Packing Fraction at Phase-Separation Transition in Hard-Core Mixtures

I relate the phase-separation transition, in binary hard-core mixtures in the limit of a small size ratio, to a bond percolation transition. It allows estimation of the packing fraction at the transition as a function of the size ratio and the composition of the mixture for different shapes of objects. The theoretical predictions are in excellent quantitative agreement with numerical simulations of binary parallel hard squares mixtures.