It is well-known that the behaviour of supercritical fluids near the critical point changes considerably in the region around the Widom lines. We have found, for pure fluids, that the relationship between the thermal expansion coefficient and the isothermal compressibility is not only highly nonlinear in this region but in a certain temperature range can also be approximated well at constant pressure by a quadratic relationship, i.e., an ellipse. In this paper, we show this analytically, and demonstrate it for the van der Waals, Berthelot and IAPWS-95 water models numerically. Furthermore, the parameters of the ellipse are discovered to obey power and linear laws. The parameters of these laws are determined for the three aforementioned models.

中文翻译：

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Widom 区域超临界流体的先导椭圆关系

众所周知，超临界流体在临界点附近的行为在 Widom 线周围区域发生很大变化。我们发现，对于纯流体，热膨胀系数和等温压缩性之间的关系不仅在该区域是高度非线性的，而且在一定温度范围内也可以在恒压下通过二次关系很好地近似，即椭圆。在本文中，我们以分析的方式展示了这一点，并在范德华、Berthelot 和 IAPWS-95 水模型中进行了数值论证。此外，椭圆的参数被发现服从幂律和线性定律。这些定律的参数是针对上述三个模型确定的。