Predicting random close packing of binary hard-disk mixtures via third-virial-based parameters

Abstract

We propose a simple and accurate approach to estimate the random close packing (RCP) fraction of binary hard-disk mixtures. By introducing a parameter based on the mixture's reduced third virial coefficient -- which effectively captures three-body correlations and excluded-area constraints -- we show that the RCP fraction depends nearly linearly on this parameter, leading to a near-universal collapse of simulation data over a wide range of size ratios and compositions. Comparisons with previous models by Brouwers and Zaccone indicate that the present approach provides more accurate and consistent predictions. The method can be naturally extended to polydisperse mixtures with continuous size distributions and is structurally consistent with the surplus equation-of-state formulation, offering a compact framework for understanding the near universality of RCP in hard-disk systems.