A simple and accurate equation of state for hard-disk fluids

A long-standing problem for hard-disk fluids is to find a simple and accurate equation of state. By observing the known updated virial coefficients from B2∗ up to B10∗, we obtain an accurate empirical formula, with errors less than 0.5%. We further assume that the empirical formula is valid for all the virial coefficients. Using this assumption, we obtain a simple and accurate equation of state. In the density range 0<ρa2≤0.830<ρa2≤0.83, the predicted pressures are in good agreement with the simulation results. For 0<ρa2≤0.700<ρa2≤0.70, the errors are less than 0.007%. Even at ρa2=0.83ρa2=0.83, the error is only 0.5%.