Model for random packing of polydisperse frictionless spheres

We propose a statistical model for the random packing of frictionless polydisperse spheres in which the complexity of the global packing is distilled into a local stochastic process. We simplify the problem by considering the "granocentric" point of view of a single particle in the bulk, thereby reducing random packing to the assembly of nearest neighbours, followed by a random choice of contacts among them. The model is based on only two parameters, the available solid angle around each particle and the ratio of contacts to neighbors, which are both directly obtainable from experiments or simulations. As a result, the model analytically predicts the microscopic distributions of nearest neighbours and contacts, the local density fluctuations as well as the global density of the packing. We find that this granocentric view captures the essential properties of the polydisperse emulsion packing. This model suggests a general principle of organization for random packing and provides a statistical tool for quantifying the effect of the particle size distribution on the geometry of random packing in a variety of contexts of industrial relevance.