Diffusion models of multicomponent mixtures in the lung^*

¹ UPMC Paris 06, UMR 7598 LJLL, Paris, F-75005, France
e-mail: laurent.boudin@upmc.fr
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
e-mail: goetz@mathematik.tu-darmstadt.de
⁴ MAP5, CNRS UMR 8145, Université Paris Descartes, F-75006 Paris, France
e-mail: berenice.grec@parisdescartes.fr
⁵ Institut Camille Jordan, CNRS UMR 5208, Université Claude Bernard Lyon 1, F-69622 Villeurbanne, France

Abstract

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.