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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Bi-velocity transport processes. Single-component liquid and gaseous continua
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Bi-velocity transport processes. Single-component liquid and gaseous continua

机译：双速运输过程。单组分液态和气态连续体

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摘要

The present contribution supplements the previous findings regarding the need for two independent velocities rather than one when quantifying mass, momentum and energy transport phenomena in fluid Continua. Explicitly, for the case of single-component fluids the present paper furnishes detailed expressions for the phenomenological coefficients appearing in the Constitutive equations governing these bi-velocity transport processes. Whereas prior analyses furnished coefficient Values only for the case of dilute monatomic gases using data from Burnett's Solution of the Boltzmann equation, the present study furnishes Values applicable to all fluids, liquids as well as densegases. Moreover, whereas prior coefficient calculations derived these values (for dilute monatomic gases) from Burnett's Solution of Boltzmann's gas-kinetic equation, the latter a molecular theory, the present analysis derives the liquid- and gas-phase Values from purely macroscopic data requiring knowledge only of the fluid's coefficients of thermal expansion, isothermal compressibility, and thermometric diffusivity. In the dilute monatomic gas case common to both levels of analysis, the respective molecularly and macroscopically derived phenomenological coefficients are found to be in excellent agreement, confirming the credibility of both bi-velocity theory and the theory establishing the Values of the phenomenological coefficients appearing in the constitutive relations derived therefrom. Whereas the preceding macroscopic calculations invoked Onsager's reciprocal theorem relating Coupled phenomenological coefficients, an alternative scheme is presented at the conclusion of the paper. one that reverses the usual order of things, at least in the present single-component fluid case. This alternate scheme enables Onsager's nonequilibrium reciprocal relation, originally derived by him using molecular arguments, to be derived using purely macroscopic arguments originating from knowledge of Maxwell's equilibrium reciprocal relations, the latter fundamental to equilibrium thermodynamics.
机译：在对流体连续体中的质量，动量和能量传输现象进行量化时，本贡献补充了先前关于需要两个独立速度而不是一个独立速度的发现。明确地，对于单组分流体，本论文提供了控制这些双速输运过程的本构方程中出现的现象学系数的详细表达式。先前的分析仅使用伯特兹曼方程的伯内特解决方案的数据为稀的单原子气体提供了系数值，而本研究则提供了适用于所有流体，液体以及稠密气体的值。此外，尽管先前的系数计算是从玻耳兹曼气体动力学方程的伯内特解决方案中得出的这些值（用于稀单原子气体），而后者是分子理论，但本分析是从仅需要知识的纯宏观数据中得出液相和气相值流体的热膨胀系数，等温可压缩性和测温扩散系数。在两种分析水平都相同的稀薄单原子气体情况下，发现从分子和宏观角度推导的各自的现象学系数具有极好的一致性，这证实了双速理论和建立在理论上出现的现象学系数的值的理论的可靠性。从中得出的本构关系。鉴于先前的宏观计算引用了与耦合现象学系数有关的Onsager互易定理，本文的结论提出了一种替代方案。至少在当前的单组分流体情况下，这种方法可以颠倒通常的顺序。这种替代方案使Onsager最初由他使用分子论证推导的非平衡倒数关系，可以使用源自麦克斯韦平衡倒数关系的纯宏观论证来推导，后者是平衡热力学的基础。

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