Abstract

Several universal fractal scaling relations are found in dense high polydispersity random packings across both a range of packing protocols and grain shapes. We derive an explicit relation between the local free volume fraction surrounding each grain and the power law exponent for the decay in the global pore space volume which is directly related to the grain shape via a renormalized adimensional volume of the grain and demonstrate that this predicts well the packing packing efficiency for a broad range of grain shapes and a wide variety of packing algorithms. We demonstrate the validity of the derived relations over a wide set of grain-anisotropies, non-convexity, and shape-mixture in large packings, of up to a million grains, for a broad range of shapes for both the classical random Apollonian packing model (RAP), for the rotational random Apollonian packing model (RRAP) and for a new variation which keeps grains at fixed orientation (FRAP).