Journal of Molecular Liquids 209 (2015) 121–133
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CFD simulation of airflow behavior and particle transport and deposition in different breathing conditions through the realistic model of human airways M. Rahimi-Gorji ⁎, O. Pourmehran, M. Gorji-Bandpy, T.B. Gorji Babol Noshirvani University of Technology, Mechanical Engineering Department, Babol, Mazandaran, Iran
a r t i c l e
i n f o
Article history: Received 17 March 2015 Received in revised form 13 May 2015 Accepted 15 May 2015 Available online xxxx Keywords: Airflow behavior Particle deposition Breathing conditions Realistic geometry CFD simulation
a b s t r a c t In this work, the airflow behavior and particle transport and deposition in different breathing conditions such as light breathing condition (15 L/min), normal breathing condition (30 L/min) and heavy breathing condition (60 L/min) are investigated. The realistic geometry data was reconstructed from CT-scan images of the human airways with 0.5 mm thickness of slices. The CT-scan images (DICOM files) are imported in the 3D-DOCTOR software and all slices were segmented. Then, the output has been imported in CATIA-V5 software. Finally, face, volume, mesh and extension tubes at inlet and outlets were created and then imported into ANSYS FLUENT 15. The Lagrangian approach is used to evaluating the transport and deposition of inhaled micro-particles. The L and for dp = 1 μm, when presented results showed that for dp = 5 μm and 10μm, when flow rate ¼ 30 min L L , the particle deposition fraction have maximum amount. For flow rate ¼ 15 min and ¼ flow rate ¼ 15 min L L , the maximum deposition occurs in the zone number 1 and for flow rate ¼ 60 min occurs in the zone 30 min L which would be acceptnumber 4. Also, the maximum pressure distribution happens when flow rate ¼ 60 min able. According to the results, the particles tended to go to the right branch and the minimum number of particles crossed the zone numbers 6 and 11. © 2015 Elsevier B.V. All rights reserved.
1. Introduction It is common for people to behold particles in the air and sense air entering into human bodies through breathing. Human lungs are one of the body's important and largest organs. Their function is gas exchange, delivering oxygen and removing wasted carbon dioxide. Air goes into the body through nostrils and mouth into trachea, which is then divided into left and right primary bronchi. The bronchus branch out into secondary bronchi and then each subdivides into tertiary bronchi and so on, reducing diameter throughout the structure until the respiratory bronchioles which scatter air to the alveoli. Today, drug delivery to the specified location is concerned. In fact, human health by controlling particles that enter human body is considered. Aerosol drug therapy, which mainly delivers the drug location of interest, is a quickly advancing field of research [1]. With the recent advances in analysis of micro- and nanoparticles, drug delivery has indicated great potential for pulmonary application, not only for local therapy but for systemic therapy as well. ⁎ Corresponding author at: Babol Noshirvani University of Technology, P.O. Box 484, Babol, Iran. E-mail addresses:
[email protected] (M. Rahimi-Gorji),
[email protected] (M. Gorji-Bandpy).
http://dx.doi.org/10.1016/j.molliq.2015.05.031 0167-7322/© 2015 Elsevier B.V. All rights reserved.
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Inhaling through the mouth, therapeutic drugs have their site of action in the large and/or small conducting airways. Inhalers designed for the delivery of therapeutic factors maximize the respiratory deposition as inhalable aerosol particles. Although, particles may deposit in another place in the respiratory tract, mainly in the upper respiratory tract or peripheral airspaces resulting in undesirable side effects and waste. Deposition of these particles in the lung periphery furthermore is being futile in this region. The amount and location of particle deposition in the respiratory tract depends on both the particle size and the human's flow patterns during inhalation [2,3]. Computational Fluid Dynamics (CFD) has been applied to characterize the fluid flow in human airway models. CFD has obtained significant interest in both the medical and engineering community because of its non-invasive character. It can predict the fluid flow characteristics when one or multiple input flow variables are changed. In addition, it permits investigation of different flow variables and fluid forces to a level of fine detail. Simple geometric configuration led to CFD simulations and gave a first vision into particle deposition and flow patterns in the airways [4–6]. Bala'sha'zy [7] investigated a wide range of submicron and micron-size particles in bifurcating tubes numerically for computing trajectories. The fluid flow and particle deposition patterns in an asymmetric single bifurcation are simulated by Gatlin et al. [8].
