Two-dimensional Simulation of Mass Transfer and Nano-Particle Deposition of Cigarette Smoke in a Human Airway

1. Introduction

2. Methods

2.1 Background information

A key parameter to asses the effects of inhalated cigarette smoke is the particle deposition in lung airway. It is costly and arduous the comprehensive particle deposition characterization in the total (upper and lower) airway using experimental methods. Therefore, the particle motion numerical simulation in the airway is an efficient method to confront with this problem, and it could indicate the patterns of particle deposition in the whole lung airway. The upper and lower airways are the divisions of the total lung. The model of airway includes of oral cavity (mouth and palate), pharynx, larynx, trachea, B1, B2 and B3. There are resemblance between the human airway model dimensions with a human cast reported by Zhang et al. [18]. As indicated in Figure 1, the glottis to the first carina length and the mouth to the trachea length were near to 14 and 12 cm, respectively [18-19]. Furthermore, 1.60 cm was the trachea diameter. In this model, the airway wall is persumed as smooth and rigid. The cartilaginous rings impacts are not considered appearing in the human airway.

2.2 Governing equations in human airway

In the total lung airway system, some doubts existed for the transition of turbulent flow on the flow rate critical Reynolds number. The approximation of turbulent flow for a flow rate more than 12 L.min^-1 was reported by Moghadas, et al. seeming rational particularly for track and field as the vibrant activities [20-22]. The Navier-Stokes equations and the continuity equation are dominant equations for the oscillating two-dimensional airflow. Zhang and Kleinstreuer [10] illustrated that it is decent for such internal laminar-to-turbulent flows. Generally, the equations of transport in tensor notation shows indirectly the double-index summation convention [10].

Figure 1. The model of airway based on the Zhang et al. model. [18, 7].

Continuity equation:

                                                                    (1)

Momentum equation:

        (2)

Turbulent kinetic energy (k) equation:

  (3)

Pseudo-vorticity  equation:

  (4)

For simplicity, summation sign is used with i, j =1, 2 where the x, y components of the velocity and the spatial coordinate vector are u₁, u₂ and x₁, x₂, respectively. Time, density, pressure, kinetic molecular viscosity of the cigarette smoke, Reynolds stress tensor, turbulence kinetic energy, and dissipation per unit turbulence kinetic energy are the t, , p, , , k and , respectively. The turbulent viscosity,  is given as , and the function  is defined as  with  while  is the dynamic molecular viscosity ; , , , , , and  are turbulence constants, i.e., , , , , .

The primary values in inlet of k and  are calculated by [10]:

  ,                            (5)

Where the turbulence intensity and the radius of inlet tube are I and R, respectively. The convection–diffusion mass transfer equation of nano-particles, where the dominant transfer mechanisms are Brownian motion and turbulent dispersion, can be written as

                       (6)

Where  is the molecular diffusivity of the cigarette smoke. The diffusivity in cigarette smoke is not very significant from compound to compound [17]. Y_w=0 is the boundary condition at the wall regarding that a perfect sink for aerosols or vapours upon touch is the airway wall. This idea is rational for fast gas-wall reaction kinetics, or vapours of high solubility and reactivity, as well as appropriate for estimating the maximum deposition of vapours in the airways. The aerosol diffusion coefficient is calculated as follows [23, 24]:

                                 (7)

Where T is the cigarette smoke temperature, k_B is the Boltzmann constant , d_p is the particle diameter and C_slip is the Cunningham slip correction factor [25]:

   (8)

where  is the air mean free path. The nano-particles local wall mass flux could be calculated as [10]

                                      (9)

Where the area of local wall cell (i) is A_i, and the direction normal to the wall is n. The local deposition fraction (DF) of nano-particles, defining as the ratio of local wall mass flux to the inlet mass flux, expressed as

              (10)

and the regional DF can be determined as

 (11)

Where the number of wall cells in one particular airway area is n_w, e.g., oral airway, first airway bifurcation, etc., as well as the flow rate and mass fraction at the mouth are Q_in and Y_in, respectively. The regional deposition fraction co uld be calculated based on the Fick’s law [7]. The model are used for a range of flow rates from 30 L/min to 80 L/min, corresponding to inlet mean velocities of 0.9417 m/s to 2.354 m/s, particle inlet velocities from 5.1 m/s to 8.4 m/s, and varying particle diameters from 1 nm to 100 nm. T_wall = 310 K. Also boundary condition no slip at the wall and Pharynx and larynx wall are rigid.

