Random space-filling-tiling: fractal properties and kinetics

Abstract

A kinetic version of random Apollonian packing model is introduced. In this model, droplets nucleate spontaneously, grow at a uniform rate and stop growing upon collisions. The fractal dimension, Df of the pore space is found to be equal to Df=d(1-exp(2-(2d+2-2)/(d+2)), a result which is confirmed exactly in 1D and numerically in 2D.