Summary
The purpose of this work was to compare experimental diffusion among three gases with the solution given by Stefan's equations to understand better how this phenomenon can work in the multi-component alveolar gas.
Experiments were performed in a cylinder full of beads open at one end and closed at the other in which a mixture of oxygen with helium or argon or sulphur hexafluoride could diffuse with ambient air through the open end. We solved Stefan's equations for the non-steady state by a finite-difference method and applied them to our experimental conditions with diffusion coefficients we had measured in binary experiments. We then made experiments and calculations to show the influence of the beads on gas transport.
Provided that diffusion is the only phenomenon, experimental and theoretical curves are very close together. Moreover beads nearly stop motions due to vortices or small differences of density.
We conclude that:
Stefan's equations should replace Fick's equations when more than two gases are involved.
One should bear in mind the possible influence of gravity and devise diffusion experiments accordingly.
In small spaces such as alveoli the influence of gravity must be negligible compared to diffusion.
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References
Boardman, L. E., Wild, N. E.: The diffusion of pairs of gases with molecules of equal mass. Proc. R. Soc. (London) A162, 511–520 (1937)
Brés, M., Hatzfeld, C.: Diffusion gazeuse dans un méaange à trois composants. Abstracts of “Distribution of pulmonary gas exchange”, 11–13, I.N.S.E.R.M., Paris 1975
Brès, M., Hatzfeld, C.: Diffusion gazeuse dans un mélange à trois composants. Comptes-rendus des colloques de l'I.N.S.E.R.M.51, 43–49, Paris 1976
Brun, E. A., Martinot-Lagarde, A., Mathieu, J.: Mécanique des Fluides. Paris: Dunod 1968
Chang, H. K., Tai, R. C., Farhi, L. E.: Some implications of ternary diffusion in the lung. Respir. Physiol.23, 109–120 (1975)
Collins, R.: Analyse numérique: application aux milieux continus. Université Paris VII, 1973
Crank, J.: The mathematics of diffusion. Oxford: Clarendon Press 1956
Cumming, G., Crank, J., Horsfield, K., Parker, I.: Gaseous diffusion in the airways of the human lung. Respir. Physiol.1, 58–74 (1966)
Fick, A.: Über Diffusion. Ann. Phys. Chem.94, 59–86 (1855)
Graham, T.: On the law of the diffusion of gases. Trans. R. Soc. Edinb.12, part 1, 222–258 (1832)
Graham, T.: On the molecular mobility of gases. Phil. Mag. S.4 (177),26, 409–434 (1863)
Krogh, A., Lindhard, J.: The volume of the dead space in breathing and the mixing of gases in the lungs of man. J. Physiol. (Lond.)51, 59–90 (1917)
Landau, E., Lifchirz, E.: Physique statistique. Moscou: Editions Mir 1967
Loschmidt, J.: Experimental-Untersuchungen über die Diffusion von Gasen ohne poröse Scheidewände. S.-B. Akad. Wiss. Wien61, 2. Abt. 367–380 and62, 2. Abt. 468–478 (1870)
Modell, H. I., Farhi, L. E.: Ternary gas diffusion — in vitro studies. Respir. Physiol.27, 65–71 (1976)
Païva, M.: Stochastic simulation of the gas diffusion in the air phase of the human lung. Bull. Math. Biophysics34, 457–466 (1972)
Radford, E. P.: The physics of gases. Handbook of Physiology, Section 3, pp. 125–152 (W. O. Fenn and H. Rahn, eds.). Washington, D.C.: American Physiological Society 1964
Rauwerda, P. E.: Unequal ventilation of different parts of the lung and the determination of cardiac output. Thesis, Groningen, Netherlands 1946
Rost, G.: Recent improvements in hypoxia warning systems. Aerospace Med.41, 865–869 (1970)
Stefan, J.: Über das Gleichgewicht und die Bewegung insbesondere die Diffusion von Gasgemengen. S.-B. Akad. Wiss. Wien63, 2. Abt., 63–124 (1871)
Toor, H. L.: Diffusion in three-component gas mixtures. A. I. Ch. E. J.3, 198–207 (1957)
Weibel, E.: Morphometry of the human lung. Berlin-Göttingen-Heidelberg: Springer 1963
Wretschko, A.: Experimental-Untersuchungen über die Diffusion von Gasgemengen. S.-B. Akad. Wiss. Wien62, 2. Abt., 575–589 (1870)
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This study was aided by grant CL 74 5 117 06 INSERM
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Bres, M., Hatzfeld, C. Three-gas diffusion — Experimental and theoretical study. Pflugers Arch. 371, 227–233 (1977). https://doi.org/10.1007/BF00586262
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DOI: https://doi.org/10.1007/BF00586262