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Nomenclature x y z ui ug up Rep ρ ρp dp CD DE p
x coordinate y coordinate z coordinate mean velocity in tensor notation (m/s) fluid (air) velocity (m/s) particle velocity (m/s) particle Reynolds number fluid density (kg/m3) particle density (kg/m3) particle diameter (m) Drag coefficient deposition efficiency mean static pressure (pa)
Greek symbols υ kinetic molecular viscosity (μ/ρ) kinetic eddy viscosity (μT/ρ) υT Reynolds stress tensor τij μ kinetic viscosity α1, α2, α3 drag constants
Although, Farag et al. [9,10], utilized a similar geometric configuration, experimentally behold flow separation in the bifurcation region under similar flow conditions. Thus bifurcation models that mentioned previously may not prepare a realistic formation of deposition in respiratory airways. Developed models have been either symmetric [11,12] or asymmetric [13]. However, these general models do not include the irregularities that every lung could have. Some researchers [14–16] have concentrated on patientspecific lung geometries and their results are more relevant to the clinical results. Longest et al. lately demonstrated a CFD-based stochastic individual path modeling moves towards to guess the delivery of pharmaceutical aerosols all over the tracheobronchial airways [17,18]. Some new characteristics of the airflow and particle deposition in complex, multi-generation healthy and diseased airways were reported such as Ref [19]. An important part of this research is considering a realistic geometry model of the human airways. Most previously proposed models involved a simplified geometry model such as Wieble model [20] or Horsfield model [21] etc. This missing information related to the three-dimensional (3D) disposition of branches had to be detected to construct a realistic model of the bronchial tree. Recent studies have used airway models that were reconstructed from magnetic resonance (MR) or computed tomography (CT) imaging data [22,23]. Fleming et al. [24] have applied 3-D radionuclide imaging with CT scanning of the airways subject to better report the deposition locations of aerosols in the respiratory system. Golshahi et al. [25] obtained interesting results with measurements of deposition of micrometer-sized particles (0.5–5.3 mm) in replicas of older children (4–14 years old) to develop correlations including geometric dimensions of airways and breathing patterns as a predictive tool for future potential improvements in environmental and pharmaceutical standards. There are fundamentally two various approaches in the analysis of the phenomenon of particles dispersed in the air flow in the respiratory system such as Euler–Lagrange method and Euler–Euler method [26]. In the Euler–Lagrange method, a particle trajectory is computed by solving equations of the motion for each particle in the Lagrangian approach [27,28]. On the other side, in the Euler–Euler method, a particle concentration distribution of the bearer fluid is calculated [29,30]. Generally, interactions between particles can be classified, based on particle
volume fraction (PVF). For PVF b 10−6, particle motion is affected by continuous phase properties while basically there is no feedback from the dispersed phase. This class is known as one-way coupling. For 10−6 b PVF b 10−3, feedback of the dispersed phase on the properties of the continuous phase fluid dynamics must also be taken into account, this class is called two-way coupling. When PVF N 10−3, a dense flow is characterized that this class is known as four-way coupling and it should be considered particle–particle interactions [31,32]. In this work, the realistic geometry data was reconstructed from CTscan images of the human airways. It can be illation from the mentioned references that there is almost no literature available in which realistic human respiratory tract model was applied for the study of the effects of the different breathing conditions on airflow behavior and particle transport and deposition. The main aim of this research is investigating the airflow behavior and particle deposition fraction in different breathing conditions such as light breathing condition (15 L/min), normal breathing condition (30 L/min) and heavy breathing condition (60 L/min). According to the results, by realizing the effects of different breathing conditions on particle deposition fraction, a deep understanding of air-particle dynamics in the tracheobronchial airway is obtained and it can be very useful for medication and drug delivery experts and committee.
Fig. 1. Flowchart of research process.
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Fig. 2. The overarching theme of research.
