A complete thermodynamical analysis for a non-reacting binary mixture exhibiting the features of a third grade fluid is analyzed. The constitutive functions are allowed to depend on the mass density of the mixture and the concentration of one of the constituents, together with their first and second order gradients, on the specific internal energy of the mixture with its first order gradient, and on the symmetric part of the gradient of barycentric velocity. Compatibility with the second law of thermodynamics is investigated by applying the extended Liu procedure. An explicit solution of the set of thermodynamic restrictions is obtained by postulating a suitable form of the constitutive relations for the diffusional mass flux, the heat flux, and the Cauchy stress tensor. Taking a first order expansion in the gradients of the specific entropy, the expression of the entropy flux is determined. It includes an additional contribution due to non-local effects.

中文翻译：

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三级流体混合物的热力学描述

对表现出三级流体特征的非反应二元混合物进行了完整的热力学分析。允许本构函数取决于混合物的质量密度和一种成分的浓度，以及它们的一阶和二阶梯度，取决于具有一阶梯度的混合物的比内能，以及对称重心速度梯度的一部分。通过应用扩展的 Liu 程序研究了与热力学第二定律的相容性。通过假设扩散质量通量、热通量和柯西应力张量的本构关系的适当形式，可以获得一组热力学限制的显式解。对特定熵的梯度进行一阶展开，确定熵通量的表达式。它包括由于非局部影响而产生的额外贡献。