Related Experiment Video
Updated: Jun 13, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
Simple relationship between the virial-route hypernetted-chain and the compressibility-route Percus-Yevick values of
1Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain. andres@unex.es
Abstract:
As is well known, approximate integral equations for liquids, such as the hypernetted chain (HNC) and Percus-Yevick (PY) theories, are in general thermodynamically inconsistent in the sense that the macroscopic properties obtained from the spatial correlation functions depend on the route followed. In particular, the values of the fourth virial coefficient B(4) predicted by the HNC and PY approximations via the virial route differ from those obtained via the compressibility route. Despite this, it is shown in this paper that the value of B(4) obtained from the virial route in the HNC theory is exactly three halves the value obtained from the compressibility route in the PY theory, irrespective of the interaction potential (whether isotropic or not), the number of components, and the dimensionality of the system. This simple relationship is confirmed in one-component systems by analytical results for the one-dimensional penetrable-square-well model and the three-dimensional penetrable-sphere model, as well as by numerical results for the one-dimensional Lennard-Jones model, the one-dimensional Gaussian core model, and the three-dimensional square-well model.
Related Concept Videos
Poiseuille's Law and Reynolds Number
Reynolds Transport Theorem
Path Between Thermodynamics States
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation
Vapor Pressure of Fluid
When a liquid is placed in a closed container with a small air space, and the space is evacuated, vapor molecules will...
Viscosity of Fluid

