Quantitative characterization of pore-scale disorder effects on transport in "homogeneous" granular media

Breakthrough curves (BTC) of a passive tracer in macroscopically homogeneous granular materials (well-sorted, unconsolidated sands or glass beads) were measured in a series of column experiments. The early and late arrival times are observed to differ systematically from theoretical predictions based on solution of the advective-dispersion equation for uniform porous media. We propose that subtle and residual pore-scale disorder effects in the porous media can account for these observations. We determine an ensemble-averaged distribution of particle transfer rates (based on a master equation for the local flux-averaged concentration) which incorporates these effects, and utilize it to calculate BTC that are in excellent agreement with the entire series of observations. Theoretical prediction of the dependence of the effective macroscopic parameters on measurable quantities is also in excellent agreement with the observations.