Fig. 3. CT-scan images of present study. Red circles indicate locations of central airway stents. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 4. (a) Three dimensional reconstructed geometry from CT-scan images. (b) Realistic 3D airway model (extended inlet and outlets with CATIA-V5 software). (c) Divided zones of geometry.
Fig. 5. 3D volume mesh generation.
Fig. 6. Comparison of the particle deposition fraction between present work's results and Nowak et al.'s work [12].
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Fig. 8. Total deposition fraction of different zones for different flow rate with dp = 5 μm.
2. Methodology 2.1. Three dimensional reconstruction of human respiratory system from CT-scan images The geometry of the human airway was obtained from computed tomography (CT) scan of a healthy 63 years old, non-smoking male. The CT-scan was started from the inlet of trachea and extended to second generation. The slice thicknesses of CT-scan images were 0.5 mm that the total 373 slices were considered for construction from the inlet of trachea to second generation (G0–G2). The CT-scan images (DICOM files) are imported in the 3D-DOCTOR software which is a strong software in field of image processing. Then, all slices segmented and exported the constructed model to .STL (Standard Tessellation Language) format. The output is prepared for importing in CATIA-V5 software for converting the .STL format to CATPART format, then has been converted to IGES format. Finally, face, volume, mesh and extension tubes at inlet and outlets were created using ANSYS-Workbench 15 and a mesh file was produced, which was then read into ANSYS FLUENT 15. Figs. 1 and 2 show a flowchart for CFD simulations of human airways and the overarching theme of research respectively.
Fig. 7. 3D view bar for deposition fraction of different zones for three particle diameter L L L with (a) flow rate ¼ 15 min , (b) flow rate ¼ 30 min , and flow rate ¼ 60 min . Fig. 9. Total deposition fraction of different flow rate with different particle diameter.
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2.2. Construction of the computational model
Momentum equations:
Fig. 3 depicts four slices of CT-scan images of present study which red circles indicate locations of central airway stents. The reconstructed model of the human airway is displayed in Fig. (4-a) which including from the trachea down to the G2. To prevent any reverse flow, the inlet and outlets were extended upstream and downstream respectively. Fig. (4-b) and (c) show the realistic 3D model for the total volume of the airway (extended inlet and outlets with CATIA-V5 software) and divided zones of geometry, respectively. As realistic human respiratory tract are irregular in shape, an unstructured tri/tetrahedral hybrid volume mesh was created inside the airway model that is depicted in Fig. 5. The cell quantity in the computational model is about 1,800,000 that obtained after the grid independency test for four different grid sizes (about 790,000, 12,500,000, 1,800,000, and 2,100,000 cells). It was observed that the computed results become almost independent of the grid size beyond 1,800,000 cells. After meshing, the CFD software package Fluent (ANSYS-FLUENT 15) was applied to solve the flow governing equations with finite volume method (FVM) on an arbitrarily shaped flow area with suitable boundary conditions. The steady-state solution of the flow field was assumed to have converged when the residuals decreased to less than 10− 6. Air was considered incompressible and Newtonian fluid with constant density ρ, viscosity μ and fluid static pressure p. The governing equations for the airflow in the respiratory tract are given as follows [33]:
" !# ∂ui ∂u 1 ∂p ∂ ∂ui ∂u j þ ðυ þ υT Þ þ þ uj i ¼ − ρ ∂xi ∂x j ∂t ∂x j ∂x j ∂xi
Continuity equation:
∂ui ¼ 0; ∂xi
ui and uj (i, j = 1, 2, 3) are the velocity components in x, y and z directions. In this study, different flow rate are assumed for inspiratory pattern. In fact, three conditions of breathing are considered such light breathing condition (15 L/min), normal breathing condition (30 L/min) and heavy breathing condition (60 L/min). Boundary conditions for fluid flow in this study are mass flow rate for inlet, pressure outlet for outlets and no slip condition for walls. The problem was calculated steady using k–ω SST turbulence model. For the pressure–velocity coupling, the SIMPLEC algorithm was used. Different terms in the transport equations were discretized using the second-order upwind numerical scheme. The governing equations of k–ω turbulence model are written as follows: Turbulent kinetic energy (k) equation:
" # ∂k ∂k ∂u ∂ ∂k ¼ τi j i þ ðυ þ σ k υT Þ þ uj ∂t ∂x j ∂x j ∂x j ∂x j
ð1Þ
Fig. 10. Cross sectional views of the velocity magnitude contour of airways for dp = 5 μm L L L with (a) 15 min , (b) 30 min and (c) 60 min .
