inertial impaction, sedimentation, and diffusion. The 15 diffusion could be ignored due to the negligible Brownian motion effect on the 16 micron-sized droplets/particles. Therefore, the main forces considered are the drag 17 force and gravity. The Saffman's lift force is ignored due to limited droplet/particle 18 rotation. The virtual mass force is ignored, considering the large droplet/particle-to-air 19 density ratio. Accordingly, the droplet/particle trajectories are determined by the 20 translation equation ( where Dd C is the drag coefficient determined by the droplet/particle Reynolds number, 3 the d m , d u and d d are the mass, velocity, and diameter of the droplet/particle, 4 respectively. The eddy-droplet/particle interaction, also known as the random walk Kleinstreuer, 2005), which can be given by: 13 Where A is the surface areas of the droplet/particle, s n is the surface averaged mass is the mass fraction of component s on the droplet/particle surface, s Y is Therefore, the mass flux of the evaporable/condensable component changes the mass 1 and volume of the droplet/particle. Thus, the density of the droplet/particle may change 2 during the simulation. In addition, the energy balance of the droplet/particle is given by (Chen, et where Nu is the Nusselt number, s L is the latent heat of species s, c k is the thermal the specific heat and temperature of the droplet/particle, respectively. where h, injecting 10, 000 particles could ensure that the deposition efficiency is independent of 9 the particle number. The droplet/particle-vapor interaction model was also validated (Chen, et al., Heat transfer between the mucus-tissue layer and the airflow was examined in our 21 recent study (Chen, et al., 2018) . The latent heat transfer occupied 84.7% of the total 1 heat transfer at the air-mucus interface. This is similar to the percentage suggested by If the droplet evaporates completely, the diameter of the solid particle containing NaCl 10 and fluorescein only would be 44.3% of its initial droplet. Parameter values for setting 11 up the simulations are provided in the Supporting Information. including 1) airway wall had a constant temperature at 37 °C, 2) ignoring the latent 20 heat due to water vapor phase change, but including convective heat transfer, and 3) the more realistic thermal boundary condition, which is the same condition we used in 1 this study. The simulated velocity distributions were highly similar due to the 2 negligible effects of the temperature and RH on the fluid density (Chen, et al., 2017) . 3 Therefore, the velocity field results and discussion were not provided in this study to 4 avoid duplicated analysis. sharply in size with the increase of Q in . As shown in Figure 4 (b), more than 1/3 area at 9 the outlet has a localized RH higher than 80%,. However, its size reduces when the 10 flow rate increases to 30 L/min. Furthermore, the region with RH > 80% almost 11 disappears and shrinks into a thin layer near the air-mucus interface, when the flow rate 12 continues to increase to 60 L/min (see Figure 4 (c)). This suggests that hygroscopic 13 growth of the droplet/particle can barely occur under high Q in condition. shown in Figure S1 in the Supporting Information. conditions remains approximately 6% for 0.018 < Stk < 0.034. When Q in further 2 increases to 60 L/min, the difference in DEs remains 5% for 0.012 < Stk < 0.025. It is well known that the deposition of the micron particle in the airway may occur 4 via impaction, including secondary airflow convecting particles to the airway walls, and particles were limited (see Figure 7 (a)) in the low RH condition (see Figure 4 (c)). 12 Therefore, the contribution of the hygroscopic growth to the deposition of the droplets 13 would be limited. This observation indicates that the inertial impaction becomes more 14 dominant on the droplet deposition when Stk increases. 15 The intensity of indoor human activity is commonly low. The inhalation flow rate 16 for possible medical applications, e.g., inhaler, nebulizer, is even lower. Therefore, the 17 focus on the inhalation flow rate should be smaller than 30 L/min, representing the 18 light activity. Neglecting the droplet hygroscopicity could underestimate the DE up to 19 20% for NaCl-water droplet at 37°C (Chen et al., 2019) . Besides, a more realistic 20 airway boundary could increase the intensity of secondary flow that enhances the heat 21 and water vapor mass transfer around the mucus-tissue layer. Therefore, it can be 1 projected that the differences in DE predictions may also increase accordingly. Thus, in 2 order to accurately predict the fate of the inhaled hygroscopic droplet/particle, the the hygroscopic growth threshold for NaCl, i.e., approximately 76% (see Figure 4 ). escaped hygroscopic droplets/particles decreases with the increase of Q in . This is in 18 accordance with the RH distributions discussed above. Higher Q in decreases the size of RH value higher than 80% at the 60 L/min condition. Thus, the droplets/particles can 1 barely absorb water before deposition when penetrating this thin layer of high RH air. 2 Besides, the lower flow rate also leads to a longer time for droplet/particle-vapor 3 interaction. Therefore, the simulation has more large droplets at Q in = 15 L/min. Also, it can be found that the average diameter of the deposited droplets is smaller 5 than that of the escaped ones under the same condition. This observation is related to 6 the droplet/particle trajectory in the airway. The airway mucus gradually humidifies the 7 inhaled air, and result in a higher average RH at the outlet. Due to a similar mechanism, 8 the maximum diameter for the deposited droplets is larger than that of escaped ones. 9 There is an interesting increase in the number of droplets having a growth ratio 10 approximately equal to 2.2 in Figure 7 (b) under 15 L/min condition. This is related to 11 the droplets and particles entrained into the tube center at the outlet (see the red circle 12 in Figure 6 (a) and green squares in Figure 7 (b) ). The growth ratio distribution of the droplets and particles within the circle indicates that these droplets are relatively large. 