Geodesic
Diffusion models of multicomponent mixtures in the lung
L. Boudin1, 2 ; D. Götz3 ; B. Grec4, 5
1UPMC Paris 06, UMR 7598 LJLL, Paris, F-75005, France
2INRIA Paris-Rocquencourt, REO Project team, BP 105, F-78153 Le Chesnay Cedex, France
3TU Darmstadt, Fachbereich Mathematik, IRTG 1529, Schloßgartenstr. 7, D-64289 Darmstadt, Germany
4MAP5, CNRS UMR 8145, Université Paris Descartes, F-75006 Paris, France
5Institut Camille Jordan, CNRS UMR 5208, Université Claude Bernard Lyon 1, F-69622 Villeurbanne, France
ESAIM. Proceedings, Tome 30 (2010), pp. 90-103
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In this work, we are interested in two different diffusion models for multicomponent mixtures. We numerically recover experimental results underlining the inadequacy of the usual Fick diffusion model, and the importance of using the Maxwell-Stefan model in various situations. This model nonlinearly couples the mole fractions and the fluxes of each component of the mixture. We then consider a subregion of the lower part of the lung, in which we compare the two different models. We first recover the fact that the Fick model is enough to model usual air breathing. In the case of chronic obstructive bronchopneumopathies, a mixture of helium and oxygen is often used to improve a patient’s situation. The Maxwell-Stefan model is then necessary to recover the experimental behaviour, and to observe the benefit for the patient, namely an oxygen peak.
DOI : 10.1051/proc/2010008

L. Boudin  1 , 2   ; D. Götz  3   ; B. Grec  4 , 5

1 UPMC Paris 06, UMR 7598 LJLL, Paris, F-75005, France
2 INRIA Paris-Rocquencourt, REO Project team, BP 105, F-78153 Le Chesnay Cedex, France
3 TU Darmstadt, Fachbereich Mathematik, IRTG 1529, Schloßgartenstr. 7, D-64289 Darmstadt, Germany
4 MAP5, CNRS UMR 8145, Université Paris Descartes, F-75006 Paris, France
5 Institut Camille Jordan, CNRS UMR 5208, Université Claude Bernard Lyon 1, F-69622 Villeurbanne, France 
@article{EP_2010_30_a7,
     author = {L. Boudin and D. G\"otz and B. Grec},
     title = {Diffusion models of multicomponent mixtures in the lung},
     journal = {ESAIM. Proceedings},
     pages = {90--103},
     year = {2010},
     volume = {30},
     doi = {10.1051/proc/2010008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2010008/}
}
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L. Boudin; D. Götz; B. Grec. Diffusion models of multicomponent mixtures in the lung. ESAIM. Proceedings, Tome 30 (2010), pp. 90-103. doi: 10.1051/proc/2010008

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