We present a systematic derivation of thermodynamically consistent hydrodynamic models for multi-component, compressible viscous fluid mixtures under isothermal conditions using the generalized Onsager principle and the one-fluid multi-component formulation. By maintaining momentum conservation while enforcing mass conservation at different levels, we obtain two compressible models. When the fluid components in the mixture are incompressible, we show that one compressible model reduces to the quasi-incompressible model via a Lagrange multiplier approach. Several different approaches to arriving at the quasi-incompressible model are discussed. Finally, we conduct a linear stability analysis on all the binary fluid models derived in the paper to show the differences of the models in near equilibrium dynamics.

中文翻译：

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多组分可压缩流体流的热力学一致流体力学模型

我们使用广义的Onsager原理和单流体多组分配方，系统地推导了等温条件下多组分可压缩粘性流体混合物的热力学一致性流体力学模型。通过在保持动量守恒的同时在不同级别执行质量守恒，我们获得了两个可压缩模型。当混合物中的流体成分不可压缩时，我们证明通过Lagrange乘数法，一个可压缩模型降为准不可压缩模型。讨论了几种到达准不可压缩模型的方法。最后，我们对本文导出的所有二元流体模型进行线性稳定性分析，以显示模型在近平衡动力学方面的差异。