Deposition of charged nano-particles in the human airways including effects from cartilaginous rings
Author(s)
Hans O. Akerstedt
ABSTRACT
This paper presents a numerical study of the deposition of spherical charged nano-particles caused by convection, Brownian diffusion and electrostatics in a pipe with a cartilaginous ring structure. The model describes the deposition of charged particles in the different generations of the tracheobronchial tree of the human lung. The upper airways are characterized by a certain wall structure called cartilaginous rings which modify the particle deposition when compared to an airway with a smooth wall. The problem is defined by solving Naver-Stokes equations in combination with a convective-diffusion equation and Gauss law for electrostatics. Three non- dimensional parameters describe the problem, the Peclet number Pe = 2ūa/D , the Reynolds number Re = ūa/v and an electrostatic parameter α=α2c0q2/(4ε0κT) . Here U is the mean velocity, a the pipe radius and D the diffusion coefficient due to Brownian motion given by D=κTCu/3πμd , where Cu is the Cunningham-factor Cu=1+λ/d(2.34+1.05exp(-0.39d/λ)) Here d is the particle diameter and λ the mean free path of the air molecules. Results are provided for generations G4-G16 of the human airways. The electrostatic parameter is varied to model different concentrations and charge numbers.
This paper presents a numerical study of the deposition of spherical charged nano-particles caused by convection, Brownian diffusion and electrostatics in a pipe with a cartilaginous ring structure. The model describes the deposition of charged particles in the different generations of the tracheobronchial tree of the human lung. The upper airways are characterized by a certain wall structure called cartilaginous rings which modify the particle deposition when compared to an airway with a smooth wall. The problem is defined by solving Naver-Stokes equations in combination with a convective-diffusion equation and Gauss law for electrostatics. Three non- dimensional parameters describe the problem, the Peclet number Pe = 2ūa/D , the Reynolds number Re = ūa/v and an electrostatic parameter α=α2c0q2/(4ε0κT) . Here U is the mean velocity, a the pipe radius and D the diffusion coefficient due to Brownian motion given by D=κTCu/3πμd , where Cu is the Cunningham-factor Cu=1+λ/d(2.34+1.05exp(-0.39d/λ)) Here d is the particle diameter and λ the mean free path of the air molecules. Results are provided for generations G4-G16 of the human airways. The electrostatic parameter is varied to model different concentrations and charge numbers.
Cite this paper
Akerstedt, H. (2011) Deposition of charged nano-particles in the human airways including effects from cartilaginous rings. Natural Science, 3, 884-888. doi: 10.4236/ns.2011.310113.
Akerstedt, H. (2011) Deposition of charged nano-particles in the human airways including effects from cartilaginous rings. Natural Science, 3, 884-888. doi: 10.4236/ns.2011.310113.
References
[1] Poland, C.A., Duffin, R., Kinloch, I. Maynard, A., Wallace, W.A.H., Seaton, A., Stone, V., Brown, S., Macnee, W. and Donaldson, K. (2008) Carbon nanotubes introduced into the abdominal cavity of mice show asbestos-like pathogenicity in a pilot study. Nature nanotechnology, 3, 423-428. doi:10.1038/nnano.2008.111 [2] Kleinstreuer, C., Zhang, Z., Donohue, J.F. (2008) Targeted drug-aerosol delivery in the human respiratory system. Annual Review of Biomedical Engineering, 10, 195- 220. doi:10.1146/annurev.bioeng.10.061807.160544 [3] Weibel, E. R. (1963). Morphometry of the human lung. Academic Press, New York. [4] Yu, C.P. (1977) Precipitation of unipolarly charged particles in cylindrical and spherical vessels. Journal of Aerosol Science, 8, 237-241. doi:10.1016/0021-8502(77)90043-X [5] Yu, C.P. and Chandra, K. (1977) Precipitation of submicron charged particles in human lung airways. Bulletin of Mathematical Biology, 39, 471-478. [6] Becker, R.S., Anderson, V.E., Allen, J.D., Birkhoff, R.D. and Ferell, T.L. (1980) Electrical image deposition of charges from laminar flow in cylinders. Journal of Aerosol Science, 11, 461-466. doi:10.1016/0021-8502(80)90118-4 [7] Ingham, D.B. (1980) Deposition of charged particles near