Effective diffusion coefficients in random packings of polydisperse hard spheres from two-point and three-point correlation functions

Abstract

We evaluate the effective diffusion coefficient Deff in random packings of polydisperse hard spheres with an analytical formula involving the three-point microstructural parameter ζ2. Bulk packings with solid volume fraction between φ = 0.54 and φ = 0.634 were computer-generated using experimentally determined particle size distributions characterized by different mean particle diameter and associated standard deviation. The parameter ζ2 was calculated from two- and three-point correlation functions S2 and S3, respectively, via an approach based on sampling templates. Results of the asymptotic analysis for S2 and S3 compare favorably with theoretical predictions. Effective diffusivities calculated by the approximate analytical formula are close to those obtained from simulations using a random-walk particle-tracking technique. The values of Deff are affected by the packings' solid volume fraction, the spatial positions of the spheres, and to a far lesser extent by the particles' polydispersity. The proposed numerical approach can be applied to evaluate effective diffusive transport properties of general two-phase materials just from the geometrical information embodied in φ and ζ2.