Volume-Explicit Equation of State for Hard Spheres, Hard Disks, and Mixtures of Hard Spheres

A simple volume-explicit equation of state for hard spheres and their mixtures is developed. The equation accurately represents the simulation data. It also predicts the correct volume at high pressures (close packing), unlike the common pressure-explicit equations which predict an unattainable volume. The new equation gives the exact second and third pressure virial coefficients. It predicts higher coefficients within 1.4% (up to the eighth coefficient) compared to 15% for the common pressure-explicit Carnahan-Starling equation. The developed equation can be used as the repulsive part in developing volume-explicit real fluid equations of state or activity coefficient models. An equation for spherical molecules in two dimensions was also developed for use in surface studies.