Correlation between random dense parking and random dense packing for determining particle coordination number in binary systems

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Abstract
An alternative method is proposed to estimate particle coordination number in a random packing of spheres. It is based on the correlation between random dense packing and random dense parking, where random dense parking is defined as the random placement of equal-size disks (or spheres) on a surface such that none overlap. Assuming that the limit for random dense parking (fraction of area covered by the projected area of particles) is independent of surface curvature, an analytical expression of the coordination number for spheres surrounding a central sphere of equal or different size is obtained. A similar analysis is achieved for a sphere touching a flat wall. Both expressions are tested through numerical simulations of bimodal, spherical particle systems.