the entrance of a cylindrical tube. Journal of Aerosol Science, 12, 47-52. doi:10.1016/0021-8502(80)90143-3 [8] H?gberg, S.M., ?kerstedt, H.O., Lundstr?m, T.S. and Freund J. (2010) Respiratory deposition of fibers in the non-inertial regime: Development and application of a semi-analytical model. Aerosol Science and Technology, 44, 847-860. doi:10.1080/02786826.2010.498455 [9] Risken, H. (1977) The Fokker-Planck equation. Springer- Verlag, Berlin. [10] ?kerstedt, H.O., H?gberg, S.M., Lundstr?m, T.S. (2011) An asymptotic approach of Brownian deposition of nanofibers fibers in pipe flow. Theoretical and Computational Fluid Dynamics. [11] ?kerstedt, H.O., H?gberg, S.M., Lundstr?m, T.S. and Sandstr?m, T. (2010) The effect of Cartilaginous rings on particle deposition by convection and Brownian diffusion. Natural Science, 2, 769-779. doi:10.4236/ns.2010.27097 [12] Martonen, T.B., Yang, Y. and Xue, Z.Q. (1994) Influence of cartilaginous rings on tracheobronchial fluid dynamics. Inhalation Toxicology, 6, 185-203. doi:10.3109/08958379408995231 [13] Zhang Y. and Finlay W.H. (2005) Measurement of the effect of cartilaginous rings on particle deposition in a proximal lung bifurcation model. Aerosol Science and Technology, 39, 394-399. doi:10.1080/027868290945785 [14] Etienne, S., Pierre, M. and Christian, D. (2010) Real time, nanometric 3D-tracking of nanoparticles made possible by second harmonic generation digital holographic microscopy. Optics Express, 18, 17392-17403. doi:10.1364/OE.18.017392
[1] Poland, C.A., Duffin, R., Kinloch, I. Maynard, A., Wallace, W.A.H., Seaton, A., Stone, V., Brown, S., Macnee, W. and Donaldson, K. (2008) Carbon nanotubes introduced into the abdominal cavity of mice show asbestos-like pathogenicity in a pilot study. Nature nanotechnology, 3, 423-428. doi:10.1038/nnano.2008.111 [2] Kleinstreuer, C., Zhang, Z., Donohue, J.F. (2008) Targeted drug-aerosol delivery in the human respiratory system. Annual Review of Biomedical Engineering, 10, 195- 220. doi:10.1146/annurev.bioeng.10.061807.160544 [3] Weibel, E. R. (1963). Morphometry of the human lung. Academic Press, New York. [4] Yu, C.P. (1977) Precipitation of unipolarly charged particles in cylindrical and spherical vessels. Journal of Aerosol Science, 8, 237-241. doi:10.1016/0021-8502(77)90043-X [5] Yu, C.P. and Chandra, K. (1977) Precipitation of submicron charged particles in human lung airways. Bulletin of Mathematical Biology, 39, 471-478. [6] Becker, R.S., Anderson, V.E., Allen, J.D., Birkhoff, R.D. and Ferell, T.L. (1980) Electrical image deposition of charges from laminar flow in cylinders. Journal of Aerosol Science, 11, 461-466. doi:10.1016/0021-8502(80)90118-4 [7] Ingham, D.B. (1980) Deposition of charged particles near the entrance of a cylindrical tube. Journal of Aerosol Science, 12, 47-52. doi:10.1016/0021-8502(80)90143-3 [8] H?gberg, S.M., ?kerstedt, H.O., Lundstr?m, T.S. and Freund J. (2010) Respiratory deposition of fibers in the non-inertial regime: Development and application of a semi-analytical model. Aerosol Science and Technology, 44, 847-860. doi:10.1080/02786826.2010.498455 [9] Risken, H. (1977) The Fokker-Planck equation. Springer- Verlag, Berlin. [10] ?kerstedt, H.O., H?gberg, S.M., Lundstr?m, T.S. (2011) An asymptotic approach of Brownian deposition of nanofibers fibers in pipe flow. Theoretical and Computational Fluid Dynamics. [11] ?kerstedt, H.O., H?gberg, S.M., Lundstr?m, T.S. and Sandstr?m, T. (2010) The effect of Cartilaginous rings on particle deposition by convection and Brownian diffusion. Natural Science, 2, 769-779. doi:10.4236/ns.2010.27097 [12] Martonen, T.B., Yang, Y. and Xue, Z.Q. (1994) Influence of cartilaginous rings on tracheobronchial fluid dynamics. Inhalation Toxicology, 6, 185-203. doi:10.3109/08958379408995231 [13] Zhang Y. and Finlay W.H. (2005) Measurement of the effect of cartilaginous rings on particle deposition in a proximal lung bifurcation model. Aerosol Science and Technology, 39, 394-399. doi:10.1080/027868290945785 [14] Etienne, S., Pierre, M. and Christian, D. (2010) Real time, nanometric 3D-tracking of nanoparticles made possible by second harmonic generation digital holographic microscopy. Optics Express, 18, 17392-17403. doi:10.1364/OE.18.017392