3.1    Characteristics of velocity structures

Selected cross sections of the 1-2 models, Profile flows, in the mouth and trachea, are displayed in figures 2a that velocity is fully develop, and 2b figures show the velocity profile for mouth and trachea at an inhalation flow rate of 60 L/min. The glottis, one of the cross-sectional areas is less than other ones of the human airway. Thus, the difference of cross-sectional areas results in the resistance against increment in various flow rates. This resistance created against the air flow decreases the mean velocity. As shown in theses figures, the central part of velocity profile is higher than the edges. The velocity of flow varies from a minimum on walls to a maximum in mouth and trachea section.

Fig. 2. The changes velocity profile for (a) mouth and (b) trachea inhalation flow rate of 60 L/min

3.2    Nano-particle deposition

The deposition fraction versus the nano-particle diameters for different rates of cigarette smoking is depicted in the Figure 3. As shown, the deposition of particle decreases with the diameter increment. The concentration of particle in cigarette smoke is totally high (~10¹² particles in one cigarette). Moreover, the hygroscopic nature of the smoke droplets leads to rapid changes in diameter of particle through condensation and coagulation [26]. Gravitational sedimentation, inertial impaction and Brownian motion (diffusion) are the three basic mechanisms that influence on the behaviour of particles in cigarette smoke within the respiratory tract. ‘Aerodynamic’ effects such as sedimentation and impaction are the important ones. They increase with size increment. Although aerodynamic impacts are negligible for particles of significantly small size, thermodynamic effects are negligible for large particles. The smoke particle deposition lies on the particle size which may vary because of the high relative-humidity condition in the respiratory tract. Although the diameter of the smoke particles is small, 60–80% efficiencies of smoke deposition in the lung have been reported [27].

Upon the high flow rate, the nano-particles are interlocked. Because of the weight increment, they deposit on airway walls. Thus, through flow rate increment, the deposition of particle decreases. Accordingly, the inhalation of cigarette smoke nano-particles in low-flow rate could results in more damage in the lung airway. The results of particle deposition in different flow rate are in good agreement with the simulation results reported by Zang and Kleinsrteuer [17].

Fig. 3. Deposition fractions of particle under different flow rates

Figure 4 indicates the selected four vapour deposition fractions of cigarette smoke in the human airways, which incorporate the representative wall absorption conditions. In this case, steady puffing with inspiratory is obtained in different flow rates from 30 to 80 L/min. During puffing (3 sec), the soft palate (or glottis) is closed for most smokers; however, some smokers, directly, inhale the aerosols in to the lung [28]. In this study, steady puffing inhalation refers to the latter (presumably worst) case, so that the aerosols are assumed to be inhaled directly in to the lung. Clearly, the impact of airway wall absorption (or vapor solubility) can be vital for vapor deposition in human airways. The deposition fractions versus the diameter of nano-particle for various cigarette smoking rates are indicated in the Figure 3. As indicated, the deposition of particle decreases with the diameter increment. The nano-particles are interlocked under the flow rates of high values. Moreover, they deposit on walls of the airway because of the weight increment. On the other hand, the deposition of particle decreases with increasing the flow rate. Consequently, the inhalation of harmful nano-particles in the flow rates of low values could result in more damage in the lung airway. As shown in figure 4, the vapor deposition fraction butadiene vapor and carbon monoxide depositions are much lower than those of acrolein and acetaldehyde. Moreover, acrolein and acetaldehyde fully deposit in the upper airways of human from the mouth to generation B3. The deposition of butadiene vapor and carbon monoxide is very low in the upper airways. It is possible that the butadiene vapor and carbon monoxide depositions are much lower than those of acrolein and acetaldehyde.

Fig.4. Vapor deposition fraction in

the human airway

Fig.5. Vapour deposition fractions of the regions in the airway model

Fig. 6. The concentration distribution of nano-particles (dp = 5 nm) in the airway model during cyclic inhalation for cigarette smoke vapors, rate: Q_in = 60 l/min, Y_in = 0.8.

