The effect of cartilaginous rings on particle deposition by convection and Brownian diffusion

ABSTRACT

The deposition of spherical nanoparticles by convection and Brownian diffusion in a pipe with a cartilaginous ring structure is studied. Analytical results for a fully developed flow are found for small amplitude rings using the interactive boundary layer theory. It is found that the local deposition rate is at maximum at a position approximately one twelfth of the spacing between the rings before the minimum cross section of the tube. For larger ring amplitudes the problem is solved numerically and separation then takes place in the depressions between the rings, and maximum deposition is found at the point of reattachment of the flow approximately at the same point as in the analytical theory. Cumulative deposition results are also provided with larger deposition rates with the inclusion of the cartilaginous rings. Deposition results for a developing flow are also provided. For the same volume flux as for fully developed flow the deposition is about 25% larger. In general conclusions about the position of maximum deposition rate from the analytic theory of fully developed flow also applies qualitatively to the case of developing flow.

The deposition of spherical nanoparticles by convection and Brownian diffusion in a pipe with a cartilaginous ring structure is studied. Analytical results for a fully developed flow are found for small amplitude rings using the interactive boundary layer theory. It is found that the local deposition rate is at maximum at a position approximately one twelfth of the spacing between the rings before the minimum cross section of the tube. For larger ring amplitudes the problem is solved numerically and separation then takes place in the depressions between the rings, and maximum deposition is found at the point of reattachment of the flow approximately at the same point as in the analytical theory. Cumulative deposition results are also provided with larger deposition rates with the inclusion of the cartilaginous rings. Deposition results for a developing flow are also provided. For the same volume flux as for fully developed flow the deposition is about 25% larger. In general conclusions about the position of maximum deposition rate from the analytic theory of fully developed flow also applies qualitatively to the case of developing flow.

KEYWORDS

Nanoparticles; Convection; Brownian Motion; Deposition; Respiratory Airways; Cartilaginous Rings

Nanoparticles; Convection; Brownian Motion; Deposition; Respiratory Airways; Cartilaginous Rings

Cite this paper

Åkerstedt, H. , Högberg, S. , Lundström, T. and Sandström, 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.

Åkerstedt, H. , Högberg, S. , Lundström, T. and Sandström, T. (2010) The effect of cartilaginous rings on particle deposition by convection and Brownian diffusion.

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(7), 423-428.

[2] Dobrovolskaia, M.A. and McNeil, S.E. (2007). Immunological properties of engineered nanomaterials. Nature Nanotechnology, 2(8), 469-478.

[3] 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(5), 394-399.

[4] H?gberg, S.M., ?kerstedt, H.O., Lundstr?m, T.S. and Freund, J.B. (2008) Numerical model for fiber transport in the respiratory airways. Proceedings of the 19th International Symposium on Transport Phenomena (ISTP-19), Reyk-javik.

[5] Risken, H. (1996) The Fokker-Planck equation. SpringerVerlag, Berlin.

[6] Ingham, D.B. (1975) Diffusion of aerosols from a stream flowing through a cylindrical tube. Journal of Aerosol Science, 6(2), 125-132.

[7] Ingham, D.B. (1984) Diffusion of aerosols from a stream flowing through a short cylindrical tube. Journal of Aerosol Science, 15(5), 637-641.

[8] Ingham, D.B. (1991) Diffusion of aerosols in the entrance region of a smooth cylindrical pipe. Journal of Aerosol Science, 22(3), 253-257.

[9] Martonen, T., Zhang, Z. and Yang, Y. (1996) Particle diffusion with entrance effects in a smooth-walled cylinder. Journal of Aerosol Science, 27(1), 139-150.

[10] Sobey, I.J. (2000) Introduction to interactive boundary layer theory. Oxford Applied Engineering and Mathematics, Oxford University Press, Oxford.

[11] Chapman, S. and Cowling, T.G. (1952) The mathematical theory of non-uniform gases. Cambridge University Press, London.

[12] Martonen, T.B., Yang, Y. and Xue, Z.Q. (1994) Influence of cartilaginous rings on tracheobronchial fluid dynamics. Inhalation Toxicology, 6(3), 185-203.

[13] Abramowitz, M. and Stegun, I.A. (1972) Handbook of Mathematical Functions, Dover, New York.

[14] Schlichting, H. and Gersten, K. (2000) Boundary layer theory. 8th Edition, Springer-Verlag, Pope.

[15] ?kerstedt, H.O., Lundstr?m, T.S. and H?gberg, S.M. (2007) Electrostatic filtration of airborne nano-particles. Journal of Nanostructured Poymers and Nanocomposites. 3(4), 111-115.

[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(7), 423-428.

[2] Dobrovolskaia, M.A. and McNeil, S.E. (2007). Immunological properties of engineered nanomaterials. Nature Nanotechnology, 2(8), 469-478.

[3] 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(5), 394-399.

[4] H?gberg, S.M., ?kerstedt, H.O., Lundstr?m, T.S. and Freund, J.B. (2008) Numerical model for fiber transport in the respiratory airways. Proceedings of the 19th International Symposium on Transport Phenomena (ISTP-19), Reyk-javik.

[5] Risken, H. (1996) The Fokker-Planck equation. SpringerVerlag, Berlin.

[6] Ingham, D.B. (1975) Diffusion of aerosols from a stream flowing through a cylindrical tube. Journal of Aerosol Science, 6(2), 125-132.

[7] Ingham, D.B. (1984) Diffusion of aerosols from a stream flowing through a short cylindrical tube. Journal of Aerosol Science, 15(5), 637-641.

[8] Ingham, D.B. (1991) Diffusion of aerosols in the entrance region of a smooth cylindrical pipe. Journal of Aerosol Science, 22(3), 253-257.

[9] Martonen, T., Zhang, Z. and Yang, Y. (1996) Particle diffusion with entrance effects in a smooth-walled cylinder. Journal of Aerosol Science, 27(1), 139-150.

[10] Sobey, I.J. (2000) Introduction to interactive boundary layer theory. Oxford Applied Engineering and Mathematics, Oxford University Press, Oxford.

[11] Chapman, S. and Cowling, T.G. (1952) The mathematical theory of non-uniform gases. Cambridge University Press, London.

[12] Martonen, T.B., Yang, Y. and Xue, Z.Q. (1994) Influence of cartilaginous rings on tracheobronchial fluid dynamics. Inhalation Toxicology, 6(3), 185-203.

[13] Abramowitz, M. and Stegun, I.A. (1972) Handbook of Mathematical Functions, Dover, New York.

[14] Schlichting, H. and Gersten, K. (2000) Boundary layer theory. 8th Edition, Springer-Verlag, Pope.

[15] ?kerstedt, H.O., Lundstr?m, T.S. and H?gberg, S.M. (2007) Electrostatic filtration of airborne nano-particles. Journal of Nanostructured Poymers and Nanocomposites. 3(4), 111-115.