INSTABILITIES IN THE EQUATIONS OF STATE OF HARD-DISK AND HARD-SPHERE FLUIDS FROM THE VIRIAL EXPANSIONS

Equations of state for hard-disk and hard-sphere fluids are obtained from a generalization of the Carnahan-Starling method of direct summation of the virial series. The equations of state thus obtained, besides reproducing all known virial coefficients, agree very accurately with simulation data for stable fluids. If appropriate values for the sixth and seventh virial coefficients are chosen within their uncertainty, the equations of state predict that the fluids become unstable at Kauzmann's density.