ð2Þ
L L L Fig. 11. Contours of pressure distribution for (a) 15 min , (b) 30 min and (c) 60 min .
ð3Þ
M. Rahimi-Gorji et al. / Journal of Molecular Liquids 209 (2015) 121–133
Pseudo-vorticity (x) equation: " # ∂ω ∂ω ω ∂u ∂ ∂ω : ¼ α τ i j i −βω2 þ ðυ þ σ ω υT Þ þ uj k ∂t ∂x j ∂x j ∂x j ∂x j
ð4Þ
Where the turbulent viscosity is given as υT = Cμfμk/ω, and the function fμ is defined as fμ = exp[−3.4/(1 + RT/50)2] with RT = ρk/(μω). The other coefficients in the above equations are: C μ ¼ 0:09;
α ¼ 0:555;
β ¼ 0:8333;
β ¼ 1;
σ k ¼ σ ω ¼ 0:5:
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on the convective/radioactive heat and mass transfer from the particle, using the local continuous phase conditions as the particle moves through the flow. Numerous applications using DPM model are particle separation and classification, spray drying, aerosol dispersion, bubble sparging of liquids, liquid fuel and coal combustion. The particle trajectory was computed through the equation of the balance of forces acting on that particle. The equation describing the particle velocity, in the Lagrange formulation, for a Cartesian coordinate system has the form g x ρp −ρ ∂up ; ¼ F D u−up þ ρp ∂t
ð5Þ
where FD(u − up) is the drag force per unit particle mass (acceleration due to drag) and
2.3. Discrete phase model (DPM) The discrete phase model (DPM) can be included in the ANSYS FLUENT model by defining the initial position, velocity, size and temperature of individual particles. These initial conditions along with the physical properties of the discrete phase are utilized to initiate trajectory and heat/mass transfer calculations. The trajectory and heat/mass transfer calculations are based on the force balance on the particle and
FD ¼
18μ C D Rer : 2 24
ρp dp
ð6Þ
Here, u is the fluid velocity, up is the particle velocity, μ is the dynamic viscosity of the fluid, ρ is the fluid density, ρp is the density of the particle
L L L Fig. 12. Streamlines of airflow in airways for (a) 15 min , (b) 30 min and (c) 60 min .
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and dp is the particle diameter. Rer is the relative Reynolds number, which is defined as ρdp up −u : Rer ¼ μ
ð7Þ
The drag coefficient, CD is obtained using the following formula: C D ¼ a1 þ
a2 a3 þ ; Rer Re2r
ð8Þ
where ai are constants that employ to smooth spherical particles over several ranges of Re given by Morsi and Alexander [34]. Eq. (3) is the particle trajectory equation. It has been solved by the same commercial software. ANSYS-FLUENT 15 guesses the trajectory of discrete phase particles by integrating the force balance on each particle, which is written in a Lagrangian reference frame. After each
iteration for each particle, the information about position, time, and three components of velocity as well as the speed with which the particles cross the control volume boundaries was obtained. Particles of specific sizes were injected in a uniform distribution at the inlet face of the computation domain, and tracked through the geometry until they met one of three fates: (1) trapping on a surface by collision, (2) escape from the domain through one of the outlet faces, or (3) continued suspension in the flow. The fate of the particles were then recorded and summarized as a particle history file. One-way coupling is assumed between the air and particle flow fields and the interaction between particles is also neglected because the particle flow is dilute [31,32]. In this work, the particle characteristics include: kg • Particle density: ρp ¼ 1000 m 3 , spherical particles. −9 • Mass flow rate: m¼ 4:2097 10−11 kg s , 5:2622 10 −8 kg 10 s.
