Geometrical aspect of susceptibility critical exponent

TL;DR

This paper explores the geometric nature of the critical exponent in real fluids, revealing that the critical point's local shape must have zero Gaussian curvature, which challenges existing empirical equations of state.

Contribution

It introduces a geometric perspective linking the critical exponent to the Gaussian curvature at the critical point, proposing a new constraint for modeling real fluids.

Findings

Critical exponent $\gamma \\geq 1.1$ relates to zero Gaussian curvature at the critical point.

Existing empirical equations of state have negative Gaussian curvature at the critical point.

The geometric constraint can improve the construction of more accurate equations of state.

Abstract

Critical exponent $\gamma \succeq 1.1$ characterizes behavior of the mechanical susceptibility of a real fluid when temperature approaches the critical one. It results in zero Gaussian curvature of the local shape of the critical point on the thermodynamic equation of state surface, which imposes a new constraint upon the construction of the potential equation of state of the real fluid from the empirical data. All known empirical equations of state suffer from a weakness that the Gaussian curvature of the critical point is negative definite instead of zero.