On the Kinetic Theory of Dense Fluids. IX. The Fluid of Rigid Spheres with a Square-Well Attraction

Abstract

By the use of methods previously introduced, we discuss in this paper the statistical theory of a dense fluid of molecules interacting with a square‐well potential. The argument proceeds via the derivation and solution of a modified Boltzmann equation. The theory is used in two ways:(a) to provide a test of the theory proposed by Rice and Allnatt; (b) to estimate the attractive force contribution to the transport of momentum and energy in a real fluid. The approach of Rice and Allnatt is shown to give a friction coefficient in agreement with experiment for liquid argon. The presence of the attraction has a marked effect on the transport of momentum and energy and the square‐well‐model fluid gives a surprisingly accurate representation of the properties of liquid argon. The computed thermal conductance and self‐diffusion coefficient are in agreement with experiment: $$\begin{array}{cc}\mathrm{\kappa (}\mathrm{calc}{\text{)\hspace{0.17em}1.33×10}}^2\hspace{0.17em}\mathrm{erg}/\mathrm{g-sec-deg},& \mathrm{\kappa (}\mathrm{obs}{\text{)\hspace{0.17em}1.26×10}}^2\mathrm{erg}/\mathrm{g-sec-deg},\\ \mathrm{D(}\mathrm{calc}{\text{)\hspace{0.17em}1.81×10}}^{\text{−5}}{\mathrm{cm}}^2/\sec ,& \mathrm{D(}\mathrm{obs}{\text{)\hspace{0.17em}1.84×10}}^{\text{−5}}\hspace{0.17em}{\mathrm{cm}}^2/\sec ,\end{array}$$ and the temperature dependence of κ/η is in qualitative agreement with the observed temperature dependence of this ratio.