L L L Fig. 13. Particles situation at t = 0.01 s after start injection with dp = 5 μm for (a) m¼ 15 min , (b) m¼ 30 min and (c) m¼ 60 min .
kg s
and 4:2097
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• Particle diameter (dp): 1, 5, and 10 μm. • Velocity: the same as inlet velocity.
conditions such as light breathing condition (15
Ns 1:8 10−5 m 2) and the flow regime is consider steady and turbulent. The deposition fraction (DF) is defined as
Number of deposited particles 100: Number of injected particles
L min),
normal breath-
L min)
kg Also, the air properties are assumed constant (ρair ¼ 1:2 m 3 andμ air ¼
DFð%Þ ¼
129
ð9Þ
3. Results and discussion The main aim of this work is investigating the airflow behavior and particle transport and deposition fraction in different breathing
L ing condition (30 and heavy breathing condition (60 min ). As early mentioned, one of the most important features of this research is using realistic geometry that reconstructed from CT-scan images. Fig. 6 shows the comparison of the particle deposition fraction between present work and Nowak et al. [12] work results. They studied particle deposition in a geometry based on the Weibel lung L model. In their steady simulations, the used flow rate was 28:3 min . It is obvious that the results of present work have good agreement with Nowak et al.'s results and little difference between these are due to the different flow rate (30 and 28.3 L/min). Fig. 7 depicts the deposition fraction in different zones for flow L L L rate ¼ 15 min (7-a), 30 min (7-b) and 60 min (7-c). As can be seen in this figure, independent of the flow rate, the maximum deposition happens
for dp = 10 μm. For flow rate ¼ 15
L min
L and 30 min , the maximum
L L L Fig. 14. Particles situation at t = 0.03 s after start injection with dp = 5 μm for (a) m¼ 15 min , (b) m¼ 30 min and (c) m¼ 60 min .
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L deposition occurs in the zone number 1 and for flow rate ¼ 60 min , it occurs in the zone number 4. For various flow rate such as 15 , 30 and L 60 min , the maximum deposition fraction of them are 6.5 %, 26.4 % and 7.94 % respectively (dp = 10 μm). The location of minimum deposition was not precisely predictable and didn't follow a specific pattern. It is L and dp = 1μm, deposition fraction is obvious, for flow rate ¼ 60 min zero due to large value of flow velocity and the small value of particle diameter. Also according to this figure, when dp = 1 μm, the maximum L in location of zone number 4 deposition fraction is for flow rate ¼ 15 min and when dp = 5μm and 10μm, the maximum deposition fraction is for L in location of zone number 1. Fig. 8 depicts the total flow rate ¼ 30 min deposition fraction of different zones for different flow rate with dp = 5 μm that clarified the illustrations of Fig. 7. Next, Fig. 9 demonstrates the total deposition fraction of different flow rate with different particle diameters by graph. As can be seen in this figure, all of the explanations of early figures (Figs. 7 and 8) could be corrected and acceptable. In fact, this figure illustrated that for dp = 5 μm and 10 μm, when flow rate ¼
L L 30 min and for dp = 1 μm, when flow rate ¼ 15 min , the particle deposition fraction is maximum. Fig. 10 shows the cross sectional views of the velocity magnitude L L contour of airways for flow rate ¼ 15 min (10-a), 30 min (10-b) and L 60 min (10-c). Because of the realistic geometry, cross sectional of different parts of the airways aren't constant and as a result, some parts are narrower. For this reason, the velocity magnitude in smaller crosssectional area is more than other locations. Contours of pressure distribution for different flow rate are displayed in Fig. 11. According to these contours, the maximum pressure distribution occurs when flow rate ¼ L 60 min that it is logical. Fig. 12 shows the streamlines of airflow in airways. The presented figure depicted that in some places of airways, vortices have been formed that causing more turbulence intensity in the flow. This phenomena happens due to the realistic human respiratory tracts are irregular in shape. Based on the observation that emerged from the figure, it can be said in first bifurcation, for all three cases L ) more fluid flows to the right branch. (flow rate = 15, 30 and 60 min
L L L Fig. 15. Particles situation at t = 0.05 s after start injection with dp = 5 μm for (a) m¼ 15 min , (b) m¼ 30 min and (c) m¼ 60 min .
