Two-dimensional percolation and cluster structure of the random packing of binary disks

In this paper we study the short-range correlated percolation and the cluster structure of two-dimensional (2D) random packing of binary disks with size ratio lambda in the range of 1-5. A Monte Carlo simulation model is used to generate the configuration of random packing first. Then a from-neighbor-to-neighbor propagation method is used to identify the number and sizes of the clusters. Results show that for lambda=1 the percolation threshold p(c) lies between the square and triangular site percolation thresholds. As lambda increases the percolation threshold p(c) (the area fraction of small disks) decreases. To characterize the cluster structure at the percolation threshold, we scale the cluster size s(c) with the cluster radius R as s(c) proportional, variant R(D). The fractal dimension D obtained lies between 1.86 and 1.88 and is independent of the size ratio lambda. This value is in good agreement with the 2D theoretical fractal dimension which is equal to 91/48.