Three-dimensional particle tracking velocimetry studies of the transition from pore dispersion to Fickian dispersion for homogeneous porous media

Fickian models developed to simulate transport in homogeneous porous media consider the flux of the contaminant species to be proportional to the concentration gradient via a constant dispersion tensor. When a solute has traveled sufficient distance or time, the mean square displacement may begin to grow linearly with time. We define the point at which the mean square displacement goes linear as the Darcy-scale Fickian limit. Prior to reaching this limit we say we are in the regime of pore-scale dispersion. In this paper we examine the transition from pore-scale dispersion to Fickian dispersion via three-dimensional particle tracking velocimetry (3D-PTV) in matched refractive index porous media. From the trajectories obtained via 3D-PTV we have computed the mean square displacements, velocity distributions, velocity correlation, and classical dispersion tensors, These data indicate the transverse components of the Darcy-scale dispersion tensor trend toward zero and that the longitudinal components go Fickian after approximately six pore diameters have been traversed.