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In second generation in right branch, for flow rate = 15 and 30
L min
more
fluid flows to the left branch of this bifurcation, but for flow rate ¼ 60 more fluid flows to the right branch of this (zone number 11). In second L generation in left branch, for flow rate = 15 and30 min more fluid flows to
L min,
the right side of this bifurcation (zone number 7), but for flow rate ¼ L 60 min , more fluid flows to the left side of this (zone number 6). Figs. 13, 14, 15 and 16 depict the particle situation at different time after injecting. According to these figures, the particles tended to go to the right branch. As can be seen in Fig. 16, the minimum number of particles crossed the zone numbers 6 and 11. Fig. 17 demonstrates the L particle situation when t = 0.4 s and dp = 5 μm for flow rate ¼ 15 min L L (17-a), flow rate ¼ 30 min (17-b) and flow rate ¼ 60 min (17-c). In fact, the total period of particle injection is 0.805 s, but this figure shows the particle position at 0.4 s after the start of injection. As can be seen L in this figure, when flow rate ¼ 15 min , the maximum deposition fraction occurs in locations of zone numbers 1 and 3. In this case, the particles L that trapped to walls were about 4.3 %. Also, when flow rate ¼ 30 min
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L and 60 min , the maximum deposition fraction occurs in location of zone number 1. In these two cases, the total trapped particles were about 8.5 % and 5.2 %, respectively. In fact, this figure confirmed the previous explanations and figures about the particle deposition.
4. Conclusion Investigation of the airflow behavior and particle transport and deposition fraction in three breathing condition such as light breathing condition (15 L/min), normal breathing condition (30 L/min) and heavy breathing condition (60 L/min) has been performed. The realistic geometry data was reconstructed from a CT-scan images of the human airways and imported into CFD simulation software. As can be seen in figures, independent of the flow rate, the maximum deposition occurs for dp = 10 μm. In fact, According to the results, for dp = 5 μm and L L 10 μm, when m¼ 30 min and for dp = 1 μm, when flow rate ¼ 15 min ,
the particle deposition fraction have maximum amount. For flow rate ¼ 15
L L min and 30 min, the maximum deposition occurs in the zone number 1
L L L Fig. 16. Particles situation at t = 0.8 second after start injection with dp = 5 μm for (a) m¼ 15 min , (b) m¼ 30 min and (c) m¼ 60 min .
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L L L Fig. 17. Particles situation when t = 0.4 s with dp = 5 μm for (a) m¼ 15 min , (b) m¼ 30 min and (c) m¼ 60 min .
and for flow rate ¼ 60
L min
occurs in the zone number 4. Also, the max-
L imum pressure distribution happens when flow rate ¼ 60 min that it is acceptable. The presented results showed that, the particles tended to go to the right branch and the minimum number of particles crossed the zone numbers 6 and 11. Also, at 0.4 s after injecting for the states L L L of flow rate ¼ 15 min , 30 min and 60 min with dp = 5 μm, the particles that trapped to the walls were about 4.3%, 8.5% and 5.2%, respectively.
Conflict of interest The authors declare that they have no conflict of interest.
Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.molliq.2015.05.031. References [1] [2] [3] [4] [5] [6] [7] [8]
Acknowledgments [9]
The authors would like to thank Mr Hosseinzadeh, expert at Sari Parto Mazand Medical Imaging Center, for providing us with the CTscan images that were used to generate the airways model. Also, we thank the reviewers for their useful and beneficial comments that improved this paper.