Fig.7. The changes of Sh number
versus Re number.

The local deposition fractions (DFs) for vapors of acetaldehyde and acrolein are shown in Figure 5. The regional deposition for acrolein and acetaldehyde might gradually decrease from the cavity of mouth to bifurcation B3 because of the heavy deposition, leading to lower vapor concentrations at the each inlet of downstream regions. Furthermore, the different airway region surface areas lead to different values of vapor deposition. For instance, while Trachea has the lowest deposition, it receives the highest vapor deposition in the Larvnx. The different airway geometries, surface areas, local flow rates and concentrations of inlet vapor are influential and the deposition fractions in individual bifurcations vary as well. Carbon monoxide and butadiene vapor deposition is very low in the airway model from the oral cavity to generation B3.

The concentration distribution of nano-particles (dp = 5 nm) in the upper airway model for the cigarette smoke vapors flow rate of 60 L/min during cyclic inhalation have been indicated in the figure 6. As indicated, the airway edges concentration profile is higher than airway center. Because of the less soluble vapors such as cigarette smoke the wall concentration would be greater than zero so that mass transport in center and in airways must be considered simultaneously when simulating vapor uptake. The most concentration distribution is in the palate, pharynx and larynx section. Because of the nano-particle deposition in the airway length, this distribution of concentration reduces slowly. The mass transfer occurs often in the mouth and palate (oral airway). Therefore, the inhalation of cigarette smoke vapors creates the more damage on the oral airway and B3 section.

The impacts of Reynolds number on Sherwood number in simulation data for cigarette smoke have been indicated in the figure 7. The Sh number, representing the ratio of convective to diffusive mass transport, can be expressed as:

                                               (12)

Where the airway segment characteristic diameter is D. Thus, obtaining h_m, the respiratory coefficient of mass transfer is vital in forecasting the vapours regional deposition accurately. The coefficient of mass transfer in terms of non-dimensional Sh number is a function of Schmidt number (Sc) and Re number, traditionally. It was developed a set of generalized Sh=f (Re, Sc) equations in respect to a model of human airway for flow rates of normal inspiratory by Zhang & Kleinstreuer [29]. However, they were partly idealized. It is noteworthy that these correlations are for constant flows and the values of realistic deposition could be deduced based on constant matching flows with corrections of time delay. The correlation curves of the Sh-Re_local have been indicated in the figure 7. They were simulated for cigarette smoke vapor. Moreover, the convection contribution impact (Re-number) on mass transfer could be observed in the figure 7.

.The diameter of local equivalent computed is  as , where average cross-sectional area is , the equivalent diameter of trachea is , and , where  is the local flow rate at peak inspiration. Figure 7 shows the effects of Re number on Sh number in simulation data for cigarette smoke. The Re number increment results to increase in the nano-particles turbulent motion, on the other hand, the stronger the convection (Re numbers) is, the higher the mass transfer. Furthermore, the flow structures and airway geometric features influence a lot on cigarette smoke mass transport. Particularly, due to the interactions among local geometric features, flow turbulence and upstream deposition, the Sh=Sh (Re) relationship may be different at various airway areas. The occurrence of upstream turbulent flows may affect both the inlet velocity and particle profiles which enter the bifurcation and could increase deposition within the model.

3. Conclusion

The mass transfer and deposition of cigarette smoke inside the human airway are investigated by the finite element method in this research. That is to say, the mass transfer and deposition of four selected tobacco-smoke vapors, acetaldehyde, acrolein, 1, 3-butadiene and carbon monoxide, in a human airway model under puffing as well as constant flow conditions have been simulated. The deposition of butadiene vapor and carbon monoxide gas is negligible in comparison to acrolein and acetaldehyde in the total human airways from mouth to generation B3. The deposition of particle decreased with increasing the diameter illustrated by the results. Moreover, the particle deposition decreased with the flowrate increment. The concentration profile of the airway edges was higher than  the airway center. This distribution of concentration reduced slowly because of the nano-particle deposition in airway length apart from B3. Moreover, the results illustrate that deposition of cigarette smoking vapor in the upper airway is more than the lower airway. The results are likely to enhance assessing the level of cigarette-smoke damage in the total lung airway.