Department of Mechanical Engineering, Stanford University, Stanford, California 94305, USA.
Phys Rev E. 2017 May;95(5-1):052120. doi: 10.1103/PhysRevE.95.052120. Epub 2017 May 12.
The coexistence line of a fluid separates liquid and gaseous states at subcritical pressures, ending at the critical point. Only recently, it became clear that the supercritical state space can likewise be divided into regions with liquidlike and gaslike properties, separated by an extension to the coexistence line. This crossover line is commonly referred to as the Widom line, and is characterized by large changes in density or enthalpy, manifesting as maxima in the thermodynamic response functions. Thus, a reliable representation of the coexistence line and the Widom line is important for sub- and supercritical applications that depend on an accurate prediction of fluid properties. While it is known for subcritical pressures that nondimensionalization with the respective species critical pressures p_{cr} and temperatures T_{cr} only collapses coexistence line data for simple fluids, this approach is used for Widom lines of all fluids. However, we show here that the Widom line does not adhere to the corresponding states principle, but instead to the extended corresponding states principle. We resolve this problem in two steps. First, we propose a Widom line functional based on the Clapeyron equation and derive an analytical, species specific expression for the only parameter from the Soave-Redlich-Kwong equation of state. This parameter is a function of the acentric factor ω and compares well with experimental data. Second, we introduce the scaled reduced pressure p_{r}^{} to replace the previously used reduced pressure p_{r}=p/p_{cr}. We show that p_{r}^{} is a function of the acentric factor only and can thus be readily determined from fluid property tables. It collapses both subcritical coexistence line and supercritical Widom line data over a wide range of species with acentric factors ranging from -0.38 (helium) to 0.34 (water), including alkanes up to n-hexane. By using p_{r}^{}, the extended corresponding states principle can be applied within corresponding states principle formalism. Furthermore, p_{r}^{} provides a theoretical foundation to compare Widom lines of different fluids.
在亚临界压力下，流体的共存线将液体和气体状态分开，在临界点结束。直到最近，人们才清楚地认识到，超临界状态空间同样可以分为具有液态和气态特性的区域，通过共存线的延伸来分隔。这条交叉线通常被称为 Widom 线，其特征是密度或焓的大幅变化，表现为热力学响应函数的最大值。因此，对于依赖于对流体特性的准确预测的亚临界和超临界应用，准确表示共存线和 Widom 线非常重要。虽然对于亚临界压力，使用各自的物质临界压力 p_{cr}和温度 T_{cr}进行无量纲化仅能使简单流体的共存线数据崩溃，但这种方法适用于所有流体的 Widom 线。然而，我们在这里表明，Widom 线不遵守相应状态原理，而是遵守扩展的相应状态原理。我们通过两步解决了这个问题。首先，我们基于 Clapeyron 方程提出了一个 Widom 线函数，并从 Soave-Redlich-Kwong 状态方程推导出了一个仅由参数的解析、物种特定表达式。该参数是偏心因子 ω的函数，与实验数据吻合较好。其次，我们引入了标度化的压缩因子 p_{r}^{}来代替以前使用的压缩因子 p_{r}=p/p_{cr}。我们表明，p_{r}^{}仅是偏心因子的函数，因此可以从流体性质表中很容易地确定。它在偏心因子范围从-0.38（氦）到 0.34（水）的各种物质中崩溃了亚临界共存线和超临界 Widom 线数据，包括正构烷烃直至正己烷。通过使用 p_{r}^{}，可以在相应状态原理形式主义内应用扩展的相应状态原理。此外，p_{r}^{}为比较不同流体的 Widom 线提供了理论基础。
