Topological and Geometrical Random Walks on Bidisperse Random Sphere Packings

Motivated by the problem of predicting the release kinetics of matrix tablets, we study random walks on the contact graph of a random sphere packing of spheres of two sizes. For a random walk on the unweighted graph that terminates in a specified target set, we compare the euclidean distance covered to the number of steps. We find a linear dependence of the former on the latter, with proportionality constant the edge length expectation of the contact graph. This result makes it possible to compare predictions of diffusion path lengths on geometric graphs.