[10] [11] [12] [13] [14]
F.Q. Hu, L. Wei, Z. Zhou, Y.L. Ran, Z. Li, M.Y. Gao, Adv. Mater. 18 (2006) 2553–2556. N. Durcan, C. Murphy, S.A. Cryan, Mol. Pharm. 5 (2008) 559–566. T.R. Flotte, B.L. Laube, Chest 120 (2001) 124S–131S. I. Balashazy, W. Hofmann, J. Aerosol Sci. 26 (1995) 273–292. I. Balashazy, W. Hofmann, J. Aerosol Sci. 24 (1993) 745–772. Z. Zhang, C. Kleinstreuer, C.S. Kim, J. Aerosol Sci. 33 (2002) 257–281. I. Bala'sha'zy, J. Comput. Phys. 110 (1994) 11–22. B. Gatlin, C. Cuicchi, J. Hammersley, D. Olson, R. Reddy, G. Burnside, ASME, vol. FEDSM971997. 1–6 (Vancouver, British Columbia, Canada). A. Farag, J. Hammersley, D. Olson, T. Ng, ASME, vol. FEDSM981998. 1–8 (Washington, DC). A. Farag, T. Ng, J. Hammersley, J. Olson, ASME, vol. FEDSM981998. 1–8 (Washington, DC). A. Li, G. Ahmadi, Aerosol Sci. Technol. 23 (1995) 201–223. N. Nowak, P.P. Kakade, A.V. Annapragada, Ann. Biomed. Eng. 31 (2003) 374–390. C. Van Eartbruggen, C. Hirsch, M. Paiva, J. Appl. Physiol. 98 (2005) 970–980. C. Kleinstreuer, Z. Zhang, L. Zhang, J. Respir. Physiol. Neurobiol. 163 (2008) 128–138.
M. Rahimi-Gorji et al. / Journal of Molecular Liquids 209 (2015) 121–133 [15] C. Kleinstreuer, Z. Zhang, Annu. Rev. Fluid Mech. 42 (2010) 301–334. [16] G. Tian, P.W. Longest, G. Su, M. Hindle, Ann. Biomed. Eng. 39 (2011) 1136–1153. [17] G. Tian, P.W. Longest, G. Su, R.L. Walenga, M. Hindle, J. Aerosol Sci. 42 (2011) 781–799. [18] P.W. Longest, S. Winchurkar, T. Martonen, J. Aerosol Sci. 37 (2006) 1234–1257. [19] A. Farkas, I. Balashazy, J. Aerosol Sci. 38 (2007) 865–884. [20] E.R Weibel, New York: Academic (1963). [21] K. Horsfield, D. Gladys, D.E. Olson, G.F. Finlay, G. Cumming, J. Appl. Phys. 31 (1971) 207–217. [22] T. Gemci, V. Ponyavin, Y. Chen, H. Chen, R. Collins, J. Biomech. 41 (2008) 2047–2054. [23] T. Sun, J. Wang, X. Li, P. Lv, F. Liu, Y. Luo, Q. Gao, H. Zhu, X. Guo, Comput. Methods Prog. Biomed. 111 (2013) 519–524. [24] J. Fleming, J. Conway, C. Majoral, L. Tossici-Bolt, I. Katz, G. Caillibotte, et al., J. Aerosol Med. Pulm. Drug Deliv. 24 (2011) 49–60.
133
[25] L. Golshahi, M.L. Noga, R.B. Thompson, W.H. Finlay, J. Aerosol Sci. 42 (2011) 474–488. [26] C. Kleinstreuer, Z. Zhang, J.F. Donohue, Annu. Rev. Biomed. Eng. 10 (2008) 195–220. [27] H. Takano, N. Nishida, M. Itoh, N. Hyo, Y. Majima, J. Aerosol Med. 19 (2006) 314–328. [28] E.A. Matida, M. Ilie, W.H. Finlay, Aerosol Sci. Technol. 42 (2008) 10–17. [29] Z. Zhang, C. Kleinstreuer, C.S. Kim, Ann. Biomed. Eng. 36 (2008) 2095–2110. [30] J. Xi, P.W. Longest, Effects of oral airway geometry characteristics on the difusional deposition of inhaled nanoparticles, J. Biomech. Eng. ASME 130 (2008). [31] S. Elghobashi, Appl. Sci. Res. 52 (1994) 309–329. [32] C. Crowe, T. Troutt, J. Chung, Annu. Rev. Fluid Mech. 28 (1996) 11–43. [33] B.R. Munson, D.F. Young, T.H. Okiishi, 5th ed., John wiley & Son, Inc. (2006). [34] S.A. Morsi, A.J. Alexander, J. Fluid Mech. 55 (1972) 193–208.
