Test of the Duh-Haymet-Henderson theory for mixtures: cavity correlation functions and excess volumes

Abstract

The accuracy of the Duh-Haymet-Henderson (DHH) integral equation theory for predicting the cavity correlation functions of mixtures has been tested by comparison with molecular simulations. We have compared the cavity correlation functions, internal energies, and pressures computed for Lennard-Jones model mixtures of Ar/Kr, Ar/Ne, and Ar/Xe with these same quantities computed from the DHH theory and also, for reference, the Percus-Yevick (PY) integral equation theory. We found that DHH gave much better accuracy than PY at high densities. At low densities DHH and PY give essentially identical predictions. We have computed excess volumes for Ar/Kr mixtures at two pressures (10 and 20 MPa) at 132.32 K, for which experimentally derived data are available. The DHH theory predicts the correct trends and is quantitatively more accurate than the PY theory for predicting the excess volumes. We have tested the local optimality of the DHH theory for pure fluids by adding two adjustable parameters to the DHH bridge function expression to see if it is possible to improve the DHH predictions of the cavity correlation function empirically, holding the form of the bridge function constant. We found that no single set of adjustable parameter values could improve the accuracy of DHH over multiple different isotherms. Furthermore, perturbing DHH leads to a decrease in accuracy of the predictions of both the pressure and energy, although small improvements in the cavity correlation functions were achieved. Thus, the DHH theory is locally optimal, given the form of the bridge function.

GRAPHICAL ABSTRACT

Keywords:

• Integral equation theory
• cavity correlation function
• molecular dynamics
• Lennard-Jones fluid mixtures

Acknowledgments

Calculations were performed using resources provided by the University of Pittsburgh's Center for Research Computing.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

J. Karl Johnson http://orcid.org/0000-0002-3608-8003

Additional information

Funding

ZG acknowledges funding provided by the University of Pittsburgh Swanson School of Engineering, Department of Chemical & Petroleum Engineering for an undergraduate summer research internship. This work was partially supported by the Defense Threat Reduction Agency (Grant no. HDTRA1-16-1-0044).