1 57% of these droplets and particles are within the growth ratio range from 1.9 to 2.3. Their average growth ratio value is 1.773, which is also higher than that of the droplets 3 and particles at the whole outlet. Besides, the droplets and particles can only absorb 4 water vapor in the high RH (>80%) region. Therefore, these large droplets are drawn 5 into the tube center by the vortices from the airway boundary, considering their spatial 6 distribution (see Figure 6 (a)). i.e., heat conduction in the airway tissue and mucus layer, the latent heat loss of mucus 18 evaporation, and heat convection induced by the airflow over the mucus layer. 19 Temperature distributions, RH distributions, droplet deposition efficiencies, deposition 20 patterns, and droplet/particle diameter changes are visualized and discussed. Major 21 conclusions are as follows: (1) High inhalation flow rate can substantially decrease the mucus temperature 2 with noticeable temperature gradients in the mucus-tissue layer. (2) High inhalation flow rate can decrease the RH in the airway, which limits the 4 hygroscopic droplet growth. No obvious hygroscopic growth of the NaCl nuclei was airway. More realistic airway geometry or lower inhalation flow rate would increase 11 this difference. Therefore, it is necessary to model the mucus-tissue layer to obtain 12 more realistic droplet deposition patterns in airways. 13 Numerical models employed in this study, especially the droplet/particle-vapor The present numerical study is subjected to the following simplifications and 9 assumptions: (1) A small region of the airway system, i.e., the mouth-to throat airway, is selected and 11 simplified; (2) The mucus-tissue layer is assumed to have a uniform thickness, and heat transfer 13 related properties are assumed to be the same as water; and 14 (3) The initial droplet components only include water, ethanol, NaCl and fluorescein. 15 In light of the limitations of this study, future work will: (1) Use larger and more realistic airway geometry to model the airflow, heat transfer 17 and water vapor mass transfer in the airway; 18 (2) Consider actual drug particle/droplet components and their hygroscopicity to 19 evaluate the deposition efficiency of the drug particle/droplet in lung; and 20 (3) Perform transient simulation to include the breathing waveform, and investigate the effect of the aerosol release time on the deposition efficiencies of the hygroscopic 1 droplets/particles. 13 where the constants 1 a , 2 a and 3 a are determined by the droplet/particle Reynolds The energy balance equation of the mucus-tissue layer can be given by: where the source term m S only existed in the mucus layer. m S is defined as: where A m is the surface area of the mucus, T m is the temperature of the mucus surface, 6 T f is the temperature of the air, L w is the latent heat of water, and J w is the mass flux of 7 water at the air-mucus interface. The two terms on the right-hand side of Eq. (S-12) 8 are the convective heat transfer term and evaporation heat term. 9 A summary of the parameter values used for the simulations is provided in Table S1 . 10 Table S1 . Inlet, boundary, and droplet conditions applied for the simulations 11 Viscosity of the air at inlet [kg/m·s] 1.786×10 -5 On the effect of anisotropy on the turbulent dispersion 13 and deposition of small particles Evaporation and movement of fine droplets in non-uniform temperature and 16 humidity field A numerical study of heat 18 and water vapor transfer in mdct-based human airway models Numerical 21 investigation of motion of sulfuric and hydrochloric droplets with phase 22 change in free-falling process Airflow and deposition of nano-particles in a human nasal 25 cavity Experimental measurement and 27 numerical study of particle deposition in highly idealized mouth-throat models Particle deposition measurements and 30 numerical simulation in a highly idealized mouth-throat Transient airflow structures and particle 33 transport in a sequentially branching lung airway model Species heat and mass transfer in a human upper 36 airway model Cyclic micron-size particle inhalation 38 and deposition in a triple bifurcation lung airway model Slip correction measurements of spherical solid 7 aerosol particles in an improved Millikan apparatus Numerical investigation of 10 the interaction, transport and deposition of multicomponent droplets in a 11 simple mouth-throat model Effects of thermal 13 airflow and mucus-layer interaction on hygroscopic droplet deposition in a 14 simple mouth-throat model Study on gas/solid flow in 16 an obstructed pulmonary airway with transient flow based on CFD-DPM Sci Improved numerical simulation 12 of aerosol deposition in an idealized mouth-throat An investigation of particle trajectories in 14 two-phase flow systems Size-change and deposition of 16 conventional and composite cigarette smoke particles during inhalation in a 17 subject-specific airway model Cyclic micron-size particle inhalation 19 and deposition in a triple bifurcation lung airway model ρ is the droplet/particle density. The energy balance of the droplet/particle is given by: