Abstract
A discussion and evaluation of the analysis describing deposition of aerosal particles due to Brownian motion and gravitational sedimentation during breath holding periods is presented. Analytic results are compared with published experimental data describing exponential recovery of aerosol with breath-holding time. Mathematical solutions for deposition with different types of assumed initial conditions are compared. Coupled simultaneous effects of diffusion with gravitational sedimentation are considered and the validity of various approximation schemes for the analysis of deposition is discussed.
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Altshuler, B. Behavior of airborne particles in the respiratory tract. InCirculatory and Respiratory Mass Transport, A Ciba Symposium, edited by G.E.W. Wolstenholme and J. Knight. Boston: Little Brown and Co., 1969, pp. 215–235.
Cinkotai, F.F. Fluid flow in a model alveolar sac.J. Appl. Physiol. 37(2):249–251, 1974.
Cunningham, E. On the velocity of steady fall of spherical particles through fluid medium.Proc. R. Soc. London, Ser. A. 83:357–365, 1910.
Davies, C.N. Definite equations for the fluid resistance of spheres.Proc. Phys. Soc. London 57:259–270, 1945.
Einstein, A. Uber die von der molecularkinetischen theorie der warmer geforderte bewegun von in ruhenden flussigkeiten suspendierten teilchen.Ann. Phys. 17:549–560, 1905.
Engel, L.A., H. Menkes, L.D.H. Wood, G. Utz, J. Joubert, and P.T. Macklem. Gas mixing during breath holding studied by intrapulmonary gas sampling.J. Appl. Physiol. 35:9–17, 1973.
Findeisen, W. Uber das absetzen kleiner, in der luft suspendierter teilchen in der menschilichen lunge bei der atmung.Pfluegers Arch. Gesamte Physiol. Menschen Tiere 236:367–379, 1935.
Fuchs, N.A.The Mechanics of Aerosols. New York: Pergamon Press, 1964, pp. 80–89 and 181–204.
Gebhart, J., J. Heyder, and W. Stahlhofen. Use of aerosol to estimate pulmonary air-space dimensions.J. Appl. Physiol: Respir. Environ. Exercise Physiol. 51 (2):465–476, 1981.
Goldberg, I.S. Deposition of aerosol particles due to simultaneous diffusion and gravitational sedimentation within a spherical chamber-Solutions to the Fokker-Planck equations.J. Aerosol Sci. 12:11–14, 1981.
Goldberg, I.S. A correction to the small-time approximation of diffusive deposition from a uniform initial concentration of particles in a circular tube with adsorbing walls.J. Aerosol Sci. 12:15–17, 1981.
Goldberg, I.S., K.Y. Lam, B. Bernstein, and J.O. Hutchens. Solutions to the Fokker-Planck equations governing simultaneous diffusion and gravitational settling of aerosol particles from a stationary gas in a horizontal circular tube.J. Aerosol Sci. 9:209–218, 1978.
Hankinson, J.L., E.D. Palmes, and N.L. Lapp. Pulmonary air space in coal miners.Am. Rev. Respir. Dis. 119:391–397, 1978.
Hatch, T.F. and P. Gross.Pulmonary Deposition and Retention of Inhaled Aerosols. New York: Academic Press, 1964, pp. 27–44.
Heyder, J. Gravitational deposition of aerosol particles within a system of randomly oriented tubes.J. Aerosol Sci. 6:133–137, 1975.
Ingham, D.B. Diffusion of aerosols from a stream flowing through a cylindrical tube.J. Aerosol Sci. 6:125–132, 1975.
Landahl, H.D. On the removal of air-borne droplets by the human respiratory tract: I. The lung.Bull. Math. Biophys. 12:43–56, 1950.
Landau, L.D. and E.M. Lifshitz.Fluid Mechanics, Vol. 6 ofCourse of Theoretical Physics. London: Pergamon Press, 1959, pp. 227–229.
Lapp, N.L., J.L. Hankinson, H. Amandus, and E.D. Palmes. Variability in the size of airspaces in normal human lungs as estimated by aerosol.Thorax 30:293–299, 1975.
Palmes, E.D., B. Altshuler, and N. Nelson. Deposition of aerosols in the human respiratory tract during breath holding. InInhaled Particles and Vapors II, edited by C.N. Davies. Oxford: Pergamon Press, 1967, pp. 339–349.
Palmes, E.D., R.M. Goldring, C.S. Wang, and B. Altshuler. Effect of chronic obstructive pulmonary disease on rate of deposition of aerosol in the lung during breath holding. InInhaled Particles III, edited by W.H. Walton. Surrey England: Unwin Bros. Ltd., 1970, Vol. 1, pp. 123–130.
Palmes, E.D., C.S. Wang, R.N. Goldring, and B. Altshuler. Effect of depth of inhalation on aerosol persistence during breath holding.J. Appl. Physiol. 34: (3):356–360, 1973.
Wang, C.S., B. Altshuler, and E.D. Palmes. The distribution and deposition of particles suspended between parallel plan surfaces.J. Colloid Interface Sci. 26:41–44, 1968.
Weibel, E.R.Morphometrics of the Human Lung. New York: Academic Press, 1963, pp. 285–307.
Yu, C.P., C.S. Liu, and D.B. Taulbee. Simultaneous diffusion and sedimentation of aerosols in a horizontal cylinder.J. Aerosol Sci. 8:309–316, 1977.
Yu, C.P. and V. Thiagarajan. Sedimentation of aerosols in closed finite tubes in random orientation.J. Aerosol Sci. 9:315–320, 1978.
Yu, C.P. and C. Thiagarajan. Decay of aerosols in the lung during breath holding.J. Aerosol Sci. 10:11–19, 1979.
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Goldberg, I.S., Smith, R.B. Settling and diffusion of aerosol particles in small airways during breath holding. Ann Biomed Eng 9, 557–575 (1981). https://doi.org/10.1007/BF02364771
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DOI: https://doi.org/10.1007/BF02364771