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Effects of volume fraction condition on thermodynamic restrictions in mixture theory

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Abstract

Volume fraction condition is a true constraint that must be taken into consideration in deducing the thermodynamic restrictions of mixture theory applying the axiom of dissipation. For a process to be admissible, the constraints imposed by the volume fraction condition include not only the equation obtained by taking its material derivative with respect to the motion of a given phase, but also those by taking its spatial gradient. The thermodynamic restrictions are deduced under the complete constraints, the results obtained are consistent for the mixtures with or without a compressible phase, and in which the free energy of each phase depends on the densities of all phases.

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Authors and Affiliations

  1. Department of Mechanics, School of Physical Science and Technology, Lanzhou University, 730000, Lanzhou, China

    Yonghong Niu & Tiande Miao

  2. State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, 730000, Lanzhou, China

    Yonghong Niu

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  1. Yonghong Niu
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  2. Tiande Miao
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Correspondence to Yonghong Niu.

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Niu, Y., Miao, T. Effects of volume fraction condition on thermodynamic restrictions in mixture theory. Sci. China Ser. A-Math. 45, 640–647 (2002). https://doi.org/10.1360/02ys9069

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  • DOI: https://doi.org/10.1360/02ys9069

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