On the fundamental derivative of gas dynamics in the vapor–liquid critical region of single-component typical fluids

This document describes the results of an investigation on the variation of the so-called fundamental derivative of gas dynamics, Γ, in the vapor–liquid critical region of well-measured substances, namely methane, carbon dioxide and water, for which accurate, scaled fundamental equations are available. The results demonstrate that for a pure fluid in the single-phase thermodynamic regime, Γ diverges to +∞ independent of the direction of approach of the vapor–liquid critical point. Furthermore, in the two-phase thermodynamic regime, Γ diverges to −∞ independent of the direction of approach of the vapor–liquid critical point. These two qualitative results, as well as the value of the exponent giving the power-law dependence of Γ along the critical isochore as a function of |T − TC|/T (T is the temperature and “C” indicates its critical point value), namely ≈−0.89, are similar for all pure, non-ionized fluids belonging to the class of 3-dimensional Ising-like systems, i.e., systems governed by short-range forces.