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Higher-Order Maxwell–Stefan Model of Diffusion

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Abstract

The paper studies a higher-order diffusion model of Maxwell–Stefan kind. The model is based upon higher-order moment equations from the kinetic theory of mixtures, which include the viscous dissipation/the pressure tensor. The governing equations are scaled using the so-called diffusive scaling, in which the Mach and Knudsen numbers are assumed to be of the same small order of magnitude. In the asymptotic limit when the small parameter vanishes, the model exhibits a coupling between the species’ partial pressure gradients, which generalizes the classical Maxwell–Stefan model. The scaled equations also lead to a higher-order model of diffusion in which inertia terms are not neglected. In that case, the model is extended by the momentum flux balance laws which determine the evolution of the pressure tensor.

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Acknowledgements

This paper was prepared during the stay of Srboljub Simić at Université Paris Cité thanks to “Guest researchers’ Faculty Programme 2022”. The research was also financially supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia (Grant No. 451-03-47/2023-01/200125) (S.S.).

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Author notes

  1. Bérénice Grec and Srboljub Simić have contributed equally to this work.

Authors and Affiliations

  1. Université Paris Cité, CNRS, MAP5, 75006, Paris, France

    Bérénice Grec

  2. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia

    Srboljub Simić

Authors
  1. Bérénice Grec
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Correspondence to Bérénice Grec.

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Grec, B., Simić, S. Higher-Order Maxwell–Stefan Model of Diffusion. La Matematica 2, 962–991 (2023). https://doi.org/10.1007/s44007-023-00071-0

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