A rigorous derivation of multicomponent diffusion laws

Zaibao Yang Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, China, 100084 Wen-An Yong Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China Yi Zhu Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, China, 100084

Mathematical Physics mathscidoc:2204.22006

2015.2
This article is concerned with the dynamics of a mixture of gases. Under the assumption that all the gases are isothermal and inviscid, we show that the governing equations have an elegant conservation-dissipation structure. With the help of this structure, a multicomponent diffusion law is derived mathematically rigorously. This clarifies a long-standing non-uniqueness issue in the field for the first time. The multicomponent diffusion law derived here takes the spatial gradient of an entropic variable as the thermodynamic forces and satisfies a nonlinear version of the Onsager reciprocal relations.
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@inproceedings{zaibao2015a,
  title={A rigorous derivation of multicomponent diffusion laws},
  author={Zaibao Yang, Wen-An Yong, and Yi Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220422142302970251100},
  year={2015},
}
Zaibao Yang, Wen-An Yong, and Yi Zhu. A rigorous derivation of multicomponent diffusion laws. 2015. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220